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HELSINKI 1995 FINNISH MARINE RESEARCH No. 264
ATMOSPHERE-SURFACE INTERACTIONS OVER POLAR OCEANS AND HETEROGENEOUS SURFACES
Timo Vihma
Academic dissertation in Geophysics, to be presented, with the permission of the Faculty of Science of the University of Helsinki, for public criticism in the Auditorium XIV of the main building, Aleksanterinkatu 5, Helsinki, on Decem ber 15th, 1995, at 12 o’clock noon.
Helsinki 1995 : •'
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Recyclable product with low emissions during production Hakapaino Oy, Helsinki 1995 DISCLAIMER
Portions of this document may be illegible in electronic image products, images are produced from the best available original document CONTENTS
1. INTRODUCTION...... 4 1.1 Aims of the study ...... 6 1.2 The author’s contribution...... 7
2. THEORETICAL BACKGROUND...... 7
2.1 Homogeneous surface...... 7 2.1.1 The atmospheric boundary layer ...... 7 2.1.2 Calculation of turbulent surface fluxes ...... 8 2.2 Heterogeneous surface...... 11 2.2.1 Neutral flow...... 11 2.2.2 Stratified flow...... 12 2.3 Momentum flux and ice dynamics ...... 15
3. OBSERVATIONS AND RESULTS...... 16
3.1 Air-sea and air-ice heat exchange ...... 16 3.1.1 Greenland Sea...... 16 3.1.2 Weddell Sea...... 17 3.2 Ice dynamics ...... 20 3.3 Interaction of ice' dynamics and heat exchange ...... 24
4. MODELLING...... 26
4.1 Neutral flow...... 26 4.2 Stratified flow...... 27
5. CONCLUSIONS...... 30
6. REFERENCES...... 35
NOTATION 40 ■i ■
This thesis is based on the following original articles, referred to in the text by % Roman numerals:
I Launiainen, J. & Vihma, T. 1990: Derivation of turbulent surface fluxes - an iterative flux-profile method allowing arbitrary observing heights. - Environmental Software 5:113-124.
II Vihma, T. & Savijrvi, H. 1991: On the effective roughness length for heterogeneous terrain. - Quarterly Journal of the Royal Meteorological Society 102: 399-407.
m Vihma, T., Launiainen, J. & Krause, G. 1991: On the air-sea interaction in areas of t r. thermal marine fronts in the Greenland Sea. - Atmosphere-Ocean 29:596-610.
IV Vihma, T. & Launiainen, J. 1993: Ice drift in the Weddell Sea in 1990-1991 as ,'Y? r Y tracked by a satellite buoy. - Journal of Geophysical Research 98: 14,471-14,485.
'i V Launiainen, J. & Vihma, T. 1994: On the surface heat fluxes in the Weddell Sea. - In: Johannessen, O.M., Muench, R.D. & Overland, J.E. (eds): The Polar Oceans and Their Role in Shaping the Global Environment, The Nansen Centennial Volume. - Geophysical Monograph, 85: 399-420. - American Geophysical Union, Washington, D.C.
VI Vihma, T. 1995: Subgrid parameterization of heat and momentum fluxes over polar oceans. - Journal of Geophysical Research. (In press)
VII Vihma, T., Launiainen, J. & Uotila, J. 1995: Weddell Sea ice drift: kinematics and u. v4 wind forcing. - manuscript submitted to Journal of Geophysical Research.
The abovementioned papers are reproduced by kind permission of the follow ing: Elsevier Science (I), the Royal Meteorological Society and Quarterly Journal (II), the Canadian Meteorological and Oceanographic Society (III), and the American Geophysical Union (IV to VII).
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Finnish Marine Research No. 264(1995):3-41
ATMOSPHERE-SURFACE INTERACTIONS OVER POLAR OCEANS AND HETEROGENEOUS SURFACES
'i Timo Vihma
Department of Geophysics University of Helsinki P.O. Box 4 FIN-00014 Helsinki, Finland
Abstract
Processes of interaction between the atmospheric boundary layer and the planetary surface have been studied with special emphasis on polar ocean surfaces: the open ocean, leads, polynyas and sea ice. The local exchange of momentum, heat and moisture has been ' »- i studied experimentally both in the Weddell Sea and in the Greenland Sea. Exchange processes over heterogeneous surfaces are addressed by modelling studies. Over a homogeneous surface, the local turbulent fluxes can be reasonably well estimated using an iterative ' ' ' I flux-profile scheme based on the Monin-Obukhov similarity theory. In the Greenland Sea. the near-surface air temperature and the generally small turbulent fluxes over the open ocean were affected by the sea surface temperature fronts. Over the sea .1 ice cover in the Weddell Sea, the turbulent sensible heat flux was generally downwards, and together with an upward oceanic heat flux through the ice it compensated the heat loss from the surface via long-wave radiation. The sensible heat flux was typically from -15 to -20 •> W/m2 in winter and -5 W/m2 in summer. Over leads and coastal polynyas in the Weddell Sea. i an upward sensible heat flux of 100 to 300 W/m2 was typical. The annual areally-averaged total vertical heat loss from the Weddell Sea was 20-30 W/m2. Ice motion in the Weddell Sea was found to be driven by the wind and the ocean current. The wind dominated on time scales of days, while the current became important on longer time scales. The drift dynamics showed apparent spatial differences between the eastern and western regions, as well as between the Antarctic Circumpolar Current and the rest of the .3 Weddell Sea. Inertial motion was present in regions of low ice concentration. The geostrophic wind provided a sound basis for the ice drift forcing. The ice dynamics, ice concentration, and the regional atmosphere-ocean heat exchange depend interactively on each other. The surface heterogeneity, arising e.g. from roughness or temperature distribution, poses a problem for the parameterization of surface exchange processes in large-scale models. In the case of neutral flow over a heterogeneous terrain, an effective roughness length can be used to parameterize the roughness effects. Considering stratified flow over a winter polynya, an extended mosaic method provides a good basis for the parameterization of the sensible i and latent heat fluxes, and parameterization of surface momentum flux seemed to be most reasonable on the basis of the surface pressure field and a geostrophic drag coefficient depending on the stability.
Key words: turbulent fluxes, air-sea interaction, heterogeneous surface, flux parameteriza tion. sea ice, ice drift, polynya, marine fronts, Weddell Sea, Greenland Sea.
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1. INTRODUCTION
■0 The atmosphere exchanges heat, moisture andmomentum with the planetary surface. The exchange may take place via turbulent, conductive or radiative processes, and the associated fluxes modify the properties of the surface and the atmospheric boundary layer. :c Over polar oceans, sea ice acts as an insulator between the generally colder atmosphere and warmer ocean, but the sea-ice cover has discontinuties: cracks, leads and polynyas, presenting strong surface heterogeneity. Thus the atmosphere-surface exchange processes depend interactively on the thermodynamics and dynamics of the sea ice. The atmos phere-surface interaction over the polar oceans has considerable climatic and environ mental importance, arising from its effect on the existence and amount of sea ice, on deep water formation and on the general oceanic and atmospheric circulation. In this thesis I especially concentrate on the turbulent surface fluxes over polar oceans, the sea ice dynamics, and the implications of surface heterogeneity. First we consider the vertical turbulent surface fluxes of momentum, heat and moisture over a horizontally-homogeneous surface. These fluxes can be directly deter mined if the covariances between the turbulent fluctuations of the vertical velocity and the horizontal wind, air temperature and air moisture are measured. In practice, however, estimates for the fluxes are needed in situations where there is no possibility of making direct measurements of the turbulent fluctuations. For example, fluxes are needed to be known over large and/or remote areas, or have to be calculated in atmospheric and oceanic models. Theories for calculating the turbulent fluxes on the basis of easily-observable quantities are therefore required. Applicable variables are the horizontal wind and the air temperature and humidity observed as averages with the turbulent fluctuations filtered /.•v; T' out. Since the fluxes are proportional to the profiles of these variables, we need information on the profiles, either in the near-surface air layer, or as differences between the surface and the air. The practical calculation of turbulent surface fluxes is usually based on the . Monin-Obukhov similarity theory (Monin and Obukhov, 1953; 1954), which provides us with dimensional forms for the flux-profile relationships. Empirical functional formulae v-. are then applied to calculate the fluxes. There exist, however, many and various formulae to describe the effects of the surface roughness and atmospheric stratification, and the flux-profile relationships are sensitive to the reference height for the wind speed, air temperature and humidity. Moreover, the relationships are implicit, requiring iterative solutions. These problems are considered in paper I, which is a theoretical review and presents a software algorithm for practical flux computations. Over polar oceans the surface can be either sea ice, open water or a floating conti nental ice shelf. The exchange processes naturally depend on the surface type, its roughness and its temperature. Over the open ocean far from the coast and sea ice, the surface is usually nearly horizontally homogeneous, and due to the enormous heat capacity of the ■' .-i ocean, the atmospheric surface layer is close to thermal equilibrium with the surface. Seasonal temperature variations and advection of heat in the ocean or in the atmosphere can, of course, locally result in a prevailing heat gain or loss at the surface, but the flux magnitudes are generally small or moderate compared to the situation in the vicinity of ice-covered regions. There may, however, exist fronts in the sea surface temperature (SST) where water masses originating from different climatological regions meet each other (e.g. Legeckis, 1978). While flowing over such a front, an air-mass is in the process of adjusting to the new surface forcing and its properties are modified. Not only the air
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temperature and humidity but also the wind speed may be altered, because horizontal pressure disturbances are created and the changed thermal stratification affects the momentum flux in the atmospheric boundary layer (ABL). The exchange processes in the regions of polar SST fronts are studied in HI. Over snow-covered sea ice, the surface heat budget is determined by fluxes via shortwave and longwave radiation, by the turbulent heat fluxes, and by the conductive heat flux through the ice and snow. The fluxes are affected e.g. by the solar elevation angle, ice and snow thickness, cloudiness, surface roughness, and the origin of the air-mass flowing over the ice. Compared to the open ocean, the heat capacity of the surface directly interacting with the atmosphere is small, and thus the surface has far less potential to modify the air-mass above (Drummer et al., 1994). Over the floating continental ice shelves the situation is comparable to that over sea ice. In V, we study the surface heat and moisture fluxes, especially the turbulent ones, over the Weddell Sea. The ice cover over the polar oceans is fractured by cracks, leads and polynyas. In the following we denote as leads all the smaller areas of open water with typical widths from 1 m to 1 km and lengths from 100 m to 10 km (chains of leads may be 100 km long). Leads are usually formed by divergent ice drift and open and close frequently. Polynyas are larger, with horizontal dimensions from 1 to 100 km. They are often recurrent or semi-permanent in nature, and form most usually along coastlines, if the wind or current carries the ice away from the cost more rapidly than new ice can be formed (Lebedev, 1968; Pease, 1987; Darby et al., 1995). Polynyas may, however, occur in the middle of the pack-ice field as well, remaining open due to oceanic heat flux and/or large-scale divergence of the ice motion. Reviews of the occurrence and characteristics of leads and polynyas are given in Zwally et al. (1985), Comiso and Gordon (1987), and Smith et al. (1990) (see also Overland et al. (1995)). In winter, the surface and air temperatures over - sea ice may drop below -30°C, while the surface temperature of a lead or polynya remains close to the freezing point of about -1.8°C. This yields extreme upward fluxes of sensible and latent heat and net long-wave radiation, which we discuss in V and VI. Thus, despite their small areal coverage, leads and polynyas may have a strong effect on the regional heat balance in winter (Maykut, 1978). Through these high heat fluxes, leads and polynyas can also affect the atmospheric circulation on a regional and even a global scale (Ledley, 1988; Simmonds and Budd, 1991; Grotzner et al., 1994; Murray and Simmonds, 1995). Ice dynamics, which is of vital importance for the formation of leads and polynyas, is addressed in IV and VII, again concentrating on the Weddell Sea. In the Southern Ocean, the general ice motion is slightly divergent, since ice is advected northward towards wider latitudinal belts. In the Weddell Sea, however, a clockwise gyre forms in the basin, as the Antarctic Peninsula prevents westward ice motion. This gives rise to strong spatial differences in the ice dynamics and concentration, and hence in the ocean-atmosphere heat exchange as well. The primary forces driving the ice motion are the wind and the ocean current. We need to know the response of the ice drift to these forcing factors and the spatial variability of the response. This would provide us with a basis on which to estimate the general ice motion, its variability, the dynamical production of areas of open water within the ice field, and hence also the surface temperature distribution and large-scale areally-avaraged surface heat fluxes. 6
The parameterization of surface fluxes is a fundamental problem in atmospheric and oceanic general circulation models (GCM) and in numerical weather prediction models. The surface heterogeneity makes the task difficult, because a well-validated theory for the surface fluxes only exists for horizontally-homogeneous surfaces. Since the grid lengths in GCMs are of the order of200-500 km, the surface is usually heterogeneous on these scales. On the global scale, spatial variations of roughness and temperature are perhaps the most important sources of surface heterogeneity, although variations in surface moisture, albedo and elevation may be very important regionally. The roughness effect is vital, for example, over the territory of Finland which consists of many lakes and forests - two surface types having extreme differences in local roughness. In II, we concentrate on the parameterization of the roughness effect by modelling neutral flow over lakes and forests. Over polar oceans, however, the heterogeneity mostly arises from the surface temperature distribution. This heterogeneity affects the turbulent fluxes of momentum, heat and moisture as well as the radiative fluxes. Surface temperature differences with small spatial dimensions (i.e. caused by leads) are not especially problematic for the parameterization, but those with larger spatial scales (caused by polynyas) already affect the sub-grid distribution of the air temperature and wind speed and therefore do pose a problem. This is studied in VI.
1.1 Aims of the study
This study has had the following aims: 1. To provide a practical calculation scheme for the turbulent surface fluxes over sea, snow and land surfaces. This scheme should be based on up-to-date knowledge on the theory and empirical functions affecting the exchange processes. The scheme should be applicable in processing experimental data. 2. To provide estimates based on experimental data for the turbulent surface fluxes of momentum, heat and moisture over the Antarctic sea ice, leads and coastal polynyas. Although these fluxes have a primary importance for the existence of sea ice, for the production of deep water, and for climatology in general, observations of them are rare, and year-round data from the Antarctic sea ice were lacking prior to paper V. 3. To study the ice motion in the Weddell Sea to get detailed information on the importance of the driving forces taking effect in various regions and on different temporal scales. The ice motion is closely connected to the heat exchange processes. 4. To analyze experimental data from the polar oceans to study the effects of surface temperature gradients on the local fluxes of momentum, heat and moisture, and on the structure of the atmospheric boundary layer. 5. To study the effects of surface heterogeneity on the areally-averaged fluxes of momentum, heat and moisture, and especially to study the parameterization of these for large-scale numerical models. The objective is to consider solely the roughness effect by modelling neutral flow, and to consider the stability effects by modelling stratified flow over a fractured sea-ice cover. 7
1.2 Author’s contribution
The author of this thesis is fully responsible for paper VI. In paper I, Jouko Lau- niainen was the main author of the theoretical review, but this author contributed to that work and programmed a large part of the software, and made experiments using the software. Paper H was mostly written by this author with some contributions, help and guidance from Hannu Savijarvi, who also provided the author with a numerical mesoscale model, which was also used in VI. In HI, the field work was performed by Jouko Lau- niainen (JL) and Gunther Krause. This author made the data analyses together with JL, but the modelling studies alone. For papers IV, V and VII, this author calibrated the buoys in Helsinki together with JL, while JL carried out the field work in the Weddell Sea. In IV and VII, this author shouldered most of the responsibility for the data analyses and drafting of the manuscripts. In V the responsibility was shared with JL. For VII, much of the practical calculations, mathematical and statistical analyses and computer program ming for the data analyses was carried out by Juba Uotila.
2. THEORETICAL BACKGROUND
2.1 Homogeneous surface
2.1.1 The atmospheric boundary layer
The atmospheric boundary layer (ABL) consists of several sublayers. The transitions between the layers are defined by the relative importance in them of the various physical processes controlling the flow and mixing. In a shallow sublayer close to the surface the exchange of momentum, heat and moisture (and other gases) takes place in the form of molecular diffusion. Above this viscous sublayer there is a transition layer where both the molecular and turbulent mixing are of importance. Over natural surfaces, the transition layer extends up to heights of from 1 mm to 1 cm, and above it the exchange is mostly due to turbulent mixing. In the turbulent layer, the flow is governed by a balance between the pressure gradient, Coriolis and frictional forces. The frictionally-induced momentum flux is almost constant with height in the lowest tens of metres. This we call the constant-flux layer or the surface layer. The concept is utilized in deriving theories for turbulent exchange. The flux-profile relationships in the surface layer are mostly based on the Monin-Obukhov similarity theory (Monin and Obukhov, 1953; 1954). According to the theory, over a horizontally- homogeneous surface and in semi-stationary circumstances any dimen sionless characteristic of the turbulence can depend only upon a dimensionless stability parameter zJL, where z is the observation height and L is the Obukhov length (Obukhov, 1946) defined as
L = «.3r0pcp / [gkH(l+0.61T aC! ,E/H)] (1) where u, is a velocity scaling parameter known as the friction velocity, and H and E are the turbulent fluxes of sensible heat and water vapour, respectively, p is the air density and cp the specific heat, g is the acceleration due to gravity, T0 a reference temperature, and parameter & is the von Karman constant, k=0.4 (Hicks, 1976; Garratt, 1977; Wieringa, 8
1980; Dyer and Bradley, 1982;H6gstrom, 1988). Thus, the dimensionless profile gradients for the wind speed (V), the potential temperature of the air (6), and the specific humidity 0q) have a mutually analogous form:
dV/dz kz/u. = (pM (z/L) (2) dd/dz z/0. = (p H (z/L) (3) dq/dz zJq. = cp E(z/L) (4)
where 0. and q. are the scaling parameters for temperature and humidity. The scaling parameters «„ 0. and q, depend on the turbulent fluxes of momentum (ta, here given as a scalar), sensible heat and water vapour (or latent heat 7JE, where X is the enthalpy of vaporization) as «. = (Vp)"2,0. = -H/(pcpku.), and q. = -E/(pku.). ■ ■' Ta = -pCDZVz = -p u, (5) H— pCpCffiCGs-GzJVz (6) E— pC^z(qs-qz)Vz (7) !•- - where the fluxes are positive upwards. The transfer coefficients, the drag coefficient CDZ, -V-V. ■ the Stanton number CHZ and the Dalton number depend on the reference height z and are relative to the roughness lengths of momentum (%), heat (zT) and moisture (zq): Cdz — z/Zo - + YmC^c/X)] 2 (8) Chz = #Vn zJzq - Vm(z/X) + X|fM(zi/L)]"I[/ii - Vh izJL) + xg H(zVL)]"' (9) Qz = 1?{ln z/zo - xj/M (Z/L) + x]/M {zJL)\\ln zJzq - xj/E(z/L) + ^(z/L)]"1 (10) where xj/M, xj/H, and \|/E are the integrated forms of the (p-functions. Integrating the profile gradients between two levels in the atmosphere,-from Z\ to z2, we get the gradient forms for the fluxes: -V * V Ta = p^(V,-V2)2 / [ln(z2/Zi) - yM(z2/L) + Ym(ziAL)]2 (11) H = pcpkM.(0r02) / [ln(z2/zd - VnCZz/X) + Vn(Z|/X)] (12) E = pku.(qrqj / [Zzz(z2/zi) - Vafe/X) + Ye(Zi/L)] (13) Above the surface layer the Earth’s rotation becomes important, and the flow is governed by a balance between the pressure gradient, Coriolis and frictional forces. This layer is called the Ekmatt layer or the outer layer (of the ABL). A drag law for the Ekman layer is provided by the Kazanski-Monin similarity theory (Kazanski and Monin, 1961), V also known as the Rossby-number similarity theory (Blackadar and Tennekes, 1968), originally derived for neutral flow and later extended to stratified conditions: In Ro = A(p) -lnCa + (^/CG2 - S2(p))1/2 (14) v > 9 where Ro is the surface Rossby number, Ro = G/(lflz„),/is the Coriolis parameter, G is the geostrophic wind speed, and CG is the geostrophic drag coefficient, CG = uJG. The stability effects are now described by the functions A and B depending on the stability parameter |A = ku,/(\f\L). Estimates for A and B are given by e.g. Zilitinkevich (1975), Clarke (1970), Melgarejo andDeardorff (1974; 1975), and Arya (1975): the neutral values are around A = 1.5 and B = 4.5. An analogous resistance law can be given for the heat flux (e.g. Zilitinkevich, 1975) 6. = 80 / [ln(CGRo) - CQi)] (15) where 50 is the temperature difference between the top of the ABL and the surface, and C is a function of stability having a neutral value around 3. 2.1.2 Calculation of turbulent surface fluxes A practical calculation of the turbulent surface fluxes may be based either on Ekman-layer scaling or on surface-layer scaling. Ekman-layer scaling provides a rea sonable basis if we lack accurate information on the surface layer variables. Considering the momentum flux, equation (14) can be solved iteratively either as CG = f(Zo,|X), or VJG - f(Zo,|i), or as Vz = f(G) with Zq and p. as parameters. If we need to estimate the surface momentum flux on the basis of the atmospheric pressure field, we apply the form CG = f(zo,|A). Simultaneous data of the pressure field, momentum flux and surface layer strat ification would also allow us to formulate a simpler empirical dependency between CG and stability for a specified surface type (zo fixed) such as sea ice. This is done e.g. by Overland and Davidson (1992) and in VII. The heat flux can be obtained by solving (15) iteratively, as we do in V, and an analogous method can be applied for the moisture flux. In the surface layer, the practical calculation of fluxes according to the Monin-Ob- ukhov theory proceeds as follows. According to (5) - (7), the fluxes depend on the transfer coefficients CDZ, CHZ, and CEZ. They in turn depend on the Obukhov length L, as stated in (8)-(10), andL depends on the fluxes according to (1). An iterative solution of equations is therefore required. The solution process is described in I. The transfer coefficients depend on height, as well as on the surface properties and stability. The literature usually provides us with values for the neutral transfer coefficients for various surface types referred to a height of 10 m. In practice, however, the measurements of wind speed, air temperature, and air moisture are often made at heights different from 10 m, and different from each other. Thus we have to iterate the set of equations of (1) - (10), or (1) - (13), not only with respect to stability, but with respect to height as well. The process has its most complex form over a water surface, since the roughness lengths depend on the wind speed. Utilizing the bulk equations, the procedure may carried out as follows. During the first loop we assume neutral stratification with 9m,h ,e = 1 Vm.h .e = 0- 10 %v .'V 1. y 10ra is calculated from the observed wind speed using the logarithmic wind profile ’! ; -•V (2). 2. the roughness lengths Zo, ZT, and Zq are calculated from V10m (e.g. Large and Pond, ' „ ' 1982; Smith 1980; 1988). y- 3. First guesses for u„ 0. and q, are obtained from (2) - (4). The same equations are • applied to calculate V, 0, and q from the arbitrary observation heights to the reference -V- •V height of the calculations. , ’ - 4. (8) - (10) are used to calculate the transfer coefficients for the reference height. -v-y ' .'J': 5. A first guess for the fluxes is obtained from (5) - (7). yy . - 6. The fluxes are used to calculate z/L from (1) X'. • " 7. z/L is used to calculate the universal functions This loop is repeated until the change in z/L or in the fluxes is below a specified limit. Over a land surface, the procedure is somewhat more straightforward, because the j •*- - roughness lengths do not depend on wind speed. They can be calculated immediately, and the iteration loop is run between sections 3 to 8 only. Over a snow surface the calculation scheme (I) assumes that the roughness length for momentum (%) does not depend on the wind speed (Banke et al., 1980) but Zj and zq do (Andreas, 1987). The calculation height does not affect the results, as long as it is kept in the constant-flux layer. We found in I that mutual differences in the observation heights of wind speed, air temperature and air humidity do not decrease the accuracy of the results, although they make the calculation procedure more complex. The calculation scheme was validated against experimental data obtained via direct eddy-correlation measurements presented in the literature, and the results were reasonable. % The scheme was utilized in calculating the turbulent surface heat fluxes in the Weddell Sea in V, and it was implemented in the numerical atmospheric boundary-layer model used in VI. In applications such as atmospheric and oceanic general circulation models, the consumption of computer time is, however, an important criterion when selecting a parameterization scheme. Alternative approaches avoiding iteration are therefore preferred. They are usually based on the bulk Richardson number and are given by e.g. Louis (1979), Large and Pond (1982), Andreas and Murphy (1986), andLauniainen (1995), the last-mentioned semi-analytical solution also taking the roughness effect into account Constant values for the transfer coefficients are used in many large-scale sea-ice models (Parkinson and Washington, 1979; Plato and Hibler, 1992). Ignoring the effect of W-iv stability may, however, lead to serious errors especially over the polar oceans, where extreme stability conditions are met in winter. Table 1 demonstrates the effects. The unstable stratification over leads has a strong effect on the transfer coefficients, whereas a stability typical over sea ice only slightly reduces the neutral values. Also note the high sensitivity to the reference height. In VI we demonstrate that even larger errors may originate in the grid-averaged fluxes, if the surface heterogeneity is ignored. Sensitivity of sea-ice models on variations in the transfer coefficients and fluxes is studied by e.g. Holland et al., (1993) and Chapman et al., (1994). m, 11 Table 1. Examples of the effects of stability and reference height on the transfer coefficients in winter conditions lead sea ice ^10m 10 m/s 10 m/s 6l0m -30°C 30°C Ts -1.8°C 32°C ref. height 2m 10 m 2m 10 m 103xCh 1.60 1.39 1.81 1.26 103xChn 1.40 1.06 1.83 1.33 103xCd 1.75 1.45 2.72 1.78 10 xCdn 1.58 1.18 2.76 1.89 2.2 Heterogeneous surface Surface heterogeneity is usually caused by spatial gradients in surface temperature, roughness, elevation, albedo, or moisture. When estimating local fluxes, the Monin-Obukhov theory can be applied in some locations where strict horizontal homo geneity is not present, at least if the change in roughness remains small, as shown by the measurements of Andreas and Murphy (1986) and Guest and Davidson (1991). Parameterization of spatially-averaged surface fluxes is, however, not as straightforward. The basic problem is that in the grid squares of GCMs the surface is usually heterogeneous, but the GCM only knows a single air temperature, surface temperature and wind speed for each grid square. 2.2.1 Neutral flow In the case of neutral flow there is no heat flux, but if there are spatial variations in surface roughness, we have to consider the spatial averaging of the momentum flux. In principle, the grid-averaging of the latent heat flux and radiative fluxes may be required in neutral conditions as well, but these will be discussed in the next section. The roughness over a heterogeneous surface may be expressed using the concept of an effective roughness length Zg cff. In practice, it can be determined on the basis of the distribution of local z„:s in the region of interest. There are, however, several possibilities of defining Z0cff, depending on what we are modelling and what is the accuracy required. The simplest way of calculating Z0cff is to take an area-weighted logarithmic average of the local roughness lengths inside the grid square (Kung, 1963), which may be areasonable method if Zq does not vary much (Taylor, 1987). Fiedler and Panofsky (1972) defined Z^ for heterogeneous terrain as the roughness length which a homogeneous terrain would have in order to produce the same surface momentum flux, essential in most modelling applications. To calculateZgcff in practice, van Dop (1983) and Wieringa (1986) suggested taking a grid-average of the local drag coefficients (CD). Since ta=-p CDZy z2, such an idea contains the assumption that wind speeds at a reference level are the same everywhere, 12 j -: above both rough and smooth surfaces. Accordingly, Mason (1988) and Claussen (1990) suggested using a blending height as a reference level. The blending height (b) is an approximate height scale at which the flow no longer depends on the local surface but is still approximately in balance with the surface (the two conditions cannot be strictly true at the same height). This yields an equation for Z0cff by Mason (1988): *' *i v [In (b/Z0ctt)Y2 = <[ln (b/zo)Y 2> (16) where < > denotes a grid-average. An alternative approach is to assume the mean flow profile in the grid square to belogarithmic. On this basis Taylor (1987) derived an equation: In Z„cff = 2.2.2 Stratified flow In the case of stratified flow, we have to consider the parameterization of grid-averages of all the surface fluxes: the turbulent fluxes of momentum, heat and moisture, as well as the short-wave and long-wave radiative fluxes. The basic problem in the parameterization of turbulent heat fluxes is that we only know a single air temperature, surface temperature and wind speed for each grid square of a GCM. We can parameterize the surface fluxes solely in terms of these grid-averaged variables, a method which we here call the mixture -v\V a method. Alternatively, we can calculate (with the help of the radiation budget) local surface temperatures for each of the uniform parts of the grid square. The surface fluxes can then be calculated separately for each part, the grid-averaged flux being some area-average of these (the mosaic method). The basic questions are: (1) what are reasonable values for 13 the transfer coefficients ? (2) how well do the grid-averaged air temperature, wind speed, and surface temperature (if the mixture method is used) represent the local values? If the scale of heterogeneity is small, the air temperature and wind speed are not too much affected by the surface temperature variations, but if the scale is large the sub-grid scale variations may be considerable. In parameterizing the radiative fluxes, problems arise from the sub-grid variations in air temperature, cloudiness and, if the mixture method is used, surface temperature and albedo. In VI we concentrate on the heterogeneity caused by the existence of both sea ice and open water in a single grid square of a GCM. From the point of view of modelling, partly ice-covered seas are in one sense simple, having no vegetation, no terrain height variations, no variations in surface moisture, and no extreme changes in surface roughness. In another sense they are more problematic than land surfaces, because the surface type varies in time and the sub-grid variations in surface temperature can be extreme, even exceeding 30°C in winter. Turbulent heat fluxes. The simplest way to parameterize a grid-averaged turbulent surface heat flux from partly ice-covered sea is: c//>=ftin (b/zin - yjb/tinv'un mn - ^b/nnr 1 m Claussen (1991a) demonstrated the applicability of (20) for sea ice with leads of the order of lO'-lO2 m wide, and the scale of polynyas is considered in VI. A practice comparable to the mosaic method is used in data analyses by Andreas and Makshtas (1985) and in V to calculate areally-averaged fluxes over a fractured sea-ice cover. If more accuracy is needed, the idea of local parameterization can be developed further. In addition to local transfer coefficients we can calculate estimates of local wind speed and air temperature over ice and open water (Vi,w and 0,,w, respectively) on the basis of the GCM’s The above formulae (18 to 21) hold for the turbulent latent heat flux (kE) as well, if we just replace 0 by the specific humidity (q), and cp by the latent heat of sublimation (X). According to present knowledge, the transfer coefficients and roughness lengths for humidity are either equal to or at least close to those for heat (e.g. Schmitt et al., 1979; Andreas, 1987; Smith, 1989). In section 4.2 we will show that (21) produces better results than (18) or (19) judged by simulations with a mesoscale model. Radiative fluxes. In the case of incoming solar (short-wave) radiation, the subgrid variations in albedo and cloudiness should be considered. If we can estimate representative values for albedo and cloudiness (if there are systematic variations in the latter) for the ice-covered and ice-free parts of the grid square, a mosaic method should work for the grid-averaged broadband net short-wave radiation flux <<2S>. The surface net long-wave radiation Qh depends on the air and surface tem peratures and on emissivity, air moisture and cloudiness. An empirical formula for QL should be selected (e.g. that of Maykut and Church, (1973)), and either the mosaic or mixture technique can be applied with respect to the surface temperature, air temperature and cloudiness. As QL changes slowly with temperature, the separation of cloudiness should be the more important, if it can be done reliably. ii: ' -L Momentumflux. In stratified flow, the grid-averaging of momentum flux poses a problem V- because the stratification is merely a local quantity while the momentum flux may depend - . ■ much on aggregated large-scale conditions (Andreas et al., 1984; Hanssen-Bauer and Gjessing, 1988; Stossel, 1992). This is due to the role of form drag. Here we restrict our analyses to grid-averaging of the skin friction. Thus, the parameterization problem is basically similar to that of heat flux. If the parameterization is based on the actual near-surface wind speed, there are four basic combinations of local and effective roughness and stability parameters available: 1. local Zq:s and an effective \|/M 2. local Zg:s and local \jrM:s 3. Zg cff and local \|/M:s 4. Zf and an effective xg M The equations are described in detail in VI. The effective roughness lengths can be calculated according to (16) or (17). Because of the lack of empirical formulae for the effective \|rM-functions, the local xg M-functions should be applied. Over the polar oceans, very little verification data is available for the actual surface wind, but the atmospheric pressure field is more reliably known for a GCM. Hence, a reasonable possibility is to parameterize the momentum flux on the basis of the geostrophic wind using the geostrophic drag coefficient: r Now we have to know the dependency of CG on the subgrid distribution of roughness and stability (over a homogeneous surface that is provided by (14)). The determination of CG is discussed in VI and VII. 15 2.3 Momentum flux and ice dynamics ■; ■ A momentum equation for a sea-ice floe written in a two-dimensional Cartesian , j coordinate system includes the following terms: j mdV-Jdt = -mfk x V,+Ta-xw +l-mgVh (23) j where m is the mass of ice per unit area, Vj is the ice velocity, ¥a is the air-ice stress, and " : ¥„ denotes the ice-water stress. I stands for the force due to the divergence of internal * i stress in the ice field, and h is the height of the sea surface with respect to a level surface. : ! The last term represents the effect of the sea surface tilt, which is usually associated with . , i a geostrophic or tidal current (the effect of an atmospheric pressure gradient is not shown). . 1 An overbar denotes a vector variable, and k is the unit vector normal to the surface. ' ■ The importance of the terms in (23) depends on the dynamic situation, but also on the scalar properties of the ice field. The thickness of the ice floe affects m dV/dt, mgVh, ,1 and the Coriolis force. The roughness of the upper surface of the floe (usually covered by , ’ snow) affects ¥,, and the roughness of the lower surface affects Tw. Stratification in the ‘ atmospheric and oceanic boundary layers also affects the momentum fluxes. I depends I on the compactness, thickness and elasticity of the ice field. The relative effect of the - j ocean current depends not only on its magnitude but also on the time scale of the analysis. The ocean current usually has a steady character when compared to the wind, and hence i becomes important in analyses with a longer time scale, of say months rather than days. % Yet, on time scales of hours instead of days the surface current may show more variability • ‘ than the wind (Lepparanta and Omstedt, 1990). . J If we consider a semi-stationary wind-driven ice drift in a gradually diverging „ | velocity field with a small /, the momentum equation approaches a balance between the air-ice and ice-water stresses and the Coriolis force. The general situation in Antarctica is not far from that, as shown in IV and VII. For thin freely-drifting ice the Coriolis force is small, and % balances t"w. Then the ratio of ice drift to wind speed is proportional to the square root of the drag coefficient ratio: V/V= (pCD/p„CH,),y2 , where is the water density • I and Cw the ice-water drag coefficient. ', •! The atmospheric influence on sea-ice motion operates through the air-ice stress. As \ % { stated in (5), Ta depends on the near-surface wind speed via a drag coefficient. In a neu- - : trally-stratified case, the drag coefficient CD is relative to the roughness length Zq as in (8) " " &- , with vj/M = 0. The surface roughness of sea ice arises from skin friction and form drag as • _ • stated by the drag partition theory (Marshall, 1971; Arya, 1975). The theory relates the ' ■ ’ drag to the distribution of geometric properties of the surface. The skin friction can be described by the roughness length and drag coefficient as in section 2.1. The form drag . ' is due to pressure forces acting against surfaces perpendicular to the flow. In practice, however, the ice and snow surface is always more or less uneven. Thus, it is not easy to make a strict distinction between the surface properties creating skin drag and those creating form drag. In general, the floe edges and pressure ridges are regarded as the major , ■ • „ sources of the form drag, and the effect of the smaller surface features is included in the parameterization of skin drag. The character and magnitude of the form drag is discussed ; inpapers by Arya(1975),Joffre(1982; 1983), Hanssen-BauerandGjessing (1988), Stossel . . and Claussen (1993), Andreas and Claffey (1995), Andreas (1995), and Dierking (1995). ' -T V ' * ■ ,'.1^ 1 16 A simple and practical model for calculating a drag coefficient, merely representing the skin drag, on the basis of the geometric properties of the surface was proposed by Banke et al. (1980). Overland (1985) reviewed air-ice drag coefficients, and Guest and Davidson (1991) gave a practical classification for various ice types and the corresponding drag coefficients. Since most of the measurements were carried out above level ice, the results mainly represent skin drag. Most of the data obtained so far have been from the Arctic. Drag coefficients over Antarctic sea ice have been studied by Martinson and Wamser (1990), Wamser andMartinson (1993), Andreas etal. (1993) Andreas and Claffey (1995), and Dierking (1995). We applied these results in IV and VII. Over a homogeneous sea-ice surface the effect of atmospheric stratification on the drag coefficient can be represented as in section 2.1.1. In modelling applications and large-scale analyses with leads occurring within the ice field the situation is, however, far more complex, since the surface is heterogeneous both in roughness and temperature. To account for this, parameterization methods such as those discussed in VI and by Stossel and Claussen (1993) could be applied. 3. OBSERVATIONS AND RESULTS The observational part of the thesis includes data analyses of the turbulent exchange between the atmosphere and the ocean in the Greenland Sea (HI) and in the Weddell Sea (IV, V, VH). In the latter, the heat and moisture exchange over both sea ice and areas of open water are considered (V). Momentum exchange and ice dynamics in the Weddell Sea are discussed in IV and VII. 3.1 Air-sea and air-ice heat exchange 3.1.1 Greenland Sea The air-sea exchange of heat and moisture in the Greenland Sea was analyzed on the basis of ship weather station data obtained during an expedition of the German R/V Polarstem in 1987. Special emphasis was laid on the influence of the SST fronts in the exchange processes and on the modification of the atmospheric surface layer. The cruise was made in a region where the Arctic front separates the warm waters of the West-Spitsbergen current and the cold waters of the Greenland Sea Gyre. The mesoscale features of this major front were traversed about 20 times. The ship weather station measured the seasurface temperature, air temperature, dew-point temperature, and relative humidity, as well as the wind speed and direction, having at least two sensors for most quantities. The surface fluxes of momentum and sensible and latent heat were calculated from the observations using the bulk equations (5) - (7) and utilizing the calculation scheme described in I. Results and discussion. The general conditions in the region in spring and early summer showed a slightly unstable atmospheric surface-layer stratification and small upward fluxes of sensible and latent heat, with average values of 13 W/m2 for H and 17 W/m2 for XE. The average wind speed at a height of 37 m was 7 m/s and the average momentum r: i 17 flux 0.060 N/m2. The SST fronts were rather distinct with an average cross-frontal change of 2.8°C and a gradient of 0.05 to 0.4°C/km. These produced a more gradual modification ■ in the air temperature with an average cross-frontal change of 0.9°C. The air temperature ■ had a diurnal cycle with an amplitude of 0.6°C; filtering this out, a standard deviation of 1.5°C remained. This could have been caused by the combined effect of frontal and : larger-scale (spatial and temporal) temperature variations. The conclusion may be reached that diurnal, frontal and larger-scale variations are of the same order of importance in controlling the atmospheric surface layer temperature in the Greenland Sea in spring and early summer. A couple of frontal crossings were studied in more detail. In one case, the SST abruptly j dropped by 4°C and the air temperature by 2°C. The wind blew from the warm side to the ,, I cold side of the front, and the stratification changed from slightly stable to moderately ,-j stable. This was accompanied by a change from evaporation on the warm side of the front /’j to condensation on the cold side. The wind speed was somewhat higher on the cold side, but the air-sea momentum flux was higher on the warm side. The latter was due to the effect of stability reducing the momentum flux on the cold side and dominating over the . effect of wind speed there. In HI we argue that the increase in wind speed on the cold | side could have resulted from the increased stability. In principle, this could be possible ; because stability reduces the momentum flux and hence the sea surface remains smoother, ,■ which tends to increase the near-surface wind speed. The direct effect of stable stratifi cation is, however, to reduce the near-surface wind speed, because less momentum is - 1 transferred down from the upper layers. A more detailed study of the relative importance , -| of these two effects, applying the relation of Chamock (1955), reveals that with small or , * moderate changes in stability the effects approximately balance each other. Thus, the "i observed change in wind speed in HI was more probably due to non-stationary conditions. V The second front analyzed was traversed twice and the situation remained almost , stationary. The wind was from the cold side to the warm side of the front and the strat ification was unstable on both sides. On the warm side it was very unstable, because the increase in the SST was again more rapid than that of the air temperature. The specific humidity increased by 30% across the front. In this case the wind speed increased on the warm water side. This we believe to be the usual behaviour, as also indicated by the observations of Sweet et al. (1981) and Mey et al. (1990), and by modelling studies (Hsu, J 1984; Huang and Raman, 1988; Wai and Stage, 1989; Warner, 1990). Several observations and modelling studies demonstrate an analogous behaviour over sea-ice margins (Over- land et al., 1983; Guest et al., 1995; paper VI). 3.1.2 Weddell Sea In the Weddell Sea, buoys were deployed on the sea ice, in the open ocean and at the , ' edge of a floating continental ice shelf (V). The buoys measured the atmospheric pressure, wind speed and direction, air temperature andhumidity, snow temperature, snow thickness ‘ - (one buoy) and the temperature profile in the oceanic surface layer. The measurements • ', and data are described in the technical reports by Launiainen et al. (1991; 1994). The -turbulent surface fluxes were estimated on the basis of these measurements. T 77 ,’>* -> • Yi-.K'.:- -■u 18 Three of the buoys were deployed on sea-ice floes, one in 1990 and two in 1992. Their data allowed us to estimate the fluxes over the whole annual cycle in both 1990 and 1992. The gradient method (12) was applied for the sensible heat flux, and the bulk method (7) for the latent heat flux. The data was also utilized to estimate the fluxes over leads, assuming that they have a surface temperature at the freezing point and are so narrow that the properties of the air-mass are not modified while flowing over a lead. Thus, the wind speed and air temperature and humidity measured over the sea ice were used when calculating the fluxes over the leads. The bulk-equations (5) - (7) were used. A buoy operating at the edge of a floating continental ice shelf provided us with data to estimate V," the heat and moisture fluxes over the ice shelf and over the coastal polynyas close to it. As over the leads, the fluxes over the coastal polynyas are hypothetical in the sense that we did not directly observe the polynyas (during the expedition the sea was open, but except in summer polynyas can be frequently detected from satellite images). From the distribution of the wind direction at the buoy site we know, however, that the air-mass was generally flowing out seawards from over the ice shelf. Thus, the wind speed and air temperature and humidity measured over the ice shelf edge were reasonable estimates for ev: those over the polynyas probably existing close to the ice shelf. In fact, in winter it is almost unnecessary to measure the air humidity for estimating the evaporation over a lead or polynya. This is because the air-surface difference in specific humidity in these conditions is almost solely determined by the air and surface temperatures. In summer, the coastal polynyas in the eastern. Weddell Sea join up with the open ocean. One of our buoys operated in this region in late summer and autumn 1990. Its data allowed us to estimate the turbulent surface fluxes using both the bulk and gradient n-.: equations, providing a basis for comparisons. We were also able to estimate the fluxes from the ABL resistance law (15) on the basis of the rawinsonde soundings made from RAf Aranda. Together with the ice shelf buoy the open ocean buoy also provided us with the possibility of studying the spatial changes in the fluxes while the air was advected away from the ice shelf. The spatially-averaged fluxes were obtained applying an integral method based on the rawinsonde soundings. Results and discussion. The estimates for the average heat fluxes over the Weddell Sea are summarized in Table 2 (adopted from paper V). Over the sea ice, the prevailing direction of the sensible heat flux was downwards, as a consequence of radiatively-based surface cooling. The average flux was from -15 to -20 W/m2 with typical variations of 10-20 W/m2 between successive days. During summer the sensible heat flux was small and variable in direction, with a mean value of -5 W/m2 (downwards). The measurements suggested slight evaporation during summer and very weak condensation during winter. The Bowen ratio was positive for 60-80% of the time. The upward heat flux through the ice and snow was of the order of 10 W/m2 from mid-February to the end of July. Over the floating continental ice shelf edge the surface heat exchange resembled that over the sea ice. The sensible heat flux was downwards, on average -17 W/m2, while the latent heat flux was close to zero. Not much annual or interannual variations were detected from r.-V. the results. The upward heat flux from the snow cover was weak - some 1-2 W/m2 only. Over leads in the sea-ice zone, the wintertime upward sensible heat flux frequently exceeded 20,0 W/m2 and the latent heat flux 100 W/m2. In summer, the fluxes were small and difficult to estimate accurately. Over coastal polynyas, the fluxes were larger than '-?• < over the leads since the air flowing from the continental ice shelf was generally colder than the air over the sea ice. In winter the average sensible heat flux was 240 W/m2 and V - ‘ Vi 19 the latent heat flux 80 W/m2. Maximum values for the sensible heat flux reached 600 W/m2, but the validity of the universal functions used in calculating them may be somewhat uncertain in such extreme conditions. A typical Bowen ratio over coastal polynyas and winter leads ranges from 2.5 to 3. In autumn, over the open ocean some 100-150 km off the ice shelf, we observed moderate turbulent heat fluxes of 30 W/m2 for both sensible and latent heat. The results obtained by the gradient method and bulk method were reasonably close to each other. Due to the cold ice shelf nearby the fluxes were approximately twice as large as those in the Greenland Sea in spring and early summer. On the other hand, the fluxes over the open ocean in these two regions resemble each other when compared to the fluxes over leads, polynyas and sea ice. Table 2. Estimates of surface heat balance components in the Weddell Sea (in W/m2, positive upwards). The mean year-round values are given for various surface types, as well as the mean values calculated for winter and summer and for the marginal ice zone and the interior of the ice field. Qs = net short-wave radiation, QL = net long-wave radiation. Adopted from V. Surface type Sensible latent heat flux Qs Ql heat flux heat flux through ice Sea ice -15 0 10 -20 20-40 MIZ +1 4 interior -17 -2 10 winter -17 -3 10 0 20-40 summer -5 3 -40 30-50 Ice shelf -17 0 1 -30 40-60 winter -16 0 1 0 30-50 summer -12 2 1 -60 50-60 onen ocean (autumn) 27 30 -100 60-70 coastal polvnvas 160 60 -100 80-110 winter 240 80 -2 100-130 summer (30) (20) -240 60-70 leads 140 60 -90 60-90 MIZ 70 30 interior 150 60 winter 190 70 -5 70-110 summer (20) (14) -190 30-50 Note: - Summer is defined as the period from December to the end of February, winter from June to the end of August. MIZ = marginal ice zone; one buoy drifted in MIZ from January to the end of April, 1990, and another one in November, 1992. During other periods analyzed the buoys drifted in the interior of the ice field. - Heat flux through the ice is calculated on the basis of two buoys only (one on the sea ice and another on the ice shelf). - Summer values over leads and coastal polynyas are uncertain due to an unknown sea surface temperature. 20 •' The radiative fluxes were not measured but estimates were given to provide a reference for the magnitudes of the surface heat balance terms. When calculating the radiation terms ' 'j the observational data of air and surface temperatures were used, but cloudiness was only estimated. Over the open ocean, sea ice and the ice shelf the radiative fluxes dominated the turbulent fluxes. Over polynyas and leads the turbulent fluxes were larger than the radiative ones, except in summer when short-wave radiation dominated. v- The air-mass modification off the ice shelf was studied during the expedition of R/V Aranda in February 1990. Cold, dry air flowed out from over the shelf towards the sea, and rawinsonde soundings were made from the research vessel. The turbulent sensible heat flux was estimated using three methods. 1) The modification in the temperature •: profile was analyzed. The change in the profile between the ABL over the ice shelf and that over the sea is related to the average heat and moisture fluxes during the traverse by the air-mass. 2) The flux was calculated from the surface-layer observations made at the ice-shelfbuoy, at the research vessel, and at an open-ocean buoy. 3) The diabatic resistance ; law for the ABL, equation (15), was applied while analyzing the rawinsonde sounding / data. The results obtained from the three methods were reasonably in accordance with each „ -1 other. The bulk-aerodynamic calculations in particular corresponded surprisingly well to . ‘ the results based on the resistance laws. The results based on air-mass modification differed 3 3 . more from these two. This was probably because we lacked detailed information on the _. temperature profile at the edge of the ice shelf, and because the exact height of the inversion base was not always easy to define. The results demonstrated that the sensible heat flux varied between 40 and 150 W/m2 and decreased with increasing distance over the open ocean. 3.2 Ice dynamics % . The drift of the buoys described in the previous section formed the basis for our analyses of the Weddell Sea ice dynamics in IV and VII. The buoy positions were determined by CLS / Argos employing the Doppler shift between consecutive messages received by the polar-orbiting NOAA satellites. We got some 20 positions a day with an average accuracy of about 350 m. In total we obtained ice drift data covering 1176 buoy days with simultaneous on-site wind data from 915 buoy days, and data on surface-layer stratification for 882 buoy days. Fig. 2 in VII gives a summary of the data processing. In addition to the winds measured by the buoys, we analyzed the geostrophic winds from the surface pressure fields of the European Centre for Medium Range Weather Forecasts % (ECMWF). Further, we estimated ABL stability from our rawinsonde soundings and from those made at the U.S.-Russian Ice Station Weddell-1 (ISW) by Claffey et al. (1994). The drift data of ISW and a U.S. buoy was also used in some analyses. In considering the ice kinematics, we studied drift speeds, their spatial and temporal variations, inertial and tidal motions, the meandering and spectral properties of the drift, ■ -U as well as deformation of the buoy grids. With respect to the ice dynamics, we analyzed ■v the drift’s response to the surface wind and the geostrophic wind. Residual ocean currents were detected from the response, and the relative importance of the wind and the currents 4 21 on various time scales was studied. A current meter deployed under the ice floe of one buoy provided information on the ice-water stress. The effects of atmospheric stratification on the air-ice stress and the ice drift were studied too. Results anddiscussion. The results of the ice kinematics study showed apparent differences between the eastern and western parts of the Weddell Sea. Close to the Antarctic Peninsula, the ice drifted as an almost non-rotating uniform field at a low speed and with reduced small-scale motions and little meandering, compared to regions further east. The mean drift rates varied from 0.15 m/s in the central Weddell Sea (CWS; here defined as the region from 25 to 45°W) to 0.11 m/s in the western Weddell Sea (WWS; west of 45°W). The fastest drift, with an average speed of -0.30 m/s was, however, observed in the region of the Antarctic Circumpolar Current (ACC; north of 63°S). The buoys drifted in the marginal ice zone in summer and autumn 1990, in 1991 and from spring 1992 to summer 1993. There the ice floes rotated actively indicating a low ice concentration. In contrast, in winter the ice pack became compact, and floe rotation was as little as 10 degrees a month. We calculated the meandering coefficient as the ratio of total trajectory length to the net transition of a buoy during the same time period. As the drift speed and its variance, so too the meandering coefficient diminished westwards, with mean values of 1.5 in the WWS and from 2 to 7 in the CWS. In the ACC, relatively straightforward drift prevailed and the meandering coefficient was about as low as in the WWS. In the CWS the values varied a lot between the years 1990 and 1992, and comparisons with the previous results of Limbert et al. (1989) and Massom (1992) also suggested that inter-annual variations are considerable and may dominate the spatial gradients. The relative amount of small- scale motions was studied by analyzing the drift velocity spectra. The spectra in general followed apower law of S=G0"“, whereSis the spectral energy and to the angular frequency. In winter the slope a was typically about 1.5 while the summer values were lower, typically between 0.5 and 1. A small a suggests a lot of activity in small-scale ice motions. A more direct measure for this is the mean spectral energy level at angular frequencies above a certain limit, for which we took to > 5x10"* rad/s. In this high-frequency region S was usually somewhat lower in winter than in summer. The drift velocity spectra indicated that inertial motions, usually superimposed on the wind drift, were apparent in the CWS in summer 1990 and in the ACC in the springs and summers of 1991 and 1992. In the CWS the observed frequency decreased during the northward ice drift, following the theoretical dependency of inertial motion on latitude. A study of the damping of the motion suggested that the inertial motion was mostly a property of the upper ocean, not only that of the sea ice. In the CWS in 1992, the drift revealed no marked signs of either inertial or tidal motions. Motions with a period of about 12 hours were somewhat more pronounced in the WWS, but it was difficult to distinguish between inertial and tidal motions, because in these latitudes the inertial period is very close to that of the semidiurnal lunar tide M2. The bottom topography and the fact that the periodic motions were more common at 50°W than at 40°W suggests, however, the presence of tides. This is also supported by other studies (Rowe et al., 1989; Genco et al., 1994; Middleton and Foster, 1977). /•V ■x "3 -:h 22 The spatial correlation of the ice drift and the geostrophic wind was analyzed on the basis of the buoy drift data and the pressure analyses of ECMWF. Using a reasonable time lag of -6 h, the patterns of eastward drift especially were in coherence over longi tudinal distances of 400-500 km. In particular, events with high drift speed correlated well, reflecting the effect of travelling cyclones that forced the ice motion. In regions west of 40°W the northward ice motion had a small mean divergence of 6-8 x 1 O'8 s"1 as calculated from the simultaneous drift of the buoys. The temporal variations in divergence were, however, much larger than the mean. The variations were not uniquely correlated with the other drift variables. High drift rates were, however, related to small \ absolute values of divergence, indicating that the ice field made its high-speed motions A as a uniform large-scale system. Further, we found that the difference between successive diurnal ratios of drift speed and geostrophic wind correlated with the divergence. An increase in the drift ratio was associated with divergence, and a decrease with convergence. We analyzed the distribution of relative drift direction with respect to the direction of the geostrophic wind and the ocean current. In 60-80% of the time the drift direction was coincident along with both the geostrophic wind and the ocean current, and in 98-99% of the time coincident with the direction of either the wind or the current. The drift speeds were reduced to half when the drift was directed against the wind. The dependency of the drift on the wind was studied both with respect to the surface ■fe' wind measured by the buoys and the geostrophic wind. The analyses showed that the ice drifted with a speed about 3% of the surface wind speed but part of the drift speed was due to the ocean current, especially in the western Weddell Sea where the wind factor to. (the coefficient in a linear regression equation) was only 1.8%. In the CWS, the average wind factor was 2.5%. In the CWS in 1990, the drift’s response to the wind varied between the summertime marginal ice zone and the wintertime inner pack-ice zone. In the former, the drift speed was 3.4% of the surface wind, while it was only 2.4% in the latter. The drift was directed about 30° left of the surface wind. The angle showed only moderate regional variations, but in 1990 the mean summer value of 47° differed a lot from the winter value of 21°. This was probably due to an increased internal ice resistance and a decreased ice thickness in winter. The latter was because the originally isolated 4-m-thick ice floe became part of a compact but generally thinner first-year ice field. The surface wind was directed on average 25° to the right of the geostrophic wind, and had 50-60% of its speed. Hence the ice drift was -5° to the left of the geostrophic wind with 2% of its speed. Due to the current, the wind factor was only 1% of the geostrophic wind. An estimate for the geostrophic drag coefficient uJG was 0.028. On time scales of days, the ice motion in the Weddell Sea is mostly controlled by the wind, butthedependency varies regionally. In the central Weddell Sea, alinear wind-based model, including a residual current, explained 60-80% of the drift velocity variance calculated from velocities at 6-hour intervals. In the western regions the degree of explanation dropped to 40-50%. There, a northward ocean current and forces due to the divergence of internal ice stress tended to have a stronger effect than in the east. The errors ' ■ . both in the observed and geostrophic winds as well as in the drift velocities tended to • .V. decrease the drift-wind correlations. Usually there were only minor differences between the two-parameter and four-parameter expressions for the dependency on wind (section 4.2 in VH), although larger differences may arise in cases sensitive to the wind direction or coastline orientation (see also Uotila et al., 1995). In general, the geostrophic wind derived from ECMWF pressure analyses provided almost as good a basis for the drift forcing as the observed surface wind. This is fortunate since data from the latter are seldom I 23 available. Occasionally and locally, however, large errors were met with in the pressure fields - in particular, deep lows were underestimated, yielding erroneous forcing for the simulated ice motion. The ratio of surface to geostrophic wind showed a dependency on the atmospheric surface-layer stratification. In near-neutral conditions the data had a lot of scatter, but strongly stable conditions were associated with a reduced ratio. This was also reflected in the ratios of drift speed to surface wind and drift speed to geostrophic wind, as well as in the geostrophic drag coefficient. The variations in the above-mentioned ratios were best explained by the local surface-layer parameter 10/L (less data were available from stability parameters related to the ABL). Fig. 1 illustrates the results (redrawn from VII). For one buoy, the periods favourable for the existence of streamlined snowdrifts on the ice were associated with reduced ratios of ice drift to wind speed. S3 0.02 0.02- y 0.005 median 10/L in each class median 10/L in each class Fig. 1. (a) Ice drift speed versus geostrophic wind speed as a function of 10IL. (b) Dependency of the geostrophic drag coefficient on 10IL. The diurnal means of 10/L were divided into five classes (< 0,0-0.2,0.2-0.4,0.4-0.6, > 0.6), each containing 25-315 diurnal means. Linear regression lines are drawn and the error bars show one standard deviation in VJG and Ca in each class of 10/L. Redrawn from VII. The linear wind-drift model allowed us to estimate an average ocean current as a residual term for various regions. The term in fact also includes the net effect of forces due to the divergence of internal ice resistance and the sea surface tilt. The resulting residual terms are in any case comparable to the currents observed e.g. by Fahrbach et al. (1994). In the CWS our data suggested a 2 cm/s current towards the northwest, while in the WWS the current was northward and had a speed of 5 cm/s. On time-scales of months, the effect of the ocean current on the ice motion is important, as can be seen from the trajectories simulated with and without the current term. An analysis of a period of free wind-induced drift in IV suggested that the ratio of air-ice to ice-water drag coefficients was of the order of 0.6, i.e Cw = 1.7 x CD. An "ef fective" ice-water drag coefficient, also implicitly containing the effect of energy dissi pation by internal ice stresses, was larger, - 3 x CD, in the central pack ice field (compare to Martinson and Wamser, 1990). 24 The ice export through a transect crossing the Weddell Sea from the tip of the Antarctic }.* Peninsula to Cape Norwegia was estimated on the basis of the ECMWF atmospheric :i pressure fields, the observed drift’s response to the wind, and literature-based information ■} on the ice concentration and thickness. The estimates for annual mean net export were ; 22,000, 8,500 and 18,000 m3/s in 1992, 1993 and 1994, respectively. Most of the net export took place in winter and spring, export prevailing west of 35°W and import east .; of that. An ice export of 20,000 m3/s would be balanced by a freshwater gain of -17,000 m3/s, which is roughly the same as estimates of the influx through precipitation and ice- <’ -- shelf melting (Fahrbach et al., 1994). 3.3 Interaction of ice dynamics and heat exchange In winter, leads and polynyas may have a dominating effect on the areally-averaged heat fluxes, as demonstrated in V and VI. The occurrence of leads and polynyas depends a great deal on the ice dynamics (e.g. Pease, 1987; Kottmeier and Engelbart, 1992). The ice motion in turn depends on the atmosphere-ice-ocean heat exchange: the momentum equation (23) is directly affected by ice growth. In addition, the salt rejection during the formation of new ice and the freshwater flux to the ocean during ice melt affect the vertical ; . and horizontal distribution of salinity in the ocean, the latter because ice usually melts in regions different to those in which it is formed. This has its implications for the formation of deep water masses and for the geostrophic ocean circulation, yielding a feedback to the ice motion. The heat exchange also affects the atmosphere-ocean momentum flux. The air-ice, ice-water and air-water momentum fluxes are directly affected by the stratification of the atmospheric and oceanic boundary layers, as demonstrated for the air-ice and air-water v. fluxes in Table 1 and in VII. The existence of ice cover can either enhance or diminish the atmosphere-ocean momentum flux depending on the thermal structures and rough- ;■ nesses of the air-ice-water interfaces and on the amount of energy dissipated through processes of ice deformation. In a neutrally-stratified case of free wind-induced ice drift, the atmosphere-ocean momentum flux tends to be increased due to the presence of ice because the ice surface is generally rougher than the open ocean surface (ice can sometimes .v<"- lo be smoother than the open water, e.g Andreas et al. (1979)). However, in other cases the ll - r' ‘ energy dissipation in the ice cover usually dominates the roughness effect: in the Weddell Sea the ice-water stress is typically only one third of the air-ice stress (Martinson and Wamser, 1990). The ice advection has a strong effect on the large-scale existence of an ice cover. In the Antarctic, new ice is formed in coastal polynyas and in leads within the pack-ice field. : At least in the Weddell Sea, however, the ice advance during autumn and winter may be primarily of thermodynamic origin in the sense that a lot of new ice is created near the northern ice margin (Hibler and Ackley, 1983; Kottmeier and Hartig, 1990; Massom, f". 1992). The results in II correspond to this: our buoy was deployed on an ice floe in the marginal ice zone, but although it drifted northward it found itself later in the interior of the ice field, indicating that the ice edge advanced more rapidly than individual ice floes. r- : > , :.,uv. v 25 In VII we observed an average divergence of 7 x 10 s s"1 for buoy grids in the Weddell Sea. As in the studies of Wadhams et al. (1989), Martinson and Wamser (1990) and Kottmeier and Sellmann (1995), the mean divergence was much smaller than the amplitude of variations around it. The wind forcing and especially the tidal and inertial motions occurring in the ice cover are of importance for local periods of divergence and conver gence (McPhee, 1978; Kottmeier and Sellmann, 1995; Geiger et al., 1994) and thus for the production of open water. The periods of divergence and convergence are therefore significant for short-term variations in the regional heat exchange. Combining the results of papers V and VII, we can calculate time series for the areally-averaged sensible and latent heat flux for a grid of platforms marked by the locations of ISW and two buoys (identification numbers 5908 and 6440, see V or VII). We apply the mosaic method, (19) and (20), in the calculations and simply assume that the local flux from leads decreases exponentially in time because new ice is formed at the lead surface (compare to Makshtas (1991), his figure 20). The initial open water fraction in the grid was -10%. The resulting fluxes are shown as time series in Fig. 2 (this can be compared to Figs. 4 and 5 in V and Fig. 20a in VII). It should be stressed that several factors may cause errors in the quantitative values, but the figure is merely to illustrate the effect of ice dynamics on the atmosphere-ocean heat exchange. The positive mean divergence is seen as an increasing trend in the areally-averaged fluxes, and the high variations, especially in the sensible heat flux, demonstrate the sensitivity of the areally-averaged flux to the drift divergence. Variations in the local flux between ice and open water are much smaller for XE than for H, and the areally-averaged XE is thus less sensitive to the divergence. Julian day in 1992 Julian day in 1992 Fig. 2. Time series of areally-averaged sensible and latent heat fluxes calculated for a grid of platforms in the western Weddell Sea. The calculation is based on the flux results in V and the results of ice drift divergence in VII. The initial lead fraction was 10%, and the heat fluxes from the leads were assumed to decrease exponentially in time, a) sensible heat flux, b) latent heat flux. 26 4. MODELLING r* The principal modelling studies were two-dimensional, and focused on the following topics. A dry ABL model was used in simulating neutral flow over a horizontally het erogeneous surface to study the effective roughness length (II). A moist version of the model was applied in a study of the subgrid-parameterization of surface fluxes over polar 3. oceans in diabatic conditions (VI). In addition, a few attempts were made with a one-dimensional ABL model to study the modification of an air-mass flowing over SST fronts in the Greenland Sea (HI). V / , Observations on the spatial averages of the turbulent surface fluxes over large het .V erogeneous surfaces are not easily available. Aircraft-based direct measurements of the covariances between the turbulent fluctuations can provide good data (e.g. Hartmann et al., 1994; Walter et al., 1995), but an adequate data set covering different conditions over large areas would require very extensive and sophisticated field programs. Hence the topic is more practically addressed by numerical modelling studies (Andre and Blondin, 1986; •fl Taylor, 1987; Mason, 1988; Claussen, 1991a,b; Glendening, 1995). The basic idea in our principal modelling studies (II and VI) was to apply a mesoscale ABL model, the whole model domain of which was intended to represent a single grid square of a hypothetical large-scale model. The mesoscale model was usually run into a steady state for given forcing and boundary conditions, and the distribution of variables in the model domain !•- ’71 represented the subgrid distribution in the large-scale model. The various methods of u* parameterizing the effective roughness length and the grid-averages of the surface fluxes were then compared against the reference values produced by the mesoscale model. - >• v 4.1 Neutral flow 3 Our objective was to model neutral flow to get an estimate for the effective roughness r * length (Zi)Cfr) for a large area, and to compare theZocff with the distribution of local roughness lengths and with the various theories for their relationship, such as (16) and (17). Further, the effects of the height of the reference level were studied, as well as the effects of internal - boundary layers. The model used was a two-dimensional dry hydrostatic ABL model with 10 levels 3 in the vertical and a 2 or 4 km horizontal gridlength. The flow was forced by a geostrophic •• •!; ' : wind and turbulence was described by a first-order closure. The model is described in '. more detail in II and in Alestalo and Savijarvi (1985). Two fixed values for the local roughness length were used in the simulations, and the proportions of the areas having • •' these two values were varied in order to find out the relationship between the z0 distribution ; { and Z0efr. The model was run to a steady state with each Zq distribution, and Z0eff was determined from the area-averaged wind profile. The values given for Zq approximately represented water and forest. The values chosen do not, however, drastically affect the 2 final results, because we were looking for the relationship between the Zq distribution and ",; Z^a, and notZo eff over any specific heterogeneous terrain. The following percentages were used for the land area: 10, 30, 50, 70 and 90%. The land area consisted of three islands j of equal size. In addition, when the proportion of land was 50%, this was in turn divided :. into one, three and ten islands. The idea was to study the effects of internal boundary layers by varying the lengths of the homogeneous surface sections. 27 The model results were compared with the values given by the various theories (see Fig. 1 in II). The uncertainty between various Z0cff estimates reached a maximum for the half land - half water case. The simple logarithmic average of local z0:s gave a lower than the model results, while the empirical methods based on terrain classification (Smith and Carson, 1977; van Dop, 1983; Kondo and Yamazawa, 1986) gave too high a Z£a when applied here. This was probably partly because the form drag due to hills and the edges of vegetation had also affected the observed winds on which the empirical equations were based (compare to Klaassen, (1992)). The equations (16) of Mason (1988) and (17) of Taylor (1987) came closest to the model results. The experiments with varying numbers of islands in the model domain showed that Z0cff increased with the decreasing scale of homogeneous surface sections, which is accounted for in (16). We did not detect any effect in Zja arising from the height of the lowest model level (compare to section 2.3.1). The model results were utilized in calculating Z£K for Finland in 150x150 km2 grid squares. The two methods judged best by the model studies, (16) and (17), were selected for use. In practice, the calculation was based on information on land use in Finland. The land use was divided into 11 categories and a representative % was estimated for each of them. The z,,:s were estimated considering a summer situation with full-grown vegetation. The three most common terrain types were the picked from squares of size 15x15 km2. Zocff was first calculated for these squares. The results were then used as local values for Zo, and the calculation was further extended to the 150x150 km2 squares. The results indicated that the most important factor for Z„cff was the amount of water surface in a grid square. Hence, coastal areas and the lake district of south-eastern Finland are characterized by small values ofZ q cK. The greatest values are found in northern Finland, where most of the smaller squares are covered by forests. Still further north Z£a decreases because vegetation becomes lower and form drag was not included in Z0cff. The results based on the calculation method of Taylor (1987) were on average 63% of the results based on Mason’s (1988) method. The relative difference was largest in grid squares with low Z0cl[. Theoretically, use of the results based on Mason’s method is better when it is important to produce the correct momentum flux, as is probably the case in general circulation modelling. In some applications it might be more important to produce correct mean-wind profiles in the surface layer, e.g in short-range forecasting and air-pollution studies. In these, (17) from Taylor (1987) might be better. In neutral flow the grid-averaged sensible heat flux is zero by definition, but the grid-averaged latent heat flux as well as the radiative fluxes may be non-zero. The latter fluxes and the other possibilities open for parameterizing the momentum flux will be addressed in the next section on stratified flow. The results can also be applied in the case of neutral flow. 4.2 Stratified flow In stratified conditions we have to consider the parameterization of grid-averages of sensible and latent heat flux, momentum flux and the radiative fluxes. In the modelling study (VI) we addressed the problem over a polar ocean with grid squares covered by sea ice and large areas of open water, which may occur due to polynyas or single ice edges. 28 The basic model used was the same as with the neutral flow, except that the air moisture and clouds were also included, and the surface layer parameterization was developed by incorporating the scheme of I in the model. A 2-km horizontal gridlength was used with 10 levels in the vertical reaching a height of 2 km with the boundary conditions applied at 3 km. Additionally, a couple of control runs were made with a 50-level version of the model, the grid extending up to 5 km. These were to certify that the 10-layer model also reliably simulates convective flow. The surface was set to be either sea ice or open water. Over the sea ice, z„ was set to 1 mm, while the surface temperature depended on the energy budget, calculated for winter (no short-wave radi ation), and ranged from -30 to -10°C depending on the flow. Over the open water, Zq depended on the wind speed (Smith, 1980) and the surface temperature was set to the freezing point of-1.8°C. As in the studies of neutral flow, the proportion of the model domain covered by the two surface types was varied between individual simulations. A total of 33 simulations were run. They consisted of 6 principal groups each having different conditions with respect to the geostrophic wind direction, location of open water, and number of polynyas. In each group the fraction of open water was altered between various model runs (or other :=< .■ -- relevant changes in the boundary conditions were made). Further, the model was run with various geostrophic wind speeds, and the sensitivity to the roughness and stability was studied. Over the sea ice, the modelled surface layer temperatures, humidities and wind speeds were comparable to those observed in the Weddell Sea in V and VII. The flow properties r > - showed an increased air temperature, moisture, wind speed and wind stress over a polynya. In addition to the direct stability effect, baroclinity and "ice breeze" (analogous to the sea breeze) were sometimes responsible for the increased wind speed. The wind and stress results qualitatively corresponded to therecentreview, data analyses and modelling studies of Guest et al. (1995). A region of upward vertical motion developed downwind of the polynya, when the geostrophic wind direction was perpendicular to it, and over the polynya in the case of a parallel geostrophic wind. Over the sea ice, the sensible heat flux was downwards, with a typical value of -20 W/m2, while over a polynya the upward flux r” •• reached values of 200-500 W/m2. In a case with an ice patch surrounded by open ocean, the wind speed and air temperature dropped over the ice, and the vertical motions remained small. The various parameterization schemes for the grid-averaged fluxes were compared i - with the model results. Some of the comparisons are shown in Fig. 3 (adopted from VI). '' The results can be summarized as follows. The use of transfer coefficients dependent on stability is essential. Neutral transfer coefficients can yield errors of 70-80 W/m2 in equations to predict it were, however, not applicable in cases of wide polynyas. The i' • blending height was of the order of 100 m in conditions of generally unstable stratification, -- / * and of the order of 10 m if the overall stratification was stable. The vertical distribution of heat rising from polynyas was analyzed as well. Although the model had its restrictions .'V * 29 in simulating the processes involved, the results in general demonstrated a need to include an algorithm in GCMs for the vertical distribution of release of the sub-grid scale surface heating (compare to Glendening (1995)). open water fraction open water fraction open water fraction Fig. 3. Applicability of the following various schemes to parameterize With respect to the surface net long-wave radiation, the grid average was more affected by the subgrid variations in cloudiness than by those in air temperature. It depends, however, on the situation (geostrophic wind speed and direction, number of polynyas, overall stability and air humidity) as to whether there are systematic variations in cloudiness above sea ice and open water. In general, clouds tend to form over open water due to local convection. In such cases, the best results were produced when a maximum estimate for the local cloudiness over the polynya (depending on the grid-averaged •t.. cloudiness and open water fraction) was used, after which the mosaic method was applied. Considering the parameterization of the skin-friction part of the momentum flux, the performance of parameterization schemes based on the surface wind varied from case to (v: case. The combination of separate roughness lengths and an effective stability function yielded results on average closest to the model results. The results based on the use of the geostrophic wind and a geostrophic drag coefficient were, however, as good as the results based on the surface wind. The uncertainty was in general of the order of 10-30 mN/m2. The modelled surface winds over the polar oceans are themselves very uncertain. Hence we feel that the most reasonable way to parameterize surface momentum flux might be •v to use the geostrophic approach and apply (22). To get accurate results it is, however, -v vital to express the dependency of CG on stability. The model results suggested that C0 ■ vt decreases with increasing air-surface temperature difference. Also the data analyses in VII indicated that CG decreases with increasing stability, with 10/L as the most relevant r-i.’v stability parameter (Fig. 1). V'*: One-dimensional modelling . Stratified flow was also modelled using the one-dimensional ABL model of Savijarvi and Vihma (1987). The model was applied in HI to simulate the air-mass modification during flow over sea-surface temperature fronts. The model results were compared against the observations made in the Greenland Sea (section 3.1.1). The ■ ■ model used resembles that of Louis (1979), which also forms the basis for ABL para ' meterization in the ECMWF model. With respect to the parameterization of turbulence (mixing length theory), the model is similar to our two-dimensional model. The vertical grid, however, consists of 15 layers and extends up to 15 km. Air moisture, condensation and simple shallow convection schemes are also included. In a simulation of a frontal crossing with unstable stratification the model results were close to those observed. An attempt to model the air-mass modification during a frontal crossing with stable stratifi cation on both sides produced, however, rather poor results. This was most probably due to an inadequate model resolution in the surface layer. 5. CONCLUSIONS Processes of interaction between the atmospheric boundary layer and the planetary surface were studied. Special emphasis was laid on polar ocean surfaces: the open ocean, f- leads, polynyas and sea ice. The local exchange of momentum, heat and moisture was studied theoretically and experimentally, and the exchange processes over heterogeneous surfaces were addressed by modelling studies. The following conclusions were drawn: !■ ‘ , ■ - . v-,.: - % 31 1. Over a homogeneous surface, the local turbulent fluxes of momentum, heat and moisture can be reasonably well estimated using bulk or gradient equations based on the Monin-Obukhov similarity theory. Solving of the equations requires an iterative calculation to consider the effects of stability and observation heights. If properly accounted for, mutual differences in the observation heights of wind speed, air temperature and air moisture do not decrease the accuracy of the -results. A possibility alternative to iteration is to apply the relationships between the Obukhov length and the Richardson number. 2. In practice, accurate data of the surface-layer quantities (wind speed, air temperature and humidity) required to utilize the bulk or gradient equations are not always available. This may be the case both in data analyses and modelling. Thus, we have to use data from higher atmospheric levels and apply the resistance laws of the ABL. Simultaneous rawinsonde soundings and surface-layer observations in the Weddell Sea allowed us to compare the methods, and for the sensible heat flux (V) the results showed good agreement. Analyses on the ice dynamics (IV and VII) and modelling studies (VI) showed that the geostrophic wind and information on the stability provide a good basis for parameterization of the ice drift and momentum flux. 3. Over the open ocean far from the coasts and ice edges, the atmospheric surface layer is generally close to thermal equilibrium with the local surface. The sensible heat flux is therefore small and may be either upwards or downwards. Sea-surface temperature fronts cause, however, surface heterogeneity yielding non-equilibrium boundary layers. The turbulent fluxes may therefore be larger and change direction over short distances. In the Greenland Sea expedition in spring and early summer, the highest turbulent fluxes we observed were 30-40 W/m2 both for H and %E. The SST change across a front was on average 2.8°C with a typical gradient of 0.05-0.4°C/km. These produced an average air temperature change of 0.9°C across a front, which was of the same order of magnitude as the changes produced by diurnal forcing and the spatial and temporal variations on larger scales. Effects of advection more vigorous than in the regions of SST fronts are observed over the open ocean in the vicinity of the edges of sea-ice and floating ice shelves. 4. Paper V provided what is though to be the first year-round data of turbulent surface fluxes over the sea-ice zone of the Weddell Sea. The sensible heat flux was generally downwards, and together with an upward oceanic heat flux through the ice it compensated the heat loss from the surface via long-wave radiation. The flux magnitude was typically from -15 to -20 W/m2 in winter and -5 W/m2 in summer. The results for latent heat flux suggested weak evaporation of 0 to 5 W/m2 in summer and weak condensation in winter. The turbulent fluxes were smaller than the fluxes via net long-wave radiation. Over leads and coastal polynyas in the Weddell Sea, an upward sensible heat flux of 100 to 300 W/m2 and a latent heat flux of 60 to 80 W/m2 were typical, except in summer when the air temperature was close to the sea surface temperature. In winter, the maximum values of the sensible heat flux reached 600 W/m2 and well exceeded the fluxes via net long-wave radiation. Over the open ocean in the vicinity of the continental ice shelf, the sensible heat flux decreased with distance away from the ice shelf. 32 5. Ice motion in the Weddell Sea is driven by the wind and a clockwise ocean gyre. The drift kinematics exhibits apparent differences between the eastern and western V parts of the Weddell Sea. Close to the Antarctic Peninsula, the ice drifts as an almost ■4 non-rotating uniform field with a low speed, reduced small-scale motions and little meandering, compared to regions further east. On time scales of days, the primary ' v -,>• effect is that of wind. Our buoys detected inertial motion in the areas east of 35°W and in the region of the Antarctic Circumpolar Current. In the west near 50°W the - periodic movements were presumably dominated by the M2-tide. Using a reasonable time lag the patterns of eastward drift were in coherence over east-west distances of 400-500 km. A linear model between the ice drift and wind (either the measured or geostrophic wind) explained 40-80% of the drift velocity variance. The degree of explanation was higher in the central Weddell Sea (here ~40°W) and lower closer V to the Antarctic Peninsula. The linear model allowed us to estimate the ocean surface •... currents, and with these residual currents the model usually provided a good basis on which to simulate the ice drift trajectories. The linear model parameters depended on the region, and the data suggested that stable stratification reduces the wind forcing on the drift. For 60-80% of the time the drift direction was coincident with that of both the geostrophic wind and the ocean current. 6. Using geostrophic wind fields, the annual mean net ice export through a transect crossing the Weddell Sea was found to be 22,000, 8,500 and 18,000 m3/s in 1992, 1993 and 1994, respectively. Most of the net export took place in winter and spring, export prevailing west of 35°W and import east of it. The associated export of fresh water is approximately balanced by precipitation and the melting of the ice shelves. 7. Based on the local turbulent fluxes over the sea ice, leads and coastal polynyas, we estimated that the annual areally-averaged total vertical heat loss from the Weddell Sea is 20-30 W/m2. The result is in close agreement with an independent estimate by Fahrbach et al. (1994) based on oceanographic observations of horizontal heat transport. Our estimate for the latent heat flux is 3-5 W/m2, accounting for a water vapour flux of 1.2xl0" 6 - 2.0x10 s kgm'V 1. 8. The sea-ice dynamics and the concentration and thickness distribution depend interactively on each other. This interaction affects the total vertical heat loss from ice-covered oceans. The differences in the local air-surface heat fluxes between the sea ice and open leads (or polynyas) are extreme, and the fluxes over sea ice depend l" on the ice thickness. The ice concentration and thickness distribution are therefore l:.:, ' i key variables affecting the areally-averaged heat fluxes. k* - 9. Surfaceheterogeneity is afundamentalproblemforthe parameterization of exchange processes both over the polar oceans, where the heterogeneity mostly arises from the uneven surface temperature distribution, and generally over the Earth’s surface, where the distribution of surface roughness is assumed to be the main source of heterogeneity. An effective roughness length calculated according to (16) or (17) provides a sound basis for the description of surface roughness over heterogeneous terrain. If the near-surface wind speeds are reliably known, the use of yields a reasonable surface momentum flux in neutral flow. The field of Z„crf over Finland depends mostly on the distribution of water and forest, and shows reduced values over grid squares in the lake district and coastal areas. ■ ;•: 33 10. Considering the surface fluxes of sensible and latent heat in stratified flow over a winter polynya, an extended mosaic method provides a good basis for the para meterization. The method uses estimates for local surface temperature, air tem perature, specific humidity and wind speed over the ice-covered and ice-free parts of the grid square. For parameterizing the net long-wave radiation, an estimate for the sub-grid distribution of cloudiness is useful. In lieu of accurate surface wind data, the parameterization of surface momentum flux seems to be reasonable on the basis of the surface pressure field and a geostrophic drag coefficient depending on stability. The parameterization methods here recommended for polar oceans are, however, not necessarily the best ones for applications over other heterogeneous surfaces (Lhomme et al., 1994). Issues to be focused upon in further research A. More data are required on Weddell Sea ice motion to distinguish between the spatial and temporal variations in the dynamics, and to study the inter-annual variations and possible climatic trends. A continuous network of buoys is therefore required in the area. The ice advection from the Weddell Sea has important implications on the heat and salt balance and further studies of it are necessary. More information is required on the drift divergence and the factors controlling it. This would provide us with a basis on which to estimate and model the dynamic production of open water within the ice field, which is essential for calculations of areally-averaged heat and moisture fluxes. B. More observations are needed on the local surface fluxes occurring over the sea ice and especially over polynyas and leads. The observations should include measure ments of both long-wave and short-wave radiation and the surface temperature to verify the parameterization schemes at low temperatures. Direct measurements of the turbulent fluctuations of the wind speed, air temperature and humidity are essential to provide more accurate data on the turbulent surface fluxes, which we have so far estimated from the bulk and gradient measurements. More data on heat conduction through the ice and snow are also required. C. Observations on the surface fluxes averaged over large heterogeneous areas are required. Measurements should be made over fractured ice cover, the marginal ice zone, leads and polynyas. The data should include vertical profiles extending through the Ekman layer (rawinsonde soundings) as well as horizontal cross-sections with simultaneous information on the surface type and temperature (helicopter and aircraft measurements). The latter should include data on the large-scale roughness and the distributions of surface temperature, ice concentration and floe size. The data would provide a basis on which to better validate the resistance laws over polar oceans, and to study the dependency of the regionally-averaged fluxes and the geostrophic drag coefficient on stability. Further, possibilities for the parameterization of the surface fluxes on the basis of easily-available data on ice concentration and surface tem perature distribution are to be studied. The experiments should cover spatial scales large enough to also provide data on the (non-turbulent) fluxes associated with mesoscale circulations. 34 D. The modelling studies should be continued by studying the mesoscale circulations - ■< induced by surface temperature discontinuities, and the fluxes associated with them. •v'-V Three-dimensional situations should be considered, and the sensitivity of large-scale models to the use of various parameterization schemes for the surface fluxes should ■ Xi be studied. Finally, the coupling of atmospheric boundary-layer models and models of sea-ice dynamics should be a principal topic of future research. Acknowledgments Help and advice from several people have made this thesis possible. I would especially like to mention the following persons. / - . I am grateful to professor Jouko Launiainen, the supervisor of my thesis, for help and advice, for infectious enthusiasm and continuous interest towards my work, for constructive and encour ■ • -« aging criticism, and for performing the field work of our project once in the Greenland Sea and twice in the Weddell Sea. Hannu Savijarvi, associate professor in the Department of Meteorology of the University of Helsinki, is the other adviser I especially wish to thank. His encouragement and advice on numerical atmospheric modelling have been important for me. Professor Juhani Virta is acknowledged for providing me excellent working conditions in the Department of Geophysics. Professor Eero Holopainen and associate professor Matti Lepparanta are acknowledged for constructive criticism. A large portion of this thesis was based on field data from three polar expeditions. I wish to thank the officers and crews of the research vessels Aranda, Polarstem and Akademik Fedorov for their efforts. Kalevi Rantanen, IVO International, is especially acknowledged for his extremely skilful field work. I wish to express my sincere gratitude to Juha Uotila, Finnish Institute of Marine i.: Research, for his help in data processing and computer programming, and especially for his co-operation while preparing paper VII. Much of the work was carried out as a part of the Finnish Antarctic Research Program, coordinated by the Finnish Institute of Marine Research, and I thank professor Pentti Malkki, the Head of FINN ARP and FIMR, for making this project possible through support in logistics and finance. The project was carried out in co-operation with several foreign research institutes, in particular the Alfred-Wegener-Institute for Polar and Marine Research (Bremerhaven, Germany), the Arctic and Antarctic Research Institute (St. Petersburg, Russia), and the Lamont-Doherty Earth Observatory (Palisades, New York, USA). I thank them for their fine co-operation. I am grateful to several scientists in the Finnish Meteorological Institute: Robin King for correcting my English in papers II, IV, V, VI, VII and in this summary, Seija Argillander for her help in preparing paper II, as well as Timo Hopeakoski and Eeva Saamilahti for putting ECMWF pressure analyses at my disposal. The staff of the Department of Geophysics and FIMR are * < " acknowledged for their co-operation, especially Jarmo Aho, who worked in our project in its early stages, and Kari Pulkkinen, for his help in some computer problems. The Academy of Finland is acknowledged for funding support. Finally, I wish to thank my parents and friends who have always supported me without ever asking "Isn’t your thesis ready yet?" ; . -V 35 6. REFERENCES Alestalo, M. & Savijarvi, H. 1985: Mesoscale circulations in a hydrostatic model: coastal conver gence and orographic lifting. - Tellus 37A: 156-162. 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Oceanology of the Antarctic Continental Shelf. ; - Antarctic Research Series 43. - AGU, Washington, D.C. * V- .}<- NOTATION < > an average over a grid square a slope coefficient in a power law for ice velocity spectral energy 88 temperature difference between the surface and the ABL top X latent heat of evaporation XE latent heat flux p. stability parameter in the ABL similarity theory co angular frequency in ice velocity spectrum a coefficient in equation (17) (= 0.09) b blending height A,B,C empirical functions describing the stability effects in the ABL cp specific heat of air CD air-surface drag coefficient CH exchange coefficient for heat CE exchange coefficient for moisture CDN neutral drag coefficient Qjn neutral exchange coefficient for heat neutral exchange coefficient for moisture CHcfr an effective exchange coefficient for heat geostrophic drag coefficient CG •v - . Cw ice-water drag coefficient i r. E water vapour flux, i.e. evaporation f Coriolis parameter ‘-.-f f„ open water fraction g acceleration due to gravity G geostrophic wind speed h height of the sea surface above a level surface H sensible heat flux I internal ice resistance X von Karman constant (= 0.4) k unit vector normal to the surface L Obukhov-length 41 m mass of ice per unit area M2 principal semidiurnal lunar tide q specific humidity of air q, scaling parameter for air moisture <2l net long-wave radiation flux <2S net short-wave radiation flux Ro surface Rossby number S spectral energy t time T0 reference temperature in eq. (1) «, friction velocity V wind speed % ice drift speed z height coordinate Zq local roughness length for momentum zr local roughness length for temperature Zq local roughness length for moisture Zncff an effective roughness length for momentum Subscripts Superscripts s surface i ice z height z in the air w water M momentum an overbar denotes a vector variable H heat omitting the overbar means the scalar value of the E moisture vector Abbreviations ABL atmospheric boundary layer ACC Antarctic Circumpolar Current (here defined as the region north of 63°S) CLS Collecte Localisation Satellites (company; CLS / Argos, Toulouse, France) CWS Central Weddell Sea (here defined as the region from 25 to 45°W) ECMWF European Centre for Medium Range Weather Forecasts (Reading, England) FIMR Finnish Institute of Marine Research FINNARP Finnish Antarctic Research Program GCM General Circulation Model ISW U.S.-Russian Ice Station Weddell-1 NOAA National Oceanic and Atmospheric Administration (of the USA) SST sea surface temperature WWS Western Weddell Sea (here defined as the region west of 45°W) Corrections paper IV: page 14,475; equation (1): + sign is missing from between Tw and 7 paper V: page 417; equation (A8): T V \r> ; 1 • V C/,' K A.- ?;■ >. -5 E t. rs 1 *1 mm © I ■k t f 3; .43: % ■V. ...i 34:4 tv: • .1 4-.v ■i v ; j.. .i -i Copyright 1995, with the kind permission from Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK. Not to be further copied without the publisher's specific permission. Derivation of Turbulent Surface Fluxes - An Iterative Flux-Profile Method Allowing Arbitrary Observing Heights J, Launiainen and T. Vihma Department of Geophysics, University of Helsinki, Fabianinkatu, 24 A, 00100 Helsinki, Finland Abstract A method for practical calculation of the turbulent surface fluxes of momentum, sensible heat and latent heat between the atmosphere and the ocean/land surface is presented. The effect of stratification is taken into account using the Monin-Obukhov similarity theory and relevant universal functions. The iterative calculation method allows the obser vation heights of wind speed, temperature and humidity to be arbitrary and different from each other. Various forms of observations of moisture can be used. In the standard form, the algorithms yield reasonable estimates for fluxes above a water and ice/snow surface. For estimates above land on-site information should be available, because of a great variety of roughness conditions and a possible displacement height involved. After proper adjustments, the algorithms might be installed e.g. into the software of an automatic station. Key Words: surface fluxes, roughness lengths, bulk-method, Monin-Obukhov similarity theory 1. INTRODUCTION AND THE THEORETICAL where z is the observation height and tr„, f?. and g. are BACKGROUND the scaling parameters of velocity, temperature and hu midity, which characterize the observation situation in The current state of art of knowledge of the surface question. Parameter k is the von Harman constant and boundary layer physics allows the effects of stratifica $;/ and are the so-called universal functions (in tion to be taken into account in the practical routine the gradient form) which characterize the effects of the determination of the surface fluxes. Utilization of the atmospheric surface layer stratification on the profile gra well recognized Monin-Obukhov similarity theory 1,2 in dients. In the argument of the universal functions, L Is volves, however, an iterative process, except in discrete the stratification parameter, the Monin-Obukhov length. cases when approximations are used. On the other hand, Utilizing the definition of the scaling parameters, the differences in observing heights of wind, temperature and integration of the profile gradients with respect to z humidity, as often is the case e.g. in ship observations yields (Appendix 1) the familiar bulk aerodynamic for and synoptic meteorological stations, raise another dif mulae for the turbulent fluxes of momentum (r), sensi ficulty which is reflected in the solution. In this paper, ble heat (H) and water vapour E (or latent heat flux £E a method and algorithms are reported to determine the where £ is the enthalpy of vaporization) surface fluxes under stratified conditions allowing the ob servation heights to be mutually different. Various forms T = PCD,VJ = pul (4) of observations of moisture can be used. In addition to the flux results, the model calculates the surface layer H = pcpCnz{0, - 0,)VZ (5) profiles and e.g. estimates the 10 m level wind speed. E = pCBz(q, -q,)V, (6) The bulk parameterization of the turbulent fluxes in the constant flux layer is based on the Monin-Obukhov where Vx is the mean wind speed at a height of z and p is \ similarity theory, which in terms of non-dimensional pro the air density and cp is the specific heat capacity of air. file gradients of wind speed (V), temperature (5) and 0t — 0X and qt — qt are the differences in potential tem perature and specific humidity between the atmosphere ,1. specific humidity (q) may be given as (cf. Appendix J). *,* and the surface, respectively. The bulk transfer coefficients, the drag coefficient Cp, the Stanton number Ch and the Dalton number Cc, may (i) be expressed as b/ t f CDl = CD(z,z0,» Af (*/£)) (7) (2) Ciiz = Q/(z,z0,ZT,’t,M(z/7'),'I,z/(z/7-)) (8 ) Cez = Cb(z,z0,z„#a /(z/L),*b(z/Z,)) (9 ) (3) Paper received 26 January 1989 and in final form 10 October 1989 Referee: Dr. A.A.M. Ifoltslay ! Environmental Software, 1990, Vol. 5, No. 3 113 ------yr •"J- ;r,‘ v-y 'v - Derivation of Turbulent Surface Fluxes: J. Launiainen and T. Vihma where z is the measuring height and zq , zp and z? nition of observation levels and calculation level, are the roughness lengths for the wind speed, tempera data sources and output devices etc. Input of ob ture and water vapour, respectively. $«,$;/ and servations of wind speed, surface temperature, air are the integrated universal functions which characterize temperature and moisture. the effects of the atmospheric surface layer stability on the bulk transfer coefficients. In cases of neutral strat 2. Calculation of humidity quantities. ification, the transfer coefficients depend on z and the roughness lengths only. 3. Sctting/calculation of roughness parameters of The flux-profile relationships introduced arc given in zo,zt and z,: Wind dependent formulae for water a functional form in Appendix 1, which also gives the surface. For snow/ice surface formulae based on motivation basis for the roughness lengths and universal observed surface roughness (f in cm). For land, zo functions adopted for the study. as estimated by the user. Instead of the "bulk" approach discussed, i.e. the use 4. Correction (if relevant) of observations to corre of the air-surface differences in flux calculations of (4) spond to the calculation level and the calculation to (6), eqs. (1) to (3) may be integrated between two of the bulk transfer coefficients Cp„ C//,, Cr* and arbitrary height levels, when using observations made •w fluxes T, // and £B (or E), and further the Monin- at two different measurement levels. This kind of ap Obukhov length L. The first quess for fluxes is cal proach is practically very difficult e.g. in studies above culated for a neutral case, i.e. the integrated uni the sea and snow, but can be proper in studies above versal functions of the Monin-Obukhov similarity land in avoiding difficulties when observing such surface theory are settled to vanish. properties as the real surface temperature. Generally, however, the demand of a high accuracy of rather small 5. Convergence of the iteration is tested as a change level differences to be measured for this "level-difference" of the argument z/L ( z = calculation level) so that or "profile ” method, is often hard to satisfy. This is the the results are regarded as stable when the differ case especially for long period and routine basis. In fact, ence between succesive values of |z/L| 1. Interactive opening; definition of the type of sur face, option for the level-difference method, defi i :vV,’ ;* 114 Environmental Software, 1990, Vol. 5, No. 3 . u •t‘* V - - Derivation of Turbulent Surface Fluxes: J. Launiainen and T. Vikma converging not converging Fig. 1. Critical wind and air-sea temperature difference for convergence Table 1. Test examples of flux calculations. OBSERVATIONS RESULTS land. %n= 10 oa £EIH/o2) tldlyta2) H(H/n z) lEUMa2) VjgfoVsl Tiora T3ra V* V" w® 100. •BitVm) HIVia-) 1QO. 5.0 10.0 7.2 4.9 0.829 13.66 -9.00 7.55 0.289 83.97 -47.66 40.57 5.0 10.0 7.2 9.9 7.4 0.830 13.65 -9.00 7.49 0.299 83.93 -47.83 40.23 5.0 10.0 7.2 70 0.829 13.66 -9.01 7.62 0.289 84.01 -47.87 40.92 ' 5.0 18.4 19.0 15.2 -0.169 32.12 3.18 46.40 -0.055 200.84 16.09 238.99 5.0 18.4 19.0 18.3 16.3 -0.169 32.13 3.18 46.79 -0.055 200.92 16.10 240.99 5.0 18.4 19.0 81 -0-169 32.13 3.18 46.65 -0.055 200.89 16.09 240.27 5.0 -3.0 5.0 -12.8 -1.411 40.74 65.51 86.21 unrealistic 5.0 -3.0 5.0 -2.9 -5.9 -1.411 40.74 *.51 86.21 situation over 1 nnrt 5.0 -3.0 5.0 42 -1.411 40.75 66.51 86.30 l 1) 1 ) 1 1 T 2 ) 3 > 4 ) 3 ) 4 ) 5) Notes : 1. Observation levels of 19, 10 and 8 m, for wind speed, temperature and humidity, respectively. The calculation level may be arbitrary, (cf. Appendix Note 1) 2. Humidity observation to be given as dew point temperature, as RH(% ) or as dry and wet bulb temperature, optionally (Appendix Note 2). 3. Dimensionless stability parameter sjL referred to a "standard ” height (z = 10 m). 4. For definition of "sea" and "land" roughness, see Appendix Note 3. 5. Latent heat flux connected with potential evaporation. I Environmental Software, 1990, Vol. 5, No. 3 115 J i Vi v-: % •k i Derivation of Turbulent Surface Fluxes: J. Launiainen and T, Vihma From the physical point of view, finally, we may see that under strongly stable stratified conditions the sta bility effectively prevents the turbulent exchange. This, accompanied with low wind speeds most frequently in volved, causes the turbulent fluxes to be small, and errors in bulk parameterization are likely to be insignificant al though the calculation procedure could not converge. S' A few numerical test examples of the calculation scheme are given in Table 1 . They correspond to cases > V. of stable, slightly unstable and strongly unstable strati fication for "sea" and "land ” conditions. In addition to the fluxes, various other results are given and an option for printing the surface layer profiles of wind speed, temperature and humidity is included (cf. Appendix Note 8). % \ i E/p <10 4. VALIDATION OF THE MODEL In order to test the reliability of the estimates gained by the calculation procedure, comparisons with field measurements were made. Unfortunately, studies report ing all the necessary data for making flux estimates and methodological comparisons arc in the literature very few. Fig. 2 gives comparisons for estimates above the sea. Fig. 2a gives the sensible heat and Fig. 2b the water vapour flux bulk estimates calculated from the NORPAX data3 and AMTEX data4, compared with the fluxes simultaneously measured3* 4 with the direct eddy correlation method. To avoid potential error sources af fecting the direct momentum flux measurements from ships and floating platforms 3* 4* 5, a comparison test for the friction velocity was made using a study based on mast measurements 6. Actually, the mean neutral drag coefficient used in the program originates from the study mentioned. Therefore, the comparison of friction veloc ity (Fig. 2c) tends to show merely a relevancy of overall parametrization, including stability effects. Generally, we think that the friction velocity or flux of momentum '• J is in average reasonably well established above the sea. Fig. 2a shows that the sensible heat flux estimates of the model fit well the data of 3 but give somewhat more scatter with respect to4. For the water vapour flux (Fig. 2b) the model gives slightly larger values, espe cially when compared to4. The latter seems to be re i 5 o o lated to a small mean Dalton number Cb obtained by 4. In addition, higher scattering is frequently accompanied with the measurements of water vapour flux originating from difficult observation praxis. As to the sensible heat and water vapour flux, strict comparisons with the mast data6 could not be made because moisture observations were not made. A rough comparison of the sensible heat flux estimates, however, fits the measured data6 quite Fig. 2. Validation tests of the model well. a) Calculated sensible heat flux (in the form of H/pcp ) versus the one measured using the eddy correlation On the basis of the reasonable flux estimates, the method (crosses from3 and circles from4) model estimates the stability parameter z/L well, which b) calculated water vapour flux (in the form E/p) versus was also found in the verification tests. the measured one (symbols as above). c) calculated friction velocity versus the one based on the observed 6 eddy momentum flux. 116 Environmental Software, 1990, Vol. 5, No. 3 Derivation of Turbulent Surface Fluxes: J. Launiainen and T. WAma Tlie calculation procedure for "ice/snow ” was tested in which k is the von Karman constant and functions of using sparse data found from7'8 for the sensible heat flux $h and are the (gradient) universal functions, under slightly stably stratified conditions. As the result, and the quantities with an asterisk arc "scaling parame the model estimates were found to agree reasonably with ters" defined as the former study, although underestimating very slightly. To the contrary, when compared with the latter one, the model yielded significantly larger flux estimates than II those observed with the eddy correlation method. The ? (A4) latter result might be accompanied more or less with an \ j > anomalistic low mean C// given by the eddy flux results8 . ”, No verification data was available for the water vapour (A5) flux. Considering the flux of momentum and friction ve pcpku * locity, one should expect reasonable estimates for them, E because they arc primarily controlled by the tested and q- = —piW. (A6) recognized drag coefficient formula 7 (A22) in the calcu lation procedure. u, called as friction velocity. Finally, because proper verification data was lacking, For a rough terrain (bushes, trees, large terrain irregu the level difference method was tested numerically using larities giving rise for a roof-top canopy) the observation an inverse test. In this method the "level differences ” height z is to be replaced by the height of z — d, where d '1 and fluxes to be tested were first calculated by the main is the displacement height12,13,14'15. model using various arbitrary meteorological conditions The profile gradients may be integrated with respect and roughness lengths. to z (or rather with z/L, where L is a stability parameter i.e. a constant characteristic of meteorological conditions in question, cf. below) between the surface and the mea 5. CONCLUSION surement level. This, together with the definitions of (A4) to (A6), yield the flux-profile relationships of An iterative method for calculating turbulent surface fluxes between the atmosphere and the ocean or a land r = pul surface was presented. It was noticed that mutual dif ferences in the observation levels of temperature, mois = pk-[ln z/z0 - *m(<) + ^/(Co)]-2^ ture and wind speed do not decrease the accuracy of the } results. The model was found to yield reasonable flux estimates when compared with those of direct eddy flux = pCoz V} (A7,a,b,c) measurements above the sea and icc/snow surface, for which verification data was available. After proper ad justments, the algorithms might be installed c.g. into II = pcpku.[ln z/zT - ’MC) + - 8.) 1 the software of an automatic station. = pcpk-[ln z/zo - *Af(C) + *A/(Co)] -1 APPENDIX 1. •[In z/zr - */,(C) + */z«t)]-1(8» ~ 8,)% 1. Formulae for flux-profile relationships (for a more detailed description sec9 ) — pcpCnt(Oa — 0x)Vt (A8,a, b,c) According to the Monin- Obukhov constant flux layer E = pku.[ln z/z, - »£«) + 'Se(C5)]-1(?. - similarity theory 1"2, which has been observed to hold true satisfactorily above the land and sea10'11,3, the dimen sionless profile gradients for velocity, temperature and = pk~[tn z/zo - I'A/tC) + 'J’m(Co )]-1 rv water vapour in the surface boundary layer may be for mulated as ■[In z/z, - *£«) + $£((,)]"'(?. - 9*)V, A = pCbi (.V> ~ In the formulae above, the stability parameter ( = zjL = $n [z/L) 1 z » ZT (A2) defined as (_:= i^//(l+0.61Tocp g/;/) = Environmental Software, 1990, Vol. 5, No. 3 117 TT Vv'-r- .-y 3s Derivation of Turbulent Surface Fluxes: J. Launiainen and T. Vihma where, in addition to the formerly introduced symbols, yield, however, somewhat larger drag coefficient esti To is commonly defined as the mean absolute temper mates than extensive oceanic data sets from sites with ature of the surface layer, g is the acceleration due to unlimited fetches. Most probably this results from the gravity. The stability parameters '/? < 118 Environmental Software, 1990, Vol. 5, No. 3 Derivation of Turbulent Surface Fluxes: J. Launiainen and T. Vihma For the heat and water vapour transfer coefficients the first order estimate (and error estimate) can be ob and roughness Icntghs, only a few experimental case tained on the basis of tables 15'48 . For the roughness results8 ’43 are available over snow or ice. For the study, lengths for temperature and water vapour, the model we adopted the results of a semi-empirical theory 44 which uses a suggestion 49 of zo/zr ~ 7 for surfaces in general. suggests the scalar roughness lengths for temperature For further technical details, see sect. 4 of Appendix and vapour as the sublayer ratios of zy/z* and z9 /z0 as a Note 3. function of the roughness Reynolds number Re (sect. 3 in Appendix Note 3). The theory gives for temperature and c) The standpoint of the "level-difference method ” in vapour roughness lengths (transfer coefficients) some our study is to use a wind velocity observation from one what larger estimates than 43 but yields for the Re-range level and temperature and moisture observations from of 10° to 10*, which come most frequently into question, two height levels (all arbitrary), respectively. For this comparable estimates with those shown by a review35 kind of solution, in addition to the observations, one has for the sublayer Stanton/Dalton number for natural and to give the roughness length zo (cf. above). In the so artificial surfaces. Accordingly, it is expectable that the lution, the program uses the same equations as in the calculation procedure introduced gives a reasonable first bulk method but hereby the heights zy and z9 and the order roughness length, transfer coefficients and bulk es co-variables accompanied are to be interpreted as real timates above snow and ice. measurement heights and not as the roughness lengths. In addition, in this case q, and 0, refer to the measure ment heights z9 and zy, respectively. Accordingly, the 2.3 Land surface, option for a level difference method program iterates the solution of the system of equations of (A76), (A86) and (A9b), in which the subscrits ”T" and Because of a great variety of roughness and canopy *q n refer to real physical heights (cf. Appendix Note 7). conditions, several complications and difficulties may arise affecting the accuracy of bulk calculations over land. For example, one may ask, above which a height In the level-difference method, one might think to use the Monin-Obukhov similarity theory is valid45,46 and two-level observations also for wind in order to be re when e.g a displacement height has to be used. Secondly, leased from using a zo. For practical observational rea on-site information about the roughness lengths should sons of detecting small vertical two-level differences, we be at hand. Thirdly, the necessary observations for the find this frequently rather inaccurate. In each applica bulk method corresponding fhe surface values, such as tion, however, sensitivity and error limits for the proce the real surface temperature, ’ may be rather difficult to dure, as for any method, should be tested. make. Accordingly, flux estimates over land using the bulk method may often remain as crude estimates, but d) Finally, one may note that although given in this they still seem to be vital and necessary for many prac section under the type "land surface", the level-difference tical and modelling purposes. Using a level difference method is directly applicable for any other surface, too method (cf. sect I. in the main text), one may try to (cf. the comment at the end of sect. 1 in the main text). surpass the last two weaknesses of the bulk method, i.e. by not including the roughness lengths and surface ob servations in the calculation procedure. On the contrary, this method has higher demands for the observational accuracy. In fact, both the methods arc included in the present algorithms, and the main physical standpoints connected with their application are outlined below: a) For the both methods, theoretically, the height co ordinate should be given in the form z — d, where d is the displacement height. Because the importance of this factor to flux calculations is dependent on the observa tion level (z), the importance of taking the displace ment height into account should be examined in each case specifically, fn practice, this is necessary for con ditions above land with large geometric irreqularities or a high canopy, e.g. higher than high crops. Most ac curately, the displacement height is to be determined from observations 15. When observations are lacking, a rather reasonable estimate for many cases may be obtained 13'14’47,48 from a simple formula of d ~ 0.7 • h, where h is the height of canopy or of predominant geo metric surface irregularities. b) After having chosen "land surface” and" bulk method ”, the program asks for z<>. If locally unknown, Environmental Software, 1990, Vol. 5, No. 3 119 Derivation of Turbulent Surface Fluxes: J. Xatmtoinen ond T. Vihma Appendix 2. Simplified flow diagram Note 6 ' •’> r.-V. :v-: I C '•, ■ '1 \5 V' 120 Environmental Software, 1990, Vo!. 5, No. 3 II. ; '> - Derivation of Turbulent Surface Fluxes: J. Launiainen and T. Vihma APPENDIX NOTES 3) Water vapour pressure e in air; (refer to the flow diagram of Appendix 2): a) if Tdtw observed then Note 1. t — c(Tfcu,) from (All) or (A12) 1) Overcome of results may be obtained on screen, disk file or on paper. b) if Tdry and Tw«t observed then (psychrometcr eqs.) 2) Input data of wind speed F(m/s), air temperature e = c(7u,c() — 0.666(7dry — TLet) 7(°C), surface temperature T^C) and air moisture (cf. point 6 below) may be given from files or from the key for Twct > 273.15 (A13) board. 3) Interactive choice of the type of the surface; "sea", and "icc/snow" or "land". After choosing "ice/snow ” the e = c(7u,e() — 0.57(7 4) Input of observing heights (in). For "land ” above where c(T) for (dry) air temperature from (All) or tall vegetation etc., the observing height must be given (A12). as z — d, where d is the displacement height (see Note 3 4) Specific humidities qs and q calculated from e, and point 4). e as 5) Choice of the calculation level; may be arbitrary (A15) and docs not affect the flux results, physically. On highly 7 — 1013- 0.378e non-neutral stratification cases, however, a slight but practically insignificant dependence of the flux results where e is e or e, from above. on the calculation level may be found. This is because of the common definition of the Monin-Obnkhov length, eq.(AlO), which defines the estimate of L to have a slight Note 3, indirect dependence on the (temperature) observation level, which is not physically the case, evidently. Definition of roughness lengths z0tzx and Zq\ G) Input of observations of moisture in any of the three 1) A common assumption of zt — s9 i.e. Cn — Ce alternative ways adopted a) as dew point temperature Tdaw(cC) b) as psychrometcr observations of 7h ry(°C) and 2) Roughness parameters; For water surface: Twd°C) a) for z„ as calculated from the neutral drag coefficient c) as relative humidity R1I (%). using the functional relationship given by (A7) tnzo = Inz — kCp'J2 (A16) Not<* 2. For the above, Cds[30) from the almost identical results 1) Saturation pressure of water vapour e(»n&) at a tem of 31 or ol6 giving for the drag coefficient a wind depen perature of T (K) is calculated from50 dent form of Cdn (10) • 103 = 0.G1 + 0.063V(10) (A17) f = cxp((—6?G3.6/T) - 4.9283 - /«7 + 54.23) (For the algorithm, actually, a smooth curve was fitted for 7 >273.15 (All) to the data of 3*. This may statistically somewhat im prove results, but may not give any significant physical e = exj)((—G141/7) + 24.3) refinement.) for 7 < 273.15 (A12) For coastal site applications, the form by 23 might be mo tivated 2) Saturation pressure e, at the temperature of a sur Cdn (10)-103 =0.80 + O.OG5V(10) (A18) face as giving somewhat larger drag coefficient and roughness e, = c(T,) lengths than (A17). Environmental Software, 1990, Vol. 5, No. 3 121 x Derivation of Turbulent Surface Fluxes: J. Launiainen and T. Vikma b) for ZqtT as calculated from the functional relationship d ~ 0.7 • h where h is the average height of vegetation. given by (A7)-(A9) as lnz,x = Inz - kC'JZCzl, (A19) Note 4. 1) Observations of Vt q and T (or rather #) are cor For the above, the Cdn as above, and for Cbn a data rected to correspond to the calculation level, using the compilation formula9 based on literature as profile equations in which the stratification effects are taken into account, as Cen (10) = 0.63Cdn (10) + 0.32 • 10~3 (A20) V(z) = f[V(zi),za,u.,i!M(z/L), <'*/(*]/£)] which with (A17) gives a slightly wind dependent form for Ceh as and Cen {1 0)-103 = 0.70 + 0.040^(10) (A21) 0(s) - 8(z) = f[8(s),8(z2)tZT,ff*,^H{z/L) f ^h{zz/L)) c) adjustment for the user defined roughness lengths zo and and ZqtT* instructions given under REM-scntences in the program listing. 5(5) - q{z) = /fo(s), *(%), zq, q.t ^(z/L), £(*>/£)] 3) For snow/ice surface where z refers to the calculation level and zj,Z2, and Z3 refer to the observation levels of wind speed, tempera a) after choosing "ice/snow" the program automatically ture and humidity, respectively (defined as RK, Y, X, asks for the observed surface roughness f i.e. the effective ZW in the algorithm). height of the roughness elements (not to be mixed with the roughness length z<>). This is a measure, the r.m.s. roughness in cm (i.e. the standard deviation of the sur Note 5. face elevations) as calculated using the height observa tions made approximately within 1 m distance intervals, 1) Limit for convergency in terms of |A(z/I>)| < I0"2. filtering out the height variations with wavelengths larger than 13 m39 . Using this height f , the drag coefficient is 2) In cases of no converge, after 25 loops a message will calculated as39 be printed. The last calculation results will be printed, Cdn{1 0) • ID3 = 1.10 + 0.072f (A22) as well. Then, z0 is calculated from (A1G) and further, the tough Note 6. ;; - • ■ ness Reynolds number is calculated as 1) For the integrated universal functions, the forms Rc = zqu.Iv = zqCJx 2VI v (A23) frequently used and tested were adopted: where v is the kinematic viscosity of air. Finally, zr.q is - for the stable region (f > 0), a recent formula of 29 calculated as the sublayer Daltou/Stanton number from the polynomial formula 44 as = #2 — — aQ — 6(C—c/d)exp(—dQ~bc/d ln{zT.q/zo) = 6o + bitn(Rc) + 62(7h Re)2 (A24) (A26) the coefficients bo = 6o(Rc),6i = bi(Rc) and 62 = 6%(Re) given in the program listing. where a = 0.7, b = 0.75, c = 5 and d = 0.35. The b) for user adjustments; instructions given in the pro equation (A26) yields in slightly and moderately stable gram listing. cases (up to C ~ 0.5) rather similar results as the well known formula of 51 = —5(, but may cover more 4) For land surface reliably the strongly stable cases. a) after choosing "land" , the program automatically asks - for the unstable region (C < 0) the Businger-Dycr for z0 in m. If unknown, the user is advised to see the type form17* 18 for tables 15'48 for rough estimates. r b) for the program uses the result given by 49 for nat = 2ln[i±f^] + - Turctan^ + f ural surfaces i.e. zojzq ~ 7 (A25) where <£*/ = (1 — 7lC)-1^4 For more accurate results, on-site information is neces and for *,/ = = 2/n[^|^], (A27) sary. The calculation procedure should not be used for mea surement levels lower than z < 50zq . Above tall vegeta where B = (1 — 72 C ) ~1 ^ ‘ tion the vertical coordinate z should be replaced by z—d, where d is the displacement height. For the first estimate 7 122 Environmental Software, 1900, Yol. 5, No. 3 r < $8 Derivation of Turbulent Surface Fluxes: J. Launtainen and T, Vikma the constant being 71 cs 72 Ci 16. The recent results27 REFERENCES suggest slightly different values of 71 = 19.3 and 72 = 12 (see sect. 1 of Appendix 1). 1. Monin, A.S. and Obukhov, A M. Osnovnye za- For the user’s adjustment of the universal functions, konomemosti turbulentnogo peremesivanija v prizem- see the program listing. nom sloe atmosfery. (Dimensionless characteristics of turbulence in the surface layer, in Russian). Trudy (7c- ofiz. Inst. Akad. Nauk. SSSR. 1954, 24,163-187. Note 7. 2. Lumley, J.L. and Panofsky, H.A. The Structure of Atmospheric Turle/cnce. Wiley (Intersdence), 1964, 1) After choosing ”Level-Difference Method ”, the pro 239pp. gram asks for measurement heights (if relevant, in the 3. Schmitt, K.F., Friehe, C.A. and Gibson, C.H. Struc form z — d) for wind (1 level), temperature (2 lev) and ture of marine surface layer turbulence. J.Atmos.Sci. moisture (2 lev) in m. 1979, 36, 602-618. 2) The program asks for z0 (m). If unknown, for esti 4. Fujitani, T. Direct measurement of turbulent fluxes mates see tables 15** 8 . over the sea during AMTEX. Papers in Meteorol. and 3) For units and forms of input data, cf. Appendix Geoph. 1981, 32, 119-134. Note 1. 5. Pond, S., Phelps, G.T., Paquin, J.E., McBean, G. and 4) For reasons of numerical calculation, a more strict Stewart, R.D. Measurements of the turbulent fluxes of limit for numerical convergency in the level-difference momentum, moisture and sensible heat over the ocean. method is necessary. In the program, a limit of J.Atmos.Sei. 1971, 28,901-917. ; |A(z/L)| < 10“* is used. 6. Smith, S.D. Wind stress and heat flux over the ocean in gale force winds. J.Phys.Oceanogr. 1980, 10, 709- 726. Note 8. 7. Banke, E.G., Smith, S.D. and Anderson, RJ. Re cent measurements of wind stress on Arctic sea ice. 1) Alternative devices for numerical output are: J.Fish.Rcs.Board Can. 1976, 33, 2307-2317. 8. Thorpe, M.R., Banke, E.G. and Smith, S.D. Eddy - screen correlation measurements of evaporation and sensible - paper heat flux over Arctic sea ice. J.Geophys.Res. 1973,78, - screen and disk files 3573-3584. Output quantities: 9. Launiainen, J. Parameterization of the water vapour flux over a water surface by the bulk aerodynamic - fluxes of T (in 10-3Nm** 2), // (in Win*" 2), E (in method. Annates Geophysicae. 1983,1, 481-492. r kgm-2s-1 and £E (in Wm** 2). // and £E as posi 10. Kaimal, J.C., Wyngaard, J.C., Izuml, Y. and Cote, tive upwards. O R. Spectral characteristics of surface-layer turbu lence. Quart. J.Roy.hfeteor.Soc. 1972, 98, 563-589. - friction velocity (cm/s) 11. Busch, N.E. The surface boundary layer. Bound.* t - stability as 10/L Layer Meteor. 1973, 4, 213-240. - bulk transfer coefficients Co and Che for calculation 12. Jackson, P.S. On the displacement height in the log level arithmic velorily profile. J.Fluid.Meeh. 1981, 111, 15-25. -T(eC), ?(g/kg) and K(m/s) for calculation level and 13. Thom, A.S. Momentum absorbation by vegetation. V also for 10 m height level Quart.J.Roy.Meteor.Soe. 1971, 97, 414-428. - several others calculated but not printed in the stan 14. Garratt, J.R. Flux profile relations above tall vegeta dard form. tion. Quart.J.Roy.Meteor.Soe. 1978,104,199-211. 15. Stull, R.B. An introduction to boundary layer mete• 2) In addition, interactive option for drawing the pro otology. Kluwer Academic Publishers, 1988, 666 pp. files of wind, temperature and specific humidity in semi- 16. Monin, A.S. and Yaglom, A.M. Statistical Fluid Me logarithmic coordination for a distance interval from chanics, Vol. /. The MIT press, 1977, 769 pp. < 10"5m to the calculation level. In the version sup 17. Businger, J.A., Wyngaard, J.C., Izumi, Y. and Bradley plied, figures are drawn in a screen of 640 • 350 pixels. E.F. Flux-profile relationships. J.Atmos.Sci. 1971, For other screen configurations and the necessary user’s 28,181-189. adjustments, cf. the program. 18. Dyer, A.J. A review of flux-profile relationships. Bound. •Layer Meteor. 1974, 7, 363-372. 19. Brulsaert, W. The roughness length for water vapour, sensible heat, and other scalars. J.Atmos.Sci. 1975, 32, 2028-2031. Acknowledgements. Constructive and encouraging 20. Hondo, J. Air-sea bulk transfer coefficients in diabatic criticism given by Dr. A.C.M. Beljaars (KNMI, Nether conditions. Bound.-Layer Meteor. 1975, 9, 91-112. lands) and by an unknown referee is kindly acknowl edged. 21. Hides, B.B. Wind profile relationships from the ‘Wan- gara* experiment. Quart.J.Roy.Meteor.Soe. 1976, 1 102, 535-551. 22. Garratt, J.R. Review of drag coefficients over oceans t and continents. Month.Wea.Rev. 1977, 105, 915-929. Environmental Software, 1990, Vol. 5, No. 3 123 Derivation of Turbulent Surface Fluxes: J. Launiainen and T. Vihma 23. Wu, J. Wind stress coefficients over sea surface in 45. Garralt, J.R. Surface influence upon verti near-neutral conditions, a revisit. J.Phys.Oceanogr. cal profiles in the atmospheric near-surface layer. 1980,10, 727-740. Quart. J.Roy.Meteor.Soc. 1980, 106, 803-819. 24. Large, W.G. and Pond, S. Sensible and latent heat 46. Beljaars, A.C.M. The derivation of fluxes from profiles flux measurements over the ocean. J.Phys.Oceanogr. in perturbed areas. Bound.-Layer Meteor. 1982, 24, . . 1 . 0 1982,12, 464-482. 35-55. 25. Blanc, T.V. Variation of bulk-derived surface flux, 47. Thom, A.S., Stewart, J.B., Oliver, H.R. and stability and roughness results due to the use of dif Cash, J.H. Comparison of aerodynamic and en ferent transfer coefficient schemes. J.Phys.Oceanogr. ergy budget estimates of fluxes over a pine forest. K * - 1985,15, 650-669. Quart.J.Roy.Meteor.Soc. 1975, 101, 93-105. 26. Holtslag, A.A.M. Estimates of diabatic wind 48. Wieringa, J. Representativeness of wind observations speed profiles from near-surface weather observations. at Airports. Bull.Am.Meteor.Soc. 1980, 61, 962-971. Bound.-Layer Meteor. 1984, 29, 225-250. 49. Garralt, J.R. Transfer characteristics for a het 27. Hogstrom, U. Non-dimensional wind and tempera erogenous surface of large aerodynamic roughness. ture profiles in the atmospheric surface layer: A re- Quart. J.Roy.Meteor.Soc. 1978, 104, 491-502. evaluation. Bound.-Layer Meteor. 1988, 42, 55-78. 50. Iribame, J.V. and Godson, W.L. Atmospheric Ther 28. Launiainen, J. Studies of energy exchange between modynamics. D.Reidel Publishing Company, 1973,222 the air and the sea surface on the coastal area of the PP* Gulf of Finland. Finnish Marine Res. 1979, 240, 3- 51. Webb, B.K- Profile relationships: the log- 110. linear range and extension to strong stability. 29. Holtslag, A.A.M. and De Bruin, H.A.R. Applied mod Quart.J.Roy.Meteor.Soc. 1970, 90, 67-90. eling of the nighttime surface energy balance over land. J. Appl. Meteor. 1988, 37, 689-704. 30. Kitaigorodsldi, S.A. The physics of air-sea interac tion. The Israel program for scientific translations. 1973, 236 pp. . 31. Hsu, S.A. A dynamic roughness equation and its ap plication to wind stress determination at the air-sea interface. J.Phys.Oceanogr. 1974, 4,116-120. 32. Csanady, G.T. Air-sea momentum transfer by means of short-crested wavelets. J.Phys.Oceanogr. 1985,15, 1486-1501. 33. Wu, J. Roughness elements of the sea surface - their spectral composition. Tellus 1986, 3SA, 178-188. 34. Large, W. G. and Pond, S. Open ocean momen tum flux measurements in moderate to strong winds. J.Phys.Oceanogr. 1980, 11, 324-336. * r 35. Gamut, J.R. and Hicks, B,B, Momentum, heat and water vapour transfer to and from natural and artificial surfaces. QuarLJ.Roy.Mcteor.Soc. 1973, 99, 680-687. 36. Smith, S.D. Water vapour flux at the sea surface. Bouni.-Layer Meteor. 1989, 47, 227-293. . 37. Lo, A.K. and McBcan, G.A. On the relative errors in methods of flux calculations. J.Appl.Meteor. 1978, 17, 1704-1711. 38. Blanc, T.V. Accuracy of bulk-method- determined flux, stability, and sea surface roughness. J.Gcophys.Res. 1987, 92, 3807-3876. 39. Banke, E G., Smith, S.D. and Anderson, R.J. Drag coefficient at AIDJBX from sonic anemometer mea j" surements. -in Pritchard, R.S. (ed.): Sea Ice Processes and Models. University of Washington Press, Seattle. 1980, 430-442. 40. Bengtsson,L. Evaporation from a snow cover. Nordic Hydrology, 1980,11, 221-234. .•V 41. Chamberlain, A.C. Roughness length of sea, sand and snow. Bound.-Layer Meteor. 1983, 25, 405-409. 42. Moore, R.D. On the use of bulk aerodynamic formulae over melting snow. Nordic Hydrology. 1983, 14, 193- 206. 43. Hondo, J. and Yamazawa, H. Bulk transfer coefficient over a snow surface. Bound.-Layer Meteor. 1986, 34, 123-135. 44. Andreas, E.L. A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice. V Bound.-Layer Meteor. 1987, 38, 159-184. r * 124 Environmental Software, 1990, Vol. 5, No. 3 f : * 11 */:* *** x y 6 ''f** " r* ’ * :n /> r- i !/■; ■ ; 'i •1 ' l Q. J. R. Meieorol, Soc. (1991), 117, pp. 399-407 551.511.6:551.588.2:551.588.4(480) On the effective roughness length for heterogeneous terrain By TIMO VIHMA' and HANNU SAVIJARVI2 'Department of Geophysics, University of Helsinki and 2 Department of Meteorology, University of Helsinki, Helsinki 00100, Finland (Received 3 March 1990: revised 21 September 1990) Summary Several theories and a mesoscale model were applied in the calculation of the effective roughness length Zf over heterogeneous flat terrain having varying proportions of land and water. Rules based on terrain classification tended to give large values of Zf, while the simple logarithmic areal average of local roughness lengths gave small values compared with the model output. The most recent theories were quite close to the model results. These theories were then used to produce a map of Zf for 150 x 150 km2 grid squares over Finland, based on a detailed knowledge of land use and water coverage. 1. Introduction A roughness length z0 is often used to describe the frictional effect of the underlying surface on the turbulent mixing in the atmospheric surface layer. za is a local value and well defined only for homogeneous terrain. The surface roughness varies, however, especially in coastal areas and archipelagos. In the case of heterogeneous terrain, an effective roughness length Zf must be determined for use, for example, on large-scale model grids. Although this might possibly be achieved over a small area by carrying out field measurements, it is clearly impracticable to obtain representative values over large , areas in this way. Alternatively, one can develop theories for calculating Zf from the distribution of local z0. Where there is a shortage of measurements, the available, partly contradictory, theories can be tested by comparison with results from small-scale and mesoscale numerical models, as has been done, for example, by Andre and Blondin (1986), Taylor (1987) and Mason (1988). In the following, a brief overview is first presented of theories found in the literature for heterogeneous but flat terrain, based mainly on the recent reviews of Taylor (1987) and Mason (1988). Then, simulations are made using a mesoscale model (that of the Department of Meteorology, University of Helsinki). The model is used to produce ‘observations’, i.e. steady-state local wind profiles (2 or 4 km apart), with a given upper- . ,1 wind forcing, flat topography, neutral stratification and various local z0 distributions. By calculating the mean flow profile over a larger area the model results can be compared ’ with the theories. Finally, two theories close to our model results were used in calculating - a tentative Zf field for 150 X 150 km2 grid squares, based on a knowledge of the local land use in Finland. •"'* This article is an abbreviated version of a longer report (Vihma and Savijarvi 1990). 2. Methods of determining the effective roughness length (a) Theories based on a known z0 field The simplest way of calculating Zf is to take an area-weighted logarithmic average (denoted by ()) of the available micrometeorological roughness lengths inside the grid square: In Zf = (In zQ). (1) 399 • .. > ■ / 400 T. VIHMA and H. SAVIJARVI This was used, for example, by Kung (1963). Taylor (1987) considers Eq. (1) to be valid if z„ does not vary much. Fiedler and Panofsky (1972) defined Zf for the heterogeneous terrain as the roughness length which a homogeneous terrain would have in order to produce the same surface stress (t). This definition can be presented as follows: « i = ((«|>I/2M ln(z, /Zf) (2) where u, stands for the wind speed at the lowest (model) level z, and k is the von Karman constant (0.4). The friction velocity (u2 distribution) should be estimated from a known z0 distribution using the surface Rossby-number similarity theory (see for example Taylor 1987). In order to simplify the problem, van Dop (1983) and Wieringa (1986) have suggested that Zf could be calculated from the grid-square average of the local drag coefficients (CD). Because r = pCD«2, such an idea contains the assumption that wind speeds at the lowest calculation level are the same everywhere, above both rough and >• smooth surfaces. (This may be true at a height of 60 m as Wieringa (1986) suggests, but the assumption is questionable if the calculation level (z,) is of the order of 10 m. Wieringa used, however, 10 m in his calculations, and regarded the error in Zf as small.) :4-' This assumption would lead to a simple relation between zQ and Zf: (lnzj/Zf)-2 = ((lnzi/z0)-2). (3) Mason (1988) has suggested calculating CD averages at a height of L/200, where the "3 wind speed no longer seems to depend on the local z„ but the flow is still approximately in balance with the surface. (L is the fetch in homogeneous surface sections. L/200 is a Vi rough approximation since the two assumptions cannot be true at the same height.) The effects of internal boundary layers would thus be taken into account: -v-v. ■ [In (L/200 Zf)] “2 = ([In (L/200 z„)] "2>. (4) Another formula rather similar to Eq. (3) was suggested by Andre and Blondin (1986): QnzJZfy' =((lnz,/z0)-1). (5) An alternative approach is to assume the mean flow profile in the grid square to be logarithmic (Taylor 1987). This leads to the relation: In Zf = (u* In z0)/(uj where there is no dependence on z, but Zf depends instead on both z„ and u . Thus knowledge about the dependence between z0 and u* is needed. Taylor (1987) made a linear approximation of the Ro-number similarity theory and derived the following formula: In Zf = (In z0) + aol !a .(6) where a is a function of Ro (typically, a = 0.09) and of„Zo = ((In zQ)2) - (In zQ)2 is the variance of In zD within the area. Equation (6) is somewhat analogous to the ‘envelope V ' • •' mountain’ topography concept. It may be noted that, according to Eq. (2), when z, increases, Zf also increases, while the opposite is true in Eqs. (3) and (5). On the other hand Eqs. (1), (4) and (6) do not change with z,. (b) Methods based on terrain classifications If one wanted to estimate Zf for a large heterogeneous area in practice, the simplest ROUGHNESS LENGTHS FOR HETEROGENEOUS TERRAIN 401 way might be to classify the area into different roughness categories, each approximately representing a uniform part. The weighting factors for the final combination (as for example Eqs. (7) and (8)) have usually been determined from (rather sparse) tower observations using regression analysis. Smith and Carson (1977) calculated geostrophic drag coefficients (CG) for Great Britain in 10 x 10 km2 grid squares. Terrain types were divided into nine groups, and CGs were obtained from standard similarity-theory relations using values of z0 typical for each terrain type. The basic analysis was done in 1 km2 squares, where the two most common terrain types were selected. The CG for a 1 km2 square was obtained by an approximate weighting of the rougher zc values and the final values for 10 x 10 km2 grid squares were then obtained as arithmetic averages. This gave values of Zf of 0.15 m for typical English countryside and =1 m for large towns. In the following, the results from their tables will be referred to as SC. Van Dop (1983) picked the three most common terrain types from each 10 x 20 km2 rectangle, and determined weighting factors on the basis of wind observations at 21 stations in The Netherlands. The calculation of Zf was based upon an average of the 10 m drag coefficients: Com ~ f\ Cdi +/z^D2 +/$Cd3 (7) where CD, is the local drag coefficient of the largest area among the three most common terrain types, CD2 that of the next largest, and CD3 that of the smallest. Determination of the weighting factors from wind observations gave/, = 0.85 ,/2 = 0.125 and/3 = 0.025. Zf was then obtained from CD10. Except for the empirical areal weighting factors, the method is thus identical to Eq. (3). Kondo and Yamazawa (1986) optimized the weighting factors with the aid of planetary-boundary-layer similarity theory and observations of the geostrophic wind (G), using surface wind observations from 30 stations in Japan. They were able to determine Zf as a function of u/G, where u is the wind at 10 m. Land areas were divided into four groups and the percentages of each group were measured in squares of 100 x 100 m2. Values of Zf based on wind observations at nearby stations were compared with the distribution of terrain groups in each square; wind direction was also taken into con sideration. The following formula was obtained by multi-linear regression: Zf (cm) = 40a + 125 b + 200c + 1KM - 30 (8 ) where a, b, c and d refer to the fractional areas of: water (and open land) (a), forests (b), areas with high buildings (c), and areas with low buildings (d). Equation (8) is simple to use, as it does not require estimates of local values of zQ. A speciality in the study of Kondo and Yamazawa (1986) was that Zf values were calculated down to very small squares. However, there is no reason why Eq. (8) should not be valid for larger grid squares as well, the weighting factors having been optimized by using wind observations at levels of about 10 m over many different kinds of surface with Eq. (8) as a summary of all of them. Note that Eq. (8) does not include terrain height variations explicitly, but these have affected the weighting factors via the observed winds. Therefore Eq. (8) may not give accurate results if applied to areas with terrain-height variations different from Japan, a mountainous country. Also, open land and water areas have been combined. In the comparisons to be made it should be borne in mind that the methods based on observed winds also include form drag, variable stabilities, etc., and are based on geostrophic analyses. They are shown for interest only. 402 T: VIHMA and H. SAVUARVI 3. Comparisons (a) Objectives and the model Model simulations were performed in order to give an independent estimate of the effective roughness over a large area. In addition, questions to be answered by the model experiments were: — what is the effect of the height of the lowest grid level? — what are the effects of one or more internal boundary layers? A two-dimensional dry hydrostatic mesoscale boundary layer model was used. It has an (x, o)-coordinate system and turbulence is described by first-order closure in the spiral layer and by drag laws in the lowest layer. The diffusion coefficient is K = P AV/ dz, where V is wind speed, mixing length / = kz/( 1 + kz)A), k = 0.4 and X = 40 m. The (neutral) flow is forced by the large-scale pressure gradient represented by the geostrophic : • v ■ i wind. The model has 10 levels in the vertical at approximate heights of 10, 17, 32, 57, v<.;, 100, 180, 330, 600, 1070 and 1900 m, with the wind becoming geostrophic at 3 km. In the present experiments there are 65 grid points in the horizontal, and flat topography. All fluxes vanish at horizontal boundaries and a = 0 at top and bottom. Gridlengths of 2 and 4 km were used, and horizontal boundary conditions were either cyclic or no- gradient, all combinations giving similar results. Vertical diffusion is solved by an implicit method, and instead of explicit horizontal diffusion a weak low-pass filter is applied to all fields. The model equations and details are given in Alpert et al. (1982) and Alestalo and Savijarvi (1985), the latter version being used here. The model has been tested and used in many studies of various mesoscale circulation systems (Alpert and Neumann 1983; Savijarvi 1985; Neumann and Savijarvi 1986; Savijarvi and Alpert 1987; Savijarvi and Alestalo 1988.) t . ' (b) Simulations The flow was neutral in all simulations, the surface temperature being constant and the temperature profile dry adiabatic. The basic flow was geostrophic and barotropic with Mg = 10 m s_I. The model was used diagnostically, i.e. it was run to a steady state, reached after the initial inertial oscillation was damped down by friction. The area- averaged wind profile was then calculated and Z®ff determined from this by extrapolating '■1' '■h the obtained curve of (n(logz)) to (n) = 0 by using the three lowest model levels (10 m, 17 m, 32 m) considered to be within or near the surface layer. The weighting was such -H v-y- that when a homogeneous za was given to the whole area, Ze0lc = zQ was obtained. To ■ 'Ji % simplify the analysis, two values of local zQ were adopted: 0.001 m and 0.5 m, approxi mately representing water and forest respectively. The proportions of areas having these r, two values of zQ were varied in order to find out the relation between Z®ff and the zG distribution. ?• The following percentages were used for the land area: 10, 30, 50, 70 and 90. The 1) land area consisted of three islands of equal size. In addition, when the proportion of land was 50%, this was in turn divided into one, three and ten islands. The idea was to study the effects of the internal boundary layers by varying the lengths of the homo geneous surface sections. (c) Results and discussion r-.; The model results (M) are shown in Fig. 1 together with the values given by the •J' theories given in Eqs. (1) to (6) and by the more empirical rules given in Eqs. (7) and (8) and by SC, using the same za distribution and lowest level (z,) which was used in the model runs. It can be seen from Fig. 1 that the scatter in the various Z%!! estimates ROUGHNESS LENGTHS FOR HETEROGENEOUS TERRAIN 403 100 % percentage of land surface Figure 1. Zln determined by various methods as a function of land-water distribution. Numbers refer to the equations, the dashed line to Eq. (1), SC to the method of Smith and Carson (1977), and M to the model result. reaches a maximum for the half land-half sea case, if the perhaps overly smooth method of Eq. (8) is excluded. As expected, the Z'ff values from the model simulations were in all cases higher than the simple logarithmic average given by Eq. (1). Taylor ’s (1987) ‘envelope roughness ’ method (Eq. (6)), i.e. adding subgrid variance to Eq. (1), results in values quite close to the model; Eq. (2) produces nearly the same values. In practice, use of Eq. (2) is tedious as one has to derive the friction velocity average from local values of z„. Equation (3), which is based on averaging the drag coefficient, is higher than the model results as might be expected. Equation (5) of Andre and Blondin (1986) gives surprisingly similar values to the model simulations. This may be a coincidence as its prerequisite, the same low-level (10 m) wind over land and sea, was certainly not true in the model runs. Mason’s (1988) suggestion (Eq. (4)) corresponds to our model results very well, especially for a small amount of rough surface. It was the only analytical formula in which the effects of internal boundary layers were considered. The values of Z%a based on model simulations cannot be regarded as faultless. The model contains idealizations, e.g. it is only two-dimensional and hydrostatic. In addition, the use of models based on mixing-length theory for flow over rapid changes in roughness has been criticized by Rao et al. (1974). However, it is interesting to note that the model results come closest to the most recent analytical theories. In Table 1 the results are presented as a function of the number of islands. In these experiments the proportion of land is 50%. The model results can now only be compared to Eq. (4). (In Eq. (6), for instance, the number of islands does not change the variance as long as the roughness is the same in all of them.) The model-produced Z£ff clearly increases with the number of islands (e.g. from 5.4 cm with one big island to 9.5 cm with 404 T. VIHMA and H. SAVIJARVI TABLE 1. Tim dependence of In Zf (Z'[f in metres) on the number OF ISLANDS WHEN HALF THE AREA IS LAND AND HALF WATER. X = WAVE LENGTH OF ROUGHNESS VARIATION IN KILOMETRES 1 island 3 islands 10 islands Model result -2.92 -2.65 -2.35 Eq. (4) method -2.42 -2.26 -2.09 X 256 73 26 10 smaller islands), as also does Eq. (4). Thus according to our model many internal boundary layers seem to increase Z£ff, as was also the case in Claussen (1987) and Mason (1988), but contrary to Jensen (1978). Another question to be addressed was whether the height of the lowest model level (z,) affects Z„c. In those theories containing a dependence on zh Eq. (2) predicts a value of Ze0n about 8% greater, while Eqs. (3) and (5) give values 10% lower for z{ = 15 m instead of 10 m. Increasing z, from 10 to 15 m, and the next level from 17 to 20 m, and repeating the experiments gave the result that the height of the lowest level does not affect Zoff at all, as long as the change is of the order of 50% and Z£;fr is determined from the profile of the mean flow in the model. This would favour Eqs. (4) and (6), which do not predict a change of Z£ff when zx is changed. 4. Calculation of effective roughness lengths for Finland As a practical example of the use of the theories, effective roughness lengths were estimated for Finland in 150 x 150 km2 grid squares. The data were extracted in the Finnish Meteorological Institute from a map made by the Finnish National Board of Survey, in which land use was divided into 11 categories: peat industry area, urban area, water, forest, arable land, lawn, open swamp, low mountains (fjelds) with and without bushes; sands and rocky islands. Every 150 x 150 km2 grid square was divided into 100 smaller squares, and the three most common terrain types in each of these small squares (about 2000 in all) were picked out from the map. The calculations were made with Taylor ’s (1987) Eq. (6) and Mason’s (1988) Eq. (4) schemes, both of which were close to the results from the model simulations. Because no accurate measurements had been made of the percentages of the terrain categories in each 15 x 15 km2 square, the following approximate values were used: 60% for the most common, 30% for the next and 10% for the third terrain type. These quotas were modified if only one or two types were present, or if the first and second or the second and third types were assumed to be equally common in a square. In Eq. (4), the following values were used for the lengths of the homogeneous surface sections: 3 km if there were three different surface types present in the grid square and 5 km if only two types were present. The fetch values were estimated on the basis of typical variations between forest, lake and arable land surfaces in Finland. The local z„ for each terrain type had also to be estimated. This was done mainly on the basis of the table of the Engineering Science Data Unit Ltd (1972). The estimates are presented in Table 2. When estimating the values for mountains, z„ was considered as representing the properties of the surface, not the terrain-height variations. The Z£fr values were first calculated for the 15 x 15 km2 squares and the calculations were further extended to the bigger squares using the former results as local values for z0. Only eight 150 x 150 km2 squares were wholly inside Finland. The following assumptions were made for the rest: if the external area was sea, zQ was taken as 0.0001 m; ROUGHNESS LENGTHS FOR HETEROGENEOUS TERRAIN 405 TABLE 2. Estimated local roughness lengths for classified terrain CATEGORIES Zo Zo metres metres ‘1 Water 0.0001 Rocky islands 0.1 Sands 0.005 Low mountains: Lawn 0.02 — without bushes 0.1 Arable land 0.05 — with bushes 0.3 Peat industry area 0.05 Urban area 0.5 Open swamp 0.1 Forest 1 if it contained both sea and terrain of another country, a value of 0.5 m was given to land areas. In the remainder of the squares the external (all land) area was assumed to be similar to the Finnish side. The results are given in Fig. 2. (It should be stressed that all values in Table 2, and consequently in Fig. 2, describe a summer situation with full-grown vegetation.) The most important factor for Z„ff is the amount of water surface in a grid square. For instance, the lake district of south-east Finland (25% of this area is covered by lakes) is characterized by small values of Z‘ff. The greatest values are found in northern Finland, where most of the smaller grid squares are covered by forests. Still further north Z£ff decreases because vegetation becomes lower and form drag is not included in Z£ff. The differences between the two calculation methods are systematic; Eq. (6) giving smaller values, on average 63% of the values of Eq. (4). The difference is largest in grid 0.11 0.28 0.081 0.20 0.11 0.32 Figure 2. Distribution of Z;n (in centimetres) for Finland in 150 x 150 km2 grid squares. The upper values in each square are based on Eq. (6) and the lower values on Eq. (4). Heavy line denotes country boundary. -.5 1 < 406 T. VIHMA and H. SAVIJARVI squares with low Z„f. This is in accordance with Fig. 1, which also suggests that the average of the two would be quite close to our model-produced Z£ff. In general the differences between Eq. (4) and Eq. (6) in Fig. 2 are minor relative to the other errors and uncertainties in the treatment of the boundary layer in large-scale models. Even the estimation of the local zQ is so uncertain that small differences in these two calculation riiethods for Z%tt are not really significant. One might speculate, however, that Eq. (4) should be used when it is important to produce a correct momentum flux. This is probably the case in general circulation modelling, where the momentum flux determines the frictional energy sink in the planetary boundary layer. In some applications it might be more important to produce correct mean-wind profiles in the surface layer, e.g. in short-range forecasting and air-pollution studies. In these, Eq. (6) might be better. 5. Conclusions Some theories for determining Z£ff were compared with simulations made by a numerical boundary-layer model. The model surface was divided into areas of different roughness (local values of zQ corresponding to land and sea), and Z‘ff was determined from the balanced profile of the neutral mean flow over the whole model area. The dependence of Z$ff on the given z„ distribution was calculated and compared to the theories. The model results were close to those of the recent theories of Mason (1988) and Taylor (1987), but differed more from those of Smith and Carson (1977), van Dop (1983) and Kondo and Yamazawa (1986), which are based on (sparse) observations. The rough land surface had a dominating effect on Z'ff in the model results. In addition, internal boundary layers, formed at shorelines in connection with rapid changes of zQ, seemed to increase Z„r. The model-produced Z„c was insensitive to the heights of the lowest model levels, gridlength and horizontal boundary conditions. The best theories (judged subjectively by our model results) were then applied to the calculation of Z£ff for Finland in 150 x 150 km2 grid squares. The calculation was based on knowledge of the distribution of different surface types, without parametrization of the form drag. The many lakes of south-east Finland contribute to a locally smaller Zf there. Acknowledgements Special thanks are due to Seija Argillander, who analyzed the terrain types of Finland. References Alcstalo, M. and Savijurvi, H. 1985 Mesoscale circulations in a hydrostatic model: coastal con vergence and orographic lifting. Tellus, 37A, 156-162 Alpcrt, P. and Neumann, J. 1983 A simulation of Lake Michigan's winter land breeze on 7 November 1978 Mon. Weather Rev., Ill, 1873-1881 Alpert, P., Cohen, A., Doron, E. 1982 A model simulation of the summer circulation from the eastern and Neumann, J. Mediterranean past Lake Kinneret in the Jordan Valley. Mon. Weather Rev., 110, 994-1006 Andre, J.-C, and Blondiri, C. 1986 On the effective roughness length for'use in numerical three- dimensional models. Boundary-Layer Meteorot., 35,231- 245 Claussen, M. 1987 The flow in a turbulent boundary layer upstream of a change in surface roughness. Boundary-Layer Meteorot., 40,31- 86 van Dop. H. 1983 Terrain classification and derived meteorological parameters for interregional transport models. Atmos. Environ., 17, 1099-1105 ROUGHNESS LENGTHS FOR HETEROGENEOUS TERRAIN 407 Engineering Science Data Unit, Ltd. 1972 ‘Characteristics of wind speed in the lowest layers of the atmosphere near the ground: strong winds ’. ESDU 72026, London Fiedler, F. and Panofsky, H. A. 1972 The geostrophic drag coefficient and the effective roughness length. Q. J. R. Meteorol. Soc., 98, 213-220 Jensen, N.-O. 1978 Change of surface roughness and the planetary boundary- layer. Q. J. R. Meteorol. Soc., 104, 351-356 ' ' « Kendo, J. and Yamazawa, H. 1986 Aerodynamic roughness over an inhomogeneous ground surface. Boundary-Layer Meteorol., 35, 331-348 Kung, E. C. 1963 Climatology of aerodynamic roughness parameter and energy dissipation in the planetary boundary layer of the northern hemisphere. In Annual report 1963. Studies of the effects of variation in boundary conditions on the atmospheric boundary layer. H. Lettau, (Ed.). Univ. of Wisconsin, Madison Mason, P. J. 1988 The formation of areally-averaged roughness lengths. Q. J. R. Meteorol. Soc., 114, 399-420 Neumann, J. and Savijarvi, H. 1986 The sea breeze on a steep coast. Beitr. Phys. Atmos., 59,375- 389 Rao, K. S., Wyngaard, J. C. and 1974 The structure of the two-dimensional internal boundary layer Cote, O. R. over a sudden change of surface roughness. J. Atmos. Sci., 31, 738-746 Savijarvi, H. 1985 The sea breeze and urban heat island circulation in a numerical model. Geophysica, 21, 115-126 Savijarvi, H. and Alcstalo, M. 1988 The sea breeze over a lake or gulf as the function of the - , prevailing flow. Beitr. Phys. Atmos., 61, 98-104 Savijarvi, H. and Alpert, P. 1987 ‘On the numerical asymmetry in calculating Coriolis terms through the splitting method in a mesoscale model’. Report No. 28. Department of Meteorology, University of Helsinki Smith, F. B. and Carson, D. J. 1977 Some thoughts on the specification of the boundary-layer relevant to numerical modelling. Boundary-Layer Meteorol., 12, 307-330 Taylor, P. A. 1987 Comments and further analysis on effective roughness lengths for use in numerical three-dimensional models. Bound ary-Layer Meteorol., 39, 403-418 Vihma, T. and Savijarvi, H. 1990 ‘On the effective roughness length for heterogeneous terrain ’. Report No. 36, Department of Meteorology, University of Helsinki. XVieringa, J. 1986 Roughness dependent geographical interpolation of surface wind speed averages. Q. J. R. Meteorol. Soc., 112, 867- 889 W i .X-- - ■:-r ' »/ ‘ y. * »v 'V* Ill % (. 'V , • iV On the Air-Sea Interaction in Areas of Thermal Marine Fronts in the Greenland Sea Timo Vihma and Jouko Launiainen Department of Geophysics, University of Helsinki Fabianinkatu 24 A, 00100 Helsinki, Finland and Gunther Krause Alfred-Wegener-Institut fur Polar- und Meeresforschung Columbusstrasse. D-2850 Bremerhaven, Federal Republic of Germany [Original manuscript received 26 June 1990; in revised form 30 January 1991] ABSTRACT The effects of marine fronts on the local atmospheric surface layer and air- sea interaction were studied. Several mesoscale fronts were crossed by a research vessel in the Greenland Sea. Air temperature, humidity and stability conditions, and the fluxes of momentum, as well as sensible and latent heat, were investigated. For relatively calm conditions, close air-sea coupling was observed in the temperature whereas for stronger winds, the air temperature of the surface layer was not markedly modified by the front below. Changes in the moisture content in the frontal area were observed and, in one case, evaporation was observed on the warm water side and condensation on the cold water side of the front. Frontal differences in heating from the sea were assumed to affect the surface-layer wind field. RESUME On etudie les effets des fronts marins sur la couche de surface atmospherique et I’interaction air-mer. Un navire de recherche a traversi plusieurs meso-fronts dans la mer du Groenland. On a analyse la temperature de Fair, Fhumidite et les conditions de stabilite, et les flux de quantile de mouvement, aussi bien que les chaleurs latente et sensible. Durant les conditons de temps relativement calme, on a observe un couplage air-mer serre de la temperature, alors que par vents forts, la temperature de Fair de la couche de surface n ‘etait pas tellement modifiee par le front en-dessous. On a observe des changements de Fhumidite et, dans un cas, de F evaporation du cote de Feau chaude et de la condensation dans Feau froide. On a suppose que le champ de vent de la couche de surface etait affecte par les differences frontales dans le richauffement par la mer. 1 Introduction Oceanic fronts are distinct boundaries between water masses exhibiting differences typically in temperature and salinity, and hence usually also in density. They can ATMOSPHERE-OCEAN 29 (3) 1991, 596-610 0705-5900/91/0000-0596S01.25/0 © Canadian Meteorological and Oceanographic Society Air-Sea Interaction in Areas of Thermal Marine Fronts / 597 be formed, for example, by coastal boundary currents, by upwelling, or by more general circulations when water masses from different climatological regions meet (Gill, 1982; Legeckis, 1978). In a survey of worldwide sea surface temperature (SST) fronts Legeckis (1978) reported on a couple of fronts where sst changes can exceed values of 5°C km-1 (the North Atlantic Polar Front in the Labrador Sea and the upwelling front along the Pacific coast of Mexico) and gradients of the order of 1°C km-1 are observed in several areas on the World Ocean. However, some of the well known global fronts are not so distinct. For example, the typical SST change across the subtropical fronts in the North Atlantic and North Pacific is 1°C (10 km)-1 (Voorhis and Mersey, 1964; van Woert, 1982). In the study area of fasinex (Frontal Air-Sea Interaction Experiment, Stage and Weller, 1985, 1986) in the western subtropical Atlantic the SST difference across the front was typically 1-2°C, mostly concentrated in a region about 6 km in width. In jasin (Joint Air-Sea Interaction Experiment, Pollard, 1978), eddies 100 km across existed in the study area between Scotland and Iceland, and sst fronts with gradients of l°C/50 km or less were located in the confluence zones of the eddy fields (Pollard et al., 1983; Guymer et al., 1983). In the Greenland Sea, the Arctic Front represents a major water mass bound ary between the warm (2.5-3.5°C) West Spitsbergen current and the water of the Greenland Sea Gyre (—1°C in springtime). This front forms mesoscale meanders and eddies in the water with characteristic length scales of 20-50 km and vertical scales of 1000-2000 m. The SST change across the front is typically 1-3°C. On a larger scale, the fronts are often quasi-stationary and, if they are accompa nied by significant variations in sea surface temperature, they may have important effects on weather and climate. The mesoscale features of the fronts are often transient and their effects on the local atmospheric boundary layer are not so well known. In experiments it has been customary to study one-dimensional air-sea in teraction and regard the local horizontal variability merely as noise, jasin (Pollard, 1978) and fasinex (Stage and Weller, 1985, 1986) were among the first major ex periments where frontal variations in sea surface conditions and their effect on the energy and mass exchange were investigated, although Knauss (1957) had already looked into the subject. An expedition of the German research ice-breaker Polarstem in 1987 involved a number of crossings of marine fronts in the Greenland Sea (Fig. 1) and offered a possibility of making frontal and air-sea interaction studies using a shipboard automatic marine weather station. Thermal and air moisture modifications, and variations in the wind field and turbulent air-sea fluxes were studied. The results reported here demonstrate various local and mesoscale effects on the air-sea bound ary in the vicinity of distinct oceanic fronts. 2 Data a Observations i.‘: Observations were made primarily by the shipboard automatic weather station, custom-made for the ship by Thiess Co. and Deutscher Wetterdienst. The station is connected to a research computer that communicates with the ship’s integrated nav igation system, in order to obtain the location, course and velocity of the ship, after •"> ■: : 598 / Timo Vihma, Jouko Launiainen and Gunther Krause - ICELAND Fig. 1 General circulation pattern of the Greenland Sea and the location of the marine fronts discussed; one at 74°N, 7°E and the other at 79°N, 5°E (broken curves). The continuous line gives the ship’s route during the Arktis IV/1 expedition. AW = Arctic water, GG = Greenland Gyre, NAW = North Atlantic water. which the computer calculates vectorial wind speed, makes the final observation message, and so forth. Fifteen different observations were made altogether. Only the methods, together with their accuracy, relevant to this study are listed in Table 1. These methods will be briefly discussed below. In Table 1, the measurement accuracies (except those of wind speed and di rection) are based on the calibrations made regularly during the experiment. The sea surface temperature was calibrated against an oceanographic CTD-sonde. Air temperature and humidity sensors were regularly calibrated against an Assmann- psychrometer, both while the ship was on station for marine observations and while it was cruising. Wind speed was compared with a hand-held, long-armed, digital tunnel-propeller microanemometer. In addition, special analysis of a comparison of the two research wind sensors on the ship (symmetrically mounted on the port and starboard sides) yielded a smooth and well defined difference curve resulting from the ship’s struc tural interference with the wind field (up to ±15%). As a result, we found that the average values from the two wind sensors give more accurate relative wind data than values from picking only one sensor, depending on the relative direction of the Air-Sea Interaction in Areas of Thermal Marine Fronts / 599 Table 1. Observation quantities, measurement heights (above sea level) and accuracies of single measurements. Observation interval: 10 min. Height Observing Quantity (m) Instrument Accuracy Remarks Sea surface temperature -2.0 Pt-100 ±0.1°C Two sensors Air temperature 28.0 Pt-100 ±0.2°C Two sensors on main mast: port side, sea side Dew-point temperature 28 Pt-100 + LiCl Using both sensors, the time and Relative humidity 28 hair hygrometer temperature-dependent calibration yields an accuracy of O.lSgkg"" 1 forspecific humidity. Wind speed 36.5 cup anemometer ±0.1 m s~' (res.) Two sensors on main mast: port ±5% (acc.) side, sea side Wind direction 36.5 wind vane ±5° ship and wind. Hence, an accuracy of ±5% in Table 1 merely means the accuracy of the instrument compared with the microanemometer. Definitely, we do not know how well our measurements from the ship represent the real undisturbed wind speed over the ocean (cf. Blanc, 1986, 1987; Pierson, 1990), but the relative accuracy of consecutive observations is of primary impor tance when frontal effects are studied, and we think that the averaged observations are accurate enough in this sense when the wind direction field remains rather stationary with respect to the ship’s course. b Calculated Quantities The turbulent fluxes of momentum (t), sensible heat (H) and water vapour E (or latent heat flux LE, where L is the enthalpy of vaporization) were calculated by the familiar bulk aerodynamic formulae: T = pCDzV2 = pV2 (1) H = —p cpCHz(Qs — 6z)Vz (2) _CE = -6pCe(*,-*)% (3) where Vz is the mean wind speed at height z, p is the air density and cp is the specific heat capacity of air. 0* —6Z and qs—qz are differences between atmospheric and surface values of the potential temperature and specific humidity, respectively. The bulk transfer coefficients, the drag coefficient Co, the Stanton number C# and the Dalton number Ce, may be expressed as CDz = Cd {z,zq ,}VmU/L)) (4) Chz = Ch(z, zo, zr, 'Pw(z/L), ^(z/L)) (5) CEz = C£(z, zo, Zq, Vm(z/L), 'F£(z/L)) (6) 6oo / Timo Vihma, Jouko Launiainen and Gunther Krause where z is the measurement height and zo, Zt and zq are the roughness lengths for wind speed, temperature and water vapour, respectively. Y^, Y# and Yg are the integrated universal functions that characterize the effects of the atmospheric surface layer stability on the bulk transfer coefficients. In situations of neutral stratification, the transfer coefficients depend on z and the roughness lengths only. The system of equations in (1) to (3) using (4) to (6) leads to an iterative solution since the argument zJL in the universal functions is dependent upon (1) to (3). That the observations of wind speed, temperature and moisture were not made on the Polarstem at the same height level, leads to another internal iteration procedure. A detailed methodological description of the solution procedure, and the basis for the physical choices of the roughness lengths and universal functions including the necessary algorithms are given in Launiainen and Vihma (1990). For reference, the formulae used yield, for a wind speed of 8 ms-1 and neutral stratification, the bulk transfer coefficients CD(10) = 1.32 x 10-3 and Cw£(10) = 1.15 x 10-3 referred to a 10-m height. The neutral bulk transfer coefficients used are slightly dependent on wind speed. The form for Q> follows the results given by Smith (1980) and Large and Pond (1980). Values for the Stanton and Dalton numbers were based on the ratio Che (Co from Launiainen (1983); the Che value above agrees well with that for a comprehensive oceanic data set published by Large and Pond (1982). For the universal functions, the so-called Businger-Dyer-type form (Businger et al., 1971; Dyer and Hicks, 1970; Dyer, 1974; Hdgstrom, 1988) was used for the unstable region and Holtslag and de Bruin’s (1988) form was adopted for the stable stratification. Unfortunately, formulae (4) to (9), which rely on the Monin-Obukhov similarity theory presuming horizontal homogeneity and (semi-) stationarity, may not be able to describe exactly the turbulent fluxes close to a front where an internal boundary layer is developing (Boyle et al., 1987). However, because direct eddy flux and eddy dissipation measurements are very difficult to make at sea (Dobson et al., 1980; Wucknitz, 1980), the literature does not provide any better theory for cal culating turbulent fluxes using ordinary marine meteorological measurements. In jasin (Guymer et al., 1983) the turbulent fluxes were determined by four differ ent techniques (eddy-correlation measurements from aircraft, shipboard dissipation method, momentum flux measurements from Seasat scatterometer, and the bulk- aerodynamic method); the uncertainty in the bulk transfer coefficients was consid ered comparable with the uncertainty in the measurements for the mean quantities, but nothing specific was reported about the effect of horizontal non-homogeneity caused by the SST fronts. 3 Air-sea interaction characteristics in frontal areas A few case studies of the frontal modification of air-sea interaction characteristics are reported below. All correspond to the Arctic Front, which is generally aligned in the north-south direction (Fig. 1), but may be rather complicated and transient •$ Air-Sea Interaction in Areas of Thermal Marine Fronts / 601 in structure, both in space and time, while it is modified by the local hydrography, depth and weather conditions. - ’-t ' a Frontal Crossing at 74°N - ,‘S- Early on 19 May 1987 the Polarstem was cruising steadily westward (strictly 1- towards 280°, at a speed of 11 knots) under rather stationary wind conditions at 74°N latitude from the warm Atlantic water to the cold Greenland Gyre water (i.e. from right to left in Fig. 2). She crossed the front at 7°20,E, as indicated by '.7 * the water and air temperature changes in Fig. 2a. In the field the front was very LT'J v; : distinct so that the sea surface temperature dropped by 4°C, the most intense change occurring over a distance of a few ship’s lengths. The influence of the marine front was clearly seen in the air temperature (at a height of 28 m, Fig. 2a), even though the cross-frontal change in air temperature is smaller. In addition, a distinct decrease in atmospheric moisture content towards the cold side (Fig. 2b) was observed. Furthermore, Fig. 2c suggests some increase in the wind speed at the front. Of course, the wind field may not have been stationary ■ji either. In the calculated quantities, given as half-hour running means, we may find that slight evaporation, seen as negative latent heat flux on the warm water side of the front in Fig. 2d, turned to condensation on the cold water side. This change was seen visually from the ship as a fog formation near the surface. The sensible heat flux, which was always directed towards the sea, was increased due to temperature relations after the front. Accordingly, after being almost near-neutral on the warm water side, the atmospheric surface layer stability (10/L) was very stable on the cold water side of the front (Fig. 2e). Recently, Mey et al. (1990) observed the : -■ i surface fluxes (of both sensible and latent heat) to change sign while crossing an SST front. Figure 2f shows the variation in the flux of momentum, i.e. the wind stress (with respect to that under neutral conditions). Owing to the increase in stability, the wind stress was drastically lower on the cold side, by 40%, although the wind speed increased. A lack of data prevents us from arriving at firm conclusions, but if we assume that the driving force for the surface layer wind remained constant during the observations, the higher wind speeds observed at the front and on the cold water side might be interpreted as a consequence of a strong stability. This reduces the vertical flux of momentum (energy) from air to sea, which is then observed as an increase in the mean wind, in an analogous manner to the behaviour of flow near a rough wall and a smooth wall when the wind is driven by an equal external pressure gradient (cf. also the theoretical considerations of Geemaert et al., 1988). b Frontal Crossing at 79°N On 4 June the Polarstem cruised eastward at 79°N towards a north-south aligned front. After the ship met the front at 5°E, the sea surface temperature increased rapidly by more than 3°C, from —0.5° up to +3°C, at a longitude of 7°E (Fig. 3a). Then, she turned back west and crossed the front again, now in the opposite 6oz / Timo Vihma, Jouko Launiainen and Gunther Krause 9 *E longitude 8 7 6 5 4 3 2h lime of 19 May Fig. 2 Time and longitudinal variation of various air-sea parameters during a warm-to-cold front crossing at 74°N on 19 May 1987: (a) sea surface temperature (7* r) and air temperature (Ta), (b) specific humidity of the air (q), (c) wind velocity (V) and alignment of the front with respect to the wind field, (d) fluxes of latent heat (LE) and sensible heat (//)• (e) atmospheric surface layer stability (10//,), and (f) flux of momentum normalized with respect to that under neutral conditions. (Note: 1° in longitude corresponds to a distance of 30 km.) Air-Sea Interaction in Areas of Thermal Marine Fronts / 603 v/m s ' back to west longitude 15h time of 4 June W nr 4*E longitude 1Sh time of 4 June Fig. 3 Temporal and longitudinal variations of various air-sea parameters during a two-way crossing of an Arctic front at 79°N. A cruising time from 7* 1 to 11* 1 40 min (or 3 to 7°E) corresponds to a change from the cold Arctic water to the warmer North Atlantic water. The graphs from the broken line onwards correspond to conditions during the immediate return cruise, (a) sea surface temperature (T,) and air temperature (Ta), (b) wind velocity (V) and alignment of the front with respect to the wind field, (c) fluxes of latent (LE) and sensible heat (H) and (d) specific humidity of the air (q). (Note: 1° in longitude corresponds to a distance of 20 km.) direction (at the same latitude). Figure 3a shows that the marine front remained in the same location during this manoeuvre, and thus the whole graph is rather symmetric. A corresponding modification in the air temperature was observed. The thermal stratification was now generally unstable, but the modification made it very unstable on the warm water side of the front. The difference between the air and water temperature modifications (i.e. compression in air temperature in Fig. 3a) reveals an effect of cold advection, as suggested by the direction of the wind with respect to the front, given in Fig. 3b. Again, a distinct variation in specific humidity was observed (Fig. 3d) in the frontal area. The observed change in specific humidity 604 / Timo Vihma, Jouko Launiainen and Gunther Krause was now 30%, but was only 10% in the frontal zone at 74°N. The difference is reasonable, since the air advection was now cold and dry and the stratification was unstable. Figure 3b suggests a slight increase in the surface wind speed towards the warm water side of the front; again the marine front had a significant effect on the calculated turbulent fluxes of latent (LE) and sensible heat (H). The wind was blowing from over the cold side of the front to over the warm side at an angle of about 45° to the front. The thermal stability changed slightly towards more unstable on the warm water side, which could have reduced the wind speed, because of an increasing tendency of skin friction. Nevertheless, the wind speed increased over the warm water area. This might be analogous to the observations of Sweet et al. (1981) and Mey et al. (1990). The former studied the north wall of the Gulf Stream and measured an increase in wind speeds over the Gulf Stream water, when the wind was blowing from over the cold slope water; the latter observed similar wind behaviour across the Subtropical Convergence - Agulhas SST front. Hsu (1984) has devised an analytic model for the phenomenon regarding it to be similar to the classical sea-breeze circulation. Later, Huang and Raman (1988) and Wai and Stage (1989) have shown in their simulations with two-dimensional models that this kind of SST distribution with respect to the wind direction results in a thermally driven direct cell with accelerated wind speeds over the warm water side. According to the model simulations of Warner et al. (1990) the SST gradient associated with the north wall of the Gulf Stream can produce horizontal velocities in excess of 7 m s'"1 when simulated from calm initial conditions. Although we cannot be sure that the situation was stationary, the above might explain the wind behaviour observed. The mechanism is not applicable at 74°N on 19 May, since the situation then was stable and the flow was from over the warm water side of the front. c Model Simulations of Air-Mass Modification A couple of interesting features in the results merited a closer look. In order to find out whether the observed air-sea modification could be roughly simulated, a one dimensional atmospheric boundary-layer model was applied. The model was that of Savijarvi and Vihma (1987) modified for application over a sea surface. (A rather similar model has been presented by Louis (1979), the boundary-layer parametriza- tion scheme of which has been used in the ecmwf global forecast model.) The model used has a first-order closure scheme for the turbulent diffusion of momentum, heat and moisture, and surface fluxes and diffusion coefficients dependent on shear and stability. An implicit numerical time integration method with a 5-min time step is used, and there are 14 levels quasi-logarithmically spaced in the vertical, the lowest levels being at 10, 35, 100 and 250 m. The simulations were based on the assumption that on time-scales, of a few hours the sea surface temperature is not affected by the atmosphere while the air temperature and humidity are modified by the turbulent surface fluxes. An air mass with temperatures, moisture and velocities corresponding to those upstream of the front was allowed to be modified by setting the water temperature equal to that observed downwind of the front. The initial temperature profile for the model Air-Sea Interaction in Areas of Thermal Marine Fronts / 605 was determined for the lowest 100 m using the observations and a flux-profile scheme (Launiainen and Vihma, 1990). The results were rather insensitive to the " ' initial profile above 100 m in short-period simulations. The modelling attempts were restricted to cases in which there seemed to be cross-frontal advection of colder or warmer air above the marine front. Of course, an optimal situation for the use of a one-dimensional model would be such that there is not much shear . *; or deformation in the large-scale flow. In such cases the modification in the air ," column is due to vertical eddy fluxes and an exchange with the sea. A number of r air-mass transformation simulations are given in the literature (e.g. Louis, 1979; Driedonks et al., 1985; Holtslag et al., 1990) having some analogy to our case studies. ; On 19 May at 74°N there was difference of about 2°C in the air temperature across the front. It was the most abrupt difference observed during the expedition: a drop of 2°C occurred over a distance of about 14 km (0.45° in longitude, cf. Fig. 2a). With a cross-frontal wind component of 5.5 m s-1 (Fig. 2c) this corresponds to a modification time of 45 min. The observations are in accord with the theoretical . ’ growth rate of the internal boundary layer (IBL) in a very stable situation, so that if /".j we estimate the fetch required for the IBL to reach the observation height of 28 m using the formula of Garratt (1987), we get a result of about 15 km. v- •; According to the model, an air-mass modification of such a magnitude would have required at least 5 h (at a height of 28 m) in the very stable conditions ; 1 corresponding to the sea surface temperatures and wind speeds observed downwind of the front. The reason is that the one-dimensional model used cannot create a sharply capped IBL, but modifies a higher air column smoothly. One interesting point shown by Fig. 2a is, however, that the temperature difference between the ; sea surface and the air at a height of 28 m remains large (about 2°C) as far as 50 km downwind of the front. The model suggested that the lack of modification is realistic, since the heat flux tends to be small in highly stable conditions, and f the heating enters into a rather high air column. In regard to the second front at 79°N (on 4 June), the model produced results v- that were rather close to those observed. The observed warming was about 2°C (from —2.6 to — 0.6°C, Fig. 3a), which happened across a fetch of 42 km (2° in longitude) over the warmer sea surface. The simulation produced a warming of 1.6°C (from —2.6 to — 1.0°C) in 2 h 45 min (corresponding to a fetch of 42 km with a 4.2 m s~l cross-frontal wind speed), i.e. slightly less than observed. The r; difference should again be due to a smooth continuous heating of an air column to a height above the supposed IBL and, in this situation, may partly be due to -;V; radiational warming that was not simulated by the model. Because the IBL grows v much faster in unstable than in stable conditions (e.g. Garratt, 1990), the model Vproduces better results than in the previous case. The radiation effect is suggested Vby the observation that the air temperature did not drop down to its initial value V x during the return cruise (Fig. 3a). The change in moisture was also satisfacto- H- rily simulated; the model produced a maximum humidity of 2.9 g kg -1,'which is •X somewhat less than that observed (cf. Fig. 3d). X* The model was not sensitive enough for any closer investigation of the frontal X: changes in wind speed. 606 / Timo Vihma, Jouko Launiainen and Gunther Krause 3 Other Frontal Crossings and Discussion During the expedition there were about 20 frontal crossings. Although often the front was a rather distinct feature in the water temperature field, it was far less frequently observed as a pronounced feature in the air temperature and humidity, comparable to the two cases discussed above. The calculated fluxes of sensible and latent heat varied almost as distinctly as the water temperature, but their effect on the air temperature and moisture was not always observable. Thus, other effects, such as heat advection by the wind, initial surface boundary-layer thickness and stratification, (radiative) diurnal air temperature variations and spatial and temporal synoptic or mesoscale weather variations must have been in many cases more dominant than the effect of the local SST front, although their importance could not be investigated in the present study. For example, in a two-way frontal crossing (during the evening of 24 May 1987), an abrupt 2°C increase in the water temperature produced practically no response in the air temperature, although the stratification was unstable on the warm wa ter side. In this case, cold advection with a wind speed of 7 m s-1 across the front was superimposed on the frontal effects. Analogous observations in fasinex were reported by Khalsa and Greenhut (1989); Davidson et al. (1988) suggest that advection can sometimes have a more important effect on the atmospheric bound ary layer than a sea surface temperature front. In one jasin case study Guymer et al. (1983) estimated that the turbulent fluxes were not dominated by local SST variations when an occluding atmospheric front crossed the study area. On 5-6 June a narrow (about 10-km wide) sharp-edged area of warmer water with a temperature difference of 2 to 3°C was crossed seven times successively in 20 h. During this time, the wind direction remained almost constant, but the wind speed varied from 3 to 6 m s-1. The air temperature modification was studied and it was found that the net change in air temperature was inversely proportional to the wind speed. The stratification was unstable on the warm water side and almost neutral on the cold water side. The average changes across the front in water and air temperature calculated from the 21 cases observed were 2.8°C for the SST and 0.9°C for the air tem perature, i.e. corresponding to a ratio of ATa /ATs = 0.3. In comparison, the mean diurnal air temperature variation, calculated as an average for the expedition period of 19 May-6 June 1987 (at the latitudes from 74 to 79°N) produced a rather smooth sine wave with an amplitude of 0.6°C. In addition, the standard deviation of the air temperature as calculated from the data, filtering out the diurnal variation, was 1.5°C, which could have been caused by the combined effect of frontal and larger scale (spatial and temporal) temperature variations. As a result it could be that diurnal, frontal and larger scale variations are approximately of the same order of importance in controlling the atmospheric surface layer temperature in the Greenland Sea during this time of the year. For comparison of the ratio of the air to sea surface temperature changes across the front, which is 0.3 in the present study, a couple of studies can be found in the literature. In fasinex, Rogers (1989) reports 2°C SST differences related to about 1°C air temperature differences measured at the height of 30 m. The air Air-Sea Interaction in Areas of Thermal Marine Fronts / 607 Table 2. Average meteorological conditions during the expedi tion in the Greenland Sea (19 May-6 June 1987). (See text for definition of symbols.) r„= -1.3°C SEE = 17 W m-2 t = 64 mN m"2 T, = 0.5°C H = 13 W m"2 q = 3.2 g kg"' V = 6.7 m s"1 10/L = -0.15 RH = 90% temperature modifications were very smooth and rather similar for different wind directions. On the contrary, in some fasinex situations Khalsa and Greenhut (1989) found highly variable air temperature modification rates with low ATa /ATs ratios. Ratios of about 0.5 can be found from the study of Mey et al. (1990). Sweet et al. (1981) studied the front between the cold Slope Water and the Gulf Stream and observed ATa /ATs ratios of 0.4 and 0.8 for two different situations. The average SST change across a front was 2.8°C in our study, which can be considered moderate. A typical SST gradient observed in the fronts was about 0.05-0.4°C km-1, which is of the same order of magnitude as the SST gradient of 0.15-0.5°C km in the Arctic Front in the Barents Sea, as observed by Johannessen and Foster (1978). To give an overview of the conditions in the Greenland Sea during the observation period, averages of the main weather characteristics are listed in Table 2. It should be stressed that the values are averages based on observations from a vessel cruising in the area bounded by 74 to 79°N and 10°E to 10°W and so cannot represent the general conditions too reliably. The average fluxes of sensible and latent heat are about the same as given by Vowinckel and Orvig (1970) for the same latitudes in the Norwegian-Barents Sea in May and June, although an exact comparison is difficult since the fluxes decrease rapidly in the area during spring and early summer (cf. also Hakkinen and Cavalieri, 1989). An interesting study of the ocean surface heat budget was made in jasin (Guymer et al., 1983). It showed that about 70% of the net radiative flux is available for heating the ocean and, of the remainder, over three quarters enters the atmosphere as latent heat, the proportion of sensible heat being less than one quarter. Un fortunately, neither proper radiation measurements nor cloud observations were made during our expedition. Therefore, we cannot determine the heat budget of the surface; however, the net radiative flux in the Greenland Sea in late May and early June can be estimated to be 100-200 W m-2 (Vowinckel and Orvig, 1970; Hakkinen and Cavalieri, 1989). Accordingly, 30 W m-2 (H+LE from Table 2) of that enters the atmosphere and most of the energy is spent for heating the ocean. In the present study the latent heat flux contributed 57% and the sensible heat flux 43% of the turbulent fluxes going into the atmosphere. The ratio is rather typical for these latitudes (Bunker and Worthington, 1976). The difference between the present study and jasin (Guymer et al., 1983) may be partly due to the non-linear modification effects in the latent heat flux when the SST increases. 4 Conclusions During the expedition, the thermal marine fronts were found to influence the local 6 o8 / Timo Vihma, Jouko Launiainen and Gunther Krause atmospheric surface layer properties and air-sea interaction. This was often promi nently noticeable in the turbulent air-sea exchange, which produced a change in air temperature and humidity. The effects were most prominent during light winds and were most readily detectable in observational data gathered under stationary weather conditions. The frontal changes in air temperature and humidity were roughly simu lated by a one-dimensional model for suitable conditions. In most of the other cases the changes were interpretable in terms of large-scale meteorological conditions. The changes observed in wind (speed and direction) and stability in the vicinity of the fronts were interesting. Although the bulk-derived stress values may be some what unreliable in horizontally non-homogeneous conditions, the frontal changes in wind and stability are most probably related to changes in wind stress and the local wind wave field. In such cases, fronts should be more detectable, e.g. by several remote sensing techniques (cf. McClain et al., 1982; Li" et al., 1989) or they can even be seen by eye (Knauss, 1957; Sweet et al., 1981; Fedorov and Ginzburg, 1986, 1988). Finally, there are some differences between the Greenland Sea Arctic Front and other SST fronts studied in more temperate areas. In high latitudes, fronts can be observed throughout the year, if there is no ice cover, whereas at latitudes lower than 35° merely seasonal SST fronts can be found (Legeckis, 1978). Accordingly, the effects of the Greenland Sea Arctic Front on the marine atmospheric boundary layer tend to be more permanent than those of the fronts at lower latitudes. Acknowledgements We would like to thank the meteorologists in charge (Deutscher Wetterdienst, Seewetteramt), under the leadership of Dr Erhard Rod, onboard the ship FS Polarstern for their, help in calibrating the instruments and obtaining data for the study. References BLANC, T.v. 1986. Superstructure flow distortion mundy . 1988. 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Davis voorhis . a .d . and j.b. hers by . 1964. Oceanic ther (Eds), Plenum Press, New York, pp. 605-626. 35 1 r ,w y-,.: ■ .•v <$ - y v ■. S' >■ *\s i,, -i & ■ m*. /*? b / •: -;- ;V- • *' • V V r53SlSS&3BSS®8ittsSslS JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. C8, PAGES 14,471-14,485, AUGUST 15,1993 Ice Drift in the Weddell Sea in 1990-1991 as Tracked by a Satellite Buoy TimoVihma Department of Geophysics, University of Helsinki JoukoLauniainen Finnish Institute of Marine Research, Helsinki Ice drift In the Weddell See hei been studied by using « satellite buoy deployed on an ice floe. The buoy survived for a 20-month period, indicating a drift trajectory of 10,000 km and yielding 13 months of marine meteorological data. The drift of the icefloe was studied with respect to the winds measured by the buoy. In the central Weddell Sea, the mean drift speed of the ice floe was 0.15 nVs, which was about 3% of the wind speed. More specifically, the drift ratio was 3.4% in the marginal ice zone and 2.4% in the inner pack icefield. On average, the drift was directed 36" kit of the wind direction, but die turning angle was larger during the austral summer and smaller during the winter. On time scales of days the drift was primarily wind-dependent, except for cases during winter periods of high ice concentration and internal ice resistance. Her time scales of several months, purely wind-based simulations of the drift resulted in a discrepancy between the observed and simulated trajectories, but the inclusion of a slow (0.02 m/s) residual current made the simulations significantly better. The geostrophic wind based on European Centre for Medium-Range Weather Forecasts pressure analyses was estimated for a 1-mcoth period, and the ice floe was found to drift almost parallel to the geostrophic wind with a speed of 2% of the geostrophic wind speed. Inertial-type motion superimposed on the wind-induced drift was found to be a characteristic feature in the marginal ice zone during the austral summer, but it could not be found from the drift in winter when kinetic energy was transfcired to larger scales of motion and dissipated into the ice field. 1. Introduction ice dynamics in the Antarctic differ from those in the Arctic lies in the characteristics of the Antarctic sea ice, which tends to be a thin, The sea ice in polar oceans has an effect of primary importance broken, and divergent first-year ice field having more local ridging on the exchange of heat, moisture, and gases between the ocean and than that in the Arctic. These characteristics result in part from the the atmosphere and it also greatly affects the momentum exchange. fact that the drift and expansion of Antarctic sea ice is not so The distribution of ice is controlled in part by the thermodynamics of the atmospbcre-ice-ocean interface and in part ty the ice drift restricted by coastal boundaries, expect in certain areas as in the driven by the wind and ocean currents. Especially in the Antarctic, western Weddell Sea by the Antarctic Peninsula. Results obtained the dynamics of ice can result in the opening or closing of polynyas from studies in the Arctic are therefore not all directly applicable to IheAntarclic. and leads both at coastal areas and in the central pack ice. These The general circulation pattern in the Weddell Seals clockwise small areas of open ocean, which are continuously opening and freezing, play an important role in the regional heat budget and elliptic [Deacon, 1979; Gordon et al., 1981; Gordon and Huber, 1984]. The sea ice consists primarily of first-year sea ice, which air-sea interaction and serve as important areas for generation of drifts with a divergent pattern around the Weddell Sea and then new ice. From the viewpoint of the momentum exchange, the ice further out to the northeast. In winter the maximum ice extent is cover acts to reduce the momentum flux from the atmosphere to the near the Antarctic Convergence; but less than one fifth of the ice ocean, as part of the momentum is dissipated in processes of ice belt survives through the summer. Winds from the continent and deformation. On the other hand, the roughness of the ice cover, the divergent motion of the sea ice cause coastal polynyas to form when larger than that of the open ocean, tends to increase the momentum flux from the atmosphere. Finally, it is noteworthy that in the eastern and southeastern Weddell Sea. In the summer when drifting divergent sea ice, such as that in the, Weddell Sea, acting as the sea ice retreats to the south, these polynyas become a part of the a negative adveedve heat source may be of importance in the beat open ocean. The eastern Weddell Sea is an area of intensive ice generation and beat and moisture exchange between the ocean and balance of largcrsrarounding sea areas. the atmosphere. Major programs, such as the Arctic Ice Dynamics Joint As a part of an air-sea interaction project within the Finnish Experiment (AIDJEX) and Marginal Ice Zone Experiment Antarctic Research Program (FINNARP-89), two drifting buoy (MIZEX) have been carried out in the Arctic in order to study the stations were deployed in the eastern Weddell Sea area during the dynamics and thermodynamics of the sea ice. In the Antarctic, austral summer of 1990 (Figure 1). In January 1990, one of the experiments have mostly been made during the last few years buoys was deployed on a small ice floe in the marginal ice zone, [Llmbcrt et al., 1989; Kottmeier and Hartig, 1990; Hoeber, 1991; some 10 km from the local ice edge, while the other was deployed Massom, 1992]. The experiment on dynamics by Martinson and in the open ocean between the continental ice shelf and the sea ice. Wamser [1990] in the eastern Weddell Sea has probably been the The buoys carried a versatile network of sensors to study air-sea most detailed one, although SAucHe/on ’s [1919] expedition already interaction and marine meteorology. The meteorological part of the noticed the tendency of the local wind to mostly control the drift of project included a third buoy at the sea edge of the continental ice their evacuation ice floe in the Weddell Sea. The main reason that shelf. The kinematics and dynamics of the drift of the buoys, especially of that on the ice floe, will be discussed in this report, while another study in preparation will concern with the aspects of Copyright 1993 by (he American Geophysical Union. air-sea heat exchange. A technical report including the primary drift Paper number 93 JC00649. data and overall marine meteorological data cdlectcd by the buoys 0I48-O227/93/93JC-00649305.00 was given by Launiainen et al. [1991]. 14,472 Vikmaand Launuinen : Weddell Sea Ice Drift 70°%. - Fig. I. Map of the research area with the drift trajectory of the ice floe from January 2,1990, to September 3,1991. Dashed lines indicate approximate ice margins in February and July 1990 as derived from satellite images. Numbers indicate the location of the ice floe in the beginning of some selected months. The drift of an ice floe is controlled by the wind, the underlying some 2 months in open water (from mid-January to March 1991). ocean current, the Coriolis force, and the internal stresses of the ice The buoys were located by the Argos satellite system, which field. Thus it may exhibit inertial and tidal motion, rotation, and determines the buoy location using polar-orbiting satellites highly irregular drift patterns superimposed on the mean drift The measuring the Doppler shift of successive buoy transmissions. In scope of this paper is to present data of ice drift and to discuss the polar regions there are 26 satellite passes a day, but to locate a buoy drift mechanisms, especially that of the wind, in an area which has the pass must be long enough for the satellite to receive at least four been sparsely observed. Emphasis is given on drift characteristics successive transmissions, with a buoy transmission interval of 90s. in summer and winter, and in the marginal ice zone and the inner Thus about 18 to 20 locations a day were collected from our buoys, padc ice field, and the data are compared with those of previous yielding an average location interval of 1.25 hour in the principal studies in the Weddell Sea and in more investigated areas. research area of 73°-65°S, 40°-25°W. The accuracy of location is of theoiderof a few hundiedmeteis. 2. Data It depends on the geometry of the satellite pass, on the transmission The ice floe tracked was 180x150 m2 in area and 4 m thick at interval and velocity of motion of the buoy and, specifically, on the the buoy ate. It was a rather heavily ridged (up to a height of 1.5 to stability of the oscillator of the buoy. The location accuracy of the 2 m over the surface) multiyear floe and had most probably been buoys was studied at a fixed place during a calibration period for fermed in the vicinity of the continental ice shelf in a sheltered the meteorological sensors [Launlalnen et a!., 1991]. To exclude "bay." The ice floe therefore differed in surface roughness from the worst location errors, observations falling in the most inaccurate floes typical of the eastern and central Weddell Sea [Wadhams el Argos location category (class 1) were not used. These comprised al„ 1987]. The hull temperature sensor and water temperature chain only 7% of the total number of observations. of the buoy indicated the period the buoy drifted in the sea ice. The For the study, locations were interpolated for time intervals of 1 ice floe survived from January 2, 1990, until at least January 16, and 6 hours, arid the mean diurnal locations were calculated as well. i * 1991. After that the readings of temperature sensors at the depths Drift speeds and directions were calculated on the basis of these of 0.6, 3, 4, and 5 m from the ice surface suddenly rose to up to •locations. Because the drift speed of a buoy was usually 0.1 to 0.4 40.3°C, indicating that the ice floe had melted. The temperatures m/s, the movement between successive locations was of the order stayed high until the end of March 1991. Then the temperature at of 0.4 to 1.2 km, i e., at worst, comparable with the magnitude of 0.6 m dropped to -3°C while the lower temperatures dropped only the location error. Accordingly, drift velocities at 1-hour intervals to the freezing point (-1.8°Q, indicating that the buoy was sometimes contain a lot of random motion. The analysis is therefore surrounded by new ice. Finally, the water temperatures increased mostly based on drift velocities at 6-hour intervals (compare section again in the beginning of September, just before the buoy was 3.1). vx ). destroyed. Thus the buoy drifted for 18 months in sea ice and fer The buoys had two wind sensors; one was a vector-averaging >- « C,: • Vihma and Launiainen :Weddeu .Sea Ice Drift 14,473 (time period of 8 min) propeller anemometer (HM. Young Co.) 0 installed at a height of 3.8 m. Additionally, a cup anemometer was installed inside a tripod sensor tower ata height of 2.4 m to ensure accurate wind observations. The anemometer heights refer to their initial values, which may have changed some tens of centimeters because of snow accumulation. The data showed the cup anemometer to be more liable for ice accretion; the cup anemometer showed 25 cases (72 days in all) when the rotation was more cr less prevented by ice accretion, whereas the propeller anemometer stopped only twice (for 15 days in all during July and August). Although the wind was measured at two height levels, the aerodynamic roughness length (zg) could not be estimated accurately on this basis because of a distortion by the tripod tower to the cup anemometer. However, when the results from the distortion analyses in the fidd (Figure 2) and in a wind tunnel were taken into account, the cup anemometer data gave support to the propeller anemometer data. In the following, the measured wind refers to the propeller anemometer at the height of 3.8 m. 180 The surface of the ice floe was covered by ice ridges with a geometric roughness of 0.5 to 1 m resulting in an aerodynamic Fig. 2. The ratio of wind speeds measured by the cup and propeller roughness length (zg) of 0.03 to 0.1 m [Andreas, 1987].Acccrding anemometer, given with respect to the wind direction relative to the tripod measuring tower. The cup anemometer was installed Inside thetripod tower. Guest and Davidson to the classification by [1991] the values Because of different height levels cf the anemometers, the asymmetry in the correspond to roughness lengths of very rough and extremely rough distortion pattern suggests the ice floe to be nonisotropic in surface multiyear ice. The roughness in question leads to an estimate of roughness. 4.7xl0"3 to 7.5xl0'3 for the drag coefficient (Cdio ). Wind speed estimates for a standard height of 10 m may be calculated from the estimated Zg. Although the roughness length and the thermal the Weddell Sea along with the Antarctic Circumpolar Current, but stability of the atmospheric surface layer above the ice floe were most further analyses of this article cover the period until the end somewhat inaccurate to define, a 10-m levd wind speed was of January 1991, until which the buoy wind sensors functioned. calculated to get results comparable with other studies. We The total length of the buoy's drift trajectory, between January computed the 10-m levd wind speed using an iterative flux-profile 2, 1990 and September 3, 1991, was of the order of 10,000 km, scheme [Launlainen and Vihma, 1990] that uses the air temperature corresponding to a mean drift speed of 0.19 mIs. Referring to the observations from 1.9- and 3.2-m levels to derive the effect of discussions above, the calculation method affects the results. The thermal stratification on the wind profile. In cases of near-neutral drift velocity and trajectory length calculated from 1-hour locations stratification the corrected wind speeds for a height of 10 m were include pseudo-movements due to errors in the determination of the 20-27% greater than those for 3.8 m. buoy location. On the other hand, calculations based on average An estimate of the ice roughness has implications for seme of diurnal locations are probably very accurate in the mean but do not the analyses to follow. The ice floe where the buoy was deployed include all small-scale dynamics. As a compromise, the results from was rougher than the surrounding ice floes. During conditions of locations at some 6-hour intervals should be the most reliable ones relatively free drift, the wind stress is determined by the roughness for overall studies, including the major part of local-scale dynamics length of that particular floe, but during winter, when the ice fidd but with the potential error in the drift velocity caused by the is compact, the drift is affected by the average stress over the large positioning inaccuracy remaning small (10%). The corresponding ice field. An estimate of the effective roughness length for a larger trajectory lengths and drift speeds arc summarized in Table 1. area is thus required. In our case it would be lower than the Zg of the The time series of the drift speeds calculated from locations at buoy floe. On the basis of visual observations, a rather sparse laser 1-, 6-, and 24-hour intervals are presented for the period from profilometry available, and results given in the literature [Overland, January 1990 to August 1991 in Figure 3. The differences between 1985; Guest and Davidson, 1991; Wamser and Martinson, 1993], the results given by the three calculations are rather comparable, the the effective roughness length may have been about 0.1 cm, i.e. 1-bour-based results being 12% greater and the diurnal-based Cotg= 1.9x10 3. speeds being 12% smaller, on average, than the 6-hour speeds. The recent paper by Massom [1992] presents drift data from almost the same area in the central Weddell Sea (from an 3. IceFLoe Drift experiment in 1980), and the data fit well with our observations. 3.1. Kinematics The diurnal mean drift speed and standard deviation of our buoy lie in the middle of the ranges of Massom ’s four buoys (0.13-0.18 m/s The overall drift trajectory of the ice floe is presented in Figure fer the mean speed, 0.06-0.14 for the standard deviation). If we 1, The general drift was to the north during the firstyear and to the compare the drift in various areas in the Weddell Sea [cf. Massom, northeast thereafter. This was somewhat contradictory to previous 1992, Tables 5-7], we can conclude that southwards of 70°S our drifterrcsults [Kotlmeier and Hartig, 1990; Crane and Bull, 1990], buoy drifted at a slower speed than Masson's, but between 70°S according to which one would have expected an initial drift more and 63°S the drift rates were very similar. North of 63°S our buoy to the west. During April and May, especially, a high speed drift drifted with a higher speed, even twice as high as Massom's buoys. was observed (Figure 3). Later, as winter approached, the ice field Maximum daily drift rates of 0.7-1 mis were found in April and May became more packed and rapid drift was prevented. In the next in both experiments. autumn the drift speed increased again as the ice drifted away from A more detailed analysis showed that parts of the trajectories v 14.474 VlHMA ANDLa UNIAINEN: WEDDELL SEA ICE DRIFT 0.45 - 1 °-25 Hg. 3. Time scries of the mcothly mean drift speeds. Results calculated from buoy locations: 1° interpolated at 6-hour intervals (solid), 2° at 1-hour intervals (dotted), 3° based on daily mean locations (dashed). Note that from January 16 to March 31,1991, the buoy drifted in open water. TABLE 1. Drift Trajectory Lengths and Speeds Calculated Using Vi BuoyP Intervals Location Total Trajectory Mean Drift Velocity and Standard Deviation, mZs Maximum Velocity, m/s Interval, hours Length, km Total Period Until Jan. 15.1991 Total Period Until Jan. 15.1991 I 10,906 <121 ±0.15 0.17 ±0.11 6 9,707 O.I9±O.I3 ai5±o.io 0.9 0.7 24 8,613 0.16 ±0.12 0.13 ±0.09 0.8 0J revealed drcularmovcments resembling inertial or tidal motion. An Actually, it was also occasionally possible to estimate a radius example of such a period is given in Figure 4. In order to study the of curvature of the circular motion from the trajectories of the most /t distribution of kinetic energy in different scales of motion and to apparent inertial movements, e.g., those shown in Figure 4. Fifteen find out whether tidal and inertial motions were present, a spectral gyres can be found from the 10-day period, the average radius of analysis was performed on the drift data. The spectra were these being 630 m. The theoretical radius for pure inertial motion calculated from the position coordinates scaled to represent is VIf where V is the drift speed and /is the Coriolis parameter. distances in north-south and east-west directions, respectively. Using the observed average drift speed, from the theoretical Accordingly, two spectra were obtained for the orthogonal velocity estimate we get a radius of 770 m. Also, the phase of the drift components. The spectra were calculated using the fast Fourier velocity components was investigated, and it did not behave like transferor (FFT) method for each month separately and also fer the that of a tide. These analyses strengthened the conclusion that the whole observation period. Calculations were based on the hourly origin of the observed cycles is indeed of inertial motion. interpolated data. i It has been demonstrated in recent literature that the trajectories * • . r-f Spectra for several months showed a peak in a frequency band of open ocean drifters may have a fractal nature [Osborne et oh, corresponding to a period of about 12.5 hours. Unfortunately, the 1989; Brown and Smith, 1990; Sanderson and Booth, 1991]. To the inertial frequency in the latitudes in question is almost the same as best of our knowledge, this kind of investigation has not been made the frequency of the principal lunar tidal component (M2). To find with respect to ice floe trajectories so far. In our experiment, the out which motion was dominant, the shift of the peak was analyzed spectra of the components of ice velocity rather well fitted a power with respect to the buoy ’s drift to the north. Figure 5 presents the law of spectral energy S = to*, where sill SSiSSSl Vihmaand Launuunen : Weddell Sea Ice Drift 14,475 the open ocean (in February and March 1991), but the differences were not remarkable enough to unravel the state of the ice floe on the basis of drift only. In addition to its translational movement, the ice floe was able to rotate more or less freely, depending on the concentration and "viscosity" of the field. The rotation was measured by a compass, and the time series is presented in Figure 7. The multiyear ice floe was in the drifting sea ice zone during the austral summer and autumn of 1990 and was able to rotate rather freely. The rotation - was prevented after the end of May 1990, when the ice field became more parked. In January 1991 the ice concentration diminished, and individual floes were once again able to rotate. The lively rotation continued while the buoy was in the open ocean, and still after the Kg. 4, Trajectory cf the ice floe revealing inertial motions during the period formation of new ice when the buoy was drifting in the northern ftbroary 4 to 13,1990. Weddell Sea. 3.2. Background to the Ice Dynamics and Magnitude of Force drift on wind and on internal and subsurface drag forcing. In the ■Terms case when the floes drift finely, without too significant an amount of collisions and compression due to other ice flees, the slope of a The forces affecting the drift of an ice floe, given as an equation drift spectrum may resemble more closely that of the wind. When of momentum balance read. i the ice field becomes more compressed, the response to the wind is more damped and kinetic energy is transferred to smaller wave m dVi/df=-m/kxVi +?* --tw /- mgVH (1) numbers, seen as an increase in the exponent a (Figure 6). Periods of higher coefficient are met with during the austral winters of 1990 The equation is written in a two-dimensional Cartesian and 1991 and in December 1990. The latter finding is somewhat coordinate system, and an overbar indicates a vector. Variables are surprising because inertial motion was apparent in the spectrum of as follows: m is the mass of ice permit area, Vf is the ice drift December 1990 and this has been regarded as a sign of free drift velocity./is the Coriolis parameter, k is the unit vector normal to [McPhee, 1978]. This should imply that the drift in December 1990 the surface, -r, is the force caused by the air stress, tw denotes the was rather free of ice stresses but that the kinetic energy force from the water stress. I denotes the force due to gradients of accumulated in small wave numbers for some other reason. In any internal stress in the ice field, and H is the height of the sea surface case, it is interesting to note that the translative drift direction in- above a level surface. The last term, accordingly, represents merely December 1990 was quite opposite to the overall observed a sea surface tilt The notation is such that-?,, assumed to be parallel direction, the latter being out from the Weddell Sea toward the open to the surface vend, is taken as positive to represent momentum ocean. The overall increasing trend of a during the 20-month period sources for the ice floe, while Tv and I represent momentum sinks. might suggest the shifting of the kinetic energy of movement In our case, only the time derivative, Le. the acceleration term . towards smaller wave numbers when going north from the Weddell and the air stress and Coriolis force, can be determined from the Sea towards the southern ocean. Both the drift speed (Figure 3) and measurements. In practice, the acceleration of the ice floe is small, the exponent a showed rather low values during the buoy ’s drift in comparable to the inaccuracy in the calculations created by the latitude Kg. 5. Theoretical period of inertial motion as a function of latitude (solid line) and the spectral "semidiurnal" peak period observed in various months. 14,476 Vihmaand Launiainen : Weddell Sea Ice Drift Period (days) > Hg. 6. Time series of the slope coefficient a of the spectral energy density of S = of* of the monthly drift spectra. Example of a spectr um (February 1990) given in the top left comer. \ \ - Fig. 7. Rotation of the ice floe with respect to compass north from January 2,1990, to September 3,1991 (diurnal means). Note that from January 16, to March 31,1991, the buoy drifted in open water. position determinations. Wind measurements from the buoy Hankins [1975] studied had a relatively low air-ice drag coefficient together with an estimate of the roughness length of the ice floe give Coltki of 1.5xl0"3, while Martinson and Wamser [1990] found it to us an estimate of the magnitude of the air stress. Unfortunately, be 2.7xl0"3 for their case (a review of drag coefficients over sea ice during the FINNARP-89 study we had no current meter under the is given by Overland [1985]). ice floe. Accordingly, the magnitudes of the oceanic shear stress Wc had no direct way of estimating the effect of a steady and the internal stress of the ice field remain uncertain. A residual gecstrophiccurrent field. In the Arctic Ocean, in studies with a small force to represent their combined effect as a momentum sink can time scale the term has been regarded as small, but because of its only be estimated. semistationary character the term may be very effective over a long A description of the momentum balance with a amplified flee time interval [c.g., Hibler and Tucker, 1979], drift equation that contains only the air and water stresses and the To summarize, the momentum balance of an ice floe can be Coriolis force should be appropriate for a first approach to the drift described as the sum of three terms that can be estimated from our of Antarctic sea ice, which, on the average, has a divergent velocity observations: the air stress, the Coriolis force and a residual term field. "The force due to the internal ice stress is significant but should (R) representing all the other terms in equation (1). The balance of not be dominant except temporarily during periods of restricted the forces can be represented schematically as in Figure 8. motions, most often found in winter [Martinson and Wamser, The air stress can be parameterized using either linear or 1990]. In the Arctic, the internal ice stress may even be of the same quadratic drag laws, the quadratic drag having a better physical order of magnitude as the air and water stresses [Hankins, 1975], baas, and being given as a scalar as According to Martinson and Wamser [1990], in the Weddell Sea the water stress is typically one third of the air stress. It should be *» = P«Cd V»2 (2) noted, however, that the roughness of the upper and lower ice boundaries and choice of drag coefficients can considerably affect where p« is the air density and Co is the drag coefficient for the ‘•/'Z the magnitude of the calculated forces. For example, the ice field observation height of wind speed V,. The ice-water stress can be ; V',,:. SsSSliSlSSIS: VlHMA AND LAUNIAINEN: WEDDELL SEA ICE DRIFT 14,477 the ice floe. Thus using the parametcrizations (2) and (3) for scmistationary_ drift, we get piCpiolV,iol 2 = pwCwHti 2, i.e„ Cdio /Cw = pwlVil 2 / p,IV,io I2. When the observed 6-hour average velocities of ice drift and wind are used for the period until January 1991, a ratio Cnio/Cw = 0.5 is obtained. The ratio differed remarkably between the periods from January to May and from June to December 1990. During the first period the drift took place in the marginal ice zone and Cdio /Cw was typically 0.7, whereas it was about 0.4 during the drift in the central pack ice. The inclusion of an estimate of an ocean current in the direction of the mean drift (compare equation (3) and section 4.1) would lower the ratios above to 0.6 and 0.3, respectively. Accordingly, Cw would be Fig, 8. Momentum balance of an ice floe. Characteristic values for relative approximately 3 times as large asCcio during the drift in the central magnitudes of air stress, Coriolis force, and residual force are given. pack ice. Bearing in mind the assumptions used, the Cw for the central pack ice should be considered as an effective drag coefficient, also containing implicitly the effect of energy parameterized analogously: dissipation by internal ice stresses. A "true" value for Cw could be Tw — pwCwl Vi-Vol2 (3) better presented by 1.7x Cdio (Cdio /0.6) as obtained from the marginal ice zone. Ratios of Cdio /Cw can be found in the literature, where pw is_ the water density and CwJs the ice-water drag such as 0.5 by McPhee [1980], 0.32 and 0.4 by Thorndike and coefficient. Vi is the ice drift velocity and V0 is the velocity of the Colony [1982], 0.7 by Fissel and Tang [1991], 0.84 (for effective ocean current. Cw and referred to 10-m air drag) by Martinson and Wamser [1990], Time series of the magnitude of the three forces of Coriolis term, and 0.28-0.59 by Hoeber [1991]. Only the last two were obtained •r, and R are now to be calculated (on the basis of 6-hour interpolated from Antarctic data. buoy locations). As was discussed in section 2, the role of the ice The period most clearly revealing inertial-type motion (see field should be taken into account when computing the air stress, Figure 4) was analyzed in the light of momentum balance. Because from January through April 1990, the ice floe drifted relatively the absolute velocity remained almost constant over the period, the freely (see Figure 7), and the air stress may be estimated using the two orthogonal velocity components of equation (1) are to be roughness length of the floe in question (q, of 3 to 10 cm), and the investigated In the case of pure inertial drift only the acceleration thickness of that particular floe (4 m) should be used when and Coriolis terms would remain. These were calculated together computing the Coriolis force. Htcsclcad to estimates of 0.16 to 0.28 with the air-ice stress from observations of drift and wind, N/m2 for the air stress, 0.07 N/m2 for the Coriolis force and 0.13 to interpolated to 1-hour intervals. Figures 9a and 96 present the time 0.24 N/m2 for the residual term, all as mean values for the period series for the terms for a part of the inertial motion period discussed from January through April. Later, when the ice field became mere and indicate that the acceleration results from the Coridis term, compact, the effective roughness length of the field (approximately although it is still exceeded by the air stress for the east-west 0.1 cm) should yield a more reasonable estimate for the air stress, component and the mean thickness of the ice field (approximately 0.8 to 1 m) An inertial-force dominant motion, as observed in the ice drift, should be used for computation of the Coriolis force. The estimates can be other that of the ice or that of the water column of the ocean. for this period are somewhat more uncertain. Mean values from Generally, the latter alternative has been regarded as more probable May through December are 0.11 N/m2 for the air stress, 0.02 N/m2 [McPhee, 1978; Hitler, 1980]. The problem might be investigated for the Coriolis force, and 0.10 N/m2 for the residual term. The on the basis of data from such periods during which the wind speed results demonstrate that the air stress and the residual force were of becomes very light If an inertial motion were a property of the ice the same magnitude, while the Coriolis force was about 20-40% of alone, a relative velocity between the ice and the ocean should exist, the air stress in the period of relatively free drift and about 15-20% and an estimate for -rw could be computed assuming the relative in the period of compact ice conditions. Thick ice floes result in velocity to equal the ice drift velocity, i.e., Vo = 0 in (3). The relatively large Coriolis force, while a rough upper surface of the damping of the drift could then be simulated on the basis of the ice leads to high air stress. The buoy floe was both thick and rough equation of momentum with the acceleration term, Coriolis term, when compared with the surrounding floes, but the thickness seems air-ice stress, and ice-water stress. to have been an especially effect! ve factor, seen as relatively large An almost calm period was found from our data set between Coriolis force during January through April. The ratio of forces was, February 11 and 13, 1990. During this time the acceleration term however, affected also by the low wind speeds observed in January and the Coridis term were dominant The velocity of the ice floe and February. In classical Ekman drift, the air stress would be was simulated using an initial velocity value at the beginning of the balanced by the Coriolis force of the whole Ekman layer. In the case period. Numerical time integration of the equation of momentum of thin, freely drifting ice the situation approaches a balance led to a damping of speed, because the air stress was smaller than between the air-ice stress and ice-water stress, i.c.,7? the water stress. The damping time is, of course, dependent on Cw. No direct measurements were available for determination of the As was discussed previously, Cw is typically somewhat greater than ice-water drag. A first-order estimate for the approximate Cdio . Therefore a first guess value of Cw=Cdio should not produce magnitude of the drag coefficient Cw may still be derived under too a rapid damping. In the simulation, the water drag overdamped certain assumptions. If the ocean underlying the ice is assumed to the speed of the ice floe in 2 hours, after which a balanced speed be at rest and internal ice stresses and the Coriolis force for the about 50% of that observed was reached. The observed drift speed relatively thin ice are ignored, the air-ice stress would be the remained almost constant during this 40-hour period of light winds. momentum source and the ice-water stress the momentum sink for The distinct discrepancy between the observed and the simulated 14,478 Vihmaand Launiainen : Weddell Sea Ice Drift speed. Additionally, the mean values of the wind factor and turning angle correspond well to classical Ekman drift, and one may suppose the wind stress to have been the dominant factor for the drift during a major part of the observation period. From Jammy to . May 1990 nearby the marginal ice zone, the mean drift ratio was 3.4% (with respect to 10-m wind), and in the inner pack ice field Vr from June 1990 onward a mean value of 2.4% was observed. Contradictory to our data, Hoeber [1991] observed in the eastern Weddell Sea a greater wind factor in October than in August (2.7% and 15%, respectively). Therefore it seems that the location of our buoy with respect to the large-scale ice field was more important in affecting the wind factor than the seasonal characteristics (ocean stratification, roughness of the lower boundary of an ice floe), which Hoeber [1991] argues to have caused the variations in his study. The drift speed ratio of about 3% is the same as observed by Martinson and Wamser [1990] for the eastern Weddell Sea and comparable to the results of 2.4 to 3.0% ty Overland et al. [1984] for the Bering Sea and of 3.4 ± 05% by Fissel and Tang [1991] for the Newfoundland shelf. Lower ratios of 0.9 to 1.9% were observed for the Arctic Ocean by Thorndike and Colony [1982], and Johannessen et al. [1983] obtained 0.9 to 2.1% for the east Greenland marginal ice zone. In the Antarctic, Bering Sea and Newfoundland shelf the ice is assumed to drift with greater freedom from internal ice resistance as compared to the common situation in Arctic areas. This could be one reason for the larger wind factors observed. Other reasons may arise from differences in floe dimensions and roughness of the floes, and from stratification of day atmospheric and oceanic boundary layers. The turning angle bad an annual variation, with smaller values Fig. 9. Time series of the acceleration term (solid), the air stress (dashed) during the austral winter (Figure 106), when the ice field had a and the Coriolis term (dotted) during an inertial motion period from higher ice concentration and was more packed. This is in accordance February 4 to7,1990. (a) East-west component, (b) North-south component with the early observations of Nansen [1902] and Sverdrup [1933], who related the variations of the turning angle to the internal ice resistance. A seasonal variation similar to our result was observed r drift speed supported the assumption that the inertial motion in the Arctic ty Thorndike and Colony [1982], with respect to the observed was a property of the ocean and not of the ice floe only. geostrophic wind. They also demonstrated bow an increase in the internal ice stress would decrease the turning angle. Additionally, 4. Ice Drift Dependenceon Wind the ice thickness affects the turning angle: drift of thicker ice tends 4.1. Drift With Respect to Surface Wind to deviate more from the wind [Zubov, 1943, p. 383]. In our case, the 4-m-thick ice floe drifted freely in summer and autumn, but in As was reported by Launiainen el al. [1991], the drift of the ice winter it became part of a larger and generally thinner first-year ice floe buoy indicated a distinct dependency on the local wind and field, which should have decreased the turning angle. Finally, one showed a drift at a turning angle to the left of the wind. The wind would expect a decrease in the turning angle as the wind speed sensor of the buoy functioned from January 2,1990, to January 28, - increases, but we did not find statistically significant support for 1991. Accordingly, the study was made for that period. Data are this from our data. More pronouncedly, a decreasing scattering in lacking from the period from July 27 to August 9,1990, because the turning angle and its convergence toward 30°-40° with .V ice accretion occurred in the anemometers. The overall average increasing wind speed was found. wind speed over the ice floe was 62 m/s (referred to 10-m height), The dependency of the ice drift on wind was further studied by and the strongest winds were measured during late winter and presenting the drift speed as a function of the average diurnal wind spring. Distribution of wind direction was rather even. speed. This resulted in a rather high correlation (of the order of The scalar ratio of the ice drift and the wind speed, and the 0.75), but the method did not include the directional dependency. turning angle between the drift and the surface wind are given as .To be more strict, the drift was analyzed in the two orthogonal time scries in Figure 10. The overall mean value was 3.6% for the (Erections (N-S and E-W) for the period from January 1990 until drift ratio and for the turning angle 36°. With respect to the wind at January 1991, when the ice floe was in the eastern and central parts a height of 10 m the ratio would be 2.8±1.9% (mean and standard of the Weddell Sea. Before the components were calculated, the deviation). Although the ratio varied with time, it did not depend wind vector was rotated 36° (left), to make the wind comparable to on wind speed. Referring to the discussions above, we do not know the drift vector. In such an analysis, a perfect correlation between the explicitratioof the forces affecting the drift, but periods of rather the component!al drift and wind velocities would mean that the drift <•-. constant values of both the drift ratio and the turning angle suggest ■ is wind-induced. The results are shown in Figure 11. The V- wind-induced Ekman-typedrifLIf the oceanic shear stress and the ■ correlations between the drift and the wind components are internal ice stress were very significant contributors to the drift in surprisingly high, the correlation coefficient being 0.88 for the the periods, the ratio of the forces would not have remained so north-south component and 0.89 for the cast-west component. The stationary, as we measured considerable variations in the wind correlation uras even higher for shorter periods and high wind -.7. '■ :v'-f v Vihmaand Launiainen : Weddell Sea Ice Drift 14.479 -100- Fig. 10. (a) Drift speed of the ice floe with respect to the local wind speed measured on the floe (6-hour averages). (6) Turning angle between thcdirectionofthcicc drift and the surface wind. Rjsitive values indicate drift directed to the left of the wind vector. speeds. For example, for wind speeds greater than 8 m/s the The time series of the geostrophic wind G and the buoy wind also correlation coefficients were 0.95 and 0.94 for the north-south and fitted each other encouragingly well. Accordingly, it was east-west components, respectively. reasonable to look for an apparent dependency between G and the The regression equations for the drift with respect to the wind ice drift velocity. The drift speed versus the geostrophic wind speed, given in Figure 11 show a constant which suggests a residual drift and the time series of the turning angle are presented in Figure 13, in cases when the wind becomes vety light. It might be interpreted The mean drift speed is 2% of the geostrophic wind, and the drift as representing the residual drift with the ocean current or, rather, direction deviates ± 30° from the geostrophic wind direction, the the velocity of the ice drift if it were affected by the underlying average being parallel to the geostrophic wind. The mean values ocean current only. Internal forces in the ice field certainly have were calculated for situations for which G > 3 m/s, because for a their own effect as well, but if this is more or less random in couple of almost calm days the direction of G was difficult to define. direction, the constant may be assumed to represent the net ocean Zubov [1943] already found that the ice drifted parallel to the current. The base drift would be 0.013 m/s for the north-south pressure isobars witha speed of about 1% of G, as was also observed component (positive northward) and -0.012 m/s for the east-west by Sobczak [1977] and Thorndike and Colony [1982]. The wind component (positive eastward). This means a current with a velocity factor based on our data is twice as large, but even higher wind of0.015 to 0.02 m/s directed to the northwest. In 13months it would factors have been observed in the Barents Sea (T. B. Loyning, have caused a net drift of 600 km. personal communication, 1992). Our result may have been affected to some extent ty the atmospheric stability, which affects the actual surface wind and stress, but this effect has to be studied on the basis 4.2. Drift With Respect to the Geostrophic Wind of a more comprehensive data set. Perhaps more importantly for our In addition to the surface wind measured by the buoy, the case, the ice floe we studied was very rough, read ting in a high geostrophic wind was derived from the pressure analysis obtained momentum flux to the ice. Moreover, April 1990 was a period of a from the European Centre for Medium-Range Weather Forecasts high drift speed, with respect to the buoy wind as well. Accordingly, (ECMWF). This was done in order to compare the buoy observed the drift was apparently not much restricted by internal ice wind and pressure with the geostrophic field and to obtain an ice resistance. It is therefore reasonable that we observed a higher drift drift ratio with respect to the geostrophic wind speed. The ratio with respect to the geostrophic wind. geostrophic wind was analyzed every 12 hours from the sea levd The data also allowed us to compute the ratio of surface to pressure fields for April 1990, when the ice wras advancing rapidly. geostrophic wind and the geostrophic drag coefficient Ca defined The ECMWF pressure analysis may be inaccurate in an area as Co = uJG, where u. is the friction velocity. The mean ratio of having only a few field observations. To check the accuracy, the Vi(3.8myG was 0.53. (Almost the same ratio was obtained with analyses ’ pressure was compared to the one measured by the buoy. respect to the wind speed above the planetary boundary layer, A rather close agreement was found, with a standard deviation of observed by a few balloon soundings from our research vessel.) The 23 hPa (Figure 12). It is to be noted that the buoy did not send the result gave 0.64 to 0.67 for V,(10 m)/G, which is comparable to the data to the Global Telecommunication System (GTS) of the World results of 0.55 to 0.62 by Thorndike and Colony [1982] and 0.52 to Meteorological Organization (WMO) (because of incompatibility 0.80 reviewed by Overland [1985], but somewhat greater than the of the structure of the data message). Thus the pressure analyzed by ratio of 0.44 ± 0.09 observed by Fissel and Tang [1991]. On the the ECMWF was independent of the buoy's pressure observation. other hand. Waiter et al. [1984] observed a ratio of OS (referred to 14,480 Vihmaand Launlunen : Weddol Sea Ice Drift v, = 0.031-v. +0.013 r=0.88 N-S comp, of 36°rotatcd wind speed (m/s) 'V ' M U; = 0.028-u.-0.012 r=0.89 E-W comp, of 36° rotated wind speed (m/s) Eg. 11. (a) North-south component (positive northward) of the drift velocity with respect to the N-S component of wind velocity rotated 36* to the left Linear regression equation given in thefigure. (6) East-west component (positive eastward) of the drift velocity with respect to the E-W component of wind velocity rotated 36® to the left. Linear regression equation given. a 10-m height). Our observation for the turning angle between the been developed especially for Arctic regions. Some of the rules for geos trophic and surface wind is 28°, which is in accordance with drift with respect to the geostropbic wind were mentioned in the values reported in the literature [cf. Overland, 1985]. The Co we preceding section. They arc especially of value for summer r obtained is 0.05 with a standard deviation of 0.02. This agrees well conditions, but the coefficients have usually been derived from with the result of 0.047 by Waller el at. [1984], but Overland and Arctic data Martinson and Wamser [1990] suggested a sample drift Davidson [1992] found a median value as low as 0.029. Generally, rule for the Weddell Sea based on surface wind and found it to fit the scatterin Co obtained in various studies is large [cf. Overland, the observed drift data well on scales of tens of kilometers. For their 1985]. data, scaling on the baas of wind resulted in almost as good a .n. 4.3. Drift and Trajectory Estimates representation of the ice drift as the use of the equation of v! Semi empirical rules for predicting the ice drift on the basis of momentum with quadratic or linear drag laws, which requires local wind observations or analysis of the geos trophic wind have information not often available. They also demonstrated that the Vjhwaand Launiainen : Weddell Sea Ice Drift 14,481 effect of internal ice stress could be described by using effective parameter values (case specific) for the drift. For our case, drift trajectories were computed to study whether the simulation is also reasonable for longer time and space scales. The simulations were encouraged by the rather steady values found for the drift to wind speed ratio and the turning angle. Accordingly, drift trajectories were calculated using the mean drift ratios and turning angles found for several periods of our drift observations. The values given by Martinson and Wamser [1990] were also tested to study how results from different areas and situations could be applied. A simulation was made for the total surviving period of the ice floe, i.e.forthc380dEy period from January 2,1990 to January 16, 1991. Additionally, three periods merited a closer look. The first was the period April-May, 1990, when the autumn drift was rapid and rather straightforward. The second period was during the spring, in November 1990, when the drift ratio and turning angle remained highly constant (sec Figure 10). The third period was during the wintertime, from June 1 to July 26, 1990, when the influence of the wind on the drift may have been weaker than usual Simulations were made with the following drift ratios and turning Buoy pressure (hPa) angles: (1) values obtained from the whole period of our drift and wind data, he., using 0.036 for the drift ratio and 36* for the turning Fig. 12. Atmospheric surface pressure from ECMWF analysis versus the angle; (2) values analyzed from the data of the specific period to be buoy pressure in April 1990 (diurnal means). simulated, values shown in figure captions, (3) values found by Martinson and Wamser [1990] for the eastern Weddell Sea (for the surface roughness of our ice floe and a 3.8-m wind height these convert to 0.041 for the drift ratio and 23* for the turning angle) and (4) for April 1990, simulated drift based on geostrophic wind. Trajectories were calculated using the observed location at the beginning of each simulation period as a starting point. The daily drift was calculated using the diurnal mean wind speed and direction to obtain the next location. Calculated trajectories together with those observed are presented in Figures 14-17. Generally, the incoherence is higher when the drift coefficients are not those obtained from the diagnostic analysis, i.e. when a data set other than that obtained from the analysis of the calculated period is used. This, of course, limits the applicability of the method. The result for the total observation period (Figure 14) shows characteristics of the overall pattern of the observed trajectory to have been reproduced by the wind-based geostrophic wind (m/s) simulation, but the distance between the observed and simulated positions at the end of the period was 590 km, the observed position being to the northwest of that simulated. This is only 12% of the total length of the trajectory but almost 80% of the total net transition. The drift simulated with the coefficients of Martinson and Wamser [1990] was directed still further east In section 4.1 we suggested, as a residual, a baric ocean current. This would have produced for the period a net drift of 600 km to the northwest. Actually, this would be the net effect of the ocean current and the internal stress of the ice field, but there is no reason to believe that the internal ice stress would have produced net drift to the northwest. Rather, the direction of its net effect would have been to the east, preventing the ice from packing against the Antarctic Peninsula. Another simulation was made adding a residual current (0.018 m/s to 317°) to the wind based model. This produced a good rcsultshowu in Figure 14. For shorter simulations the compatibility is generally better. • . : April 1990 Trajectory estimates given by various models for April and May 1990 are given in Figure 15. The best fit is for the estimate based 1 i Fig. 13. (a) Drift speed of the ice floe versus the geostrophic wind speed, on the model coefficients obtained from the diagnostic analysis of April 1990. (h)Turoingnngle between the ice driftsnd the geostrophic wind. the period in question. The rather large drift coefficient based on Positive values indicate drift directed to the left of the wind vector. Martinson and Wamser [1990] gives the next best fit. with respect , :.f ; I 7;-- I ! i .1 il t '■ ( / • ’« • V.-| On the Surface Heat Fluxes in the Weddell Sea Jouko Launiainen Finnish Institute of Marine Research, Helsinki, Finland Timo Vihma Department of Geophysics, University of Helsinki, Finland Turbulent surface fluxes of sensible and latent heat in the Weddell Sea were studied using drifting marine meteorological buoys with satellite telemetry. In 1990-1992 a total of 5 buoys were deployed on the sea ice, in the open ocean, and on the edge of a floating continental ice shelf. The buoys measured, among others, wind speed, air temperature and humidity with duplicate sensors and yielded year-round time series. The heat fluxes were calculated by the gradient and bulk methods based on the Monin-Obukhov similarity theory. Over the sea ice, a downward flux of 15 to 20 W/m2 was observed in winter (with typical variations of 10 to 20 W/m2 between successive days) and 5 W/m2 in summer. For the latent heat flux, the results suggested a small evaporation of 0 to 5 W/m2 in summer and weak condensation in winter. The highest diurnal values, up to 20 W/m2, were connected with evaporation. Because of stable stratification, the transfer coefficients of heat and moisture were reduced to 80% of their natural values, on the average. Over the leads and coastal polynyas, an upward sensible heat flux of 100 to 300 W/m2 was typical, except in summer when the air temperature was close to the sea surface temperature. Over the continental shelf ice, the sensible heat flux was predominantly downwards (15 to 20 W/m2), compensating the negative radiation balance of the snow surface. Over the snow and ice surfaces the magnitude of turbulent fluxes was smaller than that of radiative fluxes, while over the open water in winter sensible heat flux was the largest term. Modification of the continental air-mass flowing out from the shelf ice to the open sea was studied with aerological soundings made from a reaseach vessel. Associated turbulent heat exchange was estimated on the basis of three methods: modification in the temperature profiles, surface observations, and diabatic resistance laws for the atmospheric boundary layer. If we estimate an area-averaged turbulent heat exchange between the surface and the atmosphere for the whole Weddell Sea on the basis of our data, the large upward fluxes from leads and coastal polynyas (with an areal coverage of 5 to 7% in wintertime) approximately balance the downward fluxes over the sea ice. A first-order estimate for the annual area-averaged total vertical heat loss from the water mass is 20 to 30 W/m2. 1. INTRODUCTION flux from the sea to the air may reach several hundreds of watts per square meter [Bromwich and Kurtz, 1984; Polar oceans arc areas of extreme differences in the Cavalieri and Martin, 1985; Schumacher et aL, 1983]. On temperature between the ocean and the atmosphere, but the the other hand, the beat and moisture exchange affects the heat exchange is frequently restricted by sea ice cover. amount of sea ice, and controls the structure of the Over ice-free areas, cracks, leads and polynyas, the heat atmospheric and oceanic boundary layer. In certain areas of the polar oceans, the beat loss from the ocean also affects the deep water formation, especially when sea ice is The Polar Oceans and Their Role in Shaping produced increasing the surface salinity in the water. the Global Environment It is well known that^ despite the small areal coverage of Geophysical Monograph 85 Copyright 1994 by the American Geophysical Union leads and polynyas, they have a great effect on the total 399 400 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA heat loss from the ocean and even a few percent of open over open leads, die temperature difference becomes V* water or thin young ice make a dominant contribution to extreme, resulting in intensive heat exchange. The heat loss the regional heat budget in winter [Maykut, 1978; Ledley, from the leads is compensated by the enthalpy of freezing 1988]. The effect is also detectable in the output of global of the sea, and according to Arctic observations the leads climate models [Simmo/ts and Budd, 1991]. In Arctic typically remain open for a few hours only [Lebedev , 1968; regions, heat exchange over sea ice or over leads and Bauer and Marlin, 1983; Makshlas, 1991]. After that new polynyas has been studied in several field experiments, but ice is formed, but it still permits considerable heat flux observations on the meteorological variables required to from the ocean. compute the heat and moisture fluxes over Antarctic seas In summer, the marginal ice zone retreats southward and are still rare, especially from the winter period. A few westward and the coastal polynyas in the eastern Weddell analyses of heat exchange over Antarctic sea ice and coastal Sea become part of the open ocean, but the sea ice remains polynyas have been reported [Bromwich and Kurz, 1984; in the central and western Weddell Sea. Summer conditions Andreas and Makshlas, 1985; Kdnig-Langlo el al., 1990; over the sea ice are very different from those in winter, Kottmeier and Engelbart, 1992]. because incoming solar radiation warms the snow and even The Weddell Sea is totally covered by ice during the small melt-water ponds may appear. Thus the wintry austral winter, although the ice field is broken and leads are contrast between the temperature of the sea ice and the generated within the drifting divergent ice field; wider leads often vanishes and the air-sea partition of turbulent polynyas are frequent in the southeast and south near the fluxes may vary in time. For example, according to the ice shelves and the coast of the Antarctic continent [ZivaZZy arctic data of Leavitt et al. [1978, also cf. Andreas, 1989] and Comiso, 1985]. The areal coverage of the polynyas and over the Beaufort sea ice, in summer the flux of sensible leads is estimated to he about 5% [Schnack-Scltiel, 1987; heat is as often directed upwards as downwards, and the Augstein el al., 1991]. On the basis of Arctic data, the latent heat flux usually has the same direction. In the atmospheric surface layer in winter over old sea ice is Weddell Sea, the most intensive air-sea exchange still lakes typically stably stratified owing to large heat losses via place near the coasts of the continent or continental ice t longwave radiation. The turbulent heat flux is therefore shelves. The dominant wind direction on the eastern coast generally directed downwards [Vowinckel and Orvig, 1973; of the Weddell Sea is towards the ocean. The wind blowing Untersteiner, 1986; Makshlas, 1991; Serreze el al., 1992]. from the continent brings rather cold and dry air to the The simple model results of Makshlas [1991] for Arctic sea open ocean, and even in summer the difference between the ice in winter suggest tiiat over sea ice less than 1 m thick sea surface and air temperatures can reach 10 to 20°C. The W the sensible heat flux is directed upwards, and over thicker winds in the more central Weddell Sea arc more variable in ice downwards. In the Antarctic, the sea ice tends to be direction and the summertime temperature difference thinner and the stratification in the upper ocean weaker than between the sea and the atmosphere is smaller (some 5°C). in the Arctic, which should result in an increased heat flux In this paper, data obtained by automatic marine from die ocean through the ice. Accordingly, it is not meteorological buoys are analyzed to compute estimates for generally known whether the wintertime atmospheric fluxes of heat and moisture over various surfaces: the sea surface layer over Antarctic sea ice is usually stably ice, winter leads, summertime open ocean in the eastern stratified or noL Andreas and Makshlas [1985] found the Weddell Sea, and the continental ice-shelf edge. Although sensible heat flux to be as often to the atmosphere as to the involving some apparent methodological weaknesses, the extensive data sets are presumably the first ones allowing ice in the northeastern Weddell Sea in the spring, whereas .'-W'r i KOnig-Langlo el al. [1990] found, in the late winter of year-round estimates for the area. 1989, the turbulent fluxes directed into the atmosphere. Kottmeier and Engelbart [1992] reported sensible heat 2. OBSERVATIONS fluxes in both directions over pack ice in late winter and spring, but with downward-directed fluxes prevailing. Three automatic marine meteorological buoy stations However, Wamser and Martinson [1993] report were deployed in the eastern Weddell Sea area from R/V predominantly near-neutral or unstable atmospheric surface Aranda during the first Finnish Antarctic Expedition in layer stratification in the northeastern Weddell Sea in 1989-1990 (FINNARP-89). One of the buoys was deployed winter. on a small sea-ice floe, one in the open ocean 100 km from In the Weddell Sea, the surface-layer air temperature over the continental ice shelf, and one on the edge of a floating sea ice is typically -10 to -25°C in winter [Hoeber , 1989; continental ice shelf, 250 m from the "shoreline". During Launiainen el al., 1991]. When this cold air is advected the FINN ARP-91 expedition on the Russian R/V Academik --- LAUNIAINEN AND VIHMA 401 Open ocean Fig. 1. Research area, deployment sites and the drift trajectories of the marine meteorological buoys in the Weddell Sea. Dashed lines indicate approximate sea ice margins in February 1990 and in September 1992. Fedorov two more buoys were deployed in February 1992 the Argos satellite survey. In polar regions there are 26 on sea ice floes in more western parts of the Weddell Sea, satellite passes a day, about 20 of which were orbitally in connection with the U.S.-Russian Ice Station Weddell-1 suitable to receive data from our buoys, yielding an average experiment. Trajectories of the buoys are presented in observation interval of 1.2 h. Figure 1. The buoys made observations of the following Additionally, surface meteorological observations and quantities: atmospheric pressure, air temperature and aerological balloon soundings (DigiCora Rawinsonde, humidity, wind speed and direction, surface temperature of Vaisala Co.) were made from the research vessel during the snow, ice or ocean, and buoy orientation. In addition, the expeditions in the austral summers of 1989/1990 and temperature profile in the ocean was measured. Multiple 1991/1992. sensors were used to ensure data quality and to measure gradients of temperature and humidity in the atmospheric 3. COMPUTATION METHOD FOR THE FLUXES surface layer. The measurement heights, number and accuracy of sensors, and functioning periods of the buoys The ice drift dynamics and physical aspects of momentum are presented in Table 1. The buoys were manufactured by exchange in the Weddell Sea were discussed in Vihma and Defense Systems Inc. (McLean, Virginia, USA). The choice Launiainen [1993]. For this study, the fluxes of sensible and layout of the sensors were agreed in discussions and latent heat were computed by bulk methods on the between the research group and the manufacturer. A more basis of the Monin-Obukhov [1954] similarity theory using detailed description of the configuration, types and an algorithm described in detail by Launiainen and Viluna calibration of the sensors used is given in the technical data [1990]. Based on tire universal profile gradients of velocity reports by Launiainen et al. [1991] and Vihma et al. [1994]. (V), temperature (0) and specific humidity (q). the The buoys were located and the data was transmitted by Monin-Obukhov similarity theory yields for the turbulent / 402 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA TABLE 1. Marine meteorological buoy observations. Buoy identification number and lifetime, observation site, measurement heights for wind (V), temperature (T) and relative humidity (RH), observation quantities, number of sensors in each buoy (n) and accuracy are given. Buoy Lifetime obs. site height obs. quantities n Accuracy ID V T & RH Atmospheric pressure t 1 hPa 5892 2 Jan 1990-28 Jan 1991 ice floe, drifting 3.5 1.9 3 2 air temperature 4 0.05°C 5893 It Fcbr 1990- 1 Apr 1990 open sea, drifting 3.4 1.7 3.0 relative humidity of air 2 2% 5895 25 Dec 1989 • still operating^* shelf edge, fixed 3.9 2.3 3.7 buoy hull temperature 1 0.2°C 1282 14 Fcbr 1992-26 July 1992 ice floe,drilling 4.0 2.0 3.6 water temperature to" ’ o.rc 5908 6 Fcbr 1992 - 5 Jan 1993 ice floe,drifting 3.6 2.0 3.4 2 -fluxes of momentum (t), sensible heat (H) and moisture (£) or C.-C,WWz%.)). the familiar formulae of the gradient method (a) and the C„=CH(zlza£lzr'i'u(zlL),'i’ll(z/L.)), (5) " ' bulk-aerodynamic method (b) of CE=CE(zlza,zJzt.'¥tJizlL),'VlhlL)) where Zq , zt and z, are the roughness lengths for velocity, x = P“- = - PCX (1) temperature and moisture. In neutral stratification, z& zT and z, define the transfer coefficients in question [e.g. Launiainen and Viluna, 1990). 0M, d>„ and 4>E are the - P^e.-W (2) gradient forms and Y„ and Yg the integrated forms of the universal functions which give a stability correction for ■>- the profiles and transfer coefficients. In the argument z!L of B - = pC £ta,-<7t)F, (3) the universal functions, L is the stratification parameter, the Monin-Obukhov length. (a) (b) For our study, the roughness lengths z, defining the 'V/ transfer coefficients KM and the drag coefficients CD were determined as follows (for further details see the where V, is the mean wind speed at a height of z, and u. is Appendix): the friction velocity, p is the air density, and cp is the 1) For cases over the open sea the well-known slightly specific heat capacity of air. 9, - 9, and q, - qt are the wind-dependent CD values by Smith [1980, 1988] were differences in potential temperature and specific humidity used. For coastal polynyas, involving fetch-limited young between the atmosphere and the surface, respectively. (KE waves, a somewhat more strongly wind-dependent drag % gives the flux of latent heat, X being the enthalpy of form by Wu [1980] was used. . vaporization.) 2) For leads in the sea-ice zone, for taking into account .-•a The transfer coefficients " above depend on the the form drag from the ice edges and the growth of waves j measurement level, on the surface roughnesses for velocity in narrow leads, an overall CD form by Andreas and • V and scalar quantities of 9 and q, and on the surface layer Murphy [1986] was adopted. stratification. Accordingly, the transfer coefficients are 3) For ice and snow, the roughness length z, and drag ' given as a set of functions: coefficient CD were estimated using the model by Banke el at., [1980], based on the mean geometric surface roughness K^Kjxizvfi^zim, (R), which was estimated to be slightly over 10 cm. , V - =K^z/^z^z/D.^iz/L)), (4) Considering the buoy 5892, R for the specific ice floe was ,7 KE=KE(zlz0,zlZ'&H{7jL)&lz]L)) larger, but its average value in the region surrounding the floe was of the order of 10 cm. >. Vihmaand Launiainen : Weddell Sea Ice Drift 14.481 effect of internal ice stress could be described ty using effective parameter values (case specific) for the drift. For our case, drift trajectories were computed to study whether the simulation is also reasonable for longer time and space scales. 1000 - The simulations were encouraged ty the rather steady values found for the drift to wind speed ratio and the turning angle. Accordingly, drift trajectories were calculated using the mean drift ratios and turning angles found for several periods of our drift observations. The values given by Martinson and Warner [1990] were also tested to study how results from different areas and situations could be applied. 0 980 A simulation was made for the total surviving period of the ice floe, ire. for the 380 day period from January 2,1990toJanuaiy 16, 1991. Additionally, three periods merited a closer look. The first was the period April-May, 1990, when the autumn drift was rapid and rather straightforward. The second period was during the spring, in November 1990, when the drift ratio and turning angle remained highly constant (see Figure 10). The third period was during the wintertime, from June 1 to July 26, .1990, when the influence of the wind on the drift may have been weaker than usual. Simulations were made with the following drift ratios and turning Buoy pressure (hPa) angles: (1) values obtained from the whole period of our drift and wind data, i.e„ using 0.036 for the drift ratio and 36° for the turning Fig, 12, Atmospheric surface pressure from ECMWF analysis versus the angle; (2) values analyzed from the data of the spedfic period to be buoy pressure in April 1990 (diurnal means). simulated, values shown in figure captions, (3) values found by Martinson and Wamser [1990] for the eastern Weddell Sea (for the surface roughness of our ice floe and a 3.8-m wind height these convert to 0.041 for the drift ratio and 23° for the turning angle) and (4) for April 1990, simulated drift based on geostrophic wind. Trajectories were calculated using the observed location at the beginning of each simulation period as a starting point. The daily drift was calculated using the diurnal mean wind speed and direction to obtain the next location. Calculated trajectories together with those observed are presented in Figures 14-17, Generally, the incoherence is higher when the drift coefficients arc not those obtained from the diagnostic analysis, i.e. when a data set other than that obtained from the analysis of the calculated periodis used. Tins, of course, limits the applicability of the method. The result for the total observation period (Figure 14) shows characteristics of the overall pattern of the observed trajectory to have been reproduced by the wind-based geostrophic wind (m/s) simulation, but the distance between the observed and simulated positions at the end of the period was 590 km, the observed position being to the northwest of that simulated. This is only 12% of the total length of the trajectory but almost 80% of the total net transition. The drift simulated with the coefficients of Martinson and Wamser [1990] was directed still further cast. In section 4.1 we suggested, as a residual, a baric ocean current. This would have produced for the period a net drift of 600 km to the northwest Actually, this would be the net effect of the ocean current and the internal stress of the ice field, but there is no reason to believe that the internal ice stress would have produced net drift to the northwest. Rather, the direction of its net effect would have been to the east, preventing the ice from packing against the Antarctic Peninsula. Another simulation was made adding a residual current (0.018 m/s to 317°) to the wind based model. This produced a good result shown in Figure 14. For shorter simulations the compatibility is generally better. Trajectory estimates given by various modds for April and May April 1990 1990 arc given in Figure 15. The best fit is for the estimate based Fig, 13. (a) Drift speed of the ice floe vcisus the geostrophic wind speed, on the model coefficients obtained from the diagnostic analysis of April 1990. (6)Turning ingle between the ice driftandthe geostrophic wind. the period in question. The rather large drift coefficient based on Positive values indicate drift directed to the left of the wind vector. Martinson and Wamser [1990] gives the next best fit. with respect 14,482 VlHMA ANDLAUNIAINEN: WEDDELLSEA ICE DRIFT observed was smaller than usual. The drift simulated using the measured ratio fitted the observed trajectoiy well, but simulations with the overall drift ratio of our data and with those of Martinson and Wamser[199Q] produced a much faster drift than tbatobservcd (Figure 16). During the austral winter, the simulated trajectories 16 Jan 1991 differ drastically from tbatobservcd (Figure 17). The ice remained almost in one place for a 12-day period, during which the wind-based simulation produced a 70-km drift to the southeast The diurnal ice drift was, however, strongly wind-dependent during other periods of June and July. Furthermore, it is noteworthy that 2 Jan 1990 Fig. 14. Observed (solid tine) and simulated ice floe trajectories from r/.V. r* January 2,1990, to January 16,1991. Simulations are based on the wind data and die whole-period drift ratio cf Vt/Vi(3.8 m) = 3.6% and turning angle of 36* (dotted) and on the wind data with the above parameters and including a residual current (dashed). r V -r V? Fig. 16. Observed (solid line) and simulated ice floe trajectories for November 1990. Simulations are based on drift ratio and turning angle from analysis for November 1990 (2.6% and 35*) (dotted tine) and for the whole f period (dashed line), and from Martinson and Wamser [1990] (dash-dot tins). .--y 1 June •V 72* ------1------:------* ------1------1------«------1 •■t 40 38 36 34 32 30 28 °W }< Fig. 15. Observed (solid line) and simulated ice floe trajectories from April 1 to May 31,1990. Simulations arc based on drift ratio and turning angle from analysis for April and May, 1990 (4.7% and 31*) (dotted line) and for the whole period (dashed line); from Martinson and Wamser [1990] (dash-dot line); and from analysis with respect to geostrophic wind for April 1990 (2.2% and 4*) (solid line labeled “G"). Circles denote die location at the end cf April to the distance. Use of our whole-period coefficients produces a correct direction but too short a trajectory. The geostrophic 32 °W wind-based simulation for April 1990 produced a trajectory which Fig. 17. Observed (solid tine) and simulated ice tr^ectooes from June 1 to differs from the observed one rather more than the trajectories July 26,1990. Simulations are based on drift ratio and turning angle from simulated on the basis of the buoy wind, but the discrepancy is in analysis for June to July 1990(3.1% and 28*) (dotted line) and for the whole the opposite direction. In November 1990 the mean drift ratio period (dashed line), and ftomMartinson and Wamser [1990]. .a .. ; Vihmaand Launiainen : Weddell Sea Ice Drift 14.483 in all the specific cases the application of the overall period the months when it was comparable with that of the ice floe buoy, coefficients produced an error which corresponds to a residual net however, the overall pattern of the trajectory resembled rather drift of 0.01-0.02 m/s to the NW or NNW. closdy that of the ice floe, but on a smaller scale. The net transition Even when applying the correlation analysis of drift and wind of the open ocean buoy during its functioning period (from February described in section 4.1 to the periods of drift modified by apparent 11 to March 26,1990) was 160 km to the northwest (320°), while inertial motions, a puzzlingly high correlation was found between for the ice floe it was 270 km to 338° during the period. The ratio the diurnal drift and the wind. The correlation coefficients wcre0.89 of drift speed with respect to the wind wras 1.7% (referred to a 10-m for the north-south component and 0.91 for the east-west component height), i.e., 60% of that of the ice floe. It is noteworthy that after of dri ft (with respect to the 36° rotated wind velocity). This was true starting at a distance of 80 km from the ice shelf, the buoy was even though the period was one with a light mean wind of 2.6 m/s drifting perpendicular to the ice shelf and the continent. only and the presence of inertial motion was strongly supported by Trajectories of the open ocean buoy and spectral analysis the analysis in section 3.1. In principle, the high correlation could computed from the drift indicated motions with a frequency of about be caused by temporal autocorrelation of the data. We analyzed that, 12.5 hours. Because the phase did not follow the behavior of a tide, but during the inertial motion period no autocorrelation was found we believe also these motions to be mostly of inertial origin. in the wind in the inertial frequency (neither did the correlation between the drift and the wind arise from temporal autocorrelation 6. Conclusions in Figure 11). The case was further approached by applying the A 20-month-long time series of ice drift was obtained from the trajectory model. The modelled and observed trajectories are Weddell Sc a by means of a satellite location system. Such an presented in Figure 18. This gives a rather nice presentation of extended time series data set, which includes very accurate marine inertial motion superimposed on wind-induced drift and reveals meteorological observations, is a rarity from the area. why the correlation between drift and wind wras so high. The The total drift of the ice floe buoy was 10,000 km in 20 months, background clockwise circulation is induced by wind, but the but because of the highly meandering drift the net transition during smaller anticlockwise gyres arc not reproduced inthetraj ectoiy by the first year was only 660 km, toward the centre of the Weddell a wind-based model. Sea Gyre. During the 1-year period, the ice floe drifted wilhamean speed of 0.15 m/s, which was about 3% of the wind speed at the 5. Supporting Buoy Data 10-m level On average, the drift was directed 36° to the left of the For the marine meteorological and beat exchange study part of wind vector, but for the austral summer the turning angle was about the project, two additional buoys were functioning during the period 47°, decreasing to 27° during winter. The most probable reasons for in the area [cf. Launlainen el al., 1991]. One was deployed in the smaller winter value were that the internal ice stress increased February 1990 in open water in the eastern Weddell Sea, 350 km and the originally isolated 4-m-thick ice floe became a part of a east of the ice floe buoy. This buoy survived for 21/2 months before compact but generally thinner first-year ice field. The average being wrecked by autumn-formed sea ice. One other buoy was turning angle derived from the data was somewhat larger than that deployed at a fixed location on a sea edge of the Riiser-Larsen obtained by Martinson and Wamser [1990] for the eastern Weddell continental ice shelf. This buoy was still active and transmitting into Sc a in wintertime, but our winter values are in agreement with their tbeWMO/GTS as of December 1992. results. The ratio of ice drift to wind speed was comparable to that Analysis of the mechanisms controlling the drift of the open observed by Martinson and Wamser [1990]. Generally, the drift ocean buoy is more difficult. This is because the buoy had a surface ratio seems to be larger for Antarctic sea ice than for Arctic ice. This float with a meteorological mast and a 150-m-long water may result from a generally divergent velocity field leading to temperature chain. Accordingly, the drift does not represent a pure reduced internal ice stress. In our case, also the high air-ice surface current but the net effect of wind, waves and current For roughness of the icefloe yielded a high drift ratio. Fig. 18. Observed (solid) end simulated (dashed) ice floe trajectories for the inertial motion period, from February 4 to 13, 1990. Drift ratio of 4.2% and turning angle 48® were used in simulation. 14,484 VlHMA ANDLAUNIAINEN: WEDDELL SEA ICE DRIFT Factors other than the ice field affecting the ratio of drift and for the ice floe in the beginning. The drift away from the eastern wind include the stratification of the atmospheric and oceanic coast of the Weddell Sea should allow formation of coastal polyny as boundary layers. Theoretically, one might expect that the and thus creation of new ice. In addition, the generally divergent atmospheric surface layer should be less stable in the Weddell Sea ice drift with little internal ice stress in the eastern and central area than over the Arctic sea ice, because the ice is thinner and Weddell Sea should favor the formation of leads in the padc ice v; >■ broken in the Weddell Sea and the oceanic heat flux should be field. These polyny as and leads perhaps dominate the vertical larger. This could lead to larger drift ratio both with respect to the energy exchange between the atmosphere and the ocean. gcostrophic wind and to the actual surface wind, and to a larger drag Additionally, the northward ice advection transports considerable coefficient Cc- In the Arctic basin the stable stratification and amounts of (negative) latent beat to lower latitudes. According to compactness of the ice field reduce the ice drift speed with respect •the data of Kottmeier and Hartig [1990] and Uassom [1992], the to the wind speed. Less reduction takes place in the Weddell Sea. ice advance in the Weddell Sea is primarily of thermodynamic A weaker stratification of the upper ocean in the Weddell Sea might, origin in the sense that a lot of new ice is created near the northern however, increase the ice-water stress. Because it generally acts as ice margin. Our data correspond to this: our buoy was deployed on a momentum sink for the ice, this would reduce the drift speed. an icefloe in the marginal ice zone, but although it drifted northward However, more detailed data is required to estimate these effects it was later in the interior of the ice field indicating that the ice edge quantitatively. advanced mere rapidly than the ice floes. On a time scale of days the ice drift was found to be controlled Finally, we are happy to say that the project has been continued • ' V« mostly by the local wind, and explained reasonably by classical in the field, starting in February 1992. At that time, two further Ekman theory. The dependence of ice drift velocity on wind was buoys were dejioyed in the area. One of those was deployed in the presented in Figure 11. The high correlation between the wind and measuring grid of the manned U.S.-Russian "Weddell Sea Ice ice drift allowed us to deduce an estimate for a residual current not Station 1" drifting in the western Weddell Sea. Another buoy was induced by the local wind. The magnitude of the residual current deployed 300 km east, at the longitude of 40PW. The both buoys term in the equation of momentum was 3 to 5% of the wind stress. include versatile marine meteorological sensors and in the location The wind-based simulation of ice drift was not too succesful, of the first buoy a current meter was installed for making however, when applied to time scales of several months. This was measurements to estimate the ice-water drag. On the basis of vety partly because of periods of high internal ice stress, such as found, preliminary analyses of the data, three characteristics of the drift eg., in July 1990, but we assume that the final discrepancy between can be reported: (1) The buoys did not stay in the Weddell Sea until the simulated and observed ice drift trajectories was due mostly to the next summer but drifted away to the north, and after passing the the ocean current The inclusion of a residual current improved the latitude of 64°S they turned to the east. The reason for this may arise simulation significantly. A close coherency between our results and from their deployment ate in the western Weddell Sea or from Massom’s [1992] experiment from the year 1980 in the same interannual differencies in ice and meteorological conditions. (2) geographical region also supports the concept of a relatively steady Inertial motion was not found from the trajectories in the western northwestward current in the area. Weddell Sea, and the ice field rotated very little. (3) The ice drift in The Ekman-typc drift indicated that the effect of internal ice the western Weddell Sea did not depend on the wind as much as it stress in the eastern and central Weddell Sea was less significant on did in the central Weddell Sea on the baas of the experiment In average, although it is certainly significant at times. Near the 1990-1991. Particulary, the turning angle between the drift and the Antarctic Peninsula the ice is packing against the continent, and the wind was smaller in the westernmost areas. Accordingly, the ice internal stress is likely to be more important Because we had no drift in the central Weddell Sea seems to differ from that in the direct way of measuring the internal ice stress, it was not possible western Weddell Sea, but further analyses are to be made to separate to separate its magnitude from the effect of water stress. spatial differences from interannual variations. Qualitatively, the both act as momentum sinks for the ice floe. Future investigations using grids of buoys to study the strain and Acknowledgments. We wish to thank Kalevi Rantancn, Imatran deformation of the ice field are necessary. Voima Power Co., and the captain and crew of the R/V Aranda for The pressure analysis given by ECMWF for the area seemed to field assistance. Jarmo Alio and Juba Uotila are acknowledged for be rather accurate. Although encouraging, the simulation of ice drift help in processing the buoy data and Timo Hopeakoski for on the basis of the geos trophic wind was somewhatmore inaccurate providing ECMWF pressure charts. We are also grateful for than on the basis of the local wind. Local wind observations from discussions with Christoph Kottmeier, Alfred Wegener Institute for the Weddell Sea are seldom available, and without reliable model Polar and Marine Research. In the field, the project was fi nancially predictions the pressure field may be used to get a first guess for the supported by PINNARP (Finnish Antarctic Research Rrogram, -:••• - 7 • ice drift. Ministry of Trade and Industry). Finally, constructive and A notable feature found from the drift data was the presence of encouraging criticism given by three unknown referees is kindly inertial motion during both austral summers of 1990 and 1991. The acknowledged. observed frequency decreased along with the latitude, in accordance with theory, when the ice floe drifted northward, and a study of the References r. damping of the motion suggested that the inertial motion was mostly Andreas, E. L., A theory for the scalar roughness and the scalar transfer a property of the upper ocean, not only that of the sea ice. 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A, 44,54-66, 1992. *. ; types ofsea Ice, X Geophys. Res., 95,4709-4721, 1991. Overland, J. E, H. O. Mofjeld, and C. H. Pease, Wind-driven ice drift in a ■ j Hibler, W. D, IB, Sea ice growth, drift and decay, in Dynamics of Snow shallow sea, X Geophys. Res., 89,6525-6531,1984. and Ice Masses, edited by S, C Colbeck, pp. 141-209, Academic, San Sanderson, B. G„ and D. A. Booth, The fractal dimension of drifter Diego, Califs 1980. trajectories and estimates of horizontal eddy-diffusivity, Tellus, Ser. A, \ Hibler, W. D., IB, and W. B. "Ricker, Some results from a linear-viscous 43,334-349, 1991. model of the Arctic ice cover, X Glaciol, 22,293-304,1979. Shackleton, E, South. The Story of Shackleton *s Last Expedition Hoeber, H, Sea-ice dynamics in the Weddell Sea in winter, Ann. Glaciol, 1914-1917,368 pp„ Heinemann, London, 1919. 75,9-16,1991. Sobczak, L. W„ Ice movements in the Beaufort Sea 1973-1975: Hunkins, K., The oceanic boundary layer and stress beneath a drifting ice Determination by ERTS imagery, X Geophys. Res., 82, 1413-1418, floe, X Geophys. Res., 80,3425-3433, 1975. 1977. ' Johan nessen, O. M., J. A. Johannessen, J. Morison, B. A. Farrclly, and E Sverdrup, H. U., The Norwegian North Polar Expedition With the "Maud ." A.S.Svendsen, Oceanographic conditions in the marginal ice zone north voL IL Meteorology, 331 pp., Geophysical Institute, Bergen, Norway, cf Svalbard in early fall 1979 with an emphasis on mesoscale processes, 1933. X Geophys. Res., 88,2755-2769, 1983. Thorndike, A. SM and R. Colony, Sea ice motion in response to geostrophic Kottmeier, C, and R. Hartig, Winter observations of the atmosphere over winds, X Geophys. Res., 87,5845-5852, 1982. Antarctic sea Ice,X Geophys. Res., 95,16,551-16,550,1990. Wadhams, P., M. A. Lange, and S. F. Ackley, The ice thickness distribution Launialnen, J., and T. Vihma, Derivation of turbulent surface fluxes - An across the Atlantic sector of the Antarctic ocean in midwinter, X ' iterative flux-profile method allowing arbitrary observing heights, Geophys. Res. 92,14,535-14,552,1987. Environ. Software, 5,113-124,1990. Walter, B. A„ J. A. Overland, and R. O. Gilmer, Air-ice drag coefficients < Launialnen, J„ T. Vihma, J. Aho, and K. Rantanen, Air-Sea Interaction for first-year sea ioe derived from aircraft measurements, X Geophys. j Experiment In the Weddell Sea, Argos-Buoy Report from Res., 89,3550-3560.1984. - j FINNARP-5/89, 1990-1991, Antorc/. Rep. of Finland, % Min. of Trade Wamser, C, and D. G. Martinson, Drag coefficients for winter Antarctic and Ind. Helsinki, 1991. pack ice, X Geophys. Res„ in press, 1993. . ) Limbert, D. W. S., S. J. Morrison, C. B.Sear, P.Wadhams, and M.A. Rowe, Zubov, N. N., L'dy Ark tiki (Arctic Ice, in Russian), 491 pp., , 1 Pack-ice motion in the Weddell Sea in relation to weather systems and Glavsevmorputi, Moscow, 1943. (English translation, U.S. Naval determination of a Weddell Sea sea-ice budget, Ann. Glaciol., 72, Oceanographic Office, Suittand, Md. Available as NTIS AD 426972 ; 104-112,1989. from Natl. Tech. Inf. Serv., Springfield, Va.) • Martinson, D. G., and C Wamser, Ice drift and momentum exchange in | winter Antarctic pack ice, X Geophys. Res., 95,1741-1755,1990. | Massom, R. A„ Observing the ad vection of sea ice in the Weddell Sea using j buoy and satellite passive microwave data, X Geophys. Res., 97, J. Launialnen, Finnish Institute of Marine Research, P.O. Box 33, ! 15,559-15,572,1992. SF-00931 Helsinki, Finland. >1 McPhee, M. G„ A simulation of inertial oscillation in drifting pack ice, Dyn. T. Vihma, Department of Geophysics, University of Helsinki, P.O. Box Atmos. Oceans, 2,107-122,1978. 4 (Fabian in katu 24A), SF-00014 Helsinki, Finland. McPhee, M. Q., An analysis of pack ice drift in summer, in Sea-Ice ■ \ Processes and Models, edited by R.S. Pritchard, pp. 62-75, University of Washington Press, Seattle, 1980. (Received July 14,1992; Nansen, R, The Norwegian North Polar Expedition 1893-1896, Scientific revised February 9,1993; Results, vol. 3, The Oceanography of the North Polar Basin, 427 pp. accepted February 19,1993.) ( ( - i 7,1 j ' / i T" EllililiSWiS A 4 v vi ■' 4''v .. mm >? ■ V- i ,1 < $ I / 1 J ' / I 1 ‘ I f On the Surface Heat Fluxes in the Weddell Sea Jouko Launiainen Finnish Institute of Marine Research, Helsinki, Finland Timo Vihma Department of Geophysics, University of Helsinki, Finland Turbulent surface fluxes of sensible and latent heat in the Weddell Sea were studied using drifting marine meteorological buoys with satellite telemetry. In 1990-1992 a total of 5 buoys were deployed on the sea ice, in the open ocean, and on the edge of a floating continental ice shelf. The buoys measured, among others, wind speed, air temperature and humidity with duplicate sensors and yielded year-round time series. The heat fluxes were calculated by the gradient and bulk methods based on the Monin-Obukhov similarity theory. Over the sea ice, a downward flux of 15 to 20 W/m2 was observed in winter (with typical variations of 10 to 20 W/m2 between successive days) and 5 W/m2 in summer. For the latent heat flux, the results suggested a small evaporation of 0 to 5 W/m2 in summer and weak condensation in winter. The highest diurnal values, up to 20 W/m2, were connected with evaporation. Because of stable stratification, the transfer coefficients of heat and moisture were reduced to 80% of their natural values, on the average. Over the leads and coastal polynyas, an upward sensible heat flux of 100 to 300 W/m2 was typical, except in summer when the air temperature was close to the sea surface temperature. Over the continental shelf ice, the sensible heat flux was predominantly downwards (15 to 20 W/m2), compensating the negative radiation balance of the snow surface. Over the snow and ice surfaces the magnitude of turbulent fluxes was smaller than that of radiative fluxes, while over the open water in winter sensible heat flux was the largest term. Modification of the continental air-mass flowing out from the she If ice to the open sea was studied with aerological soundings made from a reaseach vessel. Associated turbulent heat exchange was estimated on the basis of three methods: modification in the temperature profiles, surface observations, and diabatic resistance laws for the atmospheric boundary layer. If we estimate an area-averaged turbulent heat exchange between the surface and the atmosphere for the whole Weddell Sea on the basis of our data, the large upward fluxes from leads and coastal polynyas (with an areal coverage of 5 to 7% in wintertime) approximately balance the downward fluxes over the sea ice. A first-order estimate for the annual area-averaged total vertical heat loss from the water mass is 20 to 30 W/m2. 1. INTRODUCTION flux from the sea to the air may reach several hundreds of watts per square meter [Bromwich and Kurtz, 1984; Polar oceans arc areas of extreme differences in the Cavalieri and Martin, 1985; Schumacher et aL, 19831. On temperature between the ocean and the atmosphere, but the the other hand, the heat and moisture exchange affects the heat exchange is frequently restricted by sea ice cover. amount of sea ice, and controls the structure of the Over ice-free areas, cracks, leads and polynyas, the heat atmospheric and oceanic boundary layer. In certain areas of the polar oceans, the heat loss from the ocean also affects the deep water formation, especially when sea ice is The Polar Oceans and Their Role in Shaping produced increasing the surface salinity in the water. the Global Environment It is well known that, despite the small areal coverage of Geophysical Monograph 85 Copyright 1994 by the American Geophysical Union leads and polynyas, they have a great effect on the total V 400 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA heat loss from the ocean and even a few percent of open over open leads, tire temperature difference becomes water or thin young ice make a dominant contribution to extreme, resulting in intensive heat exchange. The heat loss the regional heat budget in winter [Maykut, 1978; Ledley, from the leads is compensated by the enthalpy of freezing 1988]. The effect is also detectable in the output of global of the sea, and according to Arctic observations the leads climate models [Simmons and Budd, 1991]. In Arctic typically remain open for a few hours only [Lebedev, 1968; regions, beat exchange over sea ice or over leads and Bauer and Martin, 1983; Maksluas, 1991]. After that new '5 polynyas has been studied in several field experiments, but ice is formed, but it still permits considerable heat flux observations on the meteorological variables required to from the ocean. compute the heat and moisture fluxes over Antarctic seas In summer, the marginal ice zone retreats southward and are still rare, especially from the winter period. A few westward and the coastal polynyas in the eastern Weddell analyses of heat exchange over Antarctic sea ice and coastal Sea become part of the open ocean, but the sea ice remains polynyas have been reported [Bromwich and Kurz, 1984; in the central and western Weddell Sea Summer conditions Andreas and Maksluas, 1985; KGnig-Langlo et al., 1990; over the sea ice are very different from those in winter, Kotuneier and Engelbart, 1992]. because incoming solar radiation warms the snow and even The Weddell Sea is totally covered by ice during the small melt-water ponds may appear. Thus the wintry austral winter, although the ice field is broken and leads are contrast between the temperature of the sea ice and the generated within the drifting divergent ice field; wider leads often vanishes and the air-sea partition of turbulent polynyas are frequent in the southeast and south near the fluxes may vary in time. For example, according to the ice shelves and the coast of the Antarctic continent [Zwally arctic data of Leavitt et al. [1978, also cf. Andreas, 1989] and Comiso, 1985]. The areal coverage of the polynyas and over the Beaufort sea ice, in summer the flux of sensible leads is estimated to be about 5% [Schnack-Schiel, 1987; heat is as often directed upwards as downwards, and the Augstein el al., 1991]. On the basis of Arctic data, the latent heat flux usually has the same direction. In the atmospheric surface layer in winter over old sea ice is Weddell Sea, the most intensive air-sea exchange still lakes % typically stably stratified owing to large heat losses via place near the coasts of the continent or continental ice longwave radiation. The turbulent heat flux is therefore shelves. The dominant wind direction on the eastern coast generally directed downwards [Vowinckel and Orvig, 1973; of the Weddell Sea is towards the ocean. The wind blowing Untersteiner, 1986; Maksluas, 1991; Serreze et ai, 1992]. from the continent brings rather cold and dry air to the The simple model results of Maksluas [1991] for Arctic sea open ocean, and even in summer the difference between the ice in winter suggest that over sea ice less than 1 m thick sea surface and air temperatures can reach 10 to 20°C. The the sensible heat flux is directed upwards, and over thicker winds in the more central Weddell Sea are more variable in ice downwards. In the Antarctic, the sea ice lends to be direction and the summertime temperature difference thinner and the stratification in the upper ocean weaker than between the sea and the atmosphere is smaller (some 5°C). in the Arctic, which should result in an increased heat flux In this paper, data obtained by automatic marine from llie ocean through the ice. Accordingly, it is not meteorological buoys are analyzed to compute estimates for generally known whether the wintertime atmospheric fluxes of heat and moisture over various surfaces: the sea surface layer over Antarctic sea ice is usually stably ice, winter leads, summertime open ocean in the eastern stratified or noL Andreas and Maksluas [1985] found the Weddell Sea, and the continental ice-shelf edge. Although sensible heat flux to be as often to the atmosphere as to the involving some apparent methodological weaknesses, the ice in the northeastern Weddell Sea in the spring, whereas extensive data sets are presumably the first ones allowing KGnig-Langlo el al. [1990] found, in the late winter of year-round estimates for the area. 1989, the turbulent fluxes directed into the atmosphere. Kotuneier and Engelbart [1992] reported sensible heat 2. OBSERVATIONS fluxes in both directions over pack ice in late winter and spring, but with downward-directed fluxes prevailing. Three automatic marine meteorological buoy stations However, Wainser and Martinson [1993] report were deployed in the eastern Weddell Sea area from R/V predominantly near-neutral or unstable atmospheric surface Aranda during the first Finnish Antarctic Expedition in layer stratification in the northeastern Weddell Sea in 1989-1990 (FINNARP-89). One of the buoys was deployed winter. on a small sea-ice floe, one in the open ocean 100 km from In the Weddell Sea, the surface-layer air temperature over the continental ice shelf, and one on the edge of a floating sea ice is typically -10 to -25°C in winter [Hoeber, 1989; continental ice shelf, 250 m from the "shoreline". During Launiainen el al., 1991], When this cold air is advecled the FINNARP-91 expedition on the Russian R/V Academik 'V-- • u LAUNIAtNEN AND VIHMA 401 .1 'I July 91 -t Fig, 1, Research area, deployment sites and the drift trajectories of the marine meteorological buoys in the Weddell Sea, Dashed lines indicate approximate sea ice margins in February 1990 and in September 1992. Fedorov two more buoys were deployed in February 1992 the Argos satellite survey. In polar regions there are 26 on sea ice floes in more western parts of the Weddell Sea, satellite passes a day, about 20 of which were orbitally in connection with die U.S.-Russian Ice Station Weddell-1 suitable to receive data from our buoys, yielding an average experiment. Trajectories of the buoys are presented in observation interval of 1.2 h. iv- i Figure 1. The buoys made observations of the following Additionally, surface meteorological observations and / quantities: atmospheric pressure, air temperature and aerological balloon soundings (DigiCora Rawinsonde, humidity, wind speed and direction, surface temperature of Vaisala Co.) were made from the research vessel during the snow, ice or ocean, and buoy orientation. In addition, the expeditions in the austral summers of 1989/1990 and temperature profile in the ocean was measured. Multiple 1991/1992. sensors were used to ensure data quality and to measure gradients of temperature and humidity in the atmospheric 3. COMPUTATION METHOD FOR THE FLUXES surface layer. The measurement heights, number and accuracy of sensors, and functioning periods of the buoys The ice drift dynamics and physical aspects of momentum are presented in Table 1. The buoys were manufactured by exchange in the Weddell Sea were discussed in Vihma and Defense Systems Inc. (McLean, Virginia, USA). The choice Launiainen [1993]. For this study, the fluxes of sensible and layout of the sensors were agreed in discussions and latent heat were computed by bulk methods on the between the research group and the manufacturer. A more basis of the Monin-Obukhov [1954] similarity theory using detailed description of the configuration, types and an algorithm described in detail by Launiainen and Viluna calibration of the sensors used is given in the technical data [1990]. Based on die universal profile gradients of velocity reports by Launiainen et al. [1991] and Vilunaetal. [1994]. (V), temperature (0) and specific humidity (q), the The buoys were located and the data was transmitted by Monin-Obukhov similarity theory yields for the turbulent / i 7.1 ■ ! JT '*■ 402 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA TABLE I. Marine meteorological buoy observations. Buoy identification number and lifetime, observation site, measurement heights for wind (V), temperature (T) and relative humidity (RH), observation quantities, number of sensors in each buoy (n) and accuracy are given. Buoy Lifetime obs. site height obs. quantities n Accuracy ID V T & RH Atmospheric pressure i 1 hPa 5892 2 Jan 1990-28 Jan 1991 ice floe, drifting 35 1.9 32 air temperature 4 0.05°C 5893 11 Rbr 1990-1 Apr 1990 open sea, drifting 3.4 1.7 3.0 relative humidity of air 2 2% 5895 25 Dec 1989 - still operating* 4 shelf edge, fixed 3.9 2.3 3.7 buoy hull temperature 1 0.2°C 1282 14 Fcbr 1992-26 July 1992 ice floe,drifting 4.0 2.0 3.6 water temperature uf O.l’C 5908 6 Febr 1992 - 5 Jan 1993 ice floe,drifting 3.6 2.0 3.4 20*' 0.05'C wind speed 2« 03 m/s wind direction 1 5° snow depth ,(• 2 cm (* 15 Dec. 1993, for buoys 5892 and 5893, (e for buoys 1282 and 5908, (d only 1 for buoy 1282, (e only for 1282. fluxes of momentum (r), sensible heat (#) and moisture (E) or the familiar formulae of the gradient method (a) and the c„=c„(z/z0^/zr'y„(z/y.vfl(z/o), (5) bulk-aerodynamic method (b) of CE- CE(zJz0,zJZ','VjtzlL),'VE(z/L)) ;■ where Zo, zT and z, are the roughness lengths for velocity, T = pul = PcX 0) temperature and moisture. In neutral stratification, z& zT and z, define the "transfer coefficients in question [e.g. Launiainen and Vihma, 1990], 4>H, 4>„ and »E are the H = ^ p^,(0.-e,)v, (2) gradient forms and and VE the integrated forms of the universal functions which give a stability correction for the profiles and transfer coefficients. In the argument zJL of dq 1 . ' E = -p K, = P (3) the universal functions, L is the stratification parameter, the Monin-Obukhov length. (a) (b) For our study, the roughness lengths z, defining the transfer coefficients Ku and the drag coefficients CD were determined as follows (for further details see the where Vz is the mean wind speed at a height of z, and u. is Appendix): the friction velocity, p is the air density, and cp is the 1) For cases over the open sea the well-known slightly specific heat capacity of air. 8, - 8, and q, - qz are the wind-dependent CD values by Smith [1980, 1988] were differences in potential temperature and specific humidity used. For coastal polynyas, involving fetch-limited young between the atmosphere and the surface, respectively. (XE waves, a somewhat more strongly wind-dependent drag gives the flux of latent heat, X being the enthalpy of form by Wit [1980] was used. vaporization.) 2) For leads in the sea-ice zone, for taking into account The transfer coefficients ' above depend on the the form drag from the ice edges and the growth of waves - }-i- measurement level, on the surface roughnesses for velocity in narrow leads, an overall CD form by Andreas and V and scalar quantities of 8 and q, and on the surface layer Murphy [1986] was adopted. stratification. Accordingly, the transfer coefficients are 3) For ice and snow, the roughness length % and drag given as a set of functions: coefficient CD were estimated using the model by Banke et at., [1980], based on the mean geometric surface roughness Ku=Ku(z/Z', TABLE 2. The roughness lengths and neutral bulk-transfer coefficients (referred to a height of 10 m) used in the [lux calculations. Observed mean wind speed of 6 m/s used for the table. obs. site Cgandz, Che and open sea Co =1.09x10' C,B =1.01x10' (typical case) Zo = 0.05 mm Zr, = 0.02 mm coastal polynyas C„ = 1.22x10' C,B= 1.09x10 ’ (typical case) Zo = 0.09 mm Zr, = 0.02 mm leads Co = 1.49x10' C,o,= 1.26x10' Zo=03mm Zr, = 0.04mm ice and snow C„ = 1.90x10'' C,E= 1.44x10’ Zq = 1 mm z,-, = 0.05 mm ice shelf C„ = 1.46 x 10' C,E= 1.33x10’ Zo = 0.3 mm Zrq = 0.09 mm As for the vapour and heat exchange coefficients, we feel temperature was obtained from two independent sensor the common assumption of Kn - Kz and C„ - CE i.e zT - pairs on each buoy. After the sensible heat flux and the z, to be reasonable, as suggested by Martin and Yaglom snow surface temperature were estimated by the level [1971], Andreas and Murplty [1986], and Makshlas [1991]. difference method using the flux-profile relationships, the Accordingly, we compute the vapour and heat exchange flux of latent heat was computed by the bulk method. The coefficients as follows: same approach has been applied by e.g. Thorpe et al. 4) For open water surfaces a data compilation result by [1973] and Leavitt et al. [1978]. Launiainen [1983] based on a comparison of simultaneous CJCZ results, derived from direct eddy flux results in 4. SOURCES OF INACCURACY IN FLUX ESTIMATES literature is used. For the neutral transfer coefficients of vapour and heat exchange this gives Cm = 0.63-C0 + Various factors may be the potential cause of errors in 0.3210'. the flux estimates. A major difficulty in the computation 5) For ice and snow the model by Andreas [1987] is over ice was that the actual snow surface temperature was used, based on the aerodynamic roughness Zq from above. unknown. Inaccuracies resulting from the sources (a) to (g) The mean numerical values of the various roughness discussed below are summarized in Table 3. The inaccuracy lengths and neutral bulk transfer coefficients are listed in may change with meteorological conditions, but typical Table 2. It may be anticipated that an accurate estimation of situations were considered when calculating the values roughness lengths and transfer coefficients for leads given. presents the greatest difficulty. a) The gradient or level difference method had to be For the universal functions, the so-called Basinger et al. applied to estimate the sensible heat flux over ice, and the [1971] - Dyer [1974] type formulae were used for unstable result is very sensitive to the accuracy of the temperature stratification. For the stable region, a form by Holtslag and difference between the observation levels. In our case, this de Bruin [1988], not very much different from the may result in an inaccuracy of 15-20 W/m2 in the sensible well-known earlier form by Webb [1970], was used. heat flux and 10-15 W/m2 in the latent heat flux. The Because the Monin-Obukhov length L, in the argument of following discussion considers the problems in more detail. the universal functions, contains the fluxes to be The height difference between the two observation levels determined, the system of equations (1) to (5) leads to an was small, of only 1.3 to 1.6 m centered at a height of 2.5 iterative solution, described in detail in Launiainen and to 3 m, depending on the buoy. Especially above a Vihtna [1990]. Formulae for the transfer coefficients and relatively smooth surface the temperature difference within universal functions are given in the Appendix. such a distance tends to be extremely small, except in One great difficulty in the estimation of heat and moisture strongly stably stratified conditions. To determine the fluxes fluxes over the sea ice was that the actual snow surface to an accuracy of 20-30 W/m2, the temperature difference temperature was unknown. Thus, the bulk-method (i.e. should be measured with an accuracy of 0.05-0.1°C. This "b"-equations of 1 to 3) could not be used for the sensible accuracy was easily achieved in calibrations in Finland heat flux. Instead, the level-difference or gradient method before the expeditions, because the buoys measured in fact (”a"-equations) was used. The level difference of the temperature difference between the two heights (and the 404 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA TABLE 3. Inaccuracy in (he flux estimates resulting from various potential error sources. Absolute or relative inaccuracy is given, whichever more relevant in the particular case. factor measurement inaccuracy in sensible inaccuracy in latent •v (see text) inaccuracy heat flux estimate heat flux estimate - a) 0.05*0 15-20 W/m1 10-15 W/m1 b) 1% 1 W/m2 VV':-. c) ice IT 5 W/m2 water O.TC 1-2 W/m1 1 W/m2 d) 10% 10% 10% e) 100% 4-8 W/m1 4-8 W/m1 0 + 5% -1% <. % temperature at the lower level). Still, a very slight electrical drift detected from the data during the measuring periods of two buoys decreased the accuracy. Using several indirect methods of checking and correcting, and using mean values for a day or longer, an accuracy significantly better than 0.1°C is believed to have been achieved. For example, one of the methods for finding the correction to the measured level difference in the air temperature was to study the behaviour of the level difference of temperature with respect to the bulk-difference between the temperature of air and the buoy hull inside the ice. Furthermore, comparison of the results based on the level difference 11 February - 12 March method and bulk-aerodynamic method, both of which the open ocean buoy data with a measured surface temperature Fig. 2. Sensible heat flux as calculated using the made possible, also gave a rather good reference for the bulk-aerodynamic (solid line) and the level difference method accuracy of the level difference method (Figure 2). The (dashed line) for the open sea buoy (5893). Diurnal means from bulk-method was also applicable for comparison for one of February 11 to March 12, 1990. the ice floe buoys (5892, Figure 1) when it reached the open ocean after overwintering in the Weddell Sea. used in temperatures lower than -20°C. In this context one The above refers to the principal air temperature sensors. should note that the possible range of moisture content in In addition, the buoys had temperature probes in the the air at low temperatures, say below -10°C, is so small humidity sensors. Since the resolution of these probes was that the latent heat flux is in practice controlled by the only 0.7°C, they could not be used to calculate an saturation moisture of the surface (i.e. by the surface instantaneous heat flux. However, median values for the temperature). heat fluxes based on these probes corresponded to those c) Accuracy of the surface temperature. The accuracy of based on the principal air temperature sensors to an the calculated snow surface temperature affects the latent accuracy of 5 to 10 W/m2 for the buoys 5892, 5893, 5895 beat flux calculated by the bulk method. However, because and 1282. For the buoy 5908, results from the two sets of of rather large air-snow temperature differences the latent probes had a higher discrepancy. Finally, a filtering method heat flux is not very sensitive to the inaccuracy of snow for obvious errors was applied. surface temperature, see Table 3. Over open water surfaces b) It was discovered that the measurements of relative the accuracy of the difference between the air and surface >V--V humidity were not accurate enough to allow an estimate of temperature was of the order of 0.1°C. This gives an error the latent heat flux using the level difference method to be of only 1 to 2 W/m2 in the sensible heat flux and 1 W/m2 made. In calculations using the bulk-aerodynamic method, in the latent heat flux. the observed mean humidity from the two sensors was d) Ice accretion and accumulation of snow sometimes used. It was measured initially to an accuracy of 1 to 2%, prevented the collection of wind data. The data quality was but the electrical sensors did not function properly when improved using two wind sensors working on different LAUNIAINEN AND V1HMA 405 principles (propeller and cup anemometers). The cup The results over the open ocean should be the most reliable anemometer was found to be more liable to errors due to ones, while the estimates over polynyas and leads should be ice accretion. Periods when both anemometers continously regarded as having rather good relative accuracy, although showed wind speeds less Utan 1 m/s were removed from the the absolute errors may be large, because the fluxes arc analysis. A good correlation between the winds observed by large. However, the maximum values of over 400 to 600 die buoys and the gcoslrophic winds derived from ECMWF W/m2 found in our study may be erroneous, because they pressure analyses gave confidence in the wind data. are met within extremely unstable conditions for which e.g. e) Estimation of the surface roughness affects the flux the validity of the universal functions has not been results. For the open ocean, more consensus in values is to adequately proved. be found, but for cases above narrow leads and ice, values are more poorly known. Estimation of the geometric 5. RESULTS roughness (fi) of die ice and snow surface with an inaccuracy of 100% would, however, result in an The time series of air temperature and wind speed (at a inaccuracy of no more than 4-8% in the heat (luxes. height of 3 m) over the sea ice and at the edge of the 0 Changes in the observation heights due to snow floating ice shelf in 1990-1992 are given as diurnal means accumulation or melt. Exact observation heights were in Figure 3. The numerical data and further discussion are known at the time of the buoy deployments. Later, only two to be found in the technical reports [Jlauniainen el al, buoys were visited, and the one on the ice shelf edge 1991; Vihma et al, 1994]. When considering the annual showed snow accumulation of 15 to 25 cm in two years. differences over the sea ice one should note that in 1990 The snow accumulation was directiy measured by one buoy the observations (of buoy 5892) were from the central only (1282), but the rate of change, 7 to 10 cm in half a Weddell Sea, whereas in 1992 these were from more year, is assumed to be comparable to that at the sites of the western areas (Figure 1). Additionally, in July 1992 after other ice floe buoys as well. The sensitivity of estimated the two drifting buoys (5908 and 1282) crossed latitude fluxes to the measurement heights was found to be rather 63°S and started to drift east in the circumpolar current, low. The sign of error in XE is opposite to that in If, they left the wintertime Weddell Sea, which may be seen because the former is calculated by the bulk-method and the e.g. as an increase in the air temperature (compare Figures latter by the gradient method. 3 a and b). g) Finally, the requirements of horizontal quasi-homogeneity and stationarily to satisfy the 5.1. Fluxes over the sea ice Monin-Obukhov similarity theory should have been reasonably well met over the sea ice and over the open Figure 4 gives estimates of the sensible and latent heat ocean in the eastern Weddell Sea, but the narrow winter flux above the sea ice as time scries of diurnal means. leads are far more problematic in this sense. In practice, During summer, the sensible heat seems to be rather small however, no theory provides better methods for computing and may be directed either upwards or downwards. During turbulent fluxes when direct eddy-covariance or dissipation winter, the sensible heat flux tends to be downwards, from measurements are not available. Moreover, the results of the air to tire ice, as a consequence of radiatively-based Andreas el at. [1979], Smith el al. [1983] and Andreas and surface cooling, reaching -50 W/m2 or even more. On the Murpliy [1986] suggest that the effects of horizontal other hand, cases of upward fluxes of 30 to 50 W/m2 also non-homogeneity on the flux-gradient relations near the exist during winter. Large variations in the air temperature, surface are perhaps not too severe in areas where changes wind speed and cloudiness yield large variations in the heat in roughness remain small, as is the case for ice and open flux, typically 10-20 W/m2 between successive days. The water. results from the two buoys operating in 1992 are rather In the light of the various potential error sources above, coherent, giving more reliability to an estimation method one may take the inaccuracy in various flux estimates to be liable to potential inaccuracies. For the winter 1992 the around 20 W/m1 or, in the case of large fluxes, even mean sensible heat flux was -10 to -15 W/m2 downwards. significantly larger. Accordingly, the absolute values of the The estimates for latent heat flux suggest a small results given by the study should be regarded as first-order evaporation, with XE of 0 to 5 W/m2, during the summer estimates. On the other hand, relative values such as mean and very weak condensation during the winter. The highest variations between successive days and periods are to be diurnal values, up to 20 W/m2, are connected with considered more characteristic and correct. The relative evaporation. The stability parameter 10/L was typically inaccuracy is largest over ice and snow-covered surfaces. 0.05-0.5. Because of the stable stratification, the transfer —T-T- -L- Y/) -' 4: 406 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA ice shelf 1990.5 1991.5 1992.5 Fig. 3. Tune series of the air temperature and wind speed as observed by four buoys during the three-year period 1990-1992 (diurnal means) (a) Ta over sea ice (buoys 5892, 1282 and 5908), (b) Ta over ice shelf edge (buoy 5895), (c) V over sea Ice, and (d) V over ice shelf. ». v '■h -v_. , LAUNIAINEH AND VIHMA 407 -100 • 1282 — 5908 -- 1990.5 1991.5 1992.5 1282 — 5908 -- 1990.5 1991.5 1992.5 fig. 4. Time series of heat fluxes over the sea ice (positive upwards). For geographic locations of the buoys, see Fig. 1. (a) sensible heat flux and (b) latent heat flux. coefficients of heat and moisture were reduced, on the ice. The typical width of leads in the Weddell Sea is 10 to average, to 80% of their neutral values. 10’m. Near the continental ice shelves in the eastern The results are in qualitative agreement with Andreas and Weddell Sea. coastal polynyas are observed throughout the Makshlas [1985] and Koltmeier and Engelbart [1992], year [Kotlmeier and Engelbart, 1992]. In summer when the although differences in geographical areas and observation ice edge retreats to the south they are often joined to the seasons make the comparison somewhat difficult. The open ocean. Zwally and Comiso [1985] estimated 10% larger downward fluxes we obtained, especially in 1990, concentrations of open water in winter along the coast may partly result from the fact (hat (he ice floe of buoy nearby the Halley station, while Kotlmeier and Engelbart 5892 was much thicker than the typical pack ice in the [1992] reported polynyas 4-15 km wide. Pease [1987] has Weddell Sea. Over this floe the sensible heat flux was -25 developed a method of calculating the equilibrium width for W/m2 during the winter with a latent heat flux of -4 W/m2, a coastal polynya in winter, depending on the air whereas over thin floes (1282 and 5908) the winter values temperature and wind speed away from the coast. Using the were -12 W/m2 and -2 W/m2, respectively. The critical wintertime means for those quantities as measured by our effect of ice thickness was pointed out by Makshlas [1991] buoy (-25°C and 4 m/s, buoy 5895), the method would give and observed also by KOnig-Langlo and Zachek [1991], about 10 km for the equilibrium width. whose data from the Weddell Sea in September 1989 On the eastern coast of the Weddell Sea, the wind is indicated that the air temperature exceeded the surface primarily directed away from the continent or along the temperature over old ice and was lower than this over new shoreline direction [van Loon el al„ 1972; Koltmeier, 1988]. ice, when an area containing both old and new ice was The ice is therefore advected away from the coast more transversed. rapidly than it is formed and the polynyas remain open. According to Fahrbach and Rohardl [1992], heat flux from 5.2. Fluxes over leads and coastal polynyas deeper layers of the ocean may also be significant in the region. The air-sea temperature difference reaches extreme Observations allowed us to roughly estimate the heat values over the coastal polynyas, because the wind nearly fluxes over leads, which are known to exist in the Weddell always has at least a moderate component off the continent Sea ice field throughout the year. In the central Weddell [Launiainen el al., 1991]. For this reason the air-mass Sea, leads are narrow and formed by the divergent drift of measured at the buoy (5895) is advected to the open sea. V 408 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA This allows us to use, as a first approach, the properties of than a day, until the formation of new ice [Lebedev, 1968; the air mass as observed by the buoy to compute the fluxes Bauer and Martin, 1983]. According to Makshtas [1991], near the shelf, for estimation of fluxes from coastal however, fluxes through the new ice may be 2 to 3 times polynyas. The buoy is located at the floating shelf edge larger than those over multiyear ice, even two months after some 35 m above the sea surface, and the cold air mass the freezing of a polynya. In the light of the above, the flowing out from the continent drops more or less directly fluxes computed are to be seen as the potential contribution from here down to the sea surface. It is therefore difficult of leads, continously appearing and disappearing, to the to accurately define a height corresponding to the air-sea ocean-air exchange. Fluxes somewhat larger than our ■ temperature difference. To study the sensitivity of the flux estimates would be obtained for very narrow leads (less -V estimates to this height, both the observing height of the than 100 m wide), if fetch-dependent transfer coefficients buoy (Table 1) and that increased by 35 m were used. We were used. In our opinion, fetch-dependence is not crucial, found, however, that the errors are not very significant for as we do not know the distribution of the leads by width. these conditions. Makshtas [1991] came to a similar conclusion for the Arctic The surface temperature in the leads and polynyas was Ocean. On the other hand, an air mass flowing over a wider estimated to be practically at the freezing point (-1.8°C), polynya becomes warmer and moister during its traverse, and for the leads the properties of the air mass as observed and thus the temperature and moisture differences above the over the ice floes were used to compute the fluxes. The polynya decrease, resulting in reduced fluxes. Therefore the same method was used c.g. by Maykut [1986] to compute initial upwind properties of an air mass cannot be used for the fluxes over young ice. In summer, fluxes are more polynyas several kilometers wide (compare section 5.3). difficult to estimate, because the exact surface temperature The problems have been studied in some more detail by is unknown, usually exceeding the freezing temperature and Andreas and Murphy [1986], Makshtas [1991] and Serreze being closer to the air temperature. In this case, both the et al. [1992]. sensible and latent heat flux tend to be small, and a relative To compute the latent heat flux over polynyas and leads, error may be very large - even the sign i.e. the direction we assumed that the relative humidity of the air mass may be unknown, if the actual lead surface temperature is flowing out from over the ice remains constant at a height not measured. Thus we do not even attempt to estimate of 3 m. In practise this means that the humidity used in the fluxes over leads for summer. calculations is close to saturation. As pointed out by The results for heat and moisture fluxes over winter leads Andreas et al [1979], the flux of latent heat over a lead can and polynyas are presented in Figure 5. The fluxes from be estimated to within a (moisture-related) accuracy of 10% leads in the central Weddell Sea are generally smaller than without any measurements of air humidity by assuming those from coastal polynyas, although larger transfer saturation, because the flux is controlled by the large coefficients were used for the former (Table 2). The reason difference in temperature between the air and the surface. is that the air over the Weddell Sea is generally warmer We can therefore assume cither the same relative humidity than the air over the coastal polynyas, the latter flowing out as measured over the sea ice or saturation humidity. from the Antarctic continent. Wintertime sensible heat According to our data, the difference in the resulting fluxes over 200 W/m2 from leads and over 300 W/m2 from evaporation would not exceed 2% in conditions typical for \ coastal polynyas are frequent and values of latent heat up to winter leads. On the other hand, a crude assumption of 100 W/m2 and 150 W/m2 are to be found, respectively. completely dry air would typically lead to an error of 50%. Fluxes over leads were somewhat larger in winter 1992 Thus, for determining evaporation over a winter lead, it is than those in 1990 in more eastern areas of the Weddell much more important to get reasonable estimates for the Sea. In spite of this, the average heat flux from the ocean to transfer coefficient CE and the wind speed, than to measure the atmosphere is probably smaller in the western parts of the air humidity. The situation is different when evaporation the Weddell Sea, because the leads are propably rarer and is measured over the sea ice or over the open ocean. more short-lived there, where the general ice drift is not so divergent. 5.3. Fluxes over the open ocean in autumn It should be emphasized that the fluxes over leads and polynyas depend not only on fetch but also on time. The The data from buoy 5893 was used to compute the fluxes coastal polynyas may be semi-permanent [Kollmeier and for the cooling period from 11 February until the freezing Engelbart, 1992], but over leads fluxes computed with the date of 31 March, 1990. During this period the buoy drifted assumption of the surface temperature at the freezing point at a distance of 100-150 km off the ice shelf (Figure 1). typically continue for only a few hours, anyway for less The fluxes were computed by the bulk-method using the air V .V. i r. polynyas, Fig. Pig. 5. 1 and Time and the series (d) text, W /m2 a W/m2 a W/m2 S W /m2 latent 1990 K) 1990 (a) 0 of - sensible heat beat Puses Pux 1990.5 1990.5 1990.5 1990.5 heat over over Pux coastal leads over 1991 1991 and leads, polynyas. coastal (b) latent 1991.5 1991.5 1991.5 polynyas 1991.5 5908 1282 heat -- — flux (positive over 1992 1992 1282 590S leads, upwards). — -- (c) 1992.5 1992.5 1992.5 1992.5 sensible LAUNIAINEN For geographic heat 1993 1993 flux AND locations, over VIHMA coastal see 410 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA b ) 300 ' M- r V- 12 February - 1 April, 1990 Fig. 6. Time series of heat fluxes over the open sea in late summer and autumn, (a) latent and sensible heat fluxes nearby the continental ice shelf and (b) fluxes at the open sea buoy 100 to 150 km off the ice shelf (see Fig. 1). temperature, humidity, wind speed and sea surface turbulent flux results. A good set of satellite images was temperature observed by the buoy (compare Figure 2). available from January to the end of March 1990, and for Additionally, fluxes over the sea close to the ice shelf were the rest of the period the energy balance was estimated estimated on the basis of observations of buoy 5895 at the using a cloudiness of 2/8, giving a net radiation of 20 W/m2 edge of a floating ice shelf (see section 5.2 above). There, (effective outgoing longwave radiation 50 W/m2, absorbed the sea surface temperature was assumed to be practically shortwave radiation -30 W/m2, positive upwards). This is at the freezing point The resulting flux estimates are given approximately balanced by the downwards-directed sensible in Figure 6. beat flux. A beat flux from the shelf affects the surface It is distinctly seen from Figure 6 that the sensible heat energy budget as well, but its effect is small, as will be flux is greatest close to the ice shelf and decreases further discussed below. away towards the open ocean. The latent heat flux decreases slightly, but far less than the sensible heat flux. 5.5. Heat flux through ice and snow Thus the Bowen ratio, being about 2 in the vicinity of the ice shelf, diminishes to about 1 in the open sea. The total Measurements of the temperature at a depth of 0.6 to 0.7 turbulent heat flux from the ocean was typically 100-150 m below the snow surface allowed us to roughly estimate W/m2 close to the ice shelf and about 60 W/m2 at a the heat flux from the ocean through the ice and snow. In distance of 100 to 150 km from the shelf. The topic is a stationary situation with homogeneous layers of snow and r further discussed in section 7. ice, and in the absence of phase transitions, the heat flux (EH) from ice and snow can be presented as [e.g., Makshtas, 5.4. Fluxes over the floating continental ice shelf edge 1991]: Stable stratification typically prevails over the continental EH T.-T, (6) ice shelves of Antarctica. The data of buoy 5895 was used h,+(\fk)ha to compute the fluxes at the edge of an ice shelf. The level-difference method was used to estimate the sensible . V’v i' " heat flux and the snow surface temperature. Thereafter, the where h, is the snow thickness, and A, is the ice thickness latent heat flux was obtained by the bulk method with the between the ice surface and . the ice temperature help of the calculated snow surface temperature. The results measurement level. T, is the ice temperature, 7", the snow shown in Figure 7 suggest the sensible heat flux to be on surface temperature, and X, and X, are the heal conduction average -17 W/m2 (downwards), being strongest in the coefficients of ice and snow, for which we used values X, = wintertime. During the summertime of 4 to 5 months the 2.1 Wm-’K-1 and X, = 0.3 Wm'K' [Maykut, 1986: latent heat flux tends to be almost zero, but suggesting very Makshtas, 1991]. small evaporation. The results remain rather comparable The temperature at the snow surface was calculated by throughout the three-year period. the gradient method as described in section 3. The heat balance of the snow surface was estimated (see Unfortunately, the snow thickness was measured only by section 6 for the radiation budget) to get a reference for the buoy 1282. The inaccuracy estimate is based on sensitivity % .; -, V LAUNIAINEN AND VII1MA 411 a) 50 1990.5 1991.5 1992.5 1990.5 1991.5 1992.5 Fig. 7. Time scries of heat fluxes over the edge of a floating continental ice shelf, (a) sensible heat flux and (b) latent heat flux. tests for various sources of error (i.e. values of \ and X,, upwards from the snow cover. Almost zero fluxes prevailed measurement of It,, and T, as calculated by the gradient in summer and in winter the fluxes varied in direction, method). An inaccuracy of ±30% in the heat conduction reflecting the rapid response of snow surface temperature to coefficients would cause an inaccuracy of ±2 W/m2 in Ihe changes in air temperature, most pronounced in winter. The heat flux. This added to the inaccuracy caused by T, would results arc summarized in Table 5. result in a total inaccuracy of about ±4 W/m2. Additionally, ihe assumption of a linear temperature profile in snow and 6. BOWEN RATIO AND SUMMARY OF THE ice (6) may itself cause some error. Based on the analyses SURFACE HEAT BALANCE of Makshlas [1991], we estimate that the error for ice about 1 m thick would be some 20-30%, or perhaps less when It is customary to analyze the ratio of fluxes of sensible average (smoothed) meteorological parameters are used (as and latent heat using the concept of the Bowen ratio. Bo = for Table 5). HfKE, assumed to remain rather constant under certain On the basis of our calculations the conductive heat flux meteorological conditions. Knowledge of the Bowen ratio from the Weddell Sea through ihe ice and snow should be would then allow us to estimate either H or VE on the basis of the order of 10 W/m2, with a standard deviation of of measurements of one or the other. Unfortunately, data diurnal means of 5 to 10 W/m2 due to synoptic scale regarding the Bowen ratio over sea ice and polynyas is very variations in the snow surface temperature. At buoy 1282 sparse. The Bowen ratios for wintertime (in this context the heat flux remained fairly constant through the autumn to defined as the period from April to the end of October) winter period from February 15 to July 26, because the resulting from this study are given in Table 4. snow accumulation in winter compensated the increase in The results suggest somewhat larger winter values for T,-T, and prevented the flux from increasing. coastal polynyas (based on the data from the buoy 5895) For the continental ice shelf (buoy 5895), the equation for than for leads in the central Weddell Sea. The reason is to heat flux reduces to EH = where It, is now to be found in the outflow of the continental air-mass over the be interpreted as the depth of the snow temperature sensor. coastal polynyas, resulting in an intensive flux of sensible Based on two visits to the buoy after its deployment, the heat near the ice shelf. Over leads and polynyas in winter, average rate of snow accumulation is known, and values ranging from 2 to 6 have been reported by Andreas calculations resulted in a weak mean heat flux of 1-2 W/m2 el al., [1979], den Hartog el aL [1983] and Serreze et al. V' 412 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA •• • :x TABLE 4. Bowen ratios (Bo = HfkEi A summary of the estimated values of the various heat balance components is given in Table 5. The turbulent and surface type Bo conductive heat fluxes in the table are based on our data, mean std but the radiative fluxes are only first-order estimates to get a reference for the magnitudes of the heat balance terms. coastal polynyas 2.9 0.9 Our data of air and surface temperatures are used when - winter leads 2.5 0.7 calculating the radiation terms, but cloudiness is only open ocean, autumn 0.8 0.3 estimated, and is set to a constant value throughout the year v (2/8 for the ice shelf, 4/8 for the coastal polynyas, and 6/8 % [1992]. for the sea ice and leads) except for those daily values S' As for conditions above the sea ice, Andreas [1989] derived from satellite images for the open ocean buoy. The computed Bowen ratios based on the measurements of shortwave radiation was estimated using the method of van Leavitt el al. [1978] over multiyear ice in the Beaufort Sea Ulden and Hollslag [1985] with the albedo over water and found that Bo was variable in sign, but that in summer surfaces depending on the sun ’s altitude according to Payne positive values were more than twice as common as [1972]. Several methods were tested to estimate the negative values. We found that the Bowen ratio was longwave radiation [Berliand and Berliand, 1952; Budyko, positive over sea ice for 80-90% of the time. The mean 1963; Parkinson and Washington, 1979; van Ulden and values over ice are not listed above, because the flux of Hollslag, 1985; Oinsiedl, 1990]. However, an accurate latent heat is frequently close to zero. estimate for the effective outgoing longwave radiation TABLE 5. Estimates of surface heat balance components in the Weddell Sea (in W/m1, positive upwards). Net shortwave radiation is denoted by SWR and the effective outgoing longwave radiation by LWR. > Surface type Sensible latent heat flux SWR LWR heat flux heat flux through ice Sea ice -15 0 10 -20 20-40 MIZ +1 4 interior -17 -2 10 winter -17 -3 10 0 20-40 summer -5 3 -40 30-50 Ice shelf -17 0 1 -30 40-60 winter -16 0 1 0 30-50 summer -12 2 1 -60 50-60 onen ocean fautumn) 27 30 -100 60-70 •v • , coastal nolvnvas 160 60 -100 80-110 X winter 240 80 -2 100-130 summer (30) (20) -240 60-70 ' - leads 140 60 -90 60-90 MIZ 70 30 interior 150 60 winter 190 70 -5. 70-110 (20) (14) -190 30-50 : * Note: Summer defined as a period from December to end of February, winter from June to end of August. M1Z = marginal ice zone; the buoy 5892 drifted in MIZ from January to the end of April, 1990, and the buoy 5908 in November, 1992. During other periods analyzed the buoys drifted in the interior of the ice field. Heat flux through ice calculated on the basis of the buoys 1282 (sea ice) and 5895 (ice shelf) only. Summer values over leads and coastal polynyas are uncertain due to unknown sea surface temperature. . v LAUNIAINEN AND V1IIMA 413 (LWR) without knowledge of vertical profiles of T', iv’ and u' denote turbulent fluctuations of temperature temperature and humidity (reaching above the surface layer) and of vertical and horizontal velocity, respectively. (4) is impossible. Therefore the methods based on surface denotes diabatic sources and sinks of enthalpy, such as conditions and cloudiness contain some discrepancies giving radiation and condensation. rise to the uncertainity ranges shown in Table 5. (We Assuming semistationarity and (3a) » (3b) and estimated the inversion strength to be 5°C when using the neglecting (4) we get method of van Vlden and HoUslag, [1985].) Keeping in mind the potential error sources discussed and 3 (7V) the great variability in meteorological and ice conditions, -pc,- 3z die results for various energy balance components in Table 5 should be regarded as nothing more than a rough overall 3 H(xj) estimate. However, the importance of coastal polynyas and 3z leads for the local heat balance can be seen. As to their effect on the overall heat exchange in the Weddell Sea, the results must be used in connection with the areal fraction of i.e. the vertical local change in heat flux is mostly balanced polynyas and leads (normally less than 10%). The turbulent by advection. In our case this holds especially well, because fluxes are somewhat larger than the radiative fluxes over a strong inversion prevents the upward heat flux from narrow open water areas, i.e. polynyas and leads, except in penetrating through the inversion, i.e. through the height of summer when shortwave radiation dominates. Over the Zb below which 7/(z) -> 0 (see Figure 8b). Integrating up to open ocean the air temperature is adjusted to the sea surface the layer we have temperature and radiative fluxes dominate turbulent fluxes. Radiative fluxes arc larger over the sea ice and ice shelf, too. The effective outgoing longwave radiation, in p cp fu^-dz - H(xfl) particular, plays a role of essential importance throughout die year. and x A x 7. AIR-MASS MODIFICATION NEAR THE pc, J jttSj-dzdx = JH(x,0)dx ICE SHELF The location and alignment of two meteorological buoys Considering the horizontal changes with distance e.g. over and the research vessel offshore of the Riiser-Larsen ice a polynya or, as in our case, from the shelf edge downwind shelf (at 72.5°S, 17°W) offered a situation for the study of (Figure 8a) to the research vessel and to the open sea buoy air-mass modification over the sea near the ice shelf, under area, the above may be integrated to conditions of cold and dry air flowing out from over the shelf towards the sea, during the period February 11 to 12, z. 1990. The temperature and wind history of the buoy at the pc, J"u [7fX,z)-7X0,z)] dz = XH <7) shelf edge show a period of katabatic wind to have been started then, during late summer in the area. to give tiie "integral ” method heat flux, used by various 7.7. Calculation of the heat flux from the observed profiles authors for arctic leads [Badgley, 1966; Andreas et ah, 1979; Makstash, 1991], Conservation of enthalpy (pc,7) in a turbulent field gives, Accordingly, assuming the velocity not to be too under an assumption of two-dimensionality: dependent on x, the left-hand side of (7) may be easily calculated, from the temperature profiles at the shelf edge 3T 3 r 3(7V) 3(7V) Pc, -pc," -pc,- - pc,- * Qo and over the sea, to give the mean heat flux. The integral '"57 "51 3z ~sr~ heat flux provides a basis for comparing the (1) (2) (3a) (3b) (4) bulk-aerodynamic based fluxes at various observation sites. If we replace T and T by the specific humidity and its where the term (1) denotes local change and (2) advection. fluctuations, and c, by the enthalpy of vaporization, (7) Terms (3a) and (3b) describe turbulent exchange, in which gives the latent heat flux. 414 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA Fig. 8. (a) Location of meteorological buoys (5893,5895) and the RVV Aranda (A) during an air-mass modification study on February 12, 1990. Arrows give wind vectors at the shelf buoy and at the research vessel in the various case studies 1 to 3. (b) Vertical profile of wind speed and temperature given by meteorological sounding for case 2. The hatched area represents the increase in the heat content of an air column after flowing out from the shelf to the sea. TABLE 6. Aerological sounding cases on February 12,1990. z, = height of the inversion layer at the ice shelf, s, = inversion strength = T(h,)-T(3m), d = distance from the shelf to RVV Aranda, b„ = height of the modified surface layer at the site of Aranda, case no. sounding time V (m/s) air temperature z»(m) S(K) d(km) h„(m) 5895 (3m) Aranda (13m) i 00s 6.0 -7.8 -4.6 230 5 55 165 2 05" 8.5 -115 -6.9 140 7.5 41 83 3 09" 9.0 -10.7 -8.1 130 7 , 6 43 7.2 Case studies upwind shelf edge, the profile was constructed by extrapolating the ship-based balloon-observed profile Figure 8a shows the research area, giving the site of the downwards from the inversion base, to correspond to the meteorological buoys and the location of the research vessel surface-layer temperature observed by the buoy at the shelf during the cases (1 to 3) studied on February 12,1990, and edge. A comparison in case 3, when the ship was nearest to also shows the wind vectors observed at various places. The the shelf, showed the method to be rather accurate. The cases correspond to situations when aerological balloon wind profile (Figure 8b) indicates a katabatic-type wind soundings were made from the research vessel. with velocity increasing down to the surface friction layer. Figure 8b gives the wind and temperature profiles above The observations during the case studies allow us a first- the shelf edge and above the sea for case 2. The hatched order comparison of estimates of heat exchange as area shows heating of the cool air flowing out over the sea. calculated from (7). The mean characteristics of the At sea, the temperature profile was obtained from ship modification cases studied are given in Table 6. observations and a balloon sounding, direedy. For the In addition to the bulk measurements and an analysis of i LAUNIAINEN AND VIHMA 415 the ice shelf was not measured. The temperature measured by buoy 5895 was assumed to represent the air temperature case 3 3 m above the sea surface (which was assumed to be at - 0°C), but the ice shelf had a sleep 35 m high edge and a certain amount of mixing must take place when the air flows out from the ice shelf. Additionally, die exact height of die inversion base was not clearly defined in cases 2 and 3, which affects the estimates of the heat surplus (i.e. the hatched area in Figure 8b). In case 1, the modified surface case 2 layer was thick, with a well-defined inversion base, and the modification analysis gave almost the same result as the bulk-aerodynamic calculations. Similarity of the estimates given by the two methods would also require that the air temperature was constant along the shoreline of the ice shelf, as the wind did not blow directly from buoy 5895 to the research vessel. The discrepancy found in the results is thus quite natural. The results give, however, three almost independent estimates of the heat flux close to the disiancc wcsl from the ice shelf (km) continental ice shelf and the following conclusion may be drawn: the sensible heat flux varied between 40 and 150 W/m2 and decreased with increasing distance over the open Fig. 9. Sensible heat flux near the ice shelf (site of the buoy water. The problematics and data will be the subject of a 'J 5895), at the research vessel (A) and at the open ocean buoy (5893) as estimated by three different methods: (1) the specific modelling study and, hopefully, of an experimental bulk-aerodynamic method (solid lines), (2) the modification rate of verification within the next few years. temperature profiles (dashed lines), the integral method giving the average heal flux between the ice shelf and the research vessel, 8. CONCLUSIONS i (3) the diabetic resistance laws for the atmospheric boundary layer (symbols Rl, R2, and R3 for the three sounding cases described The study was based essentially on data from 5 marine in Table 6). meteorological buoys. Two of the buoys yielded high- quality data from the Weddell Sea over a period of about a air-mass modification using eq. (7), the fluxes were also year, and one buoy standing on an ice shelf edge has estimated on the basis of diabatic resistance laws for the yielded data for over 4 years so far. Among others, the data atmospheric boundary layer. For such an estimation, one permit estimation of the components of heat and moisture needs to know the sea surface temperature, the height of the exchange in the area. On the other hand, although being boundary layer and die wind speed and potential based upon very reliably-measured local quantities (air temperature at that height The height of the boundary layer temperature, air pressure, surface wind, humidity), the is taken as the inversion base (I^ in Table 6) following calculated results suffer from various potential Heinemann and Rose [1990] and Carratl [1992, p. 186]. methodological error sources (section 4). This is especially For details of the iterative method, see e.g. Komneier and true for the measurement and calculation of sensible heat Engelbart [1992], The resistance laws arc applicable only flux by the gradient or level-difference method above the for the site of R/V Aranda. The results based on all the ice. For this reason, the results given in Table 5 should be three methods are presented in Figure 9. regarded as first estimates, although two independent sensor The results of the three methods are reasonably in pairs were used in each buoy and indirect checking methods accordance with each other. The bulk-aerodynamic showed the sensors to have remained very stable. Also e.g. calculations in particular correspond surprisingly well to the the buoys in 1992 in the western Weddell Sea showed results based on the resistance laws, as was also found by mutually comparable and coherent results. Heinemann and Rose [1990] in the southern Weddell Sea. Except in the marginal ice zone, the results suggest that The results from air-mass modification differ more from the the sensible heat flux above the sea ice is most frequently otiters in cases 2 and 3. The accuracy of the results based directed downwards. This is because the radiation balance on the modification of the temperature profiles is decreased lends to be negative and it cannot be balanced by the heat e.g. by the fact dial die temperature profile at the edge of flux through the ice alone. In summertime, the average - i i 7'V • t. a : l: -T m 416 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA •V-7r. sensible beat flux is close to zero within the accuracy of the Launiainen and Vihma [1990]. Here we give the formulae measurements. For the future, a more accurate measuring or for transfer coefficients and universal functions used in the modelling of the surface temperature and radiation balance computations according to the equations (1) to (5) with (or at least observations on cloudiness) form the key notations as in the main text. V. ; problems for getting more reliable estimates of the heat balance over snow and ice. A. For practical calculations the transfer coefficients enter The turbulent heat fluxes over leads and polynyas were into eqs. (4) and (5) as the roughness lengths as V - ' large, even larger than the heat losses via longwave radiation. In summer, the lower atmosphere was almost in lnz, = lnz -kCo'n (Al) thermal equilibrium with the sea surface (except close to the continent) resulting in reduced fluxes. Thus the time (A2) series showed apparent annual cycles in the fluxes (Figure lnz,. - lnz, = In z-kC'^Cj} 5) and temporal variations over shorter periods were most pronounced in winter, when the air temperature varied far where z is the height the transfer coefficients CD and CtE more than in summer. Perhaps the most important question are referred to, and the von Karman constant k - 0.40. The in the estimation of the absolute magnitudes of the fluxes coefficients used (referred to 10 m) for the above read: above leads is to get reasonable estimates for the transfer coefficients. The importance of leads and polynyas for the a) over open sea: regional heat balance is evident, and we may anticipate that [Smith, 1980] the heat flux, especially from coastal polynyas, should CyXlO3 = 0.61 + 0.063V contribute convection and deep water formation near the ice where V is the wind speed. shelves. The above, together with studies of air-modification near the ice shelf with encouraging [Launiainen, 1983] bulk-flux comparisons, offers an interesting basis for further C„£xl0’ = 0.63C„xl05+0.32 modelling. b) over coastal polynyas: If we wish to provide a rough sketch of the overall CyXlO2 = 0.8 + 0.065V [Wu, 1980] vertical heat exchange in the Weddell Sea, a few estimates can be derived from the data given in Table 5. Estimating C„.as above the areal coverage of leads and polynyas to be 5 to 7%, except during a .3-month-long summer with an order of c) over leads in the sea-ice zone: 60% ice coverage, annual area-averages can be calculated. CyXlO1 = 1.49 [Andreas and Murphy, 1986] First, as to the sensible heat, the significant heat flux from the leads seems to be balanced by the downward flux above CH£as above yielding to =1.26x10"’ lire sea ice. In winter, the area averaged sensible heal flux would be about -5 W/m2, which is approximately in d) over ice and snow: accordance with the model results of Stdssel and Claussen Drag coefficient from the on-site mean geometric roughness [1993]. Secondly, our data yields an estimate of 20 to 30 R as W/m2 for the mean annual vertical heat loss from the CDx 103 = 1.1 + 0.072R [Banke et al, 1980] Weddell Sea. Finally, an overall estimate for the latent heat flux, 3 to 5 W/m2, accounts for a water vapour flux of Inzr ,=lnz^+h 0+h 1ln(Re) +t2(ln(/?e)) 2 [Andreas,mi] 1.2-10"6 to 2.0-10■“ kgm'V. Finally, we believe that significant advances will be made where Re is the roughness Reynolds number. in the near future, when our data are considered with other recent data sets, especially those obtained by the German Re = Zoti,"! . buoy studies in the Weddell Sea and by the studies in the U.S.-Russian Weddell Sea Ice Station I. v is the kinematic viscosity of air. APPENDIX: EMPIRICAL FORMULAE FOR B. Transfer coefficients covering diabalic cases as COMPUTATION OF TURBULENT SURFACE FLUXES c =______t______(A3) The computation algorithm is described in detail by ° [ln(z/z^-4yz/L)+4'„(z 0/L)]2- LAUNIAINEN AND VIHMA 417 Sea. J. Ceophys. Res., 94, 12,721-12,724, 1989. Andreas, E.L, C.A. Paulson, R.M. Williams, R.W. Lindsay, and m (InCz/z,,) ~'Yu(zJL) +'VtfxJL)) (A4) J.A. Businger, The turbulent heat flux from Arctic leads, x______1______■ Bound.-Layer MeteoroL, 17, 57-91, 1979. m2JzTyvm(ziL)^IIE(zjL)) Andreas, E.L, and A. P. Makshtas, Energy exchange over The Monin-Obukhov length L calculated as Antarctic sea ice in the spring, J. Geophys. Res., 90, 7119-7212, 1985. (A5) Andreas, E.L, and B. Murphy, Bulk transfer coefficients for heat gkH(\ +0.61 TacpEIH) and momentum over leads and polynyas, J. Phys. Oceanogr., 16, 1875-1883. 1986. where Ta = (T,+TJI2. Augstein, E., N. Bagriantsev, and H. W. Schenke, The expedition The formulae we use for universal functions read: Antarktis VI1I/1-2, 1989 with the Winter Weddell Gyre Study a) for the stable region (( = z/L > 0) from Holtslag and of the research vessels Polarslcm and Akademik Fedorov, deBruin [1988]: Ber. Polatforch., 84, 134 pp., 1991. = V„£ = -aX, -ZKC-c/d)exp(-tfO -hc/rf (A6) Badgley, F. J., Heat budget at the surface of the Arctic Ocean, Proc. on the Symposium on the Arctic heat budget and where a = 0.7, b = 0.75, c = 5 and d = 0.35. atmospheric circulation, edited by J. O. Fletcher, pp. b) for the unstable region (£ < 0) from Businger et al. 267-277, Rand Corporation, Santa Monica, Calif., 1966. Banke, E. G., S. D. Smith, and R. J. Anderson, Drag coefficients [1971] and Dyer [1974] type forms of: at AIDJEX from sonic anemometer measurements, in Sea Ice T„ = 21og(Jj^L) + logd^L) - 2arctan$;; +1 (A7) Processes and Models, edited by R. S. Pritchard, pp. 430-442, Univ. of Washington Press, Seattle, 1980. Bauer, J., and S. Martin, A model of grease ice growth in small where <}>M = (1-19.3Q" 1" and leads, J. Geophys. Res., 88, 2917-2925, 1983. = 2log(l(Hti)) (A8) Berliand, M.E., and T.G. Berliand, Determining the net long-wave radiation of the Earth with consideration of the effect of where = (1-12Q* I/2. In the above, the profile coefficients cloudiness, Isv. Akad. Nauk. SSSRSer. Geofis., No. 1, 1952. 19.3 and 12 are those obtained by HGgsirtitn, 119881. Bromwich, D.H., and D.D. Kurtz, Katabatic wind forcing of the The system of equations (1) to (3) and (A3) to (A8) leads Terra Nova Bay polynya, J. Geophys. Res., 89, 3561-3572, to an iterative solution, the algorithm being given in 1984. Budyko, MX, Atlas of the heat Balance of the World, Glabnaja Launiainen and Vihma [I990J. Geofiz. Observ., Moscow, 69 pp.. Also: Guide to the Atlas of the Heat Balance of the Earth, Translated by I.A. Donehoo, Acknowledgments. We wish to thank Kalevi Rantanen U.S. Wea. Bur., WB/T-I06, Washington D.C- 1963. (IVO Service Co.), Scppo Kivimaa (Technical Research Businger, J.A., J.C. Wyngaard, Y. Izumi, and E.F. Bradley, Centre of Finland) and the crews of R/V Aranda and R/V Flux-profile relationships, J.Atmos.ScL, 28, 181-189, 1971. Academik Fedorov (Russia) for field assistance. Juha Uotila Cavalieri, D. J., and S. Martin, A passive microwave study of is acknowledged for his contribution in processing the data polynyas along the Antarctic Wilkes Land Coast, in and drafting figures. The field phases of the project were Oceanology of the Antarctic Continental Shelf, Antarctic Res. financially supported by FINNARP (Finnish Antarctic Ser., vol. 43, edited by S. S. Jacobs, pp. 227-252, AGU, Research Program, Ministry of Trade and Industry), and the Washington, D.C., 1985. Academy of Finland has given some funding support for Dyer, A.J., A review of flux-profile relationships, Boundary-Layer tiie scientific work. Pentti MSlkki, chair of FINNARP and MeteoroL, 7, 363-372, 1974. Fahrbach, E., and G. Rohardt, Supression of bottom water director of the Finnish Institute of Marine Research, is formation in the southeastern Weddell Sea Shelf due to acknowledged for help and encouragement. melting of glacial ice. Deep Sea Research, 1992 Gamut, J.R., The atmospheric boundary layer, Cambridge University Press, 1992. den Hartog, G., S.D. Smith, RJ. Anderson, D.R. Topham, and REFERENCES R.G. Perkin, An investigation of a polynya in the Canadian archipelago 3, surface heat flux, J. Geophys. Res., 88, Andreas, E.L, A theory for the scalar roughness and the scalar 2911-2916, 1983. transfer coefficients over snow and sea ice, Boundary-Layer Heinemann, G., and L Rose, Surface energy balance, MeteoroL, 38, 159-184, 1987. parameterizations of boundary-layer heights and the Andreas, E.L, A year of Bowen ratios over the frozen Beaufort application of resistance laws near an Antarctic ice shelf A 7 T~ 77—7 • 418 ON THE SURFACE HEAT FLUXES IN THE WEDDELL SEA front. Boundary-layer MeteoroL, 51, 123-158, 1990. Parkinson, C.L., and W.M. Washington, A large-scale numerical Hoeber, H., One year temperature records in the atmospheric model of sea ice, J. Geophys. 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Hannover, northern Bering Sea, J. Geophys. Res., 88, 2723-2732,1983. 33, 153 pp., 1988. Serreze, M.C., J.A. Maslanik, M.C. Rehdcr, R.C. Schnell, J.D. - Kottmeier, Ch., and D. Engelbart, Generation and atmospheric Kahl, and E.L. Andreas, Theoretical heights of buoyant heat exchange of coastal polynyas in the Weddell Sea, convection above open leads in the winter Arctic pack ice Bound-Layer MeteoroL, 60, 207-234, 1992. cover, J. Geophys. Res., 97, 9411-9422, 1992. KGnig-Langlo, G., and A. Zachek, Radiation budget measurements Simmons, I., and W. F. Budd, Sensitivuty of the southern over Antarctic sea ice in late winter. World Climate hemispehre circulation to leads in the Antarctic pack ice. Programme, Research, WCRP-62, (Appendix C), 41-44,1991. Quart. J. Roy. MeteoroL Soc., 117, 1003-1024, 1991. KGnig-Langlo, G„ B. Ivanov, and A. 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Res., 88, 2900-2910, 1983. % fluxes - an iterative flux-profile method allowing arbitrary StGssel, A. and M. Claussen, On the momentum forcing of a observing heights. Environmental Software, 5, 113-124,1990. large-scale sea-ice model. Climate Dynamics, 9,71-80, 1993. Launiaincn, J., T. Vihma, J. Aho, and K. Rantanen, Air-sea Thorpe, M.R., E.G. Banke, and S.D. Smith, Eddy correlation interaction experiment in the Weddell Sea, Argos-Buoy measurements of evaporation and sensible heat flux over Report from FINNARP-5/89, 1990-1991. Antarctic Reports of Arctic sea ice, J. Geophys. Res., 78, 3573-3584, 1973. Finland no. 2, Ministry of Trade and Industry, 1991. Untersteincr, N. The geophysics of sea ice: overwiev, in Leavitt, E-, M. Albright, and F. Carsey. Report on the AIDJEX Geophysics of Sea Ice, edited by N. Untersteincr, pp. 1-8, meteorological experiment, AIDJEX Bull., 39, 121-147,1978. Plenum Press, New York, 1986. 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Webb, E.K., Profile relationships: the log-linear range and Maykut, G.A., The surface heat and mass balance, in Geophysics extension to strong stability. Quart. J. Roy. MeteoroL Soc., of Sea Ice, edited by N. Untersteincr, pp. 3xx-463, Plenum 96, 67-90, 1970. Press, New York, 1986. Vihma, T., and J. Launiaincn, Ice drift in the Weddell Sea in Monin, A. S., and A. M. Obukhov, Dimensionless characteristics 1990-1991 as tracked by a satellite buoy, J. Geophys. Res., of turbulence in the surface layer of the atmosphere (in 98, 14,471-14,485, 1993. Russian), Trudy Geoftz. Inst. Akad. Nauk SSSR, 24, 163-187, Vihma, T., J. Launiaincn, J. Uotila, and K. Rantanen, Air-sea •i • 1954. interaction experiment in the Weddell Sea, 2nd Monin, A S., and A.M. Yaglom, Statistical Fluid Mechanics, Vol. Meteorological Argos-Buoy Data Report from FINNARP, 1. The MIT press, 769 p., 1971. 1990-1993. Antarctic Reports of Finland no. 4. Ministry of Omstedt, A., A coupled one-dimensional sea ice-ocean model Trade and Industry, 1994, in press. , V ■ applied to a semi-enclosed basin, Tellus, 42A, 568-582,1990. Wu, J., Wind stress coefficients over sea surface in near-neutral fr, r 1 L 3 33 f LAUNIAINEN AND VIHMA 419 conditions, a revisit, J. Phys. Oceanogr., 10, 727-740, 1980. 43. edited by S. S. Jacobs, AGU, Washington, D C., 1985. Vowinckcl, H., and S. Orvig, Synoptic energy budgets from the Beaufort Sea, in Energy Fluxes over Polar Surfaces, edited by S. Orvig, 299 pp. World Meteorological Organization, Geneva, 1973. J. Launiainen, Finnish Institute of Marine Research, P.O. Box Zwally, HJ., and J.C. Comiso, Antarctic offshore leads and 33. FIN-00931 Helsinki, Finland. polynyas and oceanographic effects, in Oceanology of the T. Vihma, Department of Geophysics, P.O. Box 4 Antarctic Continental Shelf, Antarctic Research Series, voL (Fabianinkatu 24A), FIN-00014 University of Helsinki, Finland. .! 'V: .'1 ‘ •; W' V3M - V • V ■f ■ . V-, L :S u- •v-v. -.v i. •. « •" V V SSSti.v I VI •• i r : v* 5- > -r' .'V '-v; K Y< v.*. \S / % - : Z- < , v e ' V ; \ •. 1 Journal of Geophysical Research, in press. Copyright by the American Geophysical Union. Subgrid parameterization of surface heat and momentum fluxes over polar oceans Timo Vihma Department of Geophysics, University of Helsinki, Finland Abstract. The parameterization of heat and momentum fluxes over a heterogeneous surface consisting of sea ice and large areas of open ocean (polynyas) has been studied. Various theories required to calculate grid-averaged fluxes are discussed, and a two-dimensional mesoscale boundary layer model has been applied to simulate the flow and heat exchange processes inside a single grid element of a hypothetical atmospheric general circulation model. The theories are compared with model results. Considering the surface fluxes of sensible and latent heat, a mosaic method, based on the use of esti mates for local surface temperature, air temperature, specific humidity, and wind speed over the ice-covered and ice-free parts of the grid square, performed well in the comparison. Parameterizing the net longwave radiation, an estimate for the subgrid distribution of cloudiness was useful. Parameterization of surface momentum flux seemed to be most reasonable on the basis of the surface pressure field and a geostrophic drag coefficient depending on the air-surface temperature difference. 1. Introduction bipolar oceans, especially in wintertime, the ice cover efficiently prevents heat exchange between the relatively warm ocean and the cold atmosphere. There are, however, dis continuities in the ice cover, and these areas of open water may have horizontal dimensions ranging from 1 m to 100 km. The smaller ones, with a typical width of from 1 m to 1 km and length of from 100 m to 100 km, are here called leads and are usually formed by divergent ice drift. Here we use the term polynya for the larger areas of open water, with characteristic horizontal dimensions of from 1 to 100 km or, on rare occasions, even up to 1000 km, as in the case of the Weddell Polynya in 1974-1976. Polynyas are often recurrent or semipermanent in nature. They form most usually along coastlines, if wind carries the ice away from the coast more rapidly than new ice can be formed [Cavalieri and Martin, 1985; Pease, 1987]. A region of fast ice may remain between the coast and the polynya, as is the case, e.g., for the Laptev Sea Polynya (Figure 1). Polynyas may, however, occur in the middle of the pack-ice field as well (e.g., the Weddell Polynya, the Maud Rise Polynya, and the Cosmonaut Polynya in the Southern Ocean), remaining open 2 due to oceanic heat flux and/or large-scale divergence of surface currents. Reviews of the occurrence and characteristics of leads and polynyas are given by Zwally etal. [1985], So Comiso and Gordon [1987], and Smith etal. [1990]. .;v j--', •» V' :;v Figure 1. Landsat image showing part of the Laptev Sea Polynya (seen as a dark area) between regions of fast ice and fractured drifting ice. The size is 100x100 km, and the location is near 75°N, 137°E (the bright white, fast ice region includes parts of the snow-covered Belkovskiy and Kotelnyj Islands). The heat loss from the ocean to the atmosphere through polynyas is efficient and has been the topic of several field experiments in the Arctic [Andreas et al., 1979; den Hartog et al., 1983; Smith et al., 1983] and a few in the Antarctic [Bromwich and Kurtz, 1984; Kottmeier and Engelbart, 1992]. In wintertime the (upward) turbulent heat flux may reach 300-500 W m"2, which is almost 2 orders of magnitude larger than the heat flux through the ice. Therefore even a small amount of open water or thin young ice formed on the lead or polynya surface may dominate the regional heat budget [Maykut, 1978], In addition, the heat flux of the effective outgoing longwave radiation over polynyas in winter is of the order of 100 W m"2. These heat fluxes influence sea ice formation and ocean strat ;4v ification and thus the ocean circulation, as well as atmospheric stratification and circulation on a regional and even a global scale [Ledley, 1988; Simmons and Budd, 1991]. Since the gridlengths of large-scale atmospheric general circulation models (GCMs) are of the order of 200-500 km and those of numerical weather prediction models are about 40-100 km, the heat flux from leads and polynyas must be parameterized. The problem of parameterizing the surface fluxes over a heterogeneous surface has become f \ ■' :/ ■ "v* 3 one of the key issues in present-day research on the atmospheric boundary layer. In this context, partly ice-covered seas are in one sense simple, having no vegetation, no terrain height variations, no variations in surface moisture, and no extreme changes in surface roughness. In another sense they are more problematic than land surfaces, because subgrid variations in surface temperature can be extreme, even exceeding 30°C. The basic problem in the parameterization of turbulent heat fluxes is that we only know a single air tem perature, surface temperature and wind speed for each grid square of a GCM. We can parameterize the surface fluxes solely on the basis of these grid-averaged variables, a method which we here call the mixture method. Alternatively, we can calculate local surface temperatures for the ice-covered and ice-free parts of the grid square (with the help of the radiation budget). The surface fluxes can then be calculated separately for the ice-free and ice-covered parts, the grid-averaged flux being some area average of these (the mosaic method). The basic questions are as follows: (1) What are reasonable values for the transfer coefficients? (2) How well do the grid-averaged air temperature, wind speed, and surface temperature (if the mixture method is used) represent the local values? If the leads are narrow, the air temperature and wind speed are not too much affected by the surface temperature variations, but in the case of wide polynyas the subgrid-scale variations between the ice-covered and ice-free parts of the grid square may be con siderable. Parameterizing the radiative fluxes, problems arise from the subgrid variations in air temperature, cloudiness, and, if the mixture method is used, surface temperature and albedo. From the point of view of modeling, ice margins create an analogous problem to polynyas, because the grid boundaries of GCMs do not coincide with the ice boundaries, resulting in large subgrid variations in surface temperature. This is also the case for tongues of open water in mostly ice-covered grid squares. For example, in wintertime the Barents Sea, Greenland Sea, Baffin Bay, and Davis Strait form such tongues (see Gloersen et al. [1992, p. 46-53] for a good illustration). Similar problems are encountered in coastal areas in autumn or early winter, when the sea is still open while the surface temperature over the land has already dropped. In addition to unbroken areas of warmer surface, series of polynyas may occur in the ice field, and the response of the atmospheric boundary layer may be different from the case of a single polynya. Claussen [1991a] studied the surface heat flux parameterization on the scale of leads (lO'-lO3 m) and found relatively simple parametrization methods to work satisfactorily. In the present paper we concentrate on the scale of polynyas and simulate the airflow using a two-dimensional mesoscale planetary boundary layer (PBL) model. The model domain is intended to represent a single grid interval of a GCM. The approach is briefly introduced by Vihma [1994]. The results may naturally suffer from possible restrictions of the mesoscale model, but this is a reasonable way to test the parameterization schemes for GCMs when observations are lacking. 2. Parameterization Schemes 2.1. Turbulent Heat Fluxes The simplest way to parameterize a grid-averaged turbulent surface heat flux from partly ice-covered sea is 4 where angle brackets denotes a grid average, H is the turbulent sensible heat flux, p is the air density, and cp is the specific heat. 6sis the surface potential temperature (we assume through this paper that 6sisa variable in a GCM, not specified, e.g., climatologically). 0Z is the potential temperature of the air at height z. V is the wind speed, and CHete is an effective heat transfer coefficient, for which we need to determine an appropriate value. Perhaps the simplest way is to use where k is the von Karman constant=0.4. A more sophisticated alternative, proposed by Wood and Mason [1991], is to express CHcfr in terms of an effective roughness length for temperature Z,cfr, which is analogous to that for momentum Z„cff -v: where b is the blending height, i.e., the approximate height at which the flow is independent of horizontal position and yet is still in equilibrium with the local surface (of course, these two conditions cannot be strictly valid at the same height). Here u. is the friction velocity, Lmcff is an effective Monin-Obukhov length, and x|% is a universal function describing the Tl ■V' effect of stability on the temperature profile. The process which Wood and Mason [1991] present to determine where / is the open water fraction. Equation (2a) requires estimates for the surface temperature over the ice Qs' and water 8/. There are several ways of calculating the local transfer coefficients. In keeping with the Monin-Obukhov similarity theory, C„f> = k?[ln(b/z V’o'> = (uj’w/k) ln[b/zt - X|V6/L"1] 8 V‘w = g vVjw + (l-g v) 0-> = g e0(T + a-ge) where 0 < g^gg < 1. The optimal values for g v and g Q depend on the situation, but if (3) •V-V. • . is applied at the blending height, gg = g v=0.5 could be used as a basic estimate, because that represents an even mixture of local equilibrium and horizontal homogeneity. After computing V> and &’w we can calculate The above (formulas (la) to (4)) holds for the turbulent latent heat flux XE as well, if 4, we just replace 0 by the specific humidity q and cp by the latent heat of sublimation X According to the present knowledge, the transfer coefficients and roughness lengths for % humidity are either equal or at least close to those for heat [e.g. Schmitt et al., 1979; Andreas, 1987; Smith, 1989]. We will use (la) to (4) to parameterize 2.2. Radiative Fluxes /;v': Almost the same problems that are encountered in the parameterization of turbulent heat fluxes are also present when parameterizing the radiation balance of the surface. In the case of incoming solar (shortwave) radiation, the subgrid variations in albedo and cloudiness should be considered. If we can estimate representative values for albedo and cloudiness (if there are systematic variations in the latter) for the ice-covered and ice-free parts of the grid square (a1, a", TV, and TV", respectively), a mosaic method should work for the grid-averaged broadband shortwave radiation flux Adopting the mosaic technique for Ts results in In atmospheric GCMs the computation of longwave radiation is a far more complex process, but in many sea ice models a simple parameterization like (6) is applied. Modifications to formulas (6) and (7) can be developed, as in the case of turbulent heat fluxes. One possibility would be to go further and separate the air temperature and cloudiness analogously to (4). As QL changes slowly with temperature, the separation of cloudiness into /V and AT is, however, more important, if it can be done reliably. 2.3. Momentum Flux The turbulent surface momentum flux over an ice-covered ocean depends on skin drag and on form drag, as stated by the drag-partition theory [Marshall, 1971; Arya, 1975]. The form drag arises from floe edges, pressure ridges, and patterns of snowdrift. In the mesoscale model used for the present study, we cannot explicitly resolve the form drag from such small surface features. We set a value of 1 mm for the ice roughness length, which merely represents the effect of skin drag. We could parameterize the total wind drag on the basis of a given distribution office size, freeboard, and ridging [Hanssen-Bauer and Gjessing, 1988; Stossel and Claussen, 1993]. Parameterization schemes for a hypothetical GCM including the effect of form drag could not, however, be verified by the mesoscale model. Therefore we only discuss the problem of parameterizing the skin drag, denoted as x. The problems are basically similar to those with the heat flux. We can use an effective drag coefficient and the grid-averaged wind speed. The simplest possibility is to calculate the stability correction xj/M from the grid averages <0Z>, <0p>, and Separating Ts over ice and water to get \|/M' and \|rMw yields The separation can again be developed further by calculating a local air temperature and wind speed for the ice-covered and ice-free parts according to (3) and then applying an equation analogous to (4). A combination of an effective roughness length Z0cff and separated can be used as well. Zocff can be obtained from Taylor ’s [1987] formula as follows: ln(Zoeir) = 8 • ^ V V ' V Tctylor [1987] derived his a forementioned equation for ZJn from an idea of computing i." v< .- regional roughness from a geostrophic drag coefficient CG = uJG, where G is the A geostrophic wind speed. Another possibility is to keep using CG and parameterize Over polar oceans, very little verification data are available for the actual surface wind. The pressure field is thus more reliably known for a GCM, and the problem is to determine -V-y the geostrophic drag coefficient. OverlandandDavidson [1992] and Overlandand Colony [1994] estimated CG over the Arctic sea ice on the basis of field data, and the results showed an apparent dependence on the atmospheric stability, but the stability conditions ■l.:: over grid squares containing a large fraction of open water are out of the range of the field data. Thus a representative value for CG to be used in the present study is uncertain, but we shall first try to estimate CG using the mesoscale model results. ’ J’X 2.4. Vertical distribution of heat In addition to the problem of parameterizing the horizontal area averages, the vertical distribution of heat should be considered. The subgrid-scale upward transport of heat .y - v results partly from turbulent diffusion and partly from mesoscale circulations. The field experiments of, e.g., Schnell et al. [1989] and Dethleff [1994] showed that buoyant heat plumes originating from leads or polynyas may reach altitudes of several kilometers penetrating through the polar inversion. This is problematic for many GCMs, because the usual practice is that the subgrid-scale heat flux is released into the lowest model layer. Thus the vertical heat transfer would be underestimated, and the amount of heat returned to the ice would be overestimated. A typical height for the lowest model level in GCMs is of the order of 100 m or below that; e.g., in the 31-level model of the European Centre for Medium-Range Weather Forecasts the three lowest levels are at approximately 30, 150, and 350 m. Even a denser vertical grid could not resolve the plumes because of their small horizontal extent. Glendening and Burk [1992] studied the flow over a lead 200 m t wide using a large-eddy simulation model and gave an equation for the maximum plume height Zp : ZP = (Q,W2/Vy)m (13) -» a I where Qs = Hw/pcp, W is the lead width, and y = 30/9 z upwind of the lead. Serrezze et al. [1992] developed an equation to predict the maximum temperature that air flowing over r ■ " a lead can reach. Using this predicted temperature and sounding data, they studied the theoretical heights of buoyant convection. The theoretical height for a plume associated with a 1-km-wide lead was 985 m. A higher plume rise would require light winds, a low surface temperature, and a weak low-level temperature inversion, a combination atypical 9 of the Arctic, and conditions favoring a high plume rise do not favor the formation of large leads [Serrezze et al., 1992]. The result of 985 m is, however, already far above a typical GCM’s lowest level. Although wide polynyas should be rare in the central Arctic, they are more common in the generally divergent field of Antarctic sea ice and are potential origins for high plume rises. In section 5 we try to simulate the vertical distribution of heat originating from large polynyas. 3. Theoretical Examples In the case of narrow leads, simple considerations about the area averaging may be made, assuming that the leads are so narrow that the wind speed is not affected and the temperature of the air mass flowing from over the ice to over the lead does not change significantly. 0Z does change, of course, but the change should remain small relative to the temperature difference 8y8 z. Accordingly, the local heat flux could be calculated using <0Z> as a local 0z',lv and Figure 2. Effective heat transfer coefficient CHett with respect to the true area average of CH as a function of air temperature with (a) unstable stratification, 0/ = 0Z + 2°C; lead coverage, 1-5% and (b) stable stratification, Qs‘ = 0zf - 2°C; lead coverage 1-5%, and (c) stable stratification as in Figure 2b, but for lead coverage of 10%. 4. Mesoscale Model The airflow over polynyas was simulated using a two-dimensional hydrostatic mesoscale planetary boundary layer model. The flow is forced by a large-scale pressure gradient represented by the geostrophic wind. The model has an (x,d) coordinate system with 62 grid points in the horizontal and 10 in the vertical at the approximate heights of 2, 10, 30, 50, 100, 200, 350, 600, 1100, and 2000 m. The upper boundary condition is ■ Vi applied at 3 km, where the wind becomes geostrophic (a couple of control runs were made /n using a 50-level version of the model extending up to 6 km; see section 6.2). All fluxes vanish at the horizontal boundaries, and the vertical velocity vanishes at the top (3 km) ..Vi and bottom. In the present experiments the grid length was 2 km with flat topography. Vertical diffusion is solved by an implicit method, and instead of explicit horizontal diffusion, a weak low-pass filter is applied to all fields. The model equations and details are given by Alestalo and Savijdrvi [1985]. The main modifications to the model for the present study were an inclusion of the air moisture and a development of the surface layer description by incorporating an iterative Monin-Obukhov scheme instead of the original Louis [1979] type of transfer coefficients. In the Ekman layer, turbulence is described by first-order closure with the vertical diffusion coefficient K - l2 (dU/dz) f(Ri), where the mixing length / = kz/(l+kz/e), 8 = 30 m. Her&f(Ri) is an empirical function depending • V i V; on the Richardson number. In unstable stratification, f(Ri) = (l-l6Ri)m for momentum and f(Ri) = [1-64Ri)in for heat and moisture. In stable stratification, max(0.1, 1-5Ri) is v .: • used for momentum, heat, and moisture. Over water the surface temperature is kept at the freezing point of -1.8°C. Over ice the surface temperature change is calculated from the energy balance determined by the turbulent fluxes of sensible and latent heat, the incoming shortwave radiation (zero in the 11 winter experiments), the net longwave radiation QL, and the heat flux through ice and snow S. We calculate QL from the empirical formula by Maykut and Church [1973]. In calculating S, we assume a linear temperature profile in the ice and snow, which should be reasonable, because the model is run into a steady state before analyzing the results. The experiments and the initial and boundary conditions used are shown in Tables la and lb. A polar inversion with dT/dz = 1 K km"1 is used as the initial temperature profile, and the initial wind profile is given as an Ekman-Taylor spiral. While calculating the turbulent fluxes by the Monin-Obukhov theory, we describe the stability effects using the universal functions of Hogstrom [1988] in unstable cases and those of Holtslag and de Bruin [1988] in stable cases. The (local) roughness length for momentum is set to 1 mm over ice, and over water it is calculated from the wind speed according to Smith [1980]. The (local) roughness lengths for heat and moisture are calculated according to Andreas [1987] over ice and according to Launiainen [1983] over water. Details of the surface layer parameterizations are given by Launiainen and Vihma [1990]. This model has been used previously in several studies of mesoscale circulation systems both for the Earth and for Mars [e.g., Savijarvi and Siili, 1993]. Savijarvi [1991] validated the model against an extensive boundary layer data set both in convective and stable conditions. 5. Simulations 5.1. Experiments The 2-D PEL model was used to simulate flow associated with long polynyas, 6-108 km wide. The whole model domain (124 km) was considered as representing a single grid square of a hypothetical GCM. The grid points of the mesoscale model (2 km apart) were set to be either totally ice covered or totally ice free without any subgrid size leads or ice patches. Thus we did not have to apply any of the methods (la) to (4) to parameterize 12 each of them being 20,10, and 6 km wide, respectively. The geostrophic wind was per pendicular to the polynyas. The fifth group was the multipolynyas case but with the geostrophic wind parallel to the polynyas. In the fourth and fifth groups the horizontal grid of tiie model was extended to 82 x 2 km in order to prevent disturbances arising from changes in the surface type too close to the inflow boundary (the results were analyzed from the 60 grid points in the middle of the domain, as in the other simulations). Finally, we modeled the flow over a single ice edge in the middle of the model domain using different directions of G. The simulations are summarized in Tables la and lb. Table la. Model Experiments Simulation Description Group 1 one polynya, seven mns;/= 0,0.1,0.3,0.5 0.7,0.9, and 1; G perpendicular to the ice edge Group 2 same as 1, but G parallel to the ice edge Group 3 same as 1, but an ice patch replacing the polynya Group 4 /= 0.5; four runs; number (and width) of polynyas as follows: 1 (60 km), 3 (20 km), 6 (10 km), and 10 (6 km); G perpendicular to the ice edge Group 5 same as 4, but G parallel to the ice edge Group 6 /= 0.5, single ice edge; a, on-ice G; b, off-ice G; c, G parallel to the ice edge Here /is the open water fraction and G is geostrophic wind speed. Table lb. Initial and Boundary Conditions for Model Experiments on July 1 at 70°S Variable Value Snow surface temperature Tj, °C -33 y Water surface temperature Tg, °C -1.8 Geostrophic wind G speed m s ' 10 ice roughness length z@, mm 1 water roughness length z0“', mm =0.05' temperature profile dT/dz, K km ' lf relative humidity RH, % 90 snow depth, m 0.2 ice thickness, m 0.7 heat conductivity of ice, W m"‘ K"‘ 2.1 heat conductivity of snow, W m"‘ K"' 0.3 V * Value is wind dependent. r 1 Value was -6.5 in group 3. ! y---: ■ 13 5.2. Flow properties 5.2.1. Single polynya (group 1 simulations). The general flow properties from the simulations with the polynya in the middle of the model domain are presented in Figure 3, where we take the case with 50% open water as an example. The surface layer results are comparable to field data for that latitude and season [Kottmeier and Hartig, 1990; Launiainen and Vihma, 1994], although the air and surface temperatures over the ice are somewhat lower than the observed mean values, because large-scale heat advection was lacking from the mesoscale model. The air temperature (Figure 3a) at 2 m increased over the polynya by approximately 0. l°C/km. The rise of air temperature was naturally largest at the lowest levels, as was also its decrease downwind of the polynya, because of recapture of heat by the ice. For example, in the case of a 50% open sea fraction the maximum warming was 6.6°C at a height of 2 m, while it was 4.2°C at a height of 100 m. Yet the temperature increase between the first and last grid point was the same, 4.1°C, at both levels. The behavior of specific humidity (Figure 3b) resembled that of air temperature, except that qs exceeded qz over the ice as well. The near-surface wind speed (Figure 3c) nearly doubled over the polynya (see section 5.7 for the reasons). The PEL was very unstable over the polynya, and the surface sensible heat flux H reached 520 W m"2, the latent heat flux XE reached 160 W m"2, and the net outgoing longwave radiation Qh reached 90 W m"2 (Figure 3d). Over the sea ice upstream of the polynya, stratification was stable, with a sensible heat flux H of -14 W m'2. Over the ice downstream of the polynya, stratification was even more stable due to warming of the air mass, and H had a minimum of -22 W m"2. The variations in the longwave radiation over the polynya in Figure 3d (reflected also in the surface temperature and sensible heat flux) were due to variations in cloudiness; a grid point in the mesoscale model is either cloud covered or cloud free (the effect is even more pronounced in Figure 4). The field of vertical velocity w was interesting, with a rising motion of 5 cm s"1 over the ice downwind of the polynya (Figure 3e). The maximum resulted primarily from stability effects at the ice edge: the heated air rose over the stable surface layer above the ice, as in a synoptic-scale warm front. The roughness change was less important for w. Because of the dramatic change in stability and increase in surface wind speed, the surface momentum flux (Figure 3f) was larger over the polynya than over the ice, although the roughness was higher over the ice. The edges of the polynya induced spikes in the momentum flux, because Zq changes immediately but the wind speed does not. 5.2.2. Single polynya with parallel wind (group 2). When the geostrophic wind blew parallel to the ice edge (Figure 4), the fields of air temperature and humidity, horizontal wind speed, and turbulent surface fluxes did not differ drastically from the cases with a perpendicular wind. Yet the air temperature was 13-16°C higher and the turbulent heat fluxes over the polynya therefore smaller. Because of surface friction, the near-surface wind deviates 15-20° to the left of the geostrophic wind, and this tends to produce a weak wind component across the polynya (v 2m -2m s'). This is the reason for the asymmetry in Figure 4. The cross-polynya component was not uniform, however, even changing the wind direction. This was because the surface temperature gradient induced strong sec ondary circulations, with a maximum vertical velocity of from 10 to 31 cm s"1 and an associated cross-polynya wind component (e.g., v2m varied from -4.1 m s"1 at X=70 km to 2.2 m s'1 atX= 38 km; compare Figure 4). The intense updraft area is seen in the surface 14 G 10 m/s v - ; z- -nV 50 100 X (km) *x - X (km) X (km) V t r. ?v X(km) v; Figure 3. Flow properties in the case of one polynya in the middle of the ice field with a 50% open , Vx , water fraction and G perpendicular to the ice edges. The location of ice is marked by the thick line intheXaxis. (a) Surface temperature (solid line) and air temperature at heights of 2 m (dashed line), 30 m (dot-dashed line), and 100 m (dotted line), (b) Surface specific humidity (solid line) and specific humidity in the air at heights of 2 m (dashed line), 30 m (dot-dashed line), and 100 m (dotted . _ line), (c) Wind speed at heights of 2 m (dashed line), 30 m (dot-dashed line), and 100 m (dotted •line), (d) Turbulent surface fluxes of sensible (solid line) and latent (dashed line) heat and the net longwave radiation at the surface (dot-dashed line), (e) Cross section of vertical velocity, (f) Surface ' momentum flux. 15 G 10 m/s © -15 WVVn/ X(km) X (km) S 150- X (km) X (km) «§. 1000 X (km) X (km) Figure 4. Flow properties in the case of one polynya in the middle of the ice field with a 50% open water fraction and G parallel to the ice edges. The location of ice is marked by the thick line in the X axis, (a) Surface temperature (solid line) and air temperature at heights of 2 m (dashed line), 30 m (dot-dashed line), and 100 m (dotted line), (b) Surface specific humidity (solid line) and specific humidity in the air at heights of 2 m (dashed line), 30 m (dot-dashed line), and 100 m (dotted line), (c) Wind speed at heights of 2 m (dashed line), 30 m (dot-dashed line), and 100 m (dotted line), (d) Turbulent surface fluxes of sensible (solid line) and latent (dashed line) heat and the net longwave radiation at the surface (dot-dashed line), (e) Cross section of vertical velocity, (f) Surface momentum flux. 16 G 10 m/s y -5 :*.• X (km) X(km) f ■' O' ‘ X (km) X (km) W (cm/s) 1500 - ' X (km) -'»; Figure 5. Flow properties in the case of a single ice patch surrounded by open ocean, 50% open V water fraction. The location of ice is marked by the thick line in the X axis, (a) Surface temperature (solid line) and air temperature at heights of 2 m (dashed line), 30 m (dot-dashed line), and 100 m ' (dotted line), (b) Surface specific humidity (solid line) and specific humidity in the air at heights ■/?. of 2 m (dashed fine), 30 m (dot-dashed line), and 100 m (dotted line), (c) Wind speed at heights of 2 m (dashed fine), 30 m (dot-dashed fine), and 100 m (dotted line), (d) Turbulent surface fluxes of . sensible (solid line) and latent (dashed fine) heat and the net longwave radiation at the surface , (dot-dashed line), (e) Cross section of vertical velocity, (f) Surface momentum flux. mmm 17 layer as a maximum of air temperature but as locally reduced values of horizontal wind speed and turbulent surface fluxes. The mesoscale cell grew in strength during the first 72 hours of simulation, but it transferred heat horizontally and diminished the surface temperature difference between the ice and the polynya. Thus the cell destroyed its own driving force and became gradually less intense, with only 1-3 cm s'1 maximum updrafts after 192 hours! of simulation. For this reason we did not run the model to a steady state in these simulations. The steady state would not represent a wintertime temperature contrast and would require the wind direction to have remained constant for almost 10 days, which is unrealistic for most high-latitude sites (except, perhaps, for katabatic winds, but they are not normally parallel to polynyas). Moreover, if the ice could drift freely with the wind, the polynya would be closed in such a time (assuming an approximately 3% drift ratio and 20-30° turning angle). As a result, we analyzed the model fields after 72 hours of integration, which represents the maximum strength of the mesoscale circulations. The maximum vertical velocity in the mesoscale cell depends not only on the simulation time, but also on the grid length used, the maximum values after 72 hours being 28, 20, and 13 cm s'1 with respective grid lengths of 2, 4, and 6 km. This is mainly because the intense updraft area is narrow, although the hydrostatic assumption also may overestimate vertical velocities for relatively small grid lengths. The simulations with different grid lengths yielded otherwise similar results. 5.2.3. Ice patch (group 3). Figure 5 shows results from runs with ice in the middle (with G perpendicular to the ice edge). The initial temperature profile was now dT/dz = -6.5 K km'1 corresponding to the open-ocean conditions at the inflow boundary. Now the PEL over the open water is near neutral and becomes stable over the cold ice. The air temperature (2 m) diminishes toward the downwind edge of the ice patch by only 4°C, while the wind speed is reduced to almost half. For two reasons the modification in air temperature is now smaller than in the case with a polynya surrounded by ice. First, in the stable conditions the turbulent fluxes are smaller, and second, even the relatively small downward heat flux (Figure 5d) is able to affect the snow surface temperature, while in the polynya case the water temperature is not changed (see also Briimmer et al. [1994]). Owing to stability effects, the momentum flux over the ice is reduced to half of its value over the ocean. This agrees with the observations of Fairall and Markson [1987] in the Marginal Ice Zone Experiment. 5.2.4. Many polynyas (groups 4 and 5). The distributions of air temperature and wind speed resulting from simulations with a varying number of polynyas are presented in Figure 6. In cases with G perpendicular to the ice edges we note that the amplitude of the variations in air temperature and wind speed decreases with an increasing number of polynyas. The modification in air temperature (10 m) across one polynya with respect to the surface temperature change (80 1Om/80,y) decreases from the 0.20 of the single-polynya case down to the 0.04 of the 10-polynya case, but the total warming over the model domain remains the same. The pattern of surface wind speed (Figure 6b) resembles that of air temperature, except that the wind speed adjusts to the new conditions faster than air temperature. The grid-averaged wind speed is not especially sensitive to the number of polynyas. When G was set parallel to the ice edges, the temperatures were much higher. The asymmetry is again due to the wind component across the polynya. The distribution of surface heat fluxes appeared as square waves, as in Figures 3d and 4d. 18 f = 50%, 1-10 polynyas across G 10 m/s G 10 m/s X(km) X(km) G 10 m/s - G10 m/s X(km) X(km) Figure 6. Air temperature and wind speed at a height of 10 m across the model domain with the ' ’' . _ following numbers of polynyas: one (solid line), three (dashed line), six (dot-dashed line), and 10 S'" •:-7 (dotted line), (a) Air temperature with G perpendicular to the polynyas. (b) Wind speed with G perpendicular, (c) Air temperature with G parallel, (d) Wind speed with G parallel. ./ -. .•v- ■.*. We already saw from Figure 4e that the geostrophic wind parallel to the ice edges resulted in vigorous secondary circulations with strong updrafts and downdrafts. With parallel G the maximum updrafts were strongly reduced with increasing number (de creasing width) of polynyas, being 27.8, 24.5, 13.6, and 10.5 cm s'1 for 1, 3, 6, and 10 polynyas, respectively. With perpendicular G the maximum updrafts varied from 5.1 cm s'1 (one polynya) to 3.2 cm s'1 (10 polynyas). 5.2.5. A single ice edge. The flow properties in the experiments with a single ice edge were basically similar to those shown in Figures 3 to 5, with the exception that the features over the downstream edges were, of course, lacking. For example, there was neither heat nor momentum recapture by the ice, and in the case of an off-ice wind, the maximum vertical velocity was only 2.9 cm s'1, while it was 5.1 cm s'1 over the downwind edge of a polynya. It was interesting that a single ice edge caused rising motion over the downwind side both with on-ice and off-ice winds. In the former the small vertical velocities (maximum 1.0 cm s'1) were the result of the increase in roughness (compare to Andreas etal. [1984]), while in the latter it was the surface heat that produced the convection. 5.2.6. Cloudiness. Generally, open water induced rising motions resulting in cloud formation (relative humidity reaching 100%), but clouds were also sometimes formed upwind of polynyas (the initial relative humidity was 90% with no clouds). In the case of no open water the whole model domain was covered by fog from 2 to 600 m, while in the case of no ice a continuous cloud cover was formed at 1 km (a cloud is lifted fog in the \ S' X 19 model). With a single polynya and G perpendicular to it, a typical situation was of fog forming over the polynya and extending up to 350 m. Over the polynya and downwind of it a cloud cover existed between 200 and 600 m. With parallel G the polynya was typically covered by cloud at 1-2 km, but usually, there was no fog in the model domain. With an ice patch surrounded by open ocean a thin cloud at 1 km overcast the domain. The experiments with several polynyas resulted in basically similar cloudiness to that of a single polynya, except that the cloud cover became more uniform when the number of polynyas increased. 5.2.7. Blending height A blending height b has been suggested for surface flux calculations using equations (lc) and (2a). In our simulations the blending height was, however, not very well defined. The flow only approached horizontal homogeneity at heights at which it was already far from local equilibrium. This was probably because the extreme differences in the surface temperature considerably modified the flow field. Yet it was usually possible to find zmin, a height at which the sum of deviations from local equilibrium and deviations from horizontal homogeneity attained a minimum. Claussen [1990] derived the following equation: zmin = 0.7z0fL/z0)4/5. According to Mason [1988], b should depend on the flow and terrain as b = 2[uJV(b)]2Lc, where Lc is the horizontal length scale of each region of different Zq . In the present study, however, a strong dependence of zmin on the surface layer stability was found. In the cases with a polynya surrounded by sea ice (unstable) the average zmin was 63 m, while in the cases of an ice patch surrounded by open ocean (stable) it was 11m. Claussen’s equation, which is not sensitive to stability, yielded results differing substantially from the present model results. The discrepancy probably resulted from horizontal scales different from those in our study. The estimates based on Mason’s equation were of the right order of magnitude but were too high in strongly stable cases and too sensitive to Lc. In the following we shall para meterize the fluxes using various reference heights and compare the results. 5.3. Grid-Averaged Surface Fluxes The area-averaged surface fluxes of sensible and latent heat as a function of ice coverage in the single-polynya cases are presented in Figure 7. The marked difference between the cases of a polynya surrounded by sea ice and a sea ice patch surrounded by open ocean is very evident. (Remember that the initial 8 2m at the inflow boundary was set equal to the local Qs. Therefore cases with/= 1 and/= 0 are not drawn in Figure 7 when the upstream 0Z changes.) In general, polynya width (km) open water fraction V'7 '■) 0.4 0.5 0.6 0.7 0.8 0.9 open water fraction nolvnva width fkml / v - ; open water fraction : ✓ ! * •' 't 0.4 0.5 . 0.6 open water fraction Figure 7. Grid-averaged surface fluxes as a function of the open water fraction, (a) • ‘ ' Sensible heat flux, (b) Latent heat flux, (c) Net longwave radiation: (d) Momentum flux. ■ The solid lines denote cases with G perpendicular to a polynya surrounded by ice, the < dotted lines denote cases with G parallel to a polynya, and the dashed lines denote cases 'i V. •' with G perpendicular to an ice patch surrounded by open ocean. y -- /! . /'i ' -A . 86 WSi 21 b) 250 10 3 i "I 200 1 - r iso ' ______ a J U 0 ) 20 40 60 width ofpolynyas (km) Figure 8. Grid-averaged surface fluxes as a function of the polynya width and the number of polynyas. The lines with (without) circles represent simulations with the geostrophic wind parallel (perpendicular) to the ice edge showing (a) sensible (solid lines) and latent (dashed lines) heat flux and (b) net longwave radiation (solid lines) and momentum flux (dashed lines). 5.4. Vertical Distribution of Heat Explicit modeling for the rise of a heat plume from a polynya affected by entrainment processes would require a large-eddy resolving model. In die present model the growth of the internal boundary layer was due to turbulent diffusion (described by the mixing length theory) and mesoscale circulations. In addition, processes such as roll circulations on a scale of about 1 km could enhance the entrainment [Briimmer et al., 1994]. Accordingly, the model results merely represent a lower limit for the plume rise. A better study of the topic would also require simulations with a larger variety of initial conditions such as surface temperature, background stability, and wind speed. Despite these reser vations we briefly present the model results. G perpendicular to a polynya resulted in the highest plume rise, usually (f > 0.1) extending up to 600 m (700 m when the 50-level model was used; see section 6.2), where the air temperature above and downwind of the polynya still exceeded the upstream value by 1-2°C. Equation (13) derived for narrower leads by Glendening and Burk [1992] generally predicts a higher plume rise than obtained by the mesoscale model, for example, 2800 m for the case with/= 0.5 (single polynya). The plume rise was only slightly reduced with an increasing number (decreasing width) of polynyas n, e.g., with n = 10 the warming at the height of 600 m was some 80% of that with n= 1. With parallel G, warming of at least 1°C reached a height of 350 m (500 m with the 50-level model) with/= 0.1-0.5. When an ice patch was surrounded by open ocean, the cooling effect was smaller; even a fetch of 108 km over the ice resulted in a cooling of no more than 1°C at a height of 100 m. In general, the heights affected by the surface heating were well above the typical lowest level of a GCM. .V-‘ 22 5.5. Further Experiments The primary simulations were made to study the effects of open ocean fraction, width and number of polynyas, direction of the geostrophic wind with respect to the polynya, and the distribution of surface layer stability (polynya or ice in the middle of the model domain). In addition, there are several other topics which are of interest, and thus we made some more simulations. 5.5.1. Geostrophic wind speed. The first topic chosen is the importance of the geos trophic wind speed. The standard case with/= 0.5 and G perpendicular to a polynya (group 1) was also simulated with G = 3,5,7,15, and 20 m s'1. The flow properties were basically similar to the run with G = 10 m s'1, but naturally the turbulent fluxes were proportional to G, f - KZ weighting factors: g w = 0.5 and g e = 0.2. The values were estimated on the basis of the flow properties and are discussed in section 6.2. The parameterized results compared to those from the 2-D model are presented in Figure 9. The mean absolute deviation from the 2-D model result 1 for each parameterization scheme is given in Tables 2 and 3. Because the case with some 10% open water fraction with a polynya in the middle of the ice field represents a typical situation in polar oceans, results for this case are given separately. The mesoscale model levels close to zmin in various flow situations were used as reference heights in the calculations and are given in Tables 2 and 3. We see from the results that the parameterized Table 2. Mean Absolute Error in Grid-Averaged Turbulent Sensible Heat Flux One Polynya, /= 50%, Number of Single Ice Edge, varying width and/ Polynyas Varies /= 50% , - i Equation Unstable Cases Stable G Unstable G On-Ice Off-Ice Parallel All /= 10% Cases Parallel Cases Parallel Flow Flow Flow (lb) 83 13 8 24 74 20 9 86 29 (lc) 22 2 9 17 12 9 6 21 17 (2a) 19 1 6 15 12 13 10 20 13 (4) 5 8 4 9 10 6 7 1 7 All values are in watts per square meter. Here/is open water fraction and G is geostrophic wind speed. Reference heights used in calculations are as follows: 100 m in unstable cases, 10 min stable cases, and 30 m when G is parallel to ice edges. 24 ■; V-,,: - open water fraction open water fraction open water fraction Figure 9. Applicability of the following various schemes to parameterize Table 3. Mean Absolute Error in Grid-Averaged Turbulent Latent Heat Flux One Polynya, /= 50%, Number of Single Ice Edge, varying width and/ Polynyas Varies /= 50% Equation Unstable Cases Stable G Unstable G On-Ice Off-Ice Parallel All /= 10% Cases Parallel Cases Parallel Flow Flow Flow (lb) 23 4 1 4 20 4 1 20 5 (lc) 4 1 5 7 9 15 1 4 7 (2a) 1 0 1 1 3 1 4 2 1 (4) 5 2 1 1 8 2 3 8 1 See Table 2 footnotes. ' The accuracy of the parameterization methods is typically of the order of 10-20 W m* 2 i in simulations with a polynya surrounded by ice and about 5-10 W m"2 in cases with smaller 6.2. Sensitivity Tests 6.2.1. Vertical resolution of the mesoscale model. The principal simulations were made using a 10-level version of the mesoscale model, with a high resolution near the ground and a lower one in the upper layers. This was supposed to be adequate, because the surface fluxes are determined by the differences between the ground and the reference level of 10-100 m. The simulation of processes higher up might, however, suffer from the lower vertical resolution (although the 10-level model was well validated by Savijarvi [1991] both in convective and stable conditions). These processes may have indirect influence in the surface layer as well. A 50-level version of the model was therefore built extending the vertical grid up to 6 km, and a couple of control runs were made. The cases with 50% polynya fraction both with perpendicular and parallel wind were selected. The results demonstrated that the flow properties and the surface fluxes were very close to those produced by the 10-level model. The vertical velocities were, however, reduced, and this slightly affected the formation of clouds. This yielded local differences in the surface longwave radiation but not much in the rest of the surface fluxes (in sensible heat flux the results were the same within 3-4 W m"2). The applicability of the parameterization schemes was not affected; the best results were again produced by (4). Thus we regard the results obtained with the 10-level model as reasonably reliable. 6.2.2. Wind speed. When G ranged from 3 to 20 m s'1, the applicability of the para meterization schemes of (la) - (4) was similar to that in the cases with G = 10 m s"1. Equation (4) produced the best results, and (lb), the worst ones. T7- 7T T7^ -1' t 26 6.2.3. Roughness lengths. The sensitivity of some of the methods to different choices of roughness lengths and to functions describing the stability effects was tested. Using the method (lc) the effective roughness length for temperature Ztcfr was basically calcu lated as a logarithmic area average of the local zt. According to Wood and Mason [1991], Z?* should be less than that, but this is not supported by our results. For comparisons we also used the following methods. Zj^was first calculated by the method of Taylor [1987], and Z^[ was then obtained from the roughness Reynolds number and Z£a applying the formula of Andreas [1987] originally developed for local roughness lengths over snow and sea ice. Z,cff was now below the logarithmic area average, but the fluxes were far too low. We also made calculations with the formula of Garratt [1978] developed for rough land surfaces; Z0ea IZlett= 7. The results were about the same as those obtained using the logarithmic area average for Ztcff. 6.2.4. Stability effects. The comparison of different methods to parameterize the local stability effects is reasonable, because the iterative procedure used in the mesoscale model [LauniainenandVihma, 1990] is impractical for use in a GCM. It was used in the mesoscale r»- "■*. model to get as reliable surface fluxes as possible. In the parameterization schemes (2a) i * ■ and (4) the iteration procedure was replaced by estimating 10/Lfrom the bulk Richardson number RiB according to Donelan [1982]: 10ZL = 6.0 x RiB for the stable region and 10fL = 7.6 x RiB for the unstable region. This produced a small error of 10 W m"2 in the local sensible heat flux over a polynya. Over the stably stratified sea ice the error was close to zero. Other alternatives were to use the analogous forms of Large and Pond [1982], r- Andreas and Murphy [1986], or Launiainen [1995]. The results did not differ much from :vV those obtained using the form of Donelan [1982], the results using Launiainen [1995] being closest to the iterative solution. The differences in H’w arising from the use of various values for the turbulent Prandtl number Pr and von Karman constant k are, however, much larger. Using the xg functions of Businger et al. [1971] with Pr = 0.74 and k = 0.35, the <"■ < sensible heat flux over a winter polynya was some 50-150 W m"z higher than that based on the xg functions of Hogstrom [1988], with Pr = 1.0 and k = 0.4. We used the latter combination in the mesoscale model and in all of the parameterization schemes where xg functions are involved. 6.2.5. Subgrid variations in surface roughness. In cases with open sea surrounded or bounded by a rough land surface the grid-averaged heat fluxes are more sensitive to variations in the surface roughness. To study this, we changed the z„ of ice (1 mm) to a ' Vv value typical for a land surface (0.3 m) and simulated a flow from land to sea (analogous . T to the group 6 c case). The results demonstrated a very sensitive dependence of -' i. 27 height; the simple scheme (lb) produced far too large an 6.3. Net Longwave Radiation 1 The accuracy of the parameterization of the net longwave radiation depends above all on the distribution of cloudiness. QL was calculated using the mixture (6) and mosaic methods (7), as well as an extended mosaic method, in which the cloudiness was also separated into N’ and AT. Because the flow properties indicated that clouds typically form over the polynyas, as large a portion of Table 4. Mean Absolute Error in Grid-Averaged Longwave Radiation Flux One Polynya, /= 50%, Number of Single Ice Edge, varying width and/ Polynyas Varies /= 50% Equation Unstable Cases Stable G Unstable G On-Ice Off-Ice Parallel All /= 10% Cases Parallel Cases Parallel Flow Flow Flow (6) 9 1 3 4 1 15 1 16 15 (7) 12 1 2 4 4 16 1 20 16 (7),Ntw 8 1 2 4 4 11 1 3 12 See Table 2 footnotes. Reference height for air temperature is 30 m. Considering the results in general, the difference between the mixture and the mosaic approaches with respect to the surface temperature was small, and the reference height for air temperature in (6) and (7) had only a minor effect. The results are shown in Figure 10 (selected cases) and Table 4 (all cases). The absolute errors were usually small, mostly less than 10 W m"2 and never exceeding 20 W m*2 . The relative error was, however, large in certain cases (perpendicular G across a polynya, parallel G with several polynyas, single ice edge). These cases involved subgrid variations in cloudiness; both the mixture and mosaic methods succeeded well only if the cloud cover was uniform, as with/= 0 and 0.1 in Figure 10a. If the variations were systematic (clouds over open water, clear skies over ice), the mosaic method with separated cloudiness Ni,w considerably improved the 28 3= results. An example is given in Figure 10b: an off-ice wind results in completely clear skies over the ice and continuous cloudiness over the open ocean, and methods using b) 80 60 40 ■ V. 20 -v'V 0 -20 I 0.5 G: on-ice off-ice parallel V* *' • open water fraction Figure 10. Applicability of the following various schemes to parameterize 6.4. Momentum Flux The principal groups of simulations (1-6, compare Table la) were analyzed to para meterize CG = 0.00075(<0S> - <630m>) + 0.0286 (14) 29 The constants would vary slightly for reference heights other than 30 m. In practice, the lowest level of a GCM would be a good choice for the reference height. The results shown in Figure 11 and Table 5 were obtained using (14) with (12). We see that (12) gives practically as good results as the methods based on the surface wind, (8) - (11). The uncertainty is, in general, of the order of 10-30 mN m"2. Moreover, the surface winds over polar oceans are uncertain in any models. They depend interactively on the surface momentum flux but also on the momentum exchange at upper levels of the atmospheric boundary layer. Therefore we feel that the most reasonable way to parameterize surface momentum flux is the use of Cc. Knowledge of its dependence on stability is, however, vital to get accurate results. open water fraction open water fraction G (m/s) Figure 11. Grid-average of surface momentum flux as a function of the open water fraction (a,c) and wind speed (b,d). The mesoscale model results (solid lines) and parameterized results based on the surface wind are drawn in (a) and (b); parameterized results using equation (8), (dashed lines), (9) (dot-dashed lines), (10) (dotted lines), and (11) (dotted lines with circles). The mesoscale model results (solid lines) and parameterized results based on (12) with CG from (14) are drawn in (c) and (d); reference heights 30 m (dashed lines), 100 m (dot-dashed lines) and 1 km (dotted lines). ' " 30 > 32 if applied over a coastal area having large subgrid variations in surface roughness. In most of today ’s GCMs the grid squares in coastal areas are set to be either wholly sea or land, but they could be presented as polynyas using the fraction of land and sea in each grid square. This would allow a more realistic representation of the coastline. It should beremembered that we assumed through this paper that the surface temperature is a variable in a GCM. If it is specified, e.g., climatologically, far larger errors are to be expected in the surface fluxes . Even if 0S is calculated in the GCM, it depends interactively on the surface fluxes, and errors in calculating it cause errors in the fluxes as well. Accordingly, the real accuracy of the fluxes that can be expected in a GCM is not quite as good as the results presented in Figure 9 and Tables 2-4 would indicate. (In para ■A'V meterizing the heat fluxes, we used the true grid-averages of <05> and I::- 33 Fluxes on the scale of turbulence are not the only process affecting the vertical transport on a subgrid scale. For example, Kottmeier and Engelbart [1992] observed mesoscale circulations in the atmospheric boundary layer induced by the surface temperature gradient at an Antarctic ice shelf front. Our mesoscale model also produced such circulations, as described in section 5.2. The circulations transported heat and moisture upward, the flux divergences tending to cool and dry the lowest hundreds of meters and heat and moisten the layers above. Parameterization of these mesoscale fluxes is the topic of a paper in preparation. 8. Conclusions The basic results of this study could easily be applied in GCMs as follows. (1) Para meterize the turbulent surface heat fluxes using an extended mosaic method with estimates for the air temperature and wind speed over the ice and open water. Use a reference height of the order of 100 m, if the overall stratification is unstable, and of the order of 10 m if stable. Since the GCM does not necessarily provide values at these heights, the values at the GCM grid levels should somehow be interpolated to the blending height. (2) Para meterize the radiative flues at the surface using the mosaic method with estimates for albedo and cloudiness over the ice-covered and ice-free parts of the grid square. (3) Parameterize the skin drag portion of the surface momentum flux on the basis of the atmospheric pressure field using a geostrophic drag coefficient dependent on the air-surface temperature difference. According to the study of Chapman et al. [1994], the lead fraction and the sensible heat and momentum transfer coefficients were the parameters to which an Arctic sea ice model was most sensitive. Thus great benefit would come from efforts to discover optimal methods for calculating the heat and momentum exchange processes. As the mesoscale model results are not complete, these efforts should also include observations of the polar atmospheric boundary layer, not only over narrow leads, but also on the mesoscale. Acknowledgments. I am grateful to Hannu Savijarvi for providing me with the 2-D < mesoscale model. Jouko Launiainen and Hannu Savijarvi are acknowledged for comments on the manuscript and Alexander Makshtas, James E. Overland, and Dirk Dethleff (who also provided me with a satellite image for Figure 1) for discussions. I thank Martin Claussen and two other reviewers for their comments and suggestions. References Alestalo, M., and H. Savijarvi, Mesoscale circulations in a hydrostatic model: Coastal convergence and orographic lifting, Tellus, Ser. A, 37A, 156-162,1985. Andreas, E.L., A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice, Boundary Layer Meteoroi, 38, 159-184,1987. , Andreas, E.L., and A.P. Makshtas, Energy exchange over Antarctic sea ice in the spring, J. Geophys. Res., 90, 7119-7212,1985. ■i. "Jt 34 Andreas, E.L., and B. Murphy, Bulk transfer coefficients for heat and momentum over leads and polynyas, J. Phys. Oceanogr., 16,1875-1883,1986. Andreas, E.L., C.A. Paulson, R.M. Williams, R.W. Lindsay, and J.A. Businger, The turbulent heat flux from Arctic leads, Boundary Layer Meteorol., 17, 57-91,1979. Andreas, E.L., W.B. Tucker, and S.F. Ackley, Atmospheric boundary layer modification, drag / coefficient, and surface heat flux in the Antarctic marginal ice zone, J. Geophys. Res., 89, 649-661,1984. Ary a, S.P.S., A drag partition theory for determining the large-scale roughness parameter and wind stress on the Arctic pack ice, J. Geophys. Res., 80, 3447-3454,1975. v.-’ Bromwich, D.H., and D.D. Kurtz, Katabatic wind forcing of the Terra Nova Bay polynya, J. Geophys. Res., 89, 3561-3572,1984. Briimmer, B., B. Busack, H. Hoeber, and G. Kruspe, Boundary-layer observations over open water '■i: and Arctic sea-ice during on-ice air flow, Boundary Layer Meteorol., 68, 75-108,1994. Businger, J.A., J.C. Wyngaard, Y. Izumi, and E.F. Bradley, Flux-profile relationships in the atmospheric surface layer, J. Atmos. Sci., 28, 181-189,1971. Cavalieri, D.J., and S. Martin, A passive microwave study of polynyas along the Antarctic Wilkes Land coast, in Oceanology of the Antarctic Continental Shelf, Antarct. Res. Ser., vol. 43, edited -'V1 by S.S. Jacobs, pp. 227-252, AGU, Washington, D.C., 1985. Chapman, W.L., W.J. Welch, K.P. Bowman, J. Sacks, and J.E. Walsh, Arctic sea ice variability: Model sensitivities and a multidecadal simulation, J. Geophys. Res., 99, 919-935,1994. Claussen, M., Area-averaging of surface fluxes in a neutrally stratified, horizontally inhomogeneous atmospheric boundary layer, Atmos. Environ. Part A, 24A, 1349-1360,1990. Claussen, M., Local advection processes in the surface layer of the marginal ice zone, Boundary Layer Meteorol., 54,1-27,1991a. V - Claussen, M., Estimation of areally-averaged surface fluxes, Boundary Layer Meteorol., 54, 387-410, 1991b. •l-V. 1% Comiso, J.C., and A.L. Gordon, Recurring polynyas over the Cosmonaut Sea and the Maud Rise, J. Geophys. Res., 92, 2819-2833,1987. den Hartog, G., S.D. Smith, R.J. Anderson, D.R. Topham, and R.G. Perkin, An investigation of a i polynya in the Canadian archipelago, 3, Surface heat flux, J. Geophys. Res., 88, 2911-2916, 1983. Dethleff, D„ Polynyas as a possible source for enigmatic Bennett Island atmospheric plumes, in The Polar Oceans and Their Role in Shaping the Global Environment, Geophys. Monogr. Ser., vol. 85, edited by O.M. Johannessen, R.D. Muench, and J.E. Overland, pp. 475-483, AGU, Washington, D.C., 1994. Donelan, M.A., The dependence of the aerodynamic drag coefficient on wave parameters, in Proceedings of First International Conference on Meteorology and Air-Sea Interaction of the CoastalZone, pp. 381-387, Am. Meteorol. Soc, Boston, Mass., 1982. Fairall, C.W., and R. Markson, Mesoscale variations in surface stress, heat fluxes, and drag coefficient in the marginal ice zone during the 1983 Marginal Ice Zone Experiment, J. Geophys. Res., 92, 6921-6932,1987. Garratt, J.R., Transfer coefficients for a heterogeneous surface of large aerodynamic roughness, Q. «' < V J. R. Meteorol. Soc., 104, 491-502,1978. 'r : r\- r. rsn ■tr ' -V-; , 29 The constants would vary slightly for reference heights other than 30 m. In practice, the lowest level of a GCM would be a good choice for the reference height. The results shown in Figure 11 and Table 5 were obtained using (14) with (12). We see that (12) gives practically as good results as the methods based on the surface wind, (8) - (11). The uncertainty is, in general, of the order of 10-30 mN m*2 . Moreover, the surface winds over polar oceans are uncertain in any models. They depend interactively on the surface momentum flux but also on the momentum exchange at upper levels of the atmospheric boundary layer. Therefore we feel that the most reasonable way to parameterize surface momentum flux is the use of CG. Knowledge of its dependence on stability is, however, vital to get accurate results. open water fraction 0.15 - open water fraction G (m/s) Figure 11. Grid-average of surface momentum flux as a function of the open water fraction (a,c) and wind speed (b,d). The mesoscale model results (solid lines) and parameterized results based on the surface wind are drawn in (a) and (b); parameterized results using equation (8), (dashed lines), (9) (dot-dashed lines), (10) (dotted lines), and (11) (dotted lines with circles). The mesoscale model results (solid lines) and parameterized results based on (12) with CG from (14) are drawn in (c) and (d); reference heights 30 m (dashed lines), 100 m (dot-dashed lines) and 1 km (dotted lines). 30 Table 5. Mean Absolute Error in Grid-Averaged Skin Drag One Polynya, /= 50%, Number of Single Ice Edge, varying width and / Polynyas Varies /= 50% :(. Equation Unstable Cases Stable G Unstable G Off-Ice Flow All /= 10% Cases Parallel Cases ■ Parallel (8) 8 5 3 11 5 8 18 (9) 27 10 21 26 30 33 39 go); 30 7 17 22 30 26 59 (11) 16 7 2 17 15 11 49 (12)* 12 11 7 13 4 11 23 Reference height is 30 m with all the equations. ' Z£n from Taylor's [1987] method was used. * Equation (14) was used for CG when applying (12). 7. Discussion The parameterization of surface heat and momentum fluxes over ice-covered oceans was studied considering cases with large areas of open water. The following wide group 1 < of cases was studied: a single polynya of varying width in the middle of an ice field, an ice patch of varying width surrounded by open ocean, varying number of polynyas in the ice field, and a single ice edge. The simulations were made using different directions of the geostrophic wind. In addition to the turbulent surface heat fluxes, we examined the surface momentum flux and the net longwave radiation flux at the surface. The vertical (-V- distribution of heating was studied as well. :vv, ■ The basic problem for the study was how to produce a grid-averaged surface heat flux using the following variables known in a GCM: <6Z>, <05>, .. t—*- - • Z<- 31 ations (cold air advected over a polynya, warm air advected over ice, parallel flow), as seen in Figure 7, but the applicability of the parameterization schemes did not depend much on the flow situation. Considering the turbulent surface heat fluxes, the results can be summarized as follows. The use of transfer coefficients dependent on stability is essential. Neutral transfer coefficients (lb), which are still used in some models, can yield errors of70-80 W m'2 in if applied over a coastal area having large subgrid variations in surface roughness. In most of today ’s GCMs the grid squares in coastal areas are set to be either wholly sea or land, but they could be presented as polynyas using the fraction of land and sea in each grid square. This would allow a more realistic representation of the coastline. It should beremembered that we assumed through this paper that the surface temperature is a variable in a GCM. If it is specified, e.g., climatologically, far larger errors are to be expected in the surface fluxes. Even if Qs is calculated in the GCM, it depends interactively on the surface fluxes, and errors in calculating it cause errors in the fluxes as well. Accordingly, the real accuracy of the fluxes that can be expected in a GCM is not quite as good as the results presented in Figure 9 and Tables 2-4 would indicate. (In para meterizing the heat fluxes, we used the true grid-averages of <05> and Fluxes on the scale of turbulence are not the only process affecting the vertical transport on a subgrid scale. For example, Kottmeier and Engelbart [1992] observed mesoscale circulations in the atmospheric boundary layer induced by the surface temperature gradient at an Antarctic ice shelf front. Our mesoscale model also produced such circulations, as described in section 5.2. The circulations transported heat and moisture upward, the flux divergences tending to cool and dry the lowest hundreds of meters and heat and moisten the layers above. Parameterization of these mesoscale fluxes is the topic of a paper in preparation. 8. Conclusions The basic results of this study could easily be applied in GCMs as follows. (1) Para meterize the turbulent surface heat fluxes using an extended mosaic method with estimates for the air temperature and wind speed over the ice and open water. Use a reference height of the order of 100 m, if the overall stratification is unstable, and of the order of 10 m if stable. Since the GCM does not necessarily provide values at these heights, the values at the GCM grid levels should somehow be interpolated to the blending height. (2) Para meterize the radiative flues at the surface using the mosaic method with estimates for albedo and cloudiness over the ice-covered and ice-free parts of the grid square. (3) Parameterize the skin drag portion of the surface momentum flux on the basis of the atmospheric pressure field using a geostrophic drag coefficient dependent on the air-surface temperature difference. According to the study of Chapman etal. [1994], the lead fraction and the sensible heat and momentum transfer coefficients were the parameters to which an Arctic sea ice model was most sensitive. Thus great benefit would come from efforts to discover optimal methods for calculating the heat and momentum exchange processes. As the mesoscale model results are not complete, these efforts should also include observations of the polar atmospheric boundary layer, not only over narrow leads, but also on the mesoscale. Acknowledgments. I am grateful to Hannu Savijarvi for providing me with the 2-D mesoscale model. Jouko Launiainen and Hannu Savijarvi are acknowledged for comments on the manuscript and Alexander Makshtas, James E. Overland, and Dirk Dethleff (who also provided me with a satellite image for Figure 1) for discussions. I thank Martin Claussen and two other reviewers for their comments and suggestions. References Alestalo, M., and H. Savijarvi, Mesoscale circulations in a hydrostatic model: Coastal convergence and orographic lifting, Tellus, Ser. A, 37A, 156-162,1985. Andreas, E.L., A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice, Boundary Layer Meteorol., 38, 159-184,1987. Andreas, E.L., and A.P. Makshtas, Energy exchange over Antarctic sea ice in the spring, J. Geophys. Res., 90, 7119-7212,1985. w: A m r 34 Andreas, E.L., and B. Murphy, Bulk transfer coefficients for heat and momentum over leads and polynyas, J. Phys. Oceanogr., 16, 1875-1883,1986. Andreas, E.L., C.A. Paulson, R.M. Williams, R.W. Lindsay, and J.A. Businger, The turbulent heat flux from Arctic leads, Boundary Layer Meteorol., 17, 57-91,1979. Andreas, E.L., W.B. Tucker, and S.F. Ackley, Atmospheric boundary layer modification, drag coefficient, and surface heat flux in the Antarctic marginal ice zone, J. Geophys. Res., 89, 649-661,1984. Arya, S.P.S., A drag partition theory for determining the large-scale roughness parameter and wind stress on the Arctic pack ice, J. Geophys. Res., 80, 3447-3454,1975. Bromwich, D.H., and D.D. Kurtz, Katabatic wind forcing of the Terra Nova Bay polynya, J. Geophys. Res., 89, 3561-3572,1984. Brummer, B., B. Busack, H. Hoeber, and G. Kruspe, Boundary-layer observations over open water and Arctic sea-ice during on-ice air flow, Boundary Layer Meteorol., 68, 75-108,1994. Businger, J.A., J.C. Wyngaard, Y. Izumi, and E.F. Bradley, Flux-profile relationships in the atmospheric surface layer, J. Atmos. Sci., 28, 181-189,1971. Cavalieri, D.J., and S. Martin, A passive microwave study of polynyas along the Antarctic Wilkes Land coast, in Oceanology of the Antarctic Continental Shelf, Antarct. Res. Ser., vol. 43, edited by S.S. Jacobs, pp. 227-252, AGU, Washington, D.C., 1985. Chapman, W.L., W.J. Welch, K.P. Bowman, J. Sacks, and J.E. Walsh, Arctic sea ice variability: Model sensitivities and a multidecadal simulation, J. Geophys. Res., 99, 919-935,1994. Claussen, M., Area-averaging of surface fluxes in a neutrally stratified, horizontally inhomogeneous atmospheric boundary layer, Atmos. Environ. Part A, 24A, 1349-1360,1990. Claussen, M., Local advection processes in the surface layer of the marginal ice zone, Boundary Layer Meteorol., 54,1-27,1991a. Claussen, M., Estimation of areally-averaged surface fluxes, Boundary Layer Meteorol., 54, 387-410, 1991b. Comiso, J.C., and A.L. Gordon, Recurring polynyas over the Cosmonaut Sea and the Maud Rise, J. Geophys. Res., 92, 2819-2833,1987. den Hartog, G„S.D. Smith, R.J. Anderson, D.R. Topham, and R.G. Perkin, An investigation of a polynya in the Canadian archipelago, 3, Surface heat flux, J. Geophys. Res., 88, 2911-2916, 1983. Dethleff, D., Polynyas as a possible source for enigmatic Bennett Island atmospheric plumes, in The Polar Oceans and Their Role in Shaping the Global Environment, Geophys. Monogr. Ser., vol. 85, edited by O.M. Johannessen, R.D. Muench, and J.E. Overland, pp. 475-483, AGU, Washington, D.C., 1994. Donelan, M.A., The dependence of the aerodynamic drag coefficient on wave parameters, in Proceedings of First International Conference on Meteorology and Air-Sea Interaction of the Coastal Zone, pp. 381-387, Am. Meteorol. Soc, Boston, Mass., 1982. Fairall, C.W., and R. Markson, Mesoscale variations in surface stress, heat fluxes, and drag coefficient in the marginal ice zone during the 1983 Marginal Ice Zone Experiment, J. Geophys. Res., 92, 6921-6932,1987. Garratt, J.R., Transfer coefficients for a heterogeneous surface of large aerodynamic roughness, Q. J. R. Meteorol. Soc., 104, 491-502,1978. 35 Glendening, J.W., and S.D. Burk, Turbulent transport from an Arctic lead: A large-eddy simulation, Boundary Layer Meteorol., 59, 315-339,1992. Gloersen, P., W.J. Campbell, D.J. Cavalieri, J.G. Comiso, C.L. Parkinson, and H.J. Zwally, Arctic and Antarctic Sea Ice, 1978-1987: Satellite Passive-Microwave Observations and Analysis, NASA Publ. SP-511, Washington, D.C., 1992. Grotzner, A., R. Sausen, and M. Claussen, The impact of sub-grid scale sea-ice inhomogeneities on the performance of the atmospheric general circulation model ECHAM, Rep. No. 143, 42 pp., Max-Planck-Institut for Meteorology, Hamburg, Germany, 1994. Hanssen-Bauer, I., and Y.T. Gjessing, Observations and model calculations of aerodynamic drag on sea ice in the Pram Strait, Tellus, Ser. A, 40A, 151-161,1988. HogstrOm, U„ Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation, Boundary Layer Meteorol., 42, 55-78,1988. Holtslag, A.A.M, and H.A.R. de Bruin, Applied modeling of the nighttime surface energy balance over land, J. Appl. Meteorol., 37, 689-704, 11988. Huang, C.-Y., and S. Raman, A numerical modelling study of the marine boundary layer over the Gulf Stream during cold air advection, Boundary Layer Meteorol., 45, 251-290,1988. Kottmeier, C., and D. Engelbart, Generation and atmospheric heat exchange of coastal polynyas in the Weddell Sea, Boundary Layer Meteorol., 60, 207-234,1992. Kottmeier, C., and R. Hartig, Winter observations of the atmosphere over Antarctic sea ice, J. Geophys. Res., 95, 16,551-16,560,1990. Large, W.G., and S. Pond, Sensible and latent heat flux measurements over the ocean, J. Phys. Oceanogr., 12,464-482,1982. Launiainen, J., Parameterization of the water vapour flux over a water surface by the bulk aerodynamic method, Ann. Geophys., 1,481-492,1983. 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Claussen, On the momentum forcing of a large-scale sea-ice model, Clim. Dyn., 9, 71-80,1993. Sweet, W., R. Fett, J. Kerling, and P. LaViolette, Air-sea interaction effects in the lower troposphere across the north wall of the Gulf Stream, Mon. Weather Rev., 109, 1042-1052,1981. Taylor, P.J., Comments and future analysis on effective roughness lengths for use in numerical three-dimensional modelling, Boundary Layer Meteorol., 39, 403-418,1987. Vihma, T., Effect of polynyas on the grid-averaged heat fluxes, in Evening Sessions of the Summer School on Physics of Ice-Covered Seas, Savonlinna, Finland, 6-17 June, 1994, Rep. Ser. Geophys., vol. 28, edited by T. Vihma, pp. 29-32, Univ. of Helsinki, Helsinki, 1994. •v I @ 37 Vihma, T., and H. Savijarvi, On the effective roughness length for heterogeneous terrain, Q. J. R. Meteorol. Soc., 117, 399-407,1991. Wai,, M.M.-K., and S. A. Stage, Dynamical analysis of marine atmospheric boundary layer structure near the Gulf Stream oceanic front, Q. J. R. Meteorol. Soc., 115,29-44,1989. Wood, N., and P. Mason, The influence of static stability on the effective roughness lengths for momentum and heat transfer, Q. J. R. Meteorol. Soc., 117, 1025-1056,1991. Worby, A.P., and I. Allison, Ocean-atmosphere energy exchange over thin, variable concentration Antarctic pack ice. Ann. Glaciol., 15, 184-190,1991. Zwally, H.J., J.C. Comiso, and A.L. Gordon, Antarctic offshore leads and polynyas and oceano graphic effects, in Oceanology of the Antarctic Continental Shelf, Antarct. Res. Ser., vol. 43, edited by S.S. Jacobs, pp. 203-226, AGU, Washington, D.C., 1985. T. Vihma, Department of Geophysics, P.O. Box 4, FIN-00014 University of Helsinki, Finland, (e-mail: [email protected]) (Received November 29,1994; revised June 9,1995; accepted June 14,1995.) Copyright 1995 by the American Geophysical Union. Paper number 95JC02498. 0148-0227/95/95JC-02498$05.00 V - u- •V-V. ■' ,7 ■ v ( iv'; -) ■1 "4 7 c A r 7 , : / i k .v- -v - ' • ' x'f 1 1 . -v'Submitted to Journal of Geophysical Research, 12 June, 1995. " Copyright by the American Geophysical Union. Weddell Sea Ice Drift: Kinematics and Wind Forcing Timo Vihma0, Jouko Launiainen2) and Juha Uotila2) 0 Department of Geophysics, University of Helsinki P.O. Box 4, FIN-00014 Helsinki, Finland 2) Finnish Institute of Marine Research P.O. Box 33, FIN-00931 Helsinki, Finland Abstract Ice drift in the Weddell Sea was studied on the basis of positional and meteorological data from Argos buoys, and surface pressure analyses from the European Centre for Medium Range Weather Forecasts (ECMWF). In particular, the data from three buoys drifting in 1990-1992 was analyzed in detail. The drift kinematics showed apparent differences between the eastern and western parts of the Weddell Sea. Close to the Antarctic Peninsula, the ice drifted as an almost non-rotating uniform field at a low speed, having reduced small-scale motions with little meandering, compared to regions further to the east. On time scales of days, the effect of ytind was the prime factor, but this was less prominent in the western region, where the northward ocean current and forces due to divergence in internal ice stress tend to have a stronger effect than in the east. Inertial motion was detected from the ice drift in areas east of 35°W and in the region of the Antarctic Circumpolar Current, while far less periodic motions were detected in the central area around 40°W, while in the west around 50°W the data indicated some periodic motions presumably dominated by the M2-tide. With a reasonable time lag of ~6 h, the patterns of eastward movements especially were in coherence over longitudinal distances of 400-500 km. A linear model between the wind and ice drift explained40-80% of the drift velocity variance. The degree of explanation was higher in the central Weddell Sea (around 40°W) and lower closer to the Antarctic Peninsula. The geostrophic wind was found to provide almost as good a basis for the general drift estimation as the surface wind observed by the buoys, although deep cyclones were not well detected by the ECMWF analyses. The linear model parameters depend on the region, and the data also suggest a dependency upon atmospheric stability such that stable stratification reduces the wind forcing on the drift. For 60-80% of the time the direction of drift was that of both the geostrophic wind and the ocean current, and for 98-99% of the time coincident with the direction of either the wind or the current. Drift speeds were reduced when the drift was directed against the wind. Ice export through a transect crossing the Weddell Sea was estimated on the basis of the geostrophic winds, the drift’s observed response to the wind, and literature-based information on ice concentration and thickness. The annual mean net export in 1992-1994 varied from 8,000 to 22,000 m3/s. Most of the net export took place in winter and spring, export prevailing west of 35°W and import east of it. . K ' if .. 2 1. Introduction Ice drift in the Southern Ocean is basically divergent, as ice is advected north towards wider ■! latitudinal zones. However, in the Weddell Sea the geometry of the shoreline, especially the Antarctic Peninsula, modifies the drift. The general ocean circulation pattern is a clockwise gyre which joins with the Antarctic Circumpolar Current on its northern boundary. This results in a packing of ice towards the Antarctic Peninsula, while the drift in the central and eastern Weddell is more free, and the ice concentration is lower. Dynamic and thermodynamic processes interactively affect the ice field and its motions. New ice is formed in the leads, and especially in regions of coastal polynyas, which are kept open primarily by the wind. The circulation in the Weddell Sea is discussed by Deacon [1979], Gordon et al. [1981], Carmack [1986], Orsi et al. [1993], Farbach et al. [1994], Muench and Gordon, [1995], and Barber and Crane [1995]. s / , - Detailed knowledge of the Weddell Sea ice drift has been gained mostly from satellite-tracked drifting buoys which can survive in the ice pack through the winter. The first buoys were deployed in 1979 [Ackley, 1981], and since the late 1980s the buoy network has been almost continuous, although thenumber of buoys simultaneously presentin the areahas only been from 1 to 10. Although the individual buoy trajectories have frequently been several thousand kilometres long, it has been difficult to distinguish between features caused by spatial and temporal variations in the drift pat terns. The drift is discussed in papers by Limbert et al. [1989], Rowe et al. [1989], Wadhams et al. [1989], Martinson and Wamser [1990], Hoeber [1991], Massom [1992], Kottmeier and Engelbart [1992], Kottmeier et al., [1992], and Vihma and Launiainen [1993]. Kottmeier and Sellmann [1995] included all the existing buoy data in their analyses and provide a summary of the present state of knowledge. Passive microwave remote sensing data [Zwally et al., 1983; Gloersen et al., 1992] has increased our knowledge on the drift and extent of the Weddell Sea ice cover as well, giving us simultaneous information on broad spatial scales. This study is based on data obtained from the buoys deployed during two FINNARP =• *• i expeditions (Finnish Antarctic Research Program) in 1990 and 1992. Data from the first field phase was given in Launiainen et al. [1991], and from the second phase in Launiainen et al. [1994]. The results of heat exchange studies were discussed in Launiainen and Vihma [1994]. Vihma and Launiainen [1993] analyzed the drift of a buoy in the central Weddell Sea in 1990-1991, and this paper is a continuation of that study. Accordingly, we analyze the drift of two buoys deployed in the central and western Weddell Sea in 1992 and compare the spatial characteristics of their drift, including some comparisons with characteristics of the drift of the U.S.-Russian Ice Station Weddell-1 (hereafter referred as ISW) and the buoys near it. Comparisons are also made with the drift of our former buoy in 1990-1991. In the following, we use the term "western Weddell Sea" (WWS) for the region west of 45°W, and "central Weddell Sea" (CWS) for the region from 25 to 45"W, while the latitudes north of 63°S are called "the region of the Antarctic Circumpolar Current" (ACC). ■ / ; • ■ 2. Data The FINNARP drifting buoy data was gathered as follows. In the first stage, three marine meteorological Argos buoy stations were deployed in the central Weddell Sea (Figure 1) from RV Aranda in January 1990. One of the buoys (with ID 5892) was deployed on a small 0.2 x 0.2 km v-'.; f sea-ice floe in the marginal ice zone. A second buoy was deployed in the open ocean and a third on the edge of a floating ice shelf. In February 1992, two more buoys were deployed on sea-ice floes in the western and central Weddell Sea during the expedition of the Russian RV Akademik Fedorov. One of those (5908) was deployed on an ice floe, which was originally 0.5 x 1 km in size, \ « in the grid of the measuring network of ISW, some 50 km east of the ice camp. The other (1282) was deployed on an ice floe 0.4 x 0.5 km in extent in the central Weddell Sea. Both ice floes were covered with rather high ridges 0.2 to 1.5 m in height These floes were selected because thick, ridged multi-year floes have proved to be most conducive to long buoy survival. In addition to deployment of the buoys, marine meteorological surface observations and meteorological rawin- sonde soundings were made from the research vessel during the expeditions. . v ; ■v 3 70W, .1 Jan 93 Buoy 5908 ^26 July 92 Buoy 1282 1 July 92 Buoy 5892 1 July 91 —1 Jan 91 __ J July 90 -Open ocean 6 Fcbr 92 14Febr92 / 2 Jan 90 W^./70 ice shelf buoy r Figure 1. Research area, deployment sites and the drift trajectories of the marine meteorological buoys in the Weddell Sea. Dashed lines indicate approximate ice margins in February 1990 and July 1992. (The westernmost buoy (5908) was drifting in the vicinity of the U.S.-Russian Ice Station Weddell-1.) All the buoys were equipped with a pressure sensor and a vector averaging propeller wind sensor (R.M. Young Co.), the latter installed at the top of a meteorological mast at a height of 3.5 to 4 m. The surface wind speeds reported in this paper are referred to these heights, and are to be multiplied by a factor of about 1.2 to yield 10-m-height winds (see section 4.1). All the buoys except one (1282) were equipped with an additional cup anemometer. Duplicate air temperature sensors were installed at two different levels (for a total of 4 sensors). Additionally, the buoys were equipped with several other marine meteorological sensors, e.g for the measurement of air humidity, snow and water temperature and snow thickness, etc., as reported in the technical reports by Launiainen et al. [1991; 1994]. Detection of the periods when two of the buoys were drifting in open water (buoy 5892 from 15 January to 31 March, 1991, and buoy 5908 from late November 1992 onwards) was made possible by the availability of surface temperature and buoy rotation data. In addition the location data of ISW and a U.S. buoy (ID 6440; data from B aker and Martinson [1992]), the latter originally being deployed 50 km west of ISW, was used in certain contexts in the study. Polar regions are overpassed 26 times a day by the NOAA satellites utilized by CLS/Argos, but in practice about 18 to 20 Argos locations a day were collected for each buoy. For the study, locations interpolated for time intervals of one and six hours were used, the latter of which were . used for velocity and trajectory calculations. A long time interval removes pseudo-motions arising ;^ t from location errors, but the real small-scale dynamics are then lost as well. We found a 6-hour ' " J interval to be a reasonable first-order compromise. An average error of about 500 m in the buoy ' ■ - tv- i f 4 location yields a standard error of 0.03 m/s in the 6-hourly interpolated drift speeds and 0.008 m/s •v in the diurnal means. For more discussion about the location accuracy, high-frequency movements, and the dependency of the calculated drift speed on the interpolation period, see Vihma and Lau- niainen [1993]. The overall flow structure of the drift data processing and analysis is given in Figure 2. ;v - always studied studied when relevant * , :w’ _ Figure 2. Buoy data processing and analyses flow. ,5- 3. Kinematics 3.1 General drift and meandering $ The general properties of ice drift trajectories were distinctly different in the central Weddell Sea in 1990-1991 compared with more western areas in 1992 (Figure 1). This was seen e.g. as higher and more variable drift speeds in the central basin. Table 1 lists the basic properties of the drift kinematics for various regions and time periods, and the time series of the ice drift speeds are shown in Figure 3. Typical drift rates were of the order of 0.1 to 0.3 m/s, with the highest speeds and variances in the ACC region. Further south, values increased towards the east. These results V- - are comparable to the previous data published from the Weddell Sea [Limbert et al„ 1989; Hoeber, 1991; Massom, 1992; Kottmeier et al., 1992; Kottmeier and Sellmann, 1995], although e.g. the different time intervals for buoy location and the various ways of presenting the results make exact comparisons difficult. Ax' ' Large-scale properties of the drift are illustrated in Figure 4, in which the locations of buoys 5908 and 1282 are connected by a line at 5-day intervals. The line rotates anti-clockwise during the drift from the southernmost region to ~68°S, demonstrating a large-scale shear in the ice field with the drift speed increasing towards the east. North of ~68°S, the line mostly rotates clockwise, as the Weddell Gyre joins up with the Antarctic Circumpolar Current. ###### 5 Table 1. Principal characteristics of the drift kinematics case buoy region period Vj fm/sl inertial or tidal trajectory M = mean std motions detected length (km) I/5X 1 5892 CWS 3 Jan 1990-15 Jan 1991 0.15 0.10 inertia 4910 6.7 2 1282 CWS 15 Feb -26 July 1992 0.15 0.09 not apparent 2050 2.0 3 5908 WWS 7 Feb -14 July 1992 0.11 0.07 Mj * 1480 1.5 4 5892 ACC 1 July-3 Sep 1991 0.33 0.17 inertia 1870 1.4 5 5908 ACC 15 July 1992 - 2 Jan 1993 0.20 0.12 inertia 2950 1.4 Notation: CWS = central Weddell Sea, WWS = western Weddell Sea, ACC = region of the Antarctic Circumpolar Current, M = meandering coefficient, * inertial motion and Krtide also possible 5892 5908 and 1282 Central Weddell ACC Western Weddell ACC 1990 1991 1992 1993 Figure 3. Time series of the drift speed of the three ice floes, calculated from positions at 6-h intervals (solid line for buoy 5892, dashed line for 5908, and dotted line for 1282). .1 '/l X 19 July i f ■* 1282 Figure 4. Qualitative illustration of the large-scale shear and vorticity in the ice Held: locations of buoys 5908 and 1282 connected with a line at 5-day intervals. 6 In addition to the drift velocity, properties of the drift spectra, the buoy rotation activity, and a meandering coefficient may serve as primary quantitative measures for the kinematics of the "; • r- drift. We calculate the meandering coefficient as M = I/5X, where 8X is the net transition of a buoy V - . and I is the total trajectory length for the same time period, including all the transitions to and fro ySi; (calculated from positions at 6-hour intervals). The results are shown in Table 1. As the drift speed •' ' and its variance, so too the meandering coefficient diminishes towards the west. The meandering £ coefficients obtained are comparable to the results of Massom [1992], who obtained values of M j. >. „ ■ • from 1.2 to 3.6 for the region between 30-50°W. Limbert et al. [1989] calculated M for a buoy drifting in the southern and western Weddell Sea. Compared with our results for the same region of around 50°W (period 3 in Table 1), his results were higher, with M ranging from 2 to 5, although ; V-;,: the time-step between successive buoy positions was as long as 1 day. In our study it was 6 hours, !:; ‘■,' which ought to produce higher values of M. In general, however, both Massom’s [1992] results and ;•■; ours suggest an increase in M towards the east, and the results are relatively coherent with each ,5- other, whereas the results of Limbert et al. [1989] are quite different. It seems that interannual ... ' variations can be considerable, and may dominate over the typical spatial gradients. This is also .* supported by the distinct difference in meandering between buoys 5892 and 1282 when they drifted . '[■''[ in almost the same region of the central Weddell Sea in 1990-1991 and 1992, respectively (see -'-A ‘ Figure 1 and Table 1). In the region of the circumpolar current, both the 1991 and 1992 data sets ' ' show low meandering coefficients of 1.4. , / ’ = -0.97(j<7> 4 + (0.7855 + 0.2232
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