A Numerical Study of the Long- and Short-Term Temperature Variability and Thermal Circulation in the North Sea

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PATRICK J. LUYTEN Management Unit of the Mathematical Models, Brussels, Belgium

JOHN E. JONES AND ROGER PROCTOR Proudman Oceanographic Laboratory, Bidston, United Kingdom

(Manuscript received 3 January 2001, in ®nal form 4 April 2002)

ABSTRACT A three-dimensional numerical study is presented of the seasonal, semimonthly, and tidal-inertial cycles of temperature and density-driven circulation within the North Sea. The simulations are conducted using realistic forcing data and are compared with the 1989 data of the North Sea Project. Sensitivity experiments are performed to test the physical and numerical impact of the heat ¯ux parameterizations, turbulence scheme, and advective transport. Parameterizations of the surface ¯uxes with the Monin±Obukhov similarity theory provide a relaxation mechanism and can partially explain the previously obtained overestimate of the depth mean temperatures in summer. Temperature strati®cation and thermocline depth are reasonably predicted using a variant of the Mellor±Yamada turbulence closure with limiting conditions for turbulence variables. The results question the common view to adopt a tuned background scheme for internal wave mixing. Two mechanisms are discussed that describe the feedback of the turbulence scheme on the surface forcing and the baroclinic circulation, generated at the tidal mixing fronts. First, an increased vertical mixing increases the depth mean temperature in summer through the surface heat ¯ux, with a restoring mechanism acting during autumn. Second, the magnitude and horizontal shear of the density ¯ow are reduced in response to a higher mixing rate. Thermal and salinity fronts generate a seasonal circulation pattern in the North Sea. Their impact on the horizontal temperature distributions is found to be in good agreement with the observations. It is shown that, in the absence of strong wind forcing, both the vertical temperature distribution and the thermal circulation experience semimonthly variations in response to the spring±neap cycle in tidal mixing. At spring tides, the surface mixed layers are shallower, in agreement with observations at two mooring stations, and the baroclinic circulation intensi®es, whereas the opposite occurs at neaps.

1. Introduction A typical example is the North Sea where tidal mixing Density fronts are common features in midlatitude fronts appear from spring to autumn in the deeper central coastal and shelf seas. Thermal fronts arise as a result and northern parts and a region of freshwater in¯uence of a balance between tidal mixing and surface heating is observed throughout the year that extends along the (Simpson and Hunter 1974). The structure of these continental coasts of The Netherlands, Germany, and fronts is sensitive to the characteristics of the topog- Denmark. The principal components of the tide are the raphy and spatial and temporal variations of the tidal semidiurnal M 2 and S 2 harmonics yielding a semi- current amplitude. Salinity fronts are created by coastal monthly modulation of the tidal amplitude of about 30% discharges of freshwater. A frontal ¯ow is generated by (Davies et al. 1997). In earlier studies the location of the requirement of geostrophic equilibrium and usually tidal mixing fronts was determined at critical values of 3 takes the form of a coastal current propagating along- the parameter ␹ ϭ log(H/ut ), where H is the water depth shore or alongshelf to the right (looking seaward) of the and ut is the amplitude of the depth mean M 2 tidal cur- source in the Northern Hemisphere. rent (Pingree and Grif®ths 1978; Simpson and Bowers 1981). Although the method proved to be successful with some scatter, it is clear that a high-resolution three- Corresponding author address: Dr. Patrick J. Luyten, Management Unit of the Mathematical Models, 100 Gulledelle, B-1200 Brussels, dimensional model is needed to resolve ®nescale pro- Belgium. cesses associated with thermal fronts (James 1989; Proc- E-mail: [email protected] tor and James 1996). The density-driven residual cir-

᭧ 2003 American Meteorological Society

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Haren et al. 1999; Van Haren 2000) showed important ¯uctuations in temperature at the inertial, in response to the wind forcing, and semidiurnal tidal frequencies. As suggested by these authors these modes and their higher-order harmonics generate an important current shear across the thermocline that tends to enhance vertical mixing. The recently developed three-dimensional baroclinic COHERENS model (Luyten et al. 1999) is applied to study the annual cycle of temperature, thermal fronts, and density circulation in the North Sea. From the forcing, one deduces three different ranges in timescales, which are examined separately: seasonal (long range), semimonthly as given by the spring±neap cycle (medium range), and semidiurnal and inertial (short range). The model resolves the main frontal structures and has the ability to preserve the sharp frontal gradients. A series of simulations has been performed for the year FIG. 1. Locations of the NSP data stations. 1989. The choice is motivated by the availability of the NSP data and a fairly complete set of forcing and open culation in the North Sea can be divided into two main boundary data for that particular year, including fresh- components arising from different origins. First, a coast- water input by the main rivers discharging into the area. al current, driven by the nearshore salinity fronts and Although a study of salinity plumes and fronts is not the prevailing winds, is known to exist at the continental the prime objective, its impact on temperature via sta- coasts of The Netherlands and Germany and in the Ger- bilization of the water column and plume-driven trans- man Bight (e.g., Prandle et al. 1993). Second, a thermal port cannot be neglected. The dense spatial coverage of circulation along the tidal mixing fronts in summer has the data stations not only allows the comparison of ver- been inferred from current and density measurements tical temperature pro®les, but also provides indirect ev- at the coast of England and in the Dogger Bank area idence for the existence of a seasonal circulation pattern (Prandle and Matthews 1990; Lwiza et al. 1991). as derived from the model. First studies of the seasonal cycle of temperature and A number of sensitivity experiments is conducted to strati®cation in the North Sea were performed using analyze the separate roles of vertical mixing, surface mean forcing data and compared with climatological forcing, and advection. The importance of an adequate observations (Elliot and Clarke 1991; Pohlmann 1996). formulation for mixing in the thermocline, already ap- More realistic simulations could be performed when the parent from the numerical study of Holt and James data from the U.K. Natural Environment Research (1999), is investigated by comparing different schemes Council North Sea Project (NSP) became available for background mixing. An important outcome will be (Charnock et al. 1994). A series of cruises was per- that, while advective transport affects the vertical struc- formed during 1988±89 covering a complete seasonal ture of the water column, there exists an important feed- cycle providing monthly pro®les of temperature and sa- back from turbulence onto the surface forcing and even linity at more than 100 stations throughout the southern the frontal temperature gradients and baroclinic circu- and central North Sea (see Fig. 1). Mooring data with lation. The general nature of the analysis allows us to a high time resolution from a selected number of ®xed extend the results of the study to tidal shelf seas in stations are also available. In a recent study Holt and general. James (1999) compared the temperature data of the complete NSP dataset with a three-dimensional model and realistic surface forcing and open boundary data. The 2. Model description temperature cycle was well represented and reasonable a. General agreement was obtained for surface and bottom temperatures and thermocline depths. The coarse resolution The basic equations for momentum, continuity, tem- of the model (about 22 km) did not provide a detailed perature and salinity, written in spherical polar coor- picture of the fronts while discrepancies with the data dinates using ␴-coordinates in the vertical, are discre- 1 occurred in the German Bight because of the absence tized on an Arakawa-C grid with a resolution of ⁄15Њ in 1 of salinity in the simulation. This omission was cor- latitude, ⁄10Њ in longitude (approximately 7.3 km) and rected in the shelf sea simulations of Holt et al. (2001) 20 ␴ levels in the vertical. Density is related to tem- but the horizontal resolution (about 12 km) is still too perature and salinity via the United Nations Educational, coarse to resolve coastal fronts. Besides the variation Scienti®c and Cultural Organization equation of state on a seasonal scale, observations in the North Sea (Van of seawater (Millero et al. 1980).

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In analogy with the well-known POM model (Blum- berg and Mellor 1987) the equations are integrated in time using the mode-splitting technique with a small time step (30 s) for the 2D barotropic mode and a larger time step (10 min) for the 3D baroclinic mode. A pre- dictor±corrector scheme is implemented to ensure con- sistency between the 2D and 3D modes. The total variation diminishing (TVD) scheme is applied for the advection of momentum and scalars whereby the advective ¯ux is evaluated as a weighted average between the upwind ¯ux and either the Lax±Wendroff in the horizontal or the central ¯ux in the vertical. Compared to simpler schemes, the method has the advantage, at the expense of an increased CPU time, that it enables the simulation of frontal structures with strong horizontal gradients. Horizontal diffusion is neglected in the present FIG. 2. Bathymetry (m) of the simulated area and location of the study to avoid the broadening of frontal areas by a poorly 13 discharge sources. The Dogger Bank is the shallow triangular area parameterized physical diffusion and unphysical diffu- in the central North Sea between 54Њ and 56ЊN. The deeper Outer sion across isopycnals. Further details about the gov- Silver Pit (54ЊN, between 1Њ and 3ЊE) is visible to the south of the Dogger Bank. The area north of Germany and east of Denmark is erning equations, numerical methods, and discretization the German Bight where the Old Elbe Valley can be observed by its schemes are found in Luyten et al. (1999). wedgelike shape. Surface stress and heat ¯ux are calculated as a function of wind and sea-air temperature difference using the bulk formulas of Kondo (1975). The meteorological for most sources, except for the Wash, Humber, Seine, forcing data have been provided at 3-hourly intervals and Scheldt Rivers for which a zero transport condition by the U.K. Meteorological Of®ce, except for cloud is taken. coverage, which is obtained from satellite data with a daily value taken to be uniform over the whole domain. b. Turbulence formulation Solar irradiance is expressed as the sum of an infrared and a shortwave component. The former contains 54% The vertical eddy coef®cients ␯t for momentum and of the incoming radiation and is absorbed at the sea ␭t for temperature and salinity are expressed in terms surface whereas the latter decays exponentially with dis- of the turbulence energy K and its dissipation rate ␧ tance to the surface using an inverse attenuation depth using of 0.06 mϪ1. ␯ ϭ SK22/␧, ␭ ϭ SK/␧. (1) A quadratic friction law is applied at the seabed using tu tb a roughness length of 3.5 mm. The depth-integrated The stability coef®cients Su and Sb are functions of the 2 2 2 2 current at open sea boundaries is determined using the stability parameter ␣N ϭ K N /␧ , where N is the method of characteristics (see, e.g., Rùed and Cooper (squared) Brunt±VaÈisaÈlaÈ frequency. Their explicit forms, 1987). An equation is solved for the outgoing charac- derived from an algebraic stress model, are given by teristic while the incoming one is prescribed using an 0.108 ϩ 0.0229␣ harmonic expansion with nine tidal constituents, in- S ϭ N , u 2 cluding the principal semidiurnal, diurnal, and quarterly 1 ϩ 0.471␣NNϩ 0.0275␣ diurnal components. More details about the procedures 0.177 are given in Luyten et al. (1999). Residuals at hourly Sb ϭ . (2) intervals and the other harmonic parameters are ob- 1 ϩ 0.403␣N tained from a baroclinic model for the Continental Shelf The scheme is similar to the Galperin et al. (1988) ver- (Jones et al. 1998). To prevent spurious vertical veloc- sion of the Mellor and Yamada (1982) turbulence clo- ities at open sea boundaries, the 3D horizontal current sure. The main difference is that the critical Richardson is computed assuming a zero normal gradient for the number where turbulence ceases now takes a higher velocity deviation. value of 0.58, compared to 0.2 in the Mellor±Yamada Salinity is transported inside the domain during in- formulation. ¯ow using prescribed climatological values (Jones Turbulence energy K is obtained by solving the trans- 1994) in the form of an annually varying sine wave. In port equation the absence of reliable data for the simulated period a ␷ץu 22ץ Kץץ Kץ zero net transport is considered for temperature. River ϭ ␯ ϩ ␯ ϩ zץ zץz [] ΂΃΂΃ץz΂΃ttץ tץ input is provided from 13 sources (see Fig. 2), using daily river discharge values and assuming a uniform 2 discharge at all depths. Temperature data were available Ϫ ␭tN Ϫ␧, (3)

Unauthenticated | Downloaded 10/03/21 08:04 PM UTC 40 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 33 where advection of turbulence has been neglected. The 1, if Ri Ͻ 0; dissipation rate is computed from 3  Ri 2  ␧ϭ␧K 3/2/l. (4) f iw(Ri) ϭ 1 Ϫ ,if0Ͻ Ri Ͻ 0.7; (10) 0 []΂΃0.7 The mixing length is prescribed algebraically using a 0, if Ri Ͼ 0.7. formulation similar to the one proposed by Mellor and Yamada (1982), which takes account of both a surface Following Kantha and Clayson (1994), the background and a bottom boundary layer coef®cients are only introduced when K drops below a lower limit set by 10Ϫ6 JsϪ1. The scheme was suc- Ϫ1 Ϫ1 Ϫ1 Ϫ1 l ϭ [␬(z ϩ h)] ϩ [␬(␨ Ϫ z)] ϩ la , (5) cessfully applied by Kantha and Clayson (1994) to a where variety of oceanic mixed layer problems.

␨␨c. Model area l ϭ ␣ (␨ Ϫ z)K1/2 dz K 1/2 dz, (6) a 1 ͵͵ Ϫh ΋ Ϫh The computational domain (Fig. 2) consists of the northwest European shelf between 4ЊW and 57ЊN cov- and h and ␨ are the mean water depth and surface el- ering the Channel and the southern and central parts of evation, respectively. the North Sea. The simulated period is from 1 January The constants ␧ 0 and ␣1 are set to to 25 December 1989. The main characteristics of the bathymetry are the ␧ϭ0.19, ␣ ϭ 0.2. (7) 01 shallow area in the southern North Sea with small depth As pointed out by, for example, Kantha and Clayson variations between 20 and 40 m and two deeper parts (1994), the Mellor±Yamada type of closures (including located, respectively, in the northwest and southwest the present scheme) does not take account of mixing in area of the computational domain. The former is char- the strongly strati®ed layers where turbulence is gen- acterized by steeper gradients of bathymetry with depths erated by the shear and breaking of unresolved internal ranging from 40 up to 100 m. A notable feature is the waves. In the absence of an adequate scheme for internal shallow Dogger Bank between 54Њ and 56ЊN, which wave mixing, a uniform diffusion coef®cient is usually takes the form of a triangle with its base at the deep proposed. No agreement exists about its value or even Outer Silver Pit (54ЊN, 1Њ±3ЊE) and its top at 56ЊN, 5ЊE. about its magnitude. Two alternative approaches will be The shallowest parts with depths of about 10 m are considered in the present study. localized along the Belgian and Dutch coasts and in the The ®rst formulation is based upon limiting condi- eastern part of the German Bight (north of Germany tions for turbulence variables in the case of stable strat- and east of Denmark). The deeper Old Elbe Valley is i®cation. Following Galperin et al. (1988) an upper visible in the German Bight by its wedgelike shape. bound is imposed for the mixing length d. Model experiments l Ͻ 0.5K 1/2/N. (8) The evolution of the temperature ®eld is governed by The condition (8) is derived from the result, established four different processes. These are 1) surface forcing, from laboratory experiments, that the sizes of the largest 2) vertical distribution of temperature by turbulent mix- overturns are limited by stable strati®cation. If in ad- ing, 3) horizontal and vertical advective transport, and dition a lower bound Kmin is set for the turbulence en- 4) absorption of solar heat in the water column. A num- ergy, the diffusion coef®cients ␯t and ␭t take a back- ber of model experiments, summarized in Table 1, has ground value proportional to N Ϫ1. Burchard et al. (1998) been conducted to assess the role of these processes, and Luyten et al. (2002) found good agreement with both physically and numerically, on the long-, medium- turbulence dissipation measurements in the Irish and and short-time range. No experiment has been designed North Seas after tuning of the parameter Kmin. The value to test the formulation of optical attenuance, which in adopted here is 10Ϫ6 JsϪ1. reality should include contributions from salinity, dis- The second one is the semiempirical formulation of solved yellow substances, and small (nonsinking) sus- Large et al. (1994) where background diffusion coef- pended particles not taken into account in the present ®cients are introduced as a function of the gradient Rich- study. ardson number A standard simulation (run A) was performed using the model formulations and setup described above. 10Ϫ4 5 10Ϫ3 f (Ri), ␯tiwϭ ϩ ϫ Thermocline mixing is parameterized using limiting Ϫ5 Ϫ3 conditions for l and K. This formulation is replaced by ␭tiwϭ 5 ϫ 10 ϩ 5 ϫ 10 f (Ri), (9) the internal wave mixing (IWM) scheme of Kantha and where Clayson (1994), as given by Eqs. (9)±(10) in a second

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TABLE 1. Setup of the model experiments. Run Description A Standard simulations as described in the text and using limiting conditions for turbulence variables. B As in run A but using the IWM scheme of Kantha and Clayson (1994). C As in run A but using exchange coef®cients for the surface forcing only depending on wind speed. D As in run A but without advection of temperature. E As in run A but using a ®rst-order upwind scheme for the advection of momentum, while retaining the TVD scheme for temperature and salinity. run B. Run C is similar to the ®rst one except that the tions, where a thermocline forms during spring. The sea-air temperature difference is removed in the eval- results of the averaging, presented in Fig. 3, will be uation of the surface drag and exchange coef®cients used as general guidelines throughout the discussions used for the surface stress and heat ¯uxes. Two tests below. were performed to test the role of advection and its parameterization. In the ®rst one (run D) horizontal and vertical advection is canceled in the equation of tem- 1) SURFACE FORCING perature. In the second one (run E) currents are advected The standard simulation (run A) uses Kondo's (1975) by a more diffusive ®rst-order upwind scheme while retaining the TVD scheme for temperature and salinity. formulation for the latent and sensible heat ¯uxes. The transfer coef®cients C for the latent and C for the It is remarked that these model intercomparisons are E H intended in the ®rst place as an illustration of the phys- sensible heat ¯uxes are expressed as functions of the ical processes and second to validate the numerical wind speed and the sea-air temperature difference ⌬T T T . The expressions were derived from Monin± schemes quantitatively. ϭ s Ϫ a Obukhov (MO) similarity theory. The formulation pre-

dicts higher values for CE and CH compared to the neu- 3. Analysis of model results tral case ⌬T ϭ 0if⌬T Ͼ 0, while the opposite occurs The results of the different model experiments are if ⌬T Ͻ 0. The effect is illustrated in Figs. 4a±c for the compared with the temperature data of the North Sea case of the shallow water station AG (water depth H ϭ Project for the 1989 period. The 122 data stations are 16.6 m), where the results of run A are compared with plotted in Fig. 1 and cover most of the North Sea be- those of run C without the ⌬T dependence. From late tween 51Њ and 55Њ40ЈN. Temperature pro®les were taken winter to early summer ⌬T is mostly negative, while at nearly monthly intervals. The start and end dates of ⌬T becomes positive from day 175 until the end of the the 10 cruises conducted in 1989 are listed in Table 2. year (Fig. 4a). During the ®rst period, heating through The analysis below is split up onto three main sections the sensible and cooling through the latent heat ¯ux are each dealing with one of the different timescales (sea- both reduced in run A compared to run C. The net effect sonal, spring±neaps, semidiurnal/inertial). is that the cooling rates, predicted by run A, are slightly larger so that the depth mean temperatures (Tm) are somewhat lower during spring (Figs. 4b,c). A different a. Seasonal cycle situation arises in summer when ⌬T changes sign and A general comparison between the models and with the MO formulation increases the cooling via both the the data has been performed by averaging the measured latent and sensible heat ¯uxes, yielding a difference in and model data separately over the mixed stations, Tm between the runs upto 1.2ЊC in the beginning of where the water column remains thermally mixed September. The evolution reverses in autumn when the throughout the whole year, and the deeper strati®ed sta- lower temperatures in run A decrease the value of ⌬T and, thus, also the surface cooling at a higher rate compared to run C. One may therefore conclude that, al- TABLE 2. Start and end dates of the 1989 NSP cruises. though the MO formulation may not be too signi®cant No. Start End at the end of a yearly temperature cycle, its impact on 1 30 Dec 1988 12 Jan the seasonal temperature evolution can be substantial. 2 28 Jan 10 Feb The previous analysis is con®rmed by the station-av- 3 27 Feb 12 Mar eraged mean temperature values plotted in Fig. 3a. Al- 4 29 Mar 10 Apr though both model experiments underestimate the ob- 5 27 Apr 9 May 6 26 May 7 Jun served mean temperatures in winter changing into an 7 24 Jun 7 Jul overestimate during summer, the MO formulation re- 8 24 Jul 6 Aug duces, at least, the errors in the summer season by 20%± 9 23 Aug 4 Sep 30%. A similar analysis applies for the strati®ed sta- 10 21 Sep 3 Oct tions, as given in Fig. 3b, although the effects of the

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FIG. 3. Time series for the 10 NSP cruises in 1989 of global parameters averaged over all (a) mixed and (b)±(f) strati®ed data stations: (a),(b) depth mean temperature, (c) surface temperature, (d) bottom temperature, (e) surface minus bottom temperature difference, and (f) percentage of strati®ed stations. Values are shown according to the data (solid circles), run A (solid±plus signs), run B (dots±asterisks), run C (dashes±diamonds), run D (dash±dots± triangles), and run E (dash±three dots±squares).

surface forcing are reduced because of the larger water that the higher mean temperatures in run B now provide depths. a higher cooling rate than in run A with a consequent Since the surface heat ¯ux is calculated using the larger decrease in mean temperature. The whole evo- modeled sea surface temperature, there is an indirect lution is further illustrated in Figs. 5a,b, where the sur- in¯uence of the turbulence scheme on the surface forc- face heat ¯uxes and depth mean temperatures from runs ing and, hence, on the depth mean temperature. From A and B are compared at the deep water station CW (H Figs. 3c±e one infers that run B, using the IWM scheme, ϭ 89.2 m), and can also be derived from Fig. 3. The reduces the vertical strati®cation, yielding lower surface station-averaged values show a better agreement with and higher bottom temperatures during summer in the the observations, both for mean temperature as for ver- strati®ed areas as a result of a larger mixing in the tical strati®cation, in the standard run with limiting con- thermocline. In consequence, the cooling rates are lower ditions than in the simulation using the IWM scheme. in summer, compared to run A, giving higher mean tem- The apparent better agreement for the surface temper- peratures (Fig. 3b). The effect is reversed in late autumn ature in the latter case can therefore not be considered when the water column becomes vertically mixed so as a real improvement.

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FIG. 5. Heat ¯ux experiment at station CW: (a) downward surface heat ¯ux from run A minus its value from run B and (b) depth mean temperature difference between runs A and B. All values are averaged over 3 days.

runs where advection is included. The same conclusion can be made by inspecting the averaged values of strat- i®cation, represented by the surface minus bottom difference in Fig. 3e. A further explanation will be pro- FIG. 4. Heat ¯ux experiment at station AG: (a) sea surface minus vided in section 3c. air temperature calculated from run A (solid line) and run C (dashed line); (b) downward surface heat ¯ux from run A minus its value from run C; (c) depth mean temperature difference between runs A 3) FRONTS AND RESIDUAL CIRCULATION and C. All values are averaged over 3 days. A well-known phenomenon in the North Sea is the presence of tidal mixing fronts from spring to autumn. Thermal strati®cation arises during summer north of 2) VERTICAL STRATIFICATION 54ЊN and in the western section of the Channel (west Thermistor chains were deployed during the 1989 of 2.5ЊW), as can be observed from the distribution of North Sea Project at a limited number of stations. Time- thermocline depths (Fig. 7a), obtained using the month- depth contours of the daily averaged observed temper- ly averaged temperature pro®les for August. The mean atures at station CS (55Њ31ЈN, 0Њ54.5ЈE) are plotted in position of the fronts in the central North Sea ®rst ex- Fig. 6a and can be compared with the simulated evo- tends along the British coast and detaches from the coast lution according to the standard experiment, shown in near Flamborough Head at 0.5ЊW. A ®rst branch sur- Fig. 6b. Both the time of onset of strati®cation and the rounds the Dogger Bank while a southern branch ex- initial deepening of the thermocline are well predicted tends along 54ЊN upto 4ЊE where it curves northeast- by the model. The periodic uprising of the isothermals ward along the German Bight. These frontal positions within and below the thermocline, seen in both the data are in good agreement with the climatological data an- and the model results, occurs at semimonthly intervals alyzed by Elliot and Clarke (1991) and the numerical and can be related to the spring neap cycle. This is simulations of Holt and James (1999). A known crite- further discussed below. A notable difference is the un- rion for locating tidal mixing fronts is via critical values 3 derestimation of strati®cation in the thermocline. The of the parameter ␹ ϭ H/ut where ut represents the depth result is, as one may expect on ®rst sight, not due to an mean amplitude of the semidiurnal current. Comparing inaccurate parameterization of turbulent mixing within the position of the front in the central part with the the thermocline, but can be explained by important bathymetry in Fig. 2, one observes that the front is short-time advective effects. This is illustrated in Fig. located at a critical depth close to the 35-m isobath. 6c showing the vertical temperature pro®les on 30 Au- This is explained by the nearly homogeneous distri- gust according to the data and simulations A, B, and D. bution of tidal mixing in the central North Sea (Fig. 7b) Although run D without advection predicts too large so that ␹ only varies with the water depth. Contrary to surface and bottom values, the temperature gradients in the open ocean where the depth of the thermocline is the surface and thermocline layers are more in agree- determined by the surface forcing, the deepening of the ment with the data than the ones predicted by the other thermocline in tidal shelf seas is limited from below

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the scope of the present study, they are the driving force of density currents along the coast that advect the temperature ®eld. The intensity and direction of the salinity- induced residual circulation depend on the wind forcing (Chao 1987, 1988). During the winter and early spring the prevailing winds are strong and mainly blowing from southwesterly to westerly directions (Fig. 7e). They are thus downwelling favorable for plumes at the continental coast. The result is a narrowing of the coastal plumes, which, in combination with the high river discharges in March and April, yields stronger offshore gradients in surface salinity (Fig. 7c) and an intense northward coastal jet current (Fig. 8a). From the end of April until August the wind speeds are reduced by a factor of 2. Easterly winds are now more prevailing giving upwelling favorable conditions for continental plumes. As a result the plumes expand in offshore direction whereas the alongshore intrusion of freshwater is slowed down (Fig. 7d). The simultaneous presence of thermal and salinity fronts in shelf seas, such as the North Sea, induces an intrinsic pattern of residual circulation with variations on a seasonal scale. The residual currents are obtained from an harmonic analysis with a least squares ®tting on a monthly basis, which ®lters out the most important harmonics of the barotropic tide. The residual velocity ®elds at 15-m depth and along a transect at 55ЊN are plotted in Fig. 8 for March and August, which can be considered as typical for the winter and summer seasons. The circulation in March (Fig. 8a) is characterized by a strong northward coastal current within the shallow southern bight and the German Bight, as resulting from the westerly winds in winter and the plume-driven circulation. The residual pattern above 53ЊN can be described as a cyclonic rotation with a southeastward ¯ow in the western part, turning eastward in the central and northward in the eastern part (similar to Holt et al. 2001). The onshore winds generate a transverse circulation in the freshwater plume of the German Bight with onshore surface ¯ow, offshore bottom ¯ow, and downwelling within the plume front (Fig. 8b). The alongshore coastal jet is mainly barotropic with a maximum of about 8 cm sϪ1 (Fig. 8c). West of and above the Dogger Bank the eastward current ®rst accelerates and then de- celerates generating associated upwellings and down- wellings. The surface circulation for August (Fig. 8d) shows a

FIG. 6. Seasonal temperature evolution (ЊC) at station CS: (a) ob- dominant feature in the form of an anticyclonic gyre servations and (b) run A; Thick line denotes 12ЊC contour; (c) tem- along the thermal front around the center of the Dogger perature pro®le on 30 Aug as given by the observations (plus signs), Bank. The sense of the rotation can be deduced from run A (solid curve), run B (dotted curve), and run D (dash±dotted geostrophic equilibrium, which creates a ¯ow with the curve). White areas in (a) indicate missing data. warmer (mixed) water to the right and colder (strati®ed) water to the left. A second thermally induced circulation because of the presence of a tidally mixed bottom layer. is the southward ¯ow along the coast of Britain branch- A bottom-layer thickness of about 35 m, except for the ing eastward at 54.0ЊN just below the Outer Silver Pit deepest parts, can be deduced after comparing ther- (south of the Dogger Bank). Compared to the winter mocline and water depths. situation the salinity current in the German Bight is Although a detailed study of salinity fronts is beyond reduced in magnitude and de¯ected northwestward by

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FIG. 7. (a) Monthly averaged thermocline depth (m) for Aug, de®ned as the distance to the surface of the point where the temperature exceeds the bottom value by 0.5ЊC; (b) residual bottom stress (N m Ϫ2) for Aug; surface salinity distribution (psu) on (c) 7 Apr and (d) 5 Aug; and (e) daily averaged wind vectors at station BB.

the offshore winds. The jet stream along the western the strati®ed side of the front, changing toward down- side of the Dogger Bank (0.75ЊE) has a maximum of welling at the mixed side (Fig. 8e). In analogy with the 11 cm sϪ1 within the thermocline at 20-m depth (Fig. well-known estuarine circulation, a ¯ow, transverse to 8f). The result is in good agreement with the value of the front, is produced by tidal friction. The effect is to 13±15 cm sϪ1 measured in 1988 and reported in Lwiza reduce the alongfrontal jet and a motion directed toward et al. (1991). An important upwelling is generated on the inner mixed side of the front. A southward return

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FIG. 8. Residual circulation ®elds for (a)±(c) Mar and (d)±(f) Aug: (a),(d) horizontal current at 15-m depth; (b),(e) circulation along a transect at 55ЊN; and (c),(f) northward current (m sϪ1) at the same transect; (c),(f) thick line represents zero current.

¯ow, concentrated toward the surface, is observed along 4) ADVECTIVE TRANSPORT the eastern side of the Dogger Bank at 3.5ЊE although with a lesser magnitude, since the transect cuts the front The present simulations revealed the existence of sea- there at an angle of about 45Њ and the depth gradients sonally dependent circulation patterns in the North Sea are smaller at the eastern compared to the western side affecting the horizontal and vertical distributions of tem- of the Dogger Bank. This results in smaller cross-frontal perature. The high density of the NSP stations in the currents and upwellings. southern North Sea, the German Bight, and the frontal

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contour intervals in Fig. 9b. The main features are induced by the frontal circulation, displayed in Fig. 8d. This explains the higher temperatures observed at the Outer Silver Pit (south of the Dogger Bank), the western boundary of the Dogger Bank, and a band extending northeastward along the northern boundary of the Dog- ger Bank, while cooler water ¯ows southward along the narrow coastal front at the British coast branching eastward in front of the Humber estuary. Tendencies are, as expected, less obvious in the German Bight in view of the spring-neap modulations of the residual circulation pattern, which is further discussed below. To validate the preceding analysis the depth mean temperatures, obtained from runs A, D, and E, are compared with the corresponding data values at a number of selected stations (Fig. 10). In making the comparison one should take into account that the modeled temperatures are too low in winter and too high in summer as a consequence of the surface forcing formulation. Ev- idence for a warm current along the continental coast during winter is found at stations AV, BN, and CH. The data show agreement about warm advection at stations in the Humber area (DQ, DS) and at or near the Dogger Bank (EB, EJ, EK). The general characteristics of the frontal circulation in summer are con®rmed by the data. This applies for the advection of cool water at the coastal stations CY, DA, and DH (with a maximum cooling of more than 4ЊC in August), DQ, and the stations DS, EJ, and EK in the Humber area. Warm advection is evident at the deeper strati®ed side of the Dogger Bank mixing front (EI), whereas cold advection is seen at EB within the Dogger Bank. The temperature difference arising from advection has its maximum in July and August FIG. 9. Monthly averaged values of the depth mean temperature and diminishes when the thermal fronts decline in Sep- (ЊC) obtained from the standard run A minus the corresponding value calculated from run D without temperature advection: (a) Mar and tember. (b) Aug. Contour interval is (a) 0.25ЊC and (b) 0.5ЊC. White areas In view of the large impact of residual advection on indicate negative temperature differences (advective cooling); gray the temperature evolution near thermal fronts, it is of and black areas represent positive values (advective warming). The interest to know to what extent the results are sensitive plots show the effect of advective transport on the temperature distribution during typical winter and summer months. to the numerical discretization of advection. Time series, obtained from run E using the upwind scheme for advection of momentum, are plotted in Fig. 10 for com- areas at the western branch of the Dogger Bank and parison (dash and three-dotted curves). No difference along the British coast allows us to derive some general is seen with the standard case at most stations whereas patterns of circulation from the temperature data. The a slight difference, of the order of a few tenths of de- relative importance of seasonal advection with respect grees, can be observed at the stations EI, FJ, and EK to the surface forcing can be deduced by subtracting the within the Dogger Bank area. Although this may imply monthly averaged mean temperatures obtained by run that the expensive TVD scheme does not provide a real D, without temperature advection, from the correspond- improvement, it will be shown further below that the ing values for the standard run A. The results are il- magnitude of the thermal circulation is sensitive to the lustrated in Figs. 9a,b for March and August. The winter form of the advection scheme. distribution shows the advection of warm water along the path of the coastal jet current. Higher temperatures are observed within the Dogger Bank and an extended b. Spring±neap cycle area of shallow water in front of the Humber estuary. 1) VERTICAL STRATIFICATION This is explained by the advection from deeper areas, which generally have higher temperatures in winter than To examine the in¯uence of the different mixing pro- shallower ones. Advective effects are more localized in cesses on the vertical temperature distribution, a further summer but larger in value, as re¯ected by the larger comparison is performed with the mooring data at sta-

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FIG. 10. Time series of depth mean temperatures at a number of selected stations as obtained from the observations (solid circles), run A (solid curves), run D (dash±dotted curves), and run E (dash and three-dotted curves). tion DM (54Њ20ЈN, 24ЈE). Compared to CS (H ϭ 74 the harmonically analyzed surface amplitude, the sur- m) this station has a shallower depth of 58 m resulting face stress, and the net downward surface heat ¯ux, in a stronger impact of bottom mixing. In the absence which represent the different forcing parameters, are of advection, wind stress and surface cooling mix the given in Figs. 11d±f. When the results of the standard surface layer and deepen the thermocline. This is coun- model (Fig. 11b) are compared with the tidal evolution teracted by tidal mixing in the bottom layer, which limits (Fig. 11d), one observes a periodic downward and up- the deepening of the thermocline. The evolution of the ward lifting of the thermocline, closely related to the temperature distribution therefore depends on a balance spring±neap cycle. Bottom mixing is reduced during between surface and tidal forcing. While the latter is neaps allowing deepening of the thermocline. The op- derived from atmospheric conditions, the former strong- posite occurs during spring. Sole exception is the second ly modulates with the spring±neap cycle since the thick- spring tide when the thermocline continues to deepen. ness of the bottom layer increases during spring and This is explained by an event of strong wind and surface decreases during neap tide. cooling around day 210 (Figs. 11e,f), which effectively Daily averaged contours for July and August, ob- opposes the upward expansion of the bottom layer at tained from the observations, the standard run, and ex- this spring tide. Although high winds also prevail during periment B, are plotted in Figs. 11a±c. Time series of the third spring, deepening is now prevented by the

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FIG. 10. (Continued)

stronger tidal mixing. The evolution obtained from run 2) FRONTS AND RESIDUAL CIRCULATION B (Fig. 11c) is qualitatively similar for July but becomes dissimilar in August as a result of the wind event on To examine the in¯uence of the spring±neap cycle on days 210±212 leading to the complete destruction of the the density fronts and circulation, the M 2 tide is elim- thermocline. As expected from the previous discussions, inated from the ®eld variables using a daily harmonic the evolution, obtained from run A, gives the best agree- analysis. Results are discussed for day 187 at neaps and ment with the observations (Fig. 11a). The spring-neap day 206 at spring. The two days are characterized by cycle in temperature, clearly seen in the data, is well low winds so that there are minimal effects of wind- predicted by the model. A different behavior is, how- driven circulation. The density fronts are plotted as the ever, observed for the data in August. The low winds bottom minus surface density difference ⌬␳, which rep- during days 215±220 cannot prevent the upward lifting resents an ef®cient way to visualize thermal and salinity of the thermocline despite the occurrence of a neap tide, fronts at the same time. Figure 12a shows the neap while wind deepening dominates during the third spring distribution of ⌬␳ with the superimposed circulation at around days 220±225. This appears to indicate that the 15-m depth for the central North Sea. Besides the al- model underestimates the effects of the third neap and ready mentioned anticyclonic rotation around the Dog- spring tides, as compared to the surface forcing. ger Bank, the small gyre around the Silver Pit to the

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FIG. 11. Daily averaged temperature evolution (ЊC) at station DM for Jul and Aug according to (a) the observations, (b) run A, and (c) run B. Thick line represents 14.5ЊC contour. Time series of (d) the harmonically analyzed surface amplitude, (e) surface stress, and (f) the daily averaged downward surface heat ¯ux.

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South, and the southward current along the British coast, enhances not only the horizontal but also the vertical a strong southward ¯ow is observed in the German shear, through the thermal wind relation, of the frontal Bight, which is related to a tonguelike density front in current. Neglecting the shallow wind-driven surface the Old Elbe Valley (see Fig. 2). The origin of the latter shear layer, the result is a 19% increase of the maximum feature is the low tidal mixing at neaps so that not only current from 9.6 cm sϪ1 at neaps (Fig. 12e) to 11.4 cm temperature but also salinity becomes vertically strati- sϪ1 at spring (Fig. 12f) and a stronger upwelling at the ®ed in the deeper parts of the area with a strong density slope boundary, evidenced by the larger updoming of front as a result. The situation at spring (Fig. 12b) is the isothermals. not signi®cantly different from the previous one in the The sensitivity of the previous results on the model area west of 5ЊE, except for a strengthening of the fronts parameterizations is summarized in Figs. 12g,h. The and circulation along the western and an opposite weak- ®rst one is the same as Fig. 12c now obtained from run ening along the eastern boundary of the Dogger Bank. B using the IWM scheme. The lower degree of vertical The reason for the small variability in the southward strati®cation and of surface temperatures at the strati®ed locations of the fronts is that the higher tidal mixing side of the front reduces the frontal gradients and cir- rate below 54ЊN (Fig. 7b) prevents the onset of vertical culation. This is most readily observed by the much strati®cation throughout the semimonthly mixing cycle. smaller updoming of the isopycnals. Figure 12h, to be The main differences, observed in the German Bight, compared with Fig. 12f, is derived from run E with the are the disappearance of the previously mentioned den- TVD scheme for momentum advection replaced by the sity structure and the complete reversal of the ¯ow from more diffusive ®rst-order upwind scheme. The conse- southward toward a north±northeastward-directed cur- quence is a signi®cant reduction of the shear and mag- rent. This is explained as follows. The higher mixing nitude of the horizontal current. The maximum value rate during the spring tide suppresses the vertical tem- deduced from the ®gure is 7.4 cm sϪ1 or 35% less com- perature strati®cation over the entire Old Elbe Valley pared to run A. where water depths are between 30 and 40 m, giving a The global performances of the different runs are consequent weakening of the horizontal temperature compared in Fig. 13, representing the fraction of the gradients. Although vertical salinity strati®cation is re- total area, which is thermally strati®ed, as a function of duced as well, the salinity fronts are not destroyed be- time. The sharp increase during spring re¯ects the rapid cause of the continuous river out¯ow. The result is a initial deepening of the thermocline. The semimonthly replacement of the southward thermal ¯ow by a north- variations are clearly related to modulations of tidal ward coastal plume current. In the absence of wind- mixing during the spring-neap cycle. All models behave driven circulation this periodic ¯ow reversal would be similarly in spring and summer, except for the lower repeated for each semimonthly cycle. The long-term values in run B as a result of the higher mixing rates evolution including wind effects, seen in Fig. 8d for in the thermocline. Manifest differences are seen in au- August, is a ¯ow dominated by salinity plumes. tumn when the ®nal breakdown of strati®cation occurs The behavior of the circulation around the Dogger 25 days earlier in run B and 20 days later in run D Bank is further examined with the aid of contour plots (without advection of temperature) compared to the of the temperature (Figs. 12c,d) and northward current standard simulation. The latter result demonstrates the (Figs. 12e,f) along the 55ЊN transect. Two effects need active role of advection in the erosion of the thermal to be considered. First, at the approach of the spring fronts. Tidal advection broadens the horizontal frontal tide, the water column becomes vertically mixed at larg- gradients. This is further enhanced by numerical dif- er water depths. The front consequently recedes down- fusion due to various interpolations on the C grid and slope. Since mixing takes place across ␴ lines, aligned the coarse horizontal resolution of the model near-fron- with respect to the vertical, the water column acquires tal boundaries. Lower cross-frontal density gradients after mixing a depth mean temperature that is generally imply a smaller magnitude for the alongfrontal circu- different from a neighboring location with a different lation (as discussed above) and a reduced vertical strat- depth so that an ef®cient mechanism is provided, where- i®cation by the thermal wind relation. In this way the by vertical strati®cation is converted into horizontal one. thermocline erodes more rapidly in the runs with ad- The process is most effective at places where the slopes vection. A further comparison can be made from Fig. are largest, such as the western side of the Dogger Bank, 3f showing the percentage of strati®ed stations as ob- resulting in a strengthening of the front. The second tained from all model runs and the data. The broadening mechanism, of less general nature, is related to the deep- of the fronts explains the larger number of strati®ed ening of the thermocline, occurring prior to the spring stations for the runs with advection, except for run B on day 206, which can be inferred from Fig. 12d and where the higher mixing rate in the thermocline in- which was previously discussed at station DM (see Fig. creases the relative fraction of mixed stations. Not sur- 11a). This tends to reduce the temperature differences prisingly, the highest fraction of strati®ed stations is across the lateral fronts and can explain the weakening obtained from run E using the diffusive upwind scheme of the fronts at the eastern slope of the Dogger Bank. for momentum advection. The best overall agreement The increase of the frontal gradients at the western slope during spring and summer is found for run A. In the

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FIG. 12. (a) Bottom minus surface density difference (kg m Ϫ3) and circulation at 15-m depth on 7 Jul at neaps from run A; (b) as in (a) but for 26 Jul during spring tide; (c) neaps distribution of temperature (ЊC) along the 55ЊN transect on 7 Jul from run A; (d) as in (c) but for 26 Jul at spring; (e) as in (c) but for the northward current (m s Ϫ1); (f) as in (d) but for the northward current; (g) same as (c) but calculated from run B; (h) same as (f) but obtained from run E. Thick lines delineate the 14ЊC and zero current contours. The plots are obtained after removal of the M2 tide. absence of data after September, no validation can be previously discussed lower temperature gradients in the made for the period, covering the breakdown of strat- thermocline. i®cation, which appeared to be highly sensitive to the A notable difference between the model and the ob- model formulation. servations is that the temperature maxima and minima occur at the same time in the data whereas the modeled temperatures in the lower layer are shifted by about 90Њ. c. Semidiurnal and inertial range It is remarked that a phase difference was found in the Previous observational studies in the North Sea (van measurements, reported in Van Haren et al. (1999). No Haren et al. 1999; van Haren 2000) revealed an im- obvious explanation for the data behavior can be pro- portant variability in the temperature ®eld, on timescales vided in the absence of current observations at station up to a few days, primarily due to advection by wind DM. The model results can be explained by comparing and tidally driven currents. The data analysis, presented the temperature distribution with the time series of the by Van Haren et al. (1999), showed that the basic har- horizontal (Fig. 14c) and vertical (Fig. 14d) currents. monics in the frequency spectrum are the semidiurnal Since station DM is located south of the Dogger Bank (␻) and inertial ( f ) modes. Nonlinear interaction be- where the horizontal temperature gradient has a main tween these basic harmonics generates in turn an ad- southward component (see Figs. 12a,b), only the north- ditional series of peak harmonics (2␻ Ϫ f,2f, ␻ ϩ f, ward velocity is considered. Temperature variations in the bottom mixed layer are caused by horizontal ad- M4, . . .) down to the internal wave spectrum. The existence of such oscillations can be inferred from the vection so that the time of maximum (minimum) tem- (nonaveraged) time series of the vertical temperature perature coincides with a reversal of the current from distribution (Fig. 14a) and can be clearly observed by northward (southward) to southward (northward). In the the regular upward and downward displacements of the thermocline, vertical advection becomes more dominant thermocline. The data are displayed between days 208 giving a time of maximum (minimum) temperature and 214 covering a spring±neap cycle (see Fig. 14d) when the vertical current reverses from downwelling and the strong wind event occurring on day 212 (see (upwelling) to upwelling (downwelling). The phase dif- Fig. 11e). A rigorous inspection of the plotted data ference between thermocline and lower-layer tempera- shows that the oscillations are mainly semidiurnal dur- ture ¯uctuations can then be explained by a similar shift ing the period of the spring tide when moderate winds seen in the vertical and horizontal components of the apply (days 208, 209). The inertial mode becomes dom- current. inant during the wind event. A nonlinear 2 f harmonic The model results show a similar, although smaller, can be observed during the period of maximum wind phase shift in the surface layer. The presence of this stress on day 211. The semidiurnal oscillations reappear time delay, not observed in the data plot, induces ver- after day 212 as a result of a rapid decrease in wind tical strati®cation in the lower part of the surface mixed speed. layer and explains the advective effect at station CS, A similar evolution is obtained from the results with previously observed in Fig. 6c. the standard model (Fig. 14b), although semidiurnal har- To examine the longer-term evolution of the temper- monics appear to be more dominant throughout the ature variability, an harmonic analysis is applied with whole period, except on day 211. The lower amplitudes a least squares procedure. The semidiurnal amplitudes of the vertical temperature ¯uctuations result from the are obtained at daily intervals using hourly averaged

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FIG. 12. (Continued) temperature pro®les. Time series at 13- and 41-m depth a corresponding period of 3.3 days. In the case of run are presented in Figs. 14e,f for July and August. The B the oscillations are practically semidiurnal with a su- data values in the thermocline layer show a high dom- perimposed spring±neap modulation. The results for run inance of the inertial mode. This is observed in Fig. 14e A represent an intermediate case giving qualitatively a (where data points are plotted at daily intervals) by the good agreement with the data during most of August repeated beatings occurring at the ␻ Ϫ f frequency with and with run B between days 193 and 205. Amplitudes

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FIG. 13. Fraction of the total computational area where the surface minus bottom temperature difference exceeds 1ЊC as obtained from all model experiments: run A (solid line), run B (dotted line), run C (dashed line), run D (dash±dotted line), and run E (dash and three-dotted line). are reasonably predicted except for the period between the sensitivity study of the mixing length parameteri- days 208 and 212, which is shown in the time series zation in the MO theory, recently conducted by Wei- plots (Figs. 14a,b). The semidiurnal frequency domi- dinger et al. (2000), showed important differences in nates in the bottom layer (Fig. 14f), yielding a reason- the sensible and latent heat ¯uxes. An alternative so- able agreement between models and data. A clear lution, further discussed below, is through the feedback spring±neap signal is now observed in all cases, al- mechanism of turbulent mixing on the surface forcing. though some inertial effects are still visible in the data. It is shown that advective transport by the density The underestimation of the inertial mode with respect currents has a signi®cant impact on the seasonal tem- to the semidiurnal one can be explained in two ways. perature distributions. The tendencies, obtained from the First, vertical strati®cation is underestimated and mixing model results, are in qualitative agreement with the evo- overestimated in the thermocline. The result is a larger lution seen in the observations. Although the form of diffusive coupling between the bottom and surface lay- the numerical scheme for momentum advection is not ers and a resulting conversion of inertial into tidal shear. essential for predicting the global distributions of tem- This can explain, in particular, the behavior seen in run perature, a realistic simulation of the frontal circulation B. Second, surface winds are provided at 3-hourly in- requires the implementation of a low-diffusive scheme, tervals, which does not allow the generation of inertial such as the TVD scheme. waves caused by rapid changes in wind speed and di- The study demonstrated that the spring±neap tidal rection. mixing cycle affects the vertical temperature distribution and thermal circulation. In the absence of strong wind forcing, the surface mixed layers are shallower 4. Concluding remarks and the magnitude and shear of the baroclinic circulation The seasonal, spring±neap, and short-time variability are intensi®ed at spring while the opposite occurs at of the horizontal and vertical temperature distributions neaps. The effect is enhanced (reduced) when strong and of the residual current pattern in the North Sea have (weak) winds apply at neaps or when weak (strong) been investigated with a three-dimensional baroclinic winds prevail during spring tide. The opposing tenden- model. The simulations are performed using realistic cies of the thermally and salinity-induced currents, vary- surface and open boundary data and compared with the ing on a semimonthly scale, may be considered as typ- 1989 data of the North Sea Project. A series of sensi- ical for a shelf sea with a freshwater plume near the tivity experiments were designed to test the physical coast and an offshore thermal front. role of the heat ¯ux formulations, turbulence scheme, An important outcome of the present study is the and advective transport. Although applied to a particular feedback of the vertical diffusion scheme on the baro- area and for a speci®c year, important aspects of its clinic circulation and on the surface forcing. First, the outcome can be generalized to other shelf seas as well. magnitude of the density ¯ow is reduced in reaction to The parameterization of the surface heat ¯uxes via a higher mixing rate that weakens the horizontal density the Monin±Obukhov similarity theory provides a relax- gradients at tidal mixing fronts as a result of the larger ation mechanism for the mean temperature in summer. cross-frontal mixing at the frontal slopes. Second, in- While improving the results with respect to the data, a creasing the vertical mixing in strati®ed areas reduces signi®cant error still remains. A similar overestimation the surface temperature in summer but increases the was obtained by Holt and James (1999) with a different depth mean temperature via the surface heat ¯ux. A numerical model, but using the same meteorological restoring mechanism operates in autumn when higher forcing data. Although some doubts can be cast about cooling rates tend to lower the mean temperature again. the crude climatological data for the cloud coverage, The result is of interest since, even with the standard

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FIG. 14. Time series (nonaveraged) at station DM from 28 Jul to 3 Aug: (a) observed temperature (ЊC), (b) modeled temperature, (c) northward current (m sϪ1), and (d) vertical velocity (10 Ϫ4 msϪ1) from run A. Thick lines represent the 15ЊC and zero current contours, dashed lines the 12ЊC contour. Depths below 30 m are omitted for clarity. (a) White areas represent missing data. Harmonically analyzed temperature amplitude at (e) 13-m and (f) 41-m depth for Jul and Aug: data (solid circles), run A (solid curve), and run B (dotted curve). model, the predicted strati®cation and surface temper- the mixing in the thermocline (cf. Figs. 6a,b or Figs. atures are underpredicted, which may partially account 14a,b). The overestimation of thermocline mixing with for the overestimation of the mean temperature at the the IWM scheme supports the idea, already suggested strati®ed stations. by Van Haren et al. (1999), that, in shelf seas as the Contrary to previous ocean studies (e.g., Kantha and North Sea, most of the short-time variability in the tem- Clayson 1994; Large et al. 1994), which required a tuned perature ®eld can be attributed to the semidiurnal and background mixing scheme to simulate the deepening inertial modes and their ®rst higher-order harmonics. A of the thermocline, a better agreement is obtained from subgrid-scale turbulence model for the high-frequency a formulation using limiting conditions for turbulence spectrum can then be considered of less importance, variables. Although less diffusive, the latter scheme still provided that these basic modes are well resolved by underestimates the strati®cation and thus overestimates the model. As discussed in the paper, the inertial mode

Unauthenticated | Downloaded 10/03/21 08:04 PM UTC 56 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 33 is still underestimated. Improvement for the semidiurnal oratory, Bidston Observatory, Birkenhead, Merseyside L43 component can be made with a ®ne-grid model, resolv- 7RA, United Kingdom.] Kantha, L. H., and C. A. Clayson, 1994: An improved mixed layer ing both the horizontal and vertical tidal excursion am- model for geophysical applications. J. Geophys. Res., 99, 25 plitudes of the order of respectively 5 km and a few 235±25 266. meters. Kondo, J., 1975: Air±sea bulk transfer coef®cients in diabatic conditions. Bound.-Layer Meteor., 9, 91±112. Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic Acknowledgments. This work was supported by the vertical mixing: A review and a model with a nonlocal boundary European Union's MAST program under Contract layer parameterization. Rev. Geophys., 32, 363±403. MAS3-CT97-0088 (COHERENS). We would like to Luyten, P. J., J. E. Jones, R. Proctor, A. Tabor, and K. Wild-Allen, 1999: COHERENSÐA coupled hydrodynamical±ecological thank Paul Tett and Karen Wild-Allen from Napier Uni- model for regional and shelf seas, user documentation. MUMM versity, Edinburgh, for helpful discussions. The Met Of- Rep. 911 pp. [Available on CD-ROM at http://www.mumm. ®ce is acknowledged for providing the surface forcing ac.be/coherens.] data. ÐÐ, S. Carniel, and G. Umgiesser, 2002: Validation of turbulence closure parameterisations for stably strati®ed ¯ows using the PROVESS turbulence measurements in the North Sea. J. Sea. Res., 47, 239±267. REFERENCES Lwiza, K. M. M., D. G. Bowers, and J. H. Simpson, 1991: Residual and tidal ¯ow at a tidal mixing front in the North Sea. Cont. Blumberg, A. F., and G. L. Mellor, 1987: A description of a three- Shelf Res., 11, 1379±1395. dimensional coastal ocean circulation model. Three-Dimensional Mellor, G. L., and T. Yamada, 1982: Development of a turbulence Coastal Ocean Models, N. S. 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