Air-Sea-Ice Interactions at the Ronne Polynya, Southern Weddell Sea, Antarctica

Air-sea-ice interactions at the Ronne Polynya, southern Weddell Sea, Antarctica

Emma Kathleen Fiedler

A thesis submitted for the degree of Doctor of Philosophy

University of East Anglia School of Environmental Sciences March 2009

c This copy of the thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with the author and that no quotation from the thesis, nor any information derived therefrom, may be published without the author’s prior, written consent. Abstract

Polynyas are regions of open water or thin ice in sea ice. They play an important role in the regional meteorology and oceanography of the high latitudes and in the global ocean circulation. The surface heat budget of the Ronne Polynya, Antarctica, was investigated, using a combination of field observations and modelling. Three flights were conducted over the polynya in February 2007 using a British Antarctic Survey instrumented aircraft. The polynya was observed to be mostly covered with thin ice perforated with holes and was comprised of two distinct regimes, an inner region of newly-formed and thin ice and an outer region of thicker, more consolidated ice. The sensible heat flux over the polynya was of the order of 100 W m−2 and decreased with fetch, primarily as a result of the thickening ice cover. The Bowen ratio was 3.8 ± 0.3. The sensible heat transfer and drag coefficients were calculated,

−3 −3 at CHN10 = (0.7 ± 0.1) × 10 and CDN10 = (1.1 ± 0.2) × 10 . The heat transfer coefficient is similar to that found over heterogeneous sea ice and is significantly lower than has been used in previous studies of heat fluxes over polynyas, which are often assumed to be open water. The transfer coefficients were not found to be a function of fetch or ice conditions as represented by the surface temperature and albedo. Heat budget calculations indicated little new ice was being formed at the time of the case studies but that both regimes could potentially be important for wintertime ice production and dense water formation. The data were used to validate the output of sensible heat flux, potential temperature and boundary layer depth from a simple fetch-dependent model, showing that for these case studies, surface temperatures and transfer coefficients appropriate to an ice-covered surface were required for accurate modelling.

2 Contents

Abstract 2

Acknowledgements 7

1 Introduction 8

1.1 Air-sea-ice interactions in the Antarctic ...... 8

1.1.1 Polynyas ...... 10

1.1.2 Atmosphere - polynya interactions ...... 13

1.1.3 Ocean - polynya interactions ...... 18

1.2 The Ronne Polynya ...... 20

1.3 Project aims ...... 23

2 Aircraft Observations of the Ronne Polynya 26

2.1 Flight tracks ...... 26

2.2 Synoptic conditions ...... 27

2.3 Instrumentation and data processing ...... 32

2.3.1 The BAT probe ...... 37

3 2.3.2 Total temperature probe ...... 41

2.3.3 Humidity sensors ...... 42

2.3.4 Radiation sensors ...... 43

2.3.5 Video ...... 48

3 Observations of the Convective Internal Boundary Layer 49

3.1 Vertical proﬁles ...... 49

3.2 Ice shelf height ...... 54

3.3 Entrainment ...... 55

3.3.1 The entrainment parameter ...... 58

3.4 Summary ...... 63

4 Turbulent Fluxes over the Ronne Polynya 65

4.1 Methods ...... 65

4.1.1 Eddy covariance method ...... 65

4.1.2 Obtaining timeseries of ﬂuctuating quantities from high frequency measurements ...... 67

4.1.3 Data quality control ...... 69

4.1.4 Bulk method ...... 75

4.1.5 Transfer coeﬃcients ...... 76

4.2 Observations ...... 79

4.2.1 Sensible heat ﬂux ...... 79

4 4.2.2 Flux sampling error ...... 81

4.2.3 Observed transfer coeﬃcients ...... 83

4.2.4 Surface ice conditions ...... 85

4.2.5 Relationships between transfer coeﬃcients and ice conditions . 90

4.2.6 Latent heat ﬂux ...... 92

4.2.7 Momentum ﬂux ...... 92

4.3 Summary ...... 97

5 Modelling of the Ronne Polynya Case Studies 100

5.1 Introduction to the model ...... 100

5.2 The model construction ...... 101

5.3 Modelling of the case studies ...... 103

5.3.1 Sensible heat ﬂux ...... 104

5.3.2 Potential temperature ...... 108

5.3.3 Convective internal boundary layer depth ...... 112

5.4 Summary ...... 117

6 Surface Heat Budgets and Buoyancy Flux 119

6.1 Heat budget ...... 120

6.1.1 Background ...... 120

6.1.2 The Ronne Polynya surface heat budget ...... 129

6.2 Ice production volume ...... 132

5 6.3 Surface buoyancy ﬂux ...... 137

7 Conclusions 141

7.1 Summary ...... 141

7.2 Discussion and conclusions ...... 145

7.3 Further work ...... 147

References 150

6 Acknowledgements

I would ﬁrstly like to thank my supervisor at UEA, Ian Renfrew, for all his help- ful advice and guidance along the way. I would also very much like to thank my supervisors at BAS, John King, Tom Lachlan-Cope and Keith Nicholls for all their input to this project. Thanks also to Alex Weiss and Russ Ladkin of BAS and the support team at Rothera for their help with this research, as well as all those at BAS who made my participation in the ﬁeldwork possible. Thanks also to Dave Sproson for programming help and Nina Petersen for friendly chats about spectral analysis. Finally, I’d also like to say thanks to the ENV PhDers, particularly the climbers, quizzers and tea-break takers, as well as those at Rothera who made my time there so fantastic.

This PhD was funded by a NERC studentship with a CASE award at the British Antarctic Survey.

7 Chapter 1

Introduction

1.1 Air-sea-ice interactions in the Antarctic

Fluxes of heat and moisture between the upper surface of the ocean and the lowest layers of the atmosphere play an important role in determining the meteorological and climatological conditions of the high latitudes (King and Turner, 1997). As the specific heat capacity of the ocean is high, the heat stored has a moderating effect on the climate (King and Turner, 1997). The largest heat fluxes occur in wintertime when the ocean is significantly warmer than the atmosphere. However, the presence of sea ice significantly reduces the fluxes. In winter, the flux of heat from the ocean to the atmosphere over snow-covered pack ice can be two orders of magnitude smaller than for the open ocean (Maykut, 1978). Therefore the role of sea ice is important in many meteorological processes and has a major impact on the climatology of the polar regions.

The production of dense, saline ocean bottom water in the seas surrounding the Antarctic continent has an important inﬂuence on the global ocean circulation (King and Turner, 1997). Cooling of the ocean surface and the rejection of dense, brine- rich water during sea ice formation promotes downwelling and contributes to the transformation of intermediate and deep waters, aﬀecting the oceanic overturning

8 Figure 1.1: Map of Antarctica, showing locations referred to in the text. Image from http://blackmaps.ﬁles.wordpress.com/2009/03/antarctica-map.jpg.

9 circulation (Morales Maqueda et al., 2004).

Therefore, air-sea-ice interactions in the Antarctic play an important role in both the regional meteorology and oceanography, as well as globally through their impact on the ocean circulation.

Figure 1.1 is a map of Antarctica, showing the locations of areas mentioned in the following sections.

1.1.1 Polynyas

The presence of even small fractions of open water and thin ice in sea ice can significantly alter the surface balances of heat and moisture. These open water areas can be in the form of leads, which are linear narrow fractures in the pack ice caused by divergent motion of the ice, see figure 1.2(a), or polynyas, see figure 1.2(b). Polynyas are larger, non-linear areas of open water or thin ice in the sea ice pack ranging in area from 10 to 105 km2 (Barber et al., 2001). They are formed and maintained either through the divergent motion of sea ice due to wind stress or the action of ocean currents, or through melting due to an influx of oceanic sensible heat which also prevents the formation of new ice (Morales Maqueda et al., 2004). Polynyas have been known to exist since the early days of Antarctic exploration, because of the access they provided to the coastal areas early on in the Antarctic summer (King and Turner, 1997).

In addition to the surface heat and moisture budgets, polynyas can also modify the surface momentum balance since they allow the oceanic mixed layer direct contact with the surface winds (Morales Maqueda et al., 2004). They also have an eﬀect on biogeochemical air-sea ﬂuxes and on tracer transport by the ocean as a result of convection and vertical mixing, and, as a consequence of turbulence and freezing, can also provide conditions for the entrainment of pollutants and sedi- ments (Morales Maqueda et al., 2004). As they often recur regularly, polynyas are also important as biological habitats and, in the Arctic, have been used as hunting

10 open lead sea ice

newly-frozen sea ice

(a) An open lead in pack ice. From http://a76.dk/graﬁk/lorita 2104 open lead.jpg

Ronne Ice Shelf (Antarctic Peninsula)

wind direction (offshore) Ronne Polynya

(b) The Ronne Polynya, southern Weddell Sea, Antarctica, looking upwind towards the Ronne Ice Shelf.

Figure 1.2: Photos showing examples of a lead (a) and a polynya (b).

11 grounds by Inuit for the past 3000 years (Smith et al., 1990).

A wind-driven, or coastal, polynya is caused by the oﬀshore advection of sea ice by strong, cold, continental winds. The exposed ocean surface, which is normally at the freezing point, rapidly cools and new ice is formed, which is also advected oﬀshore, in a continuous process. The ice formed is typically frazil ice (spicules, or plates of ice which are suspended in water (Morales Maqueda et al., 2004)) due to the turbulence generated by the wind (Smith et al., 1990). The frazil ice is herded downwind and forms grease ice, a mixture of salt water and coagulating ice (Morales Maqueda et al., 2004). The action of winds above 7-8 m s−1 induces the formation of Langmuir circulations in the ocean surface, arranging the newly-formed frazil ice in characteristic rows parallel to the direction of the wind (Morales Maqueda et al., 2004).

Katabatic and synoptic winds play a signiﬁcant role in ice removal at coastal polynyas (Brown, 1990; Worby et al., 1998), and, in the case of polynyas in the vicinity of the Antarctic Peninsula, synoptically-forced barrier winds (Schwerdtfeger, 1975; Parish, 1983). Wind-driven polynyas have been in the past somewhat misleadingly termed latent heat polynyas as the mechanism for keeping these areas ice-free was thought to be the release of latent heat during ice formation. However, it has since been accepted that the release of latent heat is responsible only for maintaining the temperature of the water at the freezing point and hence cannot determine the freezing rate itself (Morales Maqueda et al., 2004). Thus the polynya is maintained through mechanically-driven ice export.

The idea that the balance between ice export and ice formation governs the areal extent of the polynya has been the basis for a number of modelling studies on polynya dynamics. The original formulation was developed by Pease (1987) who, based on an idea of Lebedev (1968), devised a simple model where frazil ice was assumed to grow within the polynya at a rate determined from the surface heat budget. The newly-formed ice was then herded downwind, where it piled up against the receding edge of the polynya. A weakness of the model however was the assumption that this piling-up occurred instantaneously. Consequently, Ou (1988) developed a

12 model which incorporated a drift rate for the frazil ice formed within the polynya. Nevertheless, owing to the simple formulation, Pease-type models have been used in a number of polynya studies, for example, coupled with ocean models (e.g. Mysak and Huang, 1992), as a basis for the investigation of the time-dependent surface buoyancy ﬂux and dense water production (Chapman, 1999) and as a comparison with polynya width derived from satellite data (Markus and Burns, 1995). Further discussion of the modelling of polynyas is provided in section 1.1.3.

1.1.2 Atmosphere - polynya interactions

During a cold-air outbreak over a coastal polynya, when cold air is advected over relatively warm open water, the large ocean-atmosphere temperature and humidity diﬀerences result in large sensible and latent heat ﬂuxes from the ocean to the atmosphere. This leads to a warming and moistening of the boundary layer above and downwind of the polynya and, owing to the change in surface conditions, the formation of a very unstable convective internal boundary layer (CIBL), which rapidly grows upwards (e.g. Stage and Businger, 1981). Figure 1.3 is a schematic showing the development of a CIBL over a coastal polynya.

The CIBL

Internal boundary layers (IBLs) are formed as a result of horizontal advection of air across a surface discontinuity, e.g. a step change in surface roughness or the availability of heat and moisture (Garratt, 1990). This aﬀects the atmospheric stability, thereby aﬀecting turbulent mixing and momentum transfer (Kaimal and Finnigan, 1994). If the surface change is perpendicular to the mean wind direction, the IBL can be assumed horizontally homogeneous in the cross-wind direction (Kaimal and Finnigan, 1994).

Over leads and polynyas, IBL growth is due mainly to the large discontinuity in surface temperature between the ice and the open water, the change in surface roughness being less signiﬁcant (Pinto et al., 1995). Under these circumstances, the

13 Figure 1.3: Growth of a CIBL due to a surface temperature discontinuity at a coastal polynya. CIBL height increases with fetch in direction of mean wind. Sensible and latent heat ﬂuxes are large because of large ocean-atmosphere temperature and humidity gradients, which decrease with fetch causing a reduction in the turbulent heat ﬂuxes.

IBL is sometimes referred to as the Thermal Internal Boundary Layer (TIBL) (e.g. Pinto et al., 1995) but use of the word convective, as in CIBL, emphasises that convection (buoyancy) is the dominant mode of turbulence. The convention CIBL will therefore be used in this study, following e.g. Hsu (1986) and Renfrew and King (2000).

As the near-surface air crosses the polynya it is warmed and moistened, primarily as a result of turbulent heat and moisture flux convergence (Stage and Businger, 1981; Chou and Zimmerman, 1989; Chang and Braham, 1991; Brümmer,1997; Renfrew and King, 2000). This reduces the surface-air temperature and moisture gradients which, given a constant surface temperature and wind speed, leads to a non-linear reduction in the surface sensible and latent heat fluxes with fetch (Andreas and Murphy, 1986; Grossman and Betts, 1990; Chang and Braham, 1991; Brümmer, 1997; Renfrew and Moore, 1999; Renfrew and King, 2000). This reduction is of the

14 order of 20 % over fetches of tens of kilometres and up to 50 % over hundreds of kilometres (Renfrew et al., 2002). Radiative heat losses will also be greatest at the upwind edge of the polynya in the presence of cloud or fog, as this increases with fetch owing to moistening of the boundary layer (Smith et al., 1990).

The depth of the CIBL increases with fetch as a consequence of the warming from the surface and additional turbulent entrainment of warm air from the free atmosphere above (Garratt, 1990). As well as the predominantly buoyancy-driven boundary layer over the polynya, wind shear will also have a modifying eﬀect on the ﬂow. The CIBL may also deepen or become thinner through the action of convergence or divergence (Stage and Businger, 1981).

The effect of the surface heat fluxes on CIBL depth is small compared with the effect of the stability of the air above the boundary layer (Brümmer, 1997) and the strength (i.e. temperature difference across it and depth) of the capping inversion (e.g. Pinto et al., 1995). The surface fluxes themselves are relatively insensitive to atmospheric stability, as well as divergence rates and cloud cover, being primarily affected by the air-sea temperature and humidity differences (Boers et al., 1991). However, they are affected to some extent by variations in the CIBL depth, and therefore atmospheric stability, as a result of variations in the layer-averaged potential temperature and humidity, as a result of heat and moisture from the surface being spread over a boundary layer of different depth (Brümmer,1997).

Polynyas can also influence the surface heat budget through the generation of ice fog (Smith et al., 1990). Clouds will form in the CIBL if the lifting condensation level is below the CIBL height, i.e. if the CIBL becomes moist and deep enough (Pinto et al., 1995). The presence of clouds increases the entrainment rate and the importance of latent heat release and radiative processes to the heat and moisture budgets. Although turbulence is still the dominant physical process affecting the evolution of a moist and cloud-filled CIBL, in modelling studies it has been shown that neglect of secondary thermodynamic processes related to radiative transfer, condensation and precipitation may result in an underestimation of boundary layer depth of 10 - 20% (Pinto et al., 1995).

15 Convective clouds and plumes generated by polynyas have been observed to reach heights of up to 4 km (Smith et al., 1990) and are frequently observed on satellite images (Morales Maqueda et al., 2004). Polynyas therefore have the potential to modify and induce mesoscale atmospheric motion, impacting on regional climate (Walter, 1989; Kottmeier and Engelbart, 1992; Alam and Curry, 1995; Pinto et al., 1995; Pinto and Curry, 1995; Gall´ee,1997; Dare and Atkinson, 1999; Morales Maqueda et al., 2004). Plumes can exist even when the polynya is covered with thin ice, provided the latent heat ﬂux does not become negligible (Morales Maqueda et al., 2004).

The surface energy balance

Owing to the diﬃculties of access, particularly during the winter months, direct measurements of the surface energy balance over polynyas are limited, and long- term measurements do not exist. Therefore, studies of the annual surface heat budget of coastal polynyas such those by Markus et al. (1998) and Renfrew et al. (2002) rely instead on remotely-sensed data and modelling. Markus et al. (1998) obtained typical values for wintertime turbulent heat losses at coastal polynyas in the southern Weddell Sea of around 200 to 300 W m−2, with radiative heat losses greater than 100 W m−2. Renfrew et al. (2002) found similar values for the Ronne Polynya, also in the southern Weddell Sea, of mean wintertime turbulent heat losses of 270 W m−2 and radiative heat losses of 50 W m−2.

The total wintertime energy loss from polynyas is therefore dominated by the turbulent fluxes, i.e. fluxes of sensible and latent heat. The latent heat flux is several times smaller than the sensible heat flux due to the low specific humidity of the saturated air at the surface in contact with the sea water at freezing point (Smith et al., 1990). Typical values for the Bowen ratio (ratio of sensible to latent heat flux) over polynyas lie between 2 and 4 (den Hartog et al., 1983; Pease, 1987; Renfrew et al., 2002).

The energy loss by polynyas is enough to dominate the winter regional heat budget and means a small change in the percentage of open water can lead to large

16 changes in the air temperature of the polar regions in winter (Smith et al., 1990). The presence of new ice, rather than open water, within a polynya does reduce the ocean-atmosphere exchange but signiﬁcant ﬂuxes still occur (Morales Maqueda et al., 2004).

Ice formation

The entire water column over the continental shelf is near freezing point in wintertime (Zwally et al., 1985), so the large ocean-atmosphere heat ﬂuxes and continual removal of the ice by the wind as quickly as it can form result in high rates of ice production, earning this type of polynya the nickname “ice factory” (e.g. Comiso and Gordon, 1998). For example, ice production rates in Weddell Sea coastal polynyas are greater than central Weddell Sea ice production rates by a factor of ten (Zwally et al., 1985; Markus et al., 1998; Renfrew et al., 2002), with estimates of polynya production rates ranging from 10 − 12 m yr−1 (per unit area) (Markus et al., 1998) up to 31.7 m yr−1 (Renfrew et al., 2002).

In spring and summer, over 90 % of incoming solar radiation over a polynya is absorbed by the open water (Smith et al., 1990) impacting on the balance of heat (as well as mass) in the ice pack and ocean (Maykut and McPhee, 1995). The snow- covered pack ice surrounding a lead or polynya has an albedo of around 0.8 (Smith et al., 1990) and thus leads and polynyas can provide centres of initial warming prior to the breakup of ice cover in the spring, allowing the pack ice to decay from ‘within’ as well as by the retreat of the ice edge from north to south (Worby et al., 1998). Melting of ice in and around a polynya transforms it into an “ice melt factory” (Ohshima et al., 1998). Frazil ice formation is also prevented by the incoming solar radiation, so the polynya is unable to reach equilibrium and increases in size for as long as the winds continue to be directed oﬀshore (Morales Maqueda et al., 2004). An example of a summer polynya of this type occurred oﬀ the Ronne Ice Shelf in January to February 1998. The polynya covered an area of 4 × 105 km2, extending 500 km north of the shelf (Morales Maqueda et al., 2004). This event was driven by an anomalous wind stress pattern and sustained by the absorption of solar radiation (Ackley et al., 2001; Hunke and Ackley, 2001).

17 Comiso and Gordon (1998) have suggested that polynyas might play an important role in the areal extent of sea ice, owing to a coherence found between Weddell Sea ice extent and peak values in the areas of coastal polynyas in the region. In addition, frazil ice has been found in cores of sea ice from the Weddell Sea (Eicken and Lange, 1989), suggesting an important amount of ice in the Weddell Sea originates in coastal polynyas (Morales Maqueda et al., 2004). However, Renfrew et al. (2002) did not ﬁnd a relationship between the annual ice production in coastal polynyas and that of the Weddell Sea. In addition, polynyas were found to contribute to only around 6 % of the total ice budget of the region, as a consequence of their small areal fraction, of about 0.2 % of the areal extent of the ice pack (Markus et al., 1998). By considering all the major Antarctic coastal polynyas together, Tamura et al. (2008) estimated ice production within the polynyas to be around 10 % of the total sea ice produced in the Southern Ocean, where the total area of the polynyas was around 1 % of the maximum ice area. However, potentially the most important impact of ice production in coastal polynyas is their inﬂuence on the production of dense water.

1.1.3 Ocean - polynya interactions

Despite their relatively small size, polynyas play an important role in the regional oceanography of the high latitudes and the ventilation of deep and bottom water both in the Southern (Grumbine, 1991; Comiso and Gordon, 1998) and Arctic Oceans (Schauer, 1995; Schauer and Fahrbach, 1999).

The high wintertime ice production rates at coastal polynyas result in extensive brine rejection, whereby sea water rejects salt on freezing, leaving the sea ice relatively fresh and the modiﬁed water column relatively salty. The salinity increase of sea water due to brine rejection as a result of frazil ice formation is up to several tenths of a part per thousand (Morales Maqueda et al., 2004). This saliniﬁcation, combined with surface cooling, increases the density of the water, leading to large buoyancy losses and the initiation of downward convection (Morales Maqueda et al., 2004).

18 The fixed location of coastal polynyas, over the relatively shallow waters of the continental shelves, allows water of enhanced salinity to accumulate without the moderating effect of mixing with other water masses. Therefore the contribution of polynyas to dense water mass formation can be significant.

Antarctic Bottom Water (AABW) is the densest water mass found in any of the free oceans (King and Turner, 1997) and the most extensive water mass, reaching as far north as 50 oN in the Pacific (Foldvik and Gammelsrød, 1988). At most sites where it is formed, coastal polynyas play an important role in the production process (Foldvik and Gammelsrød, 1988). Known sites of AABW production include the Ross Sea (Koshlyakov and Tarakanov, 2003), the Weddell Sea (Foldvik and Gammelsrød, 1988), the area off the Adelie Coast (Fukamachi et al., 2000), and potentially off the Amery Ice Shelf (Tamura et al., 2008).

In general, polynya areas are below the resolution of large-scale coupled sea ice- ocean general circulation models (Morales Maqueda et al., 2004). However studies such as those by Grigg and Holbrook (2001) and Stossel and Markus (2004) have found that poor representation of the processes taking place within polynyas may aﬀect the realistic simulation of the global thermohaline circulation (THC). Accurate parameterisations of the water mass transformation processes taking place within them (as well as the injection of heat and moisture into the lower atmosphere) based on insights provided by dynamic and thermodynamic models as well as both remote sensing and in-situ observations are therefore important.

The polar regions have been recognised as being particularly sensitive to changes in climate (Meehl et al., 2007). Future temperature increases are predicted as well as increases in precipitation, both of which could aﬀect dense water formation in polynyas and subsequent ventilation of the deep ocean, inﬂuencing the global THC (Marsland et al., 2007). Changes in the size or frequency of occurrence of polynyas could also be used as indicators of changes in the climate (Morales Maqueda et al., 2004). In addition, the interactions between polynyas and the ocean circulation beneath the ice shelves are important for investigations into future changes in ice shelf stability (Morales Maqueda et al., 2004). In order to predict how the oceans and climate

19 on a global scale might repond to future climatic change, it is vital to understand smaller scale atmospheric and oceanic processes, including those taking place within polynyas.

1.2 The Ronne Polynya

This project centres on the Ronne Polynya as a case study for the investigation of air-sea-ice interactions taking place within polynyas. The Ronne Polynya is a coastal polynya located in the southern Weddell Sea, Antarctica, adjacent to the Ronne Ice Shelf front, see figure 1.4, and driven by the prevailing offshore winds. The area of the Ronne-Filchner Ice Shelf is one of the most active in the Weddell Sea for coastal polynyas (Markus et al., 1998; Comiso and Gordon, 1998; Renfrew et al., 2002). The approximate mean surface area of the Ronne Polynya is 20 × 103 km2, with an offshore fetch of the order of 100 km, but with large inter- and intra-seasonal variability (Renfrew et al., 2002). It is thought this is related to variations in atmospheric mesoscale and synoptic features such as storm tracks, cyclones and barrier-forced winds (Renfrew et al., 2002). The Ronne Polynya is a recurring polynya, meaning it opens episodically in the same location, thereby having an important regional impact on the atmosphere and the ocean.

The Ronne Polynya can be seen in figure 1.5, an image of satellite-derived sea ice concentration in the Weddell Sea. The polynya is the entire area of low ice concentration which can be identified off the Ronne Ice Shelf. The data are obtained using the AMSR-E (Advanced Microwave Scanning Radiometer for EOS) passive satellite sensor, derived using the sea ice retrieval algorithm developed by Spreen et al. (2008).

Through the mechanism of sea ice formation and brine rejection within the polynya, as described previously, a water mass known as High Salinity Shelf Water (HSSW) is produced by saliniﬁcation of water ﬂowing onto the continental shelf at the Ronne Polynya (Nicholls et al., 2003). There are three ways in which HSSW contributes to

20 Weddell Sea

Antarctic Peninsula Approximate location of Ronne Polynya

Ronne Ice Shelf

Filchner Ice Shelf

Figure 1.4: Study Location the formation of Weddell Sea Bottom Water and Weddell Sea Deep Water, which are precursors to Antarctic Bottom Water (AABW) (Nicholls et al., 2003). Firstly, the HSSW may become dense enough to be transported offshore directly, over the continental slope to the deep ocean. Secondly, mixing with off-shelf water masses at the shelf break may enable the HSSW to penetrate the dynamic barrier of the shelf break front (Foster and Carmack, 1976). Thirdly, before reaching the shelf break, a fraction of the HSSW flows beneath the ice shelf where it is modified by heat, freshwater and momentum exchange at the base of the ice shelf and is converted to a colder, fresher water mass known as Ice Shelf Water (ISW), which then ascends as a result of positive buoyancy (Nicholls et al., 2004). This process is shown schematically on figure 1.6. With a temperature lower than the surface

21 45 oW 30 oW 15 oW

70 oS

Weddell Sea

80 oS

Ronne Ice Shelf

Figure 1.5: AMSR-E sea ice concentration, C (%), in the Weddell Sea, 27 February 2007 (data from http://iup.physik.uni-bremen.de:8084/amsr/amsre.html, see Spreen et al. (2008)). The Ronne Polynya is the area of low ice concentration located oﬀ the Ronne Ice Shelf. freezing point of -1.9 oC, the ISW is relatively dense compared to the surface water and therefore descends the continental slope.

The Weddell Sea is considered to be a major source region of AABW (Orsi et al., 2002). However, it has been recently suggested that estimates of coastal polynya ice production rates oﬀ the Ronne Ice Shelf are lower than would account for the high volume of AABW, which could instead be a cumulative eﬀect of brine rejection from the east along the Antarctic Coastal Current (Tamura et al., 2008).

22 Offshore winds

HSSW production at polynya

Figure 1.6: Sub-ice shelf oceanographic processes (after Nicholls et al., 2004). Melt- ing of deep basal ice occurs as HSSW at depth is warmer than freezing point. Addi- tion of meltwater to HSSW forms ISW, which ascends owing to positive buoyancy. Some recirculation due to density increase occurs if freezing temperature overtakes plume temperature, resulting in formation of marine ice.

However, in order to accurately quantify ice production rates and thus the amount of dense water formed at the Ronne Polynya, it is necessary to ﬁrst investigate in detail the surface heat budget, which governs the rate of ice production.

1.3 Project aims

Using the Ronne Polynya as a ‘natural laboratory’, the surface heat budget of coastal polynyas will be investigated through a combination of ﬁeldwork observations and modelling.

Aircraft-based observational data from low-level ﬂights over the Ronne Polynya during a cold-air outbreak will be analysed to provide new estimates of the surface heat budget at the Ronne Polynya and over coastal polynyas in general, as well as

23 insights into CIBL structure and development. There are only a limited number of previous aircraft-based observational datasets over leads, polynyas and sea ice, e.g. Hartmann et al. (1994), Br¨ummeret al. (2002), Schr¨oder et al. (2003), Walter et al. (2006) and all of these have been obtained in the Arctic. The Antarctic data set analysed in this study is therefore unique, owing not only to its southern hemisphere location but also to the very low-level (down to 14 m above the surface) extended transects obtained over the heterogeneous surface, providing spatially representative results. This spatial coverage can only be achieved using an aircraft measurement platform.

In addition, at the time of the ﬂights, the polynya was mostly covered with thin ice, with no extensive regions of open water. This aﬀorded the opportunity for the investigation of heat transfer over a heterogeneous ice surface, the results of which are applicable not just to studies of polynyas but to investigations of regions with similar ice concentrations, such as the marginal ice zone (MIZ). Therefore, the data and results from the analysis presented in this study make an important contribution to the currently limited body of observational data obtained under these conditions.

The potential impact of polynyas on the regional oceanography and meteorology of the high latitudes and on the global ocean circulation emphasises the importance of obtaining suitable and accurate parameterisations of the air-sea-ice interaction processes occurring within them for use in modelling studies. Owing to the paucity of observational data, the opportunites to validate smaller-scale models which can provide these parameterisations and aid understanding of the key processes govern- ing deep water formation are limited.

The observational data set obtained at the Ronne Polynya will therefore be used to validate the model developed by Renfrew and King (2000), which was designed to model CIBL depth and surface heat ﬂuxes over a coastal polynya during a cold-air outbreak. The results from this analysis will provide insights into the accuracy of the parameters required for successful modelling of the ocean-atmosphere heat ﬂuxes and CIBL depth.

24 The structure of this study is as follows. Details of data collection methods are provided in chapter 2. Chapter 3 presents an analysis of the observed structure of the CIBL, and appropriate parameters for forcing the model are also obtained. Chapter 4 covers calculation and analysis of the surface turbulent heat ﬂuxes. In chapter 5 the observational data set is used for model validation and in chapter 6 the broader applications of the preceding results are examined. A ﬁnal discussion and conclusions follow in chapter 7.

25 Chapter 2

Aircraft Observations of the Ronne Polynya

2.1 Flight tracks

In order to investigate the surface energy budget and boundary layer structure, three research flights were conducted over the Ronne Polynya between 25 and 28 February 2007. These flights were part of a wider British Antarctic Survey field campaign, measuring surface fluxes over sea ice, open water and ice shelves around the Antarctic Peninsula as part of the MASIN (Meteorological Airborne Science INstrumentation) project. Figure 2.1 shows all the flight tracks for the 2007 field season, based at Rothera research station on the Antarctic Peninsula. The three flights over the Ronne Polynya can be seen on the figure.

In total, five straight and level legs at low altitude and two sawtooth pattern legs were conducted in the along-wind direction, perpendicular to the front of the Ronne Ice Shelf. Figure 2.2 shows the Ronne Polynya flight tracks in more detail and table 2.1 the flight information for the level-flight legs, where leg 1 (L1) represents a flight out from the ice shelf and leg 2 (L2) towards. For flight F49L1 an instrument malfunction meant there were no heat or momentum flux measurements for this leg,

26 but other atmospheric data are available.

Flight Date and Mean Fetch (km)Tsfc -Tair 10 m wind speed Mean wind direction time (UTC) altitude observed observed range observed range (de- (m) range (oC) (m s−1) grees) (oﬀshore ≈ 180 - 225o)

F49L1 25/02/07 35 72.3 3.0 - 8.0 9.4 - 10.6 209.7 - 213.4 16:33 - 16:50 F49L2 25/02/07 32 84.9 2.1 - 9.0 4.8 - 6.6 195.9 - 208.1 16:52 - 17:17 F54L1 27/02/07 14 120.9 3.1 - 12.8 13.3 - 16.3 204.0 - 213.5 15:18 - 15:43 F54L2 27/02/07 33 127.5 2.9 - 12.5 8.0 - 11.5 196.0 - 208.8 15:44 - 16:27 F57L1 28/02/07 15 85.2 4.4 - 14.0 11.5 - 12.3 212.5 - 220.6 16:32 - 16:59

Table 2.1: Flight information for low-level legs. F54 and F57 also included a ‘sawtooth’ proﬁling leg, see ﬁgure 2.2.

2.2 Synoptic conditions

Figure 2.3 shows plots of mean sea level pressure from ECMWF operational analyses at 1200 hrs (before observations - see table 2.1) and 1800 hrs (after observations) for the three flight days. The plots illustrate the presence of a persistent low pressure system situated in the Weddell Sea, which induced a cold-air outbreak off the Ronne Ice Shelf at the time of the measurements. This system produced steady moderate to strong offshore winds (see table 2.1), which were responsible for the opening of the Ronne Polynya. Weather conditions during flight F57 were clear and sunny while for F54 it was sunny with some high altitude cloud. For F49 some cumulus cloud was present within the CIBL but no precipitation was observed.

The Ronne Polynya can clearly be seen in figure 2.4, AMSR-E-derived images of sea ice concentration (see section 1.2) for the dates of the three case studies. The entire area of low ice concentration located off the Ronne Ice Shelf in figure 2.4 is the polynya. The data are derived using the sea ice retrieval algorithm developed by Spreen et al. (2008), which, despite the effect of atmospheric influence, is able to utilise the higher frequency channels. This provides sea ice concentration data

27 Ronne Polynya flights

Figure 2.1: All ﬂight tracks for MASIN 2006/07 ﬁeld campaign.

28 Figure 2.2: Flight patterns over the Ronne Polynya. Flight 49 (F49) shown in blue, ﬂight 54 (F54) in green and ﬂight 57 (F57) in red.

with a ﬁner horizontal resolution than that derived from the more commonly used SSM/I (Special Sensor Microwave Imager) instrument.

Generally, synoptic-scale variability primarily sets the conditions which lead to variations in the turbulent fluxes, i.e. air-surface temperature differences and wind speed (Brümmeret al., 2002). However, under these quasi-stationary atmospheric conditions, where there is little difference between the synoptic situation before and after each flight (see figure 2.3), it is the local conditions such as fetch and ice thickness which cause the variations in the surface turbulent fluxes for these case studies. The polynya itself can be assumed to be in a steady state over each of the periods of measurement. As shown on figure 2.4, the difference in polynya size between each of the days is small. The timescale of synoptic variation as well as polynya variation, of the order of days, is therefore much greater than the time taken for each measurement leg, of a maximum of 43 min (see table 2.1). Therefore, the assumption of a steady-state polynya is valid during each flight leg and the structure of the CIBL can be assumed a function of fetch and not of time.

29 o o 984 W W 988 976 992 992 15 988 15

976 o W 972 o W 976 980 980 972 30 980 30 980 984

o W o W 984 988 984 988 45 984 45 984 988 992 980 988 980 988 988 o W 992 o W

984 976 60 984 984 60 988 980 976 988 980 976 984 988 988 980 980 W W 988 o 980 988 o 976 980 976 992

976 992 976 976 980 980 976 992 75 75 984 992 984 996 976 984 980 980 W 984 W

984 o 988 980 o 988 980 988 984 988 1000 988 o 992 996 o 988 60 S o o 60 S o o 992 66 S 72 o 66 S 72 o 1000 90 S 78 90 S 78 S 84oS S 84oS

(a) 25/02/2007 1200 (b) 25/02/2007 1800

o W o W 15 15 988 o 988 o 988 W 988 992 W 30 30 992

o W 992 o W 984 984

45 984 988 45 984 984 988 988 988 o W o W 988 984 984 980 980 992 988 984 984 60 60 984 980 980 988 984 988 988

W 988 W 988 o o 992 992 988 992 984 988 992 996 980 980 988 984 988 992 984 75992 992 996 75 984 988 988 988 988 988 996 992 988

W992 W 988 988 1004 996 o o 992 992 992 1000 996 992 1004 996996 996 1000 992 o 1008 o 996 60 S 66o o 60 S 66o o 1000 S 72 o S 72 o 1008 90 S 78 90 S 78 S 84oS S 84oS

o W o W

15 98415 992 o W o W

30 992 30 988 984 988 980 o W 980 o W

988 988

45 984 45 988 988

984 996 996 984 o W o W 992 984 988 992 984 992 60 992 988 60 992

984 992 988 988 992 992 W W 988 o o 992 988 984 984 992 988 996 996 980 988 75 988 75 1000 984 992 1000 992 1008 992 988 992 1012 992 1000 101210081004 W 1004 W 996 1000 o o 996 988 992 o 996 1004 o 992 1004 60 o 992 1008 60 o 1008 S 66 S 72o o S 66 S 72o o 996 90 S 78 90 S 78 S 84oS S 84oS

(e) 28/02/2007 1200 (f) 28/02/2007 1800

Figure 2.3: Mean sea level pressure in vicinity of the Ronne Polynya before and after ﬂight times. Wind direction oﬀshore and synoptic situation steady. All times given in UTC.

30 45 oW 30 oW 15 oW 45 oW 30 oW 15 oW 70 oS 70 oS

80 oS 80 oS

(a) 25/02/2007 (b) 27/02/2007

45 oW 30 oW 15 oW 70 oS

80 oS

Figure 2.4: AMSR-E sea ice concentration in the Weddell Sea, grid 6.25 km. Data from http://iup.physik.uni-bremen.de:8084/amsr/amsre.html, see Spreen et al. (2008). Low ice concentrations can be seen at the Ronne Polynya (around 75oS, 60oW).

31 Figures 2.5, 2.6 and 2.7 show AVHRR (Advanced Very High Resolution Radiometer) satellite images (false colour, combined visible and infra-red) of the Ronne Polynya for the three ﬂight days, captured both a few hours before and after the time of the observations in each case. The sharp edge of the Ronne Ice Shelf and the low ice concentrations of the polynya can clearly be seen on all of the images.

For F49 (figure 2.5) there is some cloud visible which was apparent during the flight. This would have affected the incoming shortwave (and longwave) radiation to the polynya, reducing the fraction of direct compared to diffuse radiation and thereby affecting the required calibration corrections for the upward-looking pyranometer (see section 2.3). F54 was conducted under cloud-free conditions, the area of cloud close to the Antarctic Peninsula (seen on figure 2.6(a)) having cleared by the time of the flight. A limited number of cumulus cloud streets were observed during the flight but not in the immediate vicinity of the measurement area and so the effect of these on the heat and moisture budgets can be ignored. F57 was conducted in the cloud-free area at the Peninsula end of the Ronne Ice Shelf seen in figures 2.7(a) and 2.7(b).

2.3 Instrumentation and data processing

Observations of the surface ﬂuxes and the CIBL (convective internal boundary layer) were conducted using an instrumented British Antarctic Survey DHC-6 Twin Otter aircraft. Table 2.2 shows a summary of the instrumentation used and variables measured and ﬁgure 2.8 shows the aircraft with the location of the instruments. Time signals from the GPS system were used to provide a common timebase for all of the sensors and all the data were recorded using an onboard computer system and interpolated onto the BAT probe frequency. The following sections give details of key instruments and data processing procedures.

32 70 oS

75 oS

60 oW

80 oW

(a) 25/02/2007 1319

70 oS

75 oS

60 oW

80 oW

(b) 25/02/2007 2012

Figure 2.5: AVHRR combined visible and infra-red satellite images of Antarctic Peninsula area on day of ﬂight F49, showing zoomed-in area of the Ronne Polynya. Figure (a) shows image captured earlier than observation times and ﬁg. (b) later.

33 70 oS

75 oS

60 oW

80 oW

(a) 27/02/2007 1054

70 oS

75 oS

60 oW

40 oW

(b) 27/02/2007 1810

Figure 2.6: As ﬁgure 2.5 but for F54.

34 70 oS

75 oS

60 oW

80 oW

(a) 28/02/2007 1210

70 oS

75 oS

60 oW

80 oW

(b) 28/02/2007 1941

Figure 2.7: As ﬁgure 2.5 but for F57.

35 a eetne ya xr 0 atclmls(185 fuel. miles nautical of 100 extra an by extended be can iao 20 t(3658 ft 12000 of tica 2.8: Figure icatadisrmnain h ln a nattd ii nAntarc- in limit altitude an has plane The instrumentation. and Aircraft

Fast thermocouple Downwelling LW and temperature sensors SW radiometers m

n ag faon 0 atclmls(926 miles nautical 500 around of range a and ) Vaisala Humicap inlet GPS GPS (roof) (tail) GPS GPS (wing) (wing)

36 BAT probe Pitot pressure Rosemount total ports (both km temperature sides) Static

sn nitra er tank ferry internal an using ) sensors pressure ports (both sides) Cooled mirror Infra-red thermometer hygrometer (other Upwelling LW and SW radiometers

km side of nose) Downward-looking video ,which ), camera Variable Instrument Sampling Rate

true airspeed, angle of at- NOAA ARL 9 hole BAT (Best Aircraft Tur- 50 Hz tack, sideslip angle bulence) probe

fast response temperature BAT probe thermocouple sensors 50 Hz

static pressure Honeywell HPA sensors 5 Hz dynamic pressure

total temperature Rosemount 102E4AL Non-Deiced 0.7 Hz Rosemount 102AU1AG Deiced

aircraft attitude, altitude Javad AT4 4-antenna GPS system 20 Hz aircraft position, velocity 10 Hz

aircraft altitude radar altimeter 0.7 Hz

humidity Buck 1011C cooled mirror hygrometer 1 Hz Vaisala Humicap sensor 0.7 Hz

radiation ﬂuxes 10 Hz shortwave Eppley PSP pyranometers longwave Eppley PIR pyrgeometers

surface temperature Downward Heimann KT 19.82 infrared radi- 10 Hz ation thermometer

visual record Sony DCR-TRV60E video cameras downward (hatch); handheld (cockpit) constant (90 min capacity) digital camera variable

Table 2.2: Instrumentation

2.3.1 The BAT probe

A Best Aircraft Turbulence, or BAT, probe (Garman et al., 2006) was used to collect measurements of temperature and wind speed at a frequency of 50 Hz, which corresponds to a sampling interval of 1.26 m at the aircraft’s level-ﬂight true airspeed of 63 m s−1. The aluminium probe can be seen on ﬁgure 2.8 mounted on the end of a 3 m boom positioned at roof level and extending along the centre line of the aircraft to just in front of the nose.

The end of the BAT probe is hemispherical and has nine holes to sense the angles and velocity of the airﬂow relative to the aircraft, making measurements of true airspeed, angle of attack and sideslip angle. As described by Lenschow (1986), and shown in ﬁgure 2.9, the angle of attack, α, is the airstream angle with respect to the vertical plane of the aircraft, positive in the downward direction. The angle of

37 Figure 2.9: Schematic showing the attack (α) and sideslip (β) angles (after Lenschow, 1986). sideslip, β, is the airstream angle with respect to the horizontal plane of the aircraft, where, looking from above, a clockwise rotation is positive. Figure 2.10 shows a close-up image of the end of the BAT probe, which also shows the two thermocouple fast temperature sensors located on the probe that measure high frequency ﬂuctuations in temperature. Two of these thermocouple wires are included to allow for redundancy as well as comparison between wires of diﬀerent thicknesses, for example 0.003” and 0.005”.

The principle behind the BAT probe is based on measurements of diﬀerential pressure between the nine ports using electronic pressure sensors (Garman et al., 2006).

The total pressure port at the centre of the probe, p0 (see ﬁgure 2.10), is located at the nominal stagnation point of the incoming airﬂow. Each of the other eight

o pressure ports surrounding p0 are displaced 45 behind the leading edge of the hemisphere. The difference between the total air pressure at port p0 and the static air pressure at ports ps (see figure 2.10) is measured, giving the dynamic pressure which is used to calculate the true airspeed of the aircraft. The other four ports, p1 to p4, are used to measure the sideslip and attack angles by measurement of the differential pressure across the pairs p1 − p3 and p2 − p4 respectively. Using these measurements of true airspeed, angle of attack and sideslip angle, the airflow can then be converted into the three-dimensional wind velocity components (u, v, w) with respect to the

38 aircraft, see e.g. Lenschow (1986) for details.

The probe is situated forward of the aircraft to minimise the effects of measuring in an airflow distorted by the aircraft itself (Lenschow, 1986). The remaining effects of the distortion on the vertical wind component (w) were corrected for following Craw- ford et al. (1996). Following Lenschow (1986), a series of in-flight manoeuvres, including known variations in aircraft speed and attitude angle, provided calibration coefficients for the BAT probe to correct the airspeed and the attack and sideslip angles for the effects of upwash ahead of the aircraft.

Using a 3 axis JAVAD AT4 four antennae GPS system, measurements of aircraft position, attitude and velocity were obtained, which allowed the aircraft velocity components with respect to the earth to be determined. Antennae were situated on the roof, tail and on both wing tips to achieve the widest separation of the antennae, improving the resolution of the attitude determination.

Using the velocity of the airﬂow relative to the aircraft, measured by the BAT probe

(Va), and the velocity of the aircraft relative to the earth, measured by the GPS system (Vp), the velocity components of the airﬂow in earth-referenced axes (V ) can then be obtained, following Lenschow (1986), where

V = Vp + Va

The horizontal wind components of V (u, v) can then be rotated from these earth- based geographic co-ordinates to the frame of reference of the mean wind, i.e. to the along- and across-wind directions respectively. Note the accuracy of this method is dependent on the assumption of a constant mean wind direction. However, calculations of the total kinematic stress require the vector sum of the two stresses u0w0 and v0w0 and are therefore independent of the choice of axes, so any introduced errors from the above rotation will not have an eﬀect on this quantity.

Errors in the GPS system occasionally occurred when the signal from one or more of the satellites was lost. These dropouts meant a loss of position, attitude and velocity outputs and consequently of wind speed data as resolution of the airﬂow

39 Figure 2.10: Head-on image of BAT probe, showing labelled pressure ports. The port labelled p0 is used to measure the total pressure and ports labelled ps are used to measure static pressure. The sideslip angle ports are labelled p1 and p3 and the attack angle ports p2 and p4. into earth-referenced coordinates was not possible.

Icing of the BAT probe can occur when flying through cloud or precipitation en-route to the study area or due to blown snow when taking off from a snow surface. As illustrated in figure 2.11, icing can block the pressure ports and alter the surface flow characteristics of the dome (Lenschow, 1986). Icing of this nature occurred during the Ronne Polynya flight F49L1 and consequently there are no flux measurements for this leg. Fortunately, using an internal heater, the probe was successfully cleared in flight, in time for the second leg. Figure 2.12 shows the flexible foil heaters fitted inside the front of the dome, which was also fitted with an insulation panel to avoid heating the electronics.

The thermocouple fast temperature measurement wires are very vulnerable to damage from snow and ice and therefore a precipitation barrier was used, a close-up image of which is shown on ﬁgure 2.13.

40 Figure 2.11: Iced BAT probe

Figure 2.12: Internal BAT probe heater for de-icing

2.3.2 Total temperature probe

Two Rosemount total temperature probes were mounted on the aircraft nose (figure 2.14). The thermometer housing measures the total air temperature, which is then corrected for adiabatic heating effects due to the aircraft motion, to obtain the ambient temperature. The correction is of the order of e.g. 5 oC for 100 m s−1 flow speed (Lenschow, 1986). The probes are situated outside of the aircraft boundary layer where viscous heating effects are negligible (Lenschow, 1986). The wire temperature sensor itself is protected from the airflow, through the inertial separation of the particles by a 90o bend in the housing.

Errors can occur in the total temperature measurements due to moistening by clouds or precipitation, which alters the dynamic heating to a wet adiabatic process. At

41 shield

wire

Figure 2.13: Thermocouple fast temperature sensor with precipitation shield

100 m s−1 this can give an error of up to 2 oC in a saturated environment (Lenschow, 1986). The correction is difficult to determine if the sensor is only partially wet. Errors can also result from salt accumulation on the sensing wire when flying in the marine boundary layer. However, due to the ice-covered ocean surface present during the Ronne Polynya flights and the consequent lack of sea spray, the likelihood of this being a problem for the temperature probe, and any of the other instrumentation, was reduced.

Figure 2.14: Rosemount total temperature probes. The sensor on the port side has a de-icing heater.

2.3.3 Humidity sensors

Humidity timeseries were determined from frostpoint temperature measurements using both a Buck cooled mirror hygrometer and a Vaisala humicap sensor. The

42 cooled mirror instrument is the standard instrument and works by chilling a mirror until water vapour saturation is reached and a thin layer of water or frost (if the temperature is below 0 oC) forms. This changes the reﬂectivity of the surface of the mirror, which is detected optically. The temperature of the mirror is then increased until this condensation starts to disappear. An equilibrium temperature is reached and is recorded as the dew/frost point temperature. The humicap sensor is a capacitive humidity device. This works by measuring variations in the dielectric constant of a porous material which absorbs water, where the mass absorbed is a function of humidity (Anderson, 1995).

The cooled mirror hygrometer (see figure 2.15) was mounted on the starboard side of the nose, near the aircraft static pressure port. The inlet for the humicap was located on the aircraft roof. Although the humicap logs at a slightly lower frequency of 0.7 Hz, compared to 1 Hz for the cooled mirror, the former has a faster response time to large humidity changes. The response time of the latter is further reduced for a frost-covered surface (NCAR, 2000). However, due to assumptions which must be made about the temperature and pressure at the humicap inlet, the timeseries produced is less accurate than that measured by the cooled mirror, leading to an offset between the two. Therefore the faster response humidity timeseries from the humicap sensor was calibrated to the mean value for the leg measured by the standard instrument, the cooled mirror hygrometer, to give an accurate, but fast response, measurement. This simple correction method is adequate, see figure 2.16.

2.3.4 Radiation sensors

Measurements of upwelling and downwelling shortwave and longwave radiation were made using hemispheric radiometers, mounted on both the bottom and top of the aircraft. Figure 2.17 shows the downwelling radiometers. Figure 2.18 shows the upwelling radiometers, as well as the infra-red thermometer which was used to obtain the surface temperature. The lens of the video camera (see section 2.3.5) can also be seen on the image.

43 Figure 2.15: Location of the cooled mirror hygrometer near the aircraft pressure ports, and closeup. The instrument location exposes it to relatively undisturbed conditions, avoiding pressure ﬂuctuations from variations in the attitude of the aircraft (NCAR, 2000).

The longwave radiation was measured using Eppley Model PIR pyrgeometers which measured within the waveband 0.3 to 50 µm. The shortwave radiation was measured using Eppley Model PSP pyranometers between 0.285 and 2.80 µm.

These dome radiometers work by the absorption of incident radiation by a thermopile coated with black optical laquer which essentially absorbs independently of wavelength. The passband of the radiation reaching the sensor can be varied by altering the filter characteristics of the dome, using silicon for LW and two glass domes for SW (Laursen, 2003). Corrections are applied for the emission effects of the dome, which artificially influence the energy detected by the sensor (Laursen, 2003). For temperatures below -20 oC, the sensitivity of the thermopile decreases, typically by about 0.15 % per oC (Laursen, 2003).

The upwelling SW radiation measured from the underbelly of the plane had a small proportion of the ﬁeld of view obscured by the aircraft skis, for which a correction of +5% was applied. Particularly at low solar elevation angles, the upward-looking radiometers may also experience some errors due to shading from features on the aircraft roof, such as the tail of the plane or cables, which are not possible to quantify.

44 −17

−18

−19

−20 C) o −21

−22 Dewpoint ( −23

−24 humicap −25 corrected humicap cooled mirror −26 0 20 40 60 80 100 120 140 Fetch (km)

Figure 2.16: Humidity timeseries for F54L1. The cooled mirror hygrometer (red) is used to correct the fast response humicap shown in black (corrected dotted).

Changes in the temperature of the instruments’ housing caused by variations in ambient temperature or ventilation eﬀects caused by the motion of the air can also contribute to an error of ± 1 % (Laursen, 2003).

Variations in aircraft attitude introduce the most significant errors in the downwelling SW radiation measured by the upward-looking pyranometers, as deviations from the horizontal affect the relative position of the sun to the instrument and alter the fractions of direct and diffuse SW radiation reaching it (Laursen, 2003). Corrections must be applied for the effect of attitude variations on the direct SW only and it is therefore important to know the relative fractions of the incoming diffuse and direct radiation. Under clear sky conditions, where the direct and diffuse components of the incoming SW can be modelled easily, the Ronne Polynya downwelling SW data has been corrected for attitude variations following Bannehr and Glover (1991). If the sky is completely cloud-covered, the direct component is zero and no correction is required. It is, however, difficult to separate the direct and diffuse components under conditions of partial cloud cover, potentially leading to errors.

45 Figure 2.17: Upward-looking dome radiometers on the aircraft roof, for the measurement of downwelling radiation.

Figure 2.18: Downward-looking dome radiometers, infra-red thermometer (lens pro- truding) and camera lens.

Since the measurement altitude of the plane was close to the surface, the pyrgeometers did not need correcting for this eﬀect as, at this level, the LW radiation is primarily diﬀuse due to atmospheric attentuation and scattering. Additionally, all the radiometers were calibrated using information supplied by the manufacturers.

Surface temperature measurements were obtained using a Heimann Model KT 19.85 infra-red radiation thermometer, or IRT, measuring within the waveband 9.6 to 11.5 µm, where atmospheric transmission is high (Laursen, 2003). Unlike the dome radiometers which have a hemispheric ﬁeld-of-view, this instrument measures over 2o, so at an altitude of e.g. 30 m the diameter of the surface target was 1.3 m. The instrument uses the Stefan-Boltzman equation to calculate surface temperature from the outgoing surface infra-red radiation, which therefore requires an appropriate correction for the emissivity of the ocean/ice surface between 9.6 and 11.5 µm. Other

46 errors associated with the emissivity of the lens itself, as well as the reﬂectance of the surface, were not corrected for. Additionally, the emission of IR radiation by water vapour in the atmosphere between the surface and the pyrometer was not corrected for. Some problems with the calibration of the instrument at low temperatures were also found, as well as problems associated with the large temperature gradient which developed across the instrument. This was especially apparent after long, cold transit ﬂights, due in part to the lens being outside of the plane, despite the instrument itself being insulated.

However, for the Ronne Polynya ﬂights, the measured surface temperature was calibrated assuming that the highest recorded temperature over the polynya corre- sponded to open water at the freezing point, i.e. -1.9 oC (e.g. Nicholls et al., 2004), see ﬁgure 2.19. For late summer/ winter conditions in this region this is a reasonable assumption.

−2 correction

−4 C) o −6

−8

−10 Surface temperature ( −12

−14

−16 0 20 40 60 80 100 120 Fetch (km)

Figure 2.19: F54L1 surface temperature measured using the infrared radiation thermometer (IRT), showing correction method as described in text.

47 2.3.5 Video

A downward-looking Sony video camera recorded the surface ice conditions to tape which was later transferred to DVD. The lens of this hatch camera can be seen on figure 2.18. The camera has a 90 minute capacity and can be switched on and off from the onboard computer system and, although the time is not logged, it can be estimated from other data which do have a time associated with it, e.g. an abrupt surface temperature change due to a boundary between different surfaces which can be seen on the video recording. The images of the surface are blurred however, due to the speed of the flight, and therefore require significant processing. A handheld cockpit video camera was also used which did not experience this problem as it was not pointed directly downwards, but at a forward-looking angle, therefore enabling qualitative assessment of the surface ice conditions to be made.

48 Chapter 3

Observations of the Convective Internal Boundary Layer

3.1 Vertical proﬁles

Figures 3.1 and 3.2 show contour plots of potential temperature, specific humidity, wind speed and wind direction over the Ronne Polynya, using the sawtooth profile data collected during F54 and F57. The profile data were averaged over 10 second intervals before interpolation between points and contouring. The interpolation was achieved using the Matlab “griddata” function, whereby a surface is fitted to the non-uniformly spaced fetch, height and variable data and, using a triangle-based linear interpolation method, values of the variable are interpolated at the points specified by a uniform two-dimensional grid of fetch and height. The data are then plotted using the uniform grid and the interpolated variable. The ice shelf edge is at 0 km fetch and 0 m height is the polynya surface. Note that the contour intervals and colour schemes for figures 3.1 and 3.2 are not necessarily the same.

The growth of a CIBL due to the surface temperature discontinuity at the ice shelf edge can be seen on the figures. zi, the top of the CIBL, is marked on each figure. Following Melfi et al. (1985), Chou and Zimmerman (1989) and Grossman and

49 −1 Potential temperature (K) Specific humidity )(g kg 600 600 0.80

550 259 550

500 500 0.75

450 450 258

400 400 0.70

350 350 257 300 300 0.65

Altitude (m) 250 Altitude (m) 250

200 256 200 0.60

150 150

100 255 100 0.55

50 50

0 20 40 60 80 100 120 0 20 40 60 80 100 120 Fetch (km) Fetch (km)

(a) Potential temperature (K) (b) Speciﬁc humidity (g kg−1)

−1 Wind speed (m) s Wind direction (degrees) 600 22 600 214

550 550

212 500 21 500

450 450 210 400 20 400

350 350 208

300 19 300

Altitude (m) 250 Altitude (m) 250 206

200 18 200 204 150 150

100 17 100 202 50 50

0 20 40 60 80 100 120 0 20 40 60 80 100 120 Fetch (km) Fetch (km)

Figure 3.1: Contoured cross-section above Ronne Polynya, during F54. x = 0 km corresponds to edge of Ronne Ice Shelf, z = 0 m is polynya surface. zi (the CIBL top) estimated from potential temperature contour plot (see text), and shown on all plots as dashed black line.

50 −1 Potential temperature (K) Specific humidity) (g kg 261 0.90

550 550

260 0.85 500 500

450 450 0.80 259

400 400 0.75 258 350 350

0.70 300 300 257

Altitude (m) 250 Altitude (m) 250 0.65

200 256 200 0.60 150 150 255 100 100 0.55

50 254 50 0.50 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Fetch (km) Fetch (km)

(a) Potential temperature (K) (b) Speciﬁc humidity (g kg−1)

−1 Wind speed )(m s Wind direction (degrees) 18 220

550 550 17 218

500 500 16 216 450 450 15 400 400 214

14 350 350 212

13 300 300 210

Altitude (m) 250 12 Altitude (m) 250

208 200 11 200

150 150 206 10

100 100 9 204

50 50 8 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Fetch (km) Fetch (km)

Figure 3.2: As for ﬁgure 3.1 but for F57.

51 Betts (1990), zi has been deﬁned as the height of the base of the capping inversion layer (the entrainment zone) above the mixed layer, i.e. the vertical limit of the mixed layer. This has been determined subjectively from the vertical proﬁles of potential temperature, where an abrupt change in stability from neutral (constant temperature, well mixed) within the CIBL to stable (increase in temperature with height) within the entrainment zone corresponds to zi.

The errors in these estimates of zi correspond to the thickness between contours, and increase with increasing fetch from the ice shelf edge. Here the temperature gradient becomes smaller and thus it becomes more diﬃcult to identify the precise location where the temperature proﬁle shifts from neutral to stable. Therefore the errors in zi are estimated to be up to 50 m (i.e. ±25 m).

The CIBL depth increases with fetch away from the ice shelf edge, mostly due to warming as a result of sensible heat ﬂux convergence from the polynya surface and the entrainment of warm air from above the CIBL (Garratt, 1990). For the longer fetch of F57 (ﬁgure 3.2), the internal boundary layer can be seen to merge into the planetary boundary layer after about 80 km fetch.

Within the mixed layer of the CIBL, the vertical gradient of potential temperature is small. This is a result of the strong turbulent mixing due to convection (Stull, 1988). This variable is not entirely constant with height however as the mixing process is not instantaneous (the convective timescale is of the order 10-20 minutes) and is also partially counteracted by the sensible heat ﬂux at the surface and at the top of the CIBL due to entrainment (Stull, 1988). Therefore the potential temperature proﬁles reach a slight minimum in the middle of the mixed layer. However, the convective timescale is relatively short and thus the top of the mixed layer can be considered in quasi-equilibrium with the surface forcings (Stull, 1988).

A strong gradient of potential temperature and speciﬁc humidity with fetch can be seen, particularly over the initial 30 km or so, as the CIBL warms and moistens. Moisture also decreases with height from the surface to the top of the CIBL as a result of the addition of moisture from the surface and the entrainment of dry

52 air from above (Stull, 1988) and remains approximately constant above zi. The measured wind speed remains approximately constant within the CIBL, increasing above it, indicating the CIBL is very well mixed. This is especially apparent for F57 (figure 3.2(c)). The higher wind speed feature positioned over the ice shelf for F57 is unexpected. This is perhaps a temporal rather than spatial feature (i.e. the wind speed was increasing overall during this final profile) but could warrant further investigation. The wind direction is fairly constant, not just within the CIBL but for the entire cross-section.

It should be noted that zi as determined from this analysis is derived from local, i.e. point measurements from the aircraft, rather than horizontally averaged measurements along the level of zi. As a result of structures such as plumes and thermals, this local top can be at a significantly different altitude than the mean CIBL top (Stull, 1988), as illustrated on figure 3.3. Therefore, as noted by Chang and Braham (1991), the averaged top is difficult to determine accurately from field data with a restricted spatial coverage, such as the Ronne Polynya data. However, using the method of interpolation between the measurements described above has allowed the CIBL top to be clearly identified on the contour plots, figures 3.1 and 3.2.

It can be seen by comparing figures 3.1 and 3.2 that the depth of the observed zi during F54 was greater than for F57. For example, at 70 km fetch, where the internal boundary layer has begun to merge into the planetary boundary layer and thus the depth can be clearly defined, zi was around 150 m higher for F54 than for F57. The ambient stability of the air above the CIBL has a large effect on the magnitude of zi (e.g. Brümmer,1997). Estimating this stability using the plots of potential temperature gives a value of 6 K km−1 for F54 compared to 14 K km−1 for F57. Therefore the difference in zi between the two flights was likely due to the difference in the ambient stability above the CIBL.

Since a profile over the ice shelf (where fetch < 0 km) was obtained for F57 (see figure 3.2), the height of the mechanically-driven boundary layer here can also be determined. Figure 3.2(a) indicates zi over the ice shelf is a maximum of 85 m, relative to the polynya (rather than the ice shelf) surface. A stable profile is seen over

53 z FA

EZ mean z i

Thermal Thermal Thermal ML

Figure 3.3: Schematic of a ‘snapshot’ of the top of the convective boundary layer, illustrating the local, rather than mean, top. Figure after Stull (1988). the ice shelf, rather than the approximately neutral proﬁles seen over the polynya itself, due to the more vigorous convective mixing over the polynya compared to the mechanical mixing over the ice shelf.

3.2 Ice shelf height

When comparing the height of the boundary layer above the ice shelf to that over the polynya (see ﬁgure 3.2), the height of the ice shelf itself needs to be taken into account, if z = 0 m is deﬁned as the polynya surface (sea level) and not the ice shelf surface. The radar altimeter and GPS altitudes can be used together to give the height of the ice shelf at the measurement location.

Figure 3.4 illustrates that

R1 + h = R2 + x (3.1)

54 Position 1 Position 2

aircraft Altitude difference (x) GPS altitude Radar altimeter aircraft

(G 1) altitude (R 1) G2 R2 Ice Shelf Ice Shelf height (h)

Geoid

Figure 3.4: Calculation of height above sea level of the Ronne Ice Shelf using aircraft data.

where x = G1 − G2

and h = R2 − R1 + G1 − G2

where Ri are radar altitudes and Gi are GPS altitudes.

For all seven points where the plane crossed over the ice shelf front during the three research flights, the observational data were substituted into equation 3.1. Results are shown in table 3.1 and the locations of the points are shown on figure 3.5, giving a rough profile of the Ronne Ice Shelf.

3.3 Entrainment

The stably stratiﬁed layer above the mixed layer acts as a lid to convection, but is also a region of downward entrainment of air, which, when the CIBL has merged into the planetary boundary layer, comes from the free atmosphere. As described by Stull (1988), buoyant thermals from the unstable surface layer rise through the mixed layer during free convection and gain momentum. On reaching the free atmosphere, despite being negatively buoyant, they overshoot a short distance. This has the

55 Point Location Ice shelf height (m)

1 75.19oS, 60.06oW 47.7 2 75.10oS, 60.48oW 36.8 3 74.99oS, 60.69oW 37.0 4 74.98oS, 60.72oW 39.7 5 74.90oS, 61.05oW 34.4 6 74.89oS, 61.12oW 29.4 7 74.88oS, 61.17oW 30.0

Table 3.1: Ronne Ice Shelf heights above polynya surface. eﬀect of pushing warmer, less turbulent free atmosphere air down into the more turbulent mixed layer where, despite having positive buoyancy, it is rapidly mixed away. There is little ambient turbulence to disperse the overshooting mixed layer air and so it sinks back down. The net result is therefore one-way entrainment of free atmosphere air into the mixed layer, so the mixed layer grows in thickness (Stull, 1988).

If there is a strong temperature inversion across the entrainment zone, penetration of thermals and therefore entrainment will be limited and the entrainment zone will be thin (Stull, 1988). Similarly, where convection is vigorous, leading to intense mixed layer turbulence, the entrainment zone will be thick (Stull, 1988). If there is no entrainment, i.e. the heat ﬂux at the top of the mixed layer is zero, then surface heating is the only source of mixed layer warming and the depth of the mixed layer increases by encroachment only. Entrainment and encroachment together en- hance the growth rate of the mixed layer by about 30 % more than encroachment alone (Garratt, 1992).

Unlike for F57, the vertical profiles did not capture the top of the entrainment zone for F54 due to its higher altitude location. For F57, the stability of the entrainment zone is estimated at about 20 K km−1, using the potential temperature plot. Using a cruder method, the stability of the entrainment zone can also be estimated for F54 by employing the two profiles obtained during descent to and ascent from the flight

56 100

40 height (m)

0 −60.2 −60.4 −74.9 −60.6 −75.0 −60.8 −75.1 longitude −61.0 latitude

Figure 3.5: Height above sea level of the Ronne Ice Shelf. level. This stability is also 20 K km−1, i.e. the strength of the capping inversion was the same for both cases. The stability of the free atmosphere for both ﬂights was also estimated using these proﬁles, at 6 K km−1 for F54 and 5 K km−1 for F57.

Figure 3.6 shows the atmospheric potential temperature with altitude (as measured by the radar altimeter) for the whole of flights F54 and F57. Comparison of figures (a) and (b) indicates that the entrainment zone is much thicker for F54 than for F57, which suggests that there was more entrainment occurring during F54 than F57. Higher wind speeds were found during F54 than for F57, promoting larger turbulent heat fluxes and hence more vigorous convective mixing. This would allow thermals to penetrate further above the mixed layer, increasing the thickness of the entrainment zone and increasing the amount of entrainment on their descent. In addition, for F54, increased mechanical mixing and wind shear due to the higher wind speeds will also generate increased turbulence and entrainment.

It should be noted that precise estimates of the thickness of the entrainment zone using these proﬁles is not possible and there is a likely uncertainty in the estimates of around 50 m. However, it is clear from ﬁgure 3.6 that the entrainment zone for

57 F54 was thicker than for F57.

3.3.1 The entrainment parameter

The entrainment parameter (β) is the ratio of the surface sensible heat ﬂux to the negative entrainment heat ﬂux at the top of the boundary layer (e.g. Garratt, 1992):

−w0T 0 β = zi (3.2) 0 0 w T sfc

0 0 where w T is the eddy covariance kinematic heat ﬂux (see chapter 4), zi is the top of the CIBL and sfc is the surface.

For

β = 0 , the CIBL grows by encroachment only β = 1 , the CIBL grows by entrainment only

β is usually assumed to lie between 0.1 and 0.3 (Stull, 1988; Chou and Zimmerman, 1989; Br¨ummer,1997).

It is assumed in this relationship that turbulence causing entrainment is directly related to the buoyancy ﬂux at the surface (Garratt, 1992). Any contribution from mechanical turbulence is thus neglected and so this relationship is valid for free convection only.

It is also assumed here that, due to the dry Antarctic atmosphere, there is little contribution to buoyancy from moisture and therefore T ≈ Tv, where Tv is the virtual temperature.

The entrainment velocity, we, is the volume of air entrained into the top of the mixed layer per unit horizontal area per unit time, i.e. a volume ﬂux, which has the same units as velocity. It is governed by the intensity of the turbulence and the strength of the capping inversion and is typically of the order 0.01 to 0.20 m s−1 (Stull, 1988).

58 EZ

(a) F54

(b) F57

Figure 3.6: Potential temperature with altitude (from radar altimeter) for F54 (a) and F57 (b), showing thicker entrainment zone (EZ) for F54 than for F57.

59 Stull (1988) gives the relationship

0 0 βw T sfc we = (3.3) ∆EZ θ where ∆EZ θ is the potential temperature jump across the top of the mixed layer, i.e. across the entrainment zone (EZ).

However, if there is a contribution from mechanically-generated turbulence, the relationship (Stull, 1988)

2θ h 3 3 3i we = c1w∗ + c2u∗ + c3(∆EZ U) (3.4) gd1∆EZ θ can be used, where θ is the mean mixed layer potential temperature, g is acceleration

−2 due to gravity (9.8 m s ) and ∆EZ θ and ∆EZ U are the mean jumps across the EZ in potential temperature and wind speed respectively. c1 = 0.0167, c2 = 0.5, c3 = 0.0006 are empirical constants.

The ﬁrst term in the square brackets parameterises the contribution of buoyancy to the entrainment velocity (using the convective velocity scale), the second surface mechanical production (using the friction velocity scale), and the third mechanical production at the top of the CIBL due to wind shear (using the wind speed jump across the EZ).

d1 is the distance between the top of the mixed layer and the height at which the heat ﬂux proﬁle crosses zero, and can be calculated using (Stull, 1988)

  − w0T 0  zi  d1 = zi (3.5) − w0T 0 + w0T 0  zi sfc

An example calculation for we is shown here, for F54 at a fetch of 60 km. Some contribution from mechanically-generated turbulence as well as convection might be expected as the wind speeds in the mixed layer were around 16 to 18 m s−1, with

60 a jump in wind speed of 4 m s−1 across the EZ. Therefore equation 3.4 should be used rather than 3.3.

Calculation:

θ = 256.5 K zi = 500 m g = 9.8 m s−2

∆EZ θ = 4.0 K −1 ∆EZ U = 4.0 m s

As calculated using the method detailed in chapter 4:

−1 u∗ = 0.5 m s

0 0 −1 −2 w T sfc = 0.07 K m s (Based on a surface sensible heat ﬂux of 100 W m )

1/3 gzi 0 0 −1 From Stull (1988), w∗ = w T = 1.10 m s θ sfc

Substituting into equation 3.4:

2(256.5) h 3 3 3i we = 0.0167(1.10) + 0.5(0.5) + 0.0006(4) 9.8d1 × 4

1.61 we = d1 or 1.61 d1 = we

But (Stull, 1988)

− w0T 0 zi we = ∆EZ θ

Using with equation 3.5 gives

" ∆ θw # d = z EZ e 1 i 0 0 ∆EZ θwe + w T sfc

61 so 4we d1 = 500 4we + 0.07

Equating for d1 gives:

2 4we = 0.0032[4we + 0.07]

−1 which can be solved to give we = 0.009 m s .

This value is low compared to the range of values given by Stull (1988) of 0.01 to 0.20 m s−1. Using this value with equation 3.3 yields a value for β of 0.53. The values used for ∆EZ θ and ∆EZ U are estimations however, and all other values are also approximate, which would introduce some error into the results. In order to estimate the magnitude of this error, the calculations were repeated using maximum and minimum values for the components.

For potential temperature, the maximum measured value within the CIBL at this fetch was 256.7 K and the minimum was 256.3 K. The error in zi was estimated previously to be ±50 m (see section 3.1) and therefore values for the minimum and maximum zi were taken here as 450 m and 550 m respectively. The error in −1 u∗ was estimated to be ±0.01 m s , which is the standard deviation of all measurements for this leg. The error in the kinematic surface heat ﬂux was estimated at ±0.007 K m s−1, based on a sampling error of 20 % for the ﬂux leg (see section 4.2.2). This gave we = 0.009 ± 0.001 with β = 0.53 ± 0.04. The errors are therefore small and the values of we and β are thus not very sensitive to the magnitude of the components chosen for the calculations. Using a similar method for

F57, we = 0.012 ± 0.002 and β = 0.48 ± 0.01.

It is not possible to calculate β using equation 3.2 directly, as there are no level-ﬂight observations of the heat ﬂux at the top of the CIBL (along the level of zi). The magnitude of the observed β is larger than the usual range given in the literature of 0.1 to 0.3 (e.g. Stull, 1988). A larger value of β might be expected however, as a result of the contribution from mechanical turbulence due to high wind speeds in

62 addition to the convective turbulence accounted for in equation 3.3.

A lower value of β was found for F57 compared to F54. This would be expected if entrainment were indeed lower for F57, as was suggested in section 3.3.

3.4 Summary

Table 3.2 summarises the CIBL parameters obtained from data collected during ﬂights F54 and F57, at an example fetch of 60 km from the edge of the Ronne Ice

−1 Shelf. γθ is the ambient stability in K km and ∆EZ θ and ∆EZ U are respectively the potential temperature (in K) and wind speed (in m s−1) jumps across the entrainment zone. θ is the mean potential temperature of the mixed layer in K

−1 and q is the mean speciﬁc humidity of the mixed layer in g kg . u∗ is the friction

−1 0 0 velocity in m s , zi is CIBL depth in m and w T sfc is the surface kinematic sensible heat flux in m s−1 K. β is the entrainment parameter. The errors given are those described in the previous section, as well as the maximum and minimum of the specific humidity at this fetch within the CIBL for each flight.

0 0 Flight γθ ∆EZ θ ∆EZ U θ q u∗ zi w T sfc β F54 6 4 4 256.5±0.2 0.72±0.12 0.5±0.1 500±50 0.07±0.007 0.53±0.04 F57 14 2 2 257.3±0.1 0.77±0.09 0.4±0.1 320±50 0.05±0.006 0.48±0.01

Table 3.2: Summary of CIBL parameters for F54 and F57.

Compared to F57, the wind speed and surface sensible heat ﬂux were higher for F54. This led to more vigorous convection during F54 and therefore a deeper CIBL and a thicker entrainment zone, demonstrated both by the larger wind speed and potential temperature jumps across it and the greater entrainment parameter than was found for F57. The higher ambient stability for F57 also acts to suppress the growth of the CIBL leading to a reduced zi compared to F54. The mean potential temperature and speciﬁc humidity are lower for F54 as they are spread out over a greater depth than for F57.

These parameters can be used to provide initial conditions with which to force ﬂux

63 and depth models of the CIBL. In addition, the observations of CIBL depth over the Ronne Polynya provide a useful data set for comparison with modelled CIBL depth. This will be investigated in chapter 5.

64 Chapter 4

Turbulent Fluxes over the Ronne Polynya

4.1 Methods

4.1.1 Eddy covariance method

The eddy covariance method can be used to directly calculate heat and momentum fluxes from high frequency wind speed and temperature data (Busch, 1973). Vertical wind fluctuations (w0) are correlated with fluctuations of temperature (T 0), humidity (q0) or horizontal wind (u0, v0) over an appropriate averaging period (see section 4.1.2). The fluctuations are defined as perturbations away from the mean. The covariance indicates the amount of common relationship between the two variables and enables kinematic fluxes of sensible heat, latent heat and momentum respectively to be obtained.

The sensible heat ﬂux is then given by

0 0 QS = ρcpw T (4.1)

65 and the latent heat ﬂux by

0 0 QL = ρLvw q (4.2)

0 0 which is sometimes written as E = QL/Lv = ρw q , where E is the moisture flux or rate of evaporation from the surface. ρ is the air density in kg m−3 (the mean over the averaging period), cp is the specific heat capacity of air at constant pressure −1 −1 o (1004 J kg K ), Lv is the latent heat of vapourisation of water (which at 0 C is 2.5 × 106J kg−1) and w0T 0, w0q0 are the kinematic fluxes as described above, where the bar denotes the mean value over the averaging period, or run.

The momentum ﬂux (Reynolds stress, or wind stress) is given by

0 02 0 02 1/2 2 τ = ρ(u w + v w ) = ρu∗ (4.3) where u0, v0 are respectively the perturbations of the along-wind and cross-wind components of the horizontal wind. The vector sum of these two stresses gives the total kinematic stress, and u∗, the friction velocity, is the square root of the

0 02 0 02 1/4 magnitude of the kinematic stress, i.e. u∗ = (u w + v w ) .

It is assumed that fluxes measured at the low flight levels (between 14 and 33 m) are representative of surface values, i.e. the aircraft was flying within the surface layer so extrapolation of the flux values to the surface is not necessary. An unstable surface layer can be observed in the vertical potential temperature profiles (see figure 3.2), the depth of which is greater than the data collection altitude for the low-level flight legs, supporting this assumption.

High frequency humidity data were not collected at the Ronne Polynya and therefore eddy covariance latent heat ﬂuxes are not presented in this study.

66 4.1.2 Obtaining timeseries of ﬂuctuating quantities from high frequency measurements

A high frequency timeseries of wind or temperature such as that measured by the aircraft sensors can be broken into a mean part and a turbulent part using Reynolds averaging (e.g. Stull, 1988). For example, for horizontal wind speed, u:

u =u ¯ + u0 (4.4) where an overbar denotes the mean part and an apostrophe the turbulent part of the flow. In this case, u0 can be thought of as short gusts superimposed on the slowly varying mean wind speed to give the total wind speed. This separation of the turbulent flow from the non-turbulent part of the flow is possible because of the existence of the ‘spectral gap’ (e.g. Kaimal and Finnigan, 1994).

Spectral Gap

Turbulence is a superposition of quasi-random eddies, which are coherent patterns of velocity, vorticity and pressure (Kaimal and Finnigan, 1994). They exist over a wide range of sizes and interact continuously, both with the mean flow and with each other. The larger, energy containing eddies derive their energy from the mean flow, through instabilities caused by existing turbulence (Stull, 1988). They are then subject themselves to instabilities due to their interaction with other eddies, causing them to break up into ever smaller eddies which also break up, in an “energy cascade”. When they are small enough, viscosity affects them directly, converting their kinetic energy into internal energy, or heat.

When turbulence is displayed as a spectrum, it can be demonstrated that turbulent eddies have wavelengths between about 50 m and 3 km (Stull, 1988). In contrast, large scale fluctuations in the flow, e.g. those associated with fronts and weather systems, can have wavelengths of the order of 102 to 103 km. There is little variation of the flow with a wavelength between about 9 km and 18 km, i.e. between

67 convectively-driven boundary layer scales and synoptic scales, and this is known as the spectral (or energy) gap (van der Hoven, 1957), see ﬁgure 4.1. However, a spectral gap may not be seen for some ﬂows, e.g. for larger cumulus clouds which act like large eddies (Stull, 1988).

Figure 4.1: Spectral, or energy, gap (van der Hoven (1957) as shown by Stull (1988)). The temporal scale is relative to the speed of advection of turbulence past the probe. Here the mean wind speed of 5 m s−1 corresponds to turbulent timescales between about 10 s to 10 min which (using speed = wavelength/time period) correspond to turbulent wavelengths of 50 m to 3 km, see text.

In order to separate these scales of motion, the data can be averaged. As follows from Taylor’s frozen turbulence hypothesis (e.g. Stull, 1988), large eddies have longer time periods than smaller eddies. Therefore, to separate the turbulent and mean flows, an averaging period should be chosen so that the small scale turbulent eddies (which are deviations about the mean) are averaged out, but the large scale mean flow remains. This mean flow can then be removed from the instantaneous timeseries to leave just the turbulent part, i.e. rearranging equation 4.4:

u0 = u − u¯

68 It is thus clearly important to choose an appropriate averaging period which incor- porates the spectral gap. The level-flight true airspeed of the plane is 63 m s−1 and the frequency of the data is 50 Hz. Assuming the spectral gap exists at around 9 km, this gives an averaging interval (or run) of approximately 140 s for detrending the data. The mean flow from each 140 s run at the constant flight level was removed, yielding the fluctuating quantities of the wind speed components and atmospheric temperature from the high frequency aircraft data. This was achieved using the Matlab ‘linear detrend’ function, which removes the best straight-line fit from each 140 s segment.

Choosing the length of the averaging period for the eddy covariances themselves is a balance between retaining a high spatial resolution but obtaining statistically significant fluxes. The chosen averaging interval must include several of the longest wavelengths of the turbulence being measured for an accurate result. In addition, a longer averaging period will reduce the flux sampling error (see section 4.2.2) and improve the spectra of the data (see section 4.1.3). However, a long averaging period will not allow the spatial variation in the surface fluxes to be resolved. For this data, the same averaging period as was used to detrend the data, 140 s, was used throughout this study.

4.1.3 Data quality control

The spectra of the data were examined to investigate the reliability of the data as well as to confirm the adequacy of the chosen averaging period of 140 s. For each 140 s run of the four low-level flux legs, for both the heat and momentum fluxes, the power spectra for the individual flux components, the cumulative summation of the covariances, as well as the cospectra and ogives and were examined for each of the sensible heat and momentum flux eddy covariance averaging periods, or runs (e.g. Friehe et al., 1991; French et al., 2007). Figures 4.2 and 4.3 provide some examples, showing high frequencies (short wavelengths, high wavenumbers) through to the lowest frequency (longest wavelength, lowest wavenumber) obtainable for the length

69 of the averaging period.

Power spectra of individual ﬂux components can be examined to assess the reliability of the data. There are three major regions of the power spectrum (Kaimal and Finnigan, 1994):

1. The energy containing range, which contains the bulk of the turbulent energy and where energy is produced by buoyancy and shear. 2. The inertial subrange, where energy is neither produced nor dissipated (no turbulent ﬂuxes, so cospectral levels vanishing or very low) but is passed down to smaller and smaller scales. The energy is proportional to a -5/3 slope. 3. The dissipation range, where kinetic energy is converted to internal energy. The transfer of energy through these ranges is controlled by the rate at which energy is coverted to heat in this range.

Figure 4.2 shows example power spectra for temperature perturbations, as used to calculate the sensible heat ﬂux. F54L1R6 is an example of a reliable, or ‘good’ run. F54L2R14 is an unreliable, or ‘bad’ run, where the T 0 spectrum dips substantially within the energy containing range. This demonstrates why the spectra for this run are also ‘bad’, see below. This poor data may either be due to measurement errors as a result of instrument problems or because conditions do not meet the strict criteria for Reynold’s averaging to be meaningful, i.e. conditions are not homogeneous and stationary.

It can be seen on ﬁgure 4.2 that the energy in the power spectra decreases along the expected -5/3 gradient of the inertial subrange, which indicates the response of the sensors was suﬃciently fast to capture all the turbulent wavelengths.

A ‘bump’ can be seen in all the T 0 spectra at wavenumbers approaching the dissipation range, which is particularly apparent in ﬁgure 4.2(a). This phenomenon is due to straining eﬀects on the eddies, and only appears in temperature spectra (Kaimal and Finnigan, 1994).

Figure 4.3(a) shows linear cumulative summations for example ‘good’ and ‘bad’

70 104 104

102 102

100 100

10−2 10−2

10−4 10−4

10−6 10−6 frequency weighted power spectrum frequency weighted power spectrum

10−8 10−8 10−4 10−3 10−2 10−1 100 10−4 10−3 10−2 10−1 100 wavenumber (m−1) wavenumber (m−1)

(a) F54L1R6 T’ power spectrum (b) F54L2R14 T’ power spectrum

Figure 4.2: Power spectra for temperature perturbation component of heat flux. Ex- amples of a reliable run (a), and an unreliable run (b) which shows dip at a wavenumber of 9 × 10−4 within energy containing range. A -5/3 gradient line shown, illustrating decrease in energy characteristic of inertial subrange. runs for the sensible heat flux, including those example runs shown in figure 4.2 for the power spectra. Similar results were obtained for the momentum flux. For these plots, a constant gradient for the entire run is desirable as this demonstrates horizontal homogeneity of the flux with distance. Large deviations from the 1:1 line indicate the presence of coherent disturbances in the flow. For some runs, this inhomogeneity affected the total energy by up to 40 % over a small proportion of the run fetch (e.g. figure 4.3(a), right), and was therefore a basis for rejection of the run.

The cospectra for the fluxes were also examined, see figure 4.3(b), to ensure all flux-carrying wavelengths were included within the averaging period and to confirm all the measured flux was present within the expected turbulent wavelengths of 50 m to 3 km (Stull, 1988), and not derived from the larger scale, e.g. synoptic disturbances. It can be seen on figure 4.3(b) (right) that there is power at relatively long wavelengths (high wavenumbers) for the ‘bad’ runs.

71 The ogives (cumulative summation of the covariance), see figure 4.3(c), should ide- ally resemble a smooth S-shape. The asymptotic values at both high and low frequencies (high and low wavenumbers) indicate where there is no contribution to the power in comparison with the other frequencies, and demonstrate the wavelengths within which the flux in the cospectrum is contained. Again, the difference between the ‘good’ and ‘bad’ runs is clear from figure 4.3(c).

Disturbances which appear in the ‘bad’ cumulative summation plots (ﬁgure 4.3(a)) are therefore often also apparent on the correspondingly ‘bad’ cospectra and ogives plots, see ﬁgures 4.3(b) and 4.3(c).

Seven heat flux runs out of a total of 49 (14 %) were discarded on the basis of the above analysis. Seven momentum flux runs were also discarded although these were not all the same as the discarded heat flux runs. As a comparison, based on a similar analysis of turbulence data collected from an aircraft platform, 17 % of sensible heat flux runs and 8 % of momentum flux runs were discarded by Petersen and Renfrew (2009), and 19 % of momentum flux runs were discarded by French et al. (2007). The rejection criteria for the Ronne Polynya data were based on one or more of the following:

• Power spectra - Dips in spectrum within energy containing range

• Cumulative summation - Large deviations from 1:1 gradient, indicating coherent disturbances in the ﬂow

• Cospectra - Highest peak in power at wavelengths larger than a few km, indicating presence of mesoscale or larger (as opposed to turbulent) variations in the ﬂow

• Ogives - Substantial deviations from a smooth S-shaped curve, and no convergence of curve which indicates power at wavelengths longer than turbulence

For both of the two lowest altitude legs in this study (see table 2.1) no runs were rejected on the basis of the spectral analysis. For these legs, a greater number of

72 (a) Cumulative Summation

(b) Cospectra

Figure 4.3: Examples of spectral analysis for good (left) and bad (right) runs for the eddy covariance sensible heat ﬂux. (a) Cumulative summation, normalised by total covariance, (b) frequency-weighted cospectra, where F57L1R11 and F54L2R14 oﬀset by -0.1 m2 s−1 for clarity, (c) ogives, normalised by total cospectra.

73 smaller eddies were sampled as a result of the lower measurement height, resulting in fluxes with a higher statistical significance. This reduces the scatter in the data, i.e. the “sampling error”, see section 4.2.2, and increases the reliability of the data. However, one run from these legs (F54L1R1) was rejected due to a malfunction in the GPS system which affected the wind measurements for this single run.

Based on the cospectra and ogives analyses, most of the flux for these runs is carried by eddies with wavelengths between about 50 m and 2 km (wavenumbers 2 × 10−2 to 5 × 10−4 m−1), i.e. the power is from turbulent eddies rather than large-scale disturbances in the flow. This is a consistent characteristic between runs, demonstrating the reliability of the data set and the confidence which can be placed in the results of this study.

The spectral analysis also indicated that the selected averaging period, or run, of 140 s was appropriate for capturing all of the turbulent flux. Choosing the length of the averaging period for the eddy covariances is a balance between retaining a high spatial resolution but obtaining statistically significant fluxes. The spectra for each run, particularly for the lower level legs, are very reliable since this averaging interval includes several of the longest wavelengths of the turbulence being measured. Therefore, using this averaging interval means fewer data points are rejected and the data can be used with confidence in its accuracy, while retaining spatial detail for investigation of the variation in the fluxes with fetch. According to Brümmeret al. (2002), fluxes averaged over longer intervals will follow the more detailed structure of the surface fluxes in a kind of smoothed curve. For this study, the spatial detail in the surface fluxes afforded by a 140 s averaging period is ideal for comparison to a model output, see chapter 5.

At the aircraft level-flight true airspeed of 63 m s−1, 140 seconds represents a sampling length of 8.8 km, which corresponds well with the 8 km sampling length used by Schröder et al. (2003), selected after analysis of the random and systematic errors in similar low level aircraft-based flux data. They also determined that values of their calculated surface transfer coefficients were not dependent on the selected sampling length.

74 4.1.4 Bulk method

If high frequency data are not available, the surface sensible heat (QS), latent heat

(QL) and momentum (τ) ﬂuxes can be estimated using bulk aerodynamic formulae, see equations 4.5, 4.6 and 4.7 (e.g. Hartmann, 1994). These equations use measurements of ‘bulk’, or mean, quantities of temperature, humidity and wind speed at the surface and at a reference height. These measurements are more readily available than high frequency data and the bulk method is therefore more appropriate than the eddy covariance method for use in many modelling studies to estimate surface wind stress, heat ﬂuxes and evaporation rates into the atmospheric surface layer.

QS = ρcpCHrUr(Tsfc − Θr) (4.5)

QL = ρLvCErUr(qsfc − qr) (4.6)

2 τ = ρCDrUr (4.7)

Subscripts sfc and r respectively denote the surface and a reference height. Fluxes are positive upwards and cp, Lv and ρ are as given previously in section 4.1.1. U is the wind speed, T the temperature, and Θ the potential temperature, which, following boundary layer convention, is deﬁned as T + Γz, where Γ is the adiabatic lapse rate (9.8×10−3 oC m−1) and z is the measurement height in m. q is the speciﬁc

−1 humidity (kg kg ) and qsfc is the saturated value at the surface at temperature

Tsfc. CH , CD and CE are empirically-determined transfer coefficients, where CH is the coefficient for sensible heat transfer (Stanton number), CE is the coefficient for latent heat transfer, or evaporation coefficient (Dalton number) and CD is the drag coefficient. Calculation of surface fluxes by this bulk method therefore requires accurate determination of these transfer coefficients appropriate to the surface, wind speed and atmospheric stability.

75 4.1.5 Transfer coeﬃcients

Using equations 4.1, 4.2 and 4.3 together with equations 4.5, 4.6 and 4.7 yields equations 4.8, 4.9 and 4.10 into which observations can be substituted to determine values for these coeﬃcients at the measurement, or reference, height.

w0T 0 CHr = (4.8) Ur(Tsfc − Θr)

w0q0 CEr = (4.9) Ur(qsfc − qr)

1/2 u0w0 + v0w0 CDr = 2 (4.10) Ur

These bulk coefficients depend not only on the measurement height but on aerodynamic surface roughness and the stratification and vertical density gradient of the atmosphere (Smith, 1988). Vertical density gradients can alter the vertical distribution of turbulent kinetic energy (TKE), altering the vertical gradients of mean temperature, humidity and momentum which support the vertical fluxes of these variables. In order to compare measurements made under different stratification conditions and at different measurement heights, values of the bulk coefficients CHr,

CEr and CDr must be converted to equivalent neutral stability values reduced to a reference height of 10 m, i.e. CHN10, CEN10 and CDN10.

Following Andreas and Cash (1999):

CDr CDN10 = 2 (4.11) n −1 1/2 o 1 − κ CDr [ln(r/10) − Ψm(r/L)]

CHr CHN10 = (4.12) 1/2 −1 −1/2 (CDr/CDN10) − κ CHrCDN10 [ln(r/10) − Ψh(r/L)]

CE is identical in form to CH .

76 L is the Obukhov (1946) length, given by

T u3 L = v ∗ 0 0 −κgw Tv

L is obtained via a balance of shear-generated and buoyancy generated/suppressed turbulence. As mechanical shear weakens, the relative importance of buoyancy increases with height. L is therefore a measure of the dynamic layer outer limit (e.g. Donelan, 1990).

κ is von Karman’s constant (0.4) and g is acceleration due to gravity (9.81 m s−2).

u∗ is the friction velocity, given by equation 4.3.

T v = T (1 + 0.61q) where T and q are representative values of temperature and speciﬁc humidity within the CIBL.

0 0 0 0 0 0 w tv = w t (1 + 0.61q) + 0.61T w q where w0q0 = cp w0t0 Lv Bo and Bo is the Bowen Ratio (ratio of sensible to latent heat, which shows the relative eﬃciency of warming to moistening, e.g. Pinto et al., 1995), for simplicity assuming

CHr ≈ CEr, giving

Bo = cp (Tsfc−Θr) Lv (qsfc−qr)

Ψm and Ψh are non-dimensional stability functions, set as the commonly used Businger-Dyer flux profile relations (or Kansas-type functions) for variation with stability in the profiles of wind and temperature (Businger et al., 1971; Dyer, 1974). Following Andreas and Cash (1999), the profiles of the mean wind speed and air temperature are:

77 u U(z) = ∗ [ln(z/z ) − Ψ (z/L)] (4.13) κ 0 m

t T (z) = T + ∗ [ln(z/z ) − Ψ (z/L)] (4.14) s κ T h

Here, z is the height by convention. u∗ and t∗ are flux scales that relate the wind speed and temperature profiles to the turbulent fluxes, where u∗ is as defined previously and t∗ = −QS/ρcpu∗, where QS is the surface sensible heat flux, as before. z0 and zT are roughness lengths for momentum and heat and are the virtual origins of the velocity and temperature profiles respectively.

The ratio r/L, or z/L, is the stability parameter, ζ, where ζ > 0 indicates stable stratiﬁcation, ζ < 0 indicates unstable stratiﬁcation and ζ = 0 indicates neutral conditions.

For the neutral case,

Ψm(ζ) = Ψh(ζ) = 0

and the proﬁles are logarithmic.

For stable stratiﬁcation (Dyer, 1974)

z Ψ (ζ) = Ψ (ζ) = −α m h L where α = 5.

For unstable stratiﬁcation (Paulson, 1970)

2 −1 Ψm(ζ) = 2ln[(1 + x)/2] + ln[(1 + x )/2] − 2tan x + π/2

78 2 Ψh(ζ) = 2ln[(1 + x )/2]

1 where x = (1 − 16ζ) 4 .

For all of the Ronne Polynya low-level data, ζ < 0 and hence only the parameterisation appropriate for unstable conditions was required.

Instrument errors in measurements of both the heat and momentum fluxes, as well as in the mean quantities of surface-air temperature difference and wind speed will have an impact on the calculated values of the heat transfer and drag coefficients. However, as noted by Schröderet al. (2003), since the magnitude of the measurement errors is much smaller than that of the measured quantities, the impact of errors in the measurements on the values of the coefficients is small.

4.2 Observations

4.2.1 Sensible heat ﬂux

Figure 4.4 shows the eddy covariance sensible heat flux over the Ronne Polynya for the four level-flight legs with fetch from the ice shelf edge at 0 km. Also shown are the flight-level potential temperature, surface temperature and surface shortwave albedo for each leg. The polynya was observed to be mostly covered with thin ice, with no extensive areas of open water, at the time of the observations. It can be seen on figure 4.4 that the surface temperature decreases with increasing fetch, while albedo increases, suggesting that ice thickness increased with fetch. Patches of thin ice and open water within the generally thicker ice are also apparent from these plots.

A decrease with fetch in the observed sensible heat flux is seen on figure 4.4, as a result of a reduction in the air-surface temperature difference. This is due in part to warming of the CIBL (by around 4 K over the polynya fetch) by sensible heat flux

79 200 200 ) ) −2 −2 100 100 (W m (W m S S Q Q 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120

0 0 C) C) o o

( −10 ( −10 air air θ θ

−20 −20 0 20 40 60 80 100 120 0 20 40 60 80 100 120

0 0 C) C) o o ( ( −10 −10 surface surface T T −20 −20 0 20 40 60 80 100 120 0 20 40 60 80 100 120

1 1

0.5 0.5 albedo albedo

0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Fetch (km) Fetch (km)

(a) F49L2 (b) F54L1

200 200 ) ) −2 −2 100 100 (W m (W m S S Q Q 0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120

0 0 C) C) o o

( −10 ( −10 air air θ θ

−20 −20 0 20 40 60 80 100 120 0 20 40 60 80 100 120

0 0 C) C) o o ( ( −10 −10 surface surface T T −20 −20 0 20 40 60 80 100 120 0 20 40 60 80 100 120

1 1

0.5 0.5 albedo albedo

0 0 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Fetch (km) Fetch (km)

Figure 4.4: For each flight leg, top to bottom: eddy covariance sensible heat flux, potential temperature, surface temperature and surface shortwave albedo, all with fetch from ice shelf edge at 0 km. Mean altitude of legs F54L1 and F57L1 are 14 m and 15 m respectively, and F49L2 and F54L2 are 32 m and 33 m. 80 convergence. However, the reduction in surface temperature with fetch of typically 9 K, as a result of the thickening ice cover, was greater than the air temperature increase, seen on figure 4.4. Therefore, for these cases, variation in the temperature of the heterogeneous surface has the greatest effect on the spatial variability of the sensible heat flux.

Following Brümmer et al. (2002), the correlation coefficient of the linear regression between the eddy sensible heat fluxes and the product (Tsfc − Θr).Ur (see bulk sensible heat flux, section 4.1.4) was used as an indication of the quality of the eddy flux measurements, as the latter is determined independently of the air-surface temperature difference. This method therefore provides an independent means of data quality control. The correlation coefficient for the four flux legs varies between 0.81 and 0.96, therefore indicating the eddy covariance heat fluxes behave as expected and the averaging length is adequate.

The effect of the decrease in the surface sensible heat flux with fetch can also be seen on figure 3.2(a), the contour plot for potential temperature for F57, where the convective mixing is seen to become weaker at a fetch of around 80 km.

4.2.2 Flux sampling error

It can be seen on figure 4.4 that even after quality control the eddy heat flux derived from the higher altitude legs (F49L2 and F54L2) is more scattered, i.e. has a greater variance, than that from the two lower altitude legs (F54L1 and F57L1). This can be explained by the “sampling error” of the data. Under stationary conditions, for each leg the sampling error of a turbulent flux (e.g. F = w0T 0) can be expressed as (Donelan, 1990; Drennan et al., 2007)

σ F = α z1/2U −1/2γ−1/2 (4.15) F¯ F

where, for each leg, σF is the standard deviation of ﬂux estimates for all runs (after ¯ quality control) and F is the mean ﬂux. αF is an empirically-derived constant. For

81 0 0 w T , Donelan (1990) gives a value for αF of 8.0. z is the measurement altitude in m and U is the speed of advection of turbulence past the probe in m s−1, equivalent in this case to the level-ﬂight true air speed of the plane, 63 m s−1. γ is the sampling interval in s, which is the averaging interval of the data, 140 s.

The left hand side of equation 4.15 represents the measured sampling error and the right hand side the predicted. The equation demonstrates that lower measurement heights, faster ﬂuid speeds relative to the measuring apparatus and longer averaging periods will yield less scattered results, i.e. a reduction in the variability of the results. In addition, a measured sampling error which is considerably larger than that predicted is a likely indication of non-stationary conditions (Drennan et al., 2007).

Equation 4.15 was used to calculate the expected and observed sampling errors for the kinematic sensible heat flux with fetch for each of the four low-level flux legs. A linear fit of the flux was removed before calculation of the standard deviation as an approximation of the expected reduction in the flux with fetch which is not due to error in the data.

Results shown in table 4.1 indicate that the measured sampling errors are all lower than the predicted sampling errors. This suggests the value of the empirical constant,

αF , at 8.0 (Donelan, 1990) is too large for this experimental set-up. Using data from all four ﬂux legs gives a mean value for this constant of 5.0.

As the L2s were conducted at a higher altitude, a larger scatter in the data is both expected and found in comparison with the L1s. This sampling error could be reduced by, for example, increasing the length of the averaging period, which will also improve the spectra of the data, reducing the number of runs which are rejected (see section 4.1.3), but will not allow the spatial variation in the surface ﬂuxes to be resolved. However, these sampling errors are of a similar magnitude to those found in other studies (Drennan et al., 2007; Petersen and Renfrew, 2009) and additionally some scatter in data from measurement of turbulent quantities is to be expected. Nevertheless, in order to produce results which are as accurate as possible, data

82 from the L1s only were used in the following section for the calculation of surface transfer coeﬃcients.

Flight Measured sampling error Predicted sampling error Measurement altitude

F49L2 32% 48% 32m F54L1 20% 32% 14m F54L2 27% 49% 33m F57L1 22% 33% 15m

Table 4.1: Measured and predicted sampling error in w0T 0, using equation 4.15.

4.2.3 Observed transfer coeﬃcients

The 10 m neutral stability heat transfer (CHN10) and drag (CDN10) coefficients were calculated using the method detailed in section 4.1.5 for each 140 s run for both F54L1 and F57L1. The results are shown on figure 4.5 with fetch from the ice shelf edge at 0 km. Despite the data being collected more than 24 hours apart, for both legs the mean values and standard deviations of these coefficients are the

−3 −3 same, at CDN10 = (1.1 ± 0.2) × 10 and CHN10 = (0.7 ± 0.1) × 10 . Therefore the measurements from the two legs can essentially be treated as the same data set.

The magnitudes of these coefficients compare very well to similar aircraft-based observations made by Schröder et al. (2003) over heterogeneous sea ice in the Arctic marginal ice zone (MIZ), under similarly unstable conditions with a comparable wind speed and surface-air temperature difference to that found at the Ronne Polynya. For their ice class of a mixture of grey and white ice and leads, which is comparable to the surface of the Ronne Polynya, they obtained mean values of CDN10 = (1.5 ± −3 −3 0.5)×10 and CHN10 = (0.8±0.2)×10 . The observed CHN10 values at the Ronne Polynya are significantly lower than those normally used in studies of heat transfer over polynyas, e.g. Walkington and Willmott (2006); Chapman (1999) at 2.0×10−3, or Renfrew et al. (2002) at 1.14 × 10−3. However, the coefficients obtained in this study of the Ronne Polynya are relevant to conditions of thin ice cover, rather than open water which is often assumed to be the case for the modelling of polynyas. Nevertheless, the magnitudes of the observed drag coefficients are similar to those

83 x 10−3 1.5

1 DN10 C 0.5

F54L1 F57L1 0 0 20 40 60 80 100 120 x 10−3 1.5

1 HN10 C 0.5

F54L1 F57L1 0 0 20 40 60 80 100 120 Fetch (km)

Figure 4.5: 10 m neutral stability drag (top) and heat transfer (bottom) coeﬃcients for F54L1 and F57L1. used in previous polynya studies, e.g. 1.0 × 10−3 as used in the Renfrew et al. (2002) study.

Despite the steadily increasing thickness of the ice with fetch, a corresponding change in CDN10 and CHN10 was not found, i.e. the regression of CDN10 and CHN10 with fetch does not have a slope significantly different from zero. However, if CDN10 for F54L1 is examined alone, the slope is found to be significantly different from zero, at the 0.05 level. This is not the case for F57L1 or for CHN10 for either leg. However, F54L1 comprises of only 9 data points and therefore examination of the two legs together is likely to produce a more statistically robust result. Therefore it can be concluded that there is no variation with fetch in CDN10 or CHN10. This at first appears to be a surprising result, given the thickening of the ice cover with fetch.

However, the sea ice roughness (and hence CDN10) cannot be characterised by a

84 single parameter such as ice thickness alone but includes other factors such as floe size, freeboard and concentration, and small variations in these do not necessarily increase momentum exchange (Schröderet al., 2003). In addition, as form drag does not affect heat exchange directly (Schröder et al., 2003), even with a large variation in z0 a relationship with CHN10 would not necessarily be seen.

The ‘step’ in the temperature and albedo plots at around 100 km for F54 (and at 60 km for F49), see figure 4.4, defines the outer edge of the polynya. Removing the single point of the transfer coefficients for F54L1 that lies outside this boundary does not however alter the mean, standard deviation or relationship with fetch for

CDN10 or CHN10.

4.2.4 Surface ice conditions

Two regions can be distinguished in a wind-driven polynya, corresponding to an inner region of open water and frazil ice and an outer region of new and young ice ﬂoes formed by frazil ice accretion, which is surrounded by ﬁrst-year ice (Morales Maqueda et al., 2004). Liu et al. (1997) refer to these regions as the “active polynya” and “young ice” regions respectively. In this study, both regions are considered to be part of the polynya.

The thickening surface ice cover with fetch observed at the Ronne Polynya can be split into two distinct areas, or regimes, which correspond to these two regions. They can be clearly identified on figure 4.6, which shows a scatter plot of the surface shortwave albedo and surface temperature for all points from F54L1 and F54L2 together. The data, which were interpolated at the time of data processing onto the GPS timebase of 50 Hz (see section 2.3), have been averaged so that each data point has a resolution of 1 km. Although the edge of the polynya could be defined as 100 km for F54 (see figure 4.4) the temperature-albedo relationship for the sea ice beyond this point is the same as for the second regime and these data have therefore been included in the figure.

85 1 First regime (0 − 35 km) 0.9 Second regime (36 − 127 km)

0.8

0.7

0.6

0.5 albedo 0.4

0.3

0.2

0.1

0 −16 −14 −12 −10 −8 −6 −4 −2 surface temperature (oC)

Figure 4.6: 1 km averaged shortwave albedo and surface temperature for F54L1 and F54L2, split into regimes where ﬁrst regime is ﬁrst 35 km.

The boundary between regimes was selected subjectively using the gradients of the best fit lines for each regime, i.e. selecting the division between the points which fitted best to these gradients. Ice conditions at a few points after this boundary are better suited to the first regime, indicating there is not an absolute cut-off point. Using a similar method, the boundary between regimes for F57 was found to be 55 km, see figure 4.7. A division between regimes for F49 is not apparent, see figure 4.8. It can be seen on the surface temperature and albedo plots with fetch for F49L2 (figure 4.4(a)) that even by the end of the 90 km leg there were still a significant number of areas of open water and thin ice within the more consolidated ice. Therefore a distinct second regime, as defined for the other legs, was not present for this case.

For both flights F54 and F57 the r-squared values (coefficient of determination, i.e. how much of the variation in albedo is related to variations in surface temperature) for the albedo-surface temperature trends are higher for the first regime than for the second, at 0.93 and 0.78 respectively for F54 and 0.95 and 0.77 for F57.

86 0.55 First regime (0 − 55 km) Second regime (56 − 115 km) 0.5

0.45

0.4

0.35 albedo

0.3

0.25

0.2

−13 −12 −11 −10 −9 −8 −7 −6 −5 −4 −3 surface temperature (oC)

Figure 4.7: 1 km averaged shortwave albedo and surface temperature for F57L1, split into regimes where ﬁrst regime is ﬁrst 55 km.

This stronger relationship indicates a more uniform ice type within the first regime, which is also evident in the similarity in the gradient of the best-fit line between the flight legs, at -0.03 for F54L1 and F54L2 and -0.04 for F57L1. This similarity is not seen for the second regime.

Figure 4.9 shows images of typical surface conditions observed within the regimes for F54 as an example. The first regime (figure 4.9(a)), i.e. the active polynya, is composed of open water, frazil ice and some thicker new ice, with open water patches, or ‘holes’. Langmuir circulations were observed in the surface distribution pattern of the frazil ice, see figure 4.9(a) and ice fog can also be observed. The second regime (figure 4.9(b)), or the young ice region, is composed of more consolidated ice, also perforated with ‘holes’. Leads and ridging of the ice floes were also observed within this region. The sensible heat flux over the second regime for these case studies remained of the order of 100 W m−2 and therefore this area is defined as part of the polynya for this study.

The perforated appearance of the ice is due to the cold air temperatures and rapid

87 0.9

0.8

0.7

0.6

0.5 albedo

0.4

0.3

0.2

0.1 −10 −9 −8 −7 −6 −5 −4 −3 −2 surface temperature (oC)

Figure 4.8: 1 km averaged shortwave albedo and surface temperature for F49L1 and F49L2, separate regimes not found. advection of the newly-formed frazil ice, which consolidates into floes before it can be piled up against the receding edge of the polynya (Smith et al., 1990). As a result of reduced turbulence, ice production in these holes would be expected to be reduced in comparison to the more open areas in the sea ice cover, where Langmuir circulations were observed, making consolidation of the frazil ice into floes less efficient, and allowing the holes to remain open (Smith et al., 1990).

Figure 4.10 is an AVHRR image of the Ronne Polynya on the day of F57, as shown previously in figure 2.7. The boundary between the first and second regimes can clearly be identified, where the darker area of the polynya corresponds to the first regime. This image was captured around 3 hours later than the time of the observations and hence the boundary between regimes on this image lies at roughly 30 km from the ice shelf, which is at a shorter fetch than during the time of the measurement flights. This implies consolidation of the frazil ice of the first regime into young ice. The boundary between the second regime and the older ice can also be identified, at a fetch of about 120 km along the polynya edge adjacent to the

88 (a) F54 First regime

(b) F54 Second regime

Figure 4.9: Photographs of Ronne Polynya surface from plane at altitude of approximately 15 m.

89 Antarctic Peninsula.

The two regimes are also clearly visible on ﬁgure 4.11, an image of sea ice concentration derived using AMSR-E data, as described in section 2.2.

1 0 0

k m

Figure 4.10: AVHRR false-colour combined visible and infra-red image of the Ronne Polynya on 28/02/2007 at 1941 UTC, around 3 hours later than F57.

4.2.5 Relationships between transfer coeﬃcients and ice conditions

A t-test shows there is no significant difference between the means of the heat transfer coefficients for the two regimes. For F54L1, there appears to be a significant difference at the 0.05 level between the means for the drag coefficient. However, for this leg, the first regime comprises of only two points and therefore this result should be treated with caution, especially as the same result is not found for F57L1. Additionally, when all of the data are considered together, thus making a larger

90 45 oW 30 oW 15 oW 70 oS

Weddell Sea

80 oS

Ronne Ice Shelf

Figure 4.11: AMSR-E sea ice concentration on 28/02/2007 (day of F57). Zoomed-in image (right) clearly shows the the two regimes.

dataset, there is no significant difference between the regimes for the different legs.

The surface temperature and surface shortwave albedo were used as indicators of the surface ice conditions, and the relationships between these factors and the calculated transfer coeﬃcients were investigated, see ﬁgure 4.12.

No significant correlations were found between the transfer coefficients and either the albedo or the surface temperature, both when considering all the data together, and under separate analysis of the two regimes. There may be a linear relationship for the transfer coefficients with surface temperatures above about -10 oC, but the range of data is limited since most of the Ronne Polynya measurements lie between surface temperatures of -10 and -12 oC with albedos of around 0.4. Therefore, to more fully examine any (possibly non-linear, see Andreas et al. (2005)) relationship between surface ice thickness or concentration and these coefficients, a greater amount and wider spread of data would be required.

It can however be concluded that, for these case studies, the two ice regimes transfer heat and momentum similarly, which suggests that under similar polynya conditions

91 to those observed, the two ice regimes can be treated in the same way, for example when modelling the surface heat ﬂuxes.

4.2.6 Latent heat ﬂux

High frequency measurements of humidity were not collected for these case studies, and therefore neither eddy covariance latent heat fluxes, nor the exchange coefficient for latent heat (CE) could be calculated for the Ronne Polynya. However, an estimate of the bulk latent heat fluxes can be determined using equation 4.6 and making the assumption, as in section 4.1.5, that CEr ≈ CHr.

Figure 4.13 shows the latent heat flux with fetch over the Ronne Polynya from the ice shelf edge for F54L1. The bulk sensible heat flux is shown for comparison. It can be seen, as described in the introduction, that the latent heat flux is smaller than the sensible heat flux. Using all four legs the mean Bowen ratio, which was found to not vary with fetch, was 3.8 ± 0.3, where the error given is the standard deviation. This value compares well to the range for polynyas given in the literature of between 2 and 4 (e.g. den Hartog et al., 1983; Pease, 1987; Renfrew et al., 2002). Note that three outlying points from F49L2 were not included in this calculation as they were 2 to 3 times larger than the mean and were thus assumed to be erroneous.

4.2.7 Momentum ﬂux

The relationship between the wind speed and the momentum flux, or wind stress, is provided by the drag coefficient, CD, see equation 4.7. Over the ocean, CD is dependent on the mean wind speed, the atmospheric stratification and on the wave state in the general case (Grachev et al., 1998). In the following form it is an equivalent measure of the roughness of the surface, under neutral stratification, at a reference height r (Donelan, 1990):

92 (a) 10 m neutral stability drag coeﬃcient (left) and sensible heat transfer coeﬃcient (right) with surface temperature

(b) 10 m neutral stability drag coeﬃcient (left) and sensible heat transfer coeﬃcient (right) with surface shortwave albedo

Figure 4.12: F54L1 and F57L1 transfer coeﬃcients with surface temperature (a) and albedo (b). Data split into the two ice regimes, as demonstrated in ﬁgure 4.6.

93 200 sensible heat flux 180 latent heat flux

160

140 )

−2 120

100

80 Heat Flux (W m

0 0 20 40 60 80 100 120 Fetch (km)

Figure 4.13: Bulk sensible and latent heat ﬂuxes over the Ronne Polynya with fetch from ice shelf edge at 0 km for F54L1.

" κ #2 CDr = (4.16) ln(r/z0)

Over an ocean, CD becomes larger at higher wind speeds as the surface becomes aerodynamically rougher as a result of waves, ranging from around 1 × 10−3 at wind speeds of 2 - 5 m s−1 up to 2 × 10−3 at speeds of 24 m s−1 (Smith, 1988). Donelan

−3 (1990) gives values of CD of 0.3 to 3 × 10 for corresponding surface roughness lengths of 1 × 10−6 mm to 10 mm (ultra-smooth to fully rough sea surface).

Measurements show that over the ocean CH can be considered independent of the wind speed (Smith, 1988), remaining fairly constant at moderate wind speeds of 4 - 18 m s−1 (Donelan, 1990). This is because the increase in surface roughness with increasing wind speed increases near-surface turbulence and therefore heat transfer on the windward sides of the waves, while simultaneously increasing the area protected in the leeward sides, thereby reducing heat transfer and balancing the eﬀect.

94 According to Charnock (1955) the surface roughness length is proportional to the wind stress which generates the waves.

For smooth conditions, e.g. Donelan (1990)

0.11ν 1/3 zs = , u∗ < 2(νg) (4.17) u∗

For rough conditions (Charnock, 1955)

au2 z = ∗ , u ≥ 2(νg)1/3 (4.18) c g ∗

−6 2 −1 where ν is the kinematic viscosity of air (14×10 m s ), u∗ is the friction velocity (see section 4.1.1), g is the acceleration due to gravity (9.8 m s−2) and a is the so- called Charnock constant, which is empirically derived. Donelan (1990) gives a value for a of 0.014 and Smith (1988) gives a range of 0.011 - 0.017, similar to the range of 0.011 to 0.018 given by Fairall et al. (2003).

Under neutral stability conditions (Smith, 1988)

z0 = zc + zs (4.19)

−1 At wind speeds below 3 m s , aerodynamic smoothness can be assumed and zs is dominant. Above 5 m s−1, there is general agreement with Charnock’s (1955) formula and it is zc which increases the drag coeﬃcient (Smith, 1988).

For a fully developed wave field, where the Charnock formula is valid, the waves which support the stress are very short in comparison to the waves carrying the energy. This is because the faster the waves travel, the weaker their direct interaction with the wind, therefore leaving the short waves to support the stress. Additionally, the large waves are not steep enough for the flow to separate and hence create enhanced form drag, and so do not contribute to the surface roughness (Donelan, 1990). The flow is able to remain attached to large features which have gentle slopes

95 but separates from small abrupt roughnesses (Smith, 1988).

For fetch-limited situations, the Charnock formula may not be valid, since the younger the waves the greater the eﬀect of the long waves on the roughness length

(Donelan, 1990) which increases the surface roughness and therefore CD (Smith, 1988). This is important for fetches under 10 km (Smith, 1980).

However, for a thin-ice covered lead or polynya, such as the Ronne Polynya at the time of the measurements, there is limited interaction between the wind and the ocean surface, and therefore the Charnock formula may not be appropriate for this situation. Figure 4.14 shows the observed surface roughness lengths at the Ronne Polynya for ﬂight legs F54L1 and F57L1, obtained using equation 4.13. They are shown with values estimated using the Charnock parameter, employing an iterative procedure to calculate u∗ and z0, based on the formulation of Smith (1988), which forms part of a heat ﬂux model designed by Renfrew and King (2000) (see chapter 5). Figure 4.14 demonstrates that the inclusion of the Charnock parameter to calculate z0 produces values larger than those observed. The wave action is ‘damped out’ by the ice cover and the Charnock formula is therefore not valid.

Although in these case studies some open water and thin ice is present which does experience some wind-induced wave action, the complete removal of the Charnock parameter from the bulk calculations provides values of z0 in reasonable agreement with the measured values. Therefore, rather than including a modified Charnock parameter in the model to account for the limited interaction between the wind and the surface, it can be assumed that the effect of the wind stress on the surface roughness is small enough to be neglected without affecting the accuracy of the calculations.

−4 The observed magnitude of z0, at around 1 × 10 m, is slightly lower than that given by Schröder et al. (2003) of 2 × 10−4 m for a heterogeneous ice surface and hence their CDN10 value is slightly larger than was found here. However, as noted previously, small variations in z0 do not necessarily affect the magnitude of CHN10 and thus values of this coefficient found in both this and the Schröder et al. (2003)

96 −3 10

10−4

−5

(m) 10 0 z

10−6

F54L1 F57L1 bulk formula (no Charnock)

−7 bulk formula (with Charnock) 10 0 20 40 60 80 100 120 Fetch (km)

Figure 4.14: Surface roughness lengths. F54L1 and F57L1 observed, and modelled with and without Charnock parameter using Smith (1988) bulk algorithm with input data from F54L1.

study are very similar.

The evaporation of sea spray can have an effect on CH and CE. According to Donelan (1990) this effect is insignificant for wind speeds below 9 m s−1 but can double these transfer coefficients for wind speeds of 18 m s−1. However, in these case studies of an ice-covered polynya with minimal wave action this effect can be assumed negligible.

4.3 Summary

Unique data from low-level aircraft-based observations of turbulence over the Ronne Polynya, Antarctica, have been presented. The observed eddy covariance sensible heat flux was shown to decrease with fetch from the ice shelf edge as a consequence of a reduction in the surface-air temperature difference. Although there was some contribution from atmospheric warming due to sensible heat flux convergence, this

97 was primarily a result of the decrease in surface temperature with fetch owing to thickening ice cover. This was illustrated by the observed decrease in surface temperature and increase in albedo with fetch.

Using the surface temperature and albedo data, it was shown that the surface ice cover can be split into two distinct regimes, termed by Liu et al. (1997) as the “active polynya” and “young ice” regions. The first regime is composed of open water, frazil ice and some thicker new ice, with open water patches, or ‘holes’. Langmuir circulations were observed in the surface distribution pattern of the frazil ice and ice fog was also seen. The second regime is composed of more consolidated ice, also perforated with ‘holes’. Leads and ridging of the ice floes were also observed within this region. The heat fluxes observed over the second regime were larger than would be expected over consolidated pack ice. This finding, coupled with the similarity in the values of both the heat transfer and drag coefficients for the two regimes, means the second regime is also considered to be part of the polynya.

The mean values for the 10 m neutral stability sensible heat transfer and drag

−3 coefficients were found to be CDN10 = (1.1 ± 0.2) × 10 and CHN10 = (0.7 ± 0.1) × 10−3, where the errors given are the standard deviations. These coefficients were not found to be a function of polynya fetch or surface ice conditions, as represented by the surface temperature and albedo. No significant difference between the values of the coefficients for the two ice regimes was found for either the heat transfer or drag coefficients which suggests the two regimes can be assumed to transfer heat and momentum similarly. This implies that, under similar conditions to those observed, the two ice regimes can be treated in the same way when modelling the surface heat fluxes. The magnitude of the observed heat transfer coefficient is similar to that

−3 found over heterogeneous sea ice, at CHN10 = (0.8 ± 0.2) × 10 (Schr¨oder et al., 2003). This is signiﬁcantly lower than the values which have been used in previous studies of heat transfer over polynyas, e.g. 2 × 10−3 (Chapman, 1999), where the polynya surface is often assumed to be open water. The Ronne Polynya CDN10 was similar however to those used in polynya studies, e.g. 1×10−3 (Renfrew et al., 2002).

Assuming that CE ≈ CH , the bulk latent heat ﬂux was calculated over the Ronne

98 Polynya, and found to be lower than the sensible heat ﬂux. The mean Bowen ratio using data from all four legs was 3.8±0.3 (where the error is the standard deviation) and did not vary with fetch. In addition, the surface roughness length was found to not be a function of the wind speed due to the surface ice cover, which limited interaction between the wind and the ocean surface. This meant the Charnock relation was not valid for this surface.

99 Chapter 5

Modelling of the Ronne Polynya Case Studies

5.1 Introduction to the model

The CIBL model of Renfrew and King (2000) was used to investigate the evolution with fetch of the surface sensible heat flux, mixed layer potential temperature and CIBL depth over the Ronne Polynya using the observational data. This one-dimensional model was designed to investigate the systematic and non-uniform modification of surface turbulent heat fluxes with fetch over polynyas. It is a zero- order jump, or slab, model, which means that the mean thermodynamic variables in the mixed layer are assumed constant with height, and fluxes vary linearly with height, so the mixed layer is assumed to be a uniform slab of air. The CIBL top is represented by a discontinuity, or sharp jump, in the variables between the mixed layer and free atmosphere, so the entrainment zone is assumed to be infinitessimally thin (e.g. Stull, 1988).

It is assumed in the model that sensible heat ﬂux convergence is responsible for warming of the boundary layer over the polynya. The variation in the surface ﬂux therefore controls the downwind changes in boundary layer depth and potential tem-

100 perature, under steady-state conditions. Given inputs of wind speed, surface and mixed layer temperatures, plus estimates of the initial boundary layer depth, ambient atmospheric stability and the entrainment parameter (ratio of the entrainment heat ﬂux at the top of the boundary layer to that at the surface), the model is able to estimate the surface sensible heat ﬂux, potential temperature and development of the CIBL depth with polynya fetch.

Effects of secondary importance such as radiative flux convergence and microphysical processes related to the formation of cloud, fog and precipitation are neglected for simplicity. The model has previously provided estimates of surface sensible heat flux and boundary layer depth that agree well with the limited observations available from sites within polynyas (Renfrew and King, 2000).

It is inaccurate to assume heat fluxes over polynyas are constant over mesoscale fetches (Smith et al., 1990; Pinto et al., 1995) and it is therefore important to include a developing boundary layer when modelling the turbulent heat fluxes with fetch. This model, which is appropriate for the investigation of cloud-free CIBLs and allows the surface sensible heat flux, mixed layer potential temperature and boundary layer depth to vary non-linearly with fetch, is therefore suitable for use in this study of the ocean-atmosphere heat fluxes over the Ronne Polynya.

5.2 The model construction

The following equations are used to model the evolution with polynya fetch of the mixed layer potential temperature (θ) and the depth of the CIBL (zi). Further model details can be found in Renfrew and King (2000).

(1 + β) Z QS(x) θm(x) = θm(0) + dx (5.1) Umcp ρ(x)zi(x)

2 Z Q (x) z2(x) = z2(0) + U γ c S dx (5.2) i i (1 + 2β) m θ p ρ(x)

101 Subscript m denotes a value representative of the mixed layer and x the fetch. β is the entrainment parameter, γθ the ambient stability, U the wind speed, cp the speciﬁc heat capacity of air, QS the surface sensible heat ﬂux and ρ the density of air.

As shown previously in section 4.1.4, the surface sensible heat ﬂux is given by

QS(x) = ρ(x)cpCHrUr(Tsfc − θm(x)) (5.3)

CHr is calculated from CHN10 using an algorithm based on the formulation of Smith

(1988). This algorithm includes an iteration scheme for the estimation of u∗ (friction velocity) and t∗ (surface-layer scaling temperature), incorporating Businger-Dyer flux-gradient relations to account for atmospheric stability effects, as were described in section 4.1.5. Although this formulation was designed for climatological use over the oceans, it can be applied to polynyas beyond microscale effects near the upwind edge (Renfrew and King, 2000).

Using numerical integration, these three equations are solved. An iteration scheme is used where firstly, the sensible heat flux (QS) is calculated using equation 5.3, using as a first guess an input value for θm at x = 0. Secondly, equations 5.1 and

5.2 are solved for θm(xi) and zi(xi). Thirdly, this new estimate of θm(xi) is then used to revise the estimate of QS(x). For the CIBL depth zi, the second and third steps are repeated until the values of zi converge.

The model is therefore able to estimate the development of CIBL depth, surface sensible heat ﬂux and air temperature with polynya fetch, given inputs of wind speed, initial temperatures of the surface and mixed layer and initial boundary layer depth. Additionally, the ambient stability of the atmosphere, γθ must be speciﬁed as well as the entrainment parameter, β.

102 5.3 Modelling of the case studies

The aircraft observational data collected at the Ronne Polynya were used to provide the initial model conditions at a fetch of 0 km, the ice shelf edge. The parameters used for the model runs are given in table 5.1 and include atmospheric stability above the CIBL (γθ), and the entrainment parameter (β), obtained as shown in sections 3.1 and 3.3 respectively. Sawtooth profiles were not conducted for F49 and so γθ and β were estimated using data obtained from the ascending and descending profiles between the measurement level and the flight transit altitude.

Flight Wind speed θair Tsfc regime 1 Tsfc regime 2 Pressure γθ β F49 8 m s−1 -14.8 oC -6.9 oC N/A 983 mb 10 K m−1 0.4 F54 17 m s−1 -18.8 oC -7.8 oC -11.7 oC 994 mb 6 K m−1 0.5 F57 14 m s−1 -19.2 oC -9.4 oC -10.8 oC 992 mb 14 K m−1 0.4

Table 5.1: Model input data from aircraft observations

The model was designed for the simple case of an open water polynya with a constant surface temperature, at the freezing point, where variation in the air temperature leads to variation in the surface sensible heat flux with fetch. However, as discussed previously, at the time of the case studies it was observed that the Ronne Polynya was mostly covered with thin ice, which increased in thickness with fetch causing a corresponding reduction in the measured surface temperature. This had a greater effect on the spatial variation of the sensible heat flux than did variations in the air temperature. A two-regime surface temperature was therefore introduced to the model, to take some account of the variation in surface temperature with fetch, using the observed mean value for each regime. For F49, where two distinct regimes were not present, the mean value of the surface temperature across the polynya was used.

−3 In addition, the mean values at the Ronne Polynya of CHN10 = 0.7 × 10 and −3 CDN10 = 1.1 × 10 as calculated in section 4.2.3, which were found to be valid for both regimes, were introduced to the model. These replaced the model default

−3 values appropriate for open water (Renfrew and King, 2000) of CHN10 = 1.14×10 −3 (DeCosmo et al., 1996) and CDN10 = 1.0 × 10 (Smith, 1988). It was also shown in

103 section 4.2.7 that the surface roughness length was not dependent on the wind speed for these case studies, and therefore the Charnock parameter was also removed from the model.

The modelled surface sensible heat ﬂux, mixed layer potential temperature and CIBL depth were then validated against the Ronne Polynya observations.

5.3.1 Sensible heat ﬂux

The model was run using a two-regime surface temperature as well as a one-regime surface temperature for comparison. In addition, the model was also run assuming the polynya consisted of open water at the freezing point, at an appropriate constant surface temperature of -1.9 oC (Nicholls et al., 2004), using firstly the original model transfer coefficients for open water and then the Ronne Polynya transfer coefficients for comparison. Results are all shown on figure 5.1, along with the observed eddy covariance sensible heat flux for F54L1 and F54L2. The magnitude of the error bars given for the observations are obtained from the measured sampling error, see table 4.1, section 4.2.2. A measured sampling error of e.g. 20 % (F54L1) corresponds to an error in the data of potentially ±10 %.

Table 5.2 shows the root-mean-square-errors (RMSE) for each of the modelled sensible heat fluxes compared to the observed eddy sensible heat flux. Also included in the table are the RMSEs for modelled heat fluxes using the observed surface temperature for each 1 km point, as shown on figure 5.2. The model run using F54L1 surface temperatures only is shown on the figure for clarity, but using the F54L2 surface data produces a very similar result, as shown in the table.

It can be seen on figure 5.1, by comparison of the dotted and dash-dotted lines, that the modelled sensible heat flux is not only very sensitive to the prescribed surface temperature but also to the value of the transfer coefficients (primarily CHN10 owing to the large difference between the DeCosmo CHN10, and that observed). Therefore, for a modelling study of the surface energy budget for example, errors in either

104 500 given model 1−regime T (Ronne C )

sfc H sfc

model 2−regime T (Ronne C ) T 450 sfc H model open water T (Ronne C ) sfc H

model open water T (DeCosmo C ) , other sfc H

400 C observed F54L1 o observed F54L2 350 is -1.9 sfc

300 T ) −2 250 (W m 105 S Q 200

150

100

50 Observed eddy sensible heat flux for F54L1 and F54L2 (error bars from 0 0 20 40 60 80 100 120 Fetch (km) in table 5.1. Figure 5.1: sampling error), and modelled sensibletemperature and heat transfer flux coefficients. shown Open with water variations in surface 250 model obs T sfc observed F54L1 observed F54L2

200

150 ) −2 (W m 106 S Q 100

50 Observed eddy sensible heat flux for F54L1 and F54L2 (error bars from 0 0 20 40 60 80 100 120 Fetch (km) Figure 5.2: sampling error), with modelled sensible heat fluxperature for using each F54L1 point. observed surface tem- the surface temperature or the heat transfer coefficient could result in a large over- or underestimate of the magnitude of the surface sensible heat flux at the Ronne Polynya.

Tsfc CHN10 RMSE 1 regime Ronne 59.6 2 regime Ronne 24.5 open water DeCosmo 273.5 open water Ronne 138.4 F54L1 observed Ronne 22.1 F54L2 observed Ronne 21.3

Table 5.2: F54 sensible heat flux RMSE (W m−2) for different model runs compared to observed eddy heat flux for F54L1 and F54L2 together.

The model run using the observed mean surface temperature for each 1 km point together with the observed mean transfer coefficients, shown on figure 5.2, gives, as would be expected, the best result when compared with the eddy covariance fluxes, see table 5.2. However, the two regime surface temperature produces a result of only slightly reduced accuracy to this, see table 5.2 and solid line, figure 5.1. In contrast, a single regime, i.e. a constant surface temperature based on the mean temperature over the first 35 km only, significantly increases the RMSE from 24.5 to 59.6 W m−2, see table 5.2 and dashed line, figure 5.1. Therefore, the two-regime method preserves the simplicity of the model while giving comparable results to inputting the surface temperature at each point. This is useful for modelling applications where high resolution surface data may not be available. Furthermore, it is possible the surface temperature could be determined from satellite observations on these spatial scales. For a two-regime polynya, a mean surface temperature over the whole polynya is close to the temperature over the longer second regime so would not capture the heat flux over the first regime if used in the model.

The use of a two-regime surface temperature has a less important effect on the modelled heat fluxes for F57, see figure 5.3, reducing the RMSE by 2 W m−2 compared to

107 the single regime. This is because there is a smaller temperature diﬀerence between the two regimes, of 1.4 oC compared to 3.9 oC for F54. Therefore, the importance of a two-regime temperature input is dependent upon the magnitude of the mean surface temperature diﬀerence between the regimes.

Figures 5.1 and 5.3 both illustrate that for these case studies the difference in the modelled heat fluxes between using an open water temperature and an ice surface temperature is significant, and indicates the importance of using the correct magnitude of heat transfer coefficient. However, for F49, using an open water surface temperature does not produce results which are as inaccurate as for the other two flights, see figure 5.4. The RMSE, using the Ronne transfer coefficients for both,

o −2 o for the observed Tsfc of -6.9 C is 26.3 W m and for open water at -1.9 C is 29.9 W m−2. This is a result of the lower surface-air temperature diﬀerence for this

flight, meaning the open water Tsfc is closer to that measured than for the other flights. Additionally, the reduced magnitude of the heat flux for this flight means the error is proportionally smaller. However, the sensible heat flux is overestimated when using a heat transfer coefficient appropriate for open water, see figure 5.4, where the RMSE for this model run is 72.7 W m−2.

As discussed previously, the Charnock parameter was not appropriate for use over the ice-covered polynya at the time of the case studies. However, the effect on the modelled sensible heat flux (and boundary layer depth) of inclusion of this parameter was found to be negligible. The magnitude of the variation in the calculated surface roughness length and friction velocity was therefore not large enough at the observed wind speed to significantly affect the modelled outcome.

5.3.2 Potential temperature

Figure 5.5 shows the modelled potential temperature (θ) with polynya fetch along with that observed for the low-level legs of F54. Using the two-regime surface temperature and the Ronne Polynya transfer coeﬃcients, the model captures the change in θ with fetch very well. Using an average of the θ observations for the two legs,

108 500 model 1−regime T (Ronne C ) sfc H model 2−regime T (Ronne C ) 450 sfc H model open water T (Ronne C ) sfc H model open water T (DeCosmo C ) 400 sfc H observed F57L1

350

300 ) −2 250 (W m 109 S Q 200

150

100

50 Observed eddy sensible heat flux for F57L1 (error bars from sampling 0 0 20 40 60 80 100 120 Fetch (km) Figure 5.3: error), and modelled sensible heat flux shownand with transfer variations coefficients. in surface temperature 500 model (Ronne C ) H model open water T (Ronne C ) 450 sfc H model open water T (DeCosmo C ) sfc H observed F49L2 400

350

300 ) −2 250 (W m 110 S Q 200

150

100

50 Observed eddy sensible heat flux for F49L2 (error bars from sampling 0 0 20 40 60 80 100 120 Fetch (km) Figure 5.4: error), and modelled sensible heat flux shownand with transfer variations coefficients. in surface temperature for the two-regime surface temperature the RMSE amounts to 0.17 K, compared with 0.34 K for the one-regime. The model also captures the observed variation in potential temperature with fetch reasonably well for F57 (see figure 5.6) using either a one- or two-regime Tsfc where the RMSE is 0.34 K or 0.31 K respectively. However, it is captured less well for F49, see figure 5.7, where the RMSE amounts to 0.54 K. For F49 the CIBL was cloud-filled and this underestimate of the warming could therefore be a result of the neglect in the model of warming due to radiative flux convergence and microphysical processes. As noted by Renfrew and King (2000) this neglect can lead to only 75 % of the boundary layer warming being captured by the model. However, in this case the error is smaller, with 85 % of the warming over the measured fetch being captured by the model.

258

257 C) o

( 256 air θ

255 observed F54L1 observed F54L2 model 1 regime T sfc model 2 regime T sfc 254 0 20 40 60 80 100 120 Fetch (km)

Figure 5.5: Modelled and observed potential temperature (θ) for F54, shown with fetch over the Ronne Polynya. Observed θ from level-ﬂight legs F54L1 and F54L2 averaged over 0.5 km sections.

111 259

258

257 C) o

( 256 air θ

255

254 observed F57L1 model 1 regime T sfc model 2 regime T sfc 253 0 20 40 60 80 100 120 Fetch (km)

Figure 5.6: Modelled and observed potential temperature (θ) for F57, shown with fetch over the Ronne Polynya. Observed θ from level-ﬂight leg F57L1 averaged over 0.5 km sections.

5.3.3 Convective internal boundary layer depth

Figure 5.8 shows the modelled CIBL depth (zi) with fetch over the Ronne Polynya for flights F54 and F57 compared to the observed zi for each flight. The observed values were derived from potential temperature profiles as discussed in section 3.1. Using the two-regime surface temperature, the model captures the observed CIBL development well for F54 (figure 5.8(a)) with an RMSE of 10.3 m compared to the observed zi, outperforming the one-regime surface temperature parameterisation which led to an RMSE of 33.2 m. For F57, the RMSE is 14.9 m using a one-regime surface temperature and marginally worse, at 16.2 m for a two-regime. This demonstrates that, as above for the surface sensible heat flux and potential temperature, the use of a one-regime or a two-regime temperature parameterisation makes little

112 263 observed F49L2 model

262

261 C) o ( air θ 260

259

258 0 20 40 60 80 100 120 Fetch (km)

Figure 5.7: Modelled and observed potential temperature (θ) for F49, shown with fetch over the Ronne Polynya. Observed θ from level-flight leg F49L2 averaged over 0.5 km sections. difference to the accuracy of the modelled results for the F57 case study owing to the small temperature difference between regimes. Measurements of zi were not collected during F49 so no discussion of this flight is presented in this section.

The modelled boundary layer depth is very sensitive to the input value of the ambient stability, i.e. the stability above the growing CIBL, and to a lesser degree the entrainment parameter (Renfrew and King, 2000). Figures 5.9(a) and 5.9(b) demonstrate this for F54. The selected values of these parameters used for the modelling in this study are shown on ﬁgure 5.9 as solid black lines. The methods used to obtain these values (see section 3.3) appear to have been appropriate, given the excellent

ﬁt of the modelled zi to the observations compared with the modelled zi using the other values. RMSE values for the various model runs shown in ﬁgure 5.9 are given in table 5.3.

113 800

700

600

500

400 Altitude (m) 300

200

observed 100 model 1 regime T sfc model 2 regime T sfc 0 0 20 40 60 80 100 120 Fetch (km)

800 observed model 1 regime T sfc 700 model 2 regime T sfc

600

500

400 Altitude (m) 300

200

100

0 0 20 40 60 80 100 120 Fetch (km)

Figure 5.8: Modelled and observed boundary layer depth (zi) for F54 (a) and F57 (b), shown with fetch over the Ronne Polynya.

114 The initial value of the modelled boundary layer depth at 0 km, zi(0), which takes into account the depth of the mechanically-driven boundary layer above the ice shelf, was set to 85 m. This was the value observed for F57 as no measurements of this parameter were obtained for F54. This could be a source of error, given that the wind speeds during F54 were stronger than for F57, which may have increased this value. However, the modelled evolution of zi, as well as θ and the sensible heat flux are not particularly sensitive to this parameter (Renfrew and King, 2000). The sensitivity of the modelled zi for F54 to a range of reasonable values of zi(0) is shown on figure 5.9(c), demonstrating that the effect of this parameter on the modelled zi is negligible for these values.

γ (K km−1) β RMS error (m)

6 0.1 84.0 6 0.3 39.9 6 0.5 10.3 6 0.7 37.5 4 0.5 92.3 6 0.5 10.3 8 0.5 53.7 10 0.5 89.5

Table 5.3: F54 modelled boundary layer depth RMSE (m) for various stabilities and entrainment parameters compared to observed boundary layer depth.

Therefore, it can be concluded that the most important parameter for the correct modelling of zi is the ambient stability, as was suggested in the introduction and was found previously in sensitivity studies for this model by Renfrew and King (2000).

115 800

700

600

500

400 Altitude (m) 300 γ −1 θ = 4 K km γ −1 200 θ = 6 K km γ −1 θ = 8 K km 100 γ −1 θ = 10 K km observed z i 0 0 20 40 60 80 100 120 Fetch (km)

(a) Ambient stability (γθ)

800

700

600

500

400 Altitude (m) 300

200 β = 0.1 β = 0.3 β 100 = 0.5 β = 0.7 observed z i 0 0 20 40 60 80 100 120 Fetch (km)

(b) Entrainment parameter (β)

800

700

600

500

400 Altitude (m) 300

200 zi(0) = 50 m zi(0) = 85 m 100 zi(0) = 100 m zi(0) = 150 m observed z i 0 0 20 40 60 80 100 120 Fetch (km)

Figure 5.9: F54 sensitivity of modelled CIBL depth to variations in ambient stability (a), entrainment parameter (b) and initial boundary layer depth (c). Solid black line indicates values used for modelling in this study. 116 5.4 Summary

The CIBL model of Renfrew and King (2000) was validated against data obtained at the Ronne Polynya. It was shown that, given appropriate input values, the model is able to accurately predict the variation in the surface sensible heat flux, potential temperature and CIBL depth with fetch across the polynya. At its best, for F54, the model was able to estimate the heat flux with an accuracy of ±24.5 W m−2, and potential temperature and CIBL depth with accuracies of ±0.17 K and ±10.3 m respectively, as given by the RMSEs. The model would not be expected to capture the variability inherent in the data exactly and this is therefore an excellent result. For F49, the modelled potential temperature was lower than was observed, with an RMSE of 0.54 K. On this day, the CIBL was cloud-filled and this underestimation could thus be a consequence of the neglect in the model of warming due to radiative and microscale processes.

The modelled boundary layer depth was shown to be sensitive to the ambient stability and, to a lesser extent, the entrainment parameter. Within a range of reasonable values, the modelled zi was relatively insensitive to the initial boundary layer depth.

It has been shown that in order to accurately model the surface sensible heat flux, potential temperature and CIBL depth for these case studies, it was important to include a suitable surface temperature parameterisation and transfer coefficients appropriate to an ice-covered surface, particularly when the surface-air temperature difference was large. It can therefore be inferred that under similar meteorological conditions where significant ice cover is expected, the heat flux over any coastal polynya should be modelled in this way. For large areas of open water within the first regime, due for example to strong winds and/or small surface-air temperature differences, a surface temperature and transfer coefficients appropriate for open water would presumably become necessary for accurate modelling of these parameters.

Therefore, for the modelling of convective heat transfer over polynyas, speciﬁcation of accurate surface temperatures and transfer coeﬃcients is crucial to achieving good results. The distinction between open water and thin ice as well as more

117 consolidated ice within the polynya is thus an important one. Without in-situ data, this is potentially a large source of error. Errors in the magnitude of the modelled ocean-atmosphere sensible heat flux will lead to significant errors in the estimation of the effect of polynyas on the regional meteorology and oceanography of the high latitudes, and consequently of their effect on the global ocean circulation.

118 Chapter 6

Surface Heat Budgets and Buoyancy Flux

The stability of the upper ocean is modified by the surface exchange of heat and moisture, including the production or ablation of ice. Consequently, the surface fluxes of heat and salinity determine the ocean surface buoyancy flux (Curry and Webster, 1999). Buoyancy flux calculations can be extended and combined with models of ocean transport and circulation to determine the amount of dense water produced within polynyas (Grumbine, 1991; Cavalieri and Martin, 1994; Markus et al., 1998; Chapman, 1999). Therefore, quantification of the surface heat and salinity budgets at coastal polynyas is a key step towards quantifying the surface buoyancy flux and, by extension, the role of coastal polynyas in the formation of dense water masses which contribute to the global ocean circulation. In addition, the surface heat budget can also be used to determine the volume of ice produced by coastal polynyas (Cavalieri and Martin, 1994; Markus et al., 1998; Renfrew et al., 2002).

In this chapter, the surface heat budget and buoyancy ﬂux for the Ronne Polynya case studies will be determined using the observational data, and the potential ice production rates at the polynya based on these results will also be investigated.

119 AIR

SWU SWD LWU LWD QS QL

Tsfc z = 0

Qci (0)

ICE

Q (H) τi(1 - α)SWD ci Tfreeze z = H QW

OCEAN

Figure 6.1: Schematic of heat budget for sea ice

6.1 Heat budget

6.1.1 Background

Figure 6.1 is a schematic of the one-dimensional energy budget for an ocean surface covered by ice of thickness H, representative of the Ronne Polynya at the time of the case studies. Tsfc is the surface temperature at z = 0 and varies in response to changes in the surface energy balance. At the bottom of the ice at z = H, the temperature is ﬁxed at the freezing point of the seawater, so the temperature of the ocean-ice interface is Tfreeze (Curry and Webster, 1999). The surface of the ice (at z = 0) is stationary, whereas H, the ice thickness, is allowed to vary.

LW is longwave radiation, SW is shortwave radiation and U and D denote upwelling and downwelling respectively. QS and QL are the surface turbulent ﬂuxes of sensible and latent heat, as discussed in chapter 4, Qw is the heat ﬂux from the ocean and

Qci is the conductive heat ﬂux through the ice, due to the temperature diﬀerence between z = 0 and z = H.

120 According to Curry and Webster (1999), during the early growth stages of ice, e.g. grease ice, the surface of the ice is wet and close to the freezing temperature of the water. Once the ice is consolidated, the surface temperature of the ice decreases in response to heat loss at the surface. If the temperature at the air-ice interface is less than the temperature of the water at the ocean-ice interface, heat will be conducted through the ice, resulting in the formation of congelation ice on the underside of the ice. The growth rate of the ice on the underside of the ice, i.e. dH/dt, therefore depends on the conduction of heat from z = H to z = 0, see ﬁgure 6.1.

Transmission of SW radiation

The quantity τi(1 − α)SW (Curry and Webster, 1999) represents the transmission of shortwave radiation through the ice, see ﬁgure 6.1, where τi is the transmissivity and α is the SW albedo of the surface. This parameter will act to reduce the ice formation rate at the underside of the ice, but is not relevant during nighttime and in the polar winter. Calculation of this contribution to the surface energy budget requires detailed information on the transmissivity of the ice, which is dependent on the ice thickness. This is unknown for the Ronne Polynya case studies.

However, generally this transmission term is not large. For example, the amount of SW radiation reaching the bottom of the ice, using τi(1 − α)SW , for a typical transmissivity for new ice of 0.2 (Perovich and Grenfell, 1981), an albedo of 0.5 and a SWD of 300 W m−2, amounts to 30 W m−2. Therefore for simplicity this term will be neglected in the following analysis. However, it should be noted that where the ice is very thin, e.g. close to the ice shelf front, or when the surface temperature is close to the freezing point of the water, this term will be considerably larger. For a more comprehensive thermodynamic treatment of sea ice growth, for example for calculation of the ice depth, H, which is beyond the scope of this study, this term would need to be included.

Precipitation

For a polynya that is mostly ice covered, it can be assumed for simplicity that there is no eﬀect on the surface heat (or salinity) budget from melting of precipitation

121 (assuming it is all in the form of snow) or blowing snow into the ocean. However, a covering of snow on sea ice will reduce the thermal conductivity, ki, of the surface, −1 −1 −1 −1 since ki for snow is 0.1 − 0.4 W m K compared to 2 W m K for sea ice. This has the effect of reducing Qci by as much as 50% (Eicken, 2003), thereby significantly reducing the rate of ice formation on the underside of the ice. The insulating properties of snow have a larger effect on the heat budget than do the albedo effects (Eicken, 2003).

Even for a polynya with a larger fraction of open water, such as may be found in the summer months, the effect on the heat budget due to melting of precipitation is in general likely to be very small, especially compared to the large contribution from the incoming radiative heat flux. For example, a relatively large snow precipitation rate of 1 m of water equivalent per year requires only 10 W m−2 of latent heat to remove it (Morales Maqueda et al., 2004). The cooling effect on the heat budget is smaller however than the freshening effect on the salinity budget (Curry and Webster, 1999). However, as the density of snowflakes is low compared to that of water, they do not submerge into the ocean but remain on the surface to form a freshwater skin, where they reduce the salinity by no more than 5 psu (Curry and Webster, 1999). Therefore, there is little effect on either the heat or salinity budgets, and therefore on the buoyancy flux, from precipitation.

Blowing snow

At the time of the case studies, snow was observed to be blown from the Ronne Ice Shelf into the Ronne Polynya, see ﬁgure 6.2.

The snow lands on the open water or very thin, wet ice of the ﬁrst few km and therefore can be assumed to melt. The latent heat required to melt this snow can be calculated. Using a parameterisation devised by Mann et al. (2000), the blowing snow transport rate, Tsn, at the upwind edge of the polynya can be modelled thus:

Tsn = 0.297(exp(2.805(u∗ − u∗t)) − 1) (6.1)

122 Ronne Ice Shelf blowing snow

Ronne Polynya

Figure 6.2: Snow blown oﬀ the Ronne Ice Shelf into the Ronne Polynya during strong winds, 27 February 2007.

where u∗ is the friction velocity, given by

κU(z) u = (6.2) ∗ ln( z ) z0 assuming a neutral surface layer due to turbulent mixing by strong winds during the blowing snow episode. κ is von Karman’s constant (0.4), U is the windspeed at the measurement height, z, and z0 is the surface roughness length. z0 is a function of the wind speed, due to saltating snow particles, similar to the dependence of z0 over open water on the wind speed due to wave height, see section 4.2.7, i.e. the

Charnock relation. Here, z0 can be described by (Mann et al., 2000)

2 z0 = z0ns(u∗/u∗t) (6.3)

where z0ns is the surface roughness length of the Ronne Ice Shelf in the absence of blowing snow, set at 5.6 × 10−5 m based on measurements made on the Brunt Ice

Shelf (King and Anderson, 1994). This equation is applicable when u∗ > u∗t, where u∗t is a threshold friction velocity, above which surface cohesion forces holding the

123 snow to the surface can be overcome. This threshold is primarily dependent on the availability of loose snow, although other factors such as the eﬀect of temperature and humidity on cohesive bonds, changes in wind direction, variations in surface features due to the drifting snow itself as well as the size, and sphericity and dendricity of the particles can also have an eﬀect (Mann et al., 2000).

Based on modelling studies of blowing snow from sea ice into open leads, Déry and Tremblay (2004) predict most of the snow will be deposited over the first 1 km, and all of the remainder over the next few km. Owing to the height of the Ronne Ice Shelf (between 30 and 40 m, see section 3.2) and consequently the trajectories of the particles blown off it, they may be expected to be deposited over a longer fetch. However, the observations of blowing snow at the Ronne Ice Shelf indicate the blowing snow can all be assumed to be deposited within the first 2 km. For simplicity in the following calculations, the snow is assumed to be deposited evenly over these 2 km.

−1 The rate of blowing snow, Rsn, in m s , deposited over a certain fetch, x, can be calculated using the following (after D´eryand Tremblay, 2004)

Tsn Rsn = (6.4) ρwx where as above Tsn is the rate of blowing snow and ρw is the density of water.

The latent heat required to melt this snow is then given by

Qb = −ρsnLilRsn (6.5)

−3 where ρsn is the density of snow, taken as 330 kg m (Fichefet and Morales Maqueda, 1999). Cooling eﬀects of the snow itself on the water due to temperature diﬀerences have been neglected.

Using equation 6.5, for a typical (10 m) wind speed at the time of the case studies

−1 −1 of 10 m s , and using a typical value for u∗t of 0.3 m s (Mann et al., 2000), the

124 latent heat required to melt this snow is only 4.4 W m−2. Changing the threshold

−1 u∗t to the minimum, 0.2 m s (Mann et al., 2000), still only amounts to a latent heat loss of 14.6 W m−2.

For the Ronne Polynya case studies, the minimum observed 10 m wind speed, 4.8 m s−1, does not reach the threshold required to initiate a blowing snow event. However, the maximum observed 10 m windspeed of 16.3 m s−1 results in a predicted latent heat loss due to melting of the blowing snow of 35.6 W m−2 using

−1 −2 −1 u∗t = 0.3 m s or 72.8 W m using u∗t = 0.2 m s . This could potentially make a signiﬁcant contribution to the surface heat (and salinity) budget. However, the contribution from blowing snow is very sporadic as a result of variations in the wind speed and for these calculations is only a factor over the ﬁrst 2 km of the polynya - a relatively small area of a typical polynya. Therefore, on average, this term could be neglected from studies of polynya surface heat and salinity budgets, and will be be neglected in this study.

Additionally, ice was observed in the lee of some areas of the Ronne Ice Shelf, see ﬁgure 6.3. In such situations a large proportion of the blowing snow is deposited here, rather than melting into the ocean. Therefore, even for strong winds and a consequently large transport rate, snow blown from the ice shelf cannot always be assumed to melt into the ocean.

Figure 6.4 shows a cornice formed at the Ronne Ice Shelf from snow blown towards the edge where it has consolidated. It appears to be unstable and close to breaking oﬀ. On falling into the water, these cornices would not be expected to immediately melt or to remain stationary, in eﬀect becoming icebergs. Therefore, they do not have a concentrated impact on the heat or salinity budgets in any one place, and the mean contribution of this form of blowing snow to the budget can be treated in the same way as the blowing snow which immediately enters the water, and be generally neglected in the mean.

The heat budget at the air-ice interface, z = 0 (see ﬁgure 6.1), can therefore be simpliﬁed to (Eicken, 2003):

125 Ronne Ice Shelf

Ronne Polynya

Figure 6.3: Snow-covered ice in the lee of the Ronne Ice Shelf, 27 February 2007.

QR − QS − QL = −Qci(0) (6.6) where a positive sign indicates a heat gain by the interface, and all heat ﬂuxes are in W m−2. It is assumed here there is no melt at the surface.

QR is the net surface radiation ﬂux, given by

QR = LW D − LW U + SWD − SWU (6.7) where, as above, a positive sign indicates a heat gain by the surface.

The surface ﬂuxes at z = 0 are balanced by the conduction of heat through the ice. Therefore the ice surface at z = 0 is in thermal equilibrium. At the underside of the ice, the conduction of heat towards or away from the ocean-ice interface at z = H results in the accretion or melt of ice.

126 Ronne Ice Shelf

cornice

Ronne Polynya

Figure 6.4: A cornice close to breaking oﬀ at the Ronne Ice Shelf, 25 February 2007.

Sea ice conduction

Most of the terms in equation 6.6 are dependent on Tsfc. Thermal equilibrium at the air-ice interface (z = 0) is the result of physical processes that adjust Tsfc, balancing all the terms in the equation (Eicken, 2003). Since the ice growth rate is dependent on the conduction of heat from z = H to z = 0, the conductive heat ﬂux, Qci can be considered a residual term which responds to variations in the other ﬂuxes into and out of the air-ice interface, which alter Tsfc, by inducing variable accretion (or melting) rates at the ice-ocean interface (Eicken, 2003).

For the simpliﬁed case where ﬂuxes in the vertical plane only are considered, Qci is given by (Eicken, 2003)

dT Q (z) = −κ (6.8) ci i dz

127 Therefore, Qci is dependent on the local temperature gradient at depth within the ice z, and on the thermal conductivity of the ice, κi.

If the ice is thin, or the variations in the surface energy balance are slow compared to the rate of conductive heat transfer through the ice, the temperature gradient can be approximated as linear (Curry and Webster, 1999; Eicken, 2003). Qci will therefore be constant with depth and there will be an immediate response of the sea ice thickness, H, at the bottom of the ice to variations in the total surface heat ﬂux (Curry and Webster, 1999; Eicken, 2003), i.e. the thermal inertia of the ice can be neglected (Morales Maqueda et al., 2004). Therefore,

Qci(0) = Qci(H) see ﬁgure 6.1, i.e. the conductive heat ﬂux at the top and bottom of the ice is equal.

At the bottom of the ice, the conductive heat ﬂux out of the ice-ocean interface and the oceanic heat ﬂux into the interface are balanced by the latent heat released during freezing or used during melting. Therefore, for a change in ice thickness of dH/dt (Eicken, 2003)

dH Q (H) + Q = ρ L (6.9) ci w i il dt

ρi is the density of young saline ice, given by e.g. Markus et al. (1998); Chapman 3 −3 (1999) as 0.95 × 10 kg m . Lil is the latent heat of fusion. For pure ice, this is 3.34 × 105 J kg−1, although it will be reduced for sea ice, and dependent on the salinity (Curry and Webster, 1999). Chapman (1999) has however used the pure ice value in calculations, an approximation which will also be used in this study.

−2 Qw, the upward oceanic heat ﬂux, is of the order 10 W m for the Antarctic sea ice zone (McPhee and Martinson, 1994) and can therefore be neglected.

Assuming Qci(0) = Qci(H) and substituting equation 6.9 into equation 6.6, neglect- ing Qw, gives

128 dH Q = Q − Q − Q = −ρ L (6.10) tot R S L i il dt

−2 where Qtot is the total atmospheric heat ﬂux, in W m (Curry and Webster, 1999).

dH Hence if Qtot < 0, then dt > 0 and ice grows, rejecting brine and increasing the dH salinity of the water column below. If Qtot > 0, dt < 0 and ablation of the ice occurs, freshening the water column. Since QR, QS and QL are all functions of dH polynya fetch, then so are Qtot, and dt .

The surface energy budget given by equation 6.10 is valid for the Ronne Polynya both for frazil ice formation on the surface under open water conditions and for growth of congelation ice on the underside of an ice surface due to surface cooling. The ice surface must either be thin (< 0.1 m (Morales Maqueda et al., 2004)) or changes in the surface energy balance must be slow compared to the rate of conduction of heat through the ice for equation 6.10 to be valid.

Equation 6.10 has been used to calculate the surface heat budget over the Ronne Polynya for the four level-ﬂight legs.

6.1.2 The Ronne Polynya surface heat budget

Net radiative ﬂux, QR

The net radiative ﬂux, QR, was obtained using equation 6.7. Unfortunately measurements of the LW U term were not reliable for the Ronne Polynya ﬂights as the downward-looking PIR dome pyrgeometer instrument (see section 2.3) had previously sustained damage. As an alternative, the LW U was calculated using measurements of surface temperature (Tsfc) obtained using the infra-red thermometer (IRT), and employing the Stefan-Boltzmann equation (Curry and Webster, 1999):

4 LW U = σTsfc (6.11)

129 300 PIR ε 295 IRT ( = 0.97) IRT (ε = 0.95) ε 290 IRT ( = 0.98) IRT (T + 0.1 K) sfc

) IRT (T + 0.5 K) 285 sfc −2 IRT (T − 0.5 K) sfc 280

275

270

Outgoing LW flux (W m 265

260

255

250 0 20 40 60 80 100 120 Fetch (km)

Figure 6.5: LWU for F57L1, showing PIR direct measurement and calculated from

IRT, demonstrating eﬀect of various errors in Tsfc and .

σ is the Stefan-Boltzmann constant, 5.67 × 10−8 W m−2 K−4 and is the emissivity of the surface, which for the Ronne Polynya was a mixture of sea ice, open water and some snow, so a representative value of 0.97 was used (King and Turner, 1997).

Figure 6.5 shows an example of the LW U timeseries for these two methods, for F57L1. This figure indicates the LW U measured by the PIR, which should be related to the surface temperature which decreased with fetch, is not reliable. However, using the IRT surface temperature instead means that any measurement errors in the surface temperature will be magnified due to the 4th power in the Stefan-Boltzmann equation. Examples of the effect of various errors in the surface temperature as well as using various emissivities on the calculated LW U are also shown on figure 6.5. This demonstrates that even within reasonable error of these parameters, it is better to use the IRT method than the data from the broken PIR, and that in using this method an error of around ±5 W m−2 is expected.

Turbulent ﬂuxes, QS, QL

The eddy covariance sensible heat ﬂux with fetch over the Ronne Polynya, QS, was

130 calculated using aircraft measurements, as discussed in detail in chapter 4. The eddy covariance latent heat flux cannot be obtained directly since measurements of humidity perturbations over the Ronne Polynya were not collected. However, as demonstrated in section 4.2.6, the Bowen ratio (ratio of sensible to latent heat fluxes) was found to be 3.8 for the Ronne Polynya. Therefore the latent heat flux,

QL, can be obtained using QS/3.8. The uncertainty in making this assumption is relatively small, due to the small magnitude of QL compared to QS and QR.

Total heat ﬂux, Qtot

The surface heat budgets for the four legs are shown on ﬁgure 6.6, where QR, QS,

QL and Qtot are all plotted separately. For clarity, error bars on Qtot only are shown.

These were obtained using the error estimates for the components of Qtot, i.e. QS,

QL and QR. As in section 5.3.1, the error in QS was assumed to be the sampling error, e.g. ±10 % for F54L1. Since here QL was calculated using QS, the error was calculated in the same way for this quantity, giving errors of 1 − 4 W m−2. For

QR, the largest error was assumed to come from the LWD as described above, and −2 was taken as ±5 W m . Thus the error in Qtot was calculated, using the standard formulation:

2 2 2 0.5 Qtot error = (QS error + QL error + QR error )

It can be seen on figure 6.6 that the total heat flux is at times close to zero but is rarely below, indicating little ice is being formed. This is due to the high levels of incoming shortwave radiation. As demonstrated by Renfrew et al. (2002), the freezing season at the Ronne Polynya begins at the end of February/ early March, when incoming solar radiation begins to decrease. The field campaign therefore took place on the very cusp of the freezing season.

A general pattern in Qtot can be seen on ﬁgure 6.6, where the magnitude towards the upwind and downwind edges of the polynya is lower than that in the middle section. At the upwind edge, the surface-air temperature (and humidity) diﬀerence was greatest, and therefore QS (and QL, calculated from QS here) is increased, leading to a greater heat loss and counteracting the radiative heat gain. Towards

131 the downwind end of the polynya, the increased surface albedo leads to a greater

SWU term and therefore a reduced net radiative heat ﬂux, QR, and a corresponding reduction in Qtot.

The monthly heat budget for polynyas along the Ronne-Filchner Ice Shelf was investigated by Markus et al. (1998) for the year 1992. The results from their Feb-

−2 ruary (March) heat budget, of a Qtot of 25 (-250) W m , where QS + QL is -75 −2 −2 (-200) W m and QR is 100 (-50) W m , are broadly consistent with the mean results calculated above for the Ronne Polynya for February 25th to 28th 2007, of

−2 −2 −2 a Qtot of 30 W m , where QS + QL is -110 W m and QR is 140 W m . For comparison, the summer maxima of these components from the Markus et al. study

−2 −2 −2 were 250 W m , 0 W m and 250 W m for Qtot, QS + QL and QR respectively.

Owing to the large ocean-atmosphere heat losses, high rates of ice formation and the oceanographic effects of brine rejection, the majority of previous studies of coastal polynya heat budgets concentrate on the winter months, where, in the absence of incoming shortwave radiation, the heat budget is dominated by the surface sensible heat flux (Cavalieri and Martin, 1994; Comiso and Gordon, 1998; Markus et al., 1998; Winsor and Björk, 2000; Renfrew et al., 2002). To give a comparison between winter and summer budgets, Renfrew et al. (2002) found maximum summer values of the total heat flux of 350 W m−2, compared with -1200 W m−2 in the winter.

6.2 Ice production volume

The Ronne Polynya heat budget data have been used to estimate the volume of ice produced by the polynya.

From equation 6.10

dH Q = −ρ L tot i il dt and therefore

132 250 250 Q Q R R Q Q 200 S 200 S Q Q L L Q Q 150 tot 150 tot

100 100 ) ) −2 −2 50 50

0 0 Heat flux (W m Heat flux (W m −50 −50

−100 −100

−150 −150

−200 −200 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Fetch (km) Fetch (km)

(a) F49L2 (b) F54L1

250 250 Q Q R R Q Q 200 S 200 S Q Q L L Q Q 150 tot 150 tot

100 100 ) ) −2 −2 50 50

0 0 Heat flux (W m Heat flux (W m −50 −50

−100 −100

−150 −150

−200 −200 0 20 40 60 80 100 120 0 20 40 60 80 100 120 Fetch (km) Fetch (km)

Figure 6.6: The surface heat budget for the four Ronne Polynya level-flight legs, showing QR (net radiative heat flux), QS (sensible heat flux), QL (latent heat flux) and Qtot (total heat flux). A positive flux indicates a flux from the atmosphere to the ocean.

133 dH Q = − tot dt ρiLil

So, following Cavalieri and Martin (1994), the volume of ice produced per polynya

3 area per day, Vi, in m is

4 (8.64 × 10 )AQtot Vi = − (6.12) ρiLil where A is the polynya area in m2. The polynya is assumed to be homogeneous in the y-direction (along the coast), i.e. Qtot varies only with fetch, x, which means Vi is also a function of fetch.

As a simpliﬁcation, the polynya is assumed rectangular, bound on two sides by the Ronne Ice Shelf and the Antarctic Peninsula. If the alongshore distance is assumed to be 300 km, the ice production volume at the Ronne Polynya can be calculated with fetch, splitting the rectangle into a number of strips, each with a diﬀerent Qtot.

However, this calculation is meaningful only for negative values of Qtot, i.e. when ice is being produced. Therefore, the ice production rates which might be expected during the polar winter (or at nighttime) were examined, where the SW radiation terms can be neglected and Qtot is negative. Therefore SW was set to zero and

Qtot was recalculated. Ice production per day was obtained using equation 6.12, and these calculations were then extended to ice production per year at the Ronne Polynya, assuming this ice production rate lasts for exactly 6 months. This is a very crude method as it assumes the wind speed and surface-air temperature diﬀerence remain constant for 6 months, which is obviously not the case. It is also based on the assumption that the LW balance measured during the ﬂights is representative of winter conditions, which is not necessarily true and does not take into account variations in LW D due to cloud cover. The most useful application of these observational data is clearly the potential for improvement of models such as the Renfrew and King (2000) CIBL model discussed in chapter 5, which can be used to make more accurate seasonal estimates of the surface energy balance than

134 this method of scaling up the measurements made on a single day. However, the calculations performed here nevertheless allow a general comparison with previous estimates of ice production rates in Weddell Sea coastal polynyas to be made and is included here for discussion purposes rather than as a serious estimate of this quantity. Figure 6.7 shows the annual ice production rates calculated using this method for each ﬂight, shown with polynya fetch.

Despite the basic method employed for these calculations, which contain a number of simpliﬁcations, these results are broadly consistent with the range of previous estimates of coastal polynya ice production rates e.g. 10 to 12 m yr−1 (Cavalieri and Martin, 1985), 11 to 13 m yr−1 (Markus et al., 1998) and 16 to 32 m yr−1 (Renfrew et al., 2002).

Since Qtot decreases with fetch, so does the ice production rate. Ice production within the first regime, as defined for F54 and F57 (see section 4.2.4) is greater than for the second, where it also levels off with fetch. However, for the second regime around 10 m of ice, a significant amount, is still produced. It is clearly important to consider the large variation in ice production rates with polynya fetch, when considering the total ice production over a polynya area.

There is also considerable variation between ice production rates calculated using F49 (25 February 2007) data and those obtained using data from the other two flights, F54 (27 February 2007) and F57 (28 February 2007). This illustrates the large temporal variability in the ice production rates of coastal polynyas, due here to a lower wind speed and a smaller air-surface temperature difference for F49 compared with the other two flights. Considerable variation in polynya size on timescales of a day has previously been determined using satellite timeseries, which therefore leads to considerable temporal variation in the total volume of ice produced by the polynya (e.g. Comiso and Gordon, 1998; Markus et al., 1998; Renfrew et al., 2002).

It can therefore be concluded using this simpliﬁed method that for detailed analyses of both ice production rates and the total volume of ice produced by coastal polynyas, spatial and temporal variations in polynya area and in the surface heat budget must

135 18 F49L2 F54L1 16 F54L2 F57L1 14

8 136

4 Ice production (m per unit area per year) unit area per (m per Ice production

2 Annual ice production rates for the Ronne Polynya, using data from the 0 0 20 40 60 80 100 120 Fetch (km) Figure 6.7: four level-ﬂight legs. be taken into account.

6.3 Surface buoyancy ﬂux

For an ice covered surface such as the Ronne Polynya, an ocean surface buoyancy

ﬂux (Bsfc) is produced by ﬂuxes of both heat and salinity due to ice formation and ablation at the ocean-ice interface. Following Curry and Webster (1999), Bsfc for an ice-covered surface is given by

! 1 gα Qtot(x) Bsfc(x) = (Qtot(x)) − gβ (s0 − si) (6.13) ρ0 cp Lil where, in order to facilitate comparison of results, following the convention of Mar- shall and Schott (1999) and Chapman (1999), Bsfc is given in relation to the initial −3 2 −3 density of the seawater at the surface ρ0 (1025 kg m ), making the units m s , i.e. a velocity times an acceleration, rather than the kg m−1 s−3 given by Curry and

Webster (1999). Bsfc is also calculated here as a function of fetch, x.

A negative value of Bsfc indicates a sinking motion in the ocean (Curry and Webster, −2 1999). g is acceleration due to gravity (9.81 m s ), cp is the speciﬁc heat capacity 3 −1 −1 of water at surface pressure and at freezing point (4.210 × 10 J kg K ) and Lil 5 −1 is the latent heat of fusion, 3.34 × 10 J kg , as previously. s0 is the initial salinity of the seawater, and si is the salinity of the newly-formed ice. si can be calculated using (Martin and Kaufmann, 1981)

s0 = 0.31si but it should be noted that the salinity of new ice is dependent on the freezing rate, where more brine is trapped during rapid freezing than during slow freezing (Smith et al., 1990). α and β are the coeﬃcients of thermal expansion and saline contraction respectively, which are dependent on salinity, temperature and pressure. At the

137 surface, for a salinity of 34.5 at the freezing point of -1.9 oC, α = 2.48 × 10−5 and β = 7.92 × 10−4 (using CSIRO “seawater” software).

The growth of ice releases latent heat to the ocean, and is also a source of salinity, thereby having opposing effects on the surface buoyancy flux (Curry and Webster, 1999). However, α is reduced at cold ocean temperatures (Curry and Webster, 1999) and therefore the effects of salinity changes would be expected to dominate the buoyancy flux. Following Curry and Webster (1999) the ratio of the heat and salinity terms in equation 6.13 can be written as

αL − il (6.14) βcp(s0 − si)

For an initial water salinity, s0, of 34.5 (representative of conditions at the Ronne

Polynya) and a new ice salinity of si = 0.31×s0 = 10.7, this ratio is -0.1. Therefore, if there are no other contributions to the heat or salinity budgets other than ice growth, the salinity term in the buoyancy ﬂux calculation is a factor of ten larger than the heat term, and therefore dominates the ocean surface buoyancy ﬂux calculation. Chapman (1999) for example neglects this heat term entirely.

The surface buoyancy ﬂux over the Ronne Polynya was calculated with fetch from the edge of the ice shelf for each of the four legs using equation 6.13, and is shown on ﬁgure 6.8. The uncertainty in these values due to uncertainty in Qtot is rela- −2 tively small, given that a typical error in Qtot of 10 W m equates to a Bsfc of −9 2 −3 −2 4.8 × 10 m s using equation 6.13. Even the largest error in Qtot of 23 W m −8 2 −3 (F54L2) equates to a Bsfc of 1.1 × 10 m s , which is an order of magnitude smaller than the calculated Bsfc for the polynya.

This figure demonstrates that the Ronne Polynya was rarely contributing a negative buoyancy flux to the ocean at the time of the case studies, as a result of the domination of the heat budget by incoming SW radiation and the consequent lack of ice formation. Although QS and QL decrease with fetch (see chapter 4), there is no discernible trend in the buoyancy flux. This is a result of the increase in albedo with fetch, which correspondingly increases the SWU, counteracting the decrease

138 x 10−7 2 F49L2 F49L2 winter 1.5 F54L1 F54L1 winter F54L2 ) 1 F54L2 winter −3

s F57L1 2 F57L1 winter 0.5

0 139

−0.5

Surface buoyancy flux (m buoyancy flux Surface −1

−1.5 Surface buoyancy flux at the Ronne Polynya for the four level-flight legs, −2 0 20 40 60 80 100 120 Fetch (km) Figure 6.8: using observed data and asnent). calculated for winter months (i.e. without SW compo- in the turbulent fluxes.

It is interesting to examine the Bsfc obtained using the wintertime heat budget, where SW is set to zero as previously, and making similar assumptions that the measured LW balance is representative of winter conditions. This wintertime Bsfc is also shown on ﬁgure 6.8 and is now negative for all four cases, with typical values between −5 × 10−8 and −1.5 × 10−7 m2 s−3. The magnitude of this sinking motion decreases with fetch, as a consequence of the decrease in QS and QL with fetch, and also to the reduction in the LW U term with fetch. Therefore, since the surface energy loss decreases with fetch, so does the ice production and the buoyancy ﬂux.

The magnitude of this buoyancy ﬂux is slightly lower than that given by Chapman

(1999) for similar analysis of the Bsfc at coastal polynyas. For an air temperature of -20 oC and a wind speed of 10 m s−1, comparable to conditions found at the Ronne

−7 2 −3 Polynya, Chapman (1999) found a value for Bsfc of −2.9 × 10 m s . However, the sensible heat transfer coefficient used in the Chapman calculation to obtain the surface sensible heat flux is 2 × 10−3. This is based on the assumption of an open water surface, whereas, as discussed in detail in chapter 4, the calculated heat transfer coefficient for the ice-covered Ronne Polynya was 0.7 × 10−3, and therefore produces a correspondingly lower Bsfc. This serves to emphasise the point discussed in chapter 5 that in order to correctly model the surface heat fluxes, and in this case the surface buoyancy flux, the surface ice conditions, be they open water, thin ice or more consolidated ice, must be taken into account.

140 Chapter 7

Conclusions

7.1 Summary

The surface heat budget of the Ronne Polynya, Antarctica has been investigated using a combination of field observations and modelling. Three flights were conducted over the polynya in February 2007, using a British Antarctic Survey instrumented aircraft. The polynya was observed to be mostly covered with thin ice. Using the surface temperature and albedo data, it was shown that the surface ice cover can be split into two distinct regimes, referred to by Liu et al. (1997) as the “active polynya” and “young ice” regions. The first regime was composed of open water, frazil ice and some thicker new ice, perforated with open water patches, or ‘holes’. Langmuir circulations were observed in the surface distribution pattern of the frazil ice and ice fog was also seen. The second regime was composed of more consolidated ice, also perforated with ‘holes’. Leads and ridging of the ice floes were also observed within this region. The perforated appearance of the ice was a result of freezing of the new ice into floes before it was able to consolidate against the receding edge of the polynya, as a result of the low air temperatures. The heat fluxes observed over the second regime were larger than would be expected over consolidated pack ice. This finding, coupled with the similarity in the values of both the heat transfer and drag coefficients for the two regimes, means the second regime was also considered

141 to be part of the polynya.

Proﬁles through the convective internal boundary layer (CIBL), formed as a result of the temperature discontinuity between the ice shelf and the polynya surface, revealed strong horizontal gradients in potential temperature and humidity, as well as an increase in the CIBL depth, zi, with fetch. Potential temperature was found to be nearly constant with height, whereas humidity decreased. Wind speed and wind direction were fairly steady throughout the CIBL.

High frequency wind speed and temperature data collected in the surface layer over the Ronne Polynya were used to calculate the eddy covariance sensible heat and momentum fluxes over the polynya surface. The sensible heat flux was found to decrease with fetch, owing to a reduction in the surface-air temperature difference. This was primarily a result of variations in the surface ice cover which, as indicated by a decrease in surface temperature and an increase in the shortwave albedo, increased in thickness with fetch. There was also some contribution from warming of the air due to sensible heat flux convergence, both from the surface and via entrainment of relatively warm air from above the CIBL.

The eddy covariance data, as well as mean, or ‘bulk’ measurements of surface and air temperatures and wind speed, were used to calculate the surface sensible heat transfer and drag coeﬃcients. These were converted to equivalent neutral stability

−3 values at 10 m altitude, where CDN10 = (1.1±0.2)×10 and CHN10 = (0.7±0.1)× 10−3. The errors given are the standard deviations. The heat transfer coefficient is significantly lower than has been used in previous studies of heat fluxes over polynyas, which are often assumed to be open water (e.g. Renfrew et al., 2002), and instead is similar to those found over a heterogeneous ice surface in the Arctic marginal ice zone (Schröderet al., 2003). This also indicates these data are not applicable solely to investigations of polynyas. The surface transfer coefficients were not found to be a function of polynya fetch, albedo or surface temperature, despite the increasing thickness of the ice cover. No significant difference between the values of the coefficients for the two ice regimes was found for either the heat transfer or drag coefficients, which suggests the two regimes transfer heat and momentum similarly.

142 This implies that, under similar conditions to those observed, the two ice regimes can be treated in the same way when modelling the surface heat ﬂuxes. In addition, as a result of the ice-covered surface, there was found to be no dependence of the surface roughness lengths on the wind stress, i.e. the Charnock parameter was not valid for these case studies.

Making the assumption that the coeﬃcients for sensible and latent heat transfer were equal, the bulk latent heat ﬂux was also calculated with fetch over the Ronne Polynya. This showed the mean Bowen ratio over the polynya to be 3.8±0.3, where the error is the standard deviation. There was no variation in the Bowen ratio with fetch.

The observations were used as input parameters for a simple model of the CIBL devised by Renfrew and King (2000). The model was designed to estimate the evolution of the surface sensible heat flux, mixed layer potential temperature and CIBL depth with fetch over a wind-driven polynya during a cold-air outbreak, such as was observed at the Ronne Polynya at the time of data collection. It was shown that given appropriate input parameters, including representation of the surface temperature difference between the two regimes where necessary, the model was able to accurately capture variations with fetch in the surface sensible heat flux, potential temperature and CIBL depth, at best to accuracies of ±24.5 W m−2, ±0.17 K and ±10.3 m respectively. For the case study of a cloud-filled CIBL, the modelled potential temperature was found to be lower than the observations, with an RMSE of 0.54 K, which could be a consequence of the neglect of radiative and microphysical processes in the model.

The use of a surface temperature and heat transfer coefficient appropriate to an ice-covered surface were found to be necessary for accurate modelling of the Ronne Polynya case studies, particularly when the surface-air temperature difference was large. This suggests that under similar meteorological conditions to those found during the case studies, where significant ice cover is expected, the heat fluxes over any coastal polynya should therefore be modelled in this way. It is thus important to distinguish between open water, thin ice and more consolidated ice within a

143 polynya for accurate modelling of the convective heat transfer. Specification of accurate surface temperatures and transfer coefficients is crucial, and without in- situ data is potentially a large source of error. Errors in the magnitude of the modelled ocean-atmosphere sensible heat flux will lead to significant errors in the estimation of the effect of polynyas on the surface heat budget, ice formation rates and regional meteorology and oceanography of the high latitudes, and consequently of their effect on the global ocean circulation.

The observational data were also used for simple thermodynamic calculations of potential ice formation rates and the surface buoyancy flux at the Ronne Polynya. It was found that at the time of the case studies there was little new ice being formed, due to the domination of the surface heat budget by incoming shortwave radiation. Therefore at this time there was little contribution by the polynya to the formation of dense water and despite the decrease in the sensible and latent heat fluxes with fetch there was no discernible trend in the buoyancy flux. During the wintertime however, when there is negligible shortwave radiation at these latitudes, even covered with thin ice (which would reduce the surface heat fluxes compared to those over open water) the calculations illustrate that ice production and the associated buoyancy flux at the polynya have the potential to be significant. The contribution of both the ice production rate and buoyancy flux was found to decrease with fetch, being more important for the first regime than for the second, where it levelled off, though still remained at a potentially significant value. It has therefore been shown in this study that, based on simple calculations, the wintertime ice production rate and surface buoyancy flux at a coastal polynya should not be assumed constant with fetch and may also be of importance in the region of consolidated new ice. However, in order to assess this more fully, a detailed study of the seasonal surface heat budget using modelling (the accuracy of which can be improved using the observations) is required.

144 7.2 Discussion and conclusions

Numerous studies of coastal polynyas have been based on the assumption that newly- formed frazil ice within the polynya is swept downwind, where it consolidates against the receding edge of the polynya. The open water surface of the polynya is then once again exposed, fostering large heat losses. Dynamic polynya models based on this idea, for example that of Pease (1987), are simple and easy to implement. However, the ‘real-world’ situation is far from being this simple. It was even noted by Pease (1987) that in reality, as was observed at the Ronne Polynya, at low temperatures the frazil ice quickly consolidates into young ice ﬂoes with holes. Thus, under these conditions, the surface of a polynya is mostly covered with thin ice. In practice, polynyas are therefore often identiﬁed as areas of low sea ice concentration (Morales Maqueda et al., 2004) and a number of studies designate the ‘open-water area’ of a polynya as e.g. sea ice of < 14% (Zwally et al., 1985) or ice of thickness < 0.3 m (Lynch et al., 1997).

However, the presence of thin ice limits the magnitude of the surface turbulent heat losses compared to those over open water. It is therefore vital to take this into account in modelling studies of surface heat transfer over polynyas, where the surface temperature and transfer coeﬃcients required for accurate modelling may well be those appropriate for a heterogeneous ice surface, rather than an open water surface. The assumption of an ice-covered surface also removes the need to include a dependence of the surface roughness lengths on the wind speed, i.e. the Charnock parameter.

It is important to note that the polynya would be expected to be covered with thin ice in this way under conditions of cold air temperatures, which are most likely to occur during the wintertime when accurate calculations of heat ﬂuxes, ice production volume and dense water formation are of greatest importance. In winter, the only extensive open water area may lie within 1 km of the coastline (Tamura et al., 2007). Tamura et al. (2007) and (2008) therefore deﬁne the combined open water and thin ice regions as the coastal polynya, as in this study, and emphasise the importance of

145 including accurate estimates of thin ice thickness in making calculations of surface heat ﬂuxes, ice production and dense water formation.

The distinction between open water and thin ice within the first regime is therefore an important one, which also has implications for problems such as that highlighted by Stossel and Markus (2004) of whether, for satellite ice concentration algorithms, to consider the thin ice of polynyas in the same way as the thicker ice of the second regime or as open water. Owing to the reduction in the modelled sensible heat flux when compared with open water and the similarity of the transfer coefficients to the second regime, this study would suggest that the thin ice should be considered in the same way as the thicker ice of the second regime, at least under conditions where the perforations develop.

In this study of the Ronne Polynya, turbulent heat fluxes over the second regime were found to be significant compared to those which might be found over the consolidated ice pack, as a result of perforations within the ice. However, frazil ice formation rates are predicted to be lower within these perforations than in more extensive areas of open water as a consequence of the reduction in wind-generated turbulence (Smith et al., 1990). Nevertheless, the magnitude of the turbulent heat fluxes means that investigation of ice production and hence dense water formation within this regime may be of importance, particularly the growth of congelation ice on the underside of the consolidated ice region, a factor taken into account by Haarpaintner et al. (2001) when estimating total ice growth and brine rejection in an Arctic polynya.

In an investigation of ice production and associated dense water formation at coastal polynyas in the Antarctic, Tamura et al. (2008) found only the relatively narrow ﬁrst regime of the Ronne Polynya to be of importance, and thus not responsible for the production of a large amount of ice or dense water. However, they did not include estimates of ice production rates in regions where the ice thickness exceeded 0.2 m, as the production rates were assumed to be much smaller than for the thinner ice. The observations at the Ronne Polynya suggest this may not always be the case, as heat ﬂuxes over the second, thicker regime of the Ronne Polynya were found to

146 be larger than might be expected, as a result of the perforations in the ice. This indicates it may be important to include ice concentration, as well as ice thickness, in the deﬁnition of a polynya area and illustrates the importance of in-situ observations to the investigation of these processes.

7.3 Further work

The novel results of this study have pointed to a number of potential avenues of further research, which are beyond the scope of this work but will be discussed in this section.

Renfrew et al. (2002) developed a climatology of the surface heat budget and ice production at the Ronne Polynya using the Renfrew and King (2000) CIBL model, forced with air temperature and wind speed data from reanalyses and an automatic weather station situated on the Ronne Ice Shelf. The polynya area was speciﬁed from satellite imagery, using the PSSM (polynya signature simulation method) algorithm (Markus and Burns, 1995). However, this algorithm was not able to estimate surface ice concentration or to specify ice thickness. In addition, in the Renfrew et al. (2002) study, the temperature of the polynya surface was held constant, at the freezing point of water and transfer coeﬃcients appropriate for open water were used.

Given appropriate input data, the simple CIBL model has been shown to be capable of accurate calculation of surface sensible heat fluxes and their variation with fetch across a polynya. Therefore, if coupled with an accurate method of specify- ing polynya size and the ice concentration field, where the surface temperature can also be determined, the seasonal surface heat budget at the Ronne Polynya, and by extension the ice production and dense water formation rates, can be accurately determined. This could potentially be achieved using either high-resolution satellite data or a prognostic sea ice model. Although it has been shown in this study that the use of a mean surface temperature for each regime is sufficient to potentially

147 achieve results accurate to ±24.5 W m−2 for the modelled surface sensible heat ﬂux, high resolution information on sea ice concentration is necessary for detection of the polynya area and to distinguish between regions of entirely open water and those which are composed of thin ice or ice perforated with holes, in order that the appropriate transfer coeﬃcients can be used.

Recently-developed high-resolution satellite ice-detection algorithms (e.g. AMSR-E) would be ideal for such studies but have the disadvantage of being short datasets and are therefore unsuitable for producing long timeseries of the surface energy budget. A long timeseries is useful owing to the large interannual variability in polynya size, and would allow investigation of any changes in the frequency or size of polynyas and hence in the ice production and dense water formation rates. However, provided data of suﬃcient accuracy could be obtained with which to force it, the use of a sea ice model would allow this to be investigated.

Walkington and Willmott (2006) coupled the Renfrew and King (2000) CIBL model to a coastal polynya sea ice model capable of varying the surface frazil ice concentration. Their study illustrated the feedbacks which take place between the polynya and the atmosphere, for example the decrease in frazil ice production with fetch due to warming of the atmosphere, which affects the width of the polynya. How- ever, it was assumed that the heat flux in the consolidated ice region was a small fraction of the heat flux in the ice-free water, and hence that ice production in the ice-covered region was 100 times less than in the ice-free region. This study of the Ronne Polynya has shown that ice production within the consolidated second regime is potentially much larger than this. In addition, the heat transfer coefficient used in the Walkington and Willmott study was 2×10−3, which is larger than the 0.7×10−3 calculated using the Ronne Polynya observations. The sea surface temperature was also held constant at -1.8 oC, which, because of the variations in the surface ice concentration, is a simplification. It would be interesting to use the Walkington and Willmott (2006) model formulation but to take into account the findings from this study of the Ronne Polynya. The coupled model could then be used to determine the seasonal surface energy budget at the Ronne Polynya and thus the contribution

148 from both regimes to ice production and the surface buoyancy ﬂux. This could also be applied to the study of other coastal polynyas.

The surface heat budget, ice formation and buoyancy flux calculations proposed above can be extended to include estimates of the volume and salinity of dense water produced at coastal polynyas. This could involve either using the results of the calculations as parameters in models of the regional ocean circulation and transport or coupling the models together. In addition, although they have been ignored for simplicity in this study owing to their secondary importance, contributions to the salinity budget from the melting of blowing snow and precipitation into areas of open water could be taken into account for detailed analysis. The contributions from melting under ice shelves and calving of icebergs could also be investigated. The contribution to the surface heat budget from radiative processes including those from convective clouds, plumes and ice fog could also be included in these investigations. The effect on the shortwave balance due to the albedo effects of fog would be interesting to investigate, given that the fog appears over surface areas with lower albedo (open water or very thin ice patches) than the rest of the ice cover. In addition, the contribution of tidal forcing to the ice cover at polynyas could also be investigated.

In conclusion, in order to accurately determine the eﬀect of coastal polynyas on the regional climate, mass balance of sea ice and accompanying dense water formation rates, future research must include accurate quantiﬁcation of the seasonal surface energy budget and ice production rate. In this way, the impact of coastal polynyas on the regional meteorology and oceanography of the high latitudes and on the global ocean circulation can be determined.

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