A parameterization of ice shelf ocean interaction for climate models

Transcription

1 Ocean Modelling 5 (2003) A parameterization of ice shelf ocean interaction for climate models A. Beckmann a, *, H. Goosse b a Alfred Wegener Institute for Polar and Marine Research, Am Handelshafen 12, 2757 Bremerhaven, Germany b Institut d Astronomie et de Geophysique G. Lema^ıtre, Universite catholique de Louvain, Louvain-la-Neuve, Belgium Abstract Model results from a regional model (BRIOS) of the Southern Ocean that includes ice shelf cavities and the interaction between ocean and ice shelves are used to derive a simple parameterization for ice shelf melting and the corresponding fresh water flux in large-scale ocean climate models. The parameterization assumes that the heat loss and fresh water gain due to the ice shelves are proportional to the difference in freezing temperature at the ice shelf edge base and the oceanic temperature on the shelf/slope area of the adjacent ocean as well as an effective area of interaction. This area is proportional to the along-shelf width of ice shelf and an effective cross-shelf distance, which turns out to be rather uniform (5 15 km) for a variety of different ice shelves. The proposed parameterization is easy to implement and valid for a wide range of circumstances. An application of the proposed scheme in a global ice ocean model (CLIO) supports our hypothesis that it can be used successfully and improves both the ocean and sea ice component of the model. This parameterization should also be used in models of the climate system that include a coupling between an ice sheet and an oceanic component. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Ice shelf melting; Fresh water forcing; Parameterization; Climate models; Southern Ocean 1. Introduction Fresh water fluxes play an important role for the oceanic water mass transformation in high latitudes (e.g., Foster and Carmack, 1976; Foldvik et al., 1985; Carmack, 2000). In addition to the net atmospheric P E fluxes, ice shelf melting contributes significantly to the fresh water balance in * Corresponding author. Tel.: ; fax: address: beckmann@awi-bremerhaven.de (A. Beckmann) /03/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S (02)

2 158 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) the shelf areas around Antarctica (Jacobs et al., 1992; Timmermann et al., 2001). Sub-ice shelf melting typically reaches a few tens of centimeters per year up to a few meters per year, and thus represents a major factor in the mass balance of ice sheets (see, e.g., Huybrechts, 2002). The total melt water input at the Antarctic coast has been estimated to about 25 msv (Jacobs et al., 1996). This is equivalent to a freshwater flux of 0.5 m/a over the circumpolar continental shelf area (the edge being defined by the 500 m isobath), exceeding P E by a factor of at least 2. Also, the injection of this fresh water occurs at the base of the ice shelf edge, i.e., m depth, and has therefore a different impact on the stability of the coastal ocean than the surface forcing. The sensitivity of the coupled sea ice ocean system in the Southern Ocean to changes in fresh water input has been shown by St ossel et al. (1998), Goosse and Fichefet (1999), Beckmann et al. (1999) and Marsland and Wolff (2001), and it seems desirable to include these interaction processes in today s ocean climate models, as well as ice sheet models. Today s ocean climate models (for a recent overview, see Griffies et al., 2000) do not include the sub-ice shelf cavities around the Antarctic continent and Greenland, because it would require substantial modification of the model code (see, e.g., Beckmann et al., 1999; Holland and Jenkins, 2001) and extension of the model domain beyond 75 S (to about 82 S in the Weddell Sea and 86 S in the Ross Sea). In addition, with horizontal resolution of a few degrees the proper representation of ice shelves seems hardly possible, even for the larger areas, the Filchner Ronne ice shelf (FRIS) in the Weddell Sea and the Ross ice shelf (RIS), and the northern part of Larsen ice shelf (LIS) and Amery ice shelf (AIS). The majority of the comparatively small shelves at ice coasts (in the eastern and northeastern Weddell Sea, the Amundsen and Bellingshausen Seas and along Adelie Land) however are clearly sub-gridscale. The interaction between ocean and ice shelves, however, is necessary for long-term sea ice ocean climate studies as well as ice sheet modelling and for the development of Earth System models (coupling atmosphere, ocean, sea ice, ice sheets, carbon cycle,...), both for an estimation of the melting of ice shelves and the impact on water mass modification. In the past, part of the effects have been implicitly included by nudging to surface salinity (e.g., DeMiranda et al., 1999), or by prescribing additional fresh water fluxes corresponding to estimates of present-day shelf melting (e.g., Goosse and Fichefet, 2001). However, this approach is only valid if the system is assumed to have no evolution through time. It cannot be used to study climate variability, climate change or in paleoclimate studies. Consequently, a more adequate parameterization is necessary. 2. Sub-ice shelf circulation and melting This section gives a brief overview of the salient features of ice shelf ocean interaction. The interaction between ice sheets and ocean is a complex phenomenon, which has been first studied in two-dimensional (x z) configurations by Hellmer and Olbers (1989) and Hellmer et al. (1998). The pressure dependence of the melting pnt of sea water leads to melting at the grounding line of the ice shelves, rising of the freshened and cooled water and hence an overturning circulation: the ice pump (see Fig. 1). Part of the waters leave the cavity as ice shelf water and mix with high salinity shelf water (HSSW) to become one of the source components of Antarctic bottom water (AABW). This interaction can be described successfully by several sys-

3 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) Fig. 1. Schematic picture of the sub-ice shelf overturning motion, induced by melting and re-freezing at the ice shelf base. tems of equations, a recent overview is given by Holland and Jenkins (1999). The modelled FRIS cavity overturning component is about 0.5 Sv., the time scale for flushing the cavity is about a decade, in general accordance with recent tracer estimates. Three-dimensional models have been developed for the large ice shelves around Antarctica: FRIS (Grosfeld et al., 1997; Gerdes et al., 1999) and AIS (Williams et al., 2001). They show strong topographic control on the horizontal circulation and confirm the observationally derived melting rates within the cavities. One of the problems is always to determine precisely the areas of in- and outflow. To date there is only one OGCM that includes the ice shelves and a realistic representation of the adjacent ocean and sea ice: the BRIOS model family (Beckmann et al., 1999; Timmermann et al., 2002a). In the stand-alone ocean ice shelf model BRIOS-1 (Beckmann et al., 1999) a system of three equations is used to compute the heat and fresh water fluxes for the major ice shelf areas in the Weddell Sea, following Hellmer et al. (1998). The coupled sea ice ocean ice shelf model BRIOS-2 uses the formulation of the sea ice module, adapted to a pressure dependent freezing pnt (see Timmermann et al., 2002a). Both ice shelf models assume that melting is exactly balanced by the glacier flow, i.e., the shape of the glacier does not change due to the melting. Consequently, the calving of icebergs is excluded from the model. Both models use a circumpolar grid with six ice shelves. The two major Antarctic ice shelves, Filchner Ronne and Ross, are included with as much detail as possible (Johnson and Smith, 1997). All other ice shelves (Larsen, Brunt, Riiser Larsen, Fimbul, Ekstr om and Amery) are included in a cruder way, due to the lack of detailed bathymetric and ice thickness data, coarse grid resolution in the relevant sector or relatively minor importance. Their thickness is assumed to be constant at 200 m. In our analysis, Fimbul, Ekstr om, Riiser Larsen and Brunt (see Beckmann et al., 1999) are treated as two separate areas called eastern Weddell ice shelf (EWIS) and northeastern Weddell ice shelf (NEWIS). In both models the expected melting patterns and amplitudes are reproduced in sufficient agreement with observations and theoretical estimates. This is especially true for FRIS, where we find an area of re-freezing in the center of the cavity (see Fig. 2). In general, the model computes

4 160 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) Fig. 2. Melting beneath Weddell Sea ice shelf cavities, from a 40-year integration driven by NCEP reanalysis atmospheric forcing (Beckmann and Timmermann, 2001), featuring large melting rates for the EWIS. Note the freezing area in the center of the Filchner Ronne cavity. Grounding line melting is generally underestimated due to the specification of a minimum water depth of 200 m. large melting at the ice shelf edge and increased values at the grounding line. 1 Interestingly, the largest melting rates are found in the smaller ice shelf areas (EWIS, NEWIS), compared to the larger ice shelf areas (FRIS, RIS, and AIS). Integral values of net melting (Fig. 3) lead us to discriminate two kinds of ice shelf cavities (Fig. 4): Type 1: FRIS, RIS; which are comparatively large and relatively far from the continental shelf break; Type 2: LIS, Riiser Larsen and Brunt ice shelves (EWIS), Fimbul, Ekstr om ice shelves (NE- WIS); which are comparatively small and relatively close to the continental shelf break. We find that the Type 2 ice shelves have generally increased oceanic heat flux at the ice shelf base due to their exposed location and the proximity of the relatively warm coastal current. Consequently, the smaller ice shelves are at least of equal importance for the large-scale stratification and water mass modification in the Antarctic marginal seas. Beckmann et al. (1999) mention that omission of the ice shelf melting will cause too warm HSSW, a weaker horizontal circulation and an increased probability for open ocean convection in the Weddell Sea. Interannual variability of the FRIS cavity circulation was investigated by Timmermann et al. (2002b), who found both cyclonic and anticyclonic circulation patterns as a result of a different stratification outside the cavity; interestingly, the annual-mean net melting rate remains largely 1 Note that tidal mixing plays a dominant role in these areas.

5 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) Fig. 3. Net melting beneath the major ice shelf cavities around Antarctica. Forty-year average values from the BRIOS NCEP model (Beckmann and Timmermann, 2001). Fig. 4. Schematic representation of ice shelf types around the Antarctic continent. The oval represents the coastal current at or near the shelf break, flowing into the page. unchanged. This suggests that the net fresh water input by ice shelf melting is rather robust to year to year changes of the shelf stratification and circulation. In general, the models results display a reasonable agreement with observations. Of course the BRIOS model can still not represent all details and may also exhibit some systematic errors (as illustrated by the differences between two- and three-equation formulations for the ice shelf ocean interaction, and climatological versus daily forcing), but the robustness of the results gives some confidence that they can be used to develop a first order parameterization of this process.

6 162 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) Parameterization of net melting In this section we investigate the possibility of parameterizing the net effects of the complex three-dimensional flow field and the water mass modification inside the ice shelf cavities. Such a parameterization will greatly help to improve both the Antarctic ice sheet models and ice ocean models of the Southern Ocean Approach The net heat flux between ocean and ice shelf Q net Z ¼ q w c pw c T T ocean ðx; yþ da Q net T f j zice ðx;yþ can be computed as ð1þ where T ocean ðx; yþ is the ocean temperature, T f j zice ðx;yþ is the freezing pnt temperature at the ice shelf base z ice and A the area of the ice shelf in contact with the ocean. Other symbols have their standard meaning: c pw ¼ 4000 J (kg C) 1, q w ¼ 1000 kg m 3 and c T ¼ 10 4 ms 1. The freezing pnt temperature at given depth (z) and salinity (S) is computed from T f ¼ 0:0939 C 0:057 CS þ 7: Cm 1 z ð2þ Our hypothesis is that the net heat flux into an ice shelf cavity can be computed as Q net ¼ q w c pw c T T ocean T f j edge z A eff ð3þ ice where Tocean is a suitably chosen oceanic temperature, and zedge ice is the depth of the ice shelf at the edge. The area A eff is an effective area for melting, as we expect the basal melting to be reduced by partial recirculation of the cavity water masses and the resulting cooling of the shelf water masses. The first step in this approach is to determine an oceanic temperature that could be used in any ocean model to compute ice shelf melting and then, in parallel, to determine the effective area for melting, which hopefully turns out to be a universal quantity. We will use various BRIOS model results to assess the suitability of such a relationship. The total net melting rate (in m 3 s 1 ) can then be diagnosed from om net ¼ Qnet ð4þ ot q i L i where L ¼ J kg 1 is the latent heat of fusion and q i ¼ 920 kg m 3 is the density of the ice shelf. The corresponding fresh water flux and the heat flux can then be applied as lateral boundary conditions to the ocean model without cavities Chce of T ocean Due to their coarse resolution and to the use of geopotential coordinates, ocean climate models tend to have no shelves or artificially wide shelves. In addition, the exchanges between shelf and deep ocean are generally not well simulated in those models. Therefore, we cannot assume a

7 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) realistic representation of the shelf water masses around Antarctica in these models. It is thus not easy to determine the temperature in BRIOS that would correspond the more closely to the temperature of the grid box adjacent to the continent in coarse resolution models. Here, we have decided to use in BRIOS the shelf break temperature, which is defined as the vertical mean below 200 m in m depth range along the slope of the continental margin. This temperature represents the coastal current with its relatively warm water masses; in case of the large ice shelf areas (FRIS, RIS) the temperature is taken from locations km north of the ice shelf edge, for all other ice shelves, it is the temperature in the grid box next to the ice edge Determination of A Using these data, the BRIOS model results have been analyzed for the net heat flux, the corresponding melting and fresh water fluxes, as well as the shelf break temperature and the resulting effective area for melting. This area is thought to be the product of the along-shelf width W, taken from the model, and the cross-shelf length L of the ice shelf. We find (see Table 1) that L amounts to a few km, much smaller than the actual ice shelf length. It is interesting to note that for the NCEP experiment with a two-equation formulation of the ice shelf ocean interaction the two largest (type 1) ice shelves FRIS and RIS have a effective length of about 11 km, while the smaller (type 2) ice shelves group around 5 km. This difference does not exist for the ECMWF experiment with its more complicated three-equation formulation; in this case all the effective lengths are about 5 km. The purpose of this study is not to evaluate different parameterizations for ocean ice shelf exchange but rather to show that the simple parameterization proposed in the previous section is robust under various conditions and with different configurations. We find relatively small and uniform values of the diagnosed L which confirms that even if a significant portion of the melting occurs at or near the grounding line, the net effect seems to be determined (and can be parameterized) by shelf ice edge processes. Physically, this suggests that the size and geometric form of an ice shelf, as well as the details of the horizontal circulation are only secondary in determining the net heat loss and fresh water input into the adjacent open ocean basin, at least at the first order. Table 1 Compilation of quantities used to determine the melting parameterization from two BRIOS simulations with different atmospheric forcing data sets and ice shelf ocean interaction schemes Ice shelf NCEP ECMWF Acronym Width (m) Q net (10 11 W) Melting (m/a) _m net (msv) T ocean ( C) L (m) Q net (10 11 W) Melting (m/a) _m net (msv) LIS ) ) FRIS ) ) EWIS ) ) NEWIS ) ) AIS ) RIS ) ) T ocean ( C) L (m)

8 164 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) Application of the parameterization in CLIO In this section we present results from a climate model where the above parameterization has been implemented. We focus on the differences between a reference experiment with 30 cm/a ice shelf related surface fresh water input on the Antarctic continental shelf and the parameterization as outlined in the preceeding section. The resulting changes in sea ice, mixed layer depth and zonally averaged fields are shown Model description The global ice ocean model used in this study (called CLIO for coupled large-scale ice ocean) is identical to Goosse et al. (2001). CLIO is made up of a primitive-equation, free-surface ocean general circulation model coupled to a dynamic thermodynamic sea ice model with viscousplastic rheology (Goosse et al., 2000). The parameterization of vertical mixing in the ocean is based on a simplified version of the Mellor and Yamada (1982) level-2.5 turbulence-closure scheme. The ocean component includes mixing along isopycnal surfaces and an eddy-induced advection term to represent the effects of quasi-horizontal meso-scale eddies (Gent and McWilliams, 1990) as well as the parameterization of Campin and Goosse (1999) designed to represent the effect of dense water flow down topographic features. The horizontal resolution is 3 in latitude and longitude, and there are 20 unevenly spaced vertical levels in the ocean. The model is driven from heat freshwater and momentum fluxes derived from various climatologies (Goosse et al., 2001). There is a 30 cm per year fresh water flux imposed on the Antarctic continental shelf in order to crudely take into account the melting from ice shelves. This model simulates reasonably well the ice extent and ice thickness in both hemispheres as well as the large-scale oceanic circulation (e.g. Goosse and Fichefet, 1999). It has been successfully used to simulate, for instance, the influence of ice ocean interactions of the global ocean circulation (Goosse and Fichefet, 1999) or the mechanism that leads to the formation of the spring polynya in the Ross Sea (Fichefet and Goosse, 1999). Nevertheless some shortcomings remain: the model tends to overestimate open ocean convection in the Southern Ocean, as do a large number of coarse-resolution oceanic models (Goosse and Fichefet, 2001). Furthermore, the bottom waters are too fresh and too cold, particularly in the Southern Ocean. Part of these problems may be related to the fresh water input from the Antarctic shelves. We will investigate this by applying the above parameterization. The parameterization proposed in Section 3 has been introduced in CLIO in the following way. Close to the ice shelves represented in BRIOS (Fig. 3), additional heat (Q net ) and fresh water fluxes ( _m net ) have been included in the CLIO grid pnt adjacent to the continent. This corresponds to the southern boundary of the model for all the ice shelves, except for LIS for which the boundary is in a North South direction in CLIO. The fluxes are applied to the ocean at the same locations, over the depth range m, that represents here the vertical extension over which ocean and sub-ice shelf cavities can interact. We use the following equation: Q net ¼ q w c pw c T T ocean T f j z edge ice L dl T ocean is the averaged temperature between 200 and 600 m. T f is the freezing pnt temperature at 200 m, i.e., at the base of the ice shelf. L is the characteristic length scale defined in Section 3.3 ð5þ

9 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) Table 2 Heat and fresh water fluxes between the ice shelf and the ocean simulated by CLIO for three values of L Ice shelf CLIO Acronym Width (m) L ¼ 5km L ¼ 10 km L ¼ 15 km Q net (10 11 W) _m net (msv) Q net (10 11 W) _m net (msv) Q net (10 11 W) _m net (msv) LIS FRIS EWIS NEWIS AIS RIS and dl is the distance along the shelf in CLIO. The fresh water flux is then deduced from an equation identical to Eq. (4). When this parameterization is used in the model, we suppress the constant fresh water flux representing the ice shelf melting in the standard case Diagnosed melting rates Three 100-year-long simulations have been performed using values of L equal to 5, 10 and 15 km, which are in the limits deduced from BRIOS. The results a summarized in Table 2. We find that within this range of values, it is possible to have melting in agreement with the ones of BRIOS for LIS, NEWIS, AIS and RIS but not for FRIS and EWIS. The total melting in the three experiments is not strictly proportional to the value of L. Any increase in L implies a larger heat flux from the ocean to the ice shelf (Eq. (5)). However, this implies a cooling of the ocean and a subsequent reduction of the ocean ice shelf heat flux (Eq. (5)). If the renewal of the oceanic water is quick, this negative feedback is relatively weak, as illustrated in CLIO for NEWIS. On the other hand, if the exchanges between the continental shelf and the open ocean are slow, the negative feedback is strong and increasing L has a smaller influence on the ocean ice shelf heat flux (FRIS and EWIS). The too weak exchanges between the continental shelf and open ocean as well as the small inflow of warm water close to the shelf in the Southern Weddell Sea in CLIO explains the underestimation of the melting rate for FRIS and EWIS using reasonable values of L. One solution to overcome this problem is to use as a temperature in (Eq. (5)) the mean over two grid pnts instead of one (averaging temperature over 600 km instead of 300 km). For a large part of FRIS, this 600-km distance still corresponds to the continental shelf in CLIO. Using this mean over 600 km and a value of L equal to 10 km, the ocean ice shelf heat flux reaches 1: W (fresh water flux of 3.79 msv) which is close to the values deduced from BRIOS Large-scale impacts of the parameterization In order to evaluate the impact of the parameterization on the characteristics of the water masses formed close to Antarctica, the simulation using L equal to 10 km has been continued for 1000 years. This version includes the modifications introduced close to FRIS as proposed above.

10 166 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) Fig. 5. Difference in ice thickness in September (m) between the two experiments with and without the parameterization (ICS STD). The results of this experiment (hereafter referred to as ICS for ice shelf) are compared to an experiment in which this parameterization is not included (hereafter referred to as STD). It must be recalled that in STD a 30 cm/a fresh water flux is applied on the continental shelf. Because the ice shelf ocean exchanges tend to cool the water column in ICS, the ice thickness is generally higher in this experiment. The difference is particularly strong in the Weddell Sea where it reaches 0.5 m close to FRIS (Fig. 5), a region where the model tends to underestimate the ice thickness. The annual-mean sea ice volume increases from 8: km 3 in STD to 9: km 3 in ICS. The changes of ice extent are much smaller: from 10: km 2 in annual mean in STD to 10: km 2 in ICS. The amount of fresh water input from the ice shelf to the ocean is roughly the same in the two experiments (see above) but the distribution, both vertically and horizontally is quite different. In particular, the ice shelf melting is quite strong in ICS for EWIS (Table 2). EWIS is located close to a region where deep open ocean convection occurs in STD (Fig. 6a), in disagreement with observations (Fahrbach et al., 1994). The large fresh water input due to the ice shelf melting in ICS is able to strongly reduce the vertical mixing there (Fig. 6). The vertical mixing is also weaker off the AIS. This decrease in the vertical exchanges amplifies the cooling at the surface and the increase in ice thickness (Fig. 5). Besides, the depth reached by convection in ICS is higher close to the continent at about 150 E, an area where no ice shelf is included in CLIO. On the continental shelf, the parameterization induces a cooling and a freshening of the water masses (Fig. 7). Off the continental shelf, at high southern latitudes, the surface also cools and becomes fresher in ICS. Furthermore, this fresh signal is incorporated in the Antarctic intermediate water (Fig. 7b). At depth, the less vigorous mixing with surface waters induces an increase of

11 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) Fig. 6. Maximum depth reached by convection (m) in the CLIO model: (a) in STD and (b) in ICS. Contour levels are drawn at 200, 500, 1000, and 2000 m. temperature and salinity. This largely overwhelms the cold and fresh signal coming form the Antarctic continental shelf and reduces the classical bias of the model that has too fresh and cold water at depth close to Antarctica. The reduction of convection implies also a decrease in the meridional overturning cell close to Antarctica from 13 Sv in STD to 9 Sv in ICS. However, the export of AABW out of the Southern Ocean (as measured by the maximum of the overturning streamfunction below 300 m at 30 S) is equal in the two experiments with a value of 12 Sv. The formation of AABW by open ocean convection is reduced. This constant export shows that this is compensated by other mechanisms of AABW production such as the ones linked with the densitydriven downsloping flows (Goosse et al., 2001).

12 168 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) Fig. 7. (a) Annual mean zonally averaged temperature. Contour interval is 0.1 K. (b) Difference in zonally averaged salinity between experiments ICS and STD (ICS STD). Contour interval is 0.01 psu between )0.01 and 0.01 and 0.02 psu outside this interval. 5. Conclusions We have derived a first order parameterization of the interaction between ice shelves and the adjacent ocean. It turns out that ice shelf melting can be reasonably well estimated knowing the oceanic temperature at the ice shelf edge as well as a characteristic length scale in the direction perpendicular to the edge. This length scale ranges typically from 5 to 15 km. It is very similar for all the ice shelves regardless of their size and much smaller than their actual cross-shelf extent. In a second step, this parameterization has been applied to a large scale coupled ice ocean model (CLIO). The improvements related to the inclusion of this parameterization are caused by the combined effects of (a) regional differences in ice shelf forcing (with the main fresh water input located in the Atlantic Sector of the Southern Ocean), (b) an additional cooling of the ocean, and (c) the sub-surface fresh water input and heat loss. As a result, a number of typical model deficiencies are reduced; these include the too fresh and cold water at depth close to Antarctica, and unrealistic areas of open ocean convection in the climatological mean. Despite its simplicity, the parameterization appears valid, at least at the first order, for different ice shelves and using different forcing fields (ECMWF, NCEP/NCAR) covering different periods. Although it is impossible to demonstrate this pnt, we expect thus the parameterization to work under a large variety of circumstances, including global warming scenarios and paleo simulations; it may also be used to ice sheet modelling studies.

13 A. Beckmann, H. Goosse / Ocean Modelling 5 (2003) Of course our simple parameterization can be improved in various ways and such improvements should be performed if a fine representation of the processes is needed. More detailed knowledge of individual ice shelves may be used to specify L and the depth of fresh water input differently for each ice shelf. The width of the continental shelf could also be taken into account. Furthermore, the transfer coefficient c T may be prescribed as a function of (tidally generated) turbulent velocities at the ice shelf edge. We also note that our parameterization can also be applied for ice shelves that cover only part of the model grid cell. In that case, L has to be chosen as a fraction of the standard value. However, we consider this a fine-tuning. If necessary, it has to be done in accordance with the (horizontal and vertical) resolution of the ocean model. In conclusion, we expect this simple parameterization to improve the circulation and water mass distribution of the Southern Ocean in the current generation of ocean climate models and that it could provide a reasonable way of producing self-adjusting fluxes in the coupling of ocean and ice sheet models. Acknowledgements Helpful discussions with members of the BRIOS team and two anonymous reviewers are gratefully acknowledged. HG was supported by the Second Multiannual Scientific Support Plan for a Sustainable Development Policy (Belgian State, Prime Minister s Services, Federal Office for Scientific, Technical, and Cultural Affairs, Contracts EV/10/7D and EV/10/9A). References Beckmann, A., Timmermann, R., Circumpolar influences on the Weddell Sea: indication of an Antarctic circumpolar coastal wave. Journal of Climate 14, Beckmann, A., Hellmer, H.H., Timmermann, R., A numerical model of the Weddell Sea: large scale circulation and water mass distribution. Journal of Geophysical Research 104, Campin, J.M., Goosse, H., Parameterization of density driven downsloping flow for a coarse resolution ocean model in z-coordinate. Tellus 51A, Carmack, E.C., The Arctic Ocean freshwater budget. In: The freshwater budget of the Arctic Ocean. In: Lewis, E.L. (Ed.), NATO Science Series, vol. 2/70. Kluwer Academic Publishers, Dordrecht, pp DeMiranda, A., Barnier, B., Dewar, W.K., Mode waters and subduction rates in a high-resolution South Atlantic simulation. Journal of Marine Research 57, Fahrbach, E., Peterson, R.G., Rohardt, G., Schlosser, P., Bayer, R., Suppression of bottom water formation in the southeastern Weddell Sea. Deep-Sea Research 41, Fichefet, T., Goosse, H., A numerical investigation of the spring Ross Sea polynya. Geophysical Research Letters 26, Foldvik, A., Kvinge, T., Tørresen, T., Bottom currents near the continental shelf break in the Weddell Sea. In: Oceanology of the Antarctic Continental Shelf. In: Jacobs, S. (Ed.), Antarctic Research Series, vol. 43. AGU, Washington, DC, pp Foster, T.D., Carmack, E.C., Frontal zone mixing and Antarctic bottom water formation in the Southern Weddell Sea. Deep-Sea Research 23, Gent, P.R., McWilliams, J., Isopycnal mixing in ocean circulation models. Journal of Physical Oceanography 20, Gerdes, R., Determann, J., Grosfeld, K., Ocean circulation beneath Filchner Ronne ice shelf from threedimensional model results. Journal of Geophysical Research 104,

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