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    Fig. 1.

    Model domain (the dots refer to the relaxation zone) and the geographic regions mentioned in this paper

  • View in gallery
    Fig. 2.

    (a) Surface mass balance ;obmm water equivalent (w.e.) yr−1;cb compilation based on in situ and satellite observations (Vaughan et al. 1999). (b) Mean calculated surface mass balance for the period 1980–84. A Laplacian filter (XX + 0.1∇2X) is used to smooth the calculated fields X

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    Fig. 3.

    A schematic representation of the method used to calculate the retreat of the sea ice. The variable λE denotes the latitude of the sea ice edge and λT refers to the latitude of the Tfreeze + ΔT isotherm, where Tfreeze is the freezing temperature of the sea water (271.46 K) and ΔT is the temperature perturbation

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    Fig. 4.

    The mean sea ice cover during the period 1980–84 for CTL (solid line) and for TEMP (dashed line). The area south of the 50% contour line is covered with sea ice for more than half of the integration period

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    Fig. 5.

    (a) 5-yr mean increase in precipitation (PTEMPPCTL). (b) 5-yr mean deviation of PTEMPPCTL from the spatially averaged relative change times PCTL (shaded areas) together with the difference in geopotential at the 700-hPa level between TEMP and CTL (contour lines). Contours are plotted every 20 m2 s−2 and the thick contour line is the 240 m2 s−2 isoline. A Laplacian smoothing filter (XX + 0.1∇2X) is used

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    Fig. 6.

    (a) Schematic representation of the moisture budget of VSSI. VSSI is the model atmosphere volume above the sea, the sea ice, and the ice shelves (SSI). (b) Annual accumulated CTL transport of moisture (km3 yr−1) during 1980–84 across the boundaries enclosing VSSI. (c) Difference between TEMP and CTL in transport of moisture across the boundaries of VSSI. A positive value defines the direction into VSSI. Transport by evaporation from SSI (Aes) and advection from outside the model domain (Aos) are positive terms, whereas transport by precipitation on SSI (Aps) and advection to the Antarctic continent (Asl) are negative terms in the moisture balance of VSSI. Asl is calculated from the precipitation and sublimation integrated over the grounded ice and Aos is calculated from the moisture balance of VSSI; Aos = Aps + AslAes

  • View in gallery
    Fig. 7.

    (a) Vertical distribution of the poleward horizontal moisture transport across the grounding line, (b) the transport by the mean flow across the grounding line, and (c) the transport by the mean flow keeping the CTL specific humidity profile to calculate the transport in TEMP. The solid lines indicate the transport in CTL and the dashed lines indicate the transport in TEMP. See text for further explanation

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    Fig. 8.

    Difference in (a) temperature and (b) specific humidity profiles between TEMP and CTL during the period 1980–84 averaged over all land ice grid points (solid lines) and all sea and sea ice grid points (dashed lines), excluding the lateral boundary grid points. The land ice grid points are a combination of grounded ice points and ice shelf points

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    Fig. 9.

    (a) Temperature sensitivity of the surface mass balance 〈ΔB〉/ΔT simulated with RACMO (solid line), estimated by f(Ti, ΔT) (dotted line) and by f(Ti, ΔTi) (dashed line). The function f is given in Eq. (6). (b) Temperature sensitivity of the moisture fluxes Aos, Asl, Aes, and Aps making up the moisture balance of VSSI. (c) Relative temperature sensitivity of Aos calculated with RACMO (solid line) and calculated with a simplified two-layer model using Eq. (7) (dashed line). (d) Temperature sensitivity of the temperature at the sea, sea ice, and ice shelves surface (ΔTSSIT). (e) Fraction of the source terms of moisture into SSI (Aes + Aos) that falls as precipitation on SSI. (f) Mean precipitation 〈P〉 (solid line), precipitation minus sublimation 〈PE〉 (dotted line), precipitation minus sublimation minus rain 〈PER〉 (dashed line), and precipitation minus sublimation minus rain minus melt 〈PERM〉 (dashed-dotted line) over the grounded ice as a function of the temperature forcing

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    Fig. 10.

    12-month centered running mean of 〈B〉 for the period 1980–84 for CTL (solid lines) and TEMP (dashed lines)

  • View in gallery
    Fig. 11.

    The relative rms deviation in mean surface mass balance over the grounded Antarctic ice of taking only τ yr of the 5-yr integration

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    Fig. A1. (a) Time series of the snow temperature at 5.7-m depth for the integration with a temperature forcing of ΔT = +10 K. The solid line indicates the integration with the original initialization and the dotted line indicates the integration with the reinitialized snow temperature profile. (b) Mean surface temperature 〈Ts〉 and (c) surface mass balance 〈B〉 for the years 1980 (solid line) and 1981 (dotted line) with original initialization and for the year 1980 (dashed line) with the reinitialized snow temperature profile as a function of the temperature forcing

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    Fig. B1. Representation of the two-layer model that is used to study advection into the model domain

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Temperature Sensitivity of the Antarctic Surface Mass Balance in a Regional Atmospheric Climate Model

Nicole P. M. van LipzigRoyal Netherlands Meteorological Institute (KNMI), de Bilt, Netherlands

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Erik van MeijgaardRoyal Netherlands Meteorological Institute (KNMI), de Bilt, Netherlands

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Johannes OerlemansInstitute for Marine and Atmospheric Research Utrecht (IMAU), Utrecht, Netherlands

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Abstract

The sensitivity of the surface mass balance of the Antarctic ice sheet to a change in temperature and a change in the sea ice extent is studied with a regional atmospheric climate model (RACMO) using a horizontal grid spacing of 55 km. The model is driven at its lateral boundaries by the reanalyses from the European Centre for Medium-Range Weather Forecasts. Sea ice extent and sea surface temperature are prescribed from observations. A control integration is performed for the 5-yr period 1980–84. In a 5-yr sensitivity run, the model is forced by a 2-K increase in temperature at the sea surface and at the lateral boundaries of the model domain, and a reduction in the sea ice extent. The relative humidity at the lateral boundaries is kept constant.

The calculated surface mass balance of the grounded Antarctic ice is found to increase by 30% due to the 2-K warming and the retreat of the sea ice. This value is two to three times as large as previous estimates, which were based on simplified atmospheric models and on statistical relations between the surface temperature and the surface mass balance.

Additional sensitivity runs show that applying the forcing throughout the atmosphere in the lateral boundary zone has a more significant effect than applying the forcing at the sea surface, especially for the interior of the ice sheet. If only an increase in the sea surface temperature or a retreat of the sea ice is prescribed, the increase in temperature and specific humidity is restricted to the lowest 2 km of the atmosphere above the ocean. Sensitivity runs with forcings in the range of −5 to +10 K indicate that the commonly used assumption stating that the surface mass balance responds in proportion to the change in continental saturation specific humidity at the inversion height is an oversimplification.

Corresponding author address: Dr. Nicole P. M. van Lipzig, British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, United Kingdom. Email: nvl@bas.ac.uk

Abstract

The sensitivity of the surface mass balance of the Antarctic ice sheet to a change in temperature and a change in the sea ice extent is studied with a regional atmospheric climate model (RACMO) using a horizontal grid spacing of 55 km. The model is driven at its lateral boundaries by the reanalyses from the European Centre for Medium-Range Weather Forecasts. Sea ice extent and sea surface temperature are prescribed from observations. A control integration is performed for the 5-yr period 1980–84. In a 5-yr sensitivity run, the model is forced by a 2-K increase in temperature at the sea surface and at the lateral boundaries of the model domain, and a reduction in the sea ice extent. The relative humidity at the lateral boundaries is kept constant.

The calculated surface mass balance of the grounded Antarctic ice is found to increase by 30% due to the 2-K warming and the retreat of the sea ice. This value is two to three times as large as previous estimates, which were based on simplified atmospheric models and on statistical relations between the surface temperature and the surface mass balance.

Additional sensitivity runs show that applying the forcing throughout the atmosphere in the lateral boundary zone has a more significant effect than applying the forcing at the sea surface, especially for the interior of the ice sheet. If only an increase in the sea surface temperature or a retreat of the sea ice is prescribed, the increase in temperature and specific humidity is restricted to the lowest 2 km of the atmosphere above the ocean. Sensitivity runs with forcings in the range of −5 to +10 K indicate that the commonly used assumption stating that the surface mass balance responds in proportion to the change in continental saturation specific humidity at the inversion height is an oversimplification.

Corresponding author address: Dr. Nicole P. M. van Lipzig, British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, United Kingdom. Email: nvl@bas.ac.uk

1. Introduction

The amount of ice stored on the Antarctic continent is of relevance for global sea level; the global mean sea level equivalent of the Antarctic ice volume is about 65 m. Only the changes in the amount of ice resting on the bedrock (grounded ice) contribute to sea level change. The ice shelves (e.g., Filchner-Ronne Ice Shelf and Ross Ice Shelf; places referred to in the text are shown in Fig. 1) are floating so changes in their mass do not alter global sea level. The mass of the grounded ice sheet is controlled by the mass balance, which is defined as the net input at the surface (surface mass balance) minus the ice flow off the continent to the ice shelves. On the century timescale, the response of the ice dynamics to variations in temperature and precipitation can be neglected (Huybrechts and de Wolde 1999; Warner and Budd 1998; O'Farrell et al. 1997); the relation between the mass of the grounded ice sheet and temperature is then controlled by the relation between surface mass balance and temperature. The objective of this paper is to study the sensitivity of the surface mass balance of the grounded Antarctic ice sheet to changes in the free-atmosphere temperature, the sea surface temperature, and the sea ice extent.

The surface mass balance is determined by the net atmospheric moisture transport to the continent. For this reason, an atmospheric model can be regarded as a suitable tool to study the relation between the Antarctic surface mass balance and temperature. Various types of models have been used previously; regression analyses between surface mass balance and surface temperature (Muszynski and Birchfield 1985; Giovinetto et al. 1990; Fortuin and Oerlemans 1990), simplified atmospheric models (e.g., Fortuin and Oerlemans 1992), global climate models (GCMs, e.g. Ohmura et al. 1996; Ye and Mather 1997), and limited area models (LAMs).

For detailed surface mass balance studies, it is most appropriate to use a model that explicitly resolves the storm processes because these processes dominate the formation of precipitation (Bromwich 1995), that is, GCMs or LAMs. Recently, integrations with GCMs have been performed in which realistic climate scenarios are calculated (e.g., Ohmura et al. 1996; Wild and Ohmura 2000; Thompson and Pollard 1997). Without doubt, these integrations are necessary to study how the atmospheric moisture transport in high latitudes responds to a possible future climate change. However, there are also some drawbacks in applying this type of GCM studies. (i) Due to the many interactions and feedbacks in the climate system, it is difficult to understand the mechanisms that are responsible for the complex response of the hydrological cycle in the Antarctic region to the forcing that is applied. (ii) Large uncertainties are involved in establishing climate scenarios that are used to force the models. (iii) Finescale aspects of precipitation are underrepresented in GCMs. (iv) The GCM integrations are not directly constrained by observations. Therefore, parallel to climate scenario integrations with GCMs, studies with well-controlled forcings are desired to understand how the atmospheric moisture transport responds to a change in temperature.

In this study, we have used an atmospheric LAM that is driven from the lateral boundaries by a host model. By using this approach, the temperature forcing in a sensitivity integration can be prescribed directly at the lateral boundaries of the model domain and at the sea surface. The nature of the temperature forcing is well controlled and one can focus on the direct response of the surface mass balance to the applied forcing. This is essentially different from GCM studies in which the temperature change is indirectly imposed by a climate forcing (e.g., a change in CO2 or aerosol concentration), making the interpretation far more complicated.

Another advantage of using a LAM is that high horizontal resolution can be achieved at reasonable computational cost. An alternative way to obtain high resolution at a reasonable cost is the use of a stretched-grid GCM (Krinner and Genthon 1997). For surface mass balance studies, it is important to resolve the orography in sufficient detail because precipitation is strongly affected by the orography. We have adopted a horizontal grid spacing of 55 km, which is finer than the grid spacing used in most of the large-scale models in climate sensitivity studies for Antarctica.

The LAM is driven from the lateral boundaries by European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analyses (ERA-15; Gibson et al. 1997). This “real weather forcing” drives the synoptic systems that are important for precipitation formation. The sea surface temperature and the sea ice extent are prescribed from observations. In this way, the model climate is constrained by observations. Model output is in close agreement with measurements from several Antarctic stations (van Lipzig et al. 1998, 1999).

In the approach that we use, the temperature forcing in a sensitivity integration is prescribed at the boundaries of the LAM. The dynamics of the atmospheric flow within the model domain (e.g., strength of the katabatic circulation) can adjust to this forcing. The circulation in the lateral boundary zone is prescribed by ERA-15, hence changes in the large-scale dynamics in response to a temperature forcing are not taken into account. As an alternative, the regional atmospheric model could have been driven from the lateral boundaries by fields from a GCM. The advantage of using GCM fields is that the effect of changes in the circulation as a response to climatic perturbations (e.g., an increase in atmospheric CO2) can be studied. On the other hand, an obvious advantage of using ERA-15 is that the occurrence of synoptic systems that are important for the precipitation distribution are correctly represented. Although it is widely accepted that changes in the dynamics of the atmospheric flow affect the precipitation processes, there exists no verification that changes inferred from climate scenario studies are correct. Therefore, results from a regional model, driven by fields that are based on measurements and thereby not taking into account changes in the large-scale dynamics of the flow, complement GCM studies to gain insight into the response of the atmospheric moisture transport in the Antarctic region to a temperature forcing.

There exists a positive feedback between temperature and sea ice extent. Ingram et al. (1989) have studied the effect of sea ice changes in an integration with doubled atmospheric CO2. In a 2 × CO2 run with a fixed sea ice extent, the global effect on the surface air temperature amounted to 81% of the temperature sensitivity found in a 2 × CO2 run allowing for the feedback to the sea ice extent. Their study and many other studies (e.g., Bintanja and Oerlemans 1995; Rind et al. 1995) indicate that the temperature sensitivity of the sea ice extent is important and should be taken into account in a realistic study. Therefore, we prescribe a change in sea ice extent in the sensitivity integration accompanying the temperature change.

A control integration and a sensitivity integration are performed for a period of 5 yr to study the effect of a +2 K change in the temperature at the lateral boundary of the LAM, a +2 K change in the sea surface temperature, and a retreat of the sea ice. The effect of the separate forcings is analyzed in detail. In addition, integrations are performed for a −5, −2, +2, +5, and +10 K temperature forcing.

2. Description of model and integrations

a. Control integration

We use a regional atmospheric climate model (RACMO; Christensen et al. 1996; Christensen and van Meijgaard 1992) covering the Antarctic continent and a large part of the Southern Ocean by a horizontal mesh counting 122 × 130 points. The shape of the domain is rectangular, with the corners at 48°S and the short axis along the 10°E meridian (Fig. 1). The horizontal grid spacing is 55 km and there are 20 levels in the vertical, with the lowest model layers centered around 7, 35, 130, and 330 m. The formulation of the dynamical processes is adopted from the High-Resolution Limited Area Model (Gustafsson 1993). The parameterizations of the physical processes (surface fluxes and vertical diffusion, gravity wave drag, cumulus convection, radiation, and stratiform clouds) are taken from the ECHAM4 model (Roeckner et al. 1996). Some adjustments are made in order to improve representation of the physical processes in Antarctica (van Lipzig et al. 1999; van Lipzig 1999).

The ECHAM4 parameterization of stratiform clouds uses tendency equations for temperature, specific humidity, and specific liquid water (Sundqvist 1978). The model treats specific liquid water as a prognostic variable, but the distinction between liquid water and ice is diagnosed from temperature. The closure relations are (i) humidity transport rate is used to moisten a preexisting cloud and (ii) the instantaneous evaporation/condensation in the cloud-free part of a grid box is equal to the liquid water transport into this grid box. The cloud cover is diagnosed from the model relative humidity and a prescribed vertical profile of relative humidity acting as a threshold for cloud formation. Boundary layer mixing employs the formulation of a moist Richardson number.

To calculate the surface fluxes over land, the snow temperatures are determined using a five-layer model and imposing a zero heat flux boundary condition at the bottom of the 10-m-deep snow column. The temperature tendency is calculated from the surface energy budget and from the heat diffusion equation, in which diffusivity and heat capacity of snow are used. When the surface is at the melting point, the residue of the surface energy balance is available for melting. Over sea, the sea ice surface temperature is calculated from the atmospheric–ice surface energy budget and the conductive heat flux through the ice. The latter is parameterized linearly in the difference between the sea ice surface temperature and the freezing point of sea water. Higher-order effects like the influence of snow on the sea ice, melting and freezing at the base of the sea ice, and changes in the sea ice thickness are not taken into account. A model grid box is either ice free or uniformly covered with sea ice of 1-m thickness. The sea ice cover is prescribed from observations.

A 5-yr control integration (CTL) is performed for the period 1980–84. At the lateral boundaries of the model domain (dots in Fig. 1), the model prognostic variables are merged with relaxation fields employing a procedure described by Davies (1976). The field that is used in the calculations is a linear combination of the field supplied by the host model and the prognostically calculated field. The weighting depends on the distance to the outer boundary. We use ERA-15 data as relaxation fields for the atmospheric temperature, the zonal and meridional components of the wind, the specific humidity, and the surface pressure. The fields are updated every 6 h.

Sea surface temperature (SST) and sea ice extent are also taken from the ERA-15 archive. Weekly data from the National Centers for Environmental Prediction (Reynolds and Smith 1994) have been used to prescribe the sea surface temperature for the period from November 1981 to the end of the ERA-15 period. The dataset is based on satellite and in situ measurements. For the period prior to November 1981, the monthly mean values of Parker et al. (1995) have been used. The sea ice mask is based on the Scanning Multichannel Microwave Radiometer and the Special Sensor Microwave Imager satellite measurements (Nomura 1995).

Figure 2 shows a comparison between the 5-yr mean calculated distribution of the surface mass balance, and the most up-to-date compilation of in situ and satellite observations (Vaughan et al. 1999). The climatology is compiled from about 1800 in situ measurements representing different time periods. The large-scale features of the compilation are reproduced by the model. The surface mass balance B (bar indicates time averaging) is largest on the west coast of the Antarctic Peninsula and on the coast of Wilkes Land. The ice shelves (especially the Ross Ice Shelf) are relatively dry. The high plateau of East Antarctica is also very dry with values for B smaller than 50 mm yr−1. Note that all the accumulation values in this paper are given in water equivalents. In mountainous areas (Transantarctic Mountains, Dronning Maud Land, and near the Amery Ice Shelf) the surface mass balance is underestimated. A more detailed evaluation shows that surface pressure, temperature, and near-surface wind are also well represented in the model (van Lipzig 1999).

b. Sensitivity integrations

A sensitivity run TEMP is performed for the same 5-yr period as the CTL run. In TEMP, the SST and the relaxation temperature profile at lateral boundaries are raised by ΔT = 2 K together with a retreat of the sea ice. We prescribe a uniform increase in temperature throughout the atmosphere to keep the forcing as simple as possible. Note that the effect of the imposed temperature increase with height is discussed in section 4b. The relaxation specific humidity is raised in such way that the relative humidity remains unchanged. The dynamics of the flow in the relaxation zone is unchanged.

The large range in model-inferred sensitivity of the sea surface temperature and sea ice extent to climate change (Ingram et al. 1989; Rind et al. 1995) justifies a simple forcing at the sea surface. The sea surface is warmed by ΔT at all grid boxes that are free of sea ice. To fit this warming, a modified sea ice mask is constructed in the following manner. To calculate the change in sea ice extent as a function of longitude and time, it is assumed that the meridional SST gradient remains unchanged as the SST increases. A schematic view of the procedure that has been used is given in Fig. 3. The CTL latitude of the sea ice edge (λE) and the CTL latitude of the (Tfreeze + ΔT)-isotherm (λT) are constructed as a function of longitude and time, where Tfreeze is the freezing temperature of the sea water (271.46 K). The functions λE and λT are smoothed in time and space. The TEMP sea ice edge is constructed by shifting the CTL sea ice edge by Δλ(=λTλE) toward the south. The TEMP Tfreeze + ΔT isotherm (λT) is identical to the CTL sea ice edge (λE). In areas where the sea ice has disappeared, the SST is assumed to vary linearly with latitude; from Tfreeze at λE to Tfreeze + ΔT at λT. Isolated areas of open water that are present in the control sea ice mask remain open.

The annual mean sea ice extent during the period 1980–84 for CTL and TEMP is shown in Fig. 4. The average reduction in sea ice cover for the 2-K temperature rise is 50%. In September, the sea ice extent is reduced by 35%. This reduction is comparable to the global mean reduction simulated in a coupled GCM that was used to study the sensitivity of the September equilibrium climate to a CO2 doubling (Thompson and Pollard 1995). They found an increase in global mean September surface temperature of 2.1 K together with a 43% reduction in sea ice.

In addition to the TEMP run, sensitivity integrations are performed for the year 1980 to study the effect of the separate forcings, namely, an increase in relaxation temperature, an increase in the SST, and a partial or total removal of the sea ice. Moreover, four integrations are performed for the years 1980 and 1981, to study the sensitivity of the surface mass balance to temperature forcings in the range of −5 to 10 K. These 2-yr integrations use values for ΔT of −5, −2, +5, and +10 K, where ΔT refers to the temperature forcing compared to the CTL integration. The forcing at the lateral boundaries and at the sea surface and the procedure to calculate the sea ice retreat as a function of ΔT are identical to that described above.

c. Initialization

In CTL, the atmospheric temperature, specific humidity, and wind profiles and the surface pressure are initialized by ERA-15 fields of 1 January 1980. The snow temperature is initialized using information from a database with climatological surface temperatures and from a 1-yr integration with RACMO (van Lipzig 1999). After initialization, the evolution of the model prognostic variables is calculated for the 5-yr period. In the interior of the model domain, no data are assimilated during the integration.

Initialization of the model prognostic variables in TEMP is consistent with the forcing at the boundaries. The atmospheric temperature is initialized by adding ΔT = 2 K to the CTL profiles, keeping the relative humidity unchanged. The snow temperatures are initialized by adding ΔT to the CTL snow temperatures. While the spin-up time in the atmosphere is short (several hours), the snow temperatures may respond more slowly; the deepest snow layer is centered at a depth of 5.7 m where the e−1 attenuation time to a stepwise increase in the surface temperature is 3.7 yr. Due to possible feedback mechanisms in the system, the annual mean snow temperature difference between TEMP and CTL could be different from the forcing ΔT. In that case, an integration of 5 yr might be too short because the snow temperature profile needs to reach equilibrium with the model physics. However, 1-yr integrations made before had already indicated that the effect of the snow temperature initialization on the calculated surface temperature and atmospheric variables is very small (see appendix A).

3. Results

a. A temperature forcing of 2 K

1) Surface mass balance

In TEMP, the mean surface mass balance 〈B〉 of the grounded Antarctic ice sheet (the bar indicates averaging in time and the brackets indicate averaging in space) has increased by 47 mm yr−1, which is 30% of 〈BCTL. The precipitation has increased by 54 mm yr−1 and the sublimation by 7 mm yr−1. The spatial distribution of the change in mean precipitation (ΔP = PTEMPPCTL) is similar to P itself; there is a large increase near the coast, especially in Ellsworth Land, Marie Byrd Land, Wilkes Land, and Enderby Land and a much smaller increase in the interior (Fig. 5a).

The sensitivity of P is studied in more detail by introducing
i1520-0442-15-19-2758-e1
which is the deviation of ΔP at a given location from the spatially averaged relative change times PCTL (Fig. 5b). The term ΔP is highly positive in Enderby Land, in Wilkes Land, and in the area of the Transantarctic Mountains, and highly negative on the Antarctic Peninsula, on the Filchner-Ronne Ice Shelf, and in the western part of Dronning Maud Land.

Further, ΔP is closely related to changes in the flow at the 700-hPa level, where the moisture advection toward the continent is largest. For example, a local maximum difference in 700-hPa geopotential (ΔΦ700) between TEMP and CTL is present at 60°E (Fig. 5b). In this area, there is a maximum sea ice retreat, resulting in heating and moistening of the atmosphere. From the hydrostatic equation it follows that this local atmospheric heating and moistening correspond to the local maximum in ΔΦ700. At the west side of this maximum in ΔΦ700 (Enderby Land), the difference in the wind vector at the 700-hPa level between TEMP and CTL is directed onshore, causing a highly positive ΔP. For the local maximum in ΔΦ700 at 60°W and the minimum at 170°E, the relation between ΔP and ΔΦ700 is clear, but in these regions, ΔΦ700 is not related to a maximum in sea ice retreat.

2) Atmospheric moisture budget

The total moisture transport to the ice sheet is the sum of the transport through the lateral model boundaries and sublimation and evaporation from sea and sea ice minus precipitation over sea and sea ice. The change in atmospheric storage of water in vapor, liquid, or solid form on a 5-yr timescale is negligible. Figure 6b shows the CTL 5-yr mean moisture balance of VSSI [the model atmosphere above the sea surface, the sea ice, and the ice shelves (SSI) excluding the lateral relaxation zone of the model domain]. Most of the incoming moisture leaves VSSI as precipitation on SSI and only 12% is transported to the grounded ice. In TEMP, both the moisture transport through the lateral model boundaries and the sublimation and evaporation from SSI are considerably enhanced (Fig. 6c). The sum of sublimation and evaporation (we will refer to this sum as evaporation from SSI in the following sections) is 83 mm yr−1 (33%) larger than in CTL. However, only 18% of the total additional moisture input into the model domain, due to enhanced evaporation and an increase in lateral transport, is transported toward the grounded Antarctic ice. The remaining part falls as precipitation on SSI.

3) Atmospheric moisture transport across the grounding line

The poleward atmospheric moisture transport across the grounding line (dividing line between the grounded ice and the ice shelves) is related to 〈B〉. The budget equation expressing the surface mass balance as a function of transport and storage terms is given by (Peixoto and Oort 1983)
i1520-0442-15-19-2758-e2
where E is the sublimation and evaporation, ρL is the density of liquid water, W is the vertically integrated specific humidity (kg m−2), and Q is the vertically integrated horizontal moisture flux vector defined as
i1520-0442-15-19-2758-e3
where q is the specific humidity, u is the horizontal wind vector, g is the acceleration due to gravity, p is the pressure, and ps is the surface pressure. Note that we divide by ρL in order to obtain water equivalents. For annual mean budgets the second term on the right-hand side of Eq. (2) is negligible (Peixoto and Oort 1983). The horizontal transport of atmospheric moisture (−〈∇·Q〉) across the boundary (l) of a closed area (e.g., the grounding line of the Antarctic ice sheet) can be estimated from vertical profiles of q and u with the use of Gauss's theorem:
i1520-0442-15-19-2758-e4
where A is the surface of the enclosed area and n the unit vector directed outward, normal to the boundary of this region.

Model output, available every 6 h, is used to calculate −〈∇·Q〉. There is a difference between the calculated −〈∇·Q〉 and 〈PE〉 because only the transport that is resolved by the model is included in −〈∇·Q〉. Transport due to horizontal diffusion, and due to eddies with timescales smaller than 6 h, are not included. For an arbitrary area the transport carried by the resolved flow is close to 100%. However, the resolved moisture transport across the grounding line (at the base of the steep slopes) turns out to be 83% of the total moisture transport. This value is much larger than the value that was found by Connolley and King (1996) in the U.K. Met Office GCM, with a grid spacing of approximately 270 km. They found that only 30% of the net accumulation in the sector between 2.4°W and 110.5°E is carried by resolved-scale transport.

The vertical distribution of the horizontal moisture transport is presented in Fig. 7. Both the transport onto the ice sheet above 850 hPa and the transport away from the ice sheet in the katabatic layer below 850 hPa have increased in TEMP. Figure 7b shows that this is also true for the transport by the mean flow. To calculate the transport by the mean flow, q and u in Eq. (4) are substituted by q and u. The increase in transport by the mean flow can arise from an increase in specific humidity or an increase in wind speed. Gallée (1996) used a mesoscale atmospheric model to study the effect of areas of open water (leads) in the southwestern Ross Sea sector. He found that the katabatic outstream, boundary layer fronts, and mesocyclone activity were all enhanced when leads in the sea ice were prescribed. In RACMO, the wind speed also increases in regions that became ice free in the TEMP run. To study whether this plays a role in the moisture transport across the grounding line, the variable q in Eq. (4) is substituted by qCTL, which is the time-averaged specific humidity in the CTL run (Fig. 7c). The change in the mean wind component normal to the grounding line turns out to be negligible, indicating that the increase in moisture transport by the mean flow almost entirely results from an increase in specific humidity.

4) Meteorological variables

So far, we have focused on the temperature sensitivity of the moisture budget. In this section, the effect of the temperature forcing on the vertical profiles of temperature and humidity and on the surface energy balance is considered. The increase in temperature in the lowest 5 km of the atmosphere is larger than the applied forcing of +2 K (Fig. 8a). This is also true for the mean land ice surface temperature, which is 3.4 K higher in TEMP than in CTL. Apparently, the positive feedback mechanisms in the system are larger than the negative feedback mechanisms. The most important positive feedback mechanism is the effect of water vapor. The greenhouse effect is stronger in TEMP, because both the specific humidity (Fig. 8b) and the specific liquid water in the atmosphere are larger. The mean vertically integrated specific humidity over land ice increases from 1.4 to 1.8 kg m−2 and the mean vertically integrated specific liquid water increases from 22 × 10−3 to 29 × 10−3 kg m−2 leading to a larger value for the emissivity in TEMP. As a result of this and due to heating of the atmosphere, the downward longwave radiation at the land ice surface changes from 144 W m−2 in CTL to 156 W m−2 in TEMP. This is almost entirely compensated by an increase in upward longwave radiation corresponding to a warming of the surface. The energy balance over land ice is hardly changed by the external temperature forcing; the mean differences over land ice between TEMP and CTL in net radiative flux, turbulent heat fluxes, and heat flux into the snow are all three smaller than 0.8 W m−2.

This is not the case for the various components of the surface energy balance over the combined open sea–sea ice region; increases of the latent (7 W m−2 upward) and sensible (3 W m−2 upward) turbulent heat exchanges are compensated by an increase of the net radiative flux (5 W m−2 downward) and an increase of the heat flux from below the surface (5 W m−2 upward). The contribution to these changes is primarily coming from the area that is covered with ice in CTL, but free of ice in TEMP. Due to the enhancement of latent heat exchange at the surface (evaporation), the specific humidity increases above the combined open sea and sea ice, with a maximum near the surface. There is a higher sensitivity of the surface temperature in the sea–sea ice region than over land ice. This is mainly caused by a high sensitivity of the surface temperature in the region where the sea ice retreats; the temperature difference between the sea ice surface in the CTL run and the sea surface at the corresponding grid point in the TEMP run after removing the sea ice is often larger than 2 K. In the area in Fig. 4 between the solid line (old sea ice edge) and dashed line (new sea ice edge), the mean surface temperature increases with 4.7 K. Although the sea surface temperature is prescribed, this large sensitivity is realistic since the ice albedo feedback amplifies the temperature sensitivity in the region where sea ice is removed (e.g., Ingram et al. 1989).

b. Relative importance of the separate forcings

For the year 1980, additional integrations are performed to study the sensitivity of 〈B〉 to each individual forcing, namely,

  • +2 K increase of the relaxation temperature keeping the relative humidity fixed;

  • +2 K warming of the sea that is free of ice; and

  • total or partial removal of the sea ice.

In the integrations where all the sea ice is removed, the areas where sea ice is removed are replaced by open water at the freezing point. The procedure to calculate the partial sea ice retreat is identical to that described above.

The results of the sensitivity runs (Table 1) indicate that the effect on 〈B〉 of a forcing is larger when this forcing is not restricted to the surface but applied throughout the whole atmospheric column at the boundaries. The yearly mean surface mass balance over the grounded land ice increases by 23 mm yr−1 when the relaxation temperature is increased by 2 K. This increase in 〈B〉 is two to three times the annual standard deviation of 〈B〉 calculated from a 14-yr integration (σ = 9 mm yr−1). When the forcing is applied at the sea surface only, most of the enhanced evaporation from SSI falls as rain and snow before it reaches the continent. Furthermore, transport of moisture from outside the model domain decreases due to an increased specific humidity inside the model domain and a corresponding smaller horizontal gradient in specific humidity. The effect of removing all the sea ice, which is an extreme case, is comparable to the effect of a 2-K increase in relaxation temperature. Only 60% of this effect is obtained by increasing the SST by 2 K.

A warming of both the relaxation zone and the sea surface keeping the sea ice extent fixed results in an increase in 〈B〉 of 28 mm yr−1. A subsequent retreat of the sea ice that corresponds to this +2 K temperature forcing adds a further 8 mm yr−1. So the retreat of the sea ice has only a modest impact on 〈B〉.

To study how far the additional moisture intrudes onto the ice sheet, we consider the area in the interior of the ice sheet with a surface elevation larger than 2.5 km. In the interior, the forcings at the sea surface are hardly noticeable. The change in B due to forcings at the sea surface is of the same order of magnitude as the standard deviation of B in this area calculated from a 14-yr integration (σ = 3 mm yr−1).

For the remaining meteorological variables it is also found that the effect of applying the forcing at the sea surface is restricted to the lowest 1–2 km of the atmosphere over the sea and the sea ice. In contrast, the effect of an increase in temperature and specific humidity in the model relaxation zone appears to penetrate throughout the entire atmosphere over land ice, sea ice, and sea. In conclusion, a forcing that is applied throughout the whole vertical atmospheric column at the boundaries has a larger effect on the atmospheric state on the continent than a forcing that is applied at the sea surface.

c. Temperature forcings in the range of −5 to +10 K

When runoff of melt water and rainwater are not considered, a first-order estimate of the relation between the increase in atmospheric temperature (T) and the increase in the surface mass balance can be made by assuming that the temperature dependency of B is linear with the saturation vapor pressure (esat) (Robin 1977). Using the Clausius–Clapeyron relation we get
i1520-0442-15-19-2758-e5
where L is the latent heat of sublimation or evaporation and Rυ is the gas constant for water vapor.
From a reference state with surface mass balance BCTL and temperature TC, the temperature sensitivity of the surface mass balance f(TC, ΔTC) can be calculated as a function of the temperature increase ΔTC, using the Taylor expansion of the term in the exponential:
i1520-0442-15-19-2758-e6
The question is which values to insert for TC and for ΔTC. Robin (1977) suggested that the temperature at the inversion (Ti) should be used; using the CTL value for Ti, which is a function of location, and the temperature forcing (ΔT) for ΔTC, we find that the temperature sensitivity of the surface mass balance increases with ΔT (dotted line in Fig. 9a).

The previous method is refined by using the temperature increase at the inversion level (ΔTi) instead of ΔT. Due to the water vapor feedback, the value for ΔTi is 1.2–1.3 times the temperature forcing ΔT, resulting in a higher temperature sensitivity of the surface mass balance (dashed line in Fig. 9a).

RACMO output from the five sensitivity integrations is used to calculate the temperature sensitivity of 〈B〉 for a temperature forcing ΔT relative to the CTL integration. Figure 9a shows that RACMO output differs from f(Ti, ΔTi), especially for large values of the forcing. To understand this behavior, we study the temperature sensitivity of the moisture balance terms into VSSI (Fig. 9b). (For a schematic representation of the moisture balance of VSSI, see Fig. 6a.) Note that the relative temperature sensitivity of the surface mass balance is identical to the relative temperature sensitivity of the moisture advection toward the grounded ice Asl (dotted line in Fig. 9b).

We use a two-layer model, in which q is linear with esat, to understand the temperature dependency of the moisture advection into the model domain Aos (solid line in Fig. 9b). In appendix B an equation is derived for the relative temperature dependency of Aos in this simplified model,
i1520-0442-15-19-2758-e7
where αm0 is the fraction of the total moisture advection that is transported by the mean circulation. In RACMO, αm0 is found to be 0.17 for the control run. For TC we use 270.4 K, which is the mean CTL temperature at the lateral model boundary at the 945-hPa level, where the moisture advection into the model domain is largest. The relative humidity, the circulation, the horizontal gradient in temperature, and the eddy diffusivity, which is used to calculate the horizontal eddy transport term as a function of the mean gradient in specific humidity, are not dependent on the temperature forcing ΔT in the simplified model. Variations in these variables are responsible for the small differences between the RACMO output and the simplified model output shown in Fig. 9c. Evidently, the relative temperature sensitivity of Aos can be largely explained by the simplified model, which means that the variations in esat determine the temperature dependency of Aos and that potential feedbacks through relative humidity, wind, eddy diffusivity, and horizontal gradient in temperature are of minor importance.
The temperature sensitivity of the transport by evaporation from SSI (Aes; irregularly dotted line in Fig. 9b) follows the temperature sensitivity of the mean surface temperature at SSI (Fig. 9d). Changes in wind speed and stability of the atmosphere are of minor importance. To analyze the effect of the temperature forcings on TSSI, we have divided SSI into three subregions: a region covered with sea ice in both integrations, a transition zone covered with sea ice in the colder integration and with open water in the warmer integration, and a region with open water in both integrations. The fractional areas of the subregions compared to the total area of SSI are αi, Δαi, and (1 − αi − Δαi), respectively. However, it turns out to be quite difficult to interpret the various contributions by comparing the five sensitivity integrations with the CTL integration, because the area of the transition zone strongly depends on the size of the temperature forcing. This effect is reduced by introducing the central difference operator D (with units of K−1), which represents the temperature sensitivity around a given temperature forcing ΔT. Hence, DTSSI is defined as the difference in TSSI between two integrations with adjacent temperature forcings divided by the difference in the corresponding temperature forcings ΔT of these integrations,
i1520-0442-15-19-2758-e8
where TTZ is the surface temperature in the transition zone, and Tsea ice is the surface temperature in the region covered with sea ice in both integrations considered. Note that the temperature sensitivity of the sea surface temperature in the model is one by construction. The second term on the right hand side of Eq. (8) (CTZ) denotes the contribution of the surface temperature change in the transition zone to DTSSI, and the third term on the right-hand side of Eq. (8) (Csea ice) denotes the contribution of the surface temperature change in the sea ice region to DTSSI.

Five values for the terms in Eq. (8) are calculated using output from the six integrations that are available. We find that CTZ dominates the temperature dependency of DTSSI. This positive term, which increases with the change in sea ice extent, is largest for perturbations around ΔT = −1 K. The area of the transition zone is largest for perturbations around ΔT = −1 K, since for warmer climates most of the SSI region is already ice free, and for colder climates the sea ice extends out of the model domain. The term Csea ice can be neglected except for ΔT = −3.5 K, at which Csea ice = −0.14 and CTZ = 0.37. The term Csea ice is negative due to the temperature dependency of the conductive heat flux through the interface of the sea ice and the underlying ocean. This heat flux is a linear function of the temperature difference between the sea ice and the freezing point of sea water and decreases with temperature. In summary, the temperature sensitivity of TSSI is primarily determined by the change in sea ice extent. The term Csea ice becomes important in the cold regime (ΔT = −3.5 K) due to an increase in heat supply from below the sea ice with decreasing temperature.

It is even more complex to explain the temperature sensitivity of the transport by precipitation on SSI Aps (dashed line in Fig. 9b). The part of the moisture input to VSSI (Aes + Aos) that is converted to rain or snow above SSI (Aps) is shown in Fig. 9e. The ratio decreases monotonically with increasing forcing. Likely, the inversion strength and the distance from the continent at which the evaporation takes place play an important role. A possible explanation is that the inversion strength decreases with ΔT. When the inversion is weaker, moisture from enhanced evaporation is transported to higher atmospheric levels, where it is more effectively transported to the continent. This mechanism leads to a decrease in Aps/Aes with ΔT, which might explain the temperature dependency of the precipitation on SSI.

From these considerations it can be concluded that the temperature sensitivity of 〈B〉 has a complex dependency on the temperature sensitivity of Aps, Aes, and Aos, and that the assumption that B is linearly dependent on esatT) is not valid for this complex system. The largest deviation (30%) from this commonly used simple assumption is found for a temperature forcing of +2 K.

Now we include melt and rain in our analysis. Melt is a negative term in the surface mass balance and the water either refreezes at some depth (internal accumulation) or runs off. Rainwater freezing upon impact with the surface provides a positive contribution to the surface mass balance. The remaining part of the rainwater either freezes internally or runs off. The total mass balance of the ice sheet is not affected by a change in melt or rain that freezes at some depth. Only the fraction that runs off is important. A refreezing model is needed to calculate this fraction. However, we can use the sensitivity runs to study two extreme cases: (i) all the liquid water freezes (already discussed) and (ii) all the liquid water runs off. Note that not only changes in runoff but also changes in the flow of ice across the grounding line probably become important for large temperature changes (larger than about 5 K).

Figure 9f shows the components contributing to the surface mass balance as a function of the temperature forcing when there is no internal accumulation and all the liquid water runs off. Melt and rain become important at ΔT = 5 K. At ΔT = 10 K, 56% of the 〈PE〉 leaves the ice sheet as liquid water. The temperature sensitivity of the surface mass balance becomes negative. However, even for ΔT = 10 K and with complete runoff, the surface mass balance is still larger that the surface mass balance in the control run. It is clear that only at very large temperature forcings would the increase in melt exceed the increase in snowfall.

4. Discussion

a. The effect of the length of the integration on the calculated sensitivity of the surface mass balance

Are 5-yr or even 2-yr time series long enough to study the effect of a forcing on the mean surface mass balance over the grounded ice? Figure 10 shows the 12-month centered running mean 〈B〉. The surface mass balance of CTL correlates reasonably well with TEMP (correlation coefficient is 0.78). The largest difference between the 12-month running mean 〈ΔB〉 and the 5-yr mean 〈ΔB〉 occurs during the year 1980 (〈ΔB1980 = 36 mm yr−1 and 〈ΔB〉 = 47 mm yr−1). The results indicate that a simulation of 5 yr should be sufficient to calculate the typical change in 〈B〉. In addition, the difference in accumulation between the 5-yr period considered and a 14-yr period (1980–93) is only 2% of the 14-yr mean accumulation, which gives confidence that the general conclusions are independent of the period considered.

We now examine the effect on the calculated value of 〈ΔB〉 of taking only a fraction of the 5-yr time series. For this, we derive the root-mean-square (rms) difference between a τ-yr running mean and the 5-yr mean surface mass balance. The mean rms deviation (δrms) from the 5-yr mean of Nm time series is given by
i1520-0442-15-19-2758-e9
where Nm = 1 + 12(tmaxτ), 〈ΔBi indicates the monthly mean difference in the surface mass balance between TEMP and CTL for the month i, and tmax is 5 yr.

In Fig. 11, the rms deviation is given as a function of the partial length τ of the time series. Taking an integration time of 2 yr, the mean rms deviation is 7% of 〈ΔB〉. The deviation of taking only the first two years of the 5-yr integration (1980–81) is also 7% of 〈ΔB〉. The result indicates that we can expect a difference in the order of 7% of 〈ΔB〉 when the 2-yr integrations described in section 3c are extended to a period of 5 yr. From this we conclude that the differences found between RACMO output and f(Ti, ΔT) or f(Ti, ΔTi) in Fig. 9a, are not an artifact of studying time series of only a two years length.

b. The effect of a vertical gradient in the temperature forcing

Wang et al. (1991) used the GCM of the National Center for Atmospheric Research (Version 1) at 4.5° × 7.5° resolution to study the response of atmospheric variables to a CO2 doubling and a change in trace gasses. They found that the response of the vertical temperature profile to a CO2 doubling is quite uniform in the troposphere, decreases with height at the tropopause, and is negative in the stratosphere. The temperature response to a change in trace gases (CH4, N2O, CFC-11, and CFC-12) is found to be different; it is positive throughout the entire atmosphere but decreases with height above the tropopause. These results suggest that the greenhouse and trace gases affect stratospheric and tropospheric temperature differently. Although we do not expect the surface mass balance to be particularly sensitive to changes in the stratospheric temperature, we have quantified this by an additional 1-month sensitivity integration. The outcome of this integration indicates that the effect of stratospheric warming on the surface mass balance is indeed very small; the difference between TEMP and an integration similar to TEMP, but with the stratospheric temperature kept unchanged, is only about 1% of the difference between TEMP and CTL. It is noted that the sensitivity found is rather the net result of small changes in dynamics of the flow and not the direct consequence of changes in the amount of stratospheric water vapor. In view of this, the sensitivity is likely to decrease with the length of the integration.

Satellite measurements (Christy et al. 2000) indicate that the recently observed warming decreases with height, but discussion on the interpretation of these data is ongoing (Folland et al. 2001). To study the effect of allowing a vertical gradient in the imposed temperature profile, we performed three sensitivity integrations of a summer, a winter, and an autumn month, respectively. These integrations (referred to as TPROF) are set up in an identical fashion as TEMP, except that the prescribed temperature perturbation in the relaxation zone decreases linearly with pressure from 2 K at the surface to 0 K at the tropopause. Relative humidity is again kept unchanged. We find that the mean absolute difference between TPROF and TEMP is about 5% of the difference between TEMP and CTL. The sign of the difference can be both positive (1 month) or negative (2 months). There are two competing effects explaining the difference between TPROF and TEMP. In TPROF (i) the specific humidity prescribed at the lateral boundaries is lower, because the imposed temperature change is smaller in the higher troposphere, resulting in a smaller moisture transport into the model domain, and (ii) evaporation above the sea, the sea ice, and the ice shelves increases due to a slightly lower static stability of the atmosphere; as a consequence convective situations are enhanced and stable situations are weakened. For all three integrations, the monthly mean evaporation above sea, sea ice, and ice shelves is 8%–11% larger in TPROF than in TEMP. Note that the integrations TPROF are relatively short and only give an indication of the effect of the vertical gradient in temperature forcing. Also for this case, the sensitivity is likely to decrease with the length of the integration.

c. Comparison with other studies

We use the 5-yr integration (TEMP) to compare the simulated temperature sensitivity with other estimates from the literature. In TEMP, the surface mass balance increased by 47 mm yr−1 for a temperature forcing of 2 K, so the temperature sensitivity is 24 mm yr−1 K−1. This value is similar to that found by linear interpolation between results of the integrations with ΔT = −2 K and ΔT = +2 K (Fig. 9a). A first-order estimate for the temperature sensitivity of 〈B〉, using the Clausius–Clapeyron equation [Eq. (6)], is 18 mm yr−1 K−1. The sensitivity found with RACMO is 30% larger than this estimate.

In recent years, several other methods have been used to estimate the temperature sensitivity of 〈B〉 (Table 2). Fortuin and Oerlemans (1992) used an axisymmetrical atmospheric model over an idealized ice sheet to study the effects of a temperature increase at the lateral boundary of the model domain. They found a sensitivity of 13 mm yr−1 K−1, about half that found here. In RACMO the transient eddies transport moisture toward the continent whereas the mean circulation removes moisture from the continent. The effect of the transport by the transient eddies was not resolved in the study of Fortuin and Oerlemans, since their model only calculates the mean meridional circulation. Another effect taken into account in RACMO, but not by Fortuin and Oerlemans, is the retreat of the sea ice. We found in a 1-yr integration with a fixed sea ice mask, and with the temperature forcing only applied at the lateral model boundaries and at the sea surface, that the total change in the surface mass balance was 78% of the value obtained with the TEMP forcings (Table 1, columns 4 and 5). However, this fraction would probably be even larger if the boundaries were located closer to the continent, as was the case in the study of Fortuin and Oerlemans, so the retreat in sea ice alone cannot explain the differences between the results of Fortuin and Oerlemans and RACMO output.

In other studies statistical relations between surface temperature and surface mass balance are used (Muszynski and Birchfield 1985; Giovinetto et al. 1990; Fortuin and Oerlemans 1990). These studies suggest sensitivities in the range of 5–9 mm yr−1 K−1. Thus, the sensitivity found with statistical methods is much smaller than the sensitivity found in this study. In RACMO, the external temperature forcing ΔT = 2 K is used to calculate the sensitivity. Using the increase in surface temperature instead of ΔT results in a 40% lower value for the sensitivity. This can be explained by the water vapor feedback causing the average land ice temperature in RACMO to increase by 3.4 K instead of ΔT = 2 K. To exclude this effect, the sensitivity of 〈B〉 (24 mm yr−1 K−1) is divided by the sensitivity of the surface temperature (1.7 K K−1) resulting in a sensitivity of 14 mm yr−1 K−1. So the water vapor feedback explains a large part of the difference between our results and the studies based on statistical relations. Differences between RACMO and the statistical analyses could also arise from the fact that the measuring sites on which the statistical analyses were based are irregularly distributed.

Evaluation of climate scenario simulations is a fourth method for assessing the sensitivity to a temperature increase. In these studies, the temperature change is a response to another type of forcing, for example an increase in greenhouse gas concentration. Church et al. (2001) give an enumeration of the surface mass balance sensitivity of the Antarctic ice sheet to a 1-K local climate warming derived from GCMs. Local climate warming is defined as the 2-m temperature increase over the ice sheet. To compare our results with the studies presented by Church et al., we divide Δ〈B〉/ΔT by the sensitivity of the 2-m temperature (1.7 K K−1) and obtain a sensitivity to a local warming of 14 mm yr−1 K−1, which corresponds to 0.48 mm yr−1 K−1 sea level equivalent. This value is similar to the values found with GCM studies; 0.41 mm yr−1 K−1 (Ohmura et al. 1996), 0.40 mm yr−1 K−1 (Smith et al. 1998), and 0.48 mm yr−1 K−1 (Wild and Ohmura 2000). Church et al. also give the slope of the temperature sensitivity of the 2-m temperature for nine GCM integrations. They find values in the range of 0.8–1.6 K K−1, so our value is at the upper end of the 2-m temperature sensitivity.

5. Summary

We have studied the sensitivity of the surface mass balance of the grounded Antarctic ice sheet to an external temperature change. The temperature forcing in the atmosphere at the lateral model boundaries is found to have a larger effect than forcings that are applied at the sea surface. This difference is caused by the mean vertical structure of the meridional moisture transport: below about 900 hPa, the moisture transport at the grounding line is directed off the ice sheet, whereas above this level poleward moisture transport occurs. Therefore, the additional moisture, resulting from enhanced evaporation at the sea surface, must first reach higher levels before it can affect the precipitation on the land ice. However, this vertical transport of moisture is found to be not very effective as the increase in specific humidity, due to enhanced evaporation from the sea surface, remains restricted to a shallow atmospheric layer of 1–2-km depth. That is why a constant supply of additional moisture throughout the atmosphere is more effective in this respect.

Integrations for a range of temperature forcings show that the temperature sensitivity of 〈PE〉 is similar for a warming of 2, 5, and 10 K (25–27 mm yr−1 K−1) but decreases with the forcing for a cooling of 2 and 5 K (17–13 mm yr−1 K−1). This relation between the temperature sensitivity of 〈PE〉 and the forcing is brought about by the complex response of the fraction of moisture input into the atmosphere that is transported to the land ice and the response of the evaporation and sublimation from sea and sea ice to the applied forcing. The assumption that 〈PE〉 responds linearly to esatT) is an oversimplification, leading to an underestimation of the sensitivity. The largest underestimation of about 30% appears when the temperature forcing ΔT = +2 K. Melt and rain only become important for temperature forcings larger than 5 K. However, even for a warming of +10 K, the increase in 〈PE〉 is still larger than the increase in rain and melt.

Globally, factors affecting sea level are oceanic thermal expansion, a change in the mass of glaciers and ice caps, a change in the mass of the Greenland and Antarctic ice sheets, and a change in the storage of surface and ground water. Warrick et al. (1996) found a sea level rise of 15–25 cm over the last 100 years, together with an increase in global mean surface temperature of 0.3–0.6 K. By the year 2100, they expect a much larger increase in sea level (13–94 cm). In the 5-yr integration with a forced warming of 2 K, including a retreat in sea ice, we find an increase of 47 mm yr−1 in the surface mass balance of the grounded Antarctic ice. Assuming that the surface accumulation processes on the ice sheet will react on a much shorter timescale than the dynamic response of the ice sheet, we can make an estimate of the Antarctic contribution to sea level change. Other assumptions are that the increase in temperature is constant with height and that circulation remains unchanged at the lateral boundaries. We find a negative contribution to the expected sea level rise of 0.7 mm yr−1 K−1.

Acknowledgments

We would like to thank Michiel van den Broeke and other scientists from IMAU and KNMI for useful discussions. We thank Dan Zwartz for correcting the English of this paper. Three anonymous reviewers are acknowledged for improving the paper. The authors are grateful to ECMWF for providing the reanalysis fields. This work was supported by the Netherlands Earth and Life Sciences Foundation (ALW) and the National Computing Facilities Foundation (NCF) for the use of supercomputer facilities with financial aid from the Netherlands Organization for Scientific Research (NWO).

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APPENDIX A

Initialization of the Snow Temperatures

The initialization of the snow temperature profile could affect the model output, because of the long spin-up time of the snow temperatures. At the lowest snow level (5.7 m depth) the e−1 attenuation time to a stepwise increase in the surface temperature is 3.7 yr. Problems could arise when the integration time is of the same order of magnitude as the spinup time. In the sensitivity runs, the temperature forcing ΔT is added to the CTL snow temperatures. However, this is not the equilibrium temperature because the water vapor feedback amplifies the temperature forcing. The effect is largest for ΔT = +10 K; the snow temperature at 5.7 m depth increases by 2.8 K during the 2-yr integration (Fig. A1). We investigated in detail how this affected the results.

The top snow layer is centered at 6.5-cm depth. For this depth, the e−1 attenuation time to a stepwise increase in the surface temperature is only 4 h. Therefore, we carried out a Fourier decomposition of the annual cycle in the surface temperature of the first year of the integration to reinitialize the snow temperature profile on the basis of the heat diffusion equation,
i1520-0442-15-19-2758-ea1
where κ is the heat diffusivity of snow (6.06 × 10−7 m2 s−1). A new integration is performed for the year 1980 with the reinitialized snow temperatures. Figure A1a shows that the reinitialization results in an additional 5.5-K heating of the deep snow layer and that the temperature increase during the year is small.

The next question is whether this new initialization affects the surface and atmospheric conditions. Figures A1b and A1c clearly show that the interannual variability (difference between the year 1980 and the year 1981) in annual mean surface temperature and surface mass balance averaged over the grounded ice is larger than the effect of the different initializations. Hence, we conclude that the error in snow temperature initialization related to omitting the excess over ΔT, due to the water vapor feedback, does not significantly affect the surface and meteorological variables.

APPENDIX B

Atmospheric Moisture Advection into the Model Domain

In this appendix, the characteristics of the atmospheric moisture advection into the model domain are illustrated with a simple conceptual model. RACMO output shows that the mean wind vector is directed into the model domain below the 700-hPa level, where the humidity is high. The mean RACMO wind vector is directed outward above this level, where the humidity is low. For this reason, we defined a two-layer model (Fig. B1) to study the moisture transport, with wind (u), temperature (T), and relative humidity (RH) prescribed. At the lateral boundaries (denoted by suffix B) u = uB, T = TB and ∂T/∂x = ∂T/∂x|x=xB. In the lower layer RH is constant and in the upper layer RH = 0.

The total transport into the model domain can be written as the transport by the mean circulation and the eddy transport:
i1520-0442-15-19-2758-eb1
where q is the specific humidity and the prime indicates the fluctuation from the mean value.
First-order closure is used to relate the horizontal eddy transport term to the mean gradient in specific humidity:
i1520-0442-15-19-2758-eb2
where parameter kB is a scalar with units m2 s−1.
We use the Clausius–Clapeyron equation to relate ∂q/∂T to the temperature:
i1520-0442-15-19-2758-eb3
where esat(T) is the saturation vapor pressure, L is the latent heat for sublimation or evaporation, p is the pressure, Rd is the gas constant for dry air, and Rυ is the gas constant for water vapor. The fraction of the total transport that is carried by the mean flow in the unperturbed situation (αm0) is used to eliminate kB and ∂T/∂x|x=xB since αm0 can be easily derived from model output,
i1520-0442-15-19-2758-eb4
where 0 denotes the unperturbed situation. Using Eqs. (B1)(B4) an expression for the total transport into the model domain is obtained:
i1520-0442-15-19-2758-eb5
Using the Taylor expansion for several terms, we get the relative sensitivity of the moisture advection into the model domain (Aos) due to the temperature increase (ΔT), without any changes in dynamics of the flow, relative humidity, horizontal gradient in temperature, and kB:
i1520-0442-15-19-2758-eb6
The first term on the right-hand side of this equation is one order of magnitude larger than the second term on the right-hand side. For αm0 = 1, the equation reduces to the formulation of Robin (1977) (Aosesat) and for αm0 = 0 it reduces to the formulation of Lorius et al. (1985) (Aos ∝ ∂esat/∂T). The sensitivity of ΔAos/(AosΔT) to the choice of αm0, the choice of TB0TB0 = 10 K) or the choice of L (value for sublimation or evaporation) is 10%–20%. The shape of the curve ΔAos/(AosΔT) as a function of ΔT is hardly affected by the specific values for αm0, TB0, or L. Use of the simple axisymmetric model clearly demonstrates that the relative temperature dependency of Aos is to a large extent determined by the linear relation between the atmospheric moisture transport and the saturation vapor pressure. Figure 9c indicates that it is plausible to draw a similar conclusion for a complex atmospheric model.

Fig. 1.
Fig. 1.

Model domain (the dots refer to the relaxation zone) and the geographic regions mentioned in this paper

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

Fig. 2.
Fig. 2.

(a) Surface mass balance ;obmm water equivalent (w.e.) yr−1;cb compilation based on in situ and satellite observations (Vaughan et al. 1999). (b) Mean calculated surface mass balance for the period 1980–84. A Laplacian filter (XX + 0.1∇2X) is used to smooth the calculated fields X

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

Fig. 3.
Fig. 3.

A schematic representation of the method used to calculate the retreat of the sea ice. The variable λE denotes the latitude of the sea ice edge and λT refers to the latitude of the Tfreeze + ΔT isotherm, where Tfreeze is the freezing temperature of the sea water (271.46 K) and ΔT is the temperature perturbation

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

Fig. 4.
Fig. 4.

The mean sea ice cover during the period 1980–84 for CTL (solid line) and for TEMP (dashed line). The area south of the 50% contour line is covered with sea ice for more than half of the integration period

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

Fig. 5.
Fig. 5.

(a) 5-yr mean increase in precipitation (PTEMPPCTL). (b) 5-yr mean deviation of PTEMPPCTL from the spatially averaged relative change times PCTL (shaded areas) together with the difference in geopotential at the 700-hPa level between TEMP and CTL (contour lines). Contours are plotted every 20 m2 s−2 and the thick contour line is the 240 m2 s−2 isoline. A Laplacian smoothing filter (XX + 0.1∇2X) is used

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

Fig. 6.
Fig. 6.

(a) Schematic representation of the moisture budget of VSSI. VSSI is the model atmosphere volume above the sea, the sea ice, and the ice shelves (SSI). (b) Annual accumulated CTL transport of moisture (km3 yr−1) during 1980–84 across the boundaries enclosing VSSI. (c) Difference between TEMP and CTL in transport of moisture across the boundaries of VSSI. A positive value defines the direction into VSSI. Transport by evaporation from SSI (Aes) and advection from outside the model domain (Aos) are positive terms, whereas transport by precipitation on SSI (Aps) and advection to the Antarctic continent (Asl) are negative terms in the moisture balance of VSSI. Asl is calculated from the precipitation and sublimation integrated over the grounded ice and Aos is calculated from the moisture balance of VSSI; Aos = Aps + AslAes

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

Fig. 7.
Fig. 7.

(a) Vertical distribution of the poleward horizontal moisture transport across the grounding line, (b) the transport by the mean flow across the grounding line, and (c) the transport by the mean flow keeping the CTL specific humidity profile to calculate the transport in TEMP. The solid lines indicate the transport in CTL and the dashed lines indicate the transport in TEMP. See text for further explanation

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

Fig. 8.
Fig. 8.

Difference in (a) temperature and (b) specific humidity profiles between TEMP and CTL during the period 1980–84 averaged over all land ice grid points (solid lines) and all sea and sea ice grid points (dashed lines), excluding the lateral boundary grid points. The land ice grid points are a combination of grounded ice points and ice shelf points

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

Fig. 9.
Fig. 9.

(a) Temperature sensitivity of the surface mass balance 〈ΔB〉/ΔT simulated with RACMO (solid line), estimated by f(Ti, ΔT) (dotted line) and by f(Ti, ΔTi) (dashed line). The function f is given in Eq. (6). (b) Temperature sensitivity of the moisture fluxes Aos, Asl, Aes, and Aps making up the moisture balance of VSSI. (c) Relative temperature sensitivity of Aos calculated with RACMO (solid line) and calculated with a simplified two-layer model using Eq. (7) (dashed line). (d) Temperature sensitivity of the temperature at the sea, sea ice, and ice shelves surface (ΔTSSIT). (e) Fraction of the source terms of moisture into SSI (Aes + Aos) that falls as precipitation on SSI. (f) Mean precipitation 〈P〉 (solid line), precipitation minus sublimation 〈PE〉 (dotted line), precipitation minus sublimation minus rain 〈PER〉 (dashed line), and precipitation minus sublimation minus rain minus melt 〈PERM〉 (dashed-dotted line) over the grounded ice as a function of the temperature forcing

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

Fig. 10.
Fig. 10.

12-month centered running mean of 〈B〉 for the period 1980–84 for CTL (solid lines) and TEMP (dashed lines)

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

Fig. 11.
Fig. 11.

The relative rms deviation in mean surface mass balance over the grounded Antarctic ice of taking only τ yr of the 5-yr integration

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

i1520-0442-15-19-2758-fa01

Fig. A1. (a) Time series of the snow temperature at 5.7-m depth for the integration with a temperature forcing of ΔT = +10 K. The solid line indicates the integration with the original initialization and the dotted line indicates the integration with the reinitialized snow temperature profile. (b) Mean surface temperature 〈Ts〉 and (c) surface mass balance 〈B〉 for the years 1980 (solid line) and 1981 (dotted line) with original initialization and for the year 1980 (dashed line) with the reinitialized snow temperature profile as a function of the temperature forcing

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

i1520-0442-15-19-2758-fb01

Fig. B1. Representation of the two-layer model that is used to study advection into the model domain

Citation: Journal of Climate 15, 19; 10.1175/1520-0442(2002)015<2758:TSOTAS>2.0.CO;2

Table 1. 

One-year mean increase in the surface mass balance (mmw.e. yr−1) averaged over the grounded ice and averaged over the area with a surface elevation higher than 2.5 km. The forcings that are applied in the five sensitivity integrations are indicated in the table with "x"

Table 1. 
Table 2. 

Increase in surface mass balance due to a temperature increase of 1 K [M&B85: Muszynski and Birchfield (1985); G90: Giovinetto et al. (1990); F90: Fortuin and Oerlemans (1990); F92: Fortuin and Oerlemans (1992)]. To calculate assuming that depends linearly on esat, we use Eq. (6) and insert the mean inversion temperature over the grounded ice (264 K) for TC and 1 K for ΔTC

Table 2. 
Save