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 (λ_E) and the CTL latitude of the (T_freeze + ΔT)-isotherm (λ_T) are constructed as a function of longitude and time, where T_freeze is the freezing temperature of the sea water (271.46 K). The functions λ_E and λ_T are smoothed in time and space. The TEMP sea ice edge is constructed by shifting the CTL sea ice edge by Δλ(=λ_T − λ_E) toward the south. The TEMP T_freeze + ΔT isotherm (λ_T) is identical to the CTL sea ice edge (λ_E). In areas where the sea ice has disappeared, the SST is assumed to vary linearly with latitude; from T_freeze at λ_E to T_freeze + ΔT at λ_T. 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).

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 〈B〉_CTL. 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 = P_TEMP − P_CTL) 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

View Expanded

which is the deviation of ΔP at a given location from the spatially averaged relative change times P_CTL (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.

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)

View Expanded

where E is the sublimation and evaporation, ρ_L 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

View Expanded

where q is the specific humidity, u is the horizontal wind vector, g is the acceleration due to gravity, p is the pressure, and p_s is the surface pressure. Note that we divide by ρ_L 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:

View Expanded

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 〈P − E〉 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 q_CTL, 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.

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.

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 (e_sat) (Robin 1977). Using the Clausius–Clapeyron relation we get

View Expanded

where L is the latent heat of sublimation or evaporation and R_υ is the gas constant for water vapor.

From a reference state with surface mass balance B_CTL and temperature T_C, the temperature sensitivity of the surface mass balance f(T_C, ΔT_C) can be calculated as a function of the temperature increase ΔT_C, using the Taylor expansion of the term in the exponential:

View Expanded

The question is which values to insert for T_C and for ΔT_C. Robin (1977) suggested that the temperature at the inversion (T_i) should be used; using the CTL value for T_i, which is a function of location, and the temperature forcing (ΔT) for ΔT_C, 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 (ΔT_i) instead of ΔT. Due to the water vapor feedback, the value for ΔT_i 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(T_i, ΔT_i), especially for large values of the forcing. To understand this behavior, we study the temperature sensitivity of the moisture balance terms into V_SSI (Fig. 9b). (For a schematic representation of the moisture balance of V_SSI, 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 A_sl (dotted line in Fig. 9b).

We use a two-layer model, in which q is linear with e_sat, to understand the temperature dependency of the moisture advection into the model domain A_os (solid line in Fig. 9b). In appendix B an equation is derived for the relative temperature dependency of A_os in this simplified model,

View Expanded

where α_m0 is the fraction of the total moisture advection that is transported by the mean circulation. In RACMO, α_m0 is found to be 0.17 for the control run. For T_C 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 A_os can be largely explained by the simplified model, which means that the variations in e_sat determine the temperature dependency of A_os 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 (A_es; 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 T_SSI, 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 α_i, Δα_i, and (1 − α_i − Δα_i), 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, DT_SSI is defined as the difference in T_SSI between two integrations with adjacent temperature forcings divided by the difference in the corresponding temperature forcings ΔT of these integrations,

View Expanded

where T_TZ is the surface temperature in the transition zone, and T_{sea 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) (C_TZ) denotes the contribution of the surface temperature change in the transition zone to DT_SSI, and the third term on the right-hand side of Eq. (8) (C_{sea ice}) denotes the contribution of the surface temperature change in the sea ice region to DT_SSI.

Five values for the terms in Eq. (8) are calculated using output from the six integrations that are available. We find that C_TZ dominates the temperature dependency of DT_SSI. 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 C_{sea ice} can be neglected except for ΔT = −3.5 K, at which C_{sea ice} = −0.14 and C_TZ = 0.37. The term C_{sea 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 T_SSI is primarily determined by the change in sea ice extent. The term C_{sea 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 A_ps (dashed line in Fig. 9b). The part of the moisture input to V_SSI (A_es + A_os) that is converted to rain or snow above SSI (A_ps) 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 A_ps/A_es 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 A_ps, A_es, and A_os, and that the assumption that B is linearly dependent on e_sat(ΔT) 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 〈P − E〉 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.

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 (〈ΔB〉₁₉₈₀ = 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 (δ_rms) from the 5-yr mean of N_m time series is given by

View Expanded

where N_m = 1 + 12(t_max − τ), 〈ΔB〉_i indicates the monthly mean difference in the surface mass balance between TEMP and CTL for the month i, and t_max 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(T_i, ΔT) or f(T_i, ΔT_i) 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.