2.1. Control integration

A 14 year integration is performed for 1980–93 with RACMO, using a grid spacing of 55 km. The grid covers the Antarctic ice sheet and a large part of the Southern Ocean with 122 × 130 gridpoints. The model uses the parameterizations of the physical processes from the European Centre/HAMburg (ECHAM) 4 model (Reference RoecknerRoeckner and others, 1996) and the formulation of the dynamical processes from the high-resolution limited-area model (HIRLAM; Reference GustafssonGustafsson, 1993). The model formulation is described in detail by Reference Christensen and van MeijgaardChristensen and Van Meijgaard (1992) and by Reference Christensen, Christensen, Lopez, van Meijgaard and BotzetChristensen and others (1996). Modifications for the Antarctic region are described byReference Van LipzigVan Lipzig (1999) and Reference Van Lipzig, van Meijgaard and OerlemansVan Lipzig and others (1999).

The model is driven from the lateral boundaries by 15 year re-analyses from ECMWF (ERA-15), which are based on observations. The fields are updated every 6 hours. Measurements are also used to prescribe sea-surface temperature and sea-ice extent (taken identical to the values used in ERA-15). The model output is in good agreement with measurements from several Antarctic stations (Reference Van Lipzig, van Meijgaard and OerlemansVan Lipzig and others, 1999, Reference Van Lipzig, van Meijgaard and Oerlemans2002a).

A comparison by Reference Schlosser, van Lipzig and OerterSchlosser and others (2002), using data from Neumayer, an Antarctic coastal station, shows that the episodic nature of the precipitation is realistically represented by RACMO (Fig. 3). Neumayer (8.4° W, 70.7° S) is on the Ekström Ice Shelf, about 7 km from the ice edge (Fig. 1). The net accumulation at Neumayer was measured approximately once a week at 25 stakes covering an area of 25 × 25 m². RACMO output for the land-ice gridbox closest to Neumayer was interpolated to the same time interval as the measurements. In RACMO, the surface mass balance or net accumulation is defined as precipitation minus sublimation. In the model, net accumulation during an event is somewhat smaller than the stake measurements indicate. It cannot be concluded whether differences between the RACMO output and Neumayer data are due to transport by wind-blown snow, which is locally important but not taken into account in RACMO, or whether they are due to too little precipitation during a model event. Clearly, windblown snow plays a role at Neumayer since net accumulation can be significantly negative during short time intervals. The effect of wind-blown snow on the scale of a model gridbox is unknown, but is assumed to be of lesser importance than on the scale of the stake array (25 × 25 m²). Generally, large precipitation events are present in both the model output and the measured time series. A comparison of model output with data from an AWS near Svea (11° 13′ W, 74°35′ S), 300 km from the coast, shows that the episodic nature of precipitation, also found at this site, is realistically represented by the model.

Fig. 3 Net accumulation rate during 1987 at Neumayer measured with a stake array (Reference SchlosserSchlosser, 1999) (solid line) and calculated with RACMO (dashed line) (see also Reference Schlosser, van Lipzig and OerterSchlosser and others, 2002). The times when the measurements were made are indicated with a dot near the upper axis. Model output is interpolated to the time interval of the measurements.

2.2. Sensitivity integration

A sensitivity integration is performed for the 5 year period 1980–84. In this integration:

1. (1) the lateral boundaries are warmed by 2°C, keeping the relative humidity fixed;

2. (2) the sea surface is warmed by 2°C; and

3. (3) a retreat of sea ice is prescribed that is consistent with the 2°C warming (Reference Van Lipzig, van Meijgaard and OerlemansVan Lipzig and others, 2002b).

The dynamics of the flow at the lateral model boundaries are identical to the control integration and changes in large-scale dynamics in response to temperature forcing are not taken into account. On the other hand, using this approach, the model is driven by large-scale flow dynamics inferred from observations and the occurrence of synoptic systems is constrained to what is observed in the present-day climate.

3.1. Variations in annual mean temperature

The δ signal in an ice core is related to the temperature at which the precipitation is formed. We estimate this temperature by the inversion temperature T _i (Reference RobinRobin, 1977), defined as a local maximum in the stably stratified atmospheric-boundary-layer temperature profile. For example, Figure 4 shows the calculated temperature profile for 1 August 1988, 12.00 UTC at Dome C. In this case, the inversion occurs at 540 m height and T _i is 27°C higher than the surface temperature (T _s).

Fig. 4 Temperature profile at Dome C for 1 August 1988, 12.00 UTC. The inversion temperature is indicated with T _i and the surface temperature with T _s . The dotted line shows the extrapolated free-atmospheric temperature profile. In the atmospheric boundary layer, the temperature deviates substantially from the extrapolated free-atmospheric temperature. The squares refer to model levels.

Having found that RACMO can represent the episodic nature of precipitation at Neumayer and Svea realistically, we believe that the model is suitable for studying the effect of the temporally irregular distribution of net accumulation (B) on signals measured in ice cores. Proxies for meteorological variables are stored in the ice during precipitation events. Therefore, the annual mean δ signal in the ice core is not directly related to T _i, but rather to the annual mean inversion temperature weighted with the net accumulation:

where T _i,j is the inversion temperature at time j, B_j is the accumulation over 6 hours at time j, and N is the number of 6 hour time intervals per year (model output is available every 6 hours). Only positive accumulation events are taken into account and when B_j is negative during a 6 hour period, this period is ignored. We have calculated T _i,w for five deep-drilling sites: Dome C (123° E, 75.1° S), Dome F (40° E, 77.3° S), DML05 (0° E, 75.0° S), Byrd (120° W, 80.0° S) and Vostok (107° E, 78.5° S) (Fig. 5). T _i,w turns out higher than T_i indicating that the correlation between temperature and precipitation is positive: precipitation events occur when relatively warm air from the sea is advected towards the ice sheet (e.g. Reference BromwichBromwich, 1988; Reference Noone, Turner and MulvaneyNoone, 1999). Ignoring unstable conditions alters T _i,w by 0.1 K, which is considered negligible.

Fig. 5 Time series of annual mean inversion temperature (solid line) and annual mean inversion temperature weighted with the net accumulation (T _i,w ) (dotted line) at (a) Dome C, (b) Dome F, (c) DML05, (d) Byrd and (e) Vostok.

The year-to-year variability of T _i,w is two to three times larger than that of T _i. This is due to year-to-year variations in modelled seasonality of accumulation. For example, at Dome F, 40% of the net accumulation in the model year 1982 occurred during the summer months December and January. In the model year 1983, the seasonality shifted so the accumulation maximum occurred during the winter month June (14% of the annual accumulation occurring in this month). Due to the shift in seasonality of precipitation, from 1982 to 1983 T _i,w decreased by 5.3°C, whereas T _i only decreased slightly by 0.2°C.

There is no significant correlation at the 95% confidence level between annual mean T _i,w and T _i, except for Byrd station. The correlation coefficients for annual mean values are −0.26, 0.40, 0.31, 0.69, and 0.21 for Dome C, Dome F, DML05, Byrd and Vostok, respectively. This implies that year-to-year variations in the δ signal in an ice core are poor indicators of year-to-year variations in the inversion temperature, except for Byrd. Byrd has the highest accumulation, 108 mm w.e.a⁻¹, whereas Dome C, Dome F and Vostok receive <30mm w.e.a⁻¹. At Byrd, the number of precipitation events exceed those for the stations in East Antarctica, so changes in the seasonality of precipitation have less effect on the signals measured in ice cores.

We investigate whether changes in seasonality of precipitation or changes in variations on a daily time-scale are responsible for the low correlation between the annual mean T _i,w and T _i. When inserting monthly mean values for the inversion temperature and accumulation into Equation (1), the weighted inversion temperature is found to be 4° to 8°C lower than T _i,w calculated on the basis of 6 hourly means. The reason for this difference is that precipitation and temperature are correlated on short time-scales. When monthly mean values are used, the positive correlation between temperature and precipitation on a daily time-scale is no longer taken into account. For all drilling sites considered, the difference between annual mean values of T _i,w, calculated on the basis of monthly means, and annual mean values of T _i,w, calculated on the basis of 6 hourly means, turns out to be approximately constant in time. From this it is concluded that year-to-year variations in seasonality of precipitation are responsible for both the larger variability of T _i,w, compared to T _i, and the low correlation between T _i,w and T _i. Year-to-year variations in the intermittent nature of daily precipitation on a daily time-scale have an insignificant effect. Further investigations show that the effect of changes in the daily cycle of precipitation is also small.

In ice-core studies, the δ signal measured along a core as a function of depth is used to derive the surface-temperature history at the drilling site. In order to make this conversion, a relationship between the δ signal and T _s is needed (a transfer function). The transfer function is derived for a reference period (present-day climate) by taking snow samples at several sites. The spatial relationship between δ and T _s, derived from the snow samples, is assumed to be identical to the temporal relationship between δ and T _s. We use model output, after Reference Krinner, Genthon and JouzelKrinner and others (1997), to mimic this procedure. The δ signal in an ice core is simulated and the surface temperature (T _s,core) is derived from the δ signal, on basis of RACMO output, using a T _i,w/T _s transfer function. The procedure for the Dome C drilling site is described below.

First, the 14 year mean T _{i, w} is calculated for 1980–93. Model output at 15 gridboxes, from Dome C northwards, is used to derive the spatial relationship between T _i,w and T _s (Fig. 6) using a least-squares method. This spatial relationship is assumed to be identical to the temporal relationship and can therefore be used to calculate T _s,core from T _{i, w}:

Fig. 6 14 year mean surface temperature (T _s ) vs 14 year mean inversion temperature weighted with the net accumulation (T _i,w ) for 15 gridboxes on a line from Dome C northwards. The solid line in the graph shows the transfer function (Equation (2)) calculated with the least-squares method.

The coefficient in this equation is > 1, since the inversion strength (T _i – T _s) increases from the coast inland (Fig. 7; see also Reference Phillpot and ZillmanPhillpot and Zillman, 1970; Reference ConnolleyConnolley, 1996). The difference between T _i,w and T _s is therefore largest in the interior.

Fig. 7 14 year mean temperature-inversion strength (T _i – T _s ) derived from model output.

Second, for each year T _s,core is calculated by inserting the annual mean value for T _i,w into Equation (2). Figure 8 shows the time series of both T _s and T _s,core; there is no significant correlation between them. Furthermore, the variability of T _s,core is 2.3 times the variability of T _s. The reason for this is the larger interannual variability of T _{i, w} compared to T _s, and the fact that the coefficient ∂T _s,core/∂T _i,w is > 1. Note that the spatial slope ∂T _s/∂T _i,w in the Dome C temperature regime is larger than the slope for the entire temperature range considered in Figure 6. If we restrict the evaluation of Equation (2) to the five coldest gridpoints, the coefficient is found to be 18% larger. This results in a 18% greater variability in the T _s,core time series, although the correlation between T _s,core and T _s is unaffected.

Fig. 8 Annual mean T _s (solid line) and T _s,core (dotted line) for Dome C. T _s,core is derived from model output with Equation (2) using Reference Krinner, Genthon and JouzelKrinner and others’ (1997) method, analogous to the retrieval of T _s from the 6 signal observed in ice cores.

Results for all five drilling sites are summarized in Table 1, showing that the transfer functions are different for each site. At Dome C, DML05 and Vostok, the ∂T _s,core/∂T _i,w coefficient is 1.7 to 1.8, whereas it is only 1.3 at Dome F and Byrd. This means that applying a transfer function derived for one region to a site elsewhere can result in errors in the interannual variations of the derived temperature up to about 40%. For all five sites considered, the variability of T _s,core is two to three times that of T _s. However, it is unlikely that the year-to-year variation in the temperature signal derived from ice-core δ measurements is overestimation, since wind mixing and isotope diffusion smooth the ice-core record. More relevant for ice-core studies is that the correlation between modelled T _s and T _s,core is significant at the 95% confidence level for only one of the five sites considered (Table 1), implying that, at most drill sites considered, the ice-core δ signal is a poor indicator for interannual variations in surface temperature.

3.2. Variations in 7 year mean temperature

We now examine whether the temporal variability of precipitation affects the proxy or tracer in an ice core when averaged over longer periods than 1 year. We consider all grounded-ice gridboxes. We use precipitation instead of net accumulation, since the modelled sublimation is unrealistically high in some mountainous areas due to an overestimation of the roughness length (Van Lipzig, 2002a). Note that the five stations considered above are in regions where sublimation is not overestimated. Since the integration covers 14 years, we divide the time series into 7 years with the highest surface temperature averaged over the entire ice sheet (1980–81, 1984, 1988, 1990–92) and 7 years with the lowest surface temperature (1982–83, 1985–87, 1989, 1993). The difference in surface temperature, 〈ΔT _s〉, averaged over the grounded ice between warm years τ _warm and cold years τ _cold was 0.9°C. The angle brackets indicate averaging in space.

We consider τ _warm as the reference years. To calculate the surface temperature during τ _cold, analogous to interpreting δ signals from ice cores, we follow the same procedure as described in the previous paragraph. The 7 year mean of T _i,w is calculated for the reference years τ _warm. For simplicity, one transfer function is derived for the entire grounded ice sheet (Fig. 9), using a least-squares method:

Fig. 9 7 year mean T _s vs 7 year mean inversion temperature weighted with the precipitation (T _i,w ) for all grounded-ice points for the τ _warm years. The solid line shows the transfer function (Equation (3)) calculated using the least-squares method.

As in Equation (2), the ∂T _s,core/∂T _i,w coefficient is > 1, since the inversion strength increases from the coast inland (see Fig. 7). To assess other effects that play a role, the relationship between the surface temperature weighted with the precipitation, (T _s,w), and T _s. is calculated. The ∂T _s,core/∂T _s,w coefficient is slightly > 1 (1.1) because the precipitation maximum in the interior occurs during summer, whereas the season with maximum precipitation varies along the coast. Therefore, T _s,w − T _s. is larger in the interior (at low temperatures) than near the coast. It is unclear whether the modelled summer precipitation maximum in the interior is realistic due to lack of reliable climatological precipitation measurements in this region, where accumulation is low.

To indicate the regional differences in transfer function, Figure 10 shows the derived surface temperature (T _s,core) calculated from Equation (3) minus T _s for the reference years τ _warm. In regions where the transfer function deviates from Equation (3), T _s,core − T _s is large. In the interior, T _s,core > T _s. This is consistent with the deviation of T _i,w from the linear regression line for the lower temperature range (interior) (Fig. 9). Other areas where T _s,core > T _s are Oates Coast and the area east of the Ross Ice Shelf. Areas where T _s,core < T _s are the interior of West Antarctica and the region east of the Amery Ice Shelf.

Fig. 10. Difference between the 7 year mean T _s,core derived with Equation (3) and the 7 year mean T _s for the τ _warm years.

The value for T _i,w is calculated for the years τ _cold. The surface temperature during τ _cold, simulating the temperature found from the δ signal in an ice core, is derived by inserting T _i,w (τ _cold) in Equation (3). The difference between T _s,core and T _s for the years τ _cold is similar to the difference for the years τ _warm, indicating that the regional differences in transfer function during τ _cold are similar to the regional differences during τ _warm. These are mainly caused by regional differences in the relationship between T _s and T _i.

The difference between τ _warm and τ _cold, 〈ΔT _s,core〉 derived with Equation (3), averaged over the grounded ice is 0.9°C, which is identical to the value found for 〈ΔT _s,core〉. However, the spatial pattern of ΔT _s,core is very different from ΔT _s (Fig. 11), its spatial variability being much larger than that of ΔT _s. At 30% of the gridboxes ΔT _s,core is negative, whereas ΔT _s is negative at only 3% of the gridboxes. In addition, at 10% of the gridboxes ΔT _s,core is > 3°C. This temperature difference never occurs for T _s. The large spatial variability of ΔT _s,core is caused by differences in flow dynamics between τ _warm and τ _cold, affecting the 7 year mean seasonality of precipitation and consequently T _i,w.

Fig. 11 Difference between τ _warm and τ _cold in (a) T _s,core derived using Equation (3) and (b) T _s .

Most of the stations considered are in a region where ΔT _s,core < ΔT _s, but for Byrd ΔT _s,core > ΔT _s. (Table 1). Using the regional coefficients in the transfer function given in the first column of Table 1, instead of the coefficient in Equation (3), can result in a ±20% change of ΔT _s,core. The correspondence between ΔT _s,core and ΔT _s improves for Byrd but deteriorates for Dome C. The mean absolute difference between ΔT _s,core and ΔT _s. for the five stations does not change using the regional coefficients. The mean absolute difference 1/M Σ_M| ΔT _s,core − ΔT _s|, where M is the number of grounded-land-ice gridboxes, is 1.2°C, which is larger than the mean temperature difference between τ _warm and τ_cold. This indicates that, in ice-core studies, an averaging period of 7 years is too short to relate the local ice core δ signal to surface temperature.

3.3. Changes in the relationship between inversion strength and surface temperature

A 5 year sensitivity integration is performed in which a temperature forcing of 2°C is prescribed at the lateral boundaries of the model domain and at the sea surface, together with a retreat of the sea ice. We have used the results of this integration to study the effect of changes in the T _i/T _s relationship on the temperature derived from the δ signal in the ice. The T _i/T _s relationship changes when the relationship between inversion strength and surface temperature changes in a different climatic regime. The inversion strength is smaller in the sensitivity integration (SENS) than in the control integration (CTL). In addition, the surface temperature averaged over the grounded ice is 3.4°C warmer in SENS than in CTL. The response of T _s is larger than the applied temperature forcing of 2°C. This is caused by the water-vapour feedback, as the amount of water vapour and specific liquid water increases in SENS, resulting in an increase in downward longwave radiation (Reference Van Lipzig, van Meijgaard and OerlemansVan Lipzig and others, 2002b). The amplification of the 2°C temperature forcing and the decrease in inversion strength are largest in the interior of the ice sheet, where the surface elevation is largest.

Although the forcings in the integration are very simple, the study is useful for identifying the mechanisms that can cause a difference between surface temperature and derived surface temperature using the δ vs T _s relationship (transfer function). Changes in the seasonality of precipitation between the two integrations are expected to be small, since changes in the circulation at the lateral-model boundaries are not taken into account.

The weighted temperature and the transfer function are derived for CTL:

This equation differs slightly from Equation (3), since a different time period (1980–85) is considered. Inserting T _i,w from SENS into Equation (4) yields the derived temperature T _s,core(SENS). Figure 12 shows ΔT _s,core = T _s,core(SENS) − T _s,core(CTL) and ΔT _s = T _s(SENS) − T _s(CTL). Again, the spatial variability of ΔT _s,core is much larger than the variability of ΔT _s, due to local changes in the 5 year mean seasonality of precipitation. Probably, the changes in seasonality averaged over the integration period decrease with the length of the integration, so the spatial variability of ΔT _s,core might be smaller for longer integration periods.

Fig. 12 Difference between SEMS and CTL in (a) T _s,core derived using Equation (4) and (b) T _s .

The increase in T _s,core averaged over the grounded ice is 4°C; 〈ΔT _s,core〉 is 18% larger than 〈ΔT _s〉. We separate the effect of changes in the T _i/T _s relation from changes in seasonality of precipitation by multiplying the difference in inversion temperature between SENS and CTL (2.7°C) by ∂T _s,core/∂T _i,w (1.56). We find a value of 4.2°C, which corresponds closely to the value found when both changes in seasonality and inversion strength are included. This indicates that changes in the T _i/T _s relationship are primarily responsible for the difference between 〈ΔT _s,core〉 and 〈ΔT _s〉.

There are two opposing effects that cause the difference between 〈ΔT _s,core〉 and 〈ΔT _s〉. First, the meridional gradient in inversion strength results in a ∂T _s,core/∂T _i,w coefficient > 1, amplifying the difference between SENS and CTL in T _i,w. Second, the inversion strength in SENS is smaller than in CTL. Therefore, the increase in T _i is smaller than the increase in T _s. The first effect dominates.

Were the temporal relation between T _s and T _i,w identical to the spatial relation, then the transfer function for the SENS integration would be identical to Equation (4). Since this is not the case, the transfer function for the SENS integration (T _s,core = −143.55 + 1.52 T _i,w) differs from the CTL integration. The difference in ∂T _s,core/∂T _i,w between CTL and SENS is significant at the 99% confidence level. The SENS value for ∂T _s,core/∂T _i,w is smaller than the CTL value since the increase in inversion strength, going from the coast into the interior, is smaller in SENS than in CTL: in CTL ∂T _s/∂T _i is 1.49 whereas in SENS it is 1.43. In both integrations, 96% of the variance in T _i is explained by a linear relation between T _s and T _i.

We conclude that the increase in simulated surface temperature, being derived with a method analogous to that used in ice-core studies, is overestimated by 18% when compared to the direct-model surface temperature. This error is of the same order of magnitude as the errors found by Reference Delaygue, Jouzel, Masson, Koster and BardDelaygue and others (2000) for a change in seasonality of precipitation (an underestimation of 15%) and a change in the temperature of the source, where evaporation took place (an overestimation of 10–30%). These errors are all less than the 100% underestimation of the temperature difference between the Last Glacial Maximum and present-day climate when the spatial δ/T _s slope was compared with borehole paleothermometry for Greenland (Reference Cuffey, Clow, Alley, Stuiver, Waddington and SaltusCuffey and others, 1995; Reference Johnsen, Dahl-Jensen, Dansgaard and GundestrupJohnsen and others, 1995).