THE SPATIAL AND TEMPORAL VARIABILITY OF THE SURFACE MASS BALANCE IN ANTARCTICA: RESULTS FROM A REGIONAL ATMOSPHERIC CLIMATE MODEL

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1 INTERNATIONAL JOURNAL OF CLIMATOLOGY Int. J. Climatol. 22: (2002) Published online in Wiley InterScience ( DOI: /joc.798 THE SPATIAL AND TEMPORAL VARIABILITY OF THE SURFACE MASS BALANCE IN ANTARCTICA: RESULTS FROM A REGIONAL ATMOSPHERIC CLIMATE MODEL NICOLE P. M. VAN LIPZIG, a, * ERIK VAN MEIJGAARD a and JOHANNES OERLEMANS b a Royal Netherlands Meteorological Institute (KNMI), de Bilt, The Netherlands b Institute for Marine and Atmospheric Research Utrecht (IMAU), The Netherlands Received 30 July 2001 Revised 15 March 2002 Accepted 20 March 2002 ABSTRACT A 14 year integration with a regional atmospheric model (RACMO) is used to obtain detailed information on the Antarctic surface mass balance and to understand the mechanisms that are responsible for the spatial and temporal distribution of the surface mass balance. The model ( x = 55 km) uses the parameterizations of the physical processes from the ECHAM4 general circulation model and is driven from the lateral boundaries by the 15 year re-analyses of the European Centre for Medium-range Weather Forecasts (ERA-15). Sea surface temperature and sea ice extent are prescribed from observations. The model is evaluated with in situ measurements of surface pressure, 2 m temperature, and surface mass balance. Generally, good agreement is found between model output and measurements, although in the interior of the ice sheet the temperatures are slightly too high in summer. The 14 year mean surface mass balance averaged over the grounded Antarctic ice B is 156 mm water equivalent per year. A statistical relation between precipitation and topographical parameters is derived from model output. Half of the spatial variance in precipitation can be explained by a relation between precipitation and distance to the coast. Locally, the direction of the atmospheric flow is important; in Ellsworth Land and Wilkes Land the surface mass balance is larger than expected on the basis of topography alone, because of flow directed inland. The year-to-year variability in B is similar to the value found in ERA-15 (standard deviation of annual mean values is 6 to 7% of the 14 year mean) and is determined by the atmospheric circulation and not by variations in temperature or humidity. In the interior of the ice sheet, seasonality of precipitation is mainly determined by temperature, but, near the coast, the dynamics of the flow are important. For example, in Dronning Maud Land the precipitation is highest in autumn, when the upslope component of the wind vector at 500 hpa is largest. Year-to-year variations in seasonality of precipitation are large and might affect proxies for meteorological variables in ice cores. Copyright 2002 Royal Meteorological Society. KEY WORDS: Antarctica; surface mass balance; precipitation; regional atmospheric model; model evaluation; climate variability; ice core analysis 1. INTRODUCTION The mass change of the Antarctic ice sheet is determined by the net input of moisture at the surface (surface mass balance) and the ice flux across the grounding line (contour line where the grounded ice turns into floating ice). The surface mass balance is the sum of precipitation, sublimation/deposition, runoff, and windblown snow. To understand past and future changes in the mass of the Antarctic ice sheet in relation to sea level, information on the present-day surface mass balance is indispensable. In this study, we focus on the primary components of the surface mass balance, namely precipitation and sublimation. Runoff is very small, because temperatures are generally below the freezing point. Wind-blown snow can be of local importance * Correspondence to: Nicole P. M. van Lipzig, British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, UK; nvl@bas.ac.uk Copyright 2002 Royal Meteorological Society

2 1198 N. P. M. VAN LIPZIG, E. VAN MEIJGAARD AND J. OERLEMANS when the wind redistributes the precipitated snow, but only contributes to the mass balance of the ice sheet when it drifts across the ice edge (Radok, 1970). Giovinetto et al. (1992) estimated that wind transport of snow across the ice edge is at least one order of magnitude smaller than the atmospheric moisture transport onto the ice sheet. Studying the temporal variability of the surface mass balance is required for a correct interpretation of signals from ice cores. In general, these cores contain important information that can be related to variations of meteorological variables in the past (e.g. Dansgaard, 1964; Johnsen et al., 1972; Peel et al., 1996). However, the isotope or tracer signal measured in ice cores represents the meteorological conditions during accumulation, which arehighly likely to be differentfrom the annualmean conditions. Therefore, the signals in the core might not be representative for annual mean conditions (Steig et al., 1994; Jouzel et al., 1997; Krinner et al., 1997; Noone and Simmonds, 1998; Schlosser, 1999; Werner et al., 2000). Information on the temporal variability of the surface mass balance on sub-annual time scales is necessary to gain insight into this problem. There is a lack of detailed information on the surface mass balance. Since it is impossible to distinguish between precipitation and wind-blown snow, the separate components of the surface mass balance cannot be derived from direct measurements. The sum of the components (net accumulation) has been measured, but measuring sites are sparse and irregularly distributed. Most sites are located near the coast, where the spatial variability is large. For example, net accumulation derived from two cores in Wilkes Land (Figure 1(a)) differ by a factor of two, whereas they were drilled only 18 km apart (Morgan et al., 1991). Measurements of the daily/monthly variations in net accumulation on a routine basis have only started recently, and time series are still short. Records of monthly variations in net accumulation exceeding a length of a decade are virtually absent (Schlosser, 1999). The objective of this paper is to obtain detailed information on the present-day spatial distribution and the temporal variation of the surface mass balance (defined here as precipitation minus sublimation), and to gain insight into the processes that are responsible for these variations. We use a regional atmospheric climate model (RACMO) as a tool to obtain this information. The model has been evaluated for Antarctic conditions by Van Lipzig et al. (1998, 1999). Synoptic-scale disturbances, which are essential for the transport of moisture towards the continent, are properly represented in the model. This is achieved by relaxing the prognostic variables at the lateral boundaries of the model domain towards European Centre for Medium-range Weather Forecasts (ECMWF) re-analyses (ERA)-15-fields (Gibson et al., 1997). In integrations with global climate models (GCMs), such a forcing, directly inferred from observations, is absent. Atmospheric analyses are constructed by assimilating irregularly distributed meteorological observations into an integration with a general circulation model, and can therefore be regarded as an interpolation of the Figure 1. Regions (a) and stations (b) mentioned in this paper

3 SURFACE MASS BALANCE IN ANTARCTICA 1199 measurements (Genthon and Braun, 1995). ERA-15-fields are suitable for studying aspects of the temporal variability in the surface mass balance (Genthon and Krinner, 1998; Noone et al., 1999; Turner et al., 1999; Marshall, 2000). However, there are also some problems in ERA-15. For example, the use of an incorrect station height for Vostok resulted in discrepancies in the interannual variations of precipitation in a sector in West Antarctica ( W) compared with the operational analyses (Bromwich et al., 1999). In addition, the winter near-surface temperature at stations in the interior is 5 to 10 C too low (Connolley and Harangozo, 2001). The re-analyses show a pronounced decoupling of the lowest atmospheric layer from the overlying atmosphere. In contrast, RACMO is able to represent the stable atmospheric boundary layer realistically over the Antarctic continent (Van Lipzig et al., 1999). In the lateral boundary zone of the RACMO domain, extending from 65 to 47 S, both satellite and in situ measurements were assimilated into the re-analysis cycle, making the ERA-15-fields less dependent on the model formulation than in the region of the Antarctic ice sheet, where the amount of observations was much smaller. The horizontal resolution presently used in re-analyses (ERA-15) and climate integrations with GCMs is about 100 km (Wild and Ohmura, 2000). By using a regional model, it was possible to perform a long integration of 14 years ( ) at 55 km horizontal resolution at reasonable computational costs. This high horizontal resolution results in improved representation of the steep edges of the ice sheet. Since precipitation is related to orographic lifting of moist air at the steep coastal slopes of the continent (Bromwich, 1988), the precipitation distribution is better resolved in RACMO than in ERA-15 and climate integrations with GCMs. In this paper, we give a description of the model formulation (Section 2), and evaluate the modelled surface mass balance and related near-surface meteorological variables (Section 3). We describe the spatial distribution (Section 4) and the temporal variations (Section 5) of the surface mass balance and discuss the mechanism behind these variations. A summary is given in Section MODEL FORMULATION A detailed description of RACMO is given by Christensen et al. (1996) and Christensen and Van Meijgaard (1992). The dynamical part of RACMO is taken from the High-Resolution Limited Area Model (Gustafsson, 1993). We adopted 20 layers in the vertical, with the lowest layers centred at about 7, 35, 130, 330, and 660 m and the highest model level centred at 10 hpa (25 30 km height). The horizontal grid spacing is 55 km. An area of km 2, including the Antarctic continent and a part of the Southern Ocean, is covered with grid points (Figure 2). In the lateral boundary zone of the model domain (larger dots in Figure 2) the temperature, the zonal and meridional components of the wind, the specific humidity, and the surface pressure are relaxed towards ERA-15-fields using a technique proposed by Davies (1976). The ERA-15 data set was composed by re-assimilating essentially all available observations on the atmospheric state for the period from 1979 to 1994 into an integration with the ECMWF global model (Gibson et al., 1997). By this approach, the regional model is driven from the lateral boundaries by a consistent time series of meteorological fields. The parameterizations of the physical processes in RACMO are taken from the ECHAM4 GCM (Roeckner et al., 1996). The ECHAM4 model parameterizes the effects of the surface exchange processes and vertical diffusion, gravity wave drag, cumulus convection, stratiform clouds, and radiation. The sub-surface temperature is determined by the surface energy budget and the vertical diffusion of heat in the snow using a five-layer model until a depth of 10 m, where a zero heat flux is prescribed. The sea-ice temperature is a prognostic variable, which is calculated from the surface energy budget and the upward heat flux from the ocean. The ocean heat flux is parameterized as a coefficient (2 W m 1 K 1 ) times the sea-ice thickness (1 m) times the temperature difference between the sea-ice surface and the ocean. Some adjustments were made to the original ECHAM4 model formulation to improve the representation of the processes in the Antarctic region (Van Lipzig et al., 1999; Van Lipzig, 1999). In particular, a better representation of the atmospheric boundary layer has been accomplished by taking out the dependency of the surface albedo on the surface temperature and by altering the values for the heat capacity and diffusivity of snow. The values adopted here are 0.8 for the albedo, Jm 3 K 1 for the heat capacity,

4 1200 N. P. M. VAN LIPZIG, E. VAN MEIJGAARD AND J. OERLEMANS Figure 2. RACMO grid with a horizontal spacing of 55 km. In the relaxation zone (indicated by larger dots), the model prognostic variables are relaxed towards ERA-15-fields. The surface geopotential height (hm) is indicated by the contour lines and m 2 s 1 for the diffusivity. Other changes in the model formulation are an extra layer in the atmosphere close to the surface (to obtain higher resolution in the generally shallow boundary layer of the Antarctic atmosphere), an improved and more detailed ice sheet orography (British Antarctic Survey et al., 1993), a more adequate initialization of the snow temperature profile, the treatment of ice shelves as land ice, and a more adequate representation of the surface roughness length. Originally, an effective roughness length z 0eff was employed to account for the effect of small-scale orographic features on the turbulent momentum and heat exchange. This z 0eff was calculated from the variance of the sub-grid-scale orography, having the disadvantage of very high values at the steep edges of the ice sheet. To avoid this, we used the ERA-15 database to prescribe the roughness length. This database shows high values for z 0eff in mountainous regions only, which we maximized at a value of 3 m. Over land, the roughness lengths for momentum and heat are identical. In the absence of sub-grid-scale orographic variance, the roughness length over land ice and ice shelves is chosen as 1 mm. An integration is performed for the 14 year period with the lateral boundaries updated every 6 h and the sea-surface temperature and sea-ice mask prescribed from daily observations. 3. EVALUATION OF THE NEAR-SURFACE CLIMATE Since this paper focuses on the surface mass balance, we evaluate variables that are related to precipitation and sublimation. Precipitation is related to the occurrence of synoptic disturbances. These disturbances are

5 SURFACE MASS BALANCE IN ANTARCTICA 1201 also reflected in time series of the surface pressure. Therefore, we evaluate the surface pressure anomalies in the model using measurements from three sites. Sublimation is influenced by temperature, since the atmospheric specific humidity depends on the atmospheric temperature. We evaluate the annual cycle of the 2 m temperature at several Antarctic stations. In addition, three different compilations of the surface mass balance based on in situ measurements are used to evaluate the model Surface pressure We evaluate the time series of surface pressure anomalies by using an extended version of the data set described by Smith and Stearns (1993). The sites of Dumont d Urville, Dome-C, and Halley were chosen for the evaluation because they are located in different areas of Antarctica: one near the coast of East Antarctica, one near the coast of the Weddell Sea, and one in the interior of the ice sheet. Most major pressure anomalies recorded at the sites are represented correctly by the model (Figure 3). Remarkably, the pressure variations at Halley were much smaller in 1980 and 1981 than in the remaining years, This feature is reproduced properly. Correlation coefficients are calculated after the removal of the annual cycle from the monthly mean time series. Correlation coefficients of 0.92, 0.88, and 0.82 are found for Dumont d Urville, Dome-C, and Halley respectively, which are all significant at the 1% level. The correlation coefficient is largest at Dumont d Urville, which is located at a distance of only 720 km from the lateral boundary of the model domain. The surface pressure at Dumont d Urville, therefore, is more directly influenced by the ERA-15-fields that are prescribed at the lateral boundaries of RACMO. The agreement between ERA-15-fields and observations from Halley is excellent (correlation coefficient with annual cycle removed is 0.97, which is significant at the 1% level), confirming the use of the measurements from this radiosonde station in the assimilation procedure to construct the ERA-15-fields. Figure 3. Time series of modelled (dashed line) and observed (solid line) monthly mean surface pressure shown as a departure from the annual mean, at (a) Dumont d Urville, (b) Dome-C, and (c) Halley. (d) Like (c), but for ERA-15-fields. Data are described by Smith and Stearns (1993). Data for Dome-C are obtained from the Antarctic Meteorological Research Center

6 1202 N. P. M. VAN LIPZIG, E. VAN MEIJGAARD AND J. OERLEMANS To test whether individual synoptic systems are properly modelled by RACMO, the surface pressure anomaly is plotted every 6 h in Figure 4 for the stations Dumont d Urville and Dome-C for an arbitrary month (January 1990). The time series of model output and measurements significantly correlate at the 1% level, with a correlation coefficient of 0.91 for both stations. The standard deviation of the measured time series is 20 to 30% larger than the standard deviation of the modelled time series. Our results indicate that individual synoptic systems are correctly represented in the model, but that the short-term time variability of surface pressure is underestimated Temperature The data set described by Smith and Stearns (1993) is used to evaluate the calculated annual cycle of the 2 m temperature. Generally, the height of the measuring site does not correspond to the elevation of the grid box, which is representative for an area of (55 km) 2 (Table I). A procedure is developed to interpolate the calculated temperature to the height of the station. Firstly, nine grid boxes are selected that are nearest to the measuring site. The sea and sea-ice grid boxes are excluded from this selection. The model output at the remaining grid boxes is used to derive a linear relation between monthly mean 2 m temperature and elevation using a least-squares method. This linear relation is derived separately for every month of the year and for every station. The monthly mean 2 m temperature at the elevation of the station is derived by substituting the elevation of the station in this linear relation. The agreement between RACMO and the measurements is good (Figure 5). The shape of the annual cycle corresponds very well to the measurements; the long coreless winter in the interior and a reduction of the annual variation going from the interior towards the coastal regions are properly represented. The amplitude of the annual cycle in the interior is slightly overestimated. The temperature increase in spring is too fast and the temperature decrease in autumn continues longer than the measurements indicate. The model overestimates the temperature at Vostok throughout the year. Unfortunately, a similar procedure to interpolate the 2 m temperature to the elevation of the station could not be applied to the ERA-15 data set, since the horizontal resolution at which ERA-15-fields were available appeared to be too coarse. As a result, the procedure gave unrealistic values for the lapse rate. For this reason, Figure 4. Time series of modelled (dashed line) and observed (solid line) surface pressure shown as a departure from the annual mean, at (a) Dumont d Urville and (b) Dome-C. Values are plotted every 6 h for the month January Data are from the Antarctic Meteorological Research Center Table I. Elevation of the station (m a.s.l.) and the elevation in RACMO and ERA-15. For the comparison, the land-ice grid box with the elevation closest to the station elevation was selected from nine grid boxes surrounding the station Faraday Mawson Halley SANAE Byrd South Pole Dome-C Vostok Station RACMO ERA

7 SURFACE MASS BALANCE IN ANTARCTICA 1203 Figure 5. Annual cycle of the observed (solid lines), RACMO (dotted lines) and ERA-15 (dashed lines) 2 m temperature for (a) Mawson, (b) Halley, (c) SANAE, (d) Byrd, (e) Amundsen Scott South Pole, and (f) Vostok (stations are shown in Figure 1(b)). Both model values and observations are averaged over the period for all stations except Byrd, where only measurements for the period were available. Observations are described by Smith and Stearns (1993). RACMO temperatures were interpolated to the height of the stations. Note that the ERA-15-fields were extracted from the ECMWF archive on a regular 1 latitude by 1.5 longitude grid, which is not identical to the resolution of the integration (T106) the land-ice grid box with the elevation closest to the elevation of the measuring site was selected from the nine ERA-15 grid boxes surrounding the measuring site. Generally, ERA-15 represents the annual cycle reasonably well. It is noted that radiosonde measurements of the stations Mawson, Halley, and Amundsen Scott are used in the assimilation procedure to construct ERA-15. For most stations, the winter temperature is underestimated by ERA-15. The bias is too large to be explained by the difference in height between the grid box and the measuring site. These findings are consistent with Connolley and Harangozo (2001), who showed that winter temperatures in ERA-15 are 5 to 10 C too low for three stations in the interior of the ice sheet. Moreover, Van Lipzig et al. (1999) showed that ERA-15 overestimates the vertical temperature gradient near the surface in summer at a site in Dronning Maud Land, about 300 km from the coast (Svea). In fact, measurements from Svea are very appropriate for an independent evaluation of ERA-15, since measurements from this station were not used in the assimilation procedure to construct ERA Surface mass balance Three different compilations based on in situ measurement are used to evaluate the modelled spatial distribution of the surface mass balance. First of all, we use one of the most comprehensive estimates of the

8 1204 N. P. M. VAN LIPZIG, E. VAN MEIJGAARD AND J. OERLEMANS mean surface mass balance (B; bar indicates time averaging) by Vaughan et al. (1999). This compilation uses roughly 1800 glaciological measurements averaged over different time periods in combination with satellite data from a passive microwave radar. In addition, we use regional compilations for two smaller regions: the flat Ross Ice Shelf, which is largely influenced by the Transantarctic Mountains (Schwerdtfeger, 1984), and east Dronning Maud Land (Takahashi et al., 1994). Figure 6(a) and (b) respectively show the compilation of Vaughan et al. (1999) and the calculated distribution of the surface mass balance. The large-scale features of the compilation are reproduced well by the model. B is largest at the west coast of the Antarctic Peninsula and at the coast of Ellsworth Land, Marie Byrd Land, and Wilkes Land. The names of the regions mentioned are indicated in Figure 1(a). 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 year 1. (Note that, throughout the paper, B, precipitation, sublimation, and snowfall are presented in water equivalents.) The precipitation exhibits the same pattern as B (Figure 6(c)). The sublimation is generally low, except near the coast, on the Antarctic Peninsula and in the Transantarctic Mountains (Figure 6(d)). Figure 6(e) shows the difference between the modelled and compiled B. The largest positive difference occurs near the coast of Marie Byrd Land, where measurements are sparse. In some mountainous areas (Transantarctic Mountains, Dronning Maud Land, and near the Amery Ice Shelf) the surface mass balance is underestimated by the model. In these areas, the drag exerted on the mean flow by the orography of scales smaller than the size of a grid box is parameterized by the introduction of an effective roughness length as described in Section 2. In RACMO, the roughness length for momentum exchange is identical to the roughness length for sensible and latent heat exchange. By this formulation, latent heat exchange is enhanced in the mountainous regions, where the effective roughness length is large, resulting in too large a value for the sublimation. The distribution of the surface mass balance on the Ross Ice Shelf has been measured by total β activity analyses (radioactive marker) of 10 m thick firn cores obtained during four seasons between 1973 and 1978 (Schwerdtfeger, 1984) (Figure 7(a)). On the west side of the shelf, isolines of equal net accumulation are nearly parallel to the Transantarctic Mountains. Net accumulation increases from less than 100 mm year 1 in the central part of the ice shelf to more than 150 mm year 1 near the mountains. This indicates that the air rises on the west side of the ice shelf. The orientation of the isolines in RACMO is similar to the observations (Figure 7(b)), indicating that the barrier effect of the Transantarctic Mountains on the precipitation is properly represented. The calculated surface mass balance increases from the central part of the shelf to the Transantarctic Mountains, with a maximum at the base. A maximum in precipitation is modelled at the same location. The calculated sublimation increases in the Transantarctic Mountains, due to an increase in the effective surface roughness length. The surface mass balance in east Dronning Maud Land has been observed for 25 years by Japanese Antarctic Research Expeditions (JARE) (Takahashi et al., 1994). Snow stakes were placed at 2349 points. The height change in time was measured to determine the net snow accumulation. A combination of this snow-stake method and the result of total β activity and tritium analyses from ice cores has been used to make a compilation of the surface mass balance (Figure 8). The surface mass balance decreases with distance to the coast to a value smaller than 50 mm year 1 south of 75 S; this feature is properly represented in the model. The calculated surface mass balance in the coastal region is somewhat underestimated. In mountainous regions, a negative surface mass balance is observed (blue ice areas). One such area is reproduced by the model. It is doubtful, however, whether this feature is simulated for the proper reason. Divergence of snow drift (caused by the deflection of the flow around an obstacle) and enhancement of sublimation (caused by a reduced surface albedo of ice compared with snow) are important for the development and maintenance of blue ice areas (Takahashi et al., 1988; Bintanja and Reijmer, 2001), but these processes are not taken into account in RACMO. Only enhancement of turbulent sensible and latent heat exchange by eddies that are generated in mountainous regions is parameterized in RACMO by the introduction of an effective roughness length in mountainous areas (Figure 8(c)). Krinner (1997) found that decreasing the roughness length for heat results in a decrease in sublimation, but it does not significantly affect the outcome of other climate parameters.

9 SURFACE MASS BALANCE IN ANTARCTICA 1205 Figure 6. (a) Surface mass balance (mm year 1 ) compilation based on in situ observations (Vaughan et al., 1999). Mean calculated (b) surface mass balance, (c) precipitation, and (d) sublimation for the period (e) Simulated minus measured surface mass balance. A Laplacian filter (X X X) is used to smooth the fields X 4. SPATIAL VARIATION The spatial distribution of the precipitation on the Antarctic continent is largely determined by the topography. In the high interior of Antarctica, precipitation is less than 50 mm year 1, whereas near the coast the

10 1206 N. P. M. VAN LIPZIG, E. VAN MEIJGAARD AND J. OERLEMANS Figure 7. (a) Measured (cm year 1 ) and (b) calculated (mm year 1 ) surface mass balance distribution on the Ross Ice Shelf. The measured distribution is derived from total β activity analyses of 10 m thick firn cores obtained during four seasons between 1973 and 1978 (Schwerdtfeger, 1984). The shading of the dots in (b) indicates the value for the surface mass balance at each ice shelf grid box and the dashed lines indicate the elevation (m) precipitation sometimes exceeds values of 500 mm year 1 (Figure 6(c)). The air in the high interior is cold and, therefore, the amount of water vapour that is available for the formation of precipitation is small. In addition, precipitation amounts in the interior are small due to the lack of synoptic forcing; the elevated terrain acts to block the penetration of synoptic disturbances onto the plateau. Another important factor that controls precipitation is the surface slope (sl), defined as h, whereh is the elevation. When the slope is steep and the large-scale wind is directed upslope, the rising of the air results in enhanced precipitation. Other topographical/geographical parameters that are likely to affect the precipitation distribution are the distance to the coast (continentality: co) and the latitude (la) (Fortuin and Oerlemans, 1990). For all topographical parameters, the correlation with the 14 year mean precipitation is significant at the 1% level (Table II). Precipitation increases with slope and latitude (defined as being negative in the Southern Hemisphere) and decreases with elevation and continentality. By using multiple linear regression analysis, Table II. Correlation coefficient r between the precipitation (mm year 1 ) and the topographical parameters elevation h, slope (sl), continentality (co), 1/ co, and latitude (la) (defined as being negative in the Southern Hemisphere). r 2 is the explained variance by one parameter. The t-value is defined as the ratio between the coefficient in the linear equation (derived using the multiple linear regression analysis) and the standard error. A high absolute t-value indicates that the predictor is useful h (km) sl (m km 1 ) co (km) 1/ co (km 0.5 ) la ( ) r r t

11 SURFACE MASS BALANCE IN ANTARCTICA 1207 Figure 8. (a) The surface mass balance (mm year 1 ) in east Dronning Maud Land compiled from snow-stake measurements by JARE (Takahashi et al., 1994). (b) RACMO surface mass balance in east Dronning Maud Land for the period (c) The roughness length (mm) as prescribed in the model we quantify which part of the spatial distribution of precipitation can be modelled as a function of the topographical parameters alone without taking into account explicitly the large-scale atmospheric flow. That some effects of the large-scale atmospheric flow are implicitly taken into account in this approach cannot be prevented. For example, a steep slope enhances precipitation only when the wind is directed upslope. Another problem is that the relation between continentality and precipitation is obviously not linear; the gradient in precipitation is largest near the coast. Using 1/ co instead of co improves the correlation from 0.54 to For this reason, we have used 1/ co in the multiple linear regression analysis. Since the predictors are dependent, we carefully analyse the result of removing predictors from the model. When all four topographical parameters are included, 50% of the variance is explained by the multiple linear regression model. The t-value (defined as the ratio between the coefficient in the linear equation and the

12 1208 N. P. M. VAN LIPZIG, E. VAN MEIJGAARD AND J. OERLEMANS Figure 9. (a) Difference between the 14 year mean precipitation calculated with RACMO and the estimate for precipitation from the multiple regression analysis with the continentality as input parameter (Equation (1)). (b) 14 year mean geopotential at 500 hpa calculated with RACMO standard error) provides information regarding the relative importance of each predictor. A high absolute t-value indicates that the predictor is useful. Consecutively removing the predictors with the lowest t-value does not significantly influence the explained variance. By only using 1/ co as a predictor, the explained variance is 49%. The equation with the smallest value of the squared vertical distances between RACMO output and the linear regression line is P = co (1) where precipitation is in millimetres per year and co is in kilometres. Note that this equation is only valid for the present-day climate. Figure 9(a) shows the difference between the RACMO output and the statistically determined precipitation using Equation (1). In Ellsworth Land, Marie Byrd Land, and Wilkes Land, the RACMO precipitation is larger than the statistical relation (Equation (1)) indicates. This can be explained by the atmospheric circulation. The mean flow at 500 hpa is directed from sea to land, indicating that locally warm moist air is advected to the ice sheet (Figure 9(b)). The most prominent area where RACMO precipitation is smaller than the precipitation derived using Equation (1) is Victoria Land, where the mean flow at 500 hpa is directed from the interior to the coast. In Dronning Maud Land, Enderby Land, and Coats Land, RACMO precipitation is slightly smaller than the topographically determined precipitation, because the westerlies in this region lie relatively far away from the continent. 5. TEMPORAL VARIABILITY 5.1. Resolved-scale atmospheric moisture transport Before studying the temporal variability of the surface mass balance averaged over the grounded Antarctic ice sheet, it is important to identify to what extent the surface mass balance differs from the resolved-scale poleward atmospheric moisture transport. In order to represent the mechanisms that cause variability correctly,

13 SURFACE MASS BALANCE IN ANTARCTICA 1209 it is desirable that the resolved-scale poleward atmospheric moisture transport does not differ greatly from the total transport. Connolley and King (1996) showed that this is not always the case; they found that in the UK Meteorological Office GCM, with a grid spacing of approximately 270 km, only 30% of the net accumulation in the Antarctic sector between 2.4 W and E is carried by resolved-scale transport. The budget equation expressing the surface mass balance as a function of transport and storage terms is given by (Peixoto and Oort, 1983): B = P E = Q 1 W (2) ρ L t where the angled brackets indicate averaging in space, the bars indicate time averaging, W (kg m 2 )isthe vertically integrated specific humidity, ρ L is the density of water, and Q is the vertically integrated horizontal moisture-flux vector, defined as Q = 1 ρ L ps 0 qu g dp (3) where q is the specific humidity, u is the horizontal wind vector, g is the acceleration due to gravity and p is the pressure. (Note that we use this definition in order to express the atmospheric poleward moisture transport ( Q ) in the same units as B, namely millimetres of water equivalent.) For annual averages, the second term on the right-hand side of Equation (2) is negligible (Peixoto and Oort, 1983). The atmospheric moisture transport across the boundary l of a closed area (for example the grounding line of the Antarctic ice sheet) can be estimated from vertical profiles of q and u with the use of the Gauss theorem: Q = 1 Q n dl (4) A where A is the surface of the enclosed area and n the unit vector directed outwards, normal to the boundary of this region. We used modelled vertical profiles of q and u to calculate the net resolved-scale poleward moisture transport across the grounding line Q RACMO. The resolved-scale transport is 127 mm year 1, whereas the mean surface mass balance within the grounding line ( B ) is 156 mm year 1. In RACMO, resolved-scale flow is responsible for 81% of the moisture transport to the grounded Antarctic ice sheet. The difference between Q RACMO and B RACMO is caused by: (i) horizontal diffusion of moisture in the model that is not included in Q RACMO ;and (ii) moisture transport by eddies on time scales that are not taken into account in calculating Q RACMO because q and u are only archived at limited temporal resolution (here 6 h). Horizontal diffusion is introduced in order to ensure computational stability and to account for the effect of sub-grid-scale horizontal moisture transport. In RACMO, horizontal diffusion is calculated along model levels (η levels). Owing to large gradients in specific humidity near steep orography, moisture is effectively transported by diffusion across the grounding line. The difference between Q RACMO and B RACMO is therefore greatest at the steep edges of the ice sheet. This is confirmed by the fact that the resolved-scale moisture flow across 65 S is responsible for 97% of the total moisture transport across 65 S. This fraction is much larger than for the flow across the grounding line, indicating that horizontal diffusion of moisture is the dominant factor for the difference between resolved-scale and total moisture transport across the grounding line. In ERA-15, the difference between resolved-scale and total moisture transport onto the grounded ice is smaller than in RACMO; it is found that Q ERA is 93% of B ERA. Beyond the effect of horizontal diffusion and eddies on time scales shorter than 6 h, there are two effects that cause additional differences between Q ERA and B ERA :

14 1210 N. P. M. VAN LIPZIG, E. VAN MEIJGAARD AND J. OERLEMANS (iii) deficiencies in the model used to construct ERA-15 are systematically corrected by assimilating data at the end of the forecast to construct the new analysis; therefore, there is no conservation of moisture in ERA-15; (iv) after Genthon and Krinner (1998), we used the last 6 h of the 12 h forecasts to calculate B ERA.These forecasts are available twice every day and, therefore, we used only a 12 h period per day to calculate the mean net ERA-15 accumulation. It is possible that these two additional effects oppose the effect of the horizontal diffusion. Genthon and Krinner (1998) studied the moisture transport in the area south of 70 S. In this area, the effects I and II play a minor role, since the enclosing boundary does not coincide with steep orography and gradients in q are small. They found that Q ERA is 12% larger than B ERA, indicating that the contribution from III and IV is negative for the area south of 70 S. From our study, it cannot be concluded whether the separate terms I to IV are small in ERA-15, or whether the separate terms are large but counteracting Year-to-year variability We study temporal variability of the surface mass balance averaged over the grounded ice using the RACMO output and the ERA-15-fields. Figure 10 shows the 12 month centred running mean of B RACMO, Q RACMO, B ERA,and Q ERA. The year-to-year variability of all the signals is similar; the standard deviation of the annual mean values is 6 to 7% of the 14 year mean value. The standard deviation of annual mean values for Q RACMO and B RACMO is 8.6 mm year 1 and 9.4 mm year 1 respectively. The correlation between the monthly mean values of Q RACMO and B RACMO with the annual cycle removed is very large (0.98). These results suggest that there is a small variability in the effect of horizontal diffusion and eddies on short time scales. ERA-15 fields are used to drive RACMO from the lateral boundaries and from the sea surface. The correlation between the monthly mean values of Q RACMO and Q ERA with the annual cycle removed is 0.75, indicating that the ERA-15 forcing fields determine some part of the variability in the moisture convergence in RACMO. The correlation between the monthly mean values of Q ERA and B ERA with the annual cycle removed is high (0.93), but, due to the effect of the assimilation procedure and the use of a 12 h sample, this correlation is smaller than for RACMO (0.98). Figure 10. The 12 month centred running mean of the atmospheric poleward moisture transport ( Q ; thin lines) and the surface mass balance ( B ; thick lines), calculated from RACMO fields (solid lines) and from ERA-15-fields (dotted lines)

15 SURFACE MASS BALANCE IN ANTARCTICA 1211 The spatial distribution of the normalized temporal standard deviation of the annual mean surface mass balance in RACMO is shown in Figure 11. There is a large temporal variability on the Ross Ice Shelf and to a lesser extent the Filchner Ronne Ice Shelf and the Amery Ice Shelf. Apart from the fact that the annual accumulation is small on the ice shelves, atmospheric disturbances are more active in these regions than higher on the ice sheet, where the disturbances penetrate less frequently. The variability is small on the plateau, in Wilkes Land, and on the east side of the Antarctic Peninsula. It is large in Dronning Maud Land. To investigate which mechanisms are responsible for the year-to-year variability in B, we study the relation between B and (near-)surface mean meteorological quantities over the grounded ice, namely: surface temperature T s, surface pressure p s, 7 m temperature T 7, 7 m specific humidity q 7,7mwind speed u 7, 500 hpa temperature T 500, 500 hpa specific humidity q 500, vertically integrated water vapour qρ dz, and vertically integrated liquid water q L ρ dz (Table III). The mean surface mass balance over the grounded ice does not significantly correlate with any of the variables considered, except for the vertically integrated liquid water. Surprisingly low is the correlation between B and T s, T 7, T 500, q 7, q 500,and qρ dz, indicating that the effect of the temperature and humidity variations on the year-to-year variations in B is small. Figure 11. The standard deviation of the annual mean surface mass balance over a period of 14 years, normalized with B Table III. Correlation coefficient between the annual mean surface mass balance B on the one hand, and, on the other hand, the annual mean surface temperature T s, surface pressure p s, temperature of the lowest model level at 7 m T 7, 7 m specific humidity q 7, 7 m wind speed u 7, temperature at the 500 hpa level T 500, 500 hpa specific humidity q 500, vertically integrated water vapour qρ dz, and vertically integrated cloud water q L ρ dz, all averaged over the grounded ice. Note that in all the tables the autocorrelation effects are taken into account to calculate the significance levels T s p s T 7 q 7 u 7 T 500 q 500 qρ dz q L ρ dz B a a Correlation is significant at the 1% level.

16 1212 N. P. M. VAN LIPZIG, E. VAN MEIJGAARD AND J. OERLEMANS Table IV. Correlation coefficient between annual mean values of the surface mass balance averaged over the grounded ice B, transport of moisture into the model domain A os, precipitation on the sea, sea ice, and ice shelves P sea, and evaporation from the sea, sea ice, and ice shelves E sea.since the matrix is symmetric, only the part above the diagonal is filled B A os P sea E sea B A os a 0.27 P sea E sea 1.00 a Correlation is significant at the 1% level. Over the grounded ice and over the sea and sea ice, p s, q, andt are mutually correlated. In warm years, the specific humidity and the surface pressure are high. In addition, when air over the sea is warm and humid with high surface pressure, these conditions also prevail over the ice sheet. B does not significantly correlate with the moisture transport from outside the model domain (A os ; r = 0.25), nor with the evaporation from sea and sea ice (r = 0.27) (Table IV). These results suggest that the year-to-year variability of B is driven by the dynamics of the flow inside the model domain. This hypothesis is confirmed by a high anti-correlation between annual mean values for B and the meridional component of the 7 m wind speed at the grounding line (r = 0.90). The wind speed at the grounding line is calculated as an average over 489 grid points that are within the grounding line and which have a nearest neighbour outside of the grounding line. On average, the meridional component of the 7 m wind speed at the grounding line is directed from land towards the sea due to the katabatic forcing. In years when synoptic systems are active, the katabatic wind is frequently interrupted by events during which moist air is transported from sea to land at low atmospheric levels. This results in a relatively low annual mean meridional wind speed. Significant negative correlations between B and meridional wind speed at the grounding line are found at the lowest four model levels up to a height of 800 m. We found no significant correlation between temperature or specific humidity at the grounding line and B. We conclude that the dynamics of the flow within the model domain influence both the year-to-year variability of the near-surface winds and the year-to-year variability of B. The forcing at the lateral boundaries affects the dynamics of the flow within the model domain (pressure anomalies at several stations are correctly represented), but does not directly impose the moisture advection towards the ice sheet (correlation between B and A os is not significant). On the time scale considered, no relation is found between B and tropospheric temperature or specific humidity Seasonality There is no clear annual cycle in the precipitation averaged over the grounded Antarctic ice (Figure 12). P is largest in autumn, but the annual variation is comparable to the standard deviation. Most of the sublimation occurs in summer, with a small year-to-year variability. The net accumulation shows a clear minimum in the summer months, due to the high sublimation in that season. Figure 13 shows for every grid box the season in which the precipitation is highest. Seasonality of precipitation appears to be much larger on a regional scale than averaged over the ice sheet. The seasonality of precipitation is determined by the amount of moisture in the atmosphere, which is a function of temperature, and the dynamics of the large-scale flow in relation with the orography. To study to what extent these factors are of importance, we calculated the correlation of the monthly mean precipitation with (i) temperature at 500 hpa (T 500 ), and (ii) the dot product of the wind vector at 500 hpa and the local slope vector (v 500 sl), which is a measure for the orographically induced lifting of the air (Table V). Precipitation in the interior is largest in summer (Figure 13), when the temperatureand the saturation specific humidity of air are highest. The correlation between monthly mean values of T 500 and P is In the interior,

17 SURFACE MASS BALANCE IN ANTARCTICA 1213 Figure 12. RACMO precipitation (dotted line), sublimation (solid line), and net accumulation (dashed line) spatially averaged over the grounded ice sheet and temporally averaged over the period The bars indicate the standard deviation, calculated from 14 monthly mean values Figure 13. The season in which the modelled precipitation is highest. Only grid boxes where this seasonal precipitation is larger than 45% of the annual accumulated precipitation are shaded. From dark to light, the maximum is simulated in summer (DJF), autumn (MAM), winter (JJA), and spring (SON) the effect of the dynamics of the flow is small because the steep edges of the ice sheet act as a barrier for low-pressure systems. This is different in the coastal areas. In Dronning Maud Land and in the area of the Ross Ice Shelf, the precipitation is highest in autumn. In the western part of Wilkes Land, the precipitation is highest in winter. In these three regions, correlations between P and v 500 sl are high, showing that the flow at 500 hpa has a distinct impact on the seasonality. Only in the area of the Ross Ice Shelf is the correlation significant at the 1% level. Near the Filchner Ronne Ice Shelf, the precipitation reaches a maximum in spring. The correlation of precipitation with both T 500 and v 500 sl is smaller than for the other regions. In summary, the seasonal cycle of precipitation is variable in space, a result that is consistent with Genthon et al. (1998), who used weather forecasts and high-resolution climate models to study seasonality of precipitation. Like in our study, Genthon et al. (1998) found large areas where the autumn peak was dominating. On the other hand, in the models used by Genthon et al. (1998), no regions with summer maxima in precipitation were found, whereas a summer maximum was found in most of the interior of the ice sheet in RACMO.

18 1214 N. P. M. VAN LIPZIG, E. VAN MEIJGAARD AND J. OERLEMANS Table V. Correlation coefficient between precipitation and both temperature at 500 hpa and the dot product between the wind vector at 500 hpa and the slope vector (v 500 sl). The correlation coefficient is calculated from climatological (14 year) monthly mean values averaged over a specific area: DML (Dronning Maud Land) is the area between 30 W and 60 E with maximum precipitation in MAM (see Figure 13); Plateau is the area with an elevation larger than 2.5 km and a maximum precipitation in DJF; Wilkes is the area between 90 and 130 E and a maximum precipitation in JJA; Ross is the area between 120 W and 120 E and a maximum precipitation in MAM; Filchner Ronne is the area between 90 and 0 W and a maximum precipitation in SON DML Plateau Wilkes Ross Filchner Ronne MAM DJF JJA MAM SON v 500 sl a 0.44 T b a Correlation is significant at the 1% level. b Correlation is significant at the 5% level A note on the effect of seasonality of precipitation on ice-core signals Signals that are stored in the ice are deposited by precipitation. Therefore, the proxy for a variable that is found in the ice core is determined by the mean of this variable, weighted by the accumulation (Krinner et al., 1997). We use model output to illustrate the effect of seasonal variations in accumulation on the proxy for temperature at the three drilling sites Dome-C, Dome-F, and DML05 (sites are indicated in Figure 1(b)). Figure 14 shows the annual mean modelled surface temperature T s, together with the temperature weighted by accumulation T weight : T weight = B i T i i (5) B i i where B i is the monthly mean accumulation and T i is the monthly mean surface temperature. Generally, the year-to-year variability of the seasonality of accumulation enhances the year-to-year variability of T weight. For example, at Dome-C, the temperature difference between 1985 and 1986 is 2 K, but due to extreme accumulation in February 1986 (28% of the annual accumulation occurred during that month), T weight suggests a difference exceeding 10 K. For all three sites, the standard deviation of T weight (which determines the proxy signal) is enhanced by a factor two to three due to variations in seasonality of accumulation. To demonstrate the effect of changes in seasonality on a time scale of 7 years, we have divided the 14 year period into two sub-periods (P 1 is the period and P 2 is the period ). Also on this time scale, changes in seasonality are found to affect the proxy for temperature in the core. For Dome-F, the weighted temperature difference between P 1 and P 2 is 2.4 times the difference in the surface temperature (1.6 K and 0.7 K respectively). For Dome-C, the difference between P 1 and P 2 is 0.6 K for T s and 0.0 K for T weight ;for DML05, the difference between P 1 and P 2 is 0.4 K for T s and 0.5 K for T weight. The effect of variations in precipitation on the ice core signals will be studied in more detail in a forthcoming paper. 6. CONCLUSIONS To gain a better understanding of the mechanisms behind spatial and temporal variations of the Antarctic surface mass balance, a 14 year ( ) integration has been performed with a regional atmospheric climate model at a horizontal resolution of 55 km. The model is driven from the boundaries (lateral boundaries and sea surface) by ECMWF re-analyses.