Annual melt duration from Special Sensor Microwave/Imager satellite data is used in a simple surface mass balance (SMB) model to estimate runoff rates, mass balance, and surface elevation changes for the Greenland ice sheet. Estimates are made using a variable accumulation rate that is based on precipitation from a dynamic climate model using European Centre for Medium-Range Weather Forecasts analysis data. The overall SMB is positive for the 1988–1999 period, but it is near the estimate of calving rates. Two years, 1995 and 1998, show a negative SMB. There is some evidence that years with higher runoff are associated with lower accumulation and that years with higher than average runoff in southern Greenland are associated with lower than average runoff in the north. Variations in accumulation rates dominate SMB variability in east and southeast Greenland, while runoff rates dominate in west Greenland. SMB is also used to estimate elevation changes resulting from trends in SMB during the 1988–1999 and 1993–1999 time periods, which in general agree with laser altimeter finding of thinning below 2000 m above sea level and near equilibrium above that elevation.
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 Predictions of how any climate change may affect the ice sheets and, therefore, global sea level is a critical question in global change research. A better understanding of the dynamics of the Greenland ice sheet, variability in its ablation rate and mass balance, and how these rates respond to changes in climate, is necessary to address the question of what role the ice sheets play in current or projected changes in global sea level. Until recently, costly and time-consuming glaciological (e.g., ablation stake) or meteorological measurements have been the most common means for assessing the ablation and runoff rates and mass balance on the ice sheets. Unfortunately, due to the paucity of these measurements, surface mass balance rates are often extrapolated across great distances.
 More recently, airborne laser altimeters [e.g., Krabill et al., 2000] and satellite radar altimeters [e.g., Zwally, 1989; Zwally et al., 1998; Davis et al., 1998] have been used to measure surface elevation changes of the ice sheet. While altimetry measurements may indicate thickening or thinning of the ice sheet, they do not indicate whether this change is due to differences in surface mass balance or ice dynamics. Measurements of the mass balance components, accumulation, sublimation, runoff and calving, are necessary as well as an understanding of ice dynamics in order to fully ascertain the role of climate change on mass balance of the ice sheet.
 Passive microwave satellite sensors have been used to map the spatial extent and frequency of snowpack melting on the ice sheet and continuous time series are available since October 1978 [Mote and Anderson, 1995; Abdalati and Steffen, 1997, 2001]. These sensors may be used to estimate the frequency with which melt occurs due to the increase in emissivity as liquid water forms in previously dry snow. With some assumptions about the distribution of daily mean temperatures, the microwave-derived annual melt duration can be used to estimate the number of positive degree days (the total sum of the number of degrees the average daily temperature exceeded 0°C.) and the potential runoff rate for use in a surface mass balance (SMB) model. While this method also requires estimates of snow accumulation rates, it takes advantage of the relatively complete spatial coverage and long time series of passive microwave satellite observations. Mote  and Hanna et al.  used this approach to make quantitative runoff estimates from the passive microwave melt frequency. This work extends that of Mote  by examining the entire ice sheet, rather than individual transects, and uses Special Sensor Microwave/Imager (SSM/I) rather than Scanning Multichannel Microwave Radiometer (SMMR) as the microwave data source. This work further improves upon Mote  and the microwave product given by Hanna et al.  by using an updated meltwater retention fraction parameterization, including a variable accumulation in SMB calculations, and estimating elevation change based on the SMB.
 The primary objective of the research project is to examine interannual variability in surface mass balance for the Greenland ice sheet using runoff rates based on annual melt duration from microwave brightness temperatures. Trends in surface mass balance are then used to examine the possible role of SMB on observed trends in surface elevation.
 Interannual variability in SMB on the Greenland ice sheet is examined by extracting runoff rates from an annual time series of melt duration based on SSM/I brightness temperature time series. The methodology can be summarized in the following steps. First, time series of daily average SSM/I 37 GHz, horizontal polarization, brightness temperatures on a 25 × 25 km grid are examined for the number of days that exceeded a critical brightness temperature. The number of days with melt are summed to arrive at the annual melt frequency. Secondly, the annual melt frequencies are used to create mean summer (May–August) temperatures and positive degree days (PDDs) based on an assumed standard deviation of 4°C in summer temperatures. The positive degree days are then used in a surface mass balance model incorporating accumulation rates from a dynamic climate model as well as global assumptions of meltwater retention fraction and sublimation rate. The fraction of liquid precipitation is estimated from the melt frequency. The PDDs are used with fixed degree-day factors for snow and ice to estimate potential runoff that is then used to drive a simple surface mass balance model. Trends in surface mass balance are used to estimate the role of SMB in recent surface elevation changes.
2.1. Melt Duration
 The first step in estimating runoff rates and surface mass balance is to create time series of annual melt duration based on the microwave radiometric observations. The gridded SSM/I data were obtained from the National Snow and Ice Data Center (NSIDC) archive of brightness temperatures on a 25 × 25 km grid on a polar stereographic projection [National Snow and Ice Data Center (NSIDC), 1992]. A raster land mask was digitized from the Quaternary Map of Greenland published by the Geological Survey of Greenland. This mask was used in conjunction with the SSM/I water and coastline masks to eliminate all grid cells not covered by at least 50 percent ice or grid cells with any permanently standing water. The unmasked grid cells available for analysis covered a total area of 1.648 million km2, including parts of ice caps separate from the ice sheet. The ice sheet covers approximately 1.701 million km2 [Weidick, 1985]. The mixed pixels included in the NSIDC polar grid mask near the margin includes some ice-free land, but the smaller footprint of the 37 GHz channel (compared to lower frequencies) minimizes any influence of land area on the SSM/I-based products. Nevertheless, it is necessary to be cautious regarding interpretation of SSM/I-derived melt frequencies near the margin.
 A simple radiative transfer model is used to estimate the SSM/I 37 GHz, horizontal polarization (37H) brightness temperatures associated with melting snow and ice [Mote and Anderson, 1995]. The modeled brightness temperatures are used as thresholds. If the observed brightness temperature (TB) exceeds the modeled TB, melt is said to have occurred that day. The number of days with melt is calculated for each of the 2,637 grid cells over the ice sheet each summer from 1988 to 1999.
 The annual accumulation data used in the SMB model are derived from annual precipitation data from Bromwich et al. . This data set is based on dynamical and topographic forcing of precipitation using European Centre for Medium Range Weather Forecasts (ECMWF) analysis data. The precipitation data are placed into the NSIDC polar grid using a nearest neighbor analysis. The precipitation for each NSIDC polar grid cell is assigned the data values from the ECMWF grid cell (on a 50 km grid) that was closest to the center of the NSIDC polar grid cell.
 The Bromwich et al.  values are total precipitation. In order to arrive at net accumulation, one must reduce the precipitation by sublimation and the fraction of precipitation falling in liquid form. Assuming an even distribution of precipitation throughout the year and a rain/snow threshold of 0°C., the frequency of days with melt is used to estimate the total fraction of precipitation falling as liquid. This amount of liquid precipitation is estimated as roughly 25 km3 yr−1 on average for the area within the masked grid. Bromwich et al.  noted a difference of 10% between glaciological and atmospheric measures of precipitation, much of which they attributed to sublimation, but they could not evaluate the sublimation loss due to the error in the precipitation estimate. In this work, sublimation is estimated based on the findings of Box and Steffen  as 12% of accumulation. This corresponds to roughly 75 km3 yr−1 on average.
 The average annual precipitation from Bromwich et al.  for 1988–1999 on the masked NSIDC polar grid is roughly 391 mm yr−1 (645 km3 yr−1). The Bromwich et al.  values agree well with glaciological measurements of accumulation along the 2000 m a.s.l. NASA PARCA transect of ice cores and reasonably well in the interior [McConnell et al., 2000a]. However, the Bromwich et al. [2001, Figure 2b] precipitation maximum values are in excess of 800 and 1000 mm yr−1 in southwest Greenland, while the Bales et al. [2001, Figure 1] map indicates maximum accumulation of only of 500 to 650 mm yr−1. In is important to note that the two data sets are based on a different “time window,” the precipitation is an average for the 1988–1999 period, whereas the ice cores average over a much longer period. A glaciological measure of accumulation, such as the Bales et al.  estimates, were not used in this study because even with the inclusion of coastal precipitation, accumulation must be interpolated into the ablation zone. Unfortunately, few reliable accumulation values exist for the ablation zone of the Greenland ice sheet. This should be addressed with additional studies of snow accumulation in the ablation zone.
2.3. Runoff and Mass Balance Modeling
 This portion of the research is designed to: (1) use the SSM/I-derived melt frequency to calculate mean summer (May–August) temperatures and annual positive degree days (PDDs), (2) use the PDDs in a degree-day model to estimate the runoff rate, and (3) incorporate accumulation from the dynamic climate model to estimate surface mass balance (SMB).
 This approach assumes that the microwave melt frequency (the percentage of days with melt), calculated on a monthly basis, is equal to the probability that the surface temperature exceeds 0°C. Mote  showed this to be a reasonable assumption for three transects on the ice sheet where detailed meteorological observations are available. The number of PDDs from a normal temperature distribution based on Braithwaite , as given by Jóhannesson et al.  may be expressed as:
where T is temperature, Tm is mean monthly temperature and σ is the standard deviation of the temperature distribution.
 The satellite-derived mean summer temperatures are calculated in a similar fashion to summer temperatures that are used to parameterize ice sheet models based on mean surface air temperature and/or 10m snowpack temperature observations [Jóhannesson et al., 1995]. A snow and ice melt model is used to account for different degree-day factors for snow and ice surfaces and to account for the formation of superimposed ice. Potential runoff rates are calculated by multiplying the number of PDDs by the appropriate degree-day factor. The model used degree-day factors of 0.008 m d−1 °C−1 for ice and 0.003 m d−1 °C−1 for snow [Braithwaite, 1995]. The degree-day factors are also the same used by Krabill et al.  to extrapolate coastal meteorological data into the ablation zone of the Greenland ice sheet. Jóhannesson et al.  used a standard deviation of 3.5°C based on a best fit with observations in west Greenland while Reeh  assumed an annual standard deviation in temperature of 4.5°C. This research uses a value of 4°C. as suggested by R. J. Braithwaite (personal communication, 1985). This value also falls within the range of standard deviation values used in previous research.
 The melt water in the firn is assumed to refreeze until the amount of superimposed ice reaches 0.291 of the annual accumulation rate. This value was suggested by Janssens and Huybrechts , which they determined was within 1% of the retention fraction (the sum of capillary water and refrozen meltwater) as determined by a more sophisticated retention model. Once the melt water retention fraction is exceeded, the model permits additional melt to runoff.
Mote  used this method to calculate runoff rates for transects from SMMR data and compare the mass balance estimates to stake ablation measurements in west Greenland. Although SMMR rather than SSM/I data were used in that study, the quantifiable sources of error for SSM/I were estimated at ±10%. This error range assumed the use of individual swath brightness temperatures rather than the gridded product used in this study and should be viewed as a lower bound for the potential error.
2.4. Surface Elevation
 The annual variations in SMB were used to estimate the component of surface elevation change that may be due to short-term changes in climate, as manifested in accumulation and runoff. SMB trends for each NSIDC polar grid cell were converted to annual changes in surface elevation by assuming fixed densities (350 kg m−3 for snow and 900 kg m−3 for ice). Trends in surface elevation were examined for the available SSM/I time period (1988–1999) as well as the time span of NASA Airborne Topographic Mapper (ATM) missions over Greenland (1993–1999).
3.1. Runoff and SMB
 A mean annual runoff rate for the Greenland ice sheet of 278 km3 yr−1 is estimated with a range in annual runoff rates from approximately 153 km3 yr−1 (1992) to 519 km3 yr−1 (1995) (Figure 1 and Table 1). Approximately 15.1% of the unmasked portion of the ice sheet experienced net ablation on average, but this varies from 9.7% in 1992 to 23.1% in 1995, using the masked NSIDC polar grid (Figure 2 and Table 1). Annual accumulation based on the Bromwich et al.  precipitation ranges from 605 km3 yr−1 (1995) to 691 km3 yr−1 (1991) (Table 1).
Table 1. Mass Balance Components and Accumulation/Ablation Areas (As a Percentage of the Ice Sheet Surface Area in the Masked NSIDC Polar Grid) Calculated Using SSM/I-Derived Runoff and a Variable Accumulation Rate Based on Bromwich et al. 
Precipitation, km3 yr−1
Accumulation-Sublimation, km3 yr−1
Runoff, km3 yr−1
SMB, km3 yr−1
 It is significant to note that in many cases the years with the lowest precipitation rates were also those years with the highest runoff rates. The year 1995 had the lowest precipitation (605 km3) and the highest runoff rate (519 km3), and 1998 had the third lowest precipitation (612 km3) and the second highest runoff rate (457 km3) (Table 1). Both of these years were likely in negative mass balance when a calving rate is included of 160 km3 yr−1 to 260 km3 yr−1 [Bigg, 1999]. The years 1991 and 1992 had the highest and second highest accumulation rates, 691 km3 and 684 km3 but had the third lowest and the lowest runoff rates of 212 km3 and 153 km3 (Table 1). A scatterplot of annual accumulation versus runoff hints at a relationship of decreasing accumulation with increasing runoff, with the exception of 1989 and, to a lesser extent, 1988 and 1994 (Figure 3). Those years had relatively low accumulation and runoff. Alternatively, if 1995 and 1998 are considered outliers, no relationship is suggested between annual runoff and accumulation. A linear regression applied to the annual accumulation and runoff data (r2 = 0.44) suggests a 1 km3 yr−1 increase in runoff for every 2.4 km3 yr−1 decrease in accumulation.
 Using the lower end of the range of calving rates given by Bigg  yields a positive mass balance in all but two years, 1995 and 1998. The higher end of the calving range also results in negative mass balance in 1997 (>−50 km3 yr−1) and near equilibrium conditions in 1988, 1993, 1996 and 1999 (−50 to +50 km3 yr−1). The overall mean surface mass balance is positive by roughly 260 km3 yr−1 during 1988–1999, which is at the upper end of the range of calving estimates.
 Changes in SMB on an interannual basis vary by region of the ice sheet. A comparison of 1995 (Figure 4) and 1998 (Figure 5) demonstrates this difference. These two years apparently had a negative SMB for the ice sheet as a whole. During 1995, the ice sheet experienced greater runoff in west Greenland, with an ELA exceeding 2000 m a.s.l. in some locations, but 1998 showed greater runoff in northern Greenland. Differences in eastern Greenland were mostly due to greater accumulation in that region in 1998. The year with the most positive SMB, 1992, exhibited lower runoff in all regions of the ice sheet and had more accumulation in southeastern and southern reaches of the ice sheet (Figure 6). Accumulation variations dominated the SMB variability in southeast Greenland, likely due to the relatively high accumulation rates due to the region's proximity to moisture influx from the Iceland Low. Variations in SMB in west Greenland were dominated by changes in runoff. This supports the findings of McConnell et al. [2000b], who used accumulation rates from shallow firn cores at approximately 2000 m a.s.l. to show that interannual variability in accumulation is large, even when averaged over broad regions of the southern ice sheet, particularly in southeast Greenland. The relatively small runoff and accumulation values in northern Greenland result in neither component dominating the SMB.
3.2. Surface Elevation Trends
Krabill et al.  analyzed ATM data and found a general pattern of thinning below 2000 m a.s.l. and a net balance at elevations above 2000 m during 1993–94 to 1998–99. They attributed this pattern mostly to a change in ice dynamics, although they did address changes in climate as a possible explanation. The trend in SMB from 1988–1999 roughly matches the elevation trends found by Krabill et al.  with a thinning generally below 2000 m a.s.l. This thinning appears to be occurring at higher elevations in the south, up to 2400 m, and lower elevations, only up to 1000–1200 m a.s.l. in the north. The most substantial thinning appears to be between 1400–1600 m in southern Greenland and 1200–1400 m in western Greenland, with thinning values exceeding 25 cm yr−1 in some locations (Figure 7). Slight thickening is mostly confined by the 70°N and 80°N parallels, above 2000m a.s.l., with the exception of the summit region of the north dome of the ice sheet. Thickening rates are generally in the range of only 2–6 cm yr−1.
 In order to make a more direct comparison with the Krabill et al.  results, this same comparison is made for SMB-derived elevation trends during 1993–1999. Because of the shorter time period, fewer locations show significant trends than for the longer time period. Nevertheless, the same pattern of thinning at lower elevations and near equilibrium to slight thickening above 2000m either side of the ice divide remains (Figure 8). There is a clearer indication of substantial thickening near 68°N, 40°W in southeast Greenland, and near the Sukkertoppen ice cap in southwest Greenland, which is also apparent in the Krabill et al.  results. This is even more evident in the 1994–1999 time period (not shown), as well as a clear SMB-induced thickening on the southwest portion of the south dome above 2000m. Regions of SMB-induced thinning are most clear between 69°N and 76°N near 1600m a.s.l. in west Greenland.
 There is evidence of SMB-induced thickening during 1993–1999 at lower elevations in east Greenland and in the west near the margin from 72°–76°N. It should be noted that the SMB trends on the western margin are not significant in this region, and that the ATM missions had few flight lines in extreme eastern Greenland. While the pattern does not perfectly match the measured elevation changes by Krabill et al. , there is some correspondence. It is in agreement with the pattern of thinning at lower elevations and near balance to slight thickening above 2000m, suggesting that elevation changes may be partially driven by short-term changes in SMB.
 These findings do not necessarily mean that all observed elevation changes can be explained by SMB. Changes in firn density, in response to temperature variations, likely play a significant role in elevation changes [e.g., Arthern and Wingham, 1998]. McConnell et al. [2000b] demonstrated that variations in accumulation and firn density were responsible for changes in surface elevation of Greenland south of 72°N and above approximately 2000 m a.s.l. identified from Seasat radar altimetry data [Davis et al., 1998]. Braithwaite et al.  estimated annual surface elevation changes of ±0.1 to ±0.2m due to changes in firn density. These values are smaller but the same order of magnitude as the −0.2m to +0.5m surface elevation changes shown here.
Braithwaite and Zhang  indicated that large interannual variability in mass balance may require long periods of record (>20 years) to determine any long-term trends in SMB driven by climate. Thus, even if the observed trends in elevation are driven by climate, they may be driven by short-term variations that do not indicate long-term climate change [e.g., Braithwaite et al., 1992; Braithwaite, 1994].
 The SMB estimated using SSM/I and accumulation based on Bromwich et al.  precipitation is roughly equal to the upper range of the calving rate suggested by Bigg . However, the results also show a large variability interannually in SMB. Spatial variation in SMB is dominated by the accumulation rate in southeast Greenland, the runoff rate in west Greenland and neither component in the north. When comparing SMB among years, often regions north and south of approximately 72°N latitude behaved in an opposite fashion. Years with higher SMB north of 72°N often had lower than average values south of that latitude. This did not apply to years, such as 1992, that had uniformly high SMB across Greenland.
 Significantly, those years with higher accumulation are more often associated with low ablation for the ice sheet as a whole. Conversely, low ablation years are more likely to be associated with high accumulation. This finding agrees with findings on individual outlet glaciers in south Greenland by Braithwaite and Olesen . This pattern may be at least partially explained by the fact that lower accumulation rates result in higher runoff rates in the SMB model due to the more rapid loss of snow mass and the higher degree day factors (and more rapid ablation) for superimposed and glacial ice.
 Changes in surface elevation inferred from the SMB trends during 1988–1999 and 1993–1999 agree in general with laser altimetry measurements of thinning at the lower reaches of the Greenland ice sheet. This would agree with assumptions that the ice sheet sees greater runoff at lower elevations and higher accumulation rates in a warmer climate.
 It is important to note that Figures 7 and 8 do not account for any difference between the mean climatic conditions during 1988–1999 and equilibrium conditions across lower elevations of the ice sheet. It may be that even the mean climatic conditions during 1988–1999 were sufficiently different from equilibrium conditions that they would have led to changes in ice sheet elevation. Krabill et al.  estimated that the warmer climate of the mid to late 1990s probably could not account for more than 50 cm yr−1 of the widespread thinning below 2000 m a.s.l. and much less in many locations, while observed thinning reached 1 m yr−1 on many glaciers. The changes observed during the 1988–1999 time period do not exceed approximately 30 cm yr−1 thinning, and in many locations the maximum thinning is not at the margin.
 Nevertheless, it appears that the general pattern of elevation changes based on SMB resembles those measured. It appears plausible that SMB changes explain a significant portion, but probably not all, of the observed elevation changes on the Greenland ice sheet. Future work should combine the surface elevation changes estimated from SMB described here with firn density changes [e.g., McConnell et al., 2000b; Braithwaite et al., 1994] to more completely describe the role of climate variations on surface elevation.
 This work was funded through NASA PARCA program (NAGW-4573) awarded to the author. SSM/I data were provided by the National Snow and Ice Data Center, Boulder, Colorado. The author thanks David Bromwich of the Byrd Polar Research Center for providing the annual precipitation data.