Introduction
Scientific interest in the magnitude of melting on the Greenland and Antarctic ice sheets has grown along with concern about the potential effects of climate change. In particular, increased melting in a warmer climate may lead to rising sea levels (Reference BindschadlerBindschadler 1985; Reference Peltier and TushinghamPeltier and Tushingham, 1989). However, Reference ZwallyZwally (1989) found that the ablation and accumulation zones of the Greenland ice sheet thickened between 1978 and 1985, as determined from radar-altimetry data, and suggested the change might be a product of increased accumulation associated with a warmer climate. This reasoning also suggests that increased melting should be associated with, but more than offset by, the increased accumulation. In contrast, Reference Braithwaite, Olesen and ThonisenBraithwaite and others (1992) used stake observations at three locations near the margin of the ice sheet to argue that thickening in the ablation zone was due to decreased ablation, primarily from decreased melting.
The question of how the ice sheet responds to variations in climate, and potential climate change, can be addressed at least partially by examining the variations in snowpack melt. Unfortunately, identification of snowpack-melt events on the Greenland ice sheet is accomplished only at a few isolated stations or by interpretation of shallow-ice-eore records that are widely scattered. Satellite remote sensing offers a means of acquiring a spatially and temporally detailed record of snowpack-melt occurrences. Passive-microwave remote sensing is especially suited to measuring melt occurrences due to the rapid change in microwave emission of a snowpack in response to the introduction of even a small amount of liquid water. Microwave emission, as described by a blackbody-equivalent radiometric temperature called a brightness temperature (T B), exhibits a distinct increase at frequencies greater than 10 GHz during snowpack melt in the West Greenland percolation zone (Reference ThomasThomas and others, 1985). This increase in T B stands in sharp contrast to the lower T B observed during non-melt conditions (Glocrsen and others, 1974) due to internal scattering within the snowpack (Reference ZwallyZwally, 1977). The emissivity of snow changes rapidly with melt due to an increase in the liquid-water content of the snow. Because of the high dielectric constant of liquid water compared to that of air and ice, melt strongly affects the dielectric constant of the ice-air-water mixture (Reference Ulaby, Moore and FungUlaby and others, 1986). The increase in the dielectric constant raises the absorptivity and, according to Kirchoff’s law, the emissivity. The result is an increase in absorption relative to volume scattering, which reduces the scattering albedo and enhances emission (Reference Chang, Gloersen, Schrnugge, Wilheit and ZwallyChang and others, 1976, Reference Chang, Foster, Owe, Hall and Rango1985; Reference Foster, Hall, Chang and RangoFoster and others 1984).
This change in T B with melt is frequency-dependent. Below approximately 10 GHz, a spectral region where volume scattering is small compared to surface scattering, the T B decreases with increasing liquid-water content; near 10 GHz the T B is nearly insensitive to liquid-water content (Reference Ulaby, Moore and FungUlaby and others, 1986). The T B becomes increasingly sensitive to water content at higher frequencies. The frequency dependence of the T B on liquid-water content has been used to identify the onset of melt in the seasonal snowpack Reference Kunzi, Patil and RottKunzi and others (1982) found the 37 GHz T B to be lower than the 18 GHz T B of dry snow, but the two values are nearly equal for wet snow. Other investigators have relied on the increase in brightness temperatures at high frequencies (37 GHz) to identify melt and quantify the liquid-water content of the snowpack (e.g Reference Stiles and UlabyStiles and Ulaby 1980).
Although snow density, temperature, crystal structure and crystal size all contribute to the snowpack’s emissivity, changes in the liquid-water content produce the most prominent changes in T B. For example, snow with 2% liquid-water content may produce a 37 GHz T B more than 100deg higher than dry snow (Reference Hofer and MätzlerHofer and Matzler, 1980). The increase in T B with melt was used to map regions of the Greenland ice sheet experiencing melt during a period of intense warming in 1989 (Reference Mote, Anderson, Kuivinen and RoweMote and others, 1993). As a continuation of that research, we use the increase in T B at 37 GHz to quantify the extent and frequency of melt on the Greenland ice sheet during the period 1979–91.
Satellite Microwave Data
Measurements of snowpack melt were made using data obtained from two satellite microwave radiometers, the Nimbus-7 Scanning Multichannel Microwave Radiometer (SMMR) and the Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave/Imager (SSM/I). The SMMR recorded radiation every other day in ten channels (Reference Gloersen, Hardis and MadridGloersen and Hardis, 1978), including both polarizations for 6.610.7, 18.0.21.0 and 37.0GHz, from October 1978 to August 1987The SSM/I, which began operation in July 1987, records radiation daily in seven channels, the vertical polarization for 22.2 GHz and both polarizations for 19.35, 37.0 and 85.5 GHz (Reference Hollinger, Lo, Poe, Savage and PierceHollinger and others, 1987). The 37 GHzhorizontally polarized (37H) channel was used for this research due to the great sensitivity of that channel to changes in snowpack liquid-water content. Additionally, the 37H channel had the smallest relative calibration difference between the two sensors, which facilitates merging the two data sets (Reference JezekJezek and others, 1991).
The two sensors differ in view angle (50.3° for SMMR vs 53.1° for SSM/I), radiometric resolution and calibration. Due to a change in swath width (approximately 1400 km for SSM/I vs 700 km for SMMR), the number of daily overpasses of a given location is greater for the SSM I than for the SMMRA systematic difference in SMMR and SSM/I brightness temperatures is primarily due to the difference in calibration of the two sensors (Reference JezekJezek and others, 1991)A linear regression of the brightness temperatures was used to remove this systematic difference . The regression was performed using daily, gridded SSM/I and SMMR brightness temperatures for locations north of 70°Ν and at elevations greater than 2700m a.s.l. This region, which approximates the dry-snow zone of the ice sheet, was selected to avoid the influence of melt on the regression. Data for 20 d between 11 July and 20 August 1987, the period when both sensors were operating concurrently, were included in the regression. The resulting equation for the 37H channel (r 2 = 0.97) is:
where T B, SMMR is the SMMR brightness temperature (K) and T B, SSMI the SSM/1 brightness temperature (K)All SMMR brightness temperatures were converted to equivalent SSM/I brightness temperatures using this regression equation.
The SMMR and SSM/I data were obtained from the National Snow and Ice Data Center (NSIDC) archive of brightness-temperature grids. The orbital data were interpolated onto a 25 km × 25 km grid on a polar stercographic projection. Any data sample located within a given grid cell on a given day, beginning at 0 Coordinated Universal Time (UTC), was averaged into the daily value for that grid cell (NSIDC, 1992). Grid cells with missing data were filled by spatially averaging the grid cells immediately adjacent. Seven days that are included in the NSIDC archive were eliminated from the analysis because of missing swaths of data.
A land mask was digitized from the Quaternary map of Greenland published by The Geological Survey of Greenland. This mask was used in conjunction with both the SMMR and SSM/I water and coastline masks to eliminate any grid cells not covered by at least 50% ice or with any permanently standing water. The unmasked grid cells available for analysis covered a total area of 1 648 125km2, including parts of ice caps separate from the ice sheet. The ice sheet covers approximately 1701000 km2 and ice caps cover another 65 000 km2 (Reference WeidickWeidick, 1985). Between 7% and 12% of the ice sheet and ice caps is removed from the analysis by the masking process.
Microwave Emission of Melting Snow
A simple microwave-emission model was employed to determine the 37H T B associated with snow cover containing a given volumetric water content (m v) for each grid cell on the Greenland ice sheet. Because T B increases with increasing mv, a simulated T B can be used as a threshold value to identify the occurrence of snowpack melt with microwave data. Given the lack of data on snow grain-size and density necessary for calculation of scattering coefficients, a semi-empirical approach was taken in which the emission model was first inverted under non-melt conditions to derive scattering coefficients Reference Ulaby and StilesUlaby and Stiles (1980) give the brightness temperature (T si) produced by the ith snow layer of thickness d i as:
where T
i, is the thermometric temperature of layer i (Κ), 
is the mass absorption coefficient (kg−1m3), 
is the mass scattering coefficient (kg−1 m3), 
is the propagation angle, h is the depth in the ith layer (m), and ρ
i is the density (kg m−3)The integral can be solved analytically and expanded for multiple snow layers, ignoring diffuse scatter and multiple reflections at boundary layers, to determine the brightness temperature at the surface of the snowpack T′
B (Reference Abdelrazik, Ulaby and StilesAbdelrazik and others, 1981).The T
B detected by the satellite sensor is the sum of T′
B, upwelling sky radiation, reflected downwelling sky radiation, and the reflected emission from free space, and is found by:
where T sky is the sky brightness temperature at 37 GHz (25 K), T sp is the averaged brightness temperature of free space (3K), τ is the atmospheric loss factor at 37 GHz (0.05), θ is the sensor view angle, and τ is the bulk emissivity of the snowpack.
The increase in microwave emission of snow undergoing melt is associated with an increase in the absorption coefficient. Therefore, the absorption coefficient must be calculated under spring pre-melt and summer-melt conditions. The absorption coefficient can be found by:
where K
a is the absorption coefficient (m−1), λ is the wavelength (m), 
is the real part of the dielectric constant of snow, and 
is the imaginary part of the dielectric constant.
The complex dielectric constant of snow was calculated using a dielectric mixing model from Reference Tinga, Voss and BlosseyTinga and others (1973), which has been used to determine the dielectric properties of snow undergoing melt (Reference Tiuri, Schultz and RangoTiuri and Schultz 1980). The complex dielectric constant can be found by:
where k s is the complex dielectric constant of snow, k w is the complex dielectric constant of water, k i is the complex dielectric constant of ice, r i is the radius of ice particles (m), r a is the radius of air pockets (m), r w is the radius of water-covered ice particles (m), m v is the volumetric water content, and ρ s is the density of snow (kg m−3)Smooth boundaries between snow layers and at the snow air boundary were assumed, and the transmission coefficients at each boundary were calculated by:
where τ s is the power transmission coefficient ε b, is the relative dielectric of the underlying layer, ε t is the relative dielectric of the overlying layer, and θ t is the propagation angle.
The model was first inverted under spring conditions to calculate scattering coefficients for each year. Scattering coefficients were estimated for individual years to account for differences in the amount of winter accumulation, which may affect the scattering properties of the snow. Observed brightness temperatures were averaged for a period before the onset of summer melt and used in the model to calculate scattering coefficients. The observed brightness temperatures were averaged for a period in each year when the temperature profile is assumed to have been nearly isothermal, and just prior to the onset of melt. This allows estimated 10 m temperatures to be used to approximate the temperature throughout the snowpack. Based on these criteria, the first 15 d of April were selected as the most appropriate period for using the observed brightness temperatures to estimate scattering coefficients.
The 10 m snowpack temperature for each grid cell was estimated from a third-order regression equation based on latitude, longitude and elevation (Reference Budd, Jacka, Jenssen, Radok and YoungBudd and others, 1982) Elevation data were from the radar altimeter aboard ERS-1 (personal communication from S. Ekholm, 1993) and from the Seasat radar altimeter (Reference Bindschadler, Zwally, Majorami and BrennerBindschadler and others, 1989).
Absorption coefficients were based on a snowpack density of 480 kg m−3, typical conditions for the top meter of moderately packed snow (Reference ZwallyZwally, 1977), and a mean grain-size of 0.5 mm, which is appropriate for fine-grained snow (Reference Stephenson and ÔuraStephenson, 1967). Changing the grain-size does not strongly affect the simulated brightness temperatures. The spatial variation in grain-size should be accounted for by the empirically derived scattering coefficients.
Using the empirically derived scattering coefficients, summer-melt conditions were simulated by the addition of 1% liquid water to the top 1 m of the snow packThe 1% value was chosen because it is near the lower limit of the radiometer’s sensitivity to changes in water content (Reference Stiles and UlabyStiles and Ulaby, 1980). The thermometrie temperature of the top 1 m was assumed to be 273 K. The model does not account for changes in the scattering coefficient due to grain growth associated with the freeze-thaw metamorphism of melt. Estimated rates of grain growth were initially incorporated into the model, and a linear increase in the scattering coefficient with grain growth was assumed, as suggested by Reference Rotman, Fisher and StaelinRotman and others (1982), but these changes had little effect on die simulated-melt T B. Because of die limited knowledge of grain-size distributions on the ice sheet, the results presented here do not include a correction to the scattering coefficient for grain growth.
A map of the mean simulated-melt brightness temperatures for the 13 years (Fig. 1) generally resembles that of the mean-emissivity map for April (Fig. 2). The emissivity map was produced from observed April brightness temperatures and 10 m snowpack temperatures using the Rayleigh Jeans approximation, which states:
where τ is the emissivity, and Τ is the thermometric temperature. The relationships between the simulated-melt T B and both the observed April T B and April emissivity are not linear. The relatively warm underlying snowpack in the southwest results in simulated-melt T B higher than would be expected from a simple linear relationship with the April emissivity. Conversely, the cold underlying snowpack in the far north results in simulated-melt T B lower than would be expected based on the April emissivity. Additionally, the high spring emissivities in the southeast, in some cases near 0.85, do not increase substantially during the simulated melt. In some locations in the southeast, the simulated-melt T B is less than 15 deg greater than the mean observed April T B, compared to differences of 30 deg in the southwest (Fig. 3).
Fig. 1. Mean values of the simulated 37 GHz brightness temperatures associated with summer-melt conditions for each year 1979–91. The brightness temperatures for each year are calculated from a simple microwave-emission model of the snowpack with 1% liquid-water content.
Fig. 2. Mean April microwave emissivities at 37 GHz determined from observed April brightness temperatures and estimated 10 m firn temperatures.
Fig. 3. Simulated summer-melt 37GHz brightness temperatures minus mean observed brightness temperatures for April 1979–91.
The use of a modeled threshold T B for each grid cell as a means of identifying melt is an improvement over the uniform step change in T B for all grid cells used by Reference Mote, Anderson, Kuivinen and RoweMote and others (1993). The use of a 31 deg change from observed January values in T B to identify melt resulted in threshold brightness temperatures near 273 Κ at some locations along the southeast margin of the ice sheet. Observed brightness temperatures in this region seldom exceed 265 K, although melt is known to occur here.
The general patterns evident in both the simulated-melt T B (Fig. 1) and April-emissivity (Fig. 2) maps result from variations in the accumulation rate across the ice sheet. The April-emissivity map (Fig. 2) closely resembles the latest accumulation map for Greenland (Reference Ohmura and ReehOhmura and Rcch, 1991). Reference Rotman, Fisher and StaelinRotman and others (1982) demonstrated that accumulation rates could be determined from Fig. 3 microwave emissivities for the dry-snow zone of the Greenland ice sheet. The southeast of the ice sheet experiences much higher emissions than the southwest (Fig. 2). This difference is due to increased accumulation in the southeast from the orographic lifting of moist air by the Icelandic low (Reference Ohmura and ReehOhmura and Rech, 1991). The microwave emissivity of the southwest is much lower due to lower accumulation rates. The regions of higher accumulation near the ice margin at 77° Ν and at 1500–2400 m a.s.l from 69° Ν to 72° N as identified by Reference Ohmura and ReehOhmura and Reeh (1991), are also evident as regions of higher emissivity (Fig. 2).
Areal Melt Extent
Values of the 37 GHz, horizontally polarized brightness temperatures for each day of available data were compared to the simulated-melt brightness temperatures for the given year. The simulated values for each year were used as threshold values to identify whether the snow pack in a given grid cell was experiencing melt. The spatial coverage of grid cells identified as experiencing melt each day was summed to quantify the areal extent of melt. The daily melt extents were then averaged on a monthly and seasonal (May-August) basis to produce mean monthly and mean seasonal melt extents. The mean melt extents are analogous to the average frequency of melt occurrence of all grid cells for a given month or season. This measurement does not indicate the intensity of the melt occurring in a grid cell on any given day. However, the climatic conditions averaged over months and seasons that produce intensive melt should usually be associated with more extensive and more frequent melt.
To merge the two data sets, the melt extents derived from each sensor for the period when both were operating (11 July-20 August 1987) are compared to determine the magnitude of error introduced by the sensor change. The comparison is made with and without the conversion of SMMR brightness temperatures using the linear regression of SMMR and SSM/I brightness temperatures. The mean melt extent detected by SMMR during the 20 d when both sensors were operating, after the conversion had been applied, is approximately 2.5% more than that detected by SSM/I. This compares favorably to a 19% greater melt area detected by SSM/I without the conversion. With the conversion applied, the SSM/I identifies more melt on the two days of greatest melt extent, but the SMMR identifies more melt on two-thirds of the remaining days (Fig. 4). Examination of the spatial pattern of the difference in melt frequency identified by the two sensors evidences no regional bias. After the conversion is applied, the difference in melt frequency appear to be randomly distrubuted. The remaining differences are likely produced by the variation in the time of overpass for each sensor. The liquid water content has a strong diurnal cycle, and as a result, the T B is also a function of the time of day during melt.
Fig. 4. Daily melt area identified in July and August 1987 with SSM/1 data vs the melt area identified by SMMR data before and after a conversion of the SMMR data to account fir calibration differences between the two sensors.
In order to determine how well the microwave data can be used to represent changes in the surface climate of the ice sheet, the microwave-derived melt-extent time series was compared to the ablation rate measured at Qamanârssûp sermia. Reference Braithwaite and OlesenBraithwaite and Olesen (1990) published monthly values of the ablation rate at Qamanârssûp sermia (64 °28′N), which were taken from a stake measurement at 790 m a.s.l. The ablation data were compared to the mean melt extent for each month for a region of the ice sheet that includes Qamanârssûp sermia. The ice sheet was divided into eight regions (Fig. 5), defined by topographic barriers that limit the transport of moisture, as shown by Reference Ohmura and ReehOhmura and Reeh (1991). Monthly mean melt extents were calculated for each region. The ablation rate for Qamanârssûp sermia was compared to the monthly mean melt extent for Region 2. The topographic barriers that define each of these regions should serve as a barrier to sensible heat advection as well as moisture advection. As a result, changes in atmospheric circulation should have a distinctly different effect on melt occurrence in each of these regions.
Fig. 5. Eight topographically defined regions of the ice sheet, based on the ice-sheet regions defined by Reference Ohmura and ReehOhmura and Reeh (1991).
An approximately linear relationship exists between the monthly mean melt extent for region 2 and the monthly ablation rate for Qamanârssûp sermia (Fig. 6). The agreement is highly significant in June (r 2 = 0.88,significant at 95% confidence interval)marginally significant in July (r 2 = 0.53, significant at 90% confidence interval), but not significant in August (r 2 = 0.31)The overall agreement was statistically significant (r 2 = 0.66, significant at 99% confidence interval). The weaker relationship later in the season is likely the result of an increasingly heterogeneous snowpack. For example, due to the low emissivity of open water, a grid cell containing numerous melt water ponds and wet snow may have a lower emissivity than is associated with wet snow alone. An increase in the amount of bare ice present in the analysis as the summer season progresses is another reason the relationship is weaker in August. At present, we cannot determine the occurrence of melt on bare ice with the passive-microwave data. Early in the summer, much of the margin of the ice sheet and the outlet glaciers with exposed ice are excluded from analysis by the land mask. As the season progresses, the expanded area of bare ice means that more grid cells containing bare ice are included in the analysis.
Fig. 6. Mean monthly melt-extent values for region 2 of the ice sheet versus stake-ablation rates measured at Qamanärssûp sermia, as given by Reference Braithwaite and OlesenBraithwaite and Olesen (1990).
Given the linear relationship between the ablation rate and mean melt extent, the same climatic conditions that result in more ice ablation at Qamanârssûp sermia apparently also result in more frequent melt of the snowpack. Reference Braithwaite and OlesenBraithwaite and Olesen (1989) used the ablation rates at Qamanârssûp sermia as a measure of surface climate on the ice sheet. Therefore, we believe the monthly and seasonal mean melt-extent values can serve as an indicator of climate variation.
In order to gain a better understanding of the spatial variation of melt occurrence, the daily melt extents were examined for extreme events, and the mean annual cycle of melt extent was calculated. The spatial extent of melt was evaluated on a daily basis first, to identify extreme events. The greatest melt extent during the 13 year period occurred on 4 and 5 July 1988. The melt extent reached 735625 km2 on 4 July and 711875 km2 on 5 July, covering approximately 44.6% and 43.2% of the unmasked area of the ice sheet, respectively. All of the ten days with the greatest melt extent during the 13 years occurred in 1988 or later (Table.1).
Table 1. Spatial extent of melt and percentage of ice sheet covered by melt for the 10 d of most extensive melt during 1979–91
The melt-extent values for each day were averaged across the 13 years to produce a mean annual cycle of melt extent. Melt begins to occur in late April, and coverage increases rapidly from mid-May until the maximum coverage occurs in mid-July (Fig. 7). The melt extent decreases rapidly from late July through mid-August, and typically terminates in late September. The time series of daily melt extent for individual years exhibit a large degree of temporal variability; this most likely results from the passage of synoptic-scale weather systems with concomitant changes in the amount of cloud cover and sensible heat advected onto the ice sheet.
Fig. 7. A time series of the mean daily melt-extent values for the years 1979–91 demonstrating the typical annual cycle of melt coverage on the ice sheet.
In order to understand the spatial variability in melt occurrence, the daily melt-extent values were compiled into a map of the frequency of melt occurrence for each grid cell. The frequency of melt occurrence is defined as the percentage of days on which melt was detected during the 4 month summer period, May-August. The total area classified as melting during at least one day for the 13 years of data includes 1090 000 km2, covering approximately 66% of the unmasked area of the ice sheet. Melt was detected across the south dome of the ice sheet and as high as 3000 m a.s.l in a region near 68°N 37° W Fig. 8). Melt occurred on more than 70% of the days in May-August along the ice sheet’s western margin from 67° N to 70° N, but 60% of the region where melt occurred experienced melt on less than one day in ten (Fig. 8).
Fig. 8. Percentage of days identified as melting during May-August 1979–91 from passive-microwave data.
The frequency of melt occurrence is probably underestimated. The land mask eliminates some snow surfaces at lower elevations that would likely experience more melt than adjacent locations at higher elevations. Also, daily averaging of the microwave data reduces the ability to identify instances in which melt occurred only during the hours of peak solar radiation or sensible-heat advection. A snowpack that experiences afternoon melt and refreezes in the evening may have a mean daily T B for the grid cell that does not exceed the threshold value. This may be especially important early and late in the season due to the fewer hours of sunlight. The tendency of refrozen snow to have a lower T B than fresh snow, due to increased volume scattering from the enlarged grain-sizes, exacerbates this melt-detection problem. Finally, snowpack heterogeneity may cause difficulties in data interpretation with grid cells as large as 625 km2 that may contain a large variation in elevation. A grid cell with both melting and refrozen snow may appear similar to a pixel with fresh snow, reducing the area classified as melting. This being said, the application of a uniform method over the entire time series should still allow the detection of tendencies in melt frequency and extent.
The daily melt-extent values were averaged into monthly and seasonal values to examine the melt-extent time series for inter-annual variations during the 13 year period. The most striking feature of the seasonal melt-extent time series (Fig. 9) is the apparent trend of increase in the area of average daily surface melt by approximately 5000 km2 year−1. The average value of the daily melt extent for the entire 13 year period is approximately 133 000 km2and the linear trend represents a 3.8% annual increase. These findings are in general agreement with Reference Braithwaite, Olesen and ThonisenBraithwaite and others (1992), who suggested that the late 1980s had higher ablation rates than the early to mid-1980s. The 5 years of SSM/I data (1988–91) have a mean seasonal melt area 26% greater than the 8 years of SMMR data (1979–87). Contrary to evidence from the sensor-overlap period, it is still possible that the sensor change has contributed to some of the increase in detected melt area. However, the SMMR data alone have a positive trend of about 2500 km2 year−1 in average daily melt area(The year 1987 is included as a SMMR year because SMMR data are used from May through July to calculate the seasonal average; SSM/I data are used only in August.). All four summer months exhibited an increase in melt extent, with the most substantial increases in July and August (Fig. 10). July has a positive trend of nearly 8200 km2 year−1, compared to approximately 5500, 5400 and 1200 km2 year−1 for August, June and May, respectively. Expressed as a percentage of the 13 year mean, August has the most positive trend, possibly indicating a longer melt season. June has the greatest variability in melt extent, from a low value of 69 800 km2 average daily melt extent during the 1979 summer season to a high of 283 900 km2 in 1987.
Fig. 9. Percentage of days identified as melting during May-August 1979–91 from passive-microwave data.
Fig. 10. Percentage of days identified as melting during May-August 1979–91 from passive-microwave data.
Examining the seasonal mean melt extents for each region, regions 2 and 3, which cover most of the western half of the ice sheet, each show a statistically significant increase. The northerly regions, 4 and 5, show a slight trend toward increasing melt, but neither is significant. The melt-extent time series for the three southeastern regions, 6–8, remain relatively fact. In fact, region 7 shows a small, though statistically insignificant, trend toward decreasing melt over the 13 year period.
Region 3, the largest of the eight regions and the one with the greatest mean melt extent (Table.2), has the largest trend in melt extent with a 6.7% annual increase (significant at the 99% confidence level). Region 2, located just south of region 3, showed a 4.2% annual increase over the 13 years (significant at the 99% confidence level). Regions 1 and 2, in the southwest, have the greatest percentage of area covered by melt, 24.4% and 17.2% respectively (Table.2). The northeastern regions, 5 and 6, have the smallest percentage of mean daily seasonal-melt coverage, each at 5.3%. Monthly trends were examined for the two regions with significant seasonal trends. Region 2 had an increase of 900 km2 year−1 (significant at the 95% confidence interval) in July and 500 km2 year−1 (significant at the 90% confidence interval) in August. Region 3 had an increase of 3000 km2 year−1 (significant at the 90% confidence interval) in July and 4900 km2 year−1 (significant at the 95% confidence interval) in August. The trends for both May and June were insignificant for regions 2 and 3.
Table 2. Mar-August mean melt area and per cent coverage for each of the eight topographically defined regions (within land/water mask)
Overall, the trend of increasing mean melt area, analogous to increasing melt frequency, is confined to the southwest and west of the ire sheet, primarily late in the season. Because a large proportion of the total melt of the ice sheet occurs in these regions, the mean annual melt extent for the entire ice sheet also shows a positive trend.
Summary and Conclusion
A threshold value of 37 GHz, horizontally polarized T B has been used to identify areas of melt on the Greenland ice sheet for 1979–91. By merging the data sets of two satellite microwave radiometers, a record of high spatial and temporal resolution of melt occurrence on the ice sheet has been developed. An examination of this detailed record provides evidence of a trend toward increasing seasonally averaged daily melt extent of about 3.8% annually. All four months examined May-August, demonstrate a positive trend in melt coverage from 1979 to 1991, but the months of July and August account for approximately 70% of the seasonal trend. However, the agreement between the mean monthly-melt extents and the measured ablation rates is weakest late in the summer season (July and August) when the trends are statistically most significant. Therefore, one must exercise caution in interpreting the melt-extent time series as indicative of increasing melt frequency or melt extent. Additionally, the apparent increase in mean melt extent is confined to the west and southwest of the ice sheet.
The loss of data near the margin of the ice sheet and the problems of diurnal variations of melt occurrence and spatial variations within a grid cell likely result in a bias toward identification of less melt than actually occurred. However, the relative melt-frequency values on a monthly and seasonal basis will prove useful in comparison to surface observations of ablation rates. These results should be used in conjunction with detailed surface meteorological observations to determine the usefulness of the passive-microwave satellite data in mass-balance studies. Continued monitoring of melt occurrence on the Greenland ice sheet is of particular value given the ongoing debate concerning global climate change. Recorded changes in melt frequency or total coverage should prove a powerful indicator of climate change in the Arctic.
Acknowledgements
The authors thank S. Ekholm and the Danish National Survey and Cadastre for providing the elevation data for Greenland from the ERS-1 radar altimeter. We also thank Dr R. Braithwaite and K. Kuivinen for their useful comments on the surface conditions on the Greenland ice sheet. Additionally, we thank Dr Braithwaite, Dr MPalecki and an anonymous reviewer for their manv constructive editorial comments on the manuscript. The SMMR and SSM/I gridded brightness-temperature data on CD-ROM were obtained from the National Snow and Ice Data Center, Boulder, CO, U.S.A. This work was supported by NASA training grant NGT-30127 and NASA grant NAGW-1266.
