The summer-fall progression of surface change

Snow metamorphism and the resulting stratigraphy of the snow and firn are principally influenced by the thermal regime during seasonal change, or the presence of meltwater. General progressions in upper ice-sheet surface properties closely follow the thermal forcing in the upper few meters of the snowpack. The warmer summer months and particularly the summer-fall transition cause rapid changes in Greenland ice-sheet surface properties. The altitude, latitude, and topography, however, modify environmental conditions such that rates of seasonal change vary spatially.

Diagenetic changes in the structure of snow and firn can take place without melt, but are accelerated with higher temperatures, until a point at which melting may take place. When summer temperatures in the upper snowpack increase above −10°C there is a significant increase in the vapor pressure of ice. In firn strata this can lead to vapor transport and sublimation. The net result is the destruction of original precipitated snow-crystal forms, increased grain-sizes and increased bonding between grains. These changes in snow and firn are common to the spring and summer months in the dry-snow zone at elevations too high to suffer actual melting.

Further downslope, as summer surface-air temperatures increase, diagenesis takes place much more rapidly and dramatically by melting. Reference Echelmeyer, Harrison, Clarke and BensonEchelmeyer and others (1992) describe the seasonal variation in surface temperatures at around 1500 m altitude and at varying depths beneath the surface. After a period of freeze–thaw fluctuations in late June, which grows grains in the lower-elevation areas to the order of 1 mm in diameter, surface temperature stabilizes at 0°C around 1 July (Julian day 183). After this date the melt front moves upslope of this altitude, as far as the dry-snow line at the height of the summer melt. Below the dry-snow line, meltwater often percolates downwards preferentially in pipes or channels. Often it encounters obstructions or simply snow below the freezing point, whereupon it filters laterally to form layers or buried ice lenses and glands (Reference Pfeffer, Illangasekare and MeierPfeffer and others, 1990) parallel to the strata. The pipes, which feed these hard ice layers with meltwater, may themselves freeze. These glands are vertically extended ice masses, and are found in association with ice lenses or layers, typically in the percolation zone.

At lower altitudes, where melting is significant, the upper snowpack typically becomes isothermal. Definitions used for wetting are applied strictly in the sense of Reference Benson and ÔuraBenson (1967) and are as follows. “Wet snow” is at 0°C and often wet throughout the upper meter of snow. When wet snow becomes saturated down to the previous summer surface it is known as “soaked snow”. Temperature cycling and fall cooling result in wet snow refreezing as “iced firn”. Such dense layers provide stratigraphic markers indicating surface melting.

Physical influences on microwave signatures

The principal parameter affecting the microwave response of the ice-sheet surface is the presence of liquid water. It changes the dielectric properties of snow and ice so significantly that it regulates the reflection or transmissivity at the surface and limits the contribution of sub-surface or volume-scattering effects by absorption and extinction within the upper layers (Reference Rott, Domik, Mätzler, Miller and LenhartRott and others, 1985). Seasonal modulations of σ° in SASS data are a demonstration of the sensitivity to the transitions in surface and sub-surface properties.

Important to the microwave scattering mechanism is the layering which develops as a consequence of the snow-accumulation patterns and the changes affected by seasons. Such stratigraphy is preserved over time, and can often be correlated over scales of tens of kilometers. A stratigraphic discontinuity forms as a consequence of seasonal changes. One such distinct boundary takes the form of a coarse-grained, low-density layer, overlain by a finer-grained, harder layer of higher density. This occurs slightly above the uppermost evidence of the previous summer’s surface melting. Reference Benson and ÔuraBenson (1967) observed the formation of this sequence under strong negative temperature gradients in mid-to late August, during the short fall season. It was normally fully formed by 10 September and could be traced over long transects, but became difficult to trace beneath the altitude at which significant melting takes place (due to obliteration by meltwater processes). In the percolation zone, the important stratigraphic horizons are seasonal markers such as iced firn or ice lenses. By this stage in the melt season, the uppermost of these boundaries are related to significant spring or summer climatic events while a relatively distinct surface may remain beneath the previous year’s annual accumulation (i.e. summer surface).

Since snow-surface wetness decreases incrementally with surface temperature and altitude there is not expected to be a large step in the observed back-scatter between the wet-and dry-snow regimes in the summer months. Rather, during fall cooling, with cooler and drier conditions (as the active surface layer refreezes and snowfall takes place), the increasing penetration of microwaves will sense the fundamental differences between the dry-snow regime and the percolation facies further downslope. Due to rapid grain growth and the formation of ice layers and lenses beneath the surface in the percolation zone, the higher resulting back-scatter should more sharply delimit the extent of surface melt (i.e. the dry-snow line) during autumn. Thus, at the end of the fall, we should begin to see the development of a sharp gradient in the back-scatter map.

Differences in physical properties between the percol-ation zone and wet-snow or saturated-snow zones after fall freeze-up has taken place should be sufficient for considerable variations in snow back-scattering. Also, the hard ice surface remaining below the equilibrium line, (i.e. in the ablation zone), should have a different appearance from the snow-covered areas. In the case of the wet snow or ice near the ice margins, surface penetration of microwaves is negligible and the shape of the surface roughness autocorrelation function is most important for determining the value of σ° obtained by SASS. The surface roughness standard-deviation and correlation-length scale used to describe this function will drive the surface scattering and the form of the back-scatter relationships.

Comparison with airborne-scatterometer measurements

Reference Swift, Hayes, Herd, Jones and DelnoreSwift and others (1985) analyzed airborne Ku-band (14.6 GHz) scatterometer data acquired over southern Green-land on 14 October 1979. They measured σ° at several incidence angles from 0° to 60° and at VV, HH, and cross-polarizations along a transect across southern Greenland (see Fig. 1). Their VV–pol plot, reproduced in Fig. 6a, was collected from east to west along transect d shown in Figure 1. Figure 6b presents W-pol SASS at σ° incidence angles from 20° to 60° along the same line, taken from SASS-derived late September A and B images. Although Figure 6b corresponds to a 2 week average earlier in the season and a year prior to the Reference Swift, Hayes, Herd, Jones and DelnoreSwift and others’ (1985) flight, it compares very favorably with Figure 6a. The same general features and σ° values are evident, although the θ dependence of σ° is linearized in the SASS-derived plots by assumptions used in the derivation of A and B. Notable features apparent in both Fig. 6a and b are the small bump between 500 and 1000 s, together with the profile step between 2000 and 3000 s along the flight line. We conclude, therefore, that application of the resolution-enhancement algorithm to SASS data provides the desired 6 km resolution while preserving the key back-scatter characteristics.

Fig. 6. Companson of VV–pol Ku-band σ° versus time along the aircraft transect shown as d in Figure 1. (a) Reproduction of Figure 5 of Reference Swift, Hayes, Herd, Jones and DelnoreSwift and others (1985) showing σ° at several incidence angles, (b) Comparison of σ° versus time computed from the SASS-derived A and B images in Figure 5 (late September) at similar incidence angles.

Comparison with SAR data

For further evaluation of the enhanced-resolution SASS images we use synthetic aperture radar (SAR) data from Seasat and aircraft. Differences between these SAR data and the SASS data include radar frequency, measurement integration time and the coverage and resolution. In addition, the aircraft SAR data were acquired over a decade after the Seasat data, in August 1989 Qezek and others, 1993), by the Jet Propulsion Laboratory (JPL) airborne Polarimetrie radar.

Airborne-SAR comparison data were collected at P-(0.4 GHz), L-(1.2 GHz) and C-bands (5.3 GHz), in contrast to the Ku-band (14.6 GHz) SASS data. In general, the higher-frequency SASS has less penetration into the ice and firn, particularly in the presence of liquid water. In effect, the different frequencies look at slightly different portions of the upper ice sheet. Previous work using normal incidence Ku-band altimeter ice-sheet returns (Reference UlanderUlander, 1985; Drinkwater, 1987; Reference Partington, Ridley, Rapley and ZwallyPartington and others, 1989) has shown that the penetration does depend upon the season and geographic location in relation to the major snow and ice facies.

A key difference between SAR and SASS data is the measurement integration time. SAR data represent an essentially instantaneous measurement in contrast to the 2 week-average SASS images used here. Thus, SASS images average out short-term temporal variations. On the other hand, because the SASS data is available over several months, it is possible to examine seasonal variations over broad regions. In addition, though the JPL aircraft SAR provides high resolution (10–30 m), it covers only a 12 km swath. Scatterometer images provide only medium-scale resolution (6 km) but cover the entire ice-sheet up to about 78° N. In effect, SASS images trade resolution for coverage and integration time.

At the end of August 1989, JPL flew a multi-band SAR over a 90 km transect across the ablation zone (see Fig. 1; transect e) in southwestern Greenland. Reference Jezek, Drinkwater, Crawford, Bindschadler and KwokJezek and others (1993) collected P-band, L-band, and C-band imagery along a 12 km wide track. They compare this data with imagery collected by the L-band (1.2 GHz) Seasat satellite-borne SAR in early October 1978. To aid in comparison, a plot of spatially averaged σ° from the C-and L-band airborne data and the L-band Seasat data was prepared. A 10 pixel (approx. 70 m) wide swath down the center of the airborne-SAR data (∼43° incidence) was extracted. Pixels along the same track were extracted from the Seasat SAR images (see Reference Jezek, Drinkwater, Crawford, Bindschadler and KwokJezek and others, 1993). Values in a 10 km long moving window were then averaged (to simulate the resolution of the SASS data) and plotted in Figure 7a, although the cross-track resolution is only approximately 70 m. The SASS curve is a plot of A of along the aircraft transect.

Fig. 7. Plots of σ° with distance along transect e in Figure 1. (a) Values of σ° derived from SEASAT Ku-band SASS and L-band HH–pol SAR data and L-band and C-band HH-pol AIRSAR data. Original SAR data from Reference Jezek, Drinkwater, Crawford, Bindschadler and KwokJezek and others (1993) are smoothed using a 10 km moving window. Superimposed are SASS data from the late August period, to correspond with the AIRSAR time window, (b) Plots of A from each of the 2 week images in Figure 5. An early August transect is not included due to the lack of adequate coverage of SASS along the transect line during this time period.

Along-track results shown in Figure 5 begin in the percolation zone and end in the wet-snow zone. Back-scatter variability near the end of the track is due to morphological features and patchy slush areas near the ice-sheet margin (Reference Jezek, Drinkwater, Crawford, Bindschadler and KwokJezek and others, 1993), An important conclusion from Figure 7a is that the value of A observed at 10 km resolution is critically dependent on the precise location of the center of the 6 km resolution element with respect to snow or ice facies or mixed surfaces near the ice-sheet periphery. Differences between them are attributed primarily to the pixel scale and measurement integration as well as the difference in imaging years. Further differences may be attributed to sampling variability.

Figure 7b illustrates change along the transect over the 3 months of the Seasat SASS mission. We note from Figure 7b that A changes rapidly between summer and fall. Seasonal variation in A accounts for more than 20 dB change over the period shown. The minimum values (<−20dB) occur in July during peak melt but, as time progresses, the wet-snow zone becomes as bright as the percolation zone, with values of about −3 dB.

Dry-snow zone

The definition in sensu stricto of this zone is the region above the dry-snow line, where negligible melting or percolation takes place (Reference BensonBenson, 1962). The mean climatological July air temperature at summit is around −10°C, and as one moves downslope to the north and west it increases to between −5° and 0°C. Reference Ohmura and ReehOhmura and Reeh (1991) demonstrated that annual accumulation in the dry-snow zone is closely dependent on precipitation patterns and wind patterns across the ice-sheet. Lower accumulation to the north and east and the patterns observed in Figure 5 support the observation that the topographic barrier imposed by the western flank of the ice cap to the predominant winds from the southwest results in a significantly different microwave scattering situation in the northeast. A line can be drawn in our Figure 5 along the western edge of the bright zone to the northwestern corner of the plots which closely follows that drawn by Reference Ohmura and ReehOhmura and Reeh (1991) in their Figure 5. The following discussion treats the differences in the micro-wave scattering between these distinct dry-snow regimes.

Northern and northeastern region

To the northeast, where the snow accumulation is lowest, we observe the highest values of dry-snow σ° (see Fig. 5). Figure 8 shows the SASS time-series from region f in Figure 1, using the same presentation as in Figure 2. Figure 8a shows A values around −5 dB and low B values around −0.1 dBdeg⁻¹. Values of A have an extremely low variance while Figure 8b shows a distinct roll-off in the values of σ°. These results illustrate the lack of seasonal variation in the dry-snow zone during the 100d period. Between Julian days 188 and 208, when surface temperatures are warmer, dielectric loss (ϵ″) in the snow rises, increasing electromagnetic absorption. Cooling, between Julian days 218 and 278, causes a small yet perceptible steady rise in A from −5 to −4 dB by early October, due to the small reduction in loss.

Fig. 8. (a) Plots of A and B for the 1° × 2° study region f in the northern dry-snow zone. The plots were computed using the same technique as described for Figure 2. (b) σ° versus θ plot for days 188–201 in region f.

Annual snow accumulation in the northeast is as low as 10 cm year⁻¹ water equivalent (w.e.), increasing gradually southwards towards the summit (at 3233m). σ° decreases correspondingly from A = −4.72 dB to −10.63 dB, with a slight increase in B from −0.1 to −0.16 (see Fig. 5). The trend mirrors the change in annual precipitation totals for these geographic locations, with the consequence that the depth of the former summer surface is shallower in the northeast of the ice-sheet. This has an important impact, with surface scattering from the wind-packed firn, or vapor-transport horizon beneath the fresh snow layer, entering into the back-scattering process.

A simple physical model (see Fig. 9) is specified, which takes into account the two primary layers involved in radar scattering (see Reference DrinkwaterDrinkwater, 1989; Reference Livingstone and DrinkwaterLivingstone and Drinkwater, 1991; Reference Winebrenner and CarseyWinebrenner and others, 1992). These are an upper layer of annual snow accumulation, upon an infinite layer of firn or ice, often with a thin upper layer of wind-slab. Both snow and buried wind-slab surfaces have roughness values specified by typical laser-measured snow surfaces (Reference Rott, Domik, Mätzler, Miller and LenhartRott and others, 1985; A. Carlstrom, personal communication). The layer parameters are specified, based upon typical field-measured values taken from Reference BensonBenson (1962) and Reference Williams, Hall and BensonWilliams and others (1991), together with annual accumulation estimates from Reference Ohmura and ReehOhmura and Reeh (1991). Dry snow is effectively transparent to microwaves so there is little or no scattering at the air/ snow boundary and consequently back-scatter is determined by the volume scatter intensity. In the northeast, the snow depth and snow grain radius have the most important influence upon the volume-scatter.

Fig. 9. Description of simple 2 layer physical model used in the simulation of microwave back-scattering. Implicitly, layer O is air. Layer 1 is snow or firn and layer 2 is a stratigraphic horizon corresponding with relatively dense snow, iced firn or glacial ice. The parameters are given in the legends of subsequent model simulations.

Model simulations of back-scatter from region f indicate that volume-scatter from an infinite Rayleigh layer of fresh snow can only give a σ° value of about −15 dB at 40°. To augment this value, in order to match the brighter observed returns with the level and gradient observed, we must either assume unrealistically large snow grains or add a distinct horizon beneath the annual layer of accumulated snow. Obviously, in relatively transparent dry snow, surface scattering from the firn beneath (of a typical density of 0.4 Mgm⁻³) is significant. It is hypothesized that this effect causes the brighter signature observed in the northeast. Supporting this argument is the fact that σ° between 30° and 60° does not decline at the rate for typical volume-scatter. Hence, surface scattering from this sub-surface layer is required to explain the observed values.

A model simulation result is shown in Figure 10 for a typical annual accumulation depth of 17.5 cm w.e. (i.e. 53 cm snow at a typical mean density of 0.33 Mgm⁻³). The dry-snow surface roughness is unimportant in the observed curves, since the transmissivity at the surface is high. To fit the value of the volume-scatter at 65°, a typical mean snow-grain radius of 0.5 mm was used together with the permittivity (ϵ′) and loss (ϵ″) for this density at a temperature of −10°C (Reference Tiuri, Sihvola, Nyfors and HallikainenTiuri and others, 1984). A denser snow layer was used for layer 2, which corresponds with the layer described by Reference Benson and ÔuraBenson (1967), to represent a stratigraphic discontinuity. The roughness of the upper surface of this boundary is specified by typical laser-measured values and shown in Figure 10. The shaded zone in Figure 10 encompasses the area in which the points from Figure 8b fall. The upper and lower bounds of this shaded area are specified by the roughest (C:) and smoothest (A:) surface roughnesses. Points from Figure 8b fall close to curve C for a rough surface. The statistics indicate a root-mean-square (rms) surface height of 5.5 mm and a correlation length of 6 cm.

Fig. 10. Plot of σ° versus θ for a simulation example corresponding to a simple 2 layer model for the northern dry-snow zone in region f Figure 1, with the data from Figure 8b superimposed. The inset describes the layer properties used as model inputs. The shaded region suggests the simulated back-scatter regime bounded by extremes for high and low sub-surface roughness values.

Western flank and summit region

At the summit, mean summer temperatures of below −10°C are experienced, together with higher annual accumulation of 30 cm w.e or an equivalent of 100cm of snow at a density (ρ) of 0.3 Mgm ⁻³. Reference BensonBenson (1962) presents results from over 100 snow pits in the dry-snow zone at high altitude on Greenland. Lower mean summer air temperatures lead to slower grain growth and grain diameters of less than 1 mm. Typical densities in the first annual unit are in the range of 0.25–0.35 Mgm ⁻³, with a mean close to 0.3 Mgm⁻³. In summary, there is a deeper light-snow layer with a smaller mean grain-size than in the northern region but resting upon firn of similar density to the northern dry-snow region.

Comparisons between the data and model simulations suggest differences with the northeastern dry-snow zone. In order to simulate the −16 dB value of σ° at 65°, the effective depth of the snow (i.e. layer 1) or the grain diameter must be reduced relative to the Figure 10 example. This reduces the proportion of the total back-scatter contributed by Rayleigh volume-scattering. However, since annual accumulation is actually higher, the increment in volume-scatter due to deeper snow must be offset by a reduction in mean grain-size. Because grain size is the primary influence upon the Rayleigh volume-scattering contribution, a reduction in diameter of only 0.16 mm is required to offset greater snow depths of up to 1 m. With a mean grain diameter of 0.23 mm and a snow depth of 1m (at ρ = 0.33 Mgm⁻³), the total volume-scattering background level is around −15 dB. This is the level observed in Figure 11 at 65°. Thus, high incidence σ° values have fallen by several dB from those plotted in Figure 8b.

Fig. 11. Plot of observed back-scatter signature from region g, Figure 1, overlaid with the results of a simulation example corresponding to a simple 2 layer model for the southern-summit dry-snow zone. The inset describes the layer properties used as model inputs. Air/snow and snow/ice interface roughness was scaled using typical published field data obtained from laser measurements.

Figure 11 presents a comparison of the SASS back-scatter and simulated data for the southern summit (centered at 70° N, 38.5° W) between days 188 and 201. Annual accumulation at the southern summit is greater than that to the north, and yet A is lower than in Figure 8b. Additionally, B is −0.16 and is larger than to the north. The model result for the summit in Figure 11b indicates that if all parameters except grain-size and snow depth remain the same, then σ° falls within the simulated range. Figure 11 shows that the data fall between curve B, for medium-rough, and A, for smooth layer 2 surfaces. This result appears to indicate that the roughness of the underlying summer surface (firn or wind-slab) is not as large as is observed in the northeastern dry-snow region, otherwise the value of B would be smaller.

For contrast, in Figure 12 another example is shown for the same time period as Figure 11. It is taken from sample window h in Figure 1 from the northwestern dry-snow zone. These data indicate a similar pattern to that observed at the southern summit and are intentionally selected from a locality where Reference Ohmura and ReehOhmura and Reeh (1991) record a 30 cm w.e. mean annual accumulation. It may be concluded from this that dry-snow regions with similar temperature and accumulation regimes give consistent microwave signatures.

Fig. 12. (a) Time-series of A and B for region h centered at 75.5° N, 49.5° W. (b) σ° versus θ plot for days 188–201 in the same northwest dry-snow area.

Dry-snow summary

The nature of the dry-snow zone back-scatter essentially does not change temporally, except for small variations due to upper-snow warming in mid-July. Modeling simulations demonstrate that, even in the areas of the deepest dry-snow cover, the snow is largely transparent and the primary source of back-scatter is a combination of surface scattering from the summer surface and Rayleigh scatter from the snow volume.

If all snow characteristics could be assumed to be homogeneous throughout the dry-snow zone, the depth of annual accumulation would have the greatest influence upon observed patterns of back-scatter, with larger values of A as annual solid accumulation increases from 10 to 50 cm w.e. south westwards across the zone of dry snow. However, instead of the back-scatter increasing as annual accumulation increases, the opposite trend takes place. The lowest dry-snow A values occur in the area of 40–50 cm w.e. accumulation on the western flank of the ice sheet to the east of Jakobshavns Isbrr. This effect requires further explanation: model simulations suggest that varying snow grain-size and density, together with the roughness of the summer surface beneath the annual accumulation, can account for this discrepancy. These variations result in a total change in A of around 8 dB within the dry-snow zone. These observations correspond with results of recent comparisons of SASS with ERS-1 data (Reference Jezek and GogieniJezek and Gogineni, 1992), where similar trends are identified in the Greenland SAR data. On the basis of snow grain-size alone, this would require a change in mean grain radius of 0.25 mm, which is extremely unlikely. Similarly, within the typical range of observed density and depth, this variability cannot be reproduced. Thus, to explain these results, further field measurements are required to describe the characteristics of the summer surface beneath the annual snow accumulation. One suggested hypothesis is that the small-scale surface roughness associated with wind-scouring of the previous summer surface or wind-slab may become significant where there is relatively low accumulation. The interface roughness is a predominant feature required in the scattering simulations from this zone.

The dry-snow zone may clearly be divided into two regions on the basis of the observed signatures and model simulations. These are: (i) the region (dry snow I) found to the north and northeast, comprising the relatively lower-elevation region in the precipitation shadow of the main ice-sheet topographic barrier; and (ii) the summit or higher-accumulation dry-snow region (dry snow II), where mid-summer mean temperatures do not exceed about −5°C. The latter extends around the western and southern summit region within a broad area above the 2500 m contour. A criterion for separating the two is the −7 dB isoline of A (Fig. 5) which follows the locus of points along the spine of the ice sheet. This line follows the topographic barrier discussed by Reference Ohmura and ReehOhmura and Reeh (1991) in their discussion of solid precipitation patterns.

Delineating the dry-snow line

Reference BensonBenson (1962) delimits the lower extent of the dry-snow zone as corresponding to the −5°C mean summer season isotherm, where it intersects the snow surface. This postulation is made on the basis of diagenesis of grains alone. If summer surface temperatures rise above −5°C, the process of equi-temperature metamorphism is accelerated, ensuring grain growth, sintering of grain clusters and often refreezing of meltwater in the snow. Such a gross change in diagenetic processes is reflected in the data since the microwaves are so sensitive to melt, we can map the dry-snow zone simply as the portion of Greenland which shows negligible change in time-series data. It has not previously been possible to map this line using visible wavelength-satellite data (Reference Williams, Hall and BensonWilliams and others, 1991); however, the penetrating capabilities of microwaves enable such a demarcation. Late in Septem-ber, the cold wave has penetrated downward into the snowpack beyond the old summer surface. After this date there is a relatively strong delineation between the dry-snow and the percolation facies downslope, where melt has occurred. The strong gradient between low values of A in dry snow and high A in the percolation zone is used as a locator, and model simulations for Figure 5 values suggest a 40° incidence back-scatter value of −5 dB as a good dry-snow line marker. The result is a map where the line closely follows the 2500 m contour in south-central Greenland (Fig. 15), falling below 2000 m at 75° N latitude on the west coast.

Fig. 15. Map showing the postulated locations of key facies and zones extracted from the high-resolution SASS maps.

Percolation zone

By late September, the contrast between the percolation zone and the dry-snow zone is large enough that mapping the upslope extent of the percolation zone is relatively straightforward. The sequence of maps in Figure 5 also demonstrates that the percolation zone becomes more extensive and marked as the 0°C isotherm moves downslope in the fall. In this region of snow, meltwater percolates downward into the snowpack. Often it refreezes at depth in cold snow, or alternatively it may penetrate freely in pipes to the depth of the first stratigraphic impediment. The further downslope, the lower the net annual accumulation, and thus the shallower this impediment becomes. The lower limit of the percolation zone therefore marks the wet-snow facies.

Southern observations

In the percolation zone, warming is detected in the early parts of the Figure 3 time-series, but A soon assumes a stable level after mid-August (Julian day 228) of −1.9 dB at 66° N, 46° W. Upslope, σ° decreases, to A = −5.4 dB (Fig. 4) at the higher altitude location of 66° N, 44° W. Annual accumulation increases with altitude, and the seasonal mean temperatures are colder, thus reducing the rate of grain growth. Above the equilibrium-line altitude (ELA) (at around 1200 m on Jakobshavns Isbrae), balance measurements can be used to infer residual snow depths at the end of the summer melt. Along the EGIG line at 1700 m altitude, the balance is typically 0.5 m w.e. year⁻¹ (i.e. over 1 m accumulation of snow at a density of 0.45 Mgm⁻³).

Reference Swift, Hayes, Herd, Jones and DelnoreSwift and others (1985) considered the volume-scattering mechanisms in simulations of the back-scatter from the percolation zone by using an unbounded half-space of scatterers. However, it is not necessary to invoke a strong volume-scattering layer to simulate the bright levels of back-scatter observed at Ku-band. Results shown in Reference Jezek, Drinkwater, Crawford, Bindschadler and KwokJezek and others (1993) suggest that there is some dominant stratigraphic feature which regulates short-wavelength percolation-zone scattering. Thcy show that there is a strong frequency dependency to back-scattering. Longer wavelengths such as L-band (21 cm wavelength) penetrate deeper, possibly penetrating the multiple layers found in this glacial regime (Reference Echelmeyer, Harrison, Clarke and BensonEchelmeyer and others, 1992) to be scattered off the ice glands and lenses found up to a few meters beneath the surface. Contrasting X-band (3 cm wavelength) measurements by Reference Forster, Davis, Rand and MooreForster and others (1991) indicate that the strongest returns come from annual layers at intervals beneath the surface which are shallower than 3 m. Recent findings from Greenland, using a Ku-band instrument during field experiments in 1991, also indicate that the largest proportion of back-scattered returns occurs from an ice layer just beneath the annual snow accumulation (Reference Jezek and GogieniJezek and Gogineni, 1992). Using a time-gated scatterometer, they demonstrate that the returns (at θ — 45°) from a depth range equal to the depth of the first ice layer were much stronger than those from either the surface of the snow or other ranges. Using the simple 2 layer ice/snow model the primary response from the upper layer is formulated in terms of a non-stratified Rayleigh layer upon an ice horizon of finite thickness. This follows work by Reference MaderMader (1991), which built on a simple scattering model applied by Reference Jezek, Drinkwater, Crawford, Bindschadler and KwokJezek and others (1993). The simulation results support these postulates.

Field measurements by Reference Echelmeyer, Harrison, Clarke and BensonEchelmeyer and others (1992) at altitudes between 1300 and 1600 m on Jakobshavns Isbrae illustrate the typical conditions during the summer months (albeit during a cold summer season). Their data indicate weakly stratified material (from net seasonal accumulation) lying upon some dominant, spatially contiguous ice layer or relatively dense internal bound-ary. For example, at 1520 m Reference Echelmeyer, Harrison, Clarke and BensonEchelmeyer and others, (1992) measured a 5 cm thick layer of ice at 30 cm depth, associated with the summer surface. Then at around 70 cm depth was another 15 cm thick ice layer this time associated with percolation to the depth of the previous summer surface. The mean density of the firn separating each ice layer was measured typically to be 0.45 Mgm ⁻³. When dry, this snow would have large grains, likely on the order of 1–2 mm diameter. Reference Echelmeyer, Harrison, Clarke and BensonEchelmeyer and others (1992) also reported that this ice layer is almost continuous at about 0.2–0.4 m depth in the elevation range from about 1300 to 1600 m. It was often a few centimeters thick and so hard that it prevented stake emplacement without drilling in many places. Moving upslope and inland to the Crawford Point site (CP. in Figure 1), occupied by Jezek and his co-workers at an altitude of 1900 m, similar stratigraphic features are found. The main real difference in snow-pit characteristics is the considerably higher annual accumulation measured at the Crawford Point site. Reference Ohmura and ReehOhmura and Reeh (1991) indicate an annual accumulation of over 50 cm w.e. at this site. If a density of 0.45 Mgm⁻³ is assumed, as appears typical from Benson’s snow pits along this transect, then this snow water equivalent represents over 1 m of snow accumulation. Indeed, Reference Jezek and GogieniJezek and Gogineni (1992) reported a value of about 140 cm of snow in June 1991.

The simulation in Figure 13 shows σ° versus θ for the medium specified. Model parameters were set using density and grain-sizes comparable to those values given for the snowpack at Crawford Point, but used to simulate fall conditions at the end of the time-series shown in Figure 3a. The data points overlaid on the simulated curves in Figure 13 are the same as shown in Figure 3b, plots (2) and (3). Notably, the annual accumulation for the region shown in Figure 3 is less than that directly east of Jakobshavns Isbrae. Reducing the snow depth to 0.7 m increases the strength of the surface returns slightly, because the surface scattering from the ice layer beneath becomes significant. The layer 2 roughness for curve B has a standard deviation of 4.5 mm and a correlation length of 7.0 cm. The match between Figure 3b and simulated scattering from this medium-rough surface is extremely good.

Fig. 13. Plot of σ° versus θ for a simulation example corresponding to a simple 2 layer model for the percolation zone. The inset describes the layer properties used as model inputs. Parameter inputs were selected to match surface-properties measurements in a region typical of region b, Figure 3. Data points from Figure 3b (2) and (3) are overlain.

Multi-layered physical models

It should be noted from the model simulations that the level of Ku-band volume-scattering from the percolation-zone snow becomes significant once snow grains reach diameters of around 1 mm. Neither deep-snow nor ice lenses are required to maintain the high incidence-angle values of around 7 dB seen in Figures 3 and 13. Together with the snow-and ice-layer scattering contributions, snow-grain volume-scatter is sufficient to match levels of scattering observed in SASS data. While this is not a comprehensive description of the multiple layers or indeed the sub-surface ice pipes and lenses, it does describe two uppermost layers which effectively impact the higher-frequency microwave scattering. There is no doubt that a more comprehensive physical description of the snow and ice layers becomes necessary in the case of longer-wavelength microwave scattering. Indeed, dipole scattering from decimeter-scale, vertically oriented ice bodies (such as ice pipes) is being investigated as a means of explaining some of the lower-frequency scattering phenomena observed by E. Rignot (personal commu-nication), Reference Jezek and GogieniJezek and Gogineni (1992) and Reference Jezek, Drinkwater, Crawford, Bindschadler and KwokJezek and others (1993).

Wet-snow zone

Moving downslope into the heart of the melt zone, the seasonal 0°C isotherm penetrates down to a few meters’ depth. AtJakobshavns Isbræ, melt rates up to 0.5 cm d⁻¹ are possible and meltwater either is suspended between snow grains or filters down to form superimposed ice on the dense iced firn or summer ice surface beneath. By definition the wet-snow zone encompasses the area where the surface is covered by wet or saturated snow at a temperature of 0°C. Further downslope, the snow cover is more patchy and the wet snow tends to survive in topographic lows in what Reference Echelmeyer, Harrison, Clarke and BensonEchelmeyer and others (1992) call “slush swamps”. The end of continuous snow and the beginnings of areas of discontinuous saturated snow mark the lower boundary of the wet-snow zone, the firn or snow line.

The presence of wetness results in limited penetration of Ku-band signals into the snow and firn. With only a few per cent liquid water by volume, absorption extinguishes the transmitted waves within a few wave-lengths. Thus, sub-surface conditions become camoufiaged and impossible to detect. Notwithstanding this deficiency, dielectric properties of wet snow change dramatically as the surface snow becomes wetted, thereby offering some potential for relating different signatures to different snow wetnesses. As soon as the snow has enough liquid water suspended between the grains (i.e. pendular regime), back-scatter becomes dominated by surface scattering and reflection and thus also the roughness of the snow surface.

Wet snow is relatively smooth in contrast to dry snow or bare ice, according to measurements by Reference Rott, Domik, Mätzler, Miller and LenhartRott and others (1985). Typical roughness values quoted by Reference Shi, Dozier and WilliamsonShi and Dozier (1992) indicate rms heights ranging from 0.4 to 1.4 cm (mean of 0.7 cm) with correlation lengths from 1.56 to 9.0 cm. For a snowpack with 6% water (by volume), Reference Rott, Domik, Mätzler, Miller and LenhartRott and others (1985) measured a rms surface height of 0.61cm and correlation length of 9.1cm (rms slope of 0.24rad), which fall within the range quoted by Reference Shi, Dozier and WilliamsonShi and Dozier (1992). These values are used as scaling parameters in the following model simulations.

Southern wet-snow zone

A model result is compared in Figure 14 with the SASS data points from region i. Though the data (thick dotted line) closely match the model result (curved solid line), two populations of points are evident, especially between 45° and 60°. One satisfies a specular surface with a small contribution by volume-scatter (at a level of around −20dB), while the other more closely traces the thin dashed curve for pure surface scattering (albeit with a higher B value). Wetter regions have saturated surfaces and negligible volume-scatter, with an absence of data points above −25 dB at angles over 60° incidence. Since surface scattering is dominant, the values of the firn/ice interface roughness are unimportant and unnecessary in Figure 14. Results show region i to have a relatively reflective surface but the resolution of the system limits the purity of the signatures. Comparisons with Figure 5 clearly demonstrate that the lowest back-scatter originates from wet snow and that mapping the wet-snow region is optimal in late June–early July.

Fig. 14. Plot of σ° versus θ for 1° × 2° study region i in the southern wet-snow zone. Model simulation results are indicated and surface and volume contributions are shaded. The thin dashed line indicates simulated surface scattering only, while the horizontal solid line at −19 dB marks the simulated volume-scattering component. The curved solid line signifies the total of surface and volume-scattering sources, and the corresponding SASS data are indicated as a thick dotted line.

To match observed wet-snow back-scatter with model simulations, it is necessary to increase extinction and almost completely switch off dry-snow volume-scattering from snow grains. This is achieved by adding only 2 or 3% liquid water by volume in firn of densities of around 0.5 Mgm⁻³ with grain diameters of 1–1.5 mm. This reduces penetration within the isothermal surface snow (at 0°C) to the order of a few wavelengths. σ° at 40° is then typically less than A = −12dB. Thus, the −12dB line may then be used as the delimiter of the upper extent of the wet-snow zone. At lower altitudes the annual accumulation depth of 0.3–0.4 m often becomes satu-rated at the end of summer. As snow-free water content climbs, the scattering loss factor increases exponentially and the permittivity climbs steadily. For a grain radius of 0.5 mm, water content of 10% by volume and density of 0.5 Mgm⁻³ (Fig. 14), the permittivity exceeds that of ice (i.e. > 3.0), while the dielectric loss attains values near 1.0. The Figure 14 simulation, with saturated firn above hard ice, shows that the volume-scattering is lowered to −20 dB or less. In this surface-scattering-dominated regime, the rms roughness and correlation function are important to B. However, increasing wetness drives up the complex dielectric constant and the reflectivity, which, even with the roughness values specified, causes decreased back-scatter at 40° (i.e. reduced A). More extreme examples in Reference Shi, Dozier and WilliamsonShi and Dozier (1992) demonstrate that if the surface is much rougher, then increased wetness could cause an increase in high-incidence back-scatter.

It should be noted that the saturation line is not evident in the mid-summer microwave data, as there is no way of sensing if the snow is saturated to the base of the annual-accumulation layer. This would require determining the snow-wetness values based upon the dielectric properties of the surface. Recent work by Shi and Dozier (personal communication) suggests that this may become possible in multi-frequency aircraft SAR data.

Wet-snow data values extracted from region j in Figure 1 show similar characteristics to SASS data points in Figure 14, confirming that the wet-snow zone has the most variable microwave signatures and thus has the most spatially variable physical properties.

Fall cooling in the wet-snow zone

Evidence supporting the hypothesis that large snow grains are the primary mechanism for dry-snow volume-scattering is found towards the end of the wet-snow time-series in Figure 2a. As the 0°C isotherm descends downslope and the wet-snow zone refreezes, A soon climbs to higher values with extremely low variability. The level of volume-scattering after Julian day 240 in Figure 2b cannot be caused by large ice lenses or glands, because originally the whole active surface layer was wet or saturated. Refreezing docs not suddenly enable ice-lens growth: instead, grains of snow bond together and grow significantly in size as irregular clusters during the summer months. Firnification processes thus cause a high level of back-scatter similar to what occurs in the percolation-zone examples from region b by the end of the time-series (cf. Figs 2b(3) and 3b(3)).

Separating the ablation and wet-snow zones

Due to a lack of contrast between the ablation zone and the wet-snow zone, it is difficult to make a distinction based upon σ° values from our time-series data. Without a longer seasonal-change cycle, and without more overlapping higher-resolution SAR data, it is currently impossible to extract the effects of mixed pixels. A small exercise was conducted on the relationship between the observed variability and individual cell signatures. It was necessary to check whether the variations in the A and B plots were a result of spatial or temporal changes in surface properties within any given sample box. It was found that it is largely differences in the rates of change of surface dielectric conditions within each cell that cause scatter in the time-series estimates of A and B.

When mixed bare-ice and slushy-snow patches are present, surface wetting causes some differences in the responses of the bare ice and wet snow. Depending upon the shape and size of the imaging cell, at any given pass of the SASS, this results in a mixture of signatures over time. The only way to extract the location of the upper boundary of the ice or ablation facies is to mark the snow line during mid-summer. Then, the ice and ablation area is simply the remainder of the ice sheet between this line and the outer extent of the ice-sheet, shown in Figure 15 as a dotted line. It is recognized that some unknown error occurs due to the lack of accounting for the superimposed ice zone. Ice-sheet extent and the lower limit of the wet-snow zone (i.e. the “snow” line) are best mapped with the high resolution offered by the SAR on board ERS-1. Even then, there is no convenient way of discriminating the ablation area or area of net melting from the remainder of the ice facies, since no recognizable physical differences exist between superimposed ice (above the equilibrium-line altitude) and ablation-zone bare ice.