Dry-snow facies

This facies is found only on the highest parts of ice sheets and some high-latitude glaciers. There is no surface melting in these regions and so the surface, consists of snow which is gradually compacted under its own weight, or metamorphosed under the effect of wind or depth-hoar development. The area is extensive over Greenland, but not necessarily uniform. In fact, recent studies (e.g. Reference Fahnestock, Bindschadler, Kwok and JezekFahnestock and others, 1993) indicate that there are systematic variations in this facies from southwest to northeast across Greenland. These regional differences may be related to corresponding variations in patterns of accumulation and wind leading to different morphological conditions in the snow, but this has not been established. The lower boundary corresponds approximately to the mean -5°C isotherm during the melt season (Benson, 1996, p.61), but according to Benson the boundary may be in the form of a 16-32 km wide transition region.

In general, SAR senses the dry-snow facies as a very dark region, as the grain-size of fresh snow is small compared to the wavelength of the C-band SAR systems (about 5 cm). Snow grain diameters above the wet-snow line are generally <5mm in diameter, with an approximate mean of 0.5-2 mm (Benson, 1996, Fig. 18). In the dry-snow facies, melting will not be a factor in the backscatter coefficient (?°). Any variations in ?° may be expected to derive largely from differences in grain-size. It is possible to derive a simple expression which, crudely, predicts the backscatter as a function of the grain-size. The backscatter coefficient for dry-snow, ?°_ds, can be defined as follows:

where T ₁ and T ₂ are the transmission coefficients in the downward and upward directions, N is the number density of scattering elements, {|f _i|²} is the scattering amplitude of a single element in the backward direction (for monostatic scattering), ? is the extinction coefficient, ??_i is the refracted incidence angle and h is distance (Reference Partington and HannaPartington and Hanna, 1994). Assuming an effective transmission coefficient in both directions of 1, a uniform size of scatterers and a half-space, the above equation can be simplified to:

where is the dielectric constant, r is the particle radius and ? is the wavelength (Ulaby and others, 1981, cq. 5.85). The extinction coefficient, ?, is defined as follows, under the assumption that the absorption coefficient is dominant (Ulaby and others, 1981, eq. 5.100):

By substituting Equations (3) and (4) into Equation (2), the following is derived:

which for ERS-1 (? = 0.056, ? _i = 23°) and assuming a dielectric constant of 3.15 - 0.0025j, simplifies to

Equation (6) suggests that the backscatter coefficient would range from -20 dB for a grain mono-distribution with mean radius of 0.25mm to -2 dB for mean grain radius of 1 mm.

It must be stressed that this is a crude approximation which neglects multiple scattering, but it provides an indication of the sensitivity of the SAR to systematic variations in grain-size, which may be related to regional variations in accumulation rate and temperature. This equation will not help to interpret the effects of rime-frost, depth hoar or other complex physical phenomena.

Percolation facies

Here, the surface snow is occasionally subject to melt which results in the percolation and refreezing of meltwater in the form of pipes and lenses (see Reference Ahlmann and sonAhlmann, 1935; Reference SharpSharp, 1951; Reference Marsh and WooMarsh and Woo, 1984), There may be no clear surface manifestation of the boundary between this facies and the dry-snow facies. The percolation facies can, however, consist of significant bodies of ice. Reference Echelmeyer, Harrison, Clarke and BensonEchelmeyer and others (1992) found a 5 cm thick layer of ice at 30 cm depth in this facies, with grains typically 1-2 mm in diameter. C. S. Benson (personal communication) has recorded photographs of pipes corresponding to a percolation facies in Alaska, where dimensions are typically 10 cm long and a few cm diameter. Over Greenland, K. G Jezek (personal communication, 1996) found that sizes of inclusions vary appreciably. At Crawford Point (just inland from Jakobshavn in the percolation facies), massive ice pipes tens of centimetres long and up to 10 cm wide were found. Once out of the jakobshavn drainage area, but still at about the same elevation, Jezek found that the ice-pipe sizes decreased dramatically to about 10 cm long and 2 cm wide, which seemed characteristic all the way up to the Dye 2 site (66.5° N, 46.3° W). At Dye 2, smaller isolated lenses were found.

The presence of ice pipes and lenses can act to increase the backscatter in SAR data substantially over that commonly found in the dry-snow facies. Ice lenses and pipes can have dimensions comparable to the wavelength of the SAR and so can produce high returns. This is confirmed by Reference Fahnestock, Bindschadler, Kwok and JezekFahnestock and others (1993), who note from their SAR mosaic of Greenland that there is a sharp contrast between the backscatter from the centre of Greenland (low) and the percolation facies which surrounds it (high). Based on the observations of K. C. Jezek (personal communication, 1996) and Reference BensonBenson (1996), it may be expected that there would be a smooth gradation of backscatter from the dry-snow facies to the percolation facies, rather than a sharp boundary, and this is confirmed by Reference Fahnestock, Bindschadler, Kwok and JezekFahnestock and others (1993).

Wet-snow facies

The wet-snow facies is defined as extending further down the glacier from the point in the percolation facies at which the entire annual accumulation of snow is subject to melt and refreeze. In this facies, the snow mass reaches melting point as a result of latent heal released by extensive refreezing of meltwater. As a result, grain-sizes are larger and re-crystallisation is the norm rather than the exception. The transition to the wet-snow facies from the percolation facies takes place over a few kilometres, according to Reference BensonBenson (1996). In general, the wet-snow facies will be damp throughout the ablation season, although refreezing at the surface will occur. In the lower altitudes of the wet-snow facies there may be lakes and areas of slush where melting is particularly vigorous.

During the ablation season, the wet-snow facies will reduce markedly in backscatter intensity, and the main scattering mechanisms will alter. The penetration depth of dry snow at the configuration of the ERS-1 SAR (C-band) is of the order of 20 m (Ulaby and others, 1981, Fig. 11.25). Very small amounts of moisture drastically reduce the penetration depth, so that a volumetric moisture content of2% will reduce the penetration depth to approximately 1 % of its dry equivalent (Reference Ulaby, Moore and FungUlaby and others, 1981). The scattering mechanism will therefore change from predominantly volume scattering to surface scattering. Ulaby and others (1986, p. 1893) note that at G-band, the Fresnel reflectivity at normal incidence for snow with 10% liquid water is 0.06. Using this, the Kirchhoff Geometric Optics model predicts that, with an rms slope of 0.2-0.4 the backscatter coefficient ranges from -9.6 to 16.2 dB, which is similar to, or even considerably less than, the backscatter expected from the dry-snow facies (Ulaby and others, 1986, eq. 21.27). Thus, we would expect the darkest, areas in a SAR image of glaciers to correspond to damp areas. A layer of damp snow under refrozen or fresh, dry snow would show little difference in backscatter as a result of the high penetration depth of radar in dry snow.

There is little reason to suppose that the wet-snow facies will show fundamentally different scattering mechanisms to the percolation facies, except during early and late summer when the melt limit is moving up- and downslope, respectively. However, Reference Fahnestock, Bindschadler, Kwok and JezekJezek (1993) found that the backscatter from the wet-snow facies was much more strongly varying than from the percolation facies. The slush which can form at the base of the wet-snow facies can cause dark patches to appear in the SAR image data (Reference Bindschadler and VornbergerBindschadler and Vornberger, 1992). In addition, it may be expected that there will be a general gradation of mean backscatter with altitude as a result of the change in density and size of lenses and pipes. Nevertheless, the wet-snow line may not be expected to be detected as a discrete boundary as it can have no influence on the sensing properties of the SAR, the line being coincident with the subsurface position where the 0° isotherm reaches the base of the previous year's accumulation, and so hereafter in this paper the percolation and wet-snow facies are treated together.

Superimposed-ice zone

Below the wet-snow facies, but still within the general accumulation area of the ice sheet, there may lie a region of superimposed ice, which is high-density refrozen melt from the previous year's accumulation. In a heavy ablation year, this facies may not exist, as the ice may be completely melted, leaving the snowline equivalent to the equilibrium line (the boundary between net accumulation and net ablation). In a lighter ablation year the equilibrium line will lie between the superimposed-ice and ice facies, giving it a different surface manifestation. G. Marshall (personal communication, 1995) suggests that the superimposed-ice facies is potentially distinguishable in SAR data as a result of its greater degree of smoothness relative to the ice facies.

Ice facies

The lowest part of an ice sheet or glacier consists of the ablation region, or ice facies. Here, the total year's accumulation, and more, is lost to melting. During winter, the ice facies will be covered by dry snow. During early summer, the snow will be melting so that by the end of the ablation season the entire accumulation of snow will have been melted, as will some of the ice from previous years' accumulation. The backscatter from SAR is likely to decrease slowly-through winter as the relatively rough ice snow interface becomes buried by attenuating dry snow (which itself generates very little backscatter). When the snow melts, the backscatter will decrease further, as was indicated above for the wet-snow facies. Once the snow has melted, leaving bare ice, the backscatter is likely to reach its yearly peak as a result of exposure of a rough, dense ice surface.

Greenland

The Greenland test area, for june 1992 January 1993, corresponds to a 100 km wide and 600 km long SAR swath (generated using six neighbouring image frames) extending from the west coast at 71°30?N, 53° W, well into the dry-snow facies at approximately 71°30? N, 43° W. The coverage includes several outlet glaciers which extend to sea level and calve icebergs. Major glaciers include (from north to south) Umiámáko Isbræ, Rink Isbræ and Kangerdluarssp sermia. These "major" glaciers have widths at their seaward margin of 5-10 km. Many smaller glaciers are also present.

There are supporting data for the study. Meteorological data provided by H. Rott of the University of Innsbruck were recorded at Godthåb/Disko (sea level). These give the air temperature and dew point at 1200 h for dates relevant to the acquisition of image products. Table 1 summarises the relevant supporting data.

As well as measurements of conditions at the time of the acquisition of data, there are the results of field surveys which provide estimates of the altitudes of glacier facies between 69° and 70° N (Table 2).

Study Techniques

Results

The colour schemes for the Greenland and Wrangell data are equivalent (blue = winter, red = early summer, green = late summer), and the resulting multi-temporal, three-band SAR images are displayed for the Mount Wrangell region in Figure 7 and for West Greenland in Figure 8. In Figure 8, contours of backscatter differences, in dB, between 23 June 1992 and 16 January 1993 are given inland of the coastal region (the coast is the lower, left side of the diagram). It can be seen from both the contours and the lack of colour that nearly the whole area in Figure 8 shows no significant multi-temporal signature. This is expected, as most of the region consists of the dry-snow facies, which appear as dark grey, and the percolation facies, which appear as white. However, there is significant temporal variation in backscatter in the coastal region and this is shown expanded in Figure 9. Recall that the dates of the component images (winter, early summer and late summer) in Figures 7-9 are given in Tables 1 and 3 and that the SAR data are terrain-corrected in Figure 7 but not in Figures 8 and 9.

Fig. 7. Terrain-corrected, map-projection multi-temporal ERS-1 image segment of Mount Wrangell and the area to the east, with north towards the top of the figure. Blue indicates data from 30 December 1992, red indicates 23 June 1993 and green indicates 1 September 1993. The background yellow-green signature in non-glaciated areas indicates a marginal increase in backscatter during the summer months which is thought to reflect growth of vegetation. The blue profile (A) shows the location of Figure 10, and the red profile (B) shows the location of Figure 11. Numbers refer to altitude above sea level, in metres.

Fig. 8. Multi-temporal image mosaic of Greenland. The image is in map projection, with north at the top of the figure. Blue indicates data from 16 January 1993, red indicates 20 June 1992 and green indicates 29 August 1992. Contours indicate backscatter coefficient differences (dB) between the 20 June 1992 and 16 January 1993 images, except in the coastal region (bottom) where the difference is >0.2dB. Nearly the whole area covered by this figure corresponds to the percolation facies (bright) and dry-snow facies (dark) and so shows no significant multi-temporal signature.

Fig. 9. The coastal (lower) portion of the multi-temporal image swath from Figure 8 (expanded to show detail). The image is in map projection, with north as the top of the figure. Blue indicates data from 16 January 1993, red indicates 20 June 1992 and green indicates 29 August 1992. The approximate position of the coastline is indicated by a white line.

As digital elevation data are available for Mount Wrangell, it is possible to generate profiles of multi-temporal backscatter signature both as a function of altitude along the Wrangell Icefield-Nabesna Glacier from source to terminus and as a function of orientation close to the summit of Mount Wrangell (4000 m a.s.l.). These profiles are located in Figure 7 and can assist in determining the boundaries of the various facies and in analyzing their characteristics. Figure 10 shows profiles of the backscatter coefficients for 30 December 1992, 23 June 1993 and 1 September 1993 as a function of altitude, for a line down Nabesna Glacier. These profiles extend from the dry-snow facies down to the ice facies. Figure 11 shows profiles of the backscatter coefficients for the same dates around the summit of Mount Wrangell at 4000 m a.s.l., in the dry-snow facies.

Fig. 10. Backscatter coefficients vs altitude along Nabesna Glacier and up to Mount Wrangell, for the three different dates. See Figure 7 for location of profile.

Fig. 11. Backscatter coefficients as a function of orientation of slope at 4000 m.a.s.l. on Mount Wrangell and for the three different times of the year. See Figure 7 for location of profile.

In the following sections, the manifestations in the multi-temporal SAR data of each of the glacier facies are described and possible explanations provided.

Dry-snow facies

Over a very wide region of the Greenland test area (Fig. 8), the dry-snow facies can be located from a combination of low backscatter and the complete absence of any multi-temporal signature (dark grey in Figure 8). The radiometric stability (over the 7 months represented in this time series) is < ±0.2 dB over most of the mapped dry-snow area of 100 km x 300 km, which is an indication from a natural, uniform distributed target of the stability of the ERS-1 SAR which is well within the design criteria for the instrument. However, an area to the north of the test region shows higher variation, up to 0.6 dB, which may be related, in some way, to the lower accumulation rate in that region.

The area bounded by a calibrated backscatter coefficient of-8dB (after correction for power loss) corresponds very closely with the dry-snow facies as defined by Reference BensonBenson (1996) in this region and estimated using the supporting data provided in this study (i.e. dry-snow line at ~2400 m a.s.l.). However, the overall range of backscatter coefficient across the dry-snow region of Greenland appears to be a minimum of about -14 dB and a maximum of about -5 dB, judging from a comparison of the Greenland facies map of Reference Long and DrinkwaterLong and Drinkwater (1994) with a map of fully calibrated ERS-1 backscatter coefficient across Greenland generated by P. J. Meadows, in Reference SephtonSephton and others (1995) (which includes power-loss correction).

These variations in backscatter coefficient across the dry-snow facies may be related to regional differences in accumulation rates. Largest grain-sizes are found in areas of lowest annual accumulation, where they may reach 1-2.5 mm in radius, through a process of depth-hoar development (Reference PatersonPaterson, 1981). However, these values are unlikely to be attained with continuity, vertically through the snowpack. If these grain-sizes were continuous, the backscatter coefficient would reach a figure of the order of-2.5 dB (Equation (6)). More typical snow sizes are radii of the order of 0.5 mm for snow which has not been subject to depth-hoar development, suggesting a backscatter coefficient of-11 dB (Equation (6)).

In the Wrangell data (Fig. 7), the dry-snow facies is indicated by patchy, dark areas near the summit. There is much less stability between the observations at different times of the season here than in Greenland.

The following equation most closely maps the extent of the dry-snow facies determined by Reference BensonBenson (1996) at the latitude associated with (his test site:

This criterion gives a mean altitude for the dry-snow line around Mount Wrangell of approximately 3460 m on the north side and above 4000 m on the south side (from the September image data). This compares with an altitude of about 2400 m for the test area in Greenland (the precise altitude cannot be measured, as a result of a lack of elevation information).

Percolation and wet-snow facies

Reference Fahnestock, Bindschadler, Kwok and JezekFahnestock and others (1993) showed that the percolation facies tends to be bright in ERS-1 SAR image data. This is true of winter image data and the highest areas of the percolation facies. In summer, however, areas of melt can extend into the percolation/wet-snow facies, reducing the backscatter coefficient (to below -15 dB in the Wrangell region). Thus, in the multi-temporal images generated here, we would expect to sec high-backscatter winter image data combined with early- and late-summer image data which will show the passage of surface melt into the wet-snow/percolation facies. In general, we will expect to find three zones within the percolation/wet-snow facies displayed in Figures 7-9. At the highest altitudes (the "upper zone") we would expect to find a uniformly high backscatter coefficient for all three dates, as at the highest altitudes in the percolation Facies we would not expert to find melt on any of the three dates. This region would appear "white" in Figures 7-9. Further down (the "middle zone"), we would expect to find a region in which melt is present in the late-summer image but not in the early-summer or winter image. This region would appear "'purple" in Figures 7-9, as the backscatter will be uniformly high during winter and early summer and low in late summer. Finally, towards the lowest altitudes in the percolation/wet-snow facies (the "lower zone"), we would expect to find melt associated with both early- and late-summer images, so the backscatter would be high in the winter data and low in both summer images. This region would appear "blue" in Figures 7-9. This is summarised in Table 4.

The upper percolation/wet-snow facies (Table 4) is extensive in Greenland (Fig. 8, white areas), indicating widespread freezing conditions on all three dates. The backscatter coefficient is of the order of-4 dB. Interestingly, the stability for the three images is as high as that of the dry-snow facies (<0.2dB). Moving down towards sea level (Fig. 9), some very limited "purple" regions indicative of the middle zone in the percolation/wet-snow facies are encountered (suggesting melt in the August data, where backscatter reduces to -10 dB) and then the "blue" lower percolation/ wet-snow zone (indicative of melt in both the June and August data), The altitudinal limit of the combined lower mid middle percolation/wet-snow zones in Greenland corresponds closely with the estimated highest altitude of melt of 1080 m on 17 June and 23 July 1992 (Table 1).

This pattern of zones is reproduced on the north- and east-facing slopes of Mount Wrangell, in an entirely analogous progression to that found in the Greenland data. On the south-facing slopes, however, the "upper zone" of the percolation/wet-snow facies appears green instead of white. This indicates higher backscatter in September than in December or June. This "green" tint extends almost to the summit of Mount Wrangell on the south-facing slopes, and includes areas that have very low backscatter in winter and so would be classified from winter data as being in the dry-snow facies. In fact, although the upper area on the south-facing slopes has very low backscatter in winter and early summer, the backscatter increases markedly in late summer by more than 5 dB. The difference in multi-temporal signature as a function of orientation is shown very clearly in Figure 11, for an altitude of 4000 m a.s.l.

This multi-temporal signature at high altitude on Mount Wrangell is extremely unlikely to be an instrument artefact, for the following reasons:

• the imaging geometry is virtually identical, and in this situation the stability of ERS-1 is a few tenths of a decibel (Reference SephtonSephton and others, 1995). The observed temporal difference (September-June backscatter coefficient) is a maximum of 5dB for slopes facing south;

• the signature is observed only on south-facing slopes and only in the percolation/wet-snow facies;

• registration errors would create similar artefacts elsewhere through the image and, in any case, cannot be large enough to account for the areal coverage associated with this multi-temporal signature.

As there is no ground truth to validate an interpretation, possible explanations are offered here for future investigation. Three possible explanations are:

• summer depth-hoar development;

• rime-frost development;

high winter accumulation over percolation facies.

Depth hoar consists of large, faceted crystals which develop from sublimation in the presence of a strong vertical gradient in vapour pressure (Reference Giddings and LaChapelleGiddings and LaChapelle, 1962). The development of depth hoar is a function of both the maximum degree of heating during the day and the diurnal range of temperature (Reference ColbeckColbeck, 1989). This would be consistent with the fact that the multi-temporal signature is found on the south sides of Mount Wrangell and not on the north or east sides, where diurnal temperature ranges are much smaller in summer. By late summer, the surface is cooling rapidly at night but the subsurface pack is still relatively warm, setting up a strong temperature gradient conducive to the formation of depth hoar (Reference PatersonPaterson, 1981). During winter, the backscatter would reduce as this depth-hoar layer is covered by a considerable attenuating layer of snow which on Mount Wrangell exceeds 100 cm w.e. on average (Reference Benson, Bingham and WhartonBenson and others, 1975). Studies by Reference BensonBenson (1968) show that depth hoar develops on Mount Wrangell each summer, but there is no direct evidence that it is better developed, to the point of being detected by the SAR, on the south-facing sides.

Rime-ice layers are also predominantly summer features which appear on Mount Wrangell, but in this case not in response to high temperature gradients but rather in response to storms (Reference BensonBenson, 1968). These layers may also form preferentially on the south side of Mount Wrangell as storms move in largely from the south. It is not clear that these features would act to increase the backscatter markedly, although Reference BensonBenson (1968) does note the frequent occurrence of these summer features on Mount Wrangell in excavated snow pits.

High winter accumulation over the percolation facies is a third possible explanation for the seasonal signature at high altitude on the south-facing slopes of Mount Wrangell. The annual accumulation rate averages 100 cm w.e. in the caldera, which equates to approximately 320 cm of snow (Reference BensonBenson, 1968), but could be higher on the south-facing slopes than on the north- and east-facing slopes (given the direction ?f predominant storm tracks).

Without validating information, it is not possible to draw a firm conclusion on whether rime-frost, depth hoar or high winter accumulation rates are causes of this multi-temporal signature in the SAR data on the south-facing slopes of Mount Wrangell. All three are mentioned simply as possibilities.

Ice facies

The ice facies lies below the equilibrium line, which is present in the Wrangell data at about 2100 m (Lingle and others, in press). There is no evidence for or against the presence of superimposed ice in the Wrangell data. In Figure 7, the ablation region can be seen to lie below the "blue" lower zone of the percolation/wet-snow facies (e.g. along the Nabesna profile) and the ice facies appears as having a green tint in the multi-temporal data. This indicates higher backscatter in September than in June or December.

Bare ice exists at the end of the ablation season (September image), but earlier in the season there remains snow cover. As explained earlier, a deep, dry- or wet-snow cover has the effect of attenuating return from the relatively strong bare-ice scattering surface, hence the green colour indicative of relatively strong scattering in September, except in areas of moraine which can be identified by longitudinal streaks in the glacier showing no multi-temporal signature.

A definition for the snowline is proposed as follows:

where subscripts "s" and "d" indicate September and December, respectively. This places the snowline on Nabesna Glacier at about 2100 m a.s.l. This compares well with the figures provided by Reference BensonBenson and others (1996) from both SAR data and air photographic data from nearby MacKeith Glacier (where it is estimated as varying in altitude between 2090 and 2230 m a.s.l.). The mean backscatter coefficients for the altitude range 950–2000 m on Nabesna Glacier (the ice facies), are shown in Table 5.

The June backscatter is consistent with scattering from a damp-snow surface. The scatter from bare ice (in September) would be expected to be greater, as the surface is rougher but will still be damp in September. In December, the scatter will be from a dry, bare-ice surface and volume attenuated by a layer of dry snow. In this area, snow depths in December are typically of the order of 2 m (personal communication from C. S. Reference Benson, Lingle and AhlnaesLingle, 1996).

An important implication of the Greenland data is that the percolation/wet-snow facies in these data extends to sea level in this region. There is no region in the Greenland data comparable to the ice facies visible in the Mount Wrangell data. This suggests a high-accumulation, or low-ablation year in 1992. Evidence in support of this result is provided by both Reference Thomas, Krabill, Frederick and JezekThomas and others (1995) and Reference Van Tatenhove, Roelfsema, Blommers and van VoordenVan Tatenhove and others (1995), who each note that 1992 was charaecerised by a very cold summer in West Greenland around Leverett Glacier and Jakobshavns Isbræ at 69° N. The average temperature at Kangerdlussuaq was 44°C from May to October, and 7.9° C from June to August, making it the fourth coldest summer between 1942 and 1992. Jakobshavns Isbræ thickened by several metres between September 1991 and April 1992 and, using aircraft-derived elevation profiles, Reference Thomas, Krabill, Frederick and JezekThomas and others (1995) found that, unusually, this was not compensated by summer melting during the following summer. Furthermore, Reference Abdalati and SteffenAbdalati and Steffen (1997) found, from passive microwave data, that there was a lack of melting during the summer of 1992 over Greenland as a whole, which they attribute to the eruption of Mount Pinatubo and the resultant increased aerosol concentrations in the atmosphere. In fact, the mean melt area (for the months of June, July and August over Greenland as a whole) in 1992 was about 0.7 x 10⁵ km²as opposed to mean melt areas during the summers of 1979-91 of about 0.9-2.25 10⁵ km² (Reference Abdalati and SteffenAbdalali and Steffen, 1997). Thus, there is strong evidence here, from a variety of sources, that ablation was unusally low in 1992, and the SAR data suggest that around 71° Non the west coast of Greenland die equilibrium line was at sea level at the end of summer that year.