C pattern

Figure 2a shows the high-pass filtered image of Ch1 (lower) and R2/1 (upper) on a coastal area of the ice sheet. Images taken under different solar azimuth are also shown to left and right.

Fig. 2. (a) C pattern in high-pass filtered albedo image in Chl (bottom ) and R2/1 (top) with resolution of 1.1 km on 4 December 1988 (left) and 3 December 1980 (right). White lines in each image show the location of profiles in Figure 3. (b) Surface contour map (NIPR, 1988) of Figure 2(a). North is N; solar azimuths of left and right figures are S and S′ respectively. A corresponds to 0 km in Figure 3.

The existence of distinct wavy structures in Ch1 is confined near the coast below 2000 m a.s.l., especially near the terminus of the outlet glacier (Shirase Glacier in Fig. 2b). The fluctuation of R2/1 develops not only below 2000 m a.s.l. but also higher. The C pattern has a wavelength of less than 10 km and is oriented normal to the ice flow lines deduced from surface contours (Fig. 2b).

Figure 3 shows profiles of the fluctuation in Ch1 and R2/1 along a flowline (white lines in Fig. 2a) of Shirase Glacier. Fluctuation in Ch1 is approximately ±3% and that in R2/1 is about ±1.5% in right images; in left images, they are both about ±1.5% except at a few points. The fluctuation in Ch1 and R2/1 is negatively and positively correlated in left and right image respectively, due to the solar azimuth (see below).

Fig. 3. High-pass filtered variations in Ch1 (thin lines) and R2/1 (thick lines) in C pattern on 4 December 1988 and 3 December 1980. Unit is 0.1%. The location of these profiles is shown in Figure 2(a) and (b).

S pattern

A well defined fluctuation in spectral ratio (R2/1) develops from 2000 m to 3000 m a.s.l. (Fig 4a). The wavelength is 10 km and 20 km at 2000 m and 3000 m a.s.l. respectively, gradually increasing with increasing altitude. The dominant alignment of stripes is at a right angle to the ice-flow lines (Fig. 4b) in the lower region around 2000 m a.s.l. or katabatic wind direction in the upper region (Reference SekoSeko and others, 1992).

Fig. 4. (a) High-pass filtered imae of S pattern in R2/1 with a resolution of 2.2 km on 4 December 1988. (b) Surface contour map of the area (NIPR, 1988). The S and N are solar azimuth and north respectively. The central line shows the traverse route corresponding to profiles in Figure 5. A is 0 km in Figure 5(a), (b) and (c).

Fig. 5. (a) High-pass filtered profiles in channels 1,2,4 and R2\l along the line in Figure 4b. Units are 0.1% in albedo or R2/1, and 0.1 K in Tb. (b) The relationship between accumulation rate (thin line) and high-pass filtered R2/1 (thick line) along the line shown in figure 4b. (c) Relationship between accumulation rate (thin) and slope gradient (thick) along the line shown in Figure 4b. Large negative values in the slope mean steep slopes.

Fluctuation is not found only in R2/1 but also in Ch1, Ch2 and Ch4. Figure 5a shows profiles of these variations along an oversnow traverse line (a line in Fig. 4b). Fluctuations in Ch1, Ch2 and R2/1 are positively correlated with each other and inversely correlated with the fluctuation in Ch4. The difference between S and C patterns is seen in the larger fluctuation in R2/1 (about ± 2%) than in Ch1 (about ± 1%) except at a few points such as 25 km from “A”. Fluctuations in Ch1 and R2/1 are positively correlated under different solar azimuth (not shown).

Figure 5b shows the relationship between R2/1 and the accumulation rate determined by measuring exposed snow-stake heights along an oversnow traverse route within four years from 1982 to 1986 (Nishio and others, 1988). Accumulation rate ranges from 0 cm a⁻¹ to 40 cm a⁻¹ snow, and there is fairly good agreement between them; low ratio corresponds to low accumulation rate.

Figure 5c shows the relationship between the net accumulation rate and the gradient of surface elevation measured by satellite Doppler positioning system and barometers (Reference Nishio, Ohmae and IshikawaNishio and others, 1988, a, b). It is also noticeable that low accumulation occurs on the steep slopes of the undulating topography. The amplitude of the undulation along this line is about a few tens of meters and slope gradient ranges from −6 × 10⁻³ to −1 × 10⁻³ except at the steepest point 27 km from “A” in Figure 4b.

Fig. 6. (a) P pattern in Ch4 image on 1 July 1988 with a resolution of 1.1 km. The white line and letter A in the center of the figure show the traverse route corresponding to profiles and 0 km in Figure 7 respectively, (b) Surface contour map (NIPR, 1988) of above.

Fig. 7. High-pass filtered variations on surface topography (thin line) and the Tb (thick lines) along the over-snow traverse route in Figure 6(a).

P pattern

P pattern can be seen on the ice-sheet surface on the further interior plateau above 3000 m a.s.l. It is clearly seen in winter Ch4 inamges, less so in summer Ch1 images and variation in R2/1 is negligible. Figure 6 shows an image on Ch4 focusing on the interior plateau of the ice sheet with a spatial resolution of 1.1 km. A band-shaped structure surrounds a summit of the ice sheet, with more than 20 km in horizontal spacing. Part of the band aligns at a right angle to ice flow lines deduced from surface contours., and part of the band is normal to katabatic wind directions which are partly seen as streak features in Ch4 (Reference SekoSeko, 1992; Reference Seko, Furukawa and WatanabeNIPR, 1992).

Figure 7 shows relationships between the fluctuations in Ch4 and the undulating topography measured by satellite Doppler positioning system and barometers during an over-snow traverse (Reference Ageta, Kikuchi, Kamiyama and OkuhiraAgeta and others, 1987). High Tb (brightness temperature) corresponds to the crest of undulating topography. The amplitude of the undulating topography along this line is deduced from the field data to be 8 m and slope gradient ranges from −2 × 10⁻³ to 1 × 10⁻³; the corresponding amplitude of fluctuation in Ch4 is about 4K. Though the fluctuation in Ch1 in summer images is much smaller than that in C and S patterns, the wavelength of the Auction in Ch1 is similar to that in Ch4 and the surface topography.

Visualization in reflectance and the spectrum

Undulating topography causes the change of solar irradiance per unit area and reflected energy is proportional to the irradiance. 1% of change in slope causes 1.7% of irradiance on unit area under 60° of the solar zenith angle. We can estimate the amplitude of undulating topography by checking the fluctuation of reflected energy in Ch1 or Ch2 unless albedo varies greatly over the undulating topography.

Actual ice sheets, however, are composed of many types of surface (Reference WatanabeWatanabe, 1978) associated with different albedos. A spectral index (R2/1) is very useful to detect the fluctuation of surface properties because the effect of undulating slope can be eliminated by taking the ratio. Reflectance in the near-infrared channel (Ch2) is more sensitive to the change of snow grain-size than that in the visible channel (Ch1) (Reference Wiscombe and WarrenWiscombe and Warren, 1980). Hence R2/1 should be the index which is proportional to the albedo on a snow surface. Reducing albedo by stronger sintering of snow particles probably occurs in lower-accumulation environment. Especially where net accumulation is almost zero, surface glazing is expected to occur. Reference Fujii, Yamanouchi, Suzuki and TanakaFujii and others (1987) found that glazed surface can be detected as relatively low-albedo (low R2/1) areas in NOAA AVHRR.

If undulating topography and change of surface properties co-exist (and considered to occur commonly on the ice sheet), it is difficult to estimate each contribution to the fluctuation in a single channel. We can deduce the relative contribution of each effect by examining both fluctuations in Chi and R2/1. As we have seen in Figure 3, C pattern varies more in Ch1 than in R2/1, and in the image under a different solar azimuth, the fluctuation in Chi appears in an opposite sense but that in R2/1 remains in a similar sense. They also suggest the widely fluctuating slope in C pattern. In S pattern, contrastingly, the amplitude of fluctuation in R2/1 is larger than in Ch1 (Fig. 5a), showing that S pattern has less variation of slope than that in C pattern, but a large variation of accumulation, which is confirmed by ground-survey data (Fig. 5b).

On the steep slopes of undulating topography, it can be deduced that katabatic wind is accelerated and it results in low accumulation rate because of the divergence of blowing snow flux. It can be said that this relationship is generally seen in both c and S patterns from the phase relationship between the fluctuation in Ch1 and R2/1.

Visualization in thermal infrared channel

The inverse correlation between fluctuations in Ch1 and Ch2, and that in Ch4 in S pattern (Fig. 5a) is probably caused by the heat budget on the snow surface. In summer when little wind and relatively stronger sunshine exist, snow surface temperature is primarily affected by short-wave radiation budget. Hence, the fluctuation of albedo and/or slope inclination determines that of surface temperature.

P pattern was clearly detected in winter Ch4 images. In winter, a surface temperature inversion exists over the ice sheet, exceeding 20 K at the lowest 100 m on the inland plateau (Reference SchwerdtfegerSchwerdtfeger, 1984). If surface undulating topography exists, part of the radiative cooled air will drain into the depression between the crests. Ground-survey data (Fig. 7) show that the amplitude of the undulating topography (2 × 10⁻³) exceeds the averaged slope gradient on the inland plateau of the ice sheet (1.5 × 10⁻³). It can be considered that a part of surface air flow on the inland plateau is controlled by the undulation and we can detect the pools of cold air in the Tb fluctuations in Ch4.

Fig. 8. Mosaic of Ch4 images with a resolution of 4.4 km constructed from 10 images in December 1988. L, M and A are Lambert Glacier, Mizuho Plateau and Dome A respectively.

Characteristics of undulating topography

It is reasonable to say that, while undulating topography can be found at every altitude on the ice sheet, causes of visualization in AVHRR differed. We classified them into three patterns. Characteristics of each pattern of undulating topography are summarized in Table 1.

Alignment and wavelength are readily observed from the images, and provide useful information of ice-sheet dynamics. The change of wavelength with altitude is similar to the ground-survey data compiled by Mclntyre (1986) and the wave length of P pattern is similar to that Reference Zwally, Bindschadler, Brenner, Martin and ThomasZwally and others (1983) found from the satellite microwave altimctry near Dome A.

Table I. Characteristics of each pattern

Although knowing their vertical scale is useful for understanding ice dynamics, it is difficult to calculate the amplitude of undulations from AVHRR, since reflectance is affected not only by undulating slope but also by albedo and/or subgrid-scale topographies such as sastrugi (Reference Wendler and KelleyWendler and Kelley, 1988). Actually, the surface properties change as seen in the fluctuation R2/1 in C and S patterns. The amplitude of P pattern cannot be estimated by fluctuations in Ch4, because the surface temperature inversion strength can vary under daily meteorological conditions. Hence, we show here the amplitudes of the undulating topography along over-snow traverse lines in S and P patterns. Concerning C pattern in which we have no ground-survey data, the amplitude was estimated as an averaged value of the fluctuation in Ch1 in two different images under almost opposite solar azimuth (Fig. 3), because, at least, the actual amplitude of the undulating topography must lie between these values.

Origins of undulating topography

A simple theoretical study (Reference NyeNye, 1959) shows that the life span of the surface undulating topography is less than 10 years, assuming 3000 m thickness of ice, 10 m a⁻¹ of ice-flow speed and no supporting force. Hence, undulating topography existing on the ice sheet must be supported by some forces. One possibility is subglacial topography, another could be accumulation anomalies.

The appearance of C pattern reflects the effect from subglacial topography. Its absence on ice shelf (NIPR, 1992) may show that it is the result of subglacial effect. On the edge of an ice sheet where ice is thinner and moves faster than inland, the effect of subglacial topography on the surface topography is greater. Some correspondence between undulating surface topography and subglacial topography was reported along a line shown in Figure 5c (Reference Nishio, Ohmae and IshikawaNishio and others, 1988a).

The relationship between accumulation and surface slope gradient (Fig. 5c) suggests a prevailing wind process. Anomalously accumulated snow changes topography, and katabatic wind can be affected by surface topography of a few tens of km in horizontal scale (Reference Kikuchi and AgetaKikuchi and Ageta, 1989). Considering the variation of accumulation is 40 cm a⁻¹ (Fig. 5b) and the surface topography has an amplitude 10 m, the wind action can alter a topography within 100 years. It could be a candidate to modify the topography primarily formed by bedrock undulation, and the alignment of undulation normal to the katabatic wind may suggest that wind processes modify this topography.