ANITA NOTE #108
Review of the Literature Regarding Small-Scale Surface
Roughness in Antarctica
Martin Griswold, David Saltzberg (UCLA)
February 12, 2016
Abstract
We conducted a survey of the literature relating to meter and centimeter scale
roughness of the Antarctic surface, a collection of relevant articles can be found at
http://www.physics.ucla.edu/~moonemp/roughness . Surface roughness in Antarctica is
created by snow accumulation and “katabatic” winds. Cold and dense air from the
interior of the Antarctic continent is pulled down the slopes of the central mountain range
creating strong winds that carve the snow to create roughness on the meter scale
(sastrugi, snow dunes) and centimeter scale (microroughness) (Remy, Legresy, Testut
2000). The meter scale roughness is generally oriented parallel to the direction of the
prevailing winds (Goodwin, 1990)
There are two common methods for quantifying the centimeter and meter scale
roughness of the Antarctic surface. The first uses observations gathered during traverses
in oversnow vehicles, and the second relies on analysis of the backscattered waveform
from satellite radar altimeters. Each method has its weaknesses: Oversnow traverses
cover a limited geographic area (mostly in East Antarctica and mostly near the coast).
Satellite altimetry yields data from 80% of the Antarctic surface, but waveform
parameters are not uniquely sensitive to surface roughness since snow density,
stratification, and surface slope also affect the waveform. However, with the combined
data from both methods it is possible to get an idea of the average surface roughness over
the entire continent.
Oversnow Traverses
Several studies have been conducted by driving oversnow vehicles across the
Antarctic surface for hundreds of kilometers and recording the features that were
encountered. (Goodwin, 1990) provides a good catalogue of the types and dimensions of
roughness features on the meter scale. He divides features into three categories based on
the processes through which they are formed:
Depositional surface features (snow dunes) are typically 50-100m long, 10 – 15m wide
and 1m high.
Redistribution surfaces are usually 20-50m long, 2-3m wide and 0.3–0.5m high.
Erosional surfaces are 0.3m in mean height.
Goodwin applies the term “sastrugi” to erosional surfaces and redistribution surfaces, and
the term “snow dunes” refers to the larger depositional features. In some papers,
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however, the term “sastrugi” is used to refer to any surface roughness on the meter scale.
A graph of average surface feature height along this traverse can be seen in Figure 1.
Roughness features appear in patches or zones, though these zones may overlap
(Watanabe, 1978). Takahashi et.al. (1984) noted that “sastrugi areas and glazed surface
[smooth] areas existed alternatively at intervals of 20 or 50 km” along the length of the
oversnow traverse he conducted. The most quantitative assessment of the distribution of
these features is provided by Furukawa et.al. (1996) who conducted a snow traverse
along a route that was approximately perpendicular to the prevailing wind direction (and
therefore approximately perpendicular to roughness features). They visually counted the
number of occurrences of sastrugi or snow dune that they crossed, and recorded the
frequency/(2km) as we can see in Figure 2.
Looking at the “small sastrugi” curve, we can see that there are sharp dips in the
frequency about every 20 -50 km between the 400 and 700 km marks, which confirm the
observations of Takahashi and Watanabe. These sastrugi zones seem to correspond
roughly to zones seen in the graph of the distribution of snow dunes. Also, we can see
that the average frequency of small sastrugi is about 250/(2km) and the average
frequency of snow dunes is approximately 150/(2km).
Combining the information on the roughness correlation length from Furukawa,
and values for the average amplitude from Goodwin, there appear to be two roughness
features: sastrugi which have a mean amplitude somewhere near 30 cm and a correlation
length of 8m and snow dunes which have a mean height of approximately 0.7 m and a
correlation length of 13m. Both features occur in zones of 20 -50 km extent, separated by
smoother surfaces of approximately the same dimension. This is in rough agreement with
the findings of Watanabe 1978, and Ohata 1984.
Satellite Altimetry
Since 1980, several satellite radar altimeters (SEAsat, ENVISAT, ERS) have been
sent over Antarctica, with the primary objective of mapping the topography. The
altimeter works by emitting a radar wave in the nadir direction, and then receiving the
reflection from the surface. The typical wavelength used is about 2.3 cm, and the
footprint size is 5 – 10 km (Remy, Legresy, Testut 2000).
The histogram of backscattered power vs. time is recorded by step of 3.125 ns.
From this, information regarding surface roughness can be extracted by looking at several
parameters: the half-leading edge width (Tr), trailing edge slope (Fl), and backscattering
coefficient (σo) (see Figure 3: Histogram of backscattered power vs. time from a satellite
altimeter.
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Maps of these parameters taken from Legresy et.al. (2005), using two different
wavelength altimeters, S (2.0 - 4.0 GHz) and Ku (12 – 18 GHz) band, are shown in
figures 4-5.
Leading Edge
The half leading edge width (Tr) corresponds to the first part of the impact of the
radar on the ground, e.g. the 1km scale (Legresy, Remy 1997). According to Remy,
Legresy, Testut (2000):
“The waveform leading edge […] is mostly controlled by snow dunes
and sastrugi height, but also by delayed subsurface scattering and the kilometric scale
surface features. It [Tr] reaches 3 m in the West Antarctic ice sheet.”
We can see in figure 6 that the leading edge width varies from 0.5 – 3.5 meters, with an
average length of about 2.2 meters over most of the continent. However, according to
data from oversnow traverses snow dunes have amplitude of approximately 1m and
sastrugi reach amplitudes of 2m only in the most extreme cases, with the average height
being closer to 0.3m (Goodwin, 1990). Given this, it seems that the leading edge width is
at best proportional, not equal, to the average height of the meter-scale roughness.
Because oversnow traverses cover such a limited geographic area, figure 6 becomes
useful in determining the relative roughness of areas where the surface roughness has not
been documented in situ.
Trailing Edge
The trailing edge slope is controlled by surface slope on the footprint scale (10 km) and
also by the ratio of volume scattering/ surface scattering (Remy, Legresy, Testut 2000).
Backscatter Coefficient
Backscattering from the ice will be a combination of surface and volume echo.
Scattering occurs in the volume of the snow cover because of stratification (layers of
different density from different snowfalls) and ice grains of finite size. This adds another
variable that affects the backscattered waveform; however, according to the literature, the
large scale variations in backscattered power are mainly due to variations in surface
scattering:
“Only a few dB of variations are expected due to the volume backscattering. Even if the
surface and subsurface are of the same order of magnitude, the geographical pattern is
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mostly controlled by the range of variations of the surface echo.” (Remy, Legresy, Testut
2000)
The total backscattered power received by the satellite is proportional to the backscatter
coefficient, σo (see Remy, Brossier, Minister 1990). In their approximation:
σo = R2/2S2
R = (n-1)/(n+1)
where R is the Fresnel coefficient at normal incidence and S is the RMS slope (in the
paper, it is referred to as the “quadratic mean” slope) of the surface on the radar
wavelength scale (Remy, Brossier, Minister 1990). The typical wavelength used is 2.3 cm
(for Ku, 7.5 cm for S); therefore the backscattering coefficient is primarily affected by
centimeter-scale “microroughness” and only marginally affected by sastrugi and snow
dunes.
The Fresnel coefficient depends on the snow density, and is estimated to be (see Remy,
Brossier, Minister 1990 or Remy, Legresy, Testut 2000):
R ≈ .137-.145
This corresponds to an index of refraction of about 1.32 for the upper snow layer. In
figures 4 and 5, we see that σo varies from 3-12 dB, this corresponds to an rms surface
slope for centimeter-scale roughness of .07 to .02.
Assuming that the amplitude of the roughness is approximately 2 cm (on the scale of the
wavelength of the Ku altimeter) yields a correlation length of 30 – 60 cm. This is in
rough agreement with the analysis given in (Remy, Brossier, Minister 1990).
Extrapolation from Snow Traverses
Because snow traverses cover only a limited area of Antarctica, it is reasonable to
question how representative their findings are of the continent as a whole. The leading
edge of the backscattered satellite waveform is controlled by meter-scale roughness such
as sastrugi and snow dunes. By comparing the leading edge values in the areas that have
been traversed with leading edge values for the rest of the continent, it is possible to
extrapolate the roughness of the continent relative to the traversed areas.
In Figure 7, the traverse routes for Goodwin (1990) and Furukawa (1996) are
indicated (roughly) on the map of leading edge width in the Ku band from Legresy et.al.
2005. The bold black lines indicate the traverse routes.
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We can see that the traverse routes are located in areas with a leading edge width
of about 2m, representative of the majority of the continent. It is therefore fair to assume
that the roughness encountered along these traverse routes is similar to roughness present
over most of the continent.
Percent Coverage of Snow vs. Ice
The indices of refraction of snow and ice differ by a nontrivial amount. It is
therefore of interest to determine how much of the Antarctic surface is covered by snow,
and how much by ice. We can see in Figure 8 (taken from Hongxing et. al. 2006) that the
vast majority of the continent is covered by dry snow.
Conclusion
After a survey of the relevant literature, it is evident that the Antarctic surface is
characterized by roughness on the meter and centimeter sale. Centimeter scale roughness
occurs over the entire continent with estimated amplitude of a few centimeters and a
correlation length of 30 – 60 cm. Meter scale roughness comes in two varieties: Sastrugi
have average amplitude of about 30 cm and a correlation length of 8m. Snow dunes have
average amplitude of approximately 70 cm and a correlation length of 13m.
This meter-scale roughness occurs in patches or zones that alternate with smoother zones
of similar size on the scale of 20 – 50 km.
With this information it is possible to judge how closely the ground glass
diffusers used in the laser scattering experiment described in ANITA note #101 match the
conditions of the Antarctic surface. The wavelength of the Cherenkov radiation in the
Antarctic ice is approximately 40 cm, so the surface roughness amplitude is on the order
of 0.1 – 1.0 wavelengths. The slope of the roughness features ranges from 0.05 – 0.1.
In the experiment described in Anita note #101, the roughness amplitude of the diffuser
was on the order of 2.5 wavelengths of the HeNe laser for the 400 grit diffuser and 1.0
wavelengths for the 1000 and 1500 grit diffusers. The roughness slopes of the diffusers
varied from 0.25 - 0.4. So, it seems that the diffusers model a surface with somewhat
larger amplitude and slopes than the average Antarctic features. However, they are close
enough to be a good qualitative model and we would like to pursue another set of data
with slightly finer diffusers.
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Figures
Figure 1: Average height of surface roughness features observed along the snow traverse route of
Goodwin (1990) plotted against distance from the start of the traverse. Roughness features are
separated into three groups based on the processes by which they are formed (depositional,
redistribution, erosional). The average height of features in each group is plotted separately.
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Figure 2: Frequency of roughness features plotted against distance (in km) from the start of the
traverse route. The frequency of snow dunes, large sastrugi (>30 cm) and small sastrugi (<30 cm) are
plotted separately (Furukawa et.al., 1996).
Figure 3: Histogram of backscattered power vs. time from a satellite altimeter.
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Figure 4: Backscatter coefficient (in dB) measured above Antarctica (using frequencies in the Ku
band) by the Envisat radar altimeter. The satellite has 2 altimeters, one uses S band radiation and
one Ku band. The measurements vary slightly between the two. (from Legresy et.al. 2005).
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Figure 5: Backscatter coefficient (in dB) measured above Antarctica (using frequencies in the S
band) by the Envisat radar altimeter. The satellite has 2 altimeters, one uses S band radiation and
one Ku band. The measurements vary slightly between the two. (from Legresy et.al. 2005).
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Figure 6: Leading edge (in meters) measured above Antarctica by the ERS satellite altimeter
(Measured using S and Ku band frequencies). (from Legresy et.al. 2005).
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Figure 7: Traverse routes of Goodwin and Furukowa indicated on the map of the leading edge (in
meters) of the waveform measured by the ERS altimeter (figure 5). We see that the leading edge
values in areas covered by the traverse routes are typical of values seen over the rest of the continent.
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Figure 8: Map of snow coverage in Antarctica from Hongxing et al. 2006. Dry snow zones are shaded black. It is clear that the vast
majority of the continent is covered by dry snow zones.
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