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F-test
parameter allows us to determine the probability that there are
coherent oscillations in the data. Both parameters can be
calculated at any frequency. For convenience the frequency f of
an oscillation will be expressed in terms of the period 1=1/f in
years.
3. MICROWAVE EMISSION FROM DRY FIRN
Microwave emission from dry firn depends on the physical
temperature of the snow and on the snow morphology over the
skin depth. According to Rott et al. (1993) the skin depth at 37
GHz is approximately 0.85 m. The observed brightness
temperatures over ice sheets are less than expected from a
black-body radiating at the in-situ temperature because of
volume scattering over the skin depth, and because of
reflection of radiation from below at the snow-air interface
(Remi and Minister, 1991). Any energy that is scattered or
reflected downward is not emitted, so scattering and reflection
decrease the observed brightness temperature.
The scattering efficiency of a layer of snow is strongly
dependent on the size distribution of the ice crystals. According
to electromagnetic wave theory the scattering efficiency of ice
grains increases with grain size. Dense medium radiative
transfer theory has shown that the larger ice grains in a snow
layer are responsible for most of the scattering (West et al.,
1993). The emissivity of a layer of coarse snow or of a refrozen
crust is thus smaller than the emissivity of a layer of new snow
(Mätzler, 1987).
Downward reflection at the snow-air interface depends on
surface roughness, surface density, incidence angle, and
polarization (Remi and Minister, 1991). Coarse grained hoar
layers on the surface of the ice sheet reduce the near surface
density and increase surface roughness at approximately the
scale of 37 GHz wavelength (Shuman et al. 1993). This
creates a surface which reduces H reflection with the result
that brightness temperature in H-band might increase despite
larger ice grains. On the other hand, V-reflection increases,
adding energy to downward scattering by the coarse ice grains.
Thus the V-signal always decreases during the formation of
hoar complexes.
Initially all computations were performed for both
polarizations. Basically the results are very similar, but there
are some differences that cannot be easily explained. We
finally decided to concentrate on V-band because we followed
the idea that meteorological conditions influence ice crystal
growth. To obtain a good correlation between the signal and
ice crystal size over the skin depth, the 37 GHz vertically
polarized channel seems to be the right choice. In addition, the
V-signal is less noisy than the H-signal.
4. RESULTS AND DISCUSSION
Maps of the absolute value of the complex amplitude, |u|, and
the F-test parameter, F, were computed for various periods.
Interannual variations in microwave emission from the ice
sheet are depicted in the maps for periods 1=2,3, and 4 years.
To investigate oscillations with a period greater than four years
does not make much sense for a nine year record. Interestingly,
745
quadrennial oscillations can be found over much larger
portions of Greenland than biennial and triennial variations,
and |u| and F are generally higher for the former one.
In Figure 1 |u| and F of the quadrennial oscillation are plotted
onto the shape of Greenland. The boundaries in the interior of
Greenland define the dry-snow facies and the percolation facies
according to Benson (1962). The dry-snow facies corresponds
to the deep interior of the ice sheet and is characterized by the
absence of seasonal melt. In the percolation zone vigorous
melting may occur near the surface. Ice pipes and massive ice
lenses are found in these regions as well as strong seasonal
modulation of ice grain size (Jezek et al., 1994). In the dark
colored patches of Figure 1a the F-test parameter is above the
99 % confidence level at 6.51. With the exception of small
clusters along the coast of Greenland, the F-test statistics
shows that the quadrennial signal can predominately be found
above the saturation line (Below the saturation line the ice
sheet surface becomes wet throughout the melting season). As
evident in Figure 1b high values of |u| are mainly found in the
percolation zone.
We now try to answer the question what caused the four-year
signal in the brightness temperature record? Let us have a look
at some time series of Ty from selected points on the ice sheet.
These points are numbered from 1 to 6 and their location can
be seen in Figure 1. The corresponding time series are
displayed in Figure 2. Comparing time series from the
percolation zone (1-5) we find that while summer brightness
temperatures are always rather similar, winter brightness
temperatures can vary significantly. This is most evident in the
brightness temperature record from point 1. There Ty varies up
to 40 K between different winters. High T, peaks in the
summers of 1981 and 1985 indicate surface melt. Since surface
melt usually results in layers of iced firn consisting of clusters
of grains bonded together by frozen melt water (Benson, 1962),
we think that the high differences in brightness temperature
measurements between the winters must be explained by
differences in the ice grain size distribution. According to
Benson (1962) grains in firn strata which have not been
exposed to melt action are predominantly less than 1 mm.
Grains exposed to temperatures within about 5 degree of
melting, but not soaked, fall in the medium size range,
between 1 and 2 mm. When surface melt and soaking occur,
individual grains are primarily larger than 2 mm and cluster
may exceed 5 mm. The size range of the individual scatterers
is thus large ( 0.1 to 5 mm). Ice grain size might therefore
serve as an index for the past climate.
New snow that buries a layer of coarse snow increases
brightness temperature. As long as the depth of the new snow
layer is low in comparison the skin depth (0.85 m), there is
always significant contribution to the signal from the coarse
snow layer below the surface. The relatively slow increase in
T» at point ] in the winters of 1981/82 and 1985/86 suggests
that winter accumulation was relatively low. According to
Ohmura and Reeh (1991) annual accumulation in the
surroundings of point 1 is around 500 mm water equivalent.
Assuming a snow density of 0.2 g/cm’ annual accumulation
expressed in snow depth is estimated to be around 2.5 m.
Considering the natural variability in precipitation and
precipitation minimum in winter (Bromwich et al., 1993) it
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996
