7 Mapping the Progression of Melt Onset and Freeze-Up
139
Long et al. (1994) have in fact begun this process using ERS-l scatterometer data from
the Weddell Sea and an adaptation of the resolution enhancement method of Long et
al. (1993)- Heuristically, Long's Scatterometer Image Reconstruction with Filtering
(SIRF) operates by combining scatterometer observations from footprints whose
backscatter values are correlated because of they share area in common. The aim is to
reconstruct the underlying, fine-scale map of backscattering cross-section, given sufficient knowledge of the overlap geometries. In practice, the scatterometer observations
are acquired over some time interval, during which the target could change; any such
temporal variation is treated as "noise" in the algorithm. The SIRF algorithm is based
on an iterative, multivariate modification of multiplicative algebraic reconstruction; the
standard version of the latter is a special case of maximum-entropy reconstruction. In
cases where footprint overlap is insufficient to completely determine all matrix elements
in the estimation problem, a maximum-entropy-based assumption is used to specify
those elements. This is, in effect, an assumption concerning the autocorrelation structure of the underlying backscattering map at subresolution scales (Jaynes 1982; see also
pages 420-426 of Percival and Walden 1993), namely that the correlation is that of the
most random, least predictable structure on those scales that is consistent with the
observations at larger scales. The assumption is likely to be more accurate when noise
is limited (Jaynes 1982). The result is a map of backscattering cross-section estimates
on a finer grid than the original data, consistent with the assumptions on that underlying map and "noise" inherent in the method.
In the case of sea ice, ice motion and possible temporal changes limit the period of
time over which observations of a given ice region may be accumulated, and therefore
the fineness of the resulting grid of backscattering cross-sections relative to the original data resolution. In the case of the study of Long et al. (1994) in the Weddell Sea, this
interval was 7 days and allowed enhancement from 50 km to 25 km. In the case of the
Seasat scatterometer, differences in predelivery processing of the data allowed greater
enhancement, to 9 km, while accumulating data over 8-day intervals.
From the preceding discussion, it is clear that high-frequency scatterometer observations of melt onset as well as freeze-up would be valuable. However the lifetime of
the Seasat, together with the unavailability of NSCAT data as of this writing, limit our
high-frequency observations for now to freeze-up during 1978. The promise of higherfrequency observations is strikingly evident, nevertheless, in the measurements we
have. Figure 7 shows temperature, precipitation, and backscattering cross section time
series from 1978, the former measured at Mould Bay in the Canadian Archipelago, the
latter from a time series of resolution-enhanced, 14.6-GHz backscattering images based
on data from the Seasat wind scatterometer. Because the location of the backscatter measurements is just west of the temperature measurement site, small temporal offsets
between events in the temperature and backscatter records might be expected.
Nonetheless, the highly variable backscattering characteristic of summer conditions
quickly gives way to high, stable backscattering after September 15 (Julian day 258), giving a clear indication of freeze-up. Even rather short, minor melting events just prior
to freeze-up seem to be reflected in the backscattering record. This appears to be consistent with the pattern seen in SAR studies at 5.3 GHz (see the previous section and
Winebrenner et al. 1996).
Figure 8 shows a series of 22 wide-area images including the Alaskan coast and the
Beaufort and Chukchi Seas, with a pixel spacing of 9 km. The series begins on July 8
139
Long et al. (1994) have in fact begun this process using ERS-l scatterometer data from
the Weddell Sea and an adaptation of the resolution enhancement method of Long et
al. (1993)- Heuristically, Long's Scatterometer Image Reconstruction with Filtering
(SIRF) operates by combining scatterometer observations from footprints whose
backscatter values are correlated because of they share area in common. The aim is to
reconstruct the underlying, fine-scale map of backscattering cross-section, given sufficient knowledge of the overlap geometries. In practice, the scatterometer observations
are acquired over some time interval, during which the target could change; any such
temporal variation is treated as "noise" in the algorithm. The SIRF algorithm is based
on an iterative, multivariate modification of multiplicative algebraic reconstruction; the
standard version of the latter is a special case of maximum-entropy reconstruction. In
cases where footprint overlap is insufficient to completely determine all matrix elements
in the estimation problem, a maximum-entropy-based assumption is used to specify
those elements. This is, in effect, an assumption concerning the autocorrelation structure of the underlying backscattering map at subresolution scales (Jaynes 1982; see also
pages 420-426 of Percival and Walden 1993), namely that the correlation is that of the
most random, least predictable structure on those scales that is consistent with the
observations at larger scales. The assumption is likely to be more accurate when noise
is limited (Jaynes 1982). The result is a map of backscattering cross-section estimates
on a finer grid than the original data, consistent with the assumptions on that underlying map and "noise" inherent in the method.
In the case of sea ice, ice motion and possible temporal changes limit the period of
time over which observations of a given ice region may be accumulated, and therefore
the fineness of the resulting grid of backscattering cross-sections relative to the original data resolution. In the case of the study of Long et al. (1994) in the Weddell Sea, this
interval was 7 days and allowed enhancement from 50 km to 25 km. In the case of the
Seasat scatterometer, differences in predelivery processing of the data allowed greater
enhancement, to 9 km, while accumulating data over 8-day intervals.
From the preceding discussion, it is clear that high-frequency scatterometer observations of melt onset as well as freeze-up would be valuable. However the lifetime of
the Seasat, together with the unavailability of NSCAT data as of this writing, limit our
high-frequency observations for now to freeze-up during 1978. The promise of higherfrequency observations is strikingly evident, nevertheless, in the measurements we
have. Figure 7 shows temperature, precipitation, and backscattering cross section time
series from 1978, the former measured at Mould Bay in the Canadian Archipelago, the
latter from a time series of resolution-enhanced, 14.6-GHz backscattering images based
on data from the Seasat wind scatterometer. Because the location of the backscatter measurements is just west of the temperature measurement site, small temporal offsets
between events in the temperature and backscatter records might be expected.
Nonetheless, the highly variable backscattering characteristic of summer conditions
quickly gives way to high, stable backscattering after September 15 (Julian day 258), giving a clear indication of freeze-up. Even rather short, minor melting events just prior
to freeze-up seem to be reflected in the backscattering record. This appears to be consistent with the pattern seen in SAR studies at 5.3 GHz (see the previous section and
Winebrenner et al. 1996).
Figure 8 shows a series of 22 wide-area images including the Alaskan coast and the
Beaufort and Chukchi Seas, with a pixel spacing of 9 km. The series begins on July 8