The Ice Altimetry Group of NASA/Goddard Space Flight Center (GSFC) and Raytheon STX have developed algorithms for retracking polar ice altimetry returns to account for the inability of the on-board tracker to follow the topography of the ice sheets. To date four versions of GSFC retracking algorithms have been used to process the polar altimetry data evolving as changes in the different radar altimeters affect the returns. Each version has been an improvement over the preceding one either from the standpoint of 1)editing out bad data, 2) reducing noise in the resultant elevation profiles, or 3) improving the accuracy of fit to the leading edge. All four versions are discussed here because GSFC and the National Snow and Ice Data Center (NSIDC) have been distributing polar altimetry data to investigators since 1980 and the scientists need to decide if the improvement gained from Version 4 could affect their results. At the end of this discussion is a comparison of the results from all 4 versions to help with this decision.
|Satellite||Source||Processing Date||GSFC Retracker version|
|Geosat||GSFC Ice Altimetry||1989 - 1992||V2|
|Geosat||GSFC Ice Altimetry||1992 - June 1996||V2 for Antarctic data, V3 for Greenland data|
|Seasat, Geosat||NSIDC CD ROM||1995||V2 for Antarctic data, V3 for Greenland data|
|Seasat, Geosat||GSFC Ice Altimetry||July 1996||Conversion to V4 in progress. Check retracking status word.|
|ERS-1, ERS-2||GSFC Ice Altimetry||1998||V4|
The GSFC algorithms are based on the concept that the ice sheet return can be represented mathematically using a modification of the function that describes the ocean returns Parsons 1979 over the Gaussian ocean surface. Typical ocean returns are shown in Figure 1:
The measurement corresponding to the midpoint of the ramp gives the median elevation within the pulse-limited footprint. The on-board tracker tries to align the return so the midpoint of the ramp occurs at the tracking gate. For the ocean surfaces this works very well as indicated by the retracking correction varying from 3-6cm. Ice sheet returns as shown in figure 2 vary greatly in shape and position within the tracking window.
The longer vertical line indicates the position of the on-board tracking gate, whereas the short vertical line indicates the midpoint of the ramp, where the tracker should have been tracking to, as determined by the the retracking process. The retracking corrections for these waveforms over the Greenland ice sheet range from 22 cm to 4.5 m. Sea ice returns, Figure 3, also differ in shape and position from the ocean return.
The near-specular sea ice surface causes a return with a sharp spike. The tracker errors for the GEOSAT returns pictured over Arctic sea ice varied from - 52 cm to -70 cm. For ERS-1 this error is usually in the 1-2 m range. GSFC Versions 1 Martin et al, 1983 and Zwally et al, 1990 and 2 treated the near-specular sea-ice waveforms separately from the diffuse-type ice sheet returns using a functional fit to the latter and a modified threshold retracker for the former. The functions representing the waveforms were altered in Versions 3 and 4 to represent both the diffuse and near-specular returns and the coarse resolution returns of TOPEX and ERS-1.
The first step is to categorize the return as either near-specular (sea ice) or diffuse (ice sheet). All returns determined by location to be within a continental mask of the Greenland or Antarctic ice sheet are categorized as diffuse. Returns outside the continental mask are categorized as diffuse if there is no significant spike in the return. To determine the existence of a significant spike, first the gate, Gmid, corresponding to the 50% threshold point is calculated as the gate where the return first passes ymid, defined as
ymid=(ymax-ynoise)/2 + ynoise where: ynoise is the average power in the first five gates ymax is the max power in any one gate
The ratio, yrat, of the total power in the n gates after ymid to that in n gates before ymid is then calculated and the return is considered specular if the ratio is less or equal to 0.7. Unless there are less than 10 gates either before or after the significant spike, n is taken as 10. Specular returns are retracked by calculating the parameters from the waveform. Details of this calculation are described in Zwally et al, 1990
The ice sheet returns are further divided into two categories, those with a distinct single sharp rise in power indicative of normal-distributed elevations within the footprint and those with two sharp rises or ramps indicative of two distinct surfaces at different elevations both within the range window. Measurements that cannot be put into one of these catagories are considered unusable. The retracking correction on the record is set to a predetermine undefined value and the surface height status flag and retracker status flag are set appropriately. For returns that pass this initial screening, the GSFC functional fit retracker strives to calculate the most accurate median elevation from the first return while preserving information about the second surface when present. Some returns are hard to distinguish between singles or doubles due to surface characteristics. Many of these returns are fit with the 9-parameter function even though the 2nd ramp is indistinct and may be indicative of volume scattering and not a second surface within the footprint.
An iterative Bayesian least squares procedure is used to fit the digitized waveform to the appropriate function. For the single ramp return, a modified version of the ocean return function is used where an additional slope parameter is added after the ramp.
The mid-point of the ramp, Beta(3), is chosen as the correct range point, and the retracking correction is the displacement of that mid-point from the tracker gate. The linear trailing-edge of the function simulates the slowly decreasing return from a diffuse reflecting surface as the pulse expands over the beam-limited footprint. A nine-parameter function is used to simulate the double-peaked returns.
Before fitting, a priori values for the coefficients are calculated from a linearly-filtered return. A set of standard deviations is assigned to these a priori values indicating how well each coefficient could be approximated from the filtered return. The digitized waveform consisting of digitized "gates" are also weighted in the solution to try to put the heaviest emphasis on fitting to the ramp location(s) which defines the retracking correction. The function coefficients are then solved for using the unfiltered digitized return by iterating until the parameters defining the ramp positions, Beta(3) and Beta(6), converge to within two percent. After the 3rd iteration some of the standard deviations on the parameters are decreased to stop the procedure from either diverging or going into a limit-cycle situation. This process usually works, but it is using a linear solution to a non-linear problem and sometimes unexpected results occur. When the functional fit process fails, the retracking correction is calculated using the threshold-type algorithm discussed above for near-specular returns. The retracker status flag is set to indicate when this occurs.
In 1985 this procedure was refined to make the initial editing tighter and change the weights on the a priori values. This became the GSFC Version 2 retracker. The form of the function remained the same and the largest effect was in the editing.
Figure 5 shows examples of ice sheet returns with the functional fit and the retracking correction marked. In Figure 5 the waveform is in green, the function is in black, the on-board tracker gate is in red and the black vertical line marks the retracker's estimate of the location of the midpoint of the first ramp of the function. The retracking correction is the difference between this mid-point and the tracker gate converted to range. Each gate for GEOSAT represents 46 cm in range. Note the large retracking corrections for returns 4-9, and 33-40. Returns 5 and 6 are typical double ramp returns from multiple elevations within the footprint.
In 1992, with the advent of the ERS-1 altimeter with its ice mode retracker, the form of the functions was altered (Eqs. 3 and 4) so that they were applicable both for the near-specular sea-ice returns and the diffuse ice sheet returns. The linear trailing edge was replaced by an exponential decay term, which simulates the antennae attenuation as the pulse expands on the surface beyond the pulse-limited footprint. The new function fits the fast-decaying ice mode returns very well, which are significantly affected by the beam attenuation and could not be fit by the linear decay term.
Typical ERS-1 waveforms over the ice sheet in both ocean and ice mode and in ocean mode over sea ice are shown in Figure 6 a-d, along with the fitted retracking function. In addition to changing the functional form, the weighting scheme for the a priori values was also altered to put more emphasis on the a priori value of the ramp positions and all the gates were given the same weight in the solution. The new algorithm reduced the noise in the sea-ice elevation profiles, however the standard deviations of the crossover differences over the ice sheet remained about the same as for the previous versions. All of the ERS-1 polar altimetry data produced prior to February 1996 by GSFC has been retracked using Version 3. In addition, all of the GEOSAT and Seasat Greenland continental data has been reprocessed using Version 3.
At the NASA-sponsored ERS-1 ice altimetry workshop held in Greenbelt, MD in November 1995, it was discussed that the GSFC Version 3 retracker caused noise in the resultant height profiles due to excessive changing between the 5 and 9 parameter fits. The GSFC Version 4 retracker was developed as an effort to reduce this noise while still maintaining the advantages of a functional fit. Some of the noise was caused by trying to make the trailing portion of the waveform conform to the function. The form of the 5 parameter fit remained the same (see Eq. 3). The 9 parameter fit was altered by placing the first exponential with a simple linear function that stops when the trailing exponential kicks in (Eq. 5).
In addition, for both the 5 and 9 parameter fit s,the gates in the vicinity of the first ramp were weighted more heavily than the rest of the return.
In version 4 we also identify measurements that pass our retracking criteria but give questionable surface elevations. These measurements were processed in previous versions and the user had no clear indication that they may cause problems. In version 4 the measurements are still processed but the surface status word indicates the retracking correction applied is based on a "high noise waveform." These are defined as waveforms where the pre-pulse noise level is elevated so that its magnitude is 15% or more of the maximum value of the waveform. Studies of many of these measurements show discrepancies between the resultant surface heights and those of other tracks that cross over the same location that do not show this elevated leading edge. This is probably caused by the altimeter tracker "missing" the first return and locking onto a surface farther away. Since the tracker is a second-order servo control system, it is dependent on history and it could lock onto different surfaces coming in from different directions. Users are cautioned that software they used to check for retracking for the earlier versions will not pick up these "high noise" measurements. Users who wish to use them will have to modify their software.
Each successive version of the GSFC retracker improved the quality of the suface elevations by either increasing the repeatability of the result at same location at different times, reducing the noise in the along-track height profile, or improving the editing to remove questionable measurements. Histograms of the differences in the retracking corrections between the various versions as a function of elevation over the ice sheets show how the revisions altered the correction applied to the observations. The differences in retracking corrections between versions 1 and 2 is portrayed in Figure 7 for Seasat data over Antarctica:
One histogram shows the ocean/sea ice data. The other 5 histograms are for different elevation envelopes stepping up in 500 m increments. The biggest improvement came in the elevations between 700 and 1200 m where the standard deviation of the differences was 49.2 cm with a mean of -5.05 cm. At these lower elevations the topography is more complex and the returns more irregular in shape. At the highest elevations near the plateaus the standard deviations of the differences is reduced to 12.50 cm with a mean of -8.32 cm. A similar set of histograms is shown in Figure 8 comparing versions 2 and 3.
This data is from GEOSAT over the Greenland ice sheet. The data in the 1200 to 1700 m elevation show the biggest improvement in retracking. This is in the ablation zone over the more complex topography.
Figure 9 shows histograms for Greenland ERS-1 data, comparing the retracking results between versions 3 and 4. Again the elevations between 700 and 1700 show the greatest improvement.
The reduction in the noise of the elevation profiles with successive retracker versions can be seen in Figure 10.
This is over sea ice near Antarctica. Unretracked data are shown in the top solid black line with no symbols, all 3 versions of the retracker shown (2,3, and 4) reduce some of the noise and lower the profile by approximately 1 m. There is also a significant reduction in noise in using either version 3 or 4 over version 2.
To test the ability of the retracker to calculate repeatable elevations from different measurements over the same location, crossover statistics are calculated. A crossover is where two passes cross over the same location. The crossover residual is the difference in surface elevations calculated from the two altimeter measurements. For same-satellite crossovers one pass is always on an ascending orbit and one on a descending orbit. Table 2 shows comparisons of crossover residuals for one month of data over the Greenland ice sheet using different versions of the GSFC retracker. The statistics are calculated after a 2 sigma convergent edit.
| GSFC Retracker
|mean||std dev||mean||std dev||mean||std dev|
|2||0.01||0.54||not used||not used|
Table 1 - Comparison of Altimeter crossover statistics using one month of data over Greenland for different retracker versions and missions.
Note that the crossover statistics did not change measurably between versions 2 and 3 of the retracker, however there is a statistical significant reduction in the standard deviations of the crossover residuals calculated using version 4. For Seasat this reduction is smaller at 8 cm compared with 16 cm for GEOSAT and 18 cm for ERS-1. Most of the differences in retracking between the two versions is evidenced in returns over the ablation zone at around 700-1700 m elevation. Seasat did not maintain acquisition as well as the other missions in this zone so the percentage of the returns here compared to those in the smoother regions is smaller than for GEOSAT and ERS-1.
Each successive version of the GSFC retracker showed improvement by either reducing the noise in the along-track profiles or by increasing the repeatability of calculating elevations from measurements over the same location at different times. However, other other corrections applied to the altimeter data have also improved over the years and may have a larger affect on the calculated elevation than the retracking, depending on the region one is studying.