Before we inverted the crossovers for these three satellites and their
pairs for their full geopotential signals
we were confronted with DSC observations,
especially for Geosat-T/P (Figure 2a),
which strongly suggested they were due to a coordinate shift
(mostly East-West)
between the
separate tracking systems of the pair (e.g., Wagner et al, 1997a,b).
If the geocenter for the orbit of one satellite were different than for
another then we presumed this difference would show up in the altimetrically
measured sea height differences for the pair as well. The expression of
this coordinate change was found in the three parameters of the first
degree (so-called "forbidden") spherical harmonics
( 
).
In addition we also found that the covariance matrix of Jgm3 (the reference orbit for the three satellites) projected anomalously small errors for Geosat-T/P crossovers at order one compared to our observations of them from harmonic analysis of the latitude banded DSCs (Klokocnik et al., 1999). While these observed (so called latitude lumped coefficient, LLC) values of order one were larger than expected for Jgm3 they could still be due reasonably to three causes (or combinations of them): (1) the geocenter shift between the tracking systems for Geosat and T/P, (2) higher than expected order-one errors in the Jgm3 geopotential, and/or (3) interannual oceanographic effects (such as El Niño/La Niña) between the Geosat and T/P mission periods.
As mentioned in a previous section we included possible geocenter shifts
for all the DSC sets in our 50x50 adjustments of Jgm3 from these data.
Table 5 shows the results for the 2 comprehensive solutions (at full and
reduced weight) together with an earlier solution only for the shifts
in Ers1-T/P and Geosat-T/P (from their separate DSCs) - compare
with Wagner et al., (1997a) and Klokocnik et al., (1998).
The most important finding from the study of the shift over
many solutions with different data sets, weights and solution parameters
was that the values changed with these circumstances. For example, in
Table 5 the Geosat-T/P geocenter shift for NOAA and Pathfinder DSCs is
not the same for X and Y in the 50x50 solutions (Z is
related to the forbidden harmonic coefficient 
and is
always poorly determined in these because zonal gravity as well as
1 cpr terms correlate strongly with Z). Yet the Geosat
Jgm3 orbits for both NOAA and Pathfinder data should have
the same coordinate basis since they used the same
(Tranet Doppler) tracking systems. Similarly
the basis for Noaa and Pathfinder sea heights for T/P should be the same
since T/P tracking for both used the same Laser, Doppler and GPS systems.
Note:
The x axis of the geocenter shift points towards Greenwich in the
equator, the y axis towards 90 degrees east longitude
and the z axis towards the North Pole.
The expression of the shift geographically
in height difference ( 
) is:
= 
+ 
.
The key to the NOAA/Pathfinder change is seen in the difference between the X, Y shifts when the weights of the DSCs are reduced to take the burden of the ordinary geopotential part of the solution off the obviously biased DSC data (Figure 2b). This change results in a significant reduction in the X, Y shifts so that from Pathfinder data they become negligible (compared to their errors). We saw previously (Figure 8) that the errors of the downweighted solution had much better agreement with the a apriori Jgm3 covariances than the solution from fully weighted DSCs. But this reduction (in the shift) with a more realistic solution and the fact that the NOAA/Pathfinder differences persist in the downweighted solution strongly suggests that (1) much of the shift itself is due to the non-geopotential bias (presumbaly oceanographic) in these DSCs and (2) the NOAA/Pathfinder differences are largely due to the different time periods for these data which have different interannual expression.
The contrast (with the time-gapped Geosat - T/P) of Ers1 - T/P geocenter shifts (Table 5b) tends to confirm this judgement. Here the NOAA DSCs (nearly contemporaneous) in the full geopotential solution show almost no geocenter shift. (Figure 2b shows the Ers1-T/P residuals to be small compared to Geosat-T/P). The change from the X, Y solution with no geopotential resolution for this pair of satellites is also dramatic. It can be attributed (as in the Geosat-T/P case) to significant correlation between the shift (representing degree one) and the other higher degree normal geopotential harmonics of order one.
Notice also in Table 5c the large change in the geocenter shift (X,Y) for the pair Geosat - Ers1 (5 year time gap) from the simplest case where the shift alone absorbs all the DSC information on this pair to the comprehensive 50x50 solutions where (again) it must share these signals with the higher degree geopotential. Just as in the Geosat-T/P results (Table 5a), when the burden of the (oceanographically?) biased DSCs on the solution are shifted to the SSCs we find the X, Y shifts are reduced for Geosat-Ers1 as well. The fact that the shifts always reduce when downweighting decorrelates them from the normal geopotential suggests the new numbers for them (with better precisons) are more realistic than the old.