Recall our data (and residuals) consist of long-term averages in 2x3 degree bins over all oceans and generally over two time periods for the sensitive multi-year gapped DSCs. For Geosat-T/P the gap is 8 years running (month by month) from April 1985 through May 1988 for the NOAA-data Geosat legs. However, with NOAA data we have no Geosat passes in October 1986 (down-time in the transition from the Geodetic to the Exact Repeat Missions), and in December 1987 (incomplete processing). The same gap (8 years) exists for NASA Pathfinder data (Geosat-T/P) but here we have a complete 2 year record (November 1986 through October 1988 for the Geosat legs). Because the NOAA data is so broken up we chose the complete Pathfinder record to compare against the gauges. For Geosat-Ers1 (only with Pathfinder altimetry) the gap is 5 years running from April 1987 through December 1988 continuously (Geosat legs).
While we took same month differences, we assumed the coverage was uniform each month over the bins and just averaged the monthly tide gauge records in the same periods. (Thus we averaged 24 months of gauge records from November 1986 through October 1988 and subtracting from these the averages of the Gauges from November 1994 through October 1996 for the 8-year Geosat-T/P comparisons).
The requirement for complete gauge records in the two averaging periods was critical because we are assessing a small interannual difference from generally much larger seasonal gauge fluctuations (e.g., Figure 10). So we started out examining the records of 44 tide gauges but the requirement for complete coverage in the gapped periods left us with only 27 for Geosat-T/P comparisons and 32 for Geosat-Ers1 (21 months with a 5 year gap). What we have then are two selected samples of interannual ocean variability over somewhat different gaps and averaging periods.
(We should remark here that we worked with pressure corrected gauge data to conform to the inverse-barometer corrected altimetry, important for comparisons at higher latitudes, all data supplied by the University of Hawaii's global network [e.g., Kilonsky and Caldwell, 1991] but predominating in the Pacific).
Figure 11 gives an overview of the results in the Pacific for the Geosat-T/P Pathfinder time period. The DSC altimeter residuals show higher elevations in the Eastern Pacific corresponding to the La Niña conditions there in 1987/88 (relative to 1995/96). Unfortunately we lack complete data in the Eastern Pacific in both periods to confirm this high but the comparison with the gauges in the Western Pacific is seen to be fairly good. (The one large discrepancy at Easter Island may be due to a gauge change during the 8 year gap). The overall correlation between gauge and altimeter residual results (27 stations) is 0.55.
Notes:
The gauge observations for the two time periods were taken by averaging
the month-month gauge means over a 5 yr gap (for Geosat-Ers1) and
8 yr (for Geosat-T/P) in the same sense and over the same months
as in the Pathfinder altimetric DSCs (21 months for Geosat-Ers1,
87 April 92 thru. 88 December 93; and 24 months for Geosat-T/P,
86 November 93 thru. 88 October 96).
The average DSCs and their residuals are averages of Xover results for
all 4 types for each 2x3 degree bin at their respective centers
interpolated bilinearly to specific gauge positions or Carton grid
points. The POCM-4B data are 1x1 dgree averages similarly
interpolated.
The Carton model assimilates some collinear T/P and Geosat altimetry
over an irregular (non edddy resolving) grid (course at high latitudes,
fine at low) below 60 degrees (absolute). The POCM-4B model assimilates
no outside source-data, is eddy resolving and extends from
65 deg. North to 75 deg. South.
The Dual Satellite Crossover residuals are from 50x50 geopotential and
geodetic solutions using altimetric crossovers and Jgm3 covariances as
a priori information. The DSC observations and residuals analysed here
are all from Pathfinder altimetry. All solutions use Pathfinder DSCs
from Geosat-T/P and Geosat-Ers1. Solution 1 (DSC-data only) also uses
Pathfinder DSCs from Ers1-T/P. Solution 2 uses NOAA Single Satellite
Crossovers from Geosat, T/P and Ers1, NOAA DSCs from all 3 pairs and
Pathfinder DSCs from G-T and G-E, weighted to yield standard errors
of fit of near 1.0 (equivalent to data errors of from
1-2 cm for
SSCs and 3-4 cm for DSCs). Solution 3 uses the same observations
as Solution 2 but with the DSCs downweighted to equivalent data
errors of 6-12 cm in order to achieve a reasonable geopotential
adjustment (of Jgm3) for orders 1 and 3.
Results:
In all cases the DSC solution residuals improve the comparison with the
independent observations from the original DSCs but only for the gauges
do these residuals reduce the power of the independent
observations on subtraction. For the gauges the comparison is for
2x3 bin averages with uncertain biases and peculiar time and space
variations (DSCs) against point monthly averages at island stations
without air pressure compensation (inverse barometer) for sealevel
(gauges).
Carton's model does well on the gauges because most of
them are in the tropical Pacific where his grid has good resolution
and benefits from both altimeter and heat assimilation (though
his altimeter data does not span missions as the independent DSC
solution residuals do).
Yet even for these gauges the improvement in the
comparison with Carton is only modest (r=0.50,
residuals somewhat smaller). Here the grid point
closest to the gauge is used for
the Carton model (grid: 2.5 deg. in longitude by
1 deg. in latitude, variable).
Table 4 summarizes the comparisons we made between the gauges and various sets of DSC residuals following geopotential inversions, as well as original DSC data (after all media corrections). In all tests the residual altimetry improves the same comparisons with the DSCs before the inversion with smaller differences from the gauges. Notice that in some cases the correlations between gauge and original altimeter data are higher than with the residuals. The original altimetry for Geosat-T/P is evidently dominated by orbit-geopotential effects of first order which by accident acts here to reinforce the oceanic differences in the Pacific to keep the correlations with them artificially high for this limited sampling. The fact that the power of the altimeter residual predictions at the gauges are always less than the power of the gauge data is probably due more to the averaging of the altimetry over the 2x3 degree bins than the aliasing of power away from the ocean effects into the geopotential solution. However, as the results of residual solution 1 shows, when DSC data alone determines the geopotential, projected power is reduced even further but not always to the detriment of the altimeter result (the gauge comparison in the Geosat-Ers1 time period actually improves).
We attribute the inconclusive results of these gauge tests to there being too few locations (some with local site problems) and also the areal (not point) nature of the altimetry. In addition it is clear from Figure 2b and 2c that the areal averages are not noise free. In fact we have made tests with spherical harmonic functions resolving the common biases in the DSC sets for a given pair (simultaneously with the Geopotential) in order to further reduce the noise in the altimeter results. The altimeter projections of the bias improve marginally with this treatment but the areal and site problems seem to preclude closer agreement.
In order to get more appropriate global ocean data for comparison with our
crossover altimetry we examined and compared three GCMs
averaged for the two periods of our Geosat-T/P and Geosat-Ers1
DSCs. In the next section we discuss these tests both with our altimetry and
with the gauge data.