Effect of orbit precision on ERS Sea State Bias models

This page presents the results of a small study into the possible aliasing of orbit errors into parameters of sea state bias models correcting ERS-1 and ERS-2 altimeter range measurements depending on sea state and wind speed.

The data

The results obtained here are based on the latest Version 6 Ocean Product (OPR) provided by CERSAT. Corrections include (corrections in bold face are not provided on the OPR data sets): After editing all measurements are converted to single-satellite crossover height differences spanning the period of 20 June 1995 till 2 June 1996 and with a maximum time interval of 17.5 days between ascending and descending tracks.

The approach

From this data we estimate the coefficient b in the simple BM1-type sea state bias model in addition to the models given above:

SSB = b * SWH

In fact, we have enhanced this model by estimating one coefficient bi for each SWH interval of 1 meter. Assuming the crossover height differences are due to errors in the bi coefficients, this leads to observation equations:

Crossover difference = SSH1 - SSH2 = SSB1 - SSB2 = bi * SWH1 - bj* SWH2

The coefficients bi (i=1...8) are solved for in a least squares minimisation of all crossover height differences.

The two alternative orbit solutions have fairly different radial precision (GFZ/D-PAF approximately 6-7 cm and DUT/DEOS approximately 4-5 cm) and differ radially by about 5 cm rms. This provides the opportunity to test the effect of orbit errors on the sea state bias estimation. At the same time, we can validate the original Gaspar and Ogor [1996] BM3-type model.

The results

The table below lists the bi coefficients (in percents) obtained from the analysis of the crossover height differences, for ERS-1 and ERS-2 and based on DUT and GFZ orbits. The one-but-last line gives the effect of the corrections to the SSB model: the variance of the changes to the derived sea height implied by these corrections. The bottom line gives the overall value in case only one b coefficient was estimated, as in a true BM1 model.

0-1 90709 0.595 0.415 42695 0.103-0.066
1-2254463 0.484 0.450198712 0.278 0.099
2-3215105 0.450 0.432207745 0.263 0.141
3-4115812 0.380 0.368122849 0.276 0.137
4-5 52027 0.216 0.237 62725 0.256 0.141
5-6 20668 0.040-0.006 28233 0.162 0.086
6-7 7343-0.033-0.130 11542 0.065 0.003
7-8 2471-0.119-0.227 4307-0.117-0.040
Var (cm2)  0.376 0.352  0.192 0.050
0-8758598 0.370 0.355678808 0.244 0.118

The values are presented in graphical form below. Circles are for ERS-1, diamonds for ERS-2. Blue (light grey) markers are for DUT orbits, red (dark grey) markers for GFZ orbits.

The conclusions


Thanks to Philippe Gaspar for his comments.
Questions or comments:
Remko Scharroo, remko.scharroo@lr.tudelft.nl.
20 May 1997.