Determining TOPEX and POSEIDON sea-state bias

Wave troughs reflect radar signals better than crests do.
Since altimeters measure the height of reflecting surfaces, the measurements are slightly biased toward troughs.
This bias, called electromagnetic, is a function of wave height.

It is typically 2% to 5% of significant wave height (H_1/3). Analyzing the waveform yields the radar signal travel time, and thus the satellite-to-ocean range. However the calculation is sometimes affected by a wave height-related effect called tracker bias. Electromagnetic bias plus tracker bias is called Sea-State Bias (SSB ).

Before TOPEX/POSEIDON (T/P) nobody was very interested in accurately evaluating sea-state bias: the error in estimating it was considerably less than the orbit radial error. Today all that has changed: T/P radial orbital error is around 3 cm rms while SSB is estimated to no better than 2 cm rms. It thus comes second in the altimeter measurement error budget.

A method for evaluating SSB based on height differences at crossover points was developed before the launch. It was used systematically for TOPEX and POSEIDON calibration and validation. The aim was to monitor bias for both altimeters, cycle by cycle, and improve the estimates if possible. The analysis clearly showed that:

1. POSEIDON SSB is significantly greater than TOPEX. The difference between the two biases is essentially a constant, 2.5 to 3% of H_1/3. Apart from this, probably a result of tracker bias, the two altimeters behave very similarly.
2. The relative bias of the two altimeters, i.e. the ratio SSB  over H_1/3, is not a constant. The ratio tends to decrease in absolute terms when H_1/3 increases.
3. The relative bias of the two altimeters varies with surface wind, increasing (in absolute values) with wind speeds up to around 10 m/s. The trend seems to be the opposite in stronger winds.

Relative bias variability according to wind is modeled well by a quadratic formula (BM4) of the type NASA uses to estimate TOPEX bias. However, the formula cannot be used to derive relative bias variability according to H_1/3. To do this we had to develop a new bias parametrization based on the NASA formula but with an extra term for relative bias variation with wave height.

The TOPEX SSB calculated with BM4 is only significantly different from the NASA bias in the GDRs for H_1/3 values greater than 5 m. Such values are observed essentially at the mid and, particularly, high latitudes. The BM4 formula also provides good results for POSEIDON. The bias estimation in the GDRs, from the 1991 Fu and Glazman model, reduces differences at crossover points considerably less effectively.

We do not recommend it for corrections.

Reference :

• Gaspar, P., Ogor, F., P.Y. Le Traon and O.Z. Zanife, 1994. Joint estimation of TOPEX and POSEIDON sea-state biases, J. Geophys. Res. (in press).