Sea State Bias Correction

Left image adapted from Satellite Altimetry and Earth Sciences, A Handbook of Techniques and Application, editors Fu and Cazenave, 2000. Right image from Relative Performance of the MLE3 and MLE4 Retracking Algorithms on Jason-2 Altimeter Waveforms. Thibaut et al. (2010). https://doi.org/10.1080/01490419.2010.491033

The Sea State Bias (effect) is caused by two reasons: 

• As waves have peaky crests and flat troughs, the radar backscattered power per unit area is larger from wave troughs than from wave crests. This leads to observing a mean scattering surface lowered by as much as tens of centimetres below the true mean sea level that we want to measure, i.e. a bias towards troughs. This effect is known as the electromagnetic (EM) bias and is a function of the electromagnetic pulse frequency and the sea state.

• Because wave troughs are flatter than wave crests due to the nonlinear, non-Gaussian, and skewed nature of ocean waves induces another bias towards the wave troughs, known as the skewness bias. For real waves, the median scattering surface (which is what the retracker finds by determining the mid point of the rising edge of the waveform) lies below the mean scattering level.

Theoretical modelling of the SSB is still a challenging problem, because SSB is a complex function of instrumental error, a wave-height-dependent bias associated with the retracking and depends on the ocean wind and wave conditions (e.g., fully developed swell waves and wind waves). This means there is no reliable theoretical model for SSB available for operational use despite numerous efforts because:​ (1) such model depends on sea surface parameters not measured by altimeter (spectral peak period, spectral width parameter, peak amplitude, fetch, wave age, …) and unavailable from numerical wave models​; (2) such parameters are required everywhere to support point-by-point SSB correction​ to range measurement; and (3) there is insufficient observational information on the space and time characteristics of the non-linear sea surface at the wave scales that are involved in the SSB. ​Therefore, currently empirical methods presently provide the only practical solution to estimate SSB.

However, using empirical methods also means including in the SSB analysis:

• The altimeter range is also affected by errors due to instrument processing and range computation methods also related to sea state; they are commonly grouped and referred to as tracker bias. In fact, we shall refer to the latter as a processing bias since the level-2 processing of the waveform data to estimate range is now always conducted on ground using a retracking algorithm as presented in the previous section.

The EM and skewness biases caused by the non-linearity of ocean surface waves should be the same for all Ku-band altimeters (Fu and Chelton, 2001), while the processing bias depends on the instrument. All these effects are generally combined all together to form the global SSB correction that needs to be modelled and removed for accurate altimetry measurement of the sea level.

Current operational SSB corrections consist in statistically-derived empirical versions that express the SSB correction as a function of significant wave height (SWH) and wind speed (WS) (Gaspar et al., 1994; Gaspar and Florens, 1998) for pragmatic reasons since the latter are also estimated from the waveform of radar altimeters.

The SSB correction is a specific case among the altimeter geophysical corrections since it depends on the altimeter characteristics and the outputs of retracking algorithms. It is not just mission and frequency specific but also processing specific because of its empirical nature. However, good consistencies between the different SSB corrections for the Jason-1 to -3 series have been reported (Tran et al., 2021), thanks to the continuity of the design of the instruments and processing techniques.

There is significant ongoing work to improve the SSB correction, including within this project and more details will be provided at later stages of the project.

Sea State Bias Correction Uncertainties

To come at later stages of this project.