Evaluating models of sea state bias in satellite altimetry

Investigations of the sea state bias (SSB) in altimeter measurements of sea surface height (SSH) have been reported by many authors based on aircraft, sea tower, and satellite-borne observations. These investigations have resulted in several proposed algorithms of the form SSB = εH, where H is the significant wave height (SWH) and ε is a nondimensional function of wind speed U and SWH available from altimeter measurements. In the present work, on the basis of the full set of Geosat and an 8-month set of TOPEX altimeter measurements, all known algorithms are examined and a conclusion is reached that the altimeter-based U and SWH are insufficient to estimate the SSB correction with uniformly high accuracy. As a criterion of model performance we employ the value (called here the accuracy gain) by which the total variance of temporal changes in surface elevation is reduced owing to an SSB correction. This quantity is estimated for global data as well as for several selected regions of sufficiently large size. The linear geophysical model function (GMF) of the form ε = a₀ + a₁U is shown to yield an improvement over the simplest GMF with a constant ε. A three-parameter linear form ε = a₀ + a₁U + a₂H produces somewhat better results. A two-parameter, physically based GMF relating ε to the pseudo wave age ξ (where ξ is estimated using altimeter wind and SWH) yields even higher accuracy, while the three-parameter GMF of form ε = a₀ + a₁U + a₂U² yields the highest accuracy gain for global data sets. However, in terms of the SSB values, the difference between different GMFs is marginal, and the accuracy gain (as a measure of the SSB models performance) is shown to have serious deficiencies. We find that for all the SSB models, globally tuned empirical parameters often yield unacceptably poor results for certain regions in which local physical conditions differ from the global average: when the globally tuned GMFs are applied to such regions, the SSB-related error in SSH may well exceed 5 cm.