Analysis of cost functions for retrieving sea surface salinity

Two kinds of Bayesian-based cost functions (i.e., the unconstrained cost function and parameter-constrained cost function) are investigated for retrieving the sea surface salinity (SSS). In low SSS regions, we have analyzed the sensitivity of the two cost functions to geophysical parameters. The results show that the unconstrained cost function is valid for retrieving several parameters (including SSS, wind speed and significant wave height), and the constrained cost function, which largely depends on the accuracy of reference values, may lead to large retrieval biases. Furthermore, as a retrieval parameter, the sea surface temperature (SST) can result in the divergence of other geophysical parameters in an unconstrained cost function due to the strong sensitivity of brightness temperature to SST. By using the unconstrained cost function and the simulated brightness temperature T _B with white noises, the retrieval biases of SSS are discussed with the following two procedures. Procedure a): the simulated T _B values are first averaged, and then SSS is retrieved. Procedure b): the SSS is directly retrieved from the simulated T _B, and then the retrieved SSS values are averaged. The results indicate that, for low SSS and SST distributions, the SSS retrieval by procedure a) has less biases compared with that by procedure b), while the two procedures give almost the same retrieval results for high SSS and SST sea regions.