Stochastic relaxation of nonlinear soil moisture ocean salinity (SMOS) soil moisture retrieval errors with maximal Lyapunov exponent optimization

Stochastic systems have received substantial attention in many disciplines ranging from various ensemble systems such as ensemble prediction system, or ensemble Kalman filter to stochastic retrievals reducing systematic errors in satellite-retrieved cloud, rainfall, or soil moisture data. However, there were few fundamental explanations of why and how the stochastic approach reduces systematic errors. We discuss how to non-locally optimize stochastic retrievals and to alleviate nonlinear error propagations of the deterministic Soil moisture ocean salinity (SMOS) soil moisture retrievals. By near-zero maximal Lyapunov exponents and rank probability skill score, the retrieval ensembles are optimized for bias correction in a computationally effective way. It is found that the diverse ensembles achieve better representativeness and structural stability than the ensembles from the majority. This stochastic property is important for effective bias correction. It is suggested that this stochastic approach independently resolves SMOS dry biases without relying on a local standard of root mean square errors from the field measurements or a relative comparison with reference data. Due to flexibility and non-determinism of surface heterogeneity this approach has a potential as a global frame.