Bayesian Time Series Approach and Its Application to Retrieve Ground and Vegetation Variables From L-Band Passive Microwave Remote Sensing

Microwave remote sensing is a widely used and effective method for observing and understanding various land, ocean, and atmospheric processes. Information on the geophysical variables associated with these processes is typically retrieved through inversion of forward models, which describe the remotely sensed observations as functions of the geophysical variables of the scene. Inversion of the forward model is often an ill-posed problem due to the limited information content of microwave measurements and the complexity of the observed scene. The Bayesian approach provides means to incorporate prior information to reduce the ill-posedness of the problem. Considering temporal information is particularly useful in this context, as the temporal characteristics of geophysical variables can be used as prior information to reduce the ill-posedness. Furthermore, considering the temporal domain is natural due to the sequential nature of remote sensing observations. To incorporate such prior information, we introduce a Bayesian inversion of a time series of geophysical variables from a time series of remote sensing observations. The method is formulated in a general form and is therefore applicable to different remote sensing problems. To demonstrate, we applied the method to Soil Moisture and Ocean Salinity (SMOS) L-band brightness temperature measurements to simultaneously retrieve, for the first time, ground permittivity, surface roughness, vegetation optical depth, and scattering albedo over a one-year period at a northern boreal forest site. We compared the retrieved geophysical variables with the ground reference: retrieved and measured ground permittivity agreed with a correlation of 0.91, and retrieved and measured vegetation optical depth agreed with a correlation of 0.68 and the standard deviation of the difference of 0.11. We demonstrated that using the time series method, we could retrieve ground surface roughness and vegetation scattering albedo. Although reference measurements were not available for these variables, the retrieved values were consistent with the ground permittivity and vegetation optical depth. In general, ground surface roughness and vegetation scattering albedo are not retrieved in the nominal case, where data from different satellite overpasses are treated separately. This demonstrates that the time series method enables the retrieval of additional information compared to the usual approach.