A Physical Deterministic Inverse Method for Operational Satellite Remote Sensing: An Application for Sea SurfaceTemperature Retrievals

We propose a new deterministic approach for remote sensing retrieval, called modified total least squares (MTLS), built upon the total least squares (TLS) technique. MTLS implicitly determines the optimal regularization strength to be applied to the normal equation first-order Newtonian retrieval using all of the noise terms embedded in the residual vector. The TLS technique does not include any constraint to prevent noise enhancement in the state space parameters from the existing noise in measurement space for an inversion with an ill-conditioned Jacobian. To stabilize the noise propagation into parameter space, we introduce an additional empirically derived regularization proportional to the logarithm of the condition number of the Jacobian and inversely proportional to the L2-norm of the residual vector. The derivation, operational advantages and use of the MTLS method are demonstrated by retrieving sea surface temperature from GOES-13 satellite measurements. An analytic equation is derived for the total retrieval error, and is shown to agree well with the observed error. This can also serve as a quality indicator for pixel-level retrievals. We also introduce additional tests from the MTLS solutions to identify contaminated pixels due to residual clouds, error in the water vapor profile and aerosols. Comparison of the performances of our new and other methods, namely, optimal estimation and regression-based retrieval, is performed to understand the relative prospects and problems associated with these methods. This was done using operational match-ups for 42 months of data, and demonstrates a relatively superior temporally consistent performance of the MTLS technique.