Microwave Integrated Retrieval System (MIRS) - 1DVAR vs Regression Technique

Advantages of Physical Retrieval wrt Regression Technique

It is important to note that if (1) the same dataset used to generate the covariance matrix and background mean vector, were also used to generate the coefficients of an algorithm based on multivariate regression technique, and if (2) the distributions of the geophysical vector and the modeling/instrument errors are both Gaussian and (3) the forward model is purely linear, then the application of the regression algorithm or the first iteration of the physical algorithm would mathematically result in the same optimal solution.

If however the problem is moderately non-linear or if the distributions non-Gaussian, the iterative-based numerical model is superior to the multivariate regression technique because it allows the use of the previous linear inversion locally and move, step by step, to the minimum-penalty solution. It is the iterative nature of the numerical method that is providing the added benefit with respect to the simple regression technique, by accommodating non-linearities and non-Normal distributions.