Synthetic Quantitative Tests of Gaussian, Lognormal, and Transform Retrieval Systems

Abstract:

A fundamental assumption of many data assimilation and retrieval systems is that errors and variables come from a Gaussian distribution. Current research indicates that this may not always be valid for positive-definite variables such as water vapor. With the recent publication of variational schemes for mixed-distributions that are designed for lognormal-distributed random variables, the goal of this research is to quantify the quality of satellite retrievals with a synthetic test case. To do this the CIRA 1-Dimensional Optimal Estimator (C1DOE), a 1DVAR satellite retrieval system, now includes a transform approach as well as a lognormal version of the cost function. Since a Gaussian distribution has the trait that its’ mean, median, and mode are all the same, it is believed that the lognormal distribution may be better suited for skewed variables because it will solve for the mode explicitly. To test this hypothesis lognormal-distributed values for mixing ratio are created and used as the true solution then randomly perturbed with synthetic noise to be retrieved with Gaussian, transform, and lognormal retrieval systems. The results of the test are analyzed.