An inversion algorithm for nonlinear retrieval problems extending Bayesian optimal estimation

Abstract

Abstract. This paper proposes effective extensions to the well-known Bayesian optimal estimation, allowing one to cope not only with the ill-posedness but also with the intrinsic nonlinearity of many geophysical inversion problems. We developed a physical-statistical retrieval algorithm, which combines nonlinear optimal estimation with further optimization techniques. Profiling of water vapor based on (synthetic) downlooking microwave sounder data as an example for a typical geophysical nonlinear optimization problem is used to demonstrate the skills of the algorithm. Starting with a nonlinear scalar penalty function derived from a Bayesian approach, the sensible guess of a priori information, the selection of useful probability density functions, the advantages of simulated annealing, and the utility of Monte Carlo methods are discussed. These techniques together furnish capability for retrieving state vectors, which depend on the data in a (highly) nonlinear manner. The sensible combination as implemented in the introduced hybrid algorithm can provide solutions to problems that could not be tackled with standard (linearized) inversion methods properly.

Retrieval of temperature and moisture profiles from AMSU-A and AMSU-B measurements

“…Rieder and Kirchengast [19] have discussed some of the advantages and limitations of Bayesian algorithms and English [20] has presented an error analysis of simulated retrievals using AMSU-A and -B frequencies. Perhaps more crucial than the method used to obtain a solution, however, is the modeling of the observation process.…”

A neural network technique for inversion of atmospheric observations from microwave limb sounders

“…If Gaussian statistics are assumed for variables and errors, selecting the maximum likelihood state or the mean state gives the following implicit equation[Rodgers, 2000]' between spectra and profiles is not linear, (11) has to be solved numerically. Different iterative schemes can be used, and Marquardt-Levenberg[Marks and Rodgers, 1993] will be used here because, although not exempt of problems[Rieder and Kirchengast, 2000], it seems to be more robust than other methods for the Odin SMR inverthe solution after iteration i, K• are the weighting functions evaluated at (xi, ha), and c is the parameter controlling the trade-off between steepest descent and NewtonJan iteration.…”