Aerosol model selection and uncertainty modelling by adaptive MCMC technique

Abstract. We present a new technique for model selection problem in atmospheric remote sensing. The technique is based on Monte Carlo sampling and it allows model selection, calculation of model posterior probabilities and model averaging in Bayesian way.

The algorithm developed here is called Adaptive Automatic Reversible Jump Markov chain Monte Carlo method (AARJ). It uses Markov chain Monte Carlo (MCMC) technique and its extension called Reversible Jump MCMC. Both of these techniques have been used extensively in statistical parameter estimation problems in wide area of applications since late 1990's. The novel feature in our algorithm is the fact that it is fully automatic and easy to use.

We show how the AARJ algorithm can be implemented and used for model selection and averaging, and to directly incorporate the model uncertainty. We demonstrate the technique by applying it to the statistical inversion problem of gas profile retrieval of GOMOS instrument on board the ENVISAT satellite. Four simple models are used simultaneously to describe the dependence of the aerosol cross-sections on wavelength. During the AARJ estimation all the models are used and we obtain a probability distribution characterizing how probable each model is. By using model averaging, the uncertainty related to selecting the aerosol model can be taken into account in assessing the uncertainty of the estimates.