Markov chain Monte Carlo methods for high dimensional inversion in remote sensing

H. Haario, M. Laine, M. Lehtinen, E. Saksman and J. Tamminen

Journal of the Royal Statistical Society Series B, 2004, vol. 66, issue 3, 591-607

Abstract: Summary. We discuss the inversion of the gas profiles (ozone, NO3, NO2, aerosols and neutral density) in the upper atmosphere from the spectral occultation measurements. The data are produced by the ‘Global ozone monitoring of occultation of stars’ instrument on board the Envisat satellite that was launched in March 2002. The instrument measures the attenuation of light spectra at various horizontal paths from about 100 km down to 10–20 km. The new feature is that these data allow the inversion of the gas concentration height profiles. A short introduction is given to the present operational data management procedure with examples of the first real data inversion. Several solution options for a more comprehensive statistical inversion are presented. A direct inversion leads to a non‐linear model with hundreds of parameters to be estimated. The problem is solved with an adaptive single‐step Markov chain Monte Carlo algorithm. Another approach is to divide the problem into several non‐linear smaller dimensional problems, to run parallel adaptive Markov chain Monte Carlo chains for them and to solve the gas profiles in repetitive linear steps. The effect of grid size is discussed, and we present how the prior regularization takes the grid size into account in a way that effectively leads to a grid‐independent inversion.

Date: 2004
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