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We use likelihood informed dimension reduction (LIS) (T. Cui et al. 2014) forinverting vertical profile information of atmospheric methane from ground basedFourier transform infrared (FTIR) measurements at Sodankyl\"a, NorthernFinland. The measurements belong to the word wide TCCON network for greenhousegas measurements and, in addition to providing accurate greenhouse gasmeasurements, they are important for validating satellite observations. LISallows construction of an efficient Markov chain Monte Carlo sampling algorithmthat explores only a reduced dimensional space but still produces a goodapproximation of the original full dimensional Bayesian posterior distribution.This in effect makes the statistical estimation problem independent of thediscretization of the inverse problem. In addition, we compare LIS to adimension reduction method based on prior covariance matrix truncation usedearlier (S. Tukiainen et al. 2016).

Likelihood informed dimension reduction for inverse problems in remote sensing of atmospheric constituent profiles