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

TL;DR

This paper applies likelihood informed dimension reduction (LIS) to efficiently invert atmospheric methane profiles from ground-based FTIR measurements, improving Bayesian inference in remote sensing applications.

Contribution

It demonstrates the use of LIS for dimension reduction in atmospheric inverse problems and compares it to prior covariance truncation methods.

Findings

LIS enables efficient MCMC sampling in reduced space.

LIS provides accurate posterior approximations.

Compared to prior truncation, LIS improves computational efficiency.

Abstract

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