3-D tomographic limb sounder retrieval techniques: irregular grids and Laplacian regularisation

Multiple limb sounder measurements of the same atmospheric region taken from different directions can be combined in a 3-D tomographic retrieval. Mathematically, this is a computationally expensive inverse modelling problem. It typically requires an introduction of some general knowledge of the atmosphere (regularisation) due to its underdetermined nature.This paper introduces a consistent, physically motivated (no ad-hoc parameters) variant of the Tikhonov regularisation scheme based on spatial derivatives of the first-order and Laplacian. As shown by a case study with synthetic data, this scheme, combined with irregular grid retrieval methods employing Delaunay triangulation, improves both upon the quality and the computational cost of 3-D tomography. It also eliminates grid dependence and the need to tune parameters for each use case. The few physical parameters required can be derived from in situ measurements and model data. Tests show that a 82 % reduction in the number of grid points and 50 % reduction in total computation time, compared to previous methods, could be achieved without compromising results. An efficient Monte Carlo technique was also adopted for accuracy estimation of the new retrievals