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

Abstract

Abstract. 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.

Orographically-Induced Spontaneous Imbalance within the Jet Causing a Large Scale Gravity Wave Event

“…This has been the first GLORIA limited angle tomography retrieval using an irregular (Delauney) grid and the Laplacian regularisation discussed in Krasauskas et al (2019). Using GLORIA, on 10 March 2016 we observed GWs over Greenland in an area, where multiple possible GW sources exist.…”

“…This continues until the synthetic measurements generated by a forward model agree within expectation to the actual measurements. The final state of this iterative process is then used as the 'retrieval' result (Krisch et al, 2017;Krasauskas et al, 2019).…”

“…The spectral windows used for the optimised retrieval are listed in Appendix A. Sixteen channels were used in the retrieval, each for a different purpose (3 for temperature, 5 for CCl 4 , 4 for HNO 3 and 4 for temperature and O 3 combined). The retrieval was conducted using Laplacian regularisation and an irregular grid (Delaunay method) (Krasauskas et al, 2019). The Laplacian (second-order derivative) regularisation replaced the traditional first spatial derivative regularisation approach.…”

3-D tomographic observations of Rossby wave breaking over the Northern Atlantic during the WISE aircraft campaign in 2017

“…The data quality and expected errors of tomographic retrieval differ depending on the position of the point where these errors are calculated with respect to the flight path (hexagonal part of pattern). The relative errors for HNO 3 and O 3 were estimated for each point on the retrieval grid grid using a Monte Carlo based technique (Ungermann, 2013;Krasauskas et al, 2019). The particular error estimate calculated here includes measurement error and error due to inaccuracies of the retrieval method, but does not include errors due to imprecise knowledge of atmospheric parameters (e.g.…”

“…Levenberg-Marquardt algorithm (Marquardt, 1963) and conjugate gradients solver (Hestenes and Stiefel, 1952) are used for inverse modelling. For more information about 3-D tomography implementation refer to Ungermann et al (2010Ungermann et al ( , 2011 and Krasauskas et al (2019). In general, 3-D tomographic retrievals are computationally expensive, typically requiring a few hundred of CPU core-hours to complete.…”