Tomographic airborne limb sounder retrievals on irregular grid with second order regularisation

Abstract

Abstract. Multiple limb sounder measurements of the same atmospheric region taken from different directions can be combined in a 3D 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 unphysical parameters) variant of the Tikhonov regularisation scheme based on spatial derivatives of first and second order. As shown by a case study with synthetic data, this scheme, 5 combined with irregular grid retrieval methods, improves both upon the quality and the computational cost of 3D tomography, while eliminating 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. An efficient Monte Carlo technique was adopted for retrieval accuracy estimation.

Answers to the Referee Comment of Dr. Vern Hart on "Limited angle tomography of mesoscale gravity waves by the infrared limb-sounder GLORIA"

“…These factors are chosen ad hoc and cannot be interpreted directly as physically meaningful correlation lengths. A more physical regularisation scheme is currently under development and will be described by Krasauskas et al (2018). This minimisation problem is solved with a truncated conjugate gradient-based trust region scheme.…”

“…The standard deviations and correlation lengths used for the different systematic errors are summarised in Table 2. The effects of instrument errors on the GLORIA retrieval are discussed in detail by Kleinert et al (2018). The covariance matrix for measurement noise is taken from theoretical estimates given by Friedl-Vallon et al (2014) that agree well with estimates derived from real measurements .…”

Answers to the Referee Comment of Dr. Ole Christensen on "Limited angle tomography of mesoscale gravity waves by the infrared limb-sounder GLORIA"

“…The standard deviations and correlation lengths used for the different systematic errors are summarised in Table 2. The effects of instrument errors on the GLORIA retrieval are discussed in detail by Kleinert et al (2018). The covariance matrix for measurement noise is taken from theoretical estimates given by Friedl-Vallon et al (2014) that agree well with estimates derived from real measurements (Kleinert et al, 2014).…”