Abstract
Abstract. In this work we discuss inclusion of a priori information about the smoothness of atmospheric profiles in inversion algorithms. The smoothness requirement can be formulated in the form of Tikhonov-type regularization, where the smoothness of atmospheric profiles is considered as a constraint or in the form of Bayesian optimal estimation (maximum a posteriori method, MAP), where the smoothness of profiles can be included as a priori information. We develop further two recently proposed retrieval methods. One of them - Tikhonov-type regularization according to the target resolution - develops the classical Tikhonov regularization. The second method - maximum a posteriori method with smoothness a priori - effectively combines the ideas of the classical MAP method and Tikhonov-type regularization. We discuss a grid-independent formulation for the proposed inversion methods, thus isolating the choice of calculation grid from the question of how strong the smoothing should be. The discussed approaches are applied to the problem of ozone profile retrieval from stellar occultation measurements by the GOMOS instrument on board the Envisat satellite. Realistic simulations for the typical measurement conditions with smoothness a priori information created from 10-years analysis of ozone sounding at Sodankylä and analysis of the total retrieval error illustrate the advantages of the proposed methods. The proposed methods are equally applicable to other profile retrieval problems from remote sensing measurements.
Highlights
The problem of profile retrieval from remote sensing measurements is always under-determined: a continuous profile of an atmospheric constituent is reconstructed from a finite number of measurements
We develop further two recently proposed methods which can be applied if the information needed for the maximum a posteriori (MAP) method is unavailable
The first method considers the smoothness of atmospheric profiles not as an ad hoc constraint, as it is done in Tikhonov regularization, but as a priori information
Summary
The problem of profile retrieval from remote sensing measurements is always under-determined: a continuous. Application of Tikhonov-type regularization ( referred to as the Twomey method) (Tikhonov and Arsenin, 1977; Twomey, 1977; Rodgers, 2000) helps to recover the stability of inversion This method assumes a smoothness of an atmospheric constituent profile and we can consider regularization as a kind of prior information. The first method considers the smoothness of atmospheric profiles not as an ad hoc constraint, as it is done in Tikhonov regularization, but as a priori information. The second method (Tamminen et al, 2004) chooses the regularization parameter in a Tikhonov-type scheme according to a target resolution, which is determined from requirements to resolve fine structures of the profiles For both methods we propose a grid-independent formulation, which is very important for measurements unevenly distributed in altitude. The resolution (Backus-Gilbert spread) is ∼2 km in the mesosphere and upper stratosphere, and is less than 1 km in the lower stratosphere and troposphere
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