Open AccessReconstructing source terms from atmospheric concentration measurements: Optimality analysis of an inversion technique
Author(s) -
Turbelin Grégory,
Singh Sarvesh Kumar,
Issartel JeanPierre
Publication year - 2014
Publication title -
journal of advances in modeling earth systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.03
H-Index - 58
ISSN - 1942-2466
DOI - 10.1002/2014ms000385
Subject(s) - inversion (geology) , inverse problem , inverse , data assimilation , renormalization , mathematics , operator (biology) , algorithm , mathematical optimization , computer science , meteorology , mathematical analysis , physics , geology , geometry , paleontology , biochemistry , chemistry , repressor , structural basin , transcription factor , mathematical physics , gene
Abstract In the event of an accidental or intentional contaminant release in the atmosphere, it is imperative, for managing emergency response, to diagnose the release parameters of the source from measured data. Reconstruction of the source information exploiting measured data is called an inverse problem. To solve such a problem, several techniques are currently being developed. The first part of this paper provides a detailed description of one of them, known as the renormalization method. This technique, proposed by Issartel (2005), has been derived using an approach different from that of standard inversion methods and gives a linear solution to the continuous Source Term Estimation (STE) problem. In the second part of this paper, the discrete counterpart of this method is presented. By using matrix notation, common in data assimilation and suitable for numerical computing, it is shown that the discrete renormalized solution belongs to a family of well‐known inverse solutions (minimum weighted norm solutions), which can be computed by using the concept of generalized inverse operator. It is shown that, when the weight matrix satisfies the renormalization condition, this operator satisfies the criteria used in geophysics to define good inverses. Notably, by means of the Model Resolution Matrix (MRM) formalism, we demonstrate that the renormalized solution fulfils optimal properties for the localization of single point sources. Throughout the article, the main concepts are illustrated with data from a wind tunnel experiment conducted at the Environmental Flow Research Centre at the University of Surrey, UK.