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Reconstruction of an atmospheric tracer source using the principle of maximum entropy. I: Theory
Author(s) -
Bocquet Marc
Publication year - 2005
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1256/qj.04.67
Subject(s) - inversion (geology) , tracer , entropy (arrow of time) , computer science , principle of maximum entropy , prior probability , minification , environmental science , meteorology , algorithm , remote sensing , mathematical optimization , mathematics , geology , physics , bayesian probability , artificial intelligence , paleontology , structural basin , quantum mechanics , nuclear physics
Abstract Over recent years, tracing back sources of chemical species dispersed through the atmosphere has been of considerable importance, with an emphasis on increasing the precision of the source resolution. This need stems from many problems: being able to estimate the emissions of pollutants; spotting the source of radionuclides; evaluating diffuse gas fluxes; etc. We study the high‐resolution retrieval on a continental scale of the source of a passive atmospheric tracer, given a set of concentration measurements. In the first of this two‐part paper, we lay out and develop theoretical grounds for the reconstruction. Our approach is based on the principle of maximum entropy on the mean . It offers a general framework in which the information input prior to the inversion is used in a flexible and controlled way. The inversion is shown to be equivalent to the minimization of an optimal cost function, expressed in the dual space of observations. Examples of such cost functions are given for different priors of interest to the retrieval of an atmospheric tracer. In this respect, variational assimilation (4D‐Var), as well as projection techniques, are obtained as biproducts of the method. The framework is enlarged to incorporate noisy data in the inversion scheme. Part II of this paper is devoted to the application and testing of these methods. Copyright © 2005 Royal Meteorological Society