Similarity transformations for fitting of geophysical properties: Application to altitude profiles of upper atmospheric species

Abstract

The similarity transform method provides a new, highly robust, and stable parametric representation of geophysical functions for use in retrieving such functions from remote sensing observations. The present discussion focuses on the approximation of altitude profiles of upper atmospheric species concentration and on the development of parametric forward models for use with discrete inverse theory (DIT). Of equal importance, the similarity transform approach provides a framework for extracting generic profile shape information, in the form of a nondimensional shape function, from observations or detailed numerical simulations. In this way the method facilitates analysis of general characteristics of species concentration variations with altitude and with other geophysical parameters. For DIT retrievals of concentration profiles from observations a similarity transformation‐based forward model embeds the generic (“basis”) shape information directly into a parametric representation of each species profile. The presentation covers the extraction of nondimensional shape functions from discrete data or simulations, the basic forward model representation, and generalizations of the basic approach. We include simple examples of similarity transform fitting calculations in which the species concentration profiles to be approximated are generated by the Mass Spectrometer Incoherent Scatter Empirical 1990 (MSISE‐90) atmospheric model, as are the basis profiles that define the shape information.