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

The similarity transform method provides a new, highly robust, and stable p arametric representation of geophysical functions for use in retrieving suc h functions from remote sensing observations. The present discussion focuse s on the approximation of altitude profiles of upper atmospheric species co ncentration and on the development of parametric forward models fur use wit h discrete inverse theory (DIT). Of equal importance, the similarity transf orm approach provides a framework fur extracting generic profile shape info rmation, in the form of a nondimensional shape function, from observations or detailed numerical simulations. In this way the method facilitates analy sis of general characteristics of species concentration variations with alt itude and with other geophysical parameters. For DIT retrievals of concentr ation profiles from observations a similarity transformation-based forward model embeds the generic ("basis") shape information directly into a parame tric representation of each species profile. The presentation covers the ex traction of nondimensional shape functions from discrete data or simulation s, tilt: basic forward model representation, and generalizations of the bas ic approach. We include simple examples of similarity transform fitting cal culations in which the species concentration profiles to he approximated ar e generated by the Mass Spectrometer Incoherent Scatter Empirical 1990 (MSI SE-90) atmospheric model, as are the basis profiles that define the shape i nformation.