The similarity transformation (ST) defines a new class of robust and stable parametric functions with embedded physical shape information to optimize flexibility in fitting or inverting data. The similarity transformation also permits the extraction of information on the shape of a particular class of physical functions, thereby providing the basis for comparing alternative models and for analyzing the information content of data. We employ these properties of similarity transformations to study differences between state-of-the-art physics-based atmospheric models (the thermosphere ionosphere electrodynamic general circulation model, or TIEGCM) and empirical atmospheric models (Mass Spectrometer Incoherent Scatter, or MSIS) and to investigate the universality of these models; we examine the role of noise in determining acceptable resolution for faithful retrieval of physical properties; and we measure the performance of MSIS-based forward models for inversion of ultraviolet remote sensing of the neutral upper atmosphere. The similarity transform method proves to be a valuable new tool for identifying common and discrepant properties of the models. Further, the ST method shows that TIEGCM and MSISE-90 profiles embody similar shape information and that a suitable ST parameterization can be constructed that approximates profiles from either model to within a few percent accuracy. ¿ 2001 American Geophysical Union