[1] This paper supports studies of low-frequency variability (LFV) within the thermosphere by deriving approximate integral and closed-form solutions of a nontrivial model of thermospheric temperature, density, and composition depending on altitude and time. We also provide a paradigm for applying dimensional analysis in such studies. The domain is the region between the mesopause and the exobase. The solutions emphasize the connectedness of the thermosphere, i.e., nonlocal influences of LFV in key physical parameters and phenomena. The present focus is seasonal variability, within which the origin of a sizable semiannual variation in the thermosphere remains under active investigation. Following from the thermodynamic differential equation for temperature is a filtered, integral solution consistent with the Π theorem of dimensional analysis. A key result is the explicit demonstration that lower thermospheric boundary conditions affect low-frequency variability throughout the thermosphere, making accurate boundary conditions essential to modeling LFV. In addition, LFV of the temperature varies inversely with variability of the net heating profile and has directly and inversely proportional contributions from variations in the thermal conductivity profile, which can include an “eddy diffusivity” component. Given a temperature profile, diffusive equilibrium defines model composition. For rapid calculations and transparency, we develop an approximate, closed-form solution for temperature, density, and composition depending only on a minimal set of observable parameters, and from that, we demonstrate the essential role of the phase and amplitude profile of the temperature LFV in determining the corresponding profile of variability in composition and density.

%B Journal of Geophysical Research: Space Physics %V 118 %P 5853 - 5873 %8 09/2013 %G eng %U http://doi.wiley.com/10.1002/jgra.v118.9http://doi.wiley.com/10.1002/jgra.50472 %N 9 %! J. Geophys. Res. Space Physics %R 10.1002/jgra.v118.910.1002/jgra.50472