The spectral characteristics of atmospheric gravity wave motions are remarkably uniform in frequency and wavenumber despite widely disparate sources, filtering environments, and altitudes of observation. This permits a convenient and useful means of describing mean spectral parameters, including energy density, anisotropy, energy and momentum fluxes, and wave influences on their environment. The purpose here is to provide a general formulation of the mean energy spectrum as well as estimates of the wave energy and momentum fluxes and the flux divergences expressed as the energy dissipation rate and the induced accelerations in the lower and middle atmosphere. These results show spectral observations to be consistent with independent estimates of energy dissipation rates and to suggest a high degree of anisotropy of the gravity wave field under conditions of strong wave filtering by large-scale, low-frequency motions. In two companion papers, these results are employed to construct a parameterizat... Abstract The spectral characteristics of atmospheric gravity wave motions are remarkably uniform in frequency and wavenumber despite widely disparate sources, filtering environments, and altitudes of observation. This permits a convenient and useful means of describing mean spectral parameters, including energy density, anisotropy, energy and momentum fluxes, and wave influences on their environment. The purpose here is to provide a general formulation of the mean energy spectrum as well as estimates of the wave energy and momentum fluxes and the flux divergences expressed as the energy dissipation rate and the induced accelerations in the lower and middle atmosphere. These results show spectral observations to be consistent with independent estimates of energy dissipation rates and to suggest a high degree of anisotropy of the gravity wave field under conditions of strong wave filtering by large-scale, low-frequency motions. In two companion papers, these results are employed to construct a parameterizat...