Water vapor continuum in the millimeter spectral region

Abstract

A theory is presented for the calculation of the continuous absorption of water molecules in the millimeter spectral region. The theory is based on a generalization of Fano’s theory in which the spectral density, the Fourier transform of the dipole‐moment correlation function, is calculated for a system consisting of a pair of molecules. The internal states are written in terms of the line space of the system, and the resolvent operator is obtained using the well‐known Lanczos algorithm. For the interaction between two water molecules, we include only the leading dipole–dipole term of the long‐range anisotropic potential, and model the isotropic interaction, used to calculate the statistical weight within the quasi‐static approximation, by a Lennard–Jones potential. Using reasonable values for the two Lennard–Jones potential parameters, and the known rotational constants and permanent dipole moment of a water molecule, we calculate the absorption coefficient for frequencies up to 450 GHz for temperatures between 282 and 315 K. The present results are in good agreement with an empirical model for the water continuum based on combined laboratory and atmospheric measurements. We conclude from our results that, contrary to some previous assertions, the strong negative temperature dependence as well as the magnitude of the continuum absorption, at least for the millimeter spectral region, can be explained in terms of the far‐wings of allowed rotational transitions.