Derive H2O window frequency bounds from quantum mechanics

Derive the mid-infrared water vapor window frequency limits ν_A and ν_B directly from the quantum mechanical vibrational–rotational spectrum of the H2O molecule, in order to replace empirically chosen bounds in the analytic expression for the clear-sky longwave climate feedback parameter λ.

Background

In the paper’s analytic treatment of the climate feedback parameter λ, the authors approximate λ by integrating the Planck spectral irradiance over the mid-infrared water vapor window between two frequency bounds, ν_A and ν_B. These bounds are assigned empirically (ν_A = 21 THz and ν_B = 36 THz) to obtain a reasonable estimate for λ consistent with observations and complex models.

The authors explicitly note that a first-principles derivation of these window limits from the quantum mechanical properties of H2O is not provided and is deferred. Establishing ν_A and ν_B from H2O’s vibrational–rotational transitions and associated line strengths, shapes, and continuum effects would enhance the theoretical foundation of the analytic λ estimate and its applicability across planetary conditions.