This study introduces nonisothermal H2O emissivity (E) and absorptivity (A) formulations for the troposphere and the stratosphere. The nonisothermal effects arise from the wavelength integration of the Planck function, evaluated at the emitting level temperature (Te), with the monochromatic absorption evaluated at the temperature of the absorbing path (Tp). In general, Te and Tp can differ by as much as 20-50 K in the atmosphere. Most of the published emissivities are essentially isothermal emissivities. We formulate a nonisothermal emissivity that satisfies the constraints posed by the monochromatic form of the transfer equation for a nonisothermal atmosphere. The new formulations employ continuous analytical expressions for E and A that retain the following H2O radiative properties: the asymptotic properties at small (≈0) and large (∞) pathlengths; temperature dependence of line parameters; nonisothermal effects; the e- and p-type continuum in the 500-1200 cm-1 region; and the overlap of the e-type continuum with the H2O line absorption. The E and A expressions are derived from a set of reference 5 cm-1 narrow-band calculations for homogeneous atmospheres. When applied to the inhomogeneous atmosphere including arctic, mid-latitude, tropics, and antarctic atmospheres, the cooling rates from 0 to 40 km computed from the emissivity approach agree within 3% of those from the narrow-band calculations; the surface downflux and the upflux at 50 km agree within 1.5%.

A major fraction (>1/2) of these small errors are due to the strong-line approximation employed in the emissivity model for the 0-800 cm-1 and the 1200-2200 cm-1 regions, and the emissivity approach itself introduces less than a 1% error in the fluxes. The excellent agreement with the narrow-band calculations essentially verifies the nonisothermal emissivity approach proposed here. We also show that emissivities, fluxes, and cooling rates computed by narrow-band models depend very strongly on the spectral resolution adopted in the model for computing transmittances.

Thus the spectral resolution in the narrow-band model is an arbitrary parameter. Furthermore, by comparing the narrow-band model fluxes with line-by-line (LBL) calculations we conclude that the 5 cm-1 resolution model underestimates atmospheric opacity due to inadequate treatment of the far wing opacity of lines. We employ a simple continuum-type opacity in our emissivity scheme to bring the present nonisothermal emissivity scheme into excellent agreement with available state-of-the-art LBL calculations.