Extension of the weak-line approximation and application to correlated-k methods

Abstract

a b s t r a c tGlobal climate models require accurate and rapid computation of the radiative transfer through the atmosphere. Correlated-k methods are often used. One of the approximations used in correlated-k models is the weakline approximation. We introduce an approximation T g which reduces to the weak-line limit when optical depths are small, and captures the deviation from the weak-line limit as the extinction deviates from the weak-line limit. This approximation is constructed to match the first two moments of the gamma distribution to the k-distribution of the transmission.We compare the errors of the weak-line approximation with T g in the context of a water vapor spectrum. The extension T g is more accurate and converges more rapidly than the weak-line approximation.

A Generalized Linear Transport Model for Spatially Correlated Stochastic Media

“…Finally, we draw attention to a serendipitous development in the atmospheric radiation literature. While our ongoing theoretical and computational work on unresolved/stochastic spatial variability of the extinction coefficient in turbulent scattering media has lead to the parameterized class of power-law propagation kernels described herein, Conley and Collins [15] have independently arrived at the very same power-law parameterization for the problem of unresolved spectral variability of the absorption coefficient due to all manner of molecules in the Earth's atmosphere that might contribute to the thermal and solar radiative processes that build up the greenhouse effect.…”

“…This violation of angular reciprocity is in fact observed in the Earth's cloudy atmosphere-the original motivation and application of the generalized RT model. In the final Section 7, we present our conclusions and an outlook on practical applications of our theoretical and computational advances, including a connection with recent work atmospheric spectroscopy [15].…”

Cloud information content in EPIC/DSCOVR’s oxygen A- and B-band channels: A physics-based approach

“…10], and references therein. Indeed this continues to be an area of active research [e.g., [18][19][20]. The simple scheme that uses exp(−τ 2) may not be the best, even for our present purposes.…”

“…Following [25], we can divide (16) by the known airmass factor (1/µ 0 + 1/µ) in (3), and thus define implicitly the "apparent" or "centroid" cloud-top altitude z in (18) simplifies to…”

“…(A 18),. we can estimate it intuitively as2 ct H ≈ cH 2 /6D = H 2 /2 t = Hτ t /2, which is H and thus ≫ t .…”