Reconciling radiation dissipation in the spatial and spectral domains under stable conditions

Abstract

Two formulations for the radiative dissipation of temperature fluctuations, in the spatial and the spectral domains, are reconciled. Both can be written in terms of a first-order decay of temperature variance. The decay constant was obtained originally by Brutsaert (1972) for stable conditions from considerations on the temperature autocovariance function (in the spatial domain). Here it is obtained directly from a spectral dissipation function, using the appropriate Monin-Obukhov dimensionless functions for a stable atmosphere. The general behavior of the constant with stability is the same for the two formulations, with Brutsaert's original formulation producing stronger dissipation than its spectral counterpart. Key Points a 1st-order decay constant is obtained from a spectral dissipation function the kaimal spectrum constant is reviewed to give an exact integral two approaches to the 1st-order decay are shown to have similar behaviors ©2013. American Geophysical Union. All Rights Reserved.