Earth’s Global Mean Energy Flow System as the Solution of Four Radiative Transfer Constraint Equations

Abstract

\n Schwarzschild’s equation in two-stream approximation provides a constraint on the net radiation at the lower boundary, as unequivocally connects it to fluxes at the upper boundary (top-of-atmosphere): surface net radiation, balanced by the non-radiative fluxes in radiative-convective equilibrium, is equal to half of the outgoing longwave radiation (OLR), independent of the optical depth. This paper controls this equation on satellite observations and proved to be valid within -2.19 W/m2 for clear-sky, in the annual global mean. The all-sky version of the relationship can easily be constructed, separating atmospheric radiation transfer from the longwave cloud radiative effect (LWCRE); it is valid with a difference of 2.76 W/m2 on the same data set. The equation provides a total (greenhouse) relationship as well, where the surface energy income is given as a function of OLR and the optical depth. This equation is controlled at a particular optical depth of two, and found to be verified with a difference of -2.72 W/m2 for clear-sky in the global mean. An all-sky form is created by including LWCRE, justified within 2.42 W/m2 on the same data set. The four equations together have a mean bias of 0.07 W/m2. This set of equations, using evident definitions between the all-sky and clear-sky fluxes has a solution for the involved components of the global mean energy flow system. Implications on the global mean clear-sky and cloudy energy flow systems are assessed, and the all-sky energy budget is constructed as a weighted sum of the clear and cloudy fluxes.