Clear-sky, Cloudy-sky and All-sky Global Mean Energy Budgets as the Solution of Classic Theoretical Radiative Transfer Constraint Equations

The clear-sky and all-sky global mean energy flow system of the Earth as the solution of four radiative transfer constraint equations were presented in Zagoni (CERES STM 2020). These equations have their theoretical origin in the concept of radiative equilibrium for stratified atmospheres (Schwarzschild 1906, Eq. 11; Milne 1930, Eq. 93-95; Goody 1964, Chamberlain 1978, Eq. 1.2.29-1.2.30; Eq. 2.115; Goody and Yung 1989, Eq. 2.146 and Eq. 9.5; Houghton 2002, Eq. 2.13; Andrews 2010, Eq. 3.50-3.51; Pierrehumbert 2010, Eq. 4.44-4.45, etc.). We showed that each of the equations is justified by 19 years of CERES data within ±3 Wm-2 and the all-sky equations by the IPCC-AR5 (2013) Fig. 2.11 global energy budget estimate within ±2 Wm-2. The individual flux components, both for clear-sky and all-sky are valid within ± 1 Wm-2 at the TOA and within ± 4 Wm-2 at the surface. A fifth equation was introduced in Zagoni (EGU 2020) showing the place of a non-observable flux component (atmospheric window radiation) in the theoretical system; and a sixth equation allowed to extend the arithmetic structure to total solar irradiance. The set of these equations has a solution for LWCRE = 1 as unit flux, and the whole system of the global mean atmospheric energy flows can be described by small integers, in their own units, separately for the clear-sky, the cloudy sky and (as their weighted sum) for the all-sky case. OLR(all) = 9, OLR(clear) = 10, ULW = 15, G(all) = 6, G(clear) = 5 units = 133.40 Wm-2 with TSI = 51 units = 1360.68 Wm-2. Here we introduce the cloudy versions of the examined classic radiative transfer constraint equations and present the all-sky global mean energy budget as the weighted sum of the clear-sky and cloudy-sky energy flow system. “Clouds” are regarded as a single IR-opaque layer, represented by an effective cloud area fraction. Essential characteristics of the climate (like the clear-cloudy energy exchange; the surface, TOA, in-atmosphere and net CREs; and the greenhouse effect) are explained as the cooperation of the clear-sky and cloudy-sky geometric arrangements expressed in the transfer equations. This way, the theoretical description of the Earth’s global mean energy budget is complete.