Solar radiation budget in the atmosphere under broken cloudy sky. An analytical model

Rosa, R. N., A. M. Silva, 2021

This study theoretically investigates the transport of broadband solar radiation in the Earth’s cloudy atmosphere (extended and broken) by considering three plane parallel layers: i) thin bottom layer adjacent to the Earth’s surface; ii) intermediate layer where clouds are most embedded; and iii) upper layer that is essentially cloud-free with possible occurrence of only thin clouds. These three layers are coupled by upwelling and downwelling radiation exchanges, including multiple retro-diffusion, and both direct beam and diffuse components are considered. The interrelation and relative magnitude of the solar radiation flux cascade across the atmosphere – αP, Ra, Rc, Rg and G/H – was established and explored as a tool for the present simulations. Two distinct radiation transport regimes through the inter-cloud gaps are identified, with the regime transition occurring when (AR*TAN(θ)+1)*CF = 1 where ARθ and CF are the cloud aspect ratio, solar zenith angle, and cloud fraction, respectively. The variation of the solar radiation fluxes with CF and θ exhibit the transition between the two radiation transport regimes, as evidenced in the flux absorbed in the cloudy layer. The effect of AR upon the solar fluxes also exhibits the two radiation transport regimes, with one regime having linear dependence of the various fluxes on AR and the other one having fluxes stay at constant levels independent of AR. The shape factor SF of cloud top and bottom boundary “surfaces” is introduced to account for the self-irradiation effect for different cloud types. It is found that increased roughness of one or both boundaries increases the cloud absorptance in all cases whereas transmittance and reflectance for upwelling and downwelling can either be diminished or enhanced.

With the proposed model the estimated impact of clouds on the enhancement of the shortwave radiation absorption in the atmospheric column was improved leading to results closer to the cloudy-sky absorptance observations reported in the literature. The ratio of the cloud radiative forcing at the surface to the cloud radiative forcing at the top of the atmosphere (Rnet), obtained by means of the present model, lead to Rnet = 1.3, closer to the estimate of 1.5 by Cess et al. than the values reported by other cloud radiative transfer models. Read the full article.