A Simple Yet More Accurate Model to Calculate Solar Radiative Flux in the Inhomogeneous Atmosphere

A simple yet more accurate semiempirical model is developed to calculate solar radiative flux in the optically inhomogeneous atmosphere. In the model a parameterized expression of spherical reflectance and transmitance of the atmosphere is confirmed, and the weighted single scatter albedo and weighted asymmetric factor are introduced to fit four empirical correction factors responsible for radiative fluxes in the inhomogeneous atmosphere. For both clean and turbid models, there are 120060 sets of radiative flux simulations for accuracy checks of the model, which cover 0-50 cloud optical depths, 0-0.8 surface reflectance, Junge and Log-normal aerosol size distributions, and 0-0.05 imaginary parts of aerosol refractive indexes. In case of the homogeneous atmosphere, standard errors of the 120060 upward fluxes from the present model are 1.08% and 1.04% for clean and turbid aerosol models, respectively; and those of the downward fluxes are 4.12% and 3.31%. In case of the inhomogeneous atmosphere, standard errors of the upward fluxes from the present model are 3.01% and 3.48% for clean and turbid aerosol models, respectively; and those of the downward fluxes are 4.54% and 4.89%, showing a much better accuracy than the results calculated by using an assumption of the homogeneous atmosphere.