Diffuse radiances under partially cloudy sky - theory and numerical modelling

摘要

Solution of radiative transfer equation under arbitrary meteorological conditions is important for modelling the solar energy at the ground, especially in the urban spaces. At present, a set of conventional computational techniques can be used to compute the diffuse and direct radiative fluxes and also the spectral radiance field under approximation of homogeneous plane-parallel atmosphere. However, an incorporation of broken clouds into theoretical and numerical models is associated with terrible difficulties, mainly due to transition from 1D to 3D geometry. In our paper, the radiative field below broken cloud array is solved theoretically introducing an approximate method of successive orders of scattering (SOS). The single-scattering radiance components originated from both broken clouds and cloud-free atmosphere are well separated, while the non-trivial superposition of these components determines the total sky radiance. The derived formulae enable to construct a rapid numerical model that can simulate the solar energy at the ground under arbitrary cloud coverage, air pollution conditions, sun elevation, or azimuthal orientation of a measuring device. The feasibility of our computational model is demonstrated in set of figures showing that radiance pattern is a function of both the cloud fraction and the physical parameters characterizing single clouds.