Clear-sky spectral radiance modeling under variable aerosol conditions

The distribution of diffuse radiance over the sky hemisphere is an important quantity that is required in many applications. Its spectral variation is useful when considering processes having a spectral dependence, such as photovoltaics (PV). Here, a clear-sky spectral radiance model is developed from radiative transfer theory, using appropriate parameterizations to make the model suitable for rapid engineering-type calculations. The phase function of various aerosol mixtures combines three conventional Henyey-Greenstein functions. This procedure provides an effective solution to the problem of modeling the strong radiance within the circumsolar region, while being also accurate in low-energy areas of the clear sky. The dependence on wavelength of the coefficients of the simplified phase functions is efficiently described by polynomial ratios. The radiance is shown to vary from a relatively isotropic distribution in the UV to a very anisotropic one over the rest of the solar spectrum. The radiance model can be used to describe either ideal atmospheric situations or dynamic situations, for which the hourly outputs from the MERRA-2 reanalysis provide the optical properties of the aerosol mixture at any location. Examples of ideal radiance distributions include those corresponding to the reference spectra used for the performance characterization of PV cells. By integrating the modeled radiance over all wavelengths with appropriate weighting, both the broadband radiance and luminance can be derived. Although these two distributions are generally not identical, they are found sufficiently close, even under hazy conditions, to make them interchangeable in practice, within reasonable error limits. Compared to common empirical luminance distributions of the literature, the model appears more universal, because responsive to strong changes in aerosol composition.