Fast scheme for determination of direct normal irradiance. Part II: Parameterization of circumsolar radiation

Abstract A method of the scattering Phase Function Scaling (PFS) for determination of the direct normal irradiance (DNI) involving the circumsolar normal irradiance (CSNI) is developed. A fraction of the normalized phase function integrated over the field of view for a pyrheliometer is introduced in the radiative transfer equation so the scaled optical depth using this phase function is derived. The PFS method is tested in a radiative transfer scheme and a simple fast parametric scheme SUNFLUX using the observational datasets at 14 Baseline Surface Radiation Network (BSRN) stations. The evaluation results show that the modelled DNI in terms of the PFS method in the radiative transfer scheme is significantly improved compared with that using the original delta-Eddington scaling method and compared well with that determined using other two radiative transfer models of DISORT and SMARTS. The modelled DNI with the PFS method in the SUNFLUX scheme is also improved compared with that without using the PFS method and compared well with that from the SMARTS model. The CSNI is also evaluated against the results from the other three models. The results are generally poor in all cases. The poor results are mainly due to the small magnitude of CSNI and uncertainties in the input data. Uncertainty in the aerosol scattering phase function could be the main reason responsible for the poor comparisons.