Finite-Surface Integration Algorithm for the Forecasting of Cloudy-Sky Direct Normal Irradiance in the Circumsolar Region

Direct Normal Irradiance (DNI) representing solar radiation along the straight line from the direction of the sun is often used to assess solar resource and is particularly crucial in evaluating the performance of concentrating solar power (CSP) systems. Numerous radiative transfer models assume DNI is related to a narrow beam only covering the solar disk where the Lambert-Bouguer law is used in the numerical computation. However, DNI is often interpreted differently in solar observation by surface-based pyrheliometers. For example, ISO-9488 standard defines direct irradiance by “the quotient of the radiant flux on a given plane receiver surface received from a small solid angle centered on the sun’s disk to the area of that surface”, which indicates the circumsolar diffuse radiation may affect the accuracy of DNI computed by the radiative transfer models. This study introduces a finite-surface integration algorithm that computes solar radiation in differential solid angles and efficiently infers its contribution to a surface perpendicular to the solar direction. A lookup table of cloud bi-directional transmittance distribution function (BTDF) is developed by the discrete ordinates radiative transfer (DISORT) model for possible solar and observation directions and various cloud optical and microphysical properties. In each solar incident direction, DNI is given by the cloud BTDFs from ~200 differential solid angles. The simulated DNI is further calibrated by considering the effect of cloud forward scattering using 10-year surface observations at the National Renewable Energy Laboratory’s (NREL’s) Solar Energy Research Laboratory (SRRL). The evaluation study using long-term Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) data suggests that this new model has significantly better accuracy than the Lambert-Bouguer law as well as models empirically separate DNI from measurements of global horizontal irradiance (GHI).