Solar Engineering of Thermal Processes, 4th Edition

2.16 Radiation on Sloped Surfaces: Anisotropic Sky

The isotropic diffuse model (Equation 2.15.1) is easy to understand, is conservative (i.e., it tends to underestimate ), and makes calculation of radiation on tilted surfaces easy. However, improved models have been developed which take into account the circumsolar diffuse and/or horizon- brightening components on a tilted surface that are shown schematically in Figure 2.16.1. Hay and Davies (1980) estimate the fraction of the diffuse that is circumsolar and consider it to be all from the same direction as the beam radiation; they do not treat horizon brightening. Reindl et al. (1990b) add a horizon-brightening term to the Hay and Davies model, as proposed by Klucher (1979), giving a model to be referred to as the HDKR model. Skartveit and Olseth (1986, 1987) and Olseth and Skartiveiz (1987) develop methods for estimating the beam and diffuse distribution and radiation on sloped surfaces starting with monthly average radiation. Perez et al. (1987, 1988, 1990) treat both circumsolar diffuse and horizon brightening in some detail in a series of models. Neumann et al. (2002) propose a model for circumsolar radiation that is of particular importance in predicting the performance of concentrating systems where the angular distribution of energy near the sun's disc is important. The circumsolar ratio (CSR; defined as the ratio of the energy ...