Evaluation of 12 models to estimate hourly diffuse irradiation on inclined surfaces

This study evaluates the performance of 12 models to estimate hourly diffuse solar irradiation on inclined surfaces from those measured on horizontal surfaces. Total solar irradiation incident on a tilted surface consists of three components including: beam, diffuse and reflected from the ground. On a semi-hourly basis, the beam component can be calculated by the ratio of the incidence angle to the solar zenith angle. The reflected component has a small effect on calculations and may be calculated with an isotropic model. In contrast, models for estimating the diffuse component show major differences, which justify the validation study that this paper discusses. Twelve models were tested against recorded south- and west-facing slope irradiances at Karaj (35°55′N55′N; 50°56′E56′E), Iran. The following models were included: Badescu [Ba], Tian et al. [Ti], Perez et al. [P9], Reindl et al. [Re], Koronakis [Kr], Perez et al. [P8], Skartveit and Olseth [SO], Steven and Unsworth [SU], Hay [Ha], Klucher [Kl], Temps and Coulson [TC], and Liu and Jordan [LJ].The relative root mean square error (RMSE), for the south-facing surface ranges from 10.16% to 54.89% for the SO and TC models, respectively. For the west-facing surface, RMSE ranges from 30.71% for the P9 model to 63.53% for the TC model. Statistical indices show that all models produce large errors for the west-facing surface. Statistical indices for the south-facing surface show reasonably good agreement with measured data.