An Improved Parametric Model for Simulating Cloudy Sky Daily Direct Solar Radiation on Tilted Surfaces

Incoming solar radiation absorbed by the Earth's surface is important for simulation models in addressing issues of ecosystem dynamics and climate change. The objective of this study was to simulate the daily direct solar radiation on tilted surfaces under cloudy sky conditions using an improved parametric model that integrates the atmospheric attenuation with the correction of three dimensional effects of cloud shadow and topographic factors. The model is validated by implementing four comparative case studies (Lhasa, Beijing, Kunming and Erjinaqi) based on the daily atmospheric products of MODIS TERRA/AQUA and SRTM DEM. The results show that the proposed parametric model is convincingly efficient, as the computed coefficients of determination (R
$^{2}$
) are relatively high for all stations except Lhasa (0.62 for Lhasa, 0.70 for Kunming, 0.70 for Beijing and 0.78 for Erjinaqi), and the RMSE (root mean square error) are 4.89 MJ/m
$^{2}$
for Lhasa, 4.09 MJ/m
$^{2}$
for Kunming, 4.02 MJ/m
$^{2}$
for Beijing and 3.79 MJ/m
$^{2}$
for Erjinaqi. A possible explanation is that the complex terrain accounts for the greater attenuation of solar radiation at Lhasa, while in our study, the data are retrieved at a spatial resolution of 1 km and the detailed terrain can not be clearly represented. The proposed model also indicates that clouds are the primary contributors to the amount and spatiotemporal distribution of solar radiation. The accuracy of the developed model is largely dependent on the temporal resolution of the data sources, especially the cloud optical thickness data. Meanwhile, the model reveals that topography and the spatial resolution of the DEM are important factors that affect the model results on tilted surfaces.