Modeling the variability of solar radiation data among weather stations by means of principal components analysis

Measurements of global terrestrial solar radiation (R_s) are commonly recorded in meteorological stations. Daily variability of R_s has to be taken into account for the design of photovoltaic systems and energy efficient buildings. Principal components analysis (PCA) was applied to R_s data recorded at 30 stations in the Mediterranean coast of Spain. Due to equipment failures and site operation problems, time series of R_s often present data gaps or discontinuities. The PCA approach copes with this problem and allows estimation of present and past values by taking advantage of R_s records from nearby stations. The gap infilling performance of this methodology is compared with neural networks and alternative conventional approaches. Four principal components explain 66% of the data variability with respect to the average trajectory (97% if non-centered values are considered). A new method based on principal components regression was also developed for R_s estimation if previous measurements are not available. By means of multiple linear regression, it was found that the latent variables associated to the four relevant principal components can be fitted according to the latitude, longitude and altitude of the station where data were recorded from. Additional geographical or climatic variables did not increase the predictive goodness-of-fit. The resulting models allow the estimation of daily R_s values at any location in the area under study and present higher accuracy than artificial neural networks and some conventional approaches considered. The proposed methodology for estimating R_s based on geographical parameters would be of interest to design solar energy systems and to select their best location.