A comparative study of ordinary and residual kriging techniques for mapping global solar radiation over southern Spain

This study presents a comparative analysis of the ordinary and residual kriging methods for mapping, on a1k m� 1 km grid size, the monthly mean of global solar radiation at the surface in Andalusia (southern Spain). The region of study is characterized by a wide range of topographic and climatic characteristic, which allows properly evaluating the two methods. The experimental dataset includes 4 years (2003– 2006) of data collected at 166 stations: 112 stations were used to train the models and 54 in an independent validation procedure. Overall, the ordinary kriging method provide fair estimates: RMSE ranges from 1.63 MJ m � 2 day � 1 (6.2%) in June to around 1.44 MJ m � 2 day � 1 (11.2%) in October. In the residual kriging procedure, we propose using an external explanatory variable (derived just based on a digital elevation model) that accounts for topographic shadows cast, and that is able to explain between 13% and 45% of the spatial variability. Based on the combined used of the elevation and the former external variable, residual kriging estimates shows a relative improvement in RMSE values ranging from 5% in the summer months to more than 20% in the autumn and winter months. Particularly, RMSE is 1.44 MJ m � 2 day � 1 (5.5%) in June and 1.31 MJ m � 2 day � 1 (10.2%) in October. Explained variance also shows a considerable improvement compared to the ordinary kriging method, with all the months showing R 2 values above 0.92. Results show that most part of these improvements is associated with a better estimation of the minimum values, particularly during the winter part of the year. It is finally concluded that the proposed residual kriging method is particularly valuable when mapping complex topography areas.