Mapping Solar Radiation in Southern Spain using residual kriging
MATRAS Group, Department of Physics, Campus Lagunillas, 23071, University of Jaen, Spain
* Corresponding Author, husain@,uiaen. es
This study presents a comparative analysis of the ordinary and residual kriging methods for mapping, on a 1 km by 1 km grid size, monthly-averaged daily global radiation (H) in the horizontal surface in Andalusia (Southern Spain). The experimental dataset includes four year (2003-2006) of data collected at 166 stations. Overall, the ordinary kriging methods proved to be able to provide fair estimates: RMSE ranging 1.63 MJ m'2day_1 (6.2%) in June to around 1.44 MJ m'2day_1 (11.2%) in October. In the residual kriging procedure, we propose the use of an external explanatory variable that accounts for topographic shadows cast, and that is able to explain between 15% and 45% of the spatial variability. Based in this 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 values of the residual kriging estimates ranges from 1.44 MJ m'2day_1 (5.5%) in June to around 1.31 MJ m'2day_1 (10.2 %) in October. It is finally concluded that the proposed residual kriging method is particularly valuable when mapping complex topography areas.
Keywords: GIS, Kriging, Global Solar Radiation, Andalusia (Southern Spain).
The interpolation techniques were the first methodologies used for mapping climate variables, such as the solar radiation. These techniques allow obtaining spatially continuous databases from isolated-stations measurements based on spatially interpolation methods. The reliability of interpolation techniques are strongly dependent on the sample size . Particularly, ordinary kriging may provide reliable estimates of climate variables, as the solar radiation, in homogeneous terrain with similar climate characteristics. Nevertheless, the reliability of the estimates decreases when the complexity of the topography increases, or when an earth-sea interface is present. In such cases, stochastic interpolation processes may not provide meaningful spatially-continuous estimates, since point-specific measurements can be affected by strong local variation. For the solar radiation, particularly, complex topography areas present a challenge. Variability in elevation, surface orientation (slope and aspect), and shadows cast by topographic features can create strong local gradients in the solar radiation that interpolation processes may not properly account for.
Many techniques have been proposed to overcome this weakness of the kriging interpolation processes. These techniques allows to take into account, prior or during the interpolation process, external variables, that may provide complementary information for the interpolation and, therefore, compensate for the lack of data and the scarce sample size . These external variables may be used locally or in the whole study area and, in most the cases, are related to geographical of
topographical characteristics. There are different ways in which the external variables can be taken into account in the kriging process. For instance, the information coming from the external variables can be considered during the interpolation process. An example of this methodology is the cokriging. This method is advantageous when the external variable is highly correlated to the studied variable, but becomes very complex when more than one covariables are considered  Instead of including the external information directly in the kriging process, it is possible to consider it during a first step, prior to the interpolation itself. There are different denominations for this technique, as ‘kriging with a guess field’  or ‘residual kriging’ . We will use this last denomination hereinafter. Basically, in a first step, a multiple linear regression is fitted between the variable of interest and some external explanatory variables. Then, an ordinary kriging procedure is applied to the residuals of this multiple regression analysis. Finally, a map is obtained integrating both the multiple regression and the kriging results. This technique, although relatively simple, is powerful, since allows including in an easy way multiple sources of external information in the interpolation procedure that may compensates for the small sample size. In this work we present an application of the residual kriging methodology for mapping monthly-averaged daily global radiation in horizontal surface in Andalusia (Southern Spain). The ordinary kriging method is also applied, to evaluate the improvement provided by the residual kriging method. The region of study is characterized by a wide range of topographic and climatic characteristic, which allows evaluating the influence of different external variables in the interpolation of the solar radiation.