External explanatory variables for the residual kriging
In this work, we have only considered explanatory variables that can be derived from DEM. This makes the results more general and useful, since these variables are readily available elsewhere. Particularly, in this study we have evaluated the effect of the elevation and shadows cast as external variables in the kriging procedure. To deal with the seasonality of the solar radiation variability, the study is carried out for each month independently. The topographic characteristics were derived based on a 1 km spatial resolution DEM and the IDRISI GIS software [6] was used to carry out the regression analysis and the whole residual kriging procedure.
Regarding the elevation, it is clear that this variable is related to the atmospheric attenuation of the incoming solar radiation at the earth surface. The higher the elevation, the lower the atmospheric layer thickness and, therefore, the lower the atmospheric attenuation. Nevertheless, the importance of this explanatory variable depends on the elevation gradient. In the present study, this gradient is relative small (minimum elevation is 4 m and maximum 1212 m).
The other external explanatory variable that has been explored in this study is related to the shadow cast caused by the topography. The slope and aspect effect on the measured values can not be evaluated in this study since the stations are located on horizontal surfaces. The sky-view factor influence, nevertheless, can be evaluated. Particularly, to assess this effect, a sky-view factor can be used. This sky-view factor can be defined as the ratio between radiation actually received by a planar surface to that received from the entire hemispheric radiating environment (without any obstruction). It represents the shadows cast by topographic features. Sky view factor can be derived from DEM using several available procedures. In the present study the sky-view factor was computed using the GRASS GIS [6] environment in the following way: given a location, the maximum elevation angle of sky obstruction were computed for 36 directions around this location. Then, a continuous curve of angle values was computed using linear interpolation. The area under this continuous curve, normalized to the entire hemisphere is considered the sky-view factor. Note that the value of the sky-view factor varies from 1, when the whole sky is obscured, to 0, when no obstructions are present. In actual cases, sky-view factor seldom are higher than 0.20.
In this study, a modified version of this sky-view factor was used. Particularly, the sky-view factor was computed just using the topographic information in the south direction. That is, the angles were only computed for the half of the sky view, from solar azimuth angles between 90° (eastern ) to -90° (western), instead of for the complete circumference (solar azimuth angles from -180° to 180°). We will call this new sky-view factor semi-sky-view factor hereinafter. As for the complete circumference, the semi-sky-view factor may take values between 0 and 1. Actual values for all the stations used in this study ranged between 0 and 0.195. This new explanatory variable reveled to be much more effective in explaining the solar radiation variability than a complete sky-view factor. The rationale behind this result is that, as it is known, in the northern hemisphere, the amount of radiation received from solar azimuth angles between below -90° and above 90° is scarce. Therefore, the topographic information associated with these angles is not relevant in explaining the solar radiation variability and just increases the noise of the explanatory variable, without adding new information. This new semi-sky-view factor was used as independent variable in the residual kriging procedure.
