Figure 1C shows a typical case of a clear day with the snow covering the Sierra Nevada Mountains. In these particular images, the method Heliosat-2 can lead to subestimations, because the pixels are considered to be covered by clouds instead of by snow. In this work, a preprocessing method is applied to perform a detection of possible snow covers. Consisting in a comparison between the mountain pixels versus the surrounding ones, where a very low albedo in the surrounding if compared with the mountain is considered to belong to a clear day with snow covers. The method offers a success of near 85% in the detection of snow covers and it will be used. Error reduction due to this detection is discussed in the Results section.

1.2. Horizon calculation

Computational cost of the horizon calculation can be a problem when dealing with large areas; that issue has been addressed by developing an algorithm that reduces drastically the time spent in this process, without loosing much information about the actual horizon. The used DTM file contains around two million values of altitude, and the horizon for a specific point should be calculated by using all that information, but in this work most of the points are skipped and only around 70000 are utilized. The skipping step is defined as a function of the distance to the studied point, and a random contribution is also added. Finally, the horizon is only calculated for those selected points which altitude is higher than the studied point one, reducing the time consumption. Figure 3 shows the random and the selected points in the calculation of the horizon.

A comparison of the calculated horizon following the described algorithm and the real horizon (calculated by using the whole set of DTM points) appears in Figure 4, where it can be noted the little influence of the selection in the final calculation. Finally, for each day, the horizon will be overlaid with the sun path, obtaining the actual sunrise and sunset hours from the solar altitudes that will be introduced to the model.

2. Results and discussion

Daily irradiation values were calculated with and without inclusion of local effects; afterwards, the error was calculated in terms of Mean Bias Error (MBE) and Root Mean Square Error (RMSE), as a percentage of the mean measured value. Table 2 shows the obtained errors for the different stations and the three considered methods: A. Heliosat-2 with no horizon and using a mean altitude for the pixel, B. Heliosat-2 considering the calculated horizon and the altitude of the point and C. same as B but including the detection of clear days with snow covers.

Error reduction is detected for all the stations, and the importance of horizon effects appears to be larger than the effect of the snow covers. In fact, the consideration of snow covers is almost negligible in the case of the stations 13 and 14, as they are located in the plane area, outside the mountains, where snow is not usually present, but it can decrease up to 2% in the upper stations.

In addition, the station 9 is the one with a major improvement in the estimates, this is ought to the fact that is placed in a gully, having the larger horizon obstructions compared with the other stations. The mean RMSE considering the whole set of stations is reduced from 16% to 11%, verifying the good behaviour of the proposed methodology.

Once the performance of the method has been analyzed and in view of the satisfactory results provided in the global radiation estimates for the 14 stations located on a complex topography area, we generated a map with daily radiation values for the zone. Figure 5 shows a map created using this methodology.

3. Conclussions

Results obtained using the proposed method showed a good agreement with the measured ones and it is interesting to note that this procedure can be applied under all kind of sky conditions. A proposed method to calculate the horizon of a point was tested with satisfactory results.

The RMSE was diminished for the whole set of stations with a mean reduction of 4.7%. MBE was also improved, with almost no over or underestimation for most of the stations. It has been observed that the improvement in the estimates is small in plane areas with almost no horizon obstructions, but becomes significant in the locations inside the mountain. The effect of the snow was also studied and it was pointed out that for the stations in the upper area it could lead to a reduction of the RMSE up to 2%, being smaller or nil in the lower stations. Finally, the method was employed over a wide area allowing the generation of an irradiation map on a complex terrain. If no additional information would be considered, the HELIOSAT 2 model would give a fixed value for the whole pixel, taking into account a mean altitude of the pixel and no horizon. On the other hand, using this methodology, the topographic variability is included in the model and a map of irradiation can be made in an easy way for a complex topography site. In future works, this method is intended to be extended to the estimation of different components of the radiation (i. e. Direct Radiation, Photosynthetically Active Radiation PAR); and also to be used together with Artificial Neural Networks.

Acknowledgements

This work has been financed by the Ministerio de Ciencia y Tecnologia of Spain (projects ENE/2004- 0786-C03-01 and ENE2007-67849-C02-02). We would like to thank CIEMAT for the use of the satellite images.

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