Ordinary kriging vs residual kriging

The comparison of the ordinary and the residual kriging models results, in terms of the validation dataset, shows several interesting features. Residual kriging provides better estimates for all the months, with relative improvement in RMSE ranging from 5% to 20%. The maximum

improvement is found for January, with (RMSE value of 0.46 versus 0.60, 23% for relative improvement). In June, relative improvement is about 5% and in October about 9%. Similar results are found for the MAE values, with relative improvements ranging from 5% to 20%. Particularly, the maximum improvement is found during December (MAE 0.31 versus 0.4, that is 22% of relative improvement). A slightly improvement is also found for the ME values, changing from a small underestimation using the ordinary kriging to almost negligible error values using the residual kriging. Finally, R2 values show an overall improvement, being particularly high for January, February and March.

Additionally, mean values are fairly reproduced by both ordinary and residual kriging methodologies, with a maximum error (overestimation) of about 0.5 MJ m-2day-1 (2.6%) during September. On the other hand, standard deviation estimation is considerable better reproduced by the residual kriging method than by the ordinary kriging. Maximum improvements are found for the winter months For instance, for January, the observed standard deviation is 0.99 MJ m-2day-1, while the value provide by the ordinary kriging is 0.62 MJ m-2day-1 (37% error) and the estimated using the residual kriging is 0.94 MJ m-2day-1 (5% error). For the summer months, residual kriging also provides better standard deviation estimates, but improvements are lower.

Regarding the maximum values, similar estimates are provided by both kriging methods during the summer months. On the other hand, residual kriging estimates are considerable better for winter months. As far as minimum values is concerned, residual kriging perform considerable better than the ordinary kriging method for all the months. Maximum differences are found for the summer months.


Overall, the ordinary kriging method is able to provide fair estimates of the solar resources in the area of the study, with RMSE values ranges from 0.63 MJ m-2day-1 (6.2%) in June to around 1.44 MJ m-2day-1 (11.2%) in October. Nevertheless, by the inclusion of external information in the interpolation procedure, the residual kriging estimates shows considerable lower errors.

Particularly, the inclusion as external explanatory variable of the semi-sky-view factor (which accounts for topographic shadows cast and is able to explain between 15% and 45% of the spatial variability) give rise to relative improvement in RMSE values ranging from 5% in the summer month 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 the June to around 1.31 MJ m - 2day-1 (10.2 %) in October. Explained variance also shows a considerable improvement compared to the ordinary kriging method, with all month showing R2 values above 0.92.


[1] J. Mubiru, K. Karume, M. Majaliwa, E. J.Banda, T. Otiti, (2006). Interpolating methods for solar radiation in Uganda. Theor. Appl. Climatol. 88, 259-263.

[2] I. O.Odeh, A. B.McBratney, D. J.Chittleborough, (1995). Further results on prediction of soil properties from terrain attributes. Geoderma, 67, 215-226.

[3] S. Ahmed, G. deMarsily, (1987). Comparison of geostatistical methods for estimating transmissivity.

Water Resour. Res. 23, 1717-1737.

[4] D. L.Phillips, J. Dolph, D. Marks, (1992). A comparison of geostatistical procedures for spatial analysis for precipitation in mountainous terrain. Agric. Forest Meteorol. 58, 1031-1047

[5] J. P.Delhomme, (1978). Kriging in the hydrosciences. Adva. Water Resour. 1, 251-266.

[6] Clark Labs, (2006). IDRISI Software, Clark University, MA, USA.



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