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Performance Comparison of Geostatistical Algorithms for Incorporating Elevation into the Mapping of Precipitation

GOOVAERTS, Pierre (goovaert@engin.umich.edu), The University of Michigan, Department of Civil and Environmental Engineering, Ann Arbor, MI 48109-2125

Key Words: geostatistics, co-kriging, precipitation, digital elevation model (DEM)

Until the late 1980s, techniques such as the inverse distance, Thiessen polygons, or isohyetals, have been used to interpolate rainfall data. Geostatistics, which is based on the theory of regionalized variables, is increasingly used because it allows one to capitalize on the spatial correlation between neighboring observations to predict attribute values at unsampled locations. Several authors have shown that geostatistics provide better estimates of precipitation than conventional methods. A major advantage of geostatistical prediction (kriging) is that sparsely sampled observations of the primary attribute can be complemented by secondary attributes that are more densely sampled. A valuable and cheap source of information for many climatic attributes is provided by digital elevation models (DEM).

In this paper, three geostatistical algorithms are introduced to incorporate an exhaustive secondary information (DEM) into the spatial prediction of precipitation: simple kriging with varying local means (SKlm), kriging with an external drift (KED) and colocated cokriging. The techniques are illustrated using annual and monthly rainfall observations measured at 36 climatic stations located in the Algarve region, Portugal. Cross validation is used to compare the prediction performances of the three geostatistical interpolation algorithms with the straightforward linear regression of rainfall against elevation and three univariate techniques: Thiessen polygons, inverse square distance, and ordinary kriging.

Larger prediction errors are obtained for the two algorithms (inverse square distance, Thiessen polygons) that ignore both elevation and rainfall records at surrounding stations. The three multivariate geostatistical algorithms outperform other interpolators, in particular linear regression, which stresses the importance of accounting for spatially dependent rainfall observations in addition to the colocated elevation. Last, ordinary kriging yields more accurate predictions than linear regression when the correlation between rainfall and elevation is moderate (less than 0.75 in the case study).