Geostatistical Methods for Prediction of Spatial Variability of Rainfall in a Mountainous Region

Reliable estimation of rainfall distribution in mountainous regions poses a great challenge not only due to highlyundulating surface terrain and complex relationships between land elevation and precipitation, but also due tonon-availability of abundant rainfall measurement points. Prediction of rainfall variability over mountainous islands is alogical step towards meaningful land use planning and water resources zoning. In this context, geostatistical techniques weredeveloped for mapping the rainfall variability over the island of St. Lucia in the Caribbean, using the elevation informationextracted from a Digital Elevation Model (DEM) and long-term mean monthly rainfall (MMR) data of 40 raingauge stationsspread over 616 km2. The ordinary co-kriging (OCK) and collocated co-kriging (CCK) methods of interpolation were appliedfor the standardized rainfall depths associated with elevation, as the primary variate, and the surface elevation values as thesecondary variate. The best semivariogram model algorithm generated, using either of the above co-kriging (CK) methods,was used to predict standardized values for the elevation points extracted from the DEM for which the rainfall depths werenot known. The predicted values were further destandardized to generate the rainfall depth at the unmeasured locations.Ordinary kriging (OK) was then performed for the destandardized and observed rainfall depths to generate the predictionmap of MMR over the entire island. These sequential steps were repeated for the MMR data of all twelve months to generaterainfall prediction maps over the island. The spherical semivariogram model fit well (0.84 < R2 < 0.98) for both the OCKand OK methods. The cross-validation error statistics of OCK presented in terms of coefficient of determination (R2), krigedroot mean square error (KRMSE), and kriged average error (KAE) were within the acceptable limits (KAE close to zero, R2close to one, and KRMSE from 0.55 to 1.45 for 40 raingauge locations) for most of the months. The exploratory data analysis,variogram model fitting, and generation of MMR prediction map through kriging were accomplished through use of ArcGISand GS+ software.