Multivariate geostatistical analysis of evapotranspiration and precipitation in mountainous terrain

Abstract This paper reports the evaluation of three geostatistical interpolation methods (ordinary kriging, cokriging and modified residual kriging) to interpolate long-term mean total annual reference evapotranspiration (AETO) and long-term mean total annual precipitation (APRE) in a mountainous region, where the stationarity hypothesis probably do not hold for the whole region, but do hold locally. AETO and APRE estimates and estimation errors were evaluated at validation stations. Estimates and computed estimation error variances (used as indicators of estimation uncertainty) were also obtained at 1913 5 km grid points. In general, estimates at validation stations were in good agreement with observed values for all interpolation methods, although modified residual kriging estimates of APRE were slightly worse than those obtained by the other two methods. Based on mean absolute error (MAE) and mean squared error (MSE) at validation stations, no method ranked clearly above other for interpolation of AETO. At grid points, AETO estimation uncertainty was improved by cokriging by about 11.5% and 8.4% compared with ordinary kriging and modified residual kriging, respectively. Likewise, cokriging was superior for interpolation of APRE in terms of MAE and MSE obtained at validation stations. At grid points, cokriging reduced estimation uncertainty by 18.7% and 24.3% compared with ordinary kriging and modified residual kriging, respectively, whereas modified residual kriging in general did not improve ordinary kriging results. Computed estimation error variance values indicated that modified residual kriging would reduce estimation uncertainty in areas where very few weather stations are available for interpolation.