Multivariate geostatistical analysis of evapotranspiration and elevation for various climatic regimes in Oregon

Abstract

This work investigated the feasibility of applying multivariate geostatistics in evapotranspiration studies. The major goals of this study were: 1) to analyze and model the spatial correlation between evapotranspiration and elevation above sea level; and 2) to investigate whether the use of cokriging improves the accuracy of the evapotranspiration estimates over a regular grid by including the effects of topography.

A total of 11 study cases for each of four different climatic regions within the state of Oregon were analyzed. The climatic regions were labeled as Willamette Valley, North Central, South Central and East. Long—term monthly averages of daily reference evapotranspiration (ETr) were available at 199 locations within those regions for the months of February to November as well as values of total annual (cumulative) ETr. Values of elevation above sea level were available at those locations and at additional 8670 locations on a grid of approximately 5 km per side.

Application of the geostatistical concept of the direct—semivariogram was required to describe the spatial variability of a single variable. The description of the spatial correlation between ETr and elevation required the application of the cross—semivariogram concept. Experimental direct—semivariograms for ETr were fit with isotropic, spherical models with small nugget effects, Experimental direct—semivariograms for elevation were fit with isotropic models with nugget effects and two nested structures (spherical and gaussian) for the Willamette Valley region, one nested structure (spherical) for the North Central region, and two nested structures (spherical and linear) for the South Central and East regions. The experimental crosssemivariograms were fit with spherical models.

The direct and crosssemivariogram models were applied to interpolate monthly and cumulative ETr using the geostatistical tools of kriging and cokriging at 8570 locations on a 5 km grid. Kriging and cokriging estimation error standard deviations were computed for each study case, ETr estimates and estimation error standard deviations were plotted as contour maps. Maximum, minimum and average kriging and cokriging estimates of ETr were in general agreement, although minimum and average values tended to be lower for cokriging. However, contour lines of cokriged ETr reflected more closely the elevation features of the climatic regions. Maximum and average estimation error standard deviations were lower for cokriging, while the minimum values being very similar for both kriging and cokriging. Average cokriging standard deviations decreased by about 20 to 30 in the Willamette Valley and North Central regions and by 5 to 13 % in the South Central and East regions. The difference between regions was caused by the lower correlation coefficient between ETr and elevation observed in the latter two regions. Contour maps of standard deviations showed cokrig-ing had a more uniform distribution of estimation errors than kriging, for which errors tended to decrease in the vicinity of the sample ETr points at the weather stations. Errors along regional borders increased for both kriging and cokriging, although maximum estimation error values were lower for cokriging.