Influence of elevation on regional evapotranspiration using multivariate geostatistics for various climatic regimes in Oregon

Abstract

An investigation of the application of multivariate geostatistics for analysis of regional evapotranspiration is reported. The focus of the research was analysis and modeling of the spatial correlation between evapotranspiration and elevation above sea level. The main goal was to investigate whether the use of cokriging could improve the accuracy of evapotranspiration estimates over a regular grid by including elevation in the estimation procedure.

A total of 11 study cases for each of four different climatic regions (Willamette Valley, North Central, South Central and East) within the state of Oregon were analyzed. Long-term monthly (February to November) averages of daily reference evapotranspiration (ETr) and values of annual ETr were available at 199 locations within the regions. Values of elevation were available at the 199 locations and at 8570 additional locations spaced at approximately 5 km intervals on a grid.

Experimental direct- and cross-semivariograms were computed to describe the spatial variability of ETr and elevation, and their correlation. Experimental direct-semivariograms for ETr showed best fit with isotropic spherical models with small nugget effects. Experimental direct-semivariograms for elevation showed best fit with isotropic models with nugget effects and two nested structures (spherical and gaussian) for the Willamette Valley region, one structure (spherical) for the North Central region, and two nested structures (spherical and linear) for the South Central and East regions. The experimental cross-semivariograms showed best fit with isotropic spherical models.

Monthly and annual ETr values were estimated at 8570 locations situated at an approximately 5 km grid spacing using kriging and cokriging in conjunction with the previously fitted direct- and cross-semivariograms. Kriging and cokriging estimation error standard deviations were computed for each study case at all locations. 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 more closely reflected the elevation features of the climatic regions. Maximum and average estimation errror standard deviations were lower for cokriging, although minimum values were very similar for both kriging and cokriging. Average cokriging standard deviations decreased by about 20–30% in the Willamette Valley and North Central regions and by 5–13% in the South Central and East regions. These differences between regions were due to the lower correlation coefficients between ET, and elevation observed in the latter two regions. Contour maps of standard deviations showed cokriging had a more uniform distribution of estimation errors than kriging, for which errord tended to decrease in the vicinity of the sample ET, points at the weather stations. Errors increased along regional borders for both kriging and cokriging, although maximum estimation error values were lower for cokriging.