Spatiotemporal Distribution of Calibration Coefficients of Hargreaves Equation for Estimating Potential Evapotranspiration in Mainland China

It is important to calibrate the potential evapotranspiration measured by the Hargreaves method (${\mathrm{ET}}_{0,\mathrm{HG}}$) using the Penman-Monteith method (${\mathrm{ET}}_{0,\mathrm{PM}}$). However, the substantial temporal variations in the calibration coefficients (${\mathrm{ET}}_0$ ratio measured by the two methods) have not been considered in the spatial analysis of the calibration coefficients. The objectives of this study were to investigate the spatiotemporal distribution of the calibration coefficient on the scale of Mainland China and to compare the accuracy of the calibrated ${\mathrm{ET}}_{0,\mathrm{HG}}$ by this spatiotemporal calibration method with three alternative methods including the calibration coefficients over space or time. One year was divided into 72 five-day periods in this study. For each five-day period, quantitative models were used to describe the spatial dependence of the calibration coefficients, and the maps of the calibration coefficients were produced by the Kriging method. The accuracies of the calibrated ${\mathrm{ET}}_0$ by this spatiotemporal calibration method and the other three methods were evaluated by criteria such as absolute bias, relative bias, root mean square error, and mean bias error. The results showed spatiotemporal changes in the parameters of the geostatistical models and the maps of the calibration coefficients of Mainland China. The maps were characterized by their divisions into two regions along a calibration coefficient contour of 1.0, and the directions of these contours showed obvious seasonal changes. The accuracy of the calibrated ${\mathrm{ET}}_{0,\mathrm{HG}}$ was highest when both the spatial and temporal variations of the calibration coefficients were considered simultaneously.