Regional calibration of the Hargreaves model for estimation of reference evapotranspiration

Abstract Estimation of reference evapotranspiration values is crucial in climatological and hydrological research, agricultural engineering, and irrigation design. The Penman-Monteith method, endorsed by the Food and Agriculture Organization (FAO) of the United Nations and numerous research studies, is widely regarded as the gold standard. However, its extensive data requirements limit its applicability in regions with sparse meteorological networks or limited measurement capabilities. The Hargreaves method, which requires only basic air temperature inputs, offers an alternative solution. The aims of this study were to calibrate the Hargreaves model for Central European climate conditions, considering altitudinal dependence, and to evaluate the temporal stability of the model parameters. In the first part of the research, we regionalized the Hargreaves coefficients using a curve-fitting method to ensure the best accuracy across 60 climatological stations in Slovakia. The regionalization of the Hargreaves coefficient improved accuracy by 10.1%, reducing the weighted absolute percentage error (WAPE) to 17.9%. However, our results showed that the accuracy of the modified Hargreaves model decreased with the increasing altitude of a climatological station. Incorporating altitude into the Hargreaves equation significantly improved model accuracy in stations at higher altitudes, providing a consistent level of accuracy across all climatological stations, regardless of their location and altitude. The results also indicated that the optimal model coefficient values change over time, showing a decreasing trend of –0.5 for the B coefficient and –0.1 for the C coefficient between the periods 1981–2000 and 2001–2020. Although regionalizing the Hargreaves model coefficients for local conditions can achieve good model performance, the model’s accuracy is not stable over time. Thus, periodic validation of the model is necessary for short-term applications.