Parameterization of the Ångström-Prescott formula based on machine learning benefit estimation of reference crop evapotranspiration with missing solar radiation data

Accurately estimated reference evapotranspiration (ET0) is essential to regional water management. The FAO recommends coupling the Penman-Monteith (P-M) model with the & Aring;ngstr & ouml;m-Prescott (A-P) formula as the standard method for ET0estimationwith missing R-s measurements. However, its application is usually restricted by the two fundamental coefficients (a and b) of the A-P formula. This paper proposes anew method for estimating ET(0)with missing R-s by combining machine learning with physical-based P-M models (PM-ET0). The benchmark values of the A-P coefficients were first determined at the daily, monthly, and yearly scales, and further evaluated in R-s and ET0estimates at 80 national R-s measuring stations. Then, three empirical models and four machine-learning methods were evaluated in estimating the A-P coefficients. Machine learning methods were also used to estimate ET0(ML-ET0)to compare with the PM-ET0. Finally, the optimal estimation method was used to estimate the A-P coefficients for the 839 regular weather stations for ET(0)estimationwithoutRsmeasurement for China. The results demonstrated a descending trend for coefficient a from northwest to southeast China, with larger values in cold seasons. However, coefficient b showed the opposite distribution as the coefficienta. The FAO has recommended a larger a but a smaller b for southeast China, which produced the region's largest R-s and ET(0)estimation errors. Additionally, the A-P coefficients calibrated at the daily scale obtained the best estimation accuracy for both R-s and ET0, and slightly outperformed the monthly and yearly coefficients without significant difference in most cases. The machine learning methods outperformed the empirical methods for estimating the A-P coefficients, especially for the sites with extreme values. Further, ML-ET(0)outperformed the PM-ET0with yearly A-P coefficients but underperformed those with daily and monthly ones. This study indicates an exciting potential for combining machine learning with physical models for estimating ET0. However, we found that using the A-P coefficients with finer time scales is unnecessary to deal with the missing R-s measurements.