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

Authors:
raw_author_name: Shang Chen
raw_affiliation_string: Jiangsu Key Laboratory of Agricultural Meteorology Nanjing University of Information Science and Technology Nanjing China; Key Laboratory for Agricultural Soil and Water Engineering in Arid Area of Ministry of Education Northwest A&amp;F University Yangling China
raw_author_name: Liang He
raw_affiliation_string: National Meteorological Center China Meteorological Administration Beijing China
raw_author_name: Wei Xiao
raw_affiliation_string: Jiangsu Key Laboratory of Agricultural Meteorology Nanjing University of Information Science and Technology Nanjing China
raw_author_name: Hao Feng
raw_affiliation_string: Key Laboratory for Agricultural Soil and Water Engineering in Arid Area of Ministry of Education Northwest A&amp;F University Yangling China; State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Water and Soil Conservation Northwest A&amp;F University Yangling China
raw_author_name: Qiang Yu
raw_affiliation_string: Key Laboratory of Eco-Environment and Meteorology for the Qinling Mountains and Loess Plateau Shaanxi Meteorological Bureau Xi'an China; State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Water and Soil Conservation Northwest A&amp;F University Yangling China
raw_author_name: Jiandong Liu
raw_affiliation_string: State Key Laboratory of Severe Weather Chinese Academy of Meteorological Sciences Beijing China
raw_author_name: Jianqiang He
raw_affiliation_string: Key Laboratory for Agricultural Soil and Water Engineering in Arid Area of Ministry of Education Northwest A&amp;F University Yangling China; State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Water and Soil Conservation Northwest A&amp;F University Yangling China

Abstract: Abstract Accurately estimated reference evapotranspiration (ET 0 ) is essential to regional water management. The FAO recommends coupling the Penman–Monteith (P‐M) model with the Ångström–Prescott (A‐P) formula as the standard method for ET 0 estimation with 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 a new method for estimating ET 0 with missing R s by combining machine learning with physical‐based P‐M models (PM‐ET 0 ). 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 ET 0 estimates 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 ET 0 (ML‐ET 0 ) to compare with the PM‐ET 0 . Finally, the optimal estimation method was used to estimate the A‐P coefficients for the 839 regular weather stations for ET 0 estimation without R s measurement 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 coefficient a . 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 ET 0 , 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‐ET 0 with 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 ET 0 . However, we found that using the A‐P coefficients with finer time scales is unnecessary to deal with the missing R s measurements.