Linear Regression Machine Learning Algorithms for Estimating Reference Evapotranspiration Using Limited Climate Data

Abstract

A linear regression machine learning model to estimate the reference evapotranspiration based on temperature data for South Korea is developed in this study. FAO56 Penman–Monteith (FAO56 P–M) reference evapotranspiration calculated with meteorological data (1981–2021) obtained from sixty-two meteorological stations nationwide is used as the label. All study datasets provide daily, monthly, or annual values based on the average temperature, daily temperature difference, and extraterrestrial radiation. Multiple linear regression (MLR) and polynomial regression (PR) are applied as machine learning algorithms, and twelve models are tested using the training data. The results of the performance evaluation of the period from 2017 to 2021 show that the polynomial regression algorithm that learns the amount of extraterrestrial radiation achieves the best performance (the minimum root-mean-square errors of 0.72 mm/day, 11.3 mm/month, and 40.5 mm/year for daily, monthly, and annual scale, respectively). Compared to temperature-based empirical equations, such as Hargreaves, Blaney–Criddle, and Thornthwaite, the model trained using the polynomial regression algorithm achieves the highest coefficient of determination and lowest error with the reference evapotranspiration of the FAO56 Penman–Monteith equation when using all meteorological data. Thus, the proposed method is more effective than the empirical equations under the condition of insufficient meteorological data when estimating reference evapotranspiration.