Exploring interpretable and non-interpretable machine learning models for estimating winter wheat evapotranspiration using particle swarm optimization with limited climatic data

Accurate estimation of crop evapotranspiration (ETc) is crucial for improving the water use efficiency and designing and operating irrigation systems. To accurately calculate winter wheat ETc with limited meteorological data, the present study proposed two interpretable machine learning (ML) models (random forest (RF) and extreme gradient boosting (XGBoost)) as well as non-interpretable ML models (support vector machine (SVM) and deep neural network (DNN)) based on the particle swarm optimization (PSO) algorithm using observed winter wheat ETc data during the period from 2007 to 2013 at Luan Cheng Agro-ecosystem Experimental Station. Mean absolute error (MAE), root mean square error (RMSE), Nash-Sutcliffe efficiency (NSE), coefficient of determination (R-2), and global performance indicator (GPI) were used to assess the performance of models. This demonstrated that the ML models based on the crop coefficient (Kc) and solar radiation (Rn) were accurate and offered a workaround for calculating winter wheat ETc in the absence of meteorological data. In four ML models, the ninth input combination, consisting of Kc, Rn, daily air maximum temperature (Tmax), daily air minimum temperature (Tmin), sunshine hours (n), and wind speed with a height of 2 m (U2), produced the best estimate of ETc. Among them, the PSO-based SVM (PSO-SVM) model obtained the best results for estimating ETc with MAE, RMSE, NSE, R2, and GPI values of 0.389 mm center dot d(-1), 0.562 mm center dot d(-1) 0.910, 0.911, and 0.975, respectively, showing the advantages of the non-interpretable ML model in ETc forecasting. Accurate descriptions of actual hydrological and climatic processes were given by local interpretable model-agnostic explanations (LIME). The inflection points of daily climatic parameters (Tmin, Tmax, Rn, n) related to ETc were determined to be 3.80 degrees C, 5.50 degrees C, 1.62 MJ center dot m(-2)center dot d(-1), 1.37 h, respectively. This work has potential to overcome the difficulty of measuring winter wheat ETc properly due to the lack of meteorological data and accomplish appropriate water management to conserve water and increase water productivity.