Extreme learning machine for reference crop evapotranspiration estimation: Model optimization and spatiotemporal assessment across different climates in China

Accurate estimation of reference crop evapotranspiration (ET) is critical for quantifying crop water requirements and irrigation schedule design. This study proposed two optimization methods, i.e., particle swarm optimization (PSO) and genetic algorithm (GA), to determine the input weights and hidden biases of extreme learning machine (ELM), and developed two novel hybrid GA-ELM and PSO-ELM models for ET estimations with limited input data. A temporal and spatial scanning strategy that can avoid misleading or partially valid results was applied to train and test the models, using daily climatic data during 1994–2016 from 96 meteorological stations across various climates of China. The results revealed that GA-ELM and PSO-ELM could quantify ET on daily, monthly, and annual time scales, with GA-ELM (with model efficiency ranging from 0.80 to 0.97) performing better than PSO-ELM (with model efficiency ranging from 0.70 to 0.93) in all climates. The temperature-based GA-ELM only with air temperature data as forcing input has relatively accurate ET estimates across different environments, and can be recommended as an alternative method when radiation data are not available. Spatial assessment reveals that the machine learning models trained by external data also offer accurate ET estimates, confirming the applicability of models for ET estimations elsewhere without the model training or when local data for model training are unavailable. Overall, the GA-ELM model provides accurate ET estimates on various time scales and exhibits superior performance than the PSO-ELM model, and thus can be recommended for ET estimations using limited data as model forcing in different climates of China. Our work presents a novel method for accurate ET estimations with limited data, which has practical implications in regional agricultural water management.