Empirical and learning machine approaches to estimating reference evapotranspiration based on temperature data

The precise estimation of reference evapotranspiration (ET0) is crucial for the planning and management of water resources and agricultural production. In this study, the applicability of the Hargreaves Samani (HS), artificial neural network (ANN), multiple linear regression (MLR) and extreme learning machine (ELM) models were evaluated to estimate ET0 based on temperature data from the Verde Grande River basin, southeastern Brazil. These models were evaluated in two scenarios: local and pooled. In the local scenario, training, calibration and validation of the models were performed separately at each station. In the pooled scenario, meteorological data from all stations were grouped for training and calibration and then separately tested at each station. The ET0 values estimated by the Penman-Monteith model (FAO-56 PM) were considered the target data. All the developed models were evaluated by cluster analysis and the following performance indices: relative root mean square error (RRMSE), Pearson correlation coefficient (r) and Nash-Sutcliffe coefficient (NS). In both scenarios evaluated, local and pooled, the results revealed the superiority of the artificial intelligence methods (ANN and ELM) and the MLR model compared to the original and adjusted HS models. In the local scenario, the ANN (with r of 0.751, NS of 0.687 and RRMSE of 0.112), ELM (with r of 0.747, NS of 0.672 and RRMSE of 0.116) and MLR (with r of 0.743, NS of 0.665 and RRMSE of 0.068) models presented the best performance, in addition to being grouped in the same cluster. Similar to the observations from the local scenario, the ANN (with r of 0.718, NS of 0.555 and RRMSE of 0.165), ELM (with r of 0.724, NS of 0.601 and RRMSE of 0.151) and MLR (with r of 0.731, NS of 0.550 and RRMSE of 0.091) models presented the best performance in the pooled scenario and were grouped in the same cluster. The locally trained models presented higher precision than the models generated with pooled data; however, the models generated in the pooled scenario could be used to estimate ET0 in cases of unavailability of local meteorological data. Although the MLR, ANN and ELM models, based on temperature data, are appropriate alternatives to accurately estimate ET0 in the Verde Grande River basin, southeastern Brazil, the MLR model presents the advantage of the use of explicit algebraic equations, facilitating its application.