Prediction of actual evapotranspiration by artificial neural network models using data from a Bowen ratio energy balance station

Abstract

Seven artificial neural network (ANN) models were developed to predict daytime actual evapotranspiration (ET) for Nissouri Creek in Oxford County, Canada, from April to July 2018, using the Bowen ratio energy balance method as target output for the first time. In total, 12 variations of each model were deployed using different combinations of model parameters, including the sigmoid and rectified linear unit (ReLU) activation functions, stochastic gradient descent (SGD), and root-mean-square-propagation (RMSprop) learning algorithms, three different network architectures, and 100 and 500 training epochs. This is the first time that ReLU has been used in ANNs that predict ET and it outperformed sigmoid in six of the seven models. This is particularly significant because until now the sigmoid activation function (or variations therein) had been exclusively employed in the ET literature. RMSprop was also used for the first time and typically demonstrated equivalent performance to that of SGD. The optimal model employs the ReLU activation function, consists of a 4-4-1 network architecture, includes the input parameters of net radiation, air temperature, soil heat flux, and wind speed, and is trained by the SGD learning algorithm for 500 training epochs. This model boasts a coefficient of determination (R2) of 0.997, root-mean-square error (RMSE) of 0.39 mm/day, and mean absolute error (MAE) of 0.18 mm/day. Furthermore, all seven models developed adequately model the ET process, with R2 ranging from 0.988 to 0.997, RMSE from 0.39 to 0.78 mm/day, and MAE from 0.18 to 0.58 mm/day.