Prediction of actual evapotranspiration by artificial neural network models using data from a Bowen ratio energy balance
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ORIGINAL ARTICLE
Prediction of actual evapotranspiration by artificial neural network models using data from a Bowen ratio energy balance station Spencer Walls1
•
Andrew D. Binns1 • Jana Levison1
•
Scott MacRitchie2
Received: 3 May 2019 / Accepted: 17 February 2020 Springer-Verlag London Ltd., part of Springer Nature 2020
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. Keywords Evapotranspiration Bowen ratio energy balance method Artificial neural networks Activation function Learning algorithm ReLU
1 Introduction
& Spencer Walls [email protected] Andrew D. Binns [email protected] Jana Levison [email protected] Scott MacRitchie [email protected] 1
School of Engineering, College of Engineering and Physical Sciences, University of Guelph, 50 Stone Rd E, Guelph, ON N1G 2W1, Canada
2
Environmental Monitoring and Reporting Branch, Ministry of the Environment, Conservation and Parks, 125 Resources Road, Toronto, ON M9P 3V6, Canada
Evapotranspiration (ET) is a term used to collectively describe the physical processes of evaporation and transpiration; the former denoted by the conversion of liquid water from the surfaces of water bodies, vegetation, and soils to water vapour, the latter comprised by the flow of liquid water from soil into the roots and through the bodies of plants, and its subsequent release as water vapour through the stomates of their leaves. An integral component of the hydrologica
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