Input dropout in product unit neural networks for stream water temperature modelling.

• Product unit neural networks (PUNN) are implemented for stream temperature modelling. • Stream temperature modelling is based on atmospheric and hydrological interactions. • Deep learning-based dropout variant is proposed for shallow PUNN. • Impact of various dropout variants is tested for PUNN. • PUNN with proposed dropout outperforms data-based and semi-physical models. For about two decades neural networks are widely used for river temperature modelling. However, in recent years one has to distinguish between the "classical" shallow neural networks, and deep learning networks. The applicability of rapidly developing deep learning networks to stream water temperature modelling may be limited, but some methods developed for deep learning, if properly re-considered, may efficiently improve performance of shallow networks. Dropout is widely considered the method that allows deep learning networks to avoid overfitting to training data, facilitating its implementations to versatile problems. Recently the successful applicability of dropout for river temperature modelling by means of shallow multilayer perceptron neural networks has been introduced. In the present study we propose to use dropout solely for input neurons of product unit neural networks for the purpose of stream temperature modelling. We perform tests on data collected from six catchments located in temperate climate zones on two continents in various orographic conditions. We show that the average performance of product unit neural networks trained with input dropout is better than the average performance of product units without dropout, product units with dropout applied to every layer of the networks, multilayer perceptron neural networks with or without dropout, and the semi-physical air2stream model. The advantage of product unit neural networks with input dropout is statistically significant on hilly or mountainous catchments; the performance on flat ones is similar to the performances obtained from competitive models. [ABSTRACT FROM AUTHOR]