Echo state networks as an alternative to traditional artificial neural networks in rainfall–runoff modelling

N J De Vos

doi:10.5194/hess-17-253-2013

Abstract

Abstract. Despite theoretical benefits of recurrent artificial neural networks over their feedforward counterparts, it is still unclear whether the former offer practical advantages as rainfall–runoff models. The main drawback of recurrent networks is the increased complexity of the training procedure due to their architecture. This work uses the recently introduced and conceptually simple echo state networks for streamflow forecasts on twelve river basins in the Eastern United States, and compares them to a variety of traditional feedforward and recurrent approaches. Two modifications on the echo state network models are made that increase the hydrologically relevant information content of their internal state. The results show that the echo state networks outperform feedforward networks and are competitive with state-of-the-art recurrent networks, across a range of performance measures. This, along with their simplicity and ease of training, suggests that they can be considered promising alternatives to traditional artificial neural networks in rainfall–runoff modelling.

Highlights

The development of rainfall–runoff (R–R) models that make accurate and reliable forecasts of river streamflow remains among the most important and difficult tasks in hydrology
In order to represent the memory of the system in feedforward artificial neural networks (ANNs), dynamical properties are commonly explicitly modelled by using tapped-delay lines on input variables so that the input space is expanded to a certain time window
It was concluded that echo state network (ESN) performed significantly better than Self-Organizing Nonlinear Auto-Regressive model with eXogenous input (SONARX), and slightly better than the SONARX-RBF and adaptive neuro-fuzzy inference system (ANFIS) models

Summary

Introduction

The development of rainfall–runoff (R–R) models that make accurate and reliable forecasts of river streamflow remains among the most important and difficult tasks in hydrology. Recurrent ANNs, on the other hand, have cyclical connections in the structure of the network that allow an implicit, more parsimonious modelling of dynamical properties They implement dynamical systems capable of representing and encoding deeply hidden states in which a network’s output depends on an arbitrary number of previous inputs, which is why their temporal representation capabilities can be better than those of feedforward ANNs with tapped-delay lines (Saad et al, 1998). Since river basins are dynamical systems, such capabilities seem to give recurrent ANNs a significant advantage over feedforward ANNs in representing a basin’s hydrological state They have been successfully tested as R–R models by, for example, Hsu et al (1997), Coulibaly et al (2000), Chang et al (2002) and Chiang et al (2004), but the number of applications using feedforward ANNs dwarfs those with recurrent ANNs. The main reason for this is that recurrency

Methods

Results

Conclusion