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Feed-forward vs recurrent neural network models for non-stationarity modelling using data assimilation and adaptivity

Abstract Artificial neural networks (ANN) are nonlinear models widely investigated in hydrology due to their properties of universal approximation and parsimony. Their performance during the training phase is very good, and their ability to generalize can be improved by using regularization methods such as early stopping and cross-validation. In our research, two kinds of generic models are implemented: the feed-forward model and the recurrent model. At first glance, the feed-forward model would seem to be more effective than the recurrent one on non-stationary datasets, because measured information on the state of the system (measured discharge) is used as input, thereby implementing a kind of data assimilation. This study investigates the feasibility and effectiveness of data assimilation and adaptivity when implemented in both feed-forward and recurrent neural networks. Based on the IAHS Workshop held in Göteborg, Sweden (July 2013), the hydrological behaviour of two watersheds of different sizes and different kind of non-stationarity will be modelled: (a) the Fernow watershed (0.2 km2) in the USA, affected by significant modifications in land cover during the study period, and (b) the Durance watershed (2170 km2) in France, affected by an increase in temperature that is causing a decrease in the extent of glaciers. Two methods were applied to evaluate the ability of ANN to adapt on the test set: (i) adaptivity using observed data to adapt parameter values in real time; and (ii) data assimilation using observed data to modify inaccurate inputs in real time. The goal of the study is thus re-analysis and not forecasting. This study highlights how effective the feed-forward model is compared to the recurrent model for dealing with non-stationarity. It also shows that adaptivity and data assimilation improve the recurrent model considerably, whereas improvement is marginal for the feed-forward model in the same conditions. Finally, this study suggests that adaptivity is effective in the case of changing conditions of the watershed, whereas data assimilation is better in the case of climate change (inputs modification).