Uncertainty Estimation in Hydrogeological Forecasting with Neural Networks: Impact of Spatial Distribution of Rainfalls and Random Initialization of the Model

Abstract

Neural networks are used to forecast hydrogeological risks, such as droughts and floods. However, uncertainties generated by these models are difficult to assess, possibly leading to a low use of these solutions by water managers. These uncertainties are the result of three sources: input data, model architecture and parameters and their initialization. The aim of the study is, first, to calibrate a model to predict Champagne chalk groundwater level at Vailly (Grand-Est, France), and, second, to estimate related uncertainties, linked both to the spatial distribution of rainfalls and to the parameter initialization. The parameter uncertainties are assessed following a previous methodology, using nine mixed probability density functions (pdf), thus creating models of correctness. Spatial distribution of rainfall uncertainty is generated by swapping three rainfall inputs and then observing dispersion of 27 model outputs. This uncertainty is incorporated into models of correctness. We show that, in this case study, an ensemble model of 40 different initializations is sufficient to estimate parameter uncertainty while preserving quality. Logistic, Gumbel and Raised Cosine laws fit the distribution of increasing and decreasing groundwater levels well, which then allows the establishment of models of correctness. These models of correctness provide a confidence interval associated with the forecasts, with an arbitrary degree of confidence chosen by the user. These methodologies have proved to have significant advantages: the rigorous design of the neural network model has allowed the realisation of models able to generalize outside of the range of the data used for training. Furthermore, it is possible to flexibly choose the confidence index according to the hydrological configuration (e.g., recession or rising water table).