Quantification of Neural Network Uncertainties on the Hydrogeological Predictions by Probability Density Functions

International audienceThe risk of drought impacting the drinking water and agricultural production is worrying in the developed countries, especially in a changing climate context. To manage and prevent this phenomenon, real-time monitoring and predictive systems are emerging as the key solutions. In the field of artificial intelligence, neural networks are one of these predictive systems. This family of parameterized models is a composition of neuronal functions, which apply a non-linear transformation from their inputs to their outputs. These networks are able to learn a hydro(geo)logical system behaviour using a database composed of observed inputs (rainfall, evapotranspiration, etc.) and outputs (groundwater level, discharge, etc.), thanks to an algorithm minimizing a cost function between observed and simulated outputs. However, it remains difficult to assess the uncertainty generated by these models, possibly leading to misinterpretations by the end users. These uncertainties are mainly of three types. The first is related to the input data. Indeed, hydrosystems are surface elements whereas meteorological inputs are punctual elements. The interpolation error can, therefore, be significant because of the lack of knowledge between gauging stations. The second is the neural network model architecture itself. It is possible to deal with this source of uncertainty using regularization methods. Finally, the neural networks are submitted to uncertainties related to parameter initialization, before the training step. The initial parameters may have an important impact on the results. In this paper, we address the prediction of the Blavet groundwater level (Bretagne, France). In order to assess uncertainties, we will first focus on the parameters initialization of the model. Neuronal models are optimized using cross-validation and early stopping. Then, an ensemble model is realized, in which each member is the result of a unique set of parameters initialization. The purpose of the study is to define how many initializations are necessary to obtain a reasonable confidence interval for forecasts, with the smallest interval and the higher rate of observed points inside this interval. The best model will be determined using cross-validation scores thereby ensuring optimal robustness. We show that, in this case study, an ensemble model of 20 different initializations is sufficient to estimate uncertainty while preserving quality. In the second part, the resulting ensemble model will be used to estimate the global model uncertainty using probability density functions (pdf) applied to the distribution of groundwater level data and cross-validation scores of forecasts. It reveals that the groundwater level predictions are composed of two mixed distributions. Therefore, we will use the expectation-maximization algorithm (EM) to obtain parameters of mixed models. Mixed normal and mixed Gumbel laws, among five mixed distributions assessed, give the best groundwater distribution and are able to generate an abacus drawing uncertainty of mode

Monitoring of Mescla karst spring French Southern Alps : a rare case of stratified waters out of coastal areas

International audienc

Monitoring of Mescla karst spring in the French Southern Alps. A rare case of stratified waters out of coastal areas

International audienc

Modélisation d'un système karstique par réseaux de neurones : simulation des débits du karst du Baget, France

After a presentation of the karstic systems modelling with neural networks, the paper is devoted to the identification of the rainfall-runoff relation of the Baget karstic system (Ariège-France) with neural networks. First, the flow simulation upon a complete year allows to illustrate the interest of the state feedback operated by neural network. In a second time, the specialisation of the neural network in the "flood" state is implemented in presenting only "flood" periods to the network. It is then satisfying to note that the performance brings results closer to those observed with a state-feedback. Flood simulation allows also to check that, the recurrent directed network having inputs containing more precise information than the static network, the complexity of the architecture may be simplified. In both cases the Nash criteria reach acceptable values between 0.6 and 0.9, which indicate that the quality of the simulation is satisfying, even if climatological data are lacking, except of course rainfall.Après une présentation de la difficulté de la modélisation des systèmes karstiques et de l'identification des systèmes avec des réseaux de neurones formels, cet article se propose d'appliquer les réseaux de neurones pour identifier la relation pluie-débit du système karstique du Baget (Ariège -France). La simulation effectuée sur une année entière permet d'illustrer l 'intérêt du retour d'état que peut apporter le réseau de neurones. Dans un deuxième temps, il est proposé de spécialiser le réseau en mode «crue» en ne lui faisant apprendre, et simuler, que les événements de crue. Il est alors satisfaisant de noter que les performances se rapprochent de celles obtenues avec un retour d 'état. La simulation des crues permet également de vérifier que le réseau récurrent dirigé, possédant des entrées plus riches en information, se satisfait alors d'une architecture simplifiée. Dans tous les cas, les simulations effectuées sont de qualité satisfaisante, conduisant, en l 'absence de données climatiques supplémentaires aux précipitations, à des critères de Nash variant entre 0.6 et 0.9.Johannet Anne, Mangin Alain, Vayssade Bernard. Modélisation d'un système karstique par réseaux de neurones : simulation des débits du karst du Baget, France. In: Collection EDYTEM. Cahiers de géographie, numéro 7, 2008. Karsts de montagne, géomorphologie, patrimoine et ressources. pp. 51-62

Modélisation des hydrosystèmes complexes par machine learning : illustrations sur la prévision des extrêmes hydrologiques (crues, étiages)

National audienc

Conception de modèles de prévision des crues éclair par apprentissage artificiel

PARIS-BIUSJ-Mathématiques rech (751052111) / SudocSudocFranceF

Taking profit of statistical modelling by neural networks: how to deal with vigilance levels prediction for flash flooding. Case study on Lez Basin (South eastern France).

International audienc

Neural networks-based operational prototype for flash flood forecasting: application to Liane flash floods (France)

The Liane River is a small costal river, famous for its floods, which can affect the city of Boulogne-sur-Mer. Due to the complexity of land cover and hydrologic processes, a black-box non-linear modelling was chosen using neural networks. The multilayer perceptron model, known for its property of universal approximation is thus chosen. Four models were designed, each one for one forecasting horizon using rainfall forecasts: 24h, 12h, 6h, 3h. The desired output of the model is original: it represents the maximal value of the water level respectively 24h, 12h, 6h, 3h ahead. Working with best forecasts of rain (the observed ones during the event in the past), on the major flood of the database in test set, the model provides excellent forecasts. Nash criteria calculated for the four lead times are 0.98 (3h), 0.97 (6h), 0.91 (12h), 0.89 (24h). Designed models were thus estimated as efficient enough to be implemented in a specific tool devoted to real time operational use. The software tool is described hereafter: designed in Java, it presents a friendly interface allowing applying various scenarios of future rainfalls, and a graphical visualization of the predicted maximum water levels and their associated real time observed values