Title
How to deal with non-stationary conditions in hydrology using neural networks - 09:45
Speaker
V. Borrell Estupina
Session
Hw15S3 - Testing simulation and forecasting models in non-stationary conditions
Author(s)
Taver, V. 1; Johannet, A. 2; Borrell Estupina, V. 3; Pistre, S. 3 - 1 Ecole des Mines d'Alès and Université
Montpellier II, Hydrosciences Montpellier, France; 2 Ecole des Mines d'Alès, France; 3 University
Montpellier II - HydroSciences Montpellier , France
Abstract number
Hw15S3.05
Abstract
Neural networks are non-linear models widely investigated in hydrology due to their universal
approximation and parsimony properties. As "black-box" models, they do not presume any a priori
behavior, given that the model construction is data-driven and the parameters are devoid of physical
significance. They thus can be applied to any watershed provided that a large dataset would be
available. Nevertheless, the excellent capabilities that neural networks prove for training must be
counterbalanced by their ability to reliably generalize to unknown dataset. This trap is well known in
machine learning and was formalized as the bias-variance tradeoff. Thanks to application of
regularization methods as early stopping and cross validation, rigorous variable and complexity
selection can be performed providing efficient generalization. In this experimentation two models
will be investigated, the feed-forward model and the recurrent one.
The feed-forward model is mathematically explained as:
s(k)=gNN(q(k-1),...q(k−r), u(k),u(k − 1)...,u(k − m))
where s is the estimated discharge, gNN is the non-linear function implemented by the neural
network, k is the discrete time (sampled each time step of the dataset) q is the measured discharge,
u is the vector of exogenous variables (rainfalls, temperature, etc), r is the order of the model, m is
the width of the sliding window of rainfalls information.
Using same notations the recurrent network is expressed as:
s(k)=gNN(s(k-1),...s(k−r), u(k),u(k − 1)...,u(k − m))
It can be considered that the feed-forward model would be more efficient than the recurrent one on
non stationary datasets, because it integrates measured information from input variables (rainfalls,
temperature, etc …) and implements data assimilation.
Classical ways to compute data assimilation will be applied in order to make the recurrent model
adaptive to the watershed evolutions.
Both models will thus be compared following the 3 protocols.