Abstract - non-stationarities

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20 Οκτ 2013 (πριν από 4 χρόνια και 7 μήνες)

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How to deal with non
stationary conditions in hydrology using neural networks




V. Borrell Estupina



Testing simulation and fore
casting models in non
stationary conditions


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 Univer
Montpellier II

HydroSciences Montpellier , France

Abstract number



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 exc
ellent 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 applicat
ion 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 re
current one.

The feed
forward model is mathematically explained as:

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:

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 inpu
t 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 followin
g the 3 protocols.