Modélisation des débits mensuels par les modèles conceptuels et les systèmes neuro-flous A monthly streamflows modelling using conceptual models and neural fuzzy system

Résumé

La modélisation pluie-débit au pas de temps mensuel, a été étudiée par le biais de quatre modèles qui appartiennent à deux catégories, les modèles conceptuels (modèles à réservoirs), et les modèles basés sur les réseaux de neurones, et la logique floue

Les modèles conceptuels mensuels utilisés sont les modèles de Thornthwaite et Arnell et le modèle GR2M, ainsi que deux modèles représentés par les réseaux de neurones à apprentissage supervisé et le modèle neuro-flou qui combine une méthode d'optimisation neuronale et une logique floue.

Une application de ces modèles a été effectuée sur le bassin de la Cheffia (Nord-Est Algérien), et a confirmé les performances du modèle basé sur la logique floue. Par sa robustesse et son pouvoir d'extrapolation non-linéaire, ce modèle a donné d'excellents résultats, et représente donc une nouvelle approche de la modélisation pluie-débit au pas de temps mensuel.

Mots-clés:

• Modèle,
• pluie-débit,
• réseaux de neurones artificiels,
• apprentissage supervisé,
• logique floue,
• cheffia

Abstract

Rainfall-runoff modelling is very important for environmental issues, as well as for water management. Due to this importance, several models have been developed to describe the transformation of rainfall to runoff. From these models, we can distinguish three categories: conceptual models; physically-based models and black box models. Conceptual models are designed to approximate within their structures the general sub-processes that govern the hydrological cycle, and they are often used because of their simplicity. The physically-based models are generally distributed models, involve complex descriptions using partial derivative equations, and need some parameter calibration to be adjusted or estimated in situ. These models can not be applied on a monthly scale. In contrast, the black box models rely on linear (or nonlinear) relationships between inputs (rainfall) and outputs (runoff), and they have been widely accepted as a practical tool on different time scales.

In this paper, rainfall-runoff modelling on a monthly scale was studied using four models, from two different categories; conceptual models (reservoir models), and models based on artificial neural network and fuzzy logic. The monthly conceptual models used were the Thornthwaite-Arnell model and the GR2M model with two reservoirs. These models are regarded as mathematical models, and are of simple conception with a reduced number of parameters. In addition, these models are considered the most valid. The two other models were based on artificial neural networks and fuzzy logic, which combine neural optimization methods and fuzzy logic. These models incorporate a flexible mathematical structure that is capable of identifying complex nonlinear relationships between input and output data sets. In contrast to conceptual deterministic models, these models proceed using data learning through input-output systems. Artificial neural network models have been often shown to provide a better representation of the rainfall-runoff relationships. However, it is necessary to investigate different learning methods used with these models.

There are two different learning modes (training). One is data learning (incremental training), which consists of training for each data set, where the weights and biases on the network model are updated each time an input is presented to the network, thus the error between simulated and target (observed) data is minimised for each input. The alternative to data learning is block learning (batch training). In block mode the weights and biases on the network model are updated only after the entire training set has been applied to the network. We have tried a block learning data method, which consisted of learning from the simulation of all data sets. Thus, it evaluates the influence of this model in the streamflow forecasting in real time.

In Algeria, the droughts recorded during the previous years resulted in a reduction of surface water and in unbalanced resources that affected the phreatic underground water due to intensive exploitation. The results from evaluation studies emphasised the instability and vulnerability of surface water resources. The government has decided to carry out an emergency plan, by constructing several reservoirs and dams over the next few years in different regions of the country. However, several hydrometric gauges are disabled, so the series of hydrometric data are short or have gaps, and thus water resource evaluation has become impossible.

One of the objectives of the monthly rainfall-runoff modelling was estimating the stream flow at the mouth of the watershed, so the rainfall-runoff relationship on a monthly scale represents a solution and a reliable method for water management projects. We have selected and applied four models on data from the Cheffia watershed situated in north-eastern Algeria. The catchment of the Cheffia river includes various sub-basins, and has an area of about 575 km². The study was carried out on a twelve-year data set, split into a six-year calibration period, and a six-year validation period. Our research compared the models based on model characteristics, like simplicity and parameterisation, and also conceptual models were compared to parsimonious models. In addition, our research compared modelling results, based on the assessment of quantitative indices and statistics, such as the Nash criterion, the root mean squared error and a comparison of means during the calibration and validation periods.

Model results have confirmed the strong performance of the fuzzy logic based model, for two periods, and this model best stimulated streamflows. Whereas the neural network model based on block learning is unable to reproduce the high runoff values, this model can to be used for simulation of the runoff only. Because of its robustness and non-linear extrapolation power, the neuro-fuzzy logic model gave better results, so it represents a new method of rainfall-runoff modelling in monthly time steps.

Keywords:

• Model,
• rainfall-runoff,
• artificial neural network,
• supervised learning,
• fuzzy logic,
• cheffia