Comparaison expérimentale des prévisions de débits mensuels obtenus, d'une part au moyen de méthodes de régression, d'autre part en utilisant un modèle déterministe

Centre Hydrométéorologique de Montpellier

Résumé

Tests have been carried out with several models adjusted in different ways with a view to determining the monthly discharge of the river Sioule at Pont-du-Bouchet in the Massif Central, involving an area of 1,170 km2. Records for a period of about twenty years were used to adjust the models, and twenty other years were considered in comparing the predicted and actual discharge data. The predicted monthly discharge data depend both on quantities known at the time of making the forecast (" predictors") and on quantities associated with events occurring between the time of making the forecast and the instant at which the flow takes place ("prediction terms"). The reliability of the forecast depends on the relative importance of these two types of quantity, but can readily be ascertained by means of a few simple correlations. Use of linear models: Regressions. Although these models are now automatic and in general use, they still give rise to a number of problems. First among these is the independence of errors, which it is often difficult to check and sometimes impossible to achieve, and which is liable to bias statistical checks and leave no alternative but to view the calculated confidence intervals with caution. Conventional methods of selecting a vector for the "predictors" are based on statistical checks requiring the same caution as the above. In addition, where the"predictors" are not independent, unstable regression coefficients with exaggerated values result. Thus, automatic methods have been found to give poor results for prediction. Experimentally, however, better results are obtained where the "prediction terms" are available when selecting the "predictors". Satisfactory results have also been obtained by making use of the main components. The methods of the future (e.g. the Ridge Regression method of system identification), however, ignore the multiple and partial multiple correlation coefficients and other conventional statistical quantities, and only take the stability of the regression coefficients into account. Use of deterministic model (Thornthwaite), This model features a production function which is none other than Thornthwaite's balance method with only one parameter adjusted to make the average available water equal to the discharge. The modulation function is a delayed-effect model adjusted by means of an optimization method (Rosenbrock) in which the sum of the relative errors is made a minimum. The predicted data supplied by this model are equivalent to those given by regression methods, and with the necessary data for a twenty-year period available, an experimental confidence interval can be calculated for both cases around the data supplied by the deterministic model. To conclude, therefore, the experimental choice of a prediction method depends on objective comparisons in which all the models to be compared start off with equal chances. However, there are still very many improvements to be made to all the different models available for use.