La prévision en temps réel des charges de polluants dans un réseau d'assainissement urbain Real-time forecasting of pollutant loads in sewer networks

Résumé

L'objectif principal du présent travail est la prévision en temps réel des charges de polluants dans un réseau d'assainissement urbain. La méthodologie préconisée dans cette étude se base sur deux outils. En premier lieu, le modèle de la courbe de tarage a été utilisé afin d'exprimer la corrélation entre les charges de polluants et les débits de ruissellement. Ce modèle a été sélectionné en raison de sa simplicité et de la disponibilité des paramètres nécessaires pour sa mise en œuvre. L'hypothèse de synchronisme systématique entre les pointes de l'hydrogramme et du pollutogramme dans ce modèle constitue une des faiblesses que nous proposons de surmonter dans le cadre du présent travail. Ainsi, le modèle de la courbe de tarage a été modifié par l'introduction d'un terme de déphasage qu'on identifie en temps réel. D'autre part, la constance des paramètres mis en jeu dans le modèle classique de la courbe de tarage constitue un autre obstacle pour la reproductibilité des phénomènes au cours du même événement et d'un événement à l'autre. Afin de surmonter cette deuxième faiblesse, le filtre de Kalman a été utilisé pour identifier les paramètres d'un modèle dynamique en fonction des erreurs de prévision constatées à chaque pas de temps. La méthodologie a été testée avec succès sur le secteur I de la ville de Verdun du Québec. Le modèle établi a été validé à l'aide de trois critères de performance, à savoir, le coefficient de Nash, le rapport des pointes mesurées/prévues et leur déphasage. Selon ces critères, les résultats trouvés par le modèle dynamique concordent bien avec les mesures.

Mots-clés:

• Prévision,
• temps réel,
• polluants,
• réseau d'assainissement,
• filtre de Kalman

Abstract

It is normally unrealistic to send the total combined water volume generated during a rainfall event to a wastewater treatment plant and this approach is not retained as a viable solution when physical and economic constraints need to be accounted for. It becomes therefore pertinent to reduce the pollution from a given area by limiting water treatment to the most polluted portion of the runoff volume. For this purpose, various municipalities have expressed an urgent need for an automated system that could dynamically manage all the hydraulic components of their urban drainage basins. However, such a system of management in real time requires short-term forecasting of the water quality in the drainage basins. The main object of this work is the development of tools for the real-time forecasting of pollutant loads in an urban sewer network. The method used in this study is based on two tools: the rating curve model and the Kalman filter.

The rating curve model is used to explain the correlation between pollutant loads and runoff. This model was selected because of its simplicity and the availability of the parameters necessary for its implementation. The rating curve model has several important characteristics. First of all, the formulation of the model is independent of the accumulation phase and the load accumulated over the basin is assumed to be unlimited. A second characteristic consists in the normalized form in which runoff is present in the model as a flow rate, so that the rating curve model can integrate the quantitative and qualitative aspects of urban runoff in a simple formulation, which requires parameters available in real time.

The assumption of systematic overlap between the hydrograph and pollutograph peaks constitutes the main weakness of this model, which we propose to overcome within the framework of this work. Thus, the rating curve model was modified by the introduction of a lag term identified in real time. In order to define the time lag parameter in real time, a mobile window has been programmed to scan the two observation vectors of flow rates and loads. Theoretically speaking, the time lag corresponds to the maximum of the cross correlation function between flow rate and load vectors observed in real time. Three cases are therefore possible. In the first case, an increase of the pollutograph precedes that of the hydrograph and the time lag is positive. In this case and in a context of real-time management, loads are determined using a forecast model for flow rates. Measured flow rates are considered in this work as forecasted flow rates. If the hydrograph precedes the pollutograph, the time lag "d" is negative and the loads are related to the flow rate measured at an instant that precedes forecast time by "d" times the time step. When, finally, the two curves are perfectly synchronous, the "d" parameter is equal to zero and the flow rates are forecasted on the basis of the flow rates measured at the time of forecasting. The model is thus sufficiently flexible and adapted to the various foreseeable conditions.

In addition, the constancy of the parameters concerned in the classic rating curve model constitutes another weakness with respect to the reproducibility of the phenomena during the same event and from one event to another. In order to overcome this second weakness, the Kalman filter was used to identify the parameters of a dynamic model according to the forecast errors noted with each time step. Use of the Kalman filter also allowed us to eliminate the calibration procedure required by the static model. With this filter, the dynamic model continuously readjusts its parameters to satisfy the non-stationary behaviour of hydrological phenomena.

The methodology was tested successfully on the sector I of the town of Verdun (Quebec). The established model was validated using three performance criteria, namely, the Nash coefficient, the peak ratio and the lag between measured and forecasted values. According to these criteria, the results obtained with the dynamic model agree well with measurements.

Keywords:

• Forecasting,
• real time,
• pollution,
• Kalman filter