La prévision en temps réel des charges de polluants dans un réseau d'assainissement urbain

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.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

Equilibrium Selection and the Rate of Convergence in Coordination Games with Simultaneous Play

We apply the dynamic stochastic framework proposed in the recent evolutionary literature to a class of coordination games played simultaneously by the entire population. In these games, payoffs whence best replies are determined by a summary statistic of the population strategy profile. We demonstrate that with simultaneous play, the equilibrium selection depends crucially on how best responses to the summary statistic remain piece-wise constant. In fact, all the strict Nash equilibria in the underlying stage game can be declared stochastically stable depending on how the best response mapping generates piece-wise constant best responses. Furthermore, we show that if the best response mapping is sufficiently asymmetric, the expected waiting time until the unique stochastically stable state is reached is of the same order as the mutation rate, even in the limit as the population size grows to infinity.equilibrium selection; stochastic stability; waiting time; rate of convergence

The Role of R&D Technology in Asymmetric Research Joint Ventures

We characterize asymmetric equilibria in two-stage process innovation games and show that they are prevalent in the different models of R&D technology considered in the literature. Indeed, cooperation in R&D may be accompanied by high concentration in the product market. We show that while such an increase may be profitable, it may be socially inefficient.Research and Development, Research Joint Ventures, Process Innovation Games

Discrete Public Goods with Incomplete Information

We investigate a simultaneous discrete public good provision game with incomplete information. To use the terminology of Admati and Perry (1991), we consider both contribution and subscription games. In the former, contributions are not refunded if the project is not completed, while in the latter they are. In the presence of complete information about individuals' valuations for the public good, the difference between the equilibrium outcomes of a subscription game and a contribution game is not significant. However, there is both casual evidence from the fund-raising literature and experimental evidence that subscription games are ``superior '', i.e., a refund increases the chance of providing the good given that it is efficient to do so. Our analysis shows that this is indeed the case in the presence of incomplete information. We compute a symmetric equilibrium for the subscription game and show that it is not necessarily efficient. This inefficiency stems from the difficulties arising in coordinating to overcome the free-rider problem in the presence of incomplete information. Although it is well known that informational disparities impose limits on the efficiency of outcomes, the novel feature of our analysis is to explicitly model the resulting trade-off --- when deciding how much to contribute towards the public good --- between increasing the likelihood of provision and creating incentives for free-riding by the other player. Moreover, we show that for the contribution game, ``contributing zero'' is the only equilibrium for a given range of the fixed cost of provision and for a family of distributions.public goods; incomplete information; continuous distribution

Stream recession curves and storage variability in small watersheds

The pattern of streamflow recession after rain events offers clues about the relationship between watershed runoff (observable as river discharge) and water storage (not directly observable) and can help in water resource assessment and prediction. However, there have been few systematic assessments of how streamflow recession varies across flow rates and how it relates to independent assessments of terrestrial water storage. We characterized the streamflow recession pattern in 61 relatively undisturbed small watersheds (1–100 km<sup>2</sup>) across the coterminous United States with multiyear records of hourly streamflow from automated gauges. We used the North American Regional Reanalysis to help identify periods where precipitation, snowmelt, and evaporation were small compared to streamflow. The order of magnitude of the recession timescale increases from 1 day at high flow rates (~1 mm h<sup>−1</sup>) to 10 days at low flow rates (~0.01 mm h<sup>−1</sup>), leveling off at low flow rates. There is significant variability in the recession timescale at a given flow rate between basins, which correlates with climate and geomorphic variables such as the ratio of mean streamflow to precipitation and soil water infiltration capacity. Stepwise multiple regression was used to construct a six-variable predictive model that explained some 80 % of the variance in recession timescale at high flow rates and 30–50 % at low flow rates. Seasonal and interannual variability in inferred storage shows similar time evolution to regional-scale water storage variability estimated from GRACE satellite gravity data and from land surface modeling forced by observed meteorology, but is up to a factor of 10 smaller. Study of this discrepancy in the inferred storage amplitude may provide clues to the range of validity of the recession curve approach to relating runoff and storage

A note on duplication of R&D and R&D subsidies

We show that the presumed incompatibility of uncoordinated R&D and competition is not fundamental, but hinges on the nature of R&D spillovers. As a consequence, R&D subsidies may be more effective than previously thought

Herniation of the Anterior Wall of the Stomach into a Congenital Postdiaphragmatic Space: An Unusual Complication following Laparoscopic Nissen Fundoplication

Postoperative herniation of the stomach into potential spaces is a rare but serious complication of Nissen fundoplication. We report a 55-year-old female who presented with persistent vomiting shortly following laparoscopic Nissen fundoplication. At laparotomy, the anterior wall of the stomach was noted to be herniating into a congenital space behind the diaphragm. Anterior gastropexy was performed following the reduction of the herniating gastric segment. A high index of suspicion followed by aggressive and timely intervention is necessary to diagnose and manage postoperative gastric herniation and reduce the subsequent morbidity and mortality

The sensitivity of land emissivity estimates from AMSR-E at C and X bands to surface properties

Microwave observations at low frequencies exhibit more sensitivity to surface and subsurface properties with little interference from the atmosphere. The objective of this study is to develop a global land emissivity product using passive microwave observations from the Advanced Microwave Scanning Radiometer – Earth Observing System (AMSR-E) and to investigate its sensitivity to land surface properties. The developed product complements existing land emissivity products from SSM/I and AMSU by adding land emissivity estimates at two lower frequencies, 6.9 and 10.65 GHz (C- and X-band, respectively). Observations at these low frequencies penetrate deeper into the soil layer. Ancillary data used in the analysis, such as surface skin temperature and cloud mask, are obtained from International Satellite Cloud Climatology Project (ISCCP). Atmospheric properties are obtained from the TIROS Operational Vertical Sounder (TOVS) observations to determine the small upwelling and downwelling atmospheric emissions as well as the atmospheric transmission. A sensitivity test confirms the small effect of the atmosphere but shows that skin temperature accuracy can significantly affect emissivity estimates. Retrieved emissivities at C- and X-bands and their polarization differences exhibit similar patterns of variation with changes in land cover type, soil moisture, and vegetation density as seen at SSM/I-like frequencies (Ka and Ku bands). The emissivity maps from AMSR-E at these higher frequencies agree reasonably well with the existing SSM/I-based product. The inherent discrepancy introduced by the difference between SSM/I and AMSR-E frequencies, incidence angles, and calibration has been assessed. Significantly greater standard deviation of estimated emissivities compared to SSM/I land emissivity product was found over desert regions. Large differences between emissivity estimates from ascending and descending overpasses were found at lower frequencies due to the inconsistency between thermal IR skin temperatures and passive microwave brightness temperatures which can originate from below the surface. The mismatch between day and night AMSR-E emissivities is greater than ascending and descending differences of SSM/I emissivity. This is because of unique orbit time of AMSR-E (01:30 a.m./p.m. LT) while other microwave sensors have orbit time of 06:00 to 09:00 (a.m./p.m.). This highlights the importance of considering the penetration depth of the microwave signal and diurnal variability of the temperature in emissivity retrieval. The effect of these factors is greater for AMSR-E observations than SSM/I observations, as AMSR-E observations exhibit a greater difference between day and night measures. This issue must be addressed in future studies to improve the accuracy of the emissivity estimates especially at AMSR-E lower frequencies