Bayesian approach for the calibration of models: application to an urban stormwater pollution model. 2003

A Kanso, and M C Gromaire, and E Gaume, and B Tassin, and G Chebbo
CEREVE (Centre d'Enseignement et de Recherche sur l'Eau, la Ville et l'Environnement), Ecole Nationale des Ponts et Chaussées, 6-8 avenue Blaise-Pascal, Cité Descartes, 77455 Marne-la-Vallée 2, France. kanso@cereve.enpc.fr

In environmental modelling, estimating the confidence level in conceptual model parameters is necessary but difficult. Having a realistic estimation of the uncertainties related to the parameters is necessary i) to assess the possible origin of the calibration difficulties (correlation between model parameters for instance), and ii) to evaluate the prediction confidence limits of the calibrated model. In this paper, an application of the Metropolis algorithm, a general Monte Carlo Markov chain sampling method, for the calibration of a four-parameter lumped urban stormwater quality model is presented. Unlike traditional optimisation approaches, the Metropolis algorithm identifies not only a "best parameter set", but a probability distribution of parameters according to measured data. The studied model includes classical formulations for the pollutant accumulation during dry weather period and their washoff during a rainfall event. Results indicate mathematical shortcomings in the pollutant accumulation formulation used.

UI MeSH Term Description Entries
D008962 Models, Theoretical Theoretical representations that simulate the behavior or activity of systems, processes, or phenomena. They include the use of mathematical equations, computers, and other electronic equipment. Experimental Model,Experimental Models,Mathematical Model,Model, Experimental,Models (Theoretical),Models, Experimental,Models, Theoretic,Theoretical Study,Mathematical Models,Model (Theoretical),Model, Mathematical,Model, Theoretical,Models, Mathematical,Studies, Theoretical,Study, Theoretical,Theoretical Model,Theoretical Models,Theoretical Studies
D011891 Rain Water particles that fall from the ATMOSPHERE. Rains
D002138 Calibration Determination, by measurement or comparison with a standard, of the correct value of each scale reading on a meter or other measuring instrument; or determination of the settings of a control device that correspond to particular values of voltage, current, frequency or other output. Calibrations
D002947 Cities A large or important municipality of a country, usually a major metropolitan center. Municipalities,Towns
D005544 Forecasting The prediction or projection of the nature of future problems or existing conditions based upon the extrapolation or interpretation of existing scientific data or by the application of scientific methodology. Futurology,Projections and Predictions,Future,Predictions and Projections
D000465 Algorithms A procedure consisting of a sequence of algebraic formulas and/or logical steps to calculate or determine a given task. Algorithm
D001499 Bayes Theorem A theorem in probability theory named for Thomas Bayes (1702-1761). In epidemiology, it is used to obtain the probability of disease in a group of people with some characteristic on the basis of the overall rate of that disease and of the likelihood of that characteristic in healthy and diseased individuals. The most familiar application is in clinical decision analysis where it is used for estimating the probability of a particular diagnosis given the appearance of some symptoms or test result. Bayesian Analysis,Bayesian Estimation,Bayesian Forecast,Bayesian Method,Bayesian Prediction,Analysis, Bayesian,Bayesian Approach,Approach, Bayesian,Approachs, Bayesian,Bayesian Approachs,Estimation, Bayesian,Forecast, Bayesian,Method, Bayesian,Prediction, Bayesian,Theorem, Bayes
D014865 Waste Disposal, Fluid The discarding or destroying of liquid waste products or their transformation into something useful or innocuous. Disposal, Fluid Waste,Disposals, Fluid Waste,Fluid Waste Disposal,Fluid Waste Disposals,Waste Disposals, Fluid
D014872 Water Movements The flow of water in enviromental bodies of water such as rivers, oceans, water supplies, aquariums, etc. It includes currents, tides, and waves. Movement, Water,Movements, Water,Water Movement
D014873 Water Pollutants Substances or organisms which pollute the water or bodies of water. Use for water pollutants in general or those for which there is no specific heading. Water Pollutant,Pollutant, Water,Pollutants, Water

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