, ACKNOWLEDGEMENT This research has been carried out under the OPUR research program. The authors gratefully acknowledge the Seine-Normandy Water Agency, Val-de-Marne Departmental Council, Seine-Saint-Denis Departmental Council, Hauts-de-Seine Departmental Council, City of Paris, and the Interdepartmental Association for Sewerage Services in the Paris Metropolitan Area (SIAAP), and the French Ministry of Ecology Sustainable Development and Energy for financial support, The authors additionally acknowledge use of the installations of the Scientific and Technical Centre for Building (CSTB)


L. M. Ahiablame, B. A. Engel, and I. Chaubey, Effectiveness of Low Impact Development Practices: Literature Review and Suggestions for Future Research, Water, Air, & Soil Pollution, vol.34, issue.3, pp.4253-4273, 2012.
DOI : 10.1016/S0043-1354(99)00290-0

W. M. Alley, Estimation of impervious-area Washoff Parameters, Water Resources Research, vol.60, issue.18, 1981.
DOI : 10.1029/WR017i004p01161

W. M. Alley and P. E. Smith, Estimation of accumulation parameters for urban runoff quality modeling, Water Resources Research, vol.97, issue.1, 1981.
DOI : 10.1093/comjnl/3.3.175

, Water Resour. Res

K. Athanasiadis, H. Horn, and B. Helmreich, A field study on the first flush effect of copper roof runoff, Corrosion Science, vol.52, issue.1, pp.21-29, 2010.
DOI : 10.1016/j.corsci.2009.08.048

S. Bertling, I. Odnevall-wallinder, C. Leygraf, and D. Berggren-kleja, Occurrence and fate of corrosion-induced zinc in runoff water from external structures, Science of The Total Environment, vol.367, issue.2-3, pp.908-923, 2006.
DOI : 10.1016/j.scitotenv.2006.01.008

K. Beven, Prophecy, reality and uncertainty in distributed hydrological modelling, Advances in Water Resources, vol.16, issue.1, pp.41-510309, 1993.
DOI : 10.1016/0309-1708(93)90028-E

K. Beven and A. Binley, The future of distributed models: Model calibration and uncertainty prediction, Hydrological Processes, vol.28, issue.3, pp.279-298, 1992.
DOI : 10.1007/978-3-642-82054-0_6

G. Bielmyer, W. R. Arnold, J. Tomasso, J. Isely, and S. Klaine, Effects of roof and rainwater characteristics on copper concentrations in roof runoff, Environmental Monitoring and Assessment, vol.52, issue.5, pp.2797-2804, 2012.
DOI : 10.1039/b402223h

A. Bressy, Flux de micropolluants dans les eaux de ruissellement urbaines. Effets de différents modes de gestion des eaux pluviales, 2010.
URL : https://hal.archives-ouvertes.fr/tel-00582379

A. Bressy, M. C. Gromaire, C. Lorgeoux, M. Saad, F. Leroy et al., Efficiency of source control systems for reducing runoff pollutant loads: Feedback on experimental catchments within Paris conurbation, Water Research, vol.57, pp.234-246, 2014.
DOI : 10.1016/j.watres.2014.03.040

URL : https://hal.archives-ouvertes.fr/hal-00981540

A. Bressy, M. C. Gromaire, C. Lorgeoux, M. Saad, F. Leroy et al., Towards the determination of an optimal scale for stormwater quality management: Micropollutants in a small residential catchment, Water Research, vol.46, issue.20, 2012.
DOI : 10.1016/j.watres.2011.12.017

URL : https://hal.archives-ouvertes.fr/hal-00759884

, Water Res, vol.46, pp.6799-6810

S. Chib and E. Greenberg, Understanding the Metropolis-Hastings algorithm, J. Am. Stat. Assoc, vol.49, pp.327-335, 1995.

D. Giudice, D. Honti, M. Scheidegger, A. Albert, C. Reichert et al., Improving uncertainty estimation in urban hydrological modeling by statistically describing bias, Hydrol. Earth Syst, 2013.

. Sci, , pp.4209-4225

A. Deletic, C. B. Dotto, D. T. Mccarthy, M. Kleidorfer, G. Freni et al., Assessing uncertainties in urban drainage models, Physics and Chemistry of the Earth, Parts A/B/C, vol.42, issue.44, pp.42-44, 2012.
DOI : 10.1016/j.pce.2011.04.007

C. B. Dotto, A. Deletic, and D. T. Mccarthy, Uncertainty analysis in urban drainage modelling: should we break our back for normally distributed residuals?, Water Science and Technology, vol.68, issue.6, pp.1271-1280, 2013.
DOI : 10.2166/wst.2013.360

C. B. Dotto, M. Kleidorfer, A. Deletic, W. Rauch, D. T. Mccarthy et al., Performance and sensitivity analysis of stormwater models using a Bayesian approach and long-term high resolution data, Environmental Modelling & Software, vol.26, issue.10, 2011.
DOI : 10.1016/j.envsoft.2011.03.013

, Environ. Model. Softw, vol.26, pp.1225-1239

F. Shorshani, M. André, M. Bonhomme, C. Seigneur, and C. , Modelling chain for the effect of road traffic on air and water quality: Techniques, current status and future prospects, Environ. Model. Softw, vol.64, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01233496

F. Shorshani, M. Bonhomme, C. Petrucci, G. André, M. Seigneur et al., Road traffic impact on urban water quality: a step towards integrated traffic, air and stormwater modelling, Environmental Science and Pollution Research, vol.16, issue.8, pp.5297-5310, 2014.
DOI : 10.1016/S1364-8152(00)00084-0

J. Förster, Patterns of roof runoff contamination and their potential implications on practice and regulation of treatment and local infiltration, Water Science and Technology, vol.33, issue.6, pp.39-48, 1996.
DOI : 10.2166/wst.1996.0079

G. Freni, G. Mannina, and G. Viviani, Urban runoff modelling uncertainty: Comparison among Bayesian and pseudo-Bayesian methods, Environmental Modelling & Software, vol.24, issue.9, 2009.
DOI : 10.1016/j.envsoft.2009.03.003

I. Gnecco, C. Berretta, L. G. Lanza, L. Barbera, and P. , Storm water pollution in the urban environment of Genoa, Italy, Atmospheric Research, vol.77, issue.1-4, pp.60-73, 2005.
DOI : 10.1016/j.atmosres.2004.10.017

M. Gromaire, P. Robert-sainte, A. Bressy, M. Saad, B. De-gouvello et al., Zn and Pb emissions from roofing materials ??? modelling and mass balance attempt at the scale of a small urban catchment, Water Science & Technology, vol.63, issue.11, 2011.
DOI : 10.2166/wst.2011.160

URL : https://hal.archives-ouvertes.fr/hal-00742329

M. C. Gromaire, S. Garnaud, M. Saad, and G. Chebbo, Contribution of different sources to the pollution of wet weather flows in combined sewers, Water Research, vol.35, issue.2, pp.521-533, 2001.
DOI : 10.1016/S0043-1354(00)00261-X

URL : https://hal.archives-ouvertes.fr/hal-00711820

M. C. Gromaire, A. Van-de-voorde, C. Lorgeoux, and G. Chebbo, Benzalkonium runoff from roofs treated with biocide products ??? In situ pilot-scale study, Water Research, vol.81, pp.279-287, 2015.
DOI : 10.1016/j.watres.2015.05.060

URL : https://hal.archives-ouvertes.fr/hal-01238344

. Doi,

W. K. Hasting, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, vol.57, issue.1, pp.97-109, 1970.
DOI : 10.1093/biomet/57.1.97

W. He, Atmospheric Corrosion and Runoff Processes on Copper and Zinc as Roofing Materials, 2002.

W. He, I. Odnevall-wallinder, and C. Leygraf, A laboratory study of copper and zinc runoff during first flush and steady-state conditions, Corrosion Science, vol.43, issue.1, pp.10-938, 2001.
DOI : 10.1016/S0010-938X(00)00066-4

A. Kanso, G. Chebbo, and B. Tassin, Application of MCMC???GSA model calibration method to urban runoff quality modeling, Reliability Engineering & System Safety, vol.91, issue.10-11, 2006.
DOI : 10.1016/j.ress.2005.11.051

A. Kanso, B. Tassin, and G. Chebbo, A benchmark methodology for managing uncertainties in urban runoff quality models, Water Science and Technology, vol.51, issue.2, pp.163-170, 2005.
DOI : 10.2166/wst.2005.0044

C. Karlén, I. Odnevall-wallinder, D. Heijerick, C. Leygraf, and C. R. Janssen, Runoff rates and ecotoxicity of zinc induced by atmospheric corrosion, Science of The Total Environment, vol.277, issue.1-3, pp.169-180, 2001.
DOI : 10.1016/S0048-9697(00)00872-X

J. G. Lee, A. Selvakumar, K. Alvi, J. Riverson, J. X. Zhen et al., A watershed-scale design optimization model for stormwater best management practices, Environmental Modelling & Software, vol.37, pp.6-18, 2012.
DOI : 10.1016/j.envsoft.2012.04.011

. Doi,

A. U. Leuenberger-minger, B. Buchmann, M. Faller, P. Richner, and M. Zöbeli, Dose???response functions for weathering steel, copper and zinc obtained from a four-year exposure programme in Switzerland, Corrosion Science, vol.44, issue.4, 2002.
DOI : 10.1016/S0010-938X(01)00097-X

, Corros. Sci, vol.44, pp.675-68700097

J. E. Nash and J. V. Sutcliffe, River flow forecasting through conceptual models part I ??? A discussion of principles, Journal of Hydrology, vol.10, issue.3, pp.282-290, 1970.
DOI : 10.1016/0022-1694(70)90255-6

O. Wallinder, I. Leygraf, C. Karlén, C. Heijerick, D. Janssen et al., Atmospheric corrosion of zinc-based materials: runoff rates, chemical speciation and ecotoxicity effects, Corrosion Science, vol.43, issue.5, pp.809-816, 2001.
DOI : 10.1016/S0010-938X(00)00136-0

O. Wallinder, I. Verbiest, P. He, W. Leygraf, and C. , The influence of patina age and pollutant levels on the runoff rate of zinc from roofing materials, Corros. Sci, vol.40, issue.98, pp.1977-1982, 1998.

D. Persson and V. Kucera, Release of Metals from Buildings, Constructions and Products during Atmospheric Exposure in Stockholm, Water, Air and Soil Pollution: Focus, vol.1, issue.3/4, pp.133-150, 2001.
DOI : 10.1023/A:1017556105259

D. Reiss, B. Rihm, C. Thöni, and M. Faller, Mapping Stock at Risk and Release of Zinc and Copper in Switzerland???Dose Response Functions for Runoff Rates derived from Corrosion Rate Data, Water, Air, & Soil Pollution, vol.159, issue.1, pp.101-113, 2004.
DOI : 10.1023/B:WATE.0000049163.18416.ec

P. Robert-sainte, Contribution des matériaux de couverture à la contamination métallique des eaux de ruissellement [Contribution of roofing materials to the metal contamination of runoff], 2009.

P. Robert-sainte, M. C. Gromaire, B. De-gouvello, M. Saad, and G. Chebbo, Annual Metallic Flows in Roof Runoff from Different Materials: Test-Bed Scale in Paris Conurbation, Environmental Science & Technology, vol.43, issue.15, pp.5612-561810, 1021.
DOI : 10.1021/es9002108

URL : https://hal.archives-ouvertes.fr/hal-00739900

J. Sage, C. Bonhomme, A. Ali, S. Gromaire, and M. , Performance assessment of a commonly used ???accumulation and wash-off??? model from long-term continuous road runoff turbidity measurements, Water Research, vol.78, pp.47-59, 2015.
DOI : 10.1016/j.watres.2015.03.030

URL : https://hal.archives-ouvertes.fr/hal-01145853

G. Schoups and J. A. Vrugt, A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non-Gaussian errors, Water Resources Research, vol.44, issue.8, 2010.
DOI : 10.1029/2008WR006833

A. Schriewer, H. Horn, and B. Helmreich, Time focused measurements of roof runoff quality, Corrosion Science, vol.50, issue.2, pp.384-391, 2008.
DOI : 10.1016/j.corsci.2007.08.011

M. Thyer, B. Renard, D. Kavetski, G. Kuczera, S. W. Franks et al., Critical evaluation of parameter consistency and predictive uncertainty in hydrological modeling: A case study using Bayesian total error analysis, Water Resources Research, vol.43, issue.1, 2009.
DOI : 10.1029/2006WR005497

URL : https://hal.archives-ouvertes.fr/hal-00456158

V. A. Tsihrintzis and R. Hamid, Modeling and Management of Urban Stormwater Runoff Quality: A Review, pp.137-164, 2001.

A. Van-de-voorde, Incidence des pratiques d'entretien des toitures sur la qualité des eaux de ruissellement : cas des traitements par produits biocides [Effect of roof maintenance practices on runoff quality : case of biocidal treatments, 2012.

L. Vezzaro and P. S. Mikkelsen, Application of global sensitivity analysis and uncertainty quantification in??dynamic modelling of micropollutants in stormwater runoff, Environmental Modelling & Software, vol.27, issue.28, pp.27-28, 2012.
DOI : 10.1016/j.envsoft.2011.09.012

. Doi,

L. Vezzaro, A. K. Sharma, A. Ledin, and P. S. Mikkelsen, Evaluation of stormwater micropollutant source control and end-of-pipe control strategies using an uncertainty-calibrated integrated dynamic simulation model, Journal of Environmental Management, vol.151, pp.56-64, 2015.
DOI : 10.1016/j.jenvman.2014.12.013

Q. J. Wang, D. L. Shrestha, D. E. Robertson, and P. Pokhrel, A log-sinh transformation for data normalization and variance stabilization, Water Resources Research, vol.340, issue.3-4, 2012.
DOI : 10.1016/j.jhydrol.2007.04.006

D. Wicke, Effect of age and rainfall pH on contaminant yields from metal roofs, Water Science & Technology, vol.69, issue.10, 2014.
DOI : 10.2166/wst.2014.124

J. Yang, P. Reichert, and K. C. Abbaspour, Bayesian uncertainty analysis in distributed hydrologic modeling: A case study in the Thur River basin (Switzerland), Water Resources Research, vol.340, issue.1, pp.10-1029, 2007.
DOI : 10.1016/j.jhydrol.2007.04.006

M. I. Yaziz, H. Gunting, N. Sapari, and A. W. Ghazali, Variations in rainwater quality from roof catchments, Water Research, vol.23, issue.6, pp.10-1016, 1989.
DOI : 10.1016/0043-1354(89)90211-X

X. Zhang, W. He, I. Odnevall-wallinder, J. Pan, and C. Leygraf, Determination of instantaneous corrosion rates and runoff rates of copper from naturally patinated copper during continuous rain events, Corrosion Science, vol.44, issue.9, pp.2131-2151, 2002.
DOI : 10.1016/S0010-938X(02)00015-X

J. Zobrist, S. R. Müller, A. Ammann, T. D. Bucheli, V. Mottier et al., Quality of roof runoff for groundwater infiltration, Water Research, vol.34, issue.5, pp.1455-1462, 2000.
DOI : 10.1016/S0043-1354(99)00290-0