Scope of the present paper is to provide an assessment of the state of the art of predictive uncertainty in flood forecasting. After defining what is meant by predictive uncertainty, the role and the importance of estimating predictive uncertainty within the context of flood management and in particular flood emergency management, is here discussed. Furthermore, the role of model and parameter uncertainty is presented together with alternative approaches aimed at taking them into account in the estimation of predictive uncertainty. In terms of operational tools, the paper also describes three of the recently developed Hydrological Uncertainty Processors. Finally, given the increased interest in meteorological ensemble precipitation forecasts, the paper discusses possible approaches aimed at incorporating input forecasting uncertainty in predictive uncertainty.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bertalanffy, L., General System Theory, George Braziller, New York, New York, 1968.
Beven, K.J. and Binley, A.M., 1992. The future of distributed models: model calibration and uncertainty prediction, Hydrol. Processes, 6, 279–298.
Beven, K.J. and Freer, J., 2001. Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems, J. Hydrol., 249, 11–29.
Buizza, R., Miller, M., and Palmer, T.N., 1999. Stochastic representation of model uncertainties in the ECMWF Ensemble Prediction System. Quart. J. Roy. Meteorol. Soc., 125, 2887–2908.
de Finetti, B., 1975. Theory of Probability, vol. 2. Wiley, Chichester, UK.
De Groot, M.H., 1970. Optimal Statistical Decisions, McGraw-Hill, New York.
Dempster, A.P., Laird, N.M., and Rubin, D.B., 1977. Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Stat. Soc. Series B, 39, 1–39.
Draper, D., 1995. Assessment and propagation of model uncertainty. J.Roy. Stat. Soc. Series B (Methodological), 57(1), 45–97.
Evensen, G., 2003. The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dynamics, 53, 343–367. DOI 10.1007/s10236-003-0036-9.
Krzysztofowicz, R., 1999. Bayesian theory of probabilistic forecasting via deterministic hydrologic model. Water Resour. Res., 35, 2739–2750.
Krzysztofowicz, R. and Kelly, K.S., 2000. Hydrologic uncertainty processor for probabilistic river stage Forecasting. Water Resour. Res., 36(11), 3265–3277.
Lindley, D.V., 1968. The choice of variables in multiple regression (with discussion). J.R. Statist. Soc. B, 30, 31–66.
Liu, Z., Martina, M.V.L., and Todini, E., 2005. Flood forecasting using a fully distributed model: application of the TOPKAPI model to the Upper Xixian Catchment. Hydrol. Earth Syst. Sci., 9, 347–364.
Mantovan, P. and Todini, E., 2006. Hydrological forecasting uncertainty assessment: incoherence of the GLUE methodology. J. Hydrol., 330, 368–381.
Mantovan, P., Todini, E., and Martina, M.V.L., 2007. Reply to comment by Keith Beven, Paul Smith and Jim Freer on “Hydrological forecasting uncertainty assessment: incoherence of the GLUE methodology”. J. Hydrol., 338, 319–324.
Mardia, K.V., Kent, J.T., and Bibby, J.M., 1979. Multivariate Analysis. Probability and Mathematical Statistics. Academic Press, London.
Martina, M.L.V., Todini, E., and Libralon, A., 2006. A Bayesian decision approach to rainfall thresholds based flood warning. Hydrol. Earth Syst. Sci., 10, 413–426.
Qian, S.S., Stow, C.A., and Borsuk, M.E., 2003. On Monte Carlo methods for Bayesian inference. Ecological Modelling, 159, 269–277.
Raftery, A.E., 1993. Bayesian model selection in structural equation models. In Bollen, K.A. and Long, J.S. (Eds.), Testing Structural Equation Models, pp. 163–180. Newbury Park, CA. Sage.
Raftery, A.E., Balabdaoui, F., Gneiting, T., and Polakowski, M., 2003. Using Bayesian model averaging to calibrate forecast ensembles, Tech. Rep., 440, Dep. of Stat., Univ. of Wash., Seattle.
Raftery, A.E., Gneiting, T., Balabdaoui, F., and Polakowski, M., 2005. Using Bayesian model averaging to calibrate forecast ensembles, Mon. Weather Rev., 133, 1155– 1174.
Raiffa, H. and Schlaifer, R., 1961. Applied Statistical Decision Theory. The MIT Press, Cambridge, MA.
Rougier, J., 2007. Probabilistic inference for future climate using an ensemble of climate model evaluations. Climatic Change, 81, 247–264.
Todini E., 1999. Using phase-space modeling for inferring forecasting uncertainty in nonlinear stochastic decision schemes. J. Hydroinformatics, 01.2, 75–82.
Todini, E., 2007. Hydrological modelling: past, present and future. Hydrol. Earth Syst. Sci., 11(1), 468–482
Todini, E., 2008. A model conditional processor to assess predictive uncertainty in flood forecasting, accepted JRBM, in press.
Van der Waerden, B.L., 1952. Order tests for two-sample problem and their power I. Indagationes Mathematicae, 14, 453–458.
Van der Waerden, B.L., 1953a. Order tests for two-sample problem and their power II. Indagationes Mathematicae, 15, 303–310.
Van der Waerden, B.L., 1953b. Order tests for two-sample problem and their power III. Indagationes Mathematicae, 15, 311–316.
Vrugt, J.A., Gupta, H.V., Bouten, W., and Sorooshian, S., 2003. A shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrological model parameters. Water Resour. Res., 39, 1201, doi: 10.1029/2002WR001642.
Vrugt, J.A. and Robinson, B.A., 2007. Treatment of uncertainty using ensemble methods: comparison of sequential data assimilation and Bayesian model averaging, Water Resour. Res., 43, W01411, doi: 10.1029/2005WR004838.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer Science + Business Media B.V
About this paper
Cite this paper
Todini, E. (2009). Predictive uncertainty assessment in real time flood forecasting. In: Baveye, P.C., Laba, M., Mysiak, J. (eds) Uncertainties in Environmental Modelling and Consequences for Policy Making. NATO Science for Peace and Security Series C: Environmental Security. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2636-1_9
Download citation
DOI: https://doi.org/10.1007/978-90-481-2636-1_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-2635-4
Online ISBN: 978-90-481-2636-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)