Advertisement

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.

Keyword

forecasting 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bertalanffy, L., General System Theory, George Braziller, New York, New York, 1968.Google Scholar
  2. Beven, K.J. and Binley, A.M., 1992. The future of distributed models: model calibration and uncertainty prediction, Hydrol. Processes, 6, 279–298.Google Scholar
  3. 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.CrossRefGoogle Scholar
  4. 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.CrossRefGoogle Scholar
  5. de Finetti, B., 1975. Theory of Probability, vol. 2. Wiley, Chichester, UK.Google Scholar
  6. De Groot, M.H., 1970. Optimal Statistical Decisions, McGraw-Hill, New York.Google Scholar
  7. 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.Google Scholar
  8. Draper, D., 1995. Assessment and propagation of model uncertainty. J.Roy. Stat. Soc. Series B (Methodological), 57(1), 45–97.Google Scholar
  9. Evensen, G., 2003. The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dynamics, 53, 343–367. DOI 10.1007/s10236-003-0036-9.CrossRefGoogle Scholar
  10. Krzysztofowicz, R., 1999. Bayesian theory of probabilistic forecasting via deterministic hydrologic model. Water Resour. Res., 35, 2739–2750.CrossRefGoogle Scholar
  11. Krzysztofowicz, R. and Kelly, K.S., 2000. Hydrologic uncertainty processor for probabilistic river stage Forecasting. Water Resour. Res., 36(11), 3265–3277.CrossRefGoogle Scholar
  12. Lindley, D.V., 1968. The choice of variables in multiple regression (with discussion). J.R. Statist. Soc. B, 30, 31–66.Google Scholar
  13. 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.Google Scholar
  14. Mantovan, P. and Todini, E., 2006. Hydrological forecasting uncertainty assessment: incoherence of the GLUE methodology. J. Hydrol., 330, 368–381.CrossRefGoogle Scholar
  15. 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.CrossRefGoogle Scholar
  16. Mardia, K.V., Kent, J.T., and Bibby, J.M., 1979. Multivariate Analysis. Probability and Mathematical Statistics. Academic Press, London.Google Scholar
  17. 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.Google Scholar
  18. Qian, S.S., Stow, C.A., and Borsuk, M.E., 2003. On Monte Carlo methods for Bayesian inference. Ecological Modelling, 159, 269–277.CrossRefGoogle Scholar
  19. 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.Google Scholar
  20. 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.Google Scholar
  21. 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.CrossRefGoogle Scholar
  22. Raiffa, H. and Schlaifer, R., 1961. Applied Statistical Decision Theory. The MIT Press, Cambridge, MA.Google Scholar
  23. Rougier, J., 2007. Probabilistic inference for future climate using an ensemble of climate model evaluations. Climatic Change, 81, 247–264.CrossRefGoogle Scholar
  24. Todini E., 1999. Using phase-space modeling for inferring forecasting uncertainty in nonlinear stochastic decision schemes. J. Hydroinformatics, 01.2, 75–82.Google Scholar
  25. Todini, E., 2007. Hydrological modelling: past, present and future. Hydrol. Earth Syst. Sci., 11(1), 468–482CrossRefGoogle Scholar
  26. Todini, E., 2008. A model conditional processor to assess predictive uncertainty in flood forecasting, accepted JRBM, in press.Google Scholar
  27. Van der Waerden, B.L., 1952. Order tests for two-sample problem and their power I. Indagationes Mathematicae, 14, 453–458.Google Scholar
  28. Van der Waerden, B.L., 1953a. Order tests for two-sample problem and their power II. Indagationes Mathematicae, 15, 303–310.Google Scholar
  29. Van der Waerden, B.L., 1953b. Order tests for two-sample problem and their power III. Indagationes Mathematicae, 15, 311–316.Google Scholar
  30. 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.CrossRefGoogle Scholar
  31. 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.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media B.V 2009

Authors and Affiliations

  • Ezio Todini
    • 1
  1. 1.Dipartimento di Scienze della Terra e Geologico-AmbientaliPiazza Di Porta S. Donato1 BolognaItaly

Personalised recommendations