Skip to main content

Advertisement

SpringerLink
Log in

Flood risk curves and uncertainty bounds

  • ORIGINAL PAPER
  • Published:
Natural Hazards Aims and scope Submit manuscript

Abstract

Although flood risk assessments are frequently associated with significant uncertainty, formal uncertainty analyses are the exception rather than the rule. We propose to separate two fundamentally different types of uncertainty in flood risk analyses: aleatory and epistemic uncertainty. Aleatory uncertainty refers to quantities that are inherently variable in time, space or populations of individuals or objects. Epistemic uncertainty results from incomplete knowledge and is related to our inability to understand, measure and describe the system under investigation. The separation between aleatory and epistemic uncertainty is exemplified for the flood risk analysis of the city of Cologne, Germany. This flood risk assessment consists of three modules: (1) flood frequency analysis, (2) inundation estimation and (3) damage estimation. By the concept of parallel models, the epistemic uncertainty of each module is quantified. The epistemic uncertainty associated with the risk estimate is reduced by introducing additional information into the risk analysis. Finally, the contribution of different modules to the total uncertainty is quantified. The flood risk analysis results in a flood risk curve, representing aleatory uncertainty, and in associated uncertainty bounds, representing epistemic uncertainty. In this way, the separation reveals the uncertainty (epistemic) that can be reduced by more knowledge and the uncertainty (aleatory) that is not reducible.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Apel H, Thieken A, Merz B, Blöschl G (2004) Flood risk assessment and associated uncertainty. Nat Hazards Earth Syst Sci 4:295–308

    Google Scholar 

  • Apel H, Merz B, Thieken AH (2008) Quantification of uncertainties in flood risk assessments. J River Basin Manag 6(2):149–162

    Google Scholar 

  • Bárdossy A, Markovic D (2002) Extremwertstatistik—Bericht des Instituts für Wasserbau, Universität Stuttgart für die Bundesanstalt für Gewässerkunde (unpublished)

  • Bobee B, Ashkar F (1988) Review of statistical methods for estimating flood risk with special emphasis on the Log Pearson Type 3 distribution. In: El-Sabh MI, Murty TS (eds) Natural and man-made hazards. D. Reidel Publishing Company, pp 357–367

  • Büchele B, Kreibich H, Kron A, Thieken AH, Ihringer J, Oberle P, Merz B, Nestmann F (2006) Flood-risk mapping: contributions towards an enhanced assessment of extreme events and associated risks. NHESS 6:485–503

    Google Scholar 

  • Cullen AC, Frey HC (1999) Probabilistic techniques in exposure assessment. A handbook for dealing with variability and uncertainty in models and inputs. Plenum Press, New York, p 335

    Google Scholar 

  • Disse M, Engel H (2001) Flood events in the Rhine basins: genesis, influences and mitigation. Nat Hazards 23:271–290

    Article  Google Scholar 

  • Downton MW, Morss RE, Wilhelmi OV, Gruntfest E, Higgings ML (2005) Interactions between scientific uncertainty and flood management decisions: two case studies in Colorado. Environ Hazards 6:134–146

    Article  Google Scholar 

  • DVWK (1999) Statistische Analyse von Hochwasserabflüssen. Wirtschafts- und Verlags-Ges. Gas und Wasser, Bonn, p 42

    Google Scholar 

  • El Adlouni S, Bobée B, Ouarda TBMJ (2008) On the tails of extreme event distributions in hydrology. J Hydrol 355:16–33

    Article  Google Scholar 

  • Ferson S, Ginzburg LR (1996) Different methods are needed to propagate ignorance and variability. Reliab Eng Syst Saf 54:133–144

    Article  Google Scholar 

  • Fink A, Ulbrich U, Engel H (1996) Aspects of the January 1995 flood in Germany. Weather 51:34–39

    Google Scholar 

  • Geomer (2009) http://www.geomer.de/produkte/floodarea/index.html. Accessed 12 June 2009

  • Gouldby B, Sayers P, Mulet-Marti J, Hassan MAAM, Benwell D (2008) A methodology for regional-scale flood risk assessment. Water Manag 161(WM3):169–182

    Article  Google Scholar 

  • Grünthal G, Thieken AH, Schwarz J, Radtke K, Smolka A, Merz B (2006) Comparative risk assessment for the city of Cologne, Germany—storms, floods, earthquakes. Nat Hazards 38(1–2):21–44

    Article  Google Scholar 

  • Haimes YY (1998) Risk modeling, assessment, and management, Wiley series in systems engineering. Wiley, New York, p 726

    Google Scholar 

  • Hall JW (2003) Handling uncertainty in the hydroinformatic process. J Hydroinformatics 05.4:215–232

    Google Scholar 

  • Hall J, Anderson M (2002) Handling uncertainty in extreme unrepeatable hydrological processes—the need for an alternative paradigm. Hydrol Process 16:1867–1870

    Article  Google Scholar 

  • Hammitt JK, Shlyakhter AI (1999) The expected value of information and the probability of surprise. Risk Anal 19(1):135–152

    Google Scholar 

  • Helton JC, Oberkampf WL (2004) Alternative representations of epistemic uncertainty. Reliab Eng Syst Saf 85:1–10

    Article  Google Scholar 

  • Hoffman FO, Hammonds JS (1994) Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. Risk Anal 14(5):707–712

    Article  Google Scholar 

  • Hora SC (1996) Aleatory and epistemic uncertainty in probability elicitation with an example from hazardous waste management. Reliab Eng Syst Saf 54:217–223

    Article  Google Scholar 

  • Hosking JRM, Wallis JR (1997) Regional frequency analysis. An approach based on L-moments. Cambridge University Press, Cambridge

    Google Scholar 

  • Hydrotec (2001) Hochwasser-Aktionsplan Angerbach. Teil I: Berichte und Anlagen. Studie im Auftrag des StUA Düsseldorf, Aachen (unpublished report)

  • ICPR (2001) Atlas of flood danger and potential damage due to extreme floods of the Rhine. International Commission for the Protection of the Rhine (ICPR), ISBN 9-935324-43-x

  • Institute of Hydrology (1999) Flood estimation handbook, vol 1–5. Institute of Hydrology, Crowmarsh Gifford

    Google Scholar 

  • Kleeberg H-B, Schumann AH (2001) Ableitung von Bemessungsabflüssen kleiner Überschreitungswahrscheinlichkeiten. Wasserwirtschaft 91(2):90–94

    Google Scholar 

  • Kleist L, Thieken A, Köhler P, Müller M, Seifert I, Borst D, Werner U (2006) Estimation of the regional stock of residential buildings as a basis for comparative risk assessment for Germany. NHESS 6:541–552

    Google Scholar 

  • Krahe P (1997) Hochwasser und Klimafluktuationen am Rhein seit dem Mittelalter. In: Immendorf R (ed) Hochwasser—Natur im Überfluß?. Müller, Heidelberg, pp 57–82

    Google Scholar 

  • Kundzewicz ZW, Robson AJ (2004) Change detection in hydrological records—a review of the methodology. J Hydrol Sci 49(1):7–19

    Article  Google Scholar 

  • Lammersen R, Engel H, Van de Langemheen W, Buiteveld H (2002) Impact of river training and retention measures on flood peaks along the Rhine. J Hydrol 267(1–2):115–124

    Article  Google Scholar 

  • Merz B, Thieken A (2005) Separating natural and epistemic uncertainty in flood frequency analysis. J Hydrol 309(1–4):114–132

    Article  Google Scholar 

  • Merz B, Thieken A, Blöschl G (2002) Uncertainty analysis for flood risk estimation, International Commission for the Hydrology of the Rhine basin, Proceedings of the International Conference on Flood Estimation, 6–8 March 2002, Berne, CHR Report II-17, pp 577–585

  • Merz B, Kreibich H, Thieken A, Schmidtke R (2004) Estimation uncertainty of direct monetary flood damage to buildings. Nat Hazards Earth Syst Sci 4:153–163

    Google Scholar 

  • Mosley M, McKerchar AI (1992) Streamflow. In: Maidment DR (ed) Handbook of hydrology. McGraw-Hill, New York, pp 8.1–8.39

    Google Scholar 

  • MURL (2000) Potentielle Hochwasserschäden am Rhein in NRW. Ministerium für Umwelt. Raumordnung und Landwirtschaft des Landes Nordrhein-Westfalen. Düsseldorf (unpublished report)

  • Palmer TN (2000) Predicting uncertainty in forecasts of weather and climate. Rep Prog Phys 63:71–116

    Article  Google Scholar 

  • Parry GW (1996) The characterization of uncertainty in probabilistic risk assessment of complex systems. Reliab Eng Syst Saf 54:119–126

    Article  Google Scholar 

  • Petrow T, Merz B (2009) Trends in flood magnitude, frequency and seasonality in Germany in the period 1951–2002. J Hydrol 371:129–141

    Article  Google Scholar 

  • Petrow T, Zimmer J, Merz B (2009) Changes in the flood hazard through changing frequency and persistence of circulation patterns. Nat Hazards Earth Syst Sci 9:1409–1423

    Google Scholar 

  • Pfister L, Kwadijk J, Musy A, Bronstert A, Hoffmann L (2004) Climate change, land use change and runoff prediction in the Rhine-Meuse Basins. River Res Appl 20:229–241. doi:10.1002/rra.775

    Article  Google Scholar 

  • Pinter N, van der Ploeg RR, Schweigert P, Hoefer G (2006) Flood magnification on the River Rhine. Hydrol Process 20:147–164

    Article  Google Scholar 

  • Stanescu VA (2002) Outstanding floods in Europe: a regionalization and comparison. International Conference on Flood Estimation, Berne, Switzerland CHR-Report II-17, pp 697–706

  • Stedinger JR, Vogel RM, Foufoula-Georgiou E (1992) Frequency analysis of extreme events. In: Maidment DR (ed) Handbook of hydrology. McGraw-Hill, New York, pp 18.1–18.66

    Google Scholar 

  • Svensson C, Kundzewicz ZW, Maurer T (2005) Trend detection in river flow 697 series: 2. Flood and low-flow index series. J Hydrol Sci 50(5):811–824

    Article  Google Scholar 

  • Thieken AH, Müller M, Kleist L, Seifert I, Borst D, Werner U (2006) Regionalisation of asset values for risk analyses. Nat Hazards Earth Syst Sci 6:167–178

    Article  Google Scholar 

  • Thieken AH, Olschewski A, Kreibich H, Kobsch S, Merz B (2008) Development and evaluation of FLEMOps—a new Flood Loss Estimation MOdel for the private sector. In: Proverbs D, Brebbia CA, Penning-Rowsell E (eds) Flood recovery, innovation and response. WIT Press, London, pp 315–324

    Chapter  Google Scholar 

  • Van Asselt MBA, Rotmans J (2002) Uncertainty in integrated assessment modelling. Clim Chang 54(1):75–105

    Article  Google Scholar 

  • Visser H, Folkert RJM, Hoekstra J, de Wolff JJ (2000) Identifying key sources of uncertainty in climate change projections. Clim Chang 45(3–4):421–457

    Article  Google Scholar 

  • Vogt R (1995) Hochwasser in Köln. In: Dokumentation der Fachtagung “Mit dem Hochwasser leben”, Baden-Baden, pp 48–55

  • Von Storch H, Zwiers FW (1999) Statistical analysis in climate research. Cambridge University Press, New York, p 484

    Google Scholar 

  • Watson SR (1994) The meaning of probability in probabilistic safety analysis. Reliab Eng Syst Saf 45:261–269

    Article  Google Scholar 

Download references

Acknowledgments

We gratefully acknowledge the provision of data by Hochwasserschutzzentrale Köln (Flood Defence Centre Cologne).

Author information

Authors and Affiliations

  1. GFZ German Research Centre for Geosciences, Telegrafenberg, 14473, Potsdam, Germany

    Bruno Merz

  2. Centre for Natural Hazard and Risk Management, Leopold-Franzens-University Innsbruck and alpS, Grabenweg 3, 6020, Innsbruck, Austria

    Annegret H. Thieken

Authors
  1. Bruno Merz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Annegret H. Thieken
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bruno Merz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Merz, B., Thieken, A.H. Flood risk curves and uncertainty bounds. Nat Hazards 51, 437–458 (2009). https://doi.org/10.1007/s11069-009-9452-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11069-009-9452-6

Keywords

Search

Navigation