TECHNICAL PAPERS
Mar 1, 1997

Expected Probability and Annual Damage Estimators

Publication: Journal of Water Resources Planning and Management
Volume 123, Issue 2

Abstract

Controversy continues over the relative merits of traditional frequency estimators and the “expected probability” estimator of flood risk that incorporates an adjustment for parameter uncertainty. Both have solid theoretical motivation, but address different concerns. The description of hydrologic risk and uncertainty provided by new risk and uncertainty procedures adopted by the U.S. Army Corps of Engineers, and risk-based design procedures developed by others, are shown to be equivalent to the expected probability model in simple cases. A 1995 National Research Council (NRC) report recommended against use of the expected probability model for evaluating expected annual damages and the probability of flooding; in particular, the NRC analysis and the 1989 Arnell analysis demonstrated that expected probability estimators yield risk and damage estimators that generally have large positive biases. Historical arguments and related issues are reviewed. Resolution of this controversy and success of the new U.S. Army Corps of Engineers (USACE) risk and uncertainty procedures require a clear framework for understanding what is meant by risk, variability, and uncertainty. Such risk analyses can better represent a community's vulnerability to flooding and the large uncertainty in estimates of expected damages and residual flood risk.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Afshar, A., and Mariño, M. A.(1994). “Optimizing river diversion under hydraulic and hydrologic uncertainties.”J. Water Resour. Plng. and Mgmt., ASCE, 120(1), 36–47.
2.
Arnell, N.(1989). “Expected annual damages and uncertainties in flood frequency estimation.”J. Water Resour. Plng. and Mgmt., ASCE, 115(1), 94–107.
3.
Bao, Y., Tung, Y.-K., and Hasfurther, V. R.(1987). “Evaluation of uncertainty in glood magnitude estimator and annual expected damage costs of hydraulic structures.”Water Resour. Res., 23(11), 2023–2029.
4.
Beard, L. R.(1960). “Probability estimates based on small normal-distribution samples.”J. Geophy. Res., 65(7), 2143–2148.
5.
Beard, L. R.(1978). “Impact of hydrologic uncertainties on flood insurance.”J. Hydr. Div., ASCE, Am. Soc. Civ. Eng., 104(11), 1473–1483.
6.
Beard, L. R.(1990). “Discussion of expected annual damages and uncertainties in flood frequency estimation.”J. Water Res. Plng. and Mgmt., ASCE, 116(6), 847–850.
7.
Beard, L. R.(1997). “Estimated flood frequency and average annual damage.”J. Water Resour. Plng. and Mgmt., 123(2), 84–88.
8.
Benjamin, J. R., and Cornell, C. A. (1970). Probability, statistics and decisions for civil engineers. McGraw-Hill Book Co., Inc., N.Y.
9.
Berger, J. (1980). Statistical decision theory, foundations, concepts and methods. Springer-Verlag New York, Inc., New York, N.Y.
10.
Bernier, J. M. (1987). “Elements of Bayesian analysis of uncertainty in hydrological reliability and risk models.”Engineering reliability and risk in water resources, L. Duckstein, and E. Plate, eds., M. Nijhoff, The Hague, The Netherlands, 405–422.
11.
Bobée, B., and Rasmussen, P. F. (1995). “Recent advances in flood frequency analysis.”Reviews of Geophysics; Supplement, U.S. Nat. Rep. to Int. Union of Geodesy and Geophys., Am. Geophys. Union, Washington, D.C., 1111–1116.
12.
Burnham, M. W., and Davis, D. W. (1995). “Risk-based analysis for flood studies.”Integrated Water Resources Planning for the 21st Century; Proc., 22nd Conf., Water Resour. Plng. and Mgmt. Div., ASCE, New York, N.Y., 686–689.
13.
Chowdhury, J. U., and Stedinger, J. R.(1991). “Confidence intervals for design floods with estimated skew coefficient.”J. Hydr. Engrg., ASCE, 117(7), 811–831.
14.
Cohn, T. A., and Stedinger, J. R.(1987). “Use of historical information in a maximum-likelihood framework.”J. Hydro., Amsterdam, The Netherlands, 96, 215–223.
15.
Davis, D. W. (1991). “A risk and uncertainty based concept for sizing levee projects.”Proc., Hydro. and Hydr. Workshop on Riverine Levee Freeboard. SP-24.
16.
Davis, D. R., Kisiel, C. C., and Duckstein, L.(1972). “Bayesian decision theory applied to design in hydrology.”Water Resour. Res., 8(1), 33–41.
17.
Doran, D. G., and Irish, J. L. (1980). “On the nature and extent of bias in flood damage estimation.”Proc., Hydro. and Water Resour. Symp.
18.
Duckstein, L., Bogárdi, I., Szidarovszky, F., and Davis, D. R.(1975). “Sample uncertainty in flood levee design: Bayesian versus nonBayesian methods.”Water Resour. Bull., 11(3), 425–435.
19.
Gould, B. W.(1973). “Discussion of `Bias in computed flood risk,' by C. H. Hardison and M. E. Jennings.”J. Hydr. Div., ASCE, 99(1), 415–427.
20.
Gunasekara, T. A. G., and Cunnane, C.(1991). “Expected probabilities of exceedance for non-normal flood distributions.”J. Hydro., Amsterdam, The Netherlands, 128, 101–113.
21.
Hardison, C. H., and Jennings, M. E.(1972). “Bias in computed flood risk.”J. Hydr. Div., ASCE, 98(3), 415–427.
22.
Hardison, C. H., and Jennings, M. E.(1973). “Bias in computed flood risk-closure.”J. Hydr. Div., ASCE, 99(7), 1157–1158.
23.
Hirsch, R. M., Helsel, D. R., Cohn, T. A., and Gilroy, E. J. (1993). “Statistical analysis of hydrologic data.”Handbook of hydrology, D. Maidment, ed., McGraw-Hill Book Co., Inc., New York, N.Y.
24.
Interagency Advisory Committee on Water Data (IACWD). (1982). “Guidelines for determining flood flow frequency,”Bull. No. 17B, Hydro. Subcommittee, U.S. Geological Survey, Reston, Va.
25.
Interagency Floodplain Management Review Committee (IFMRC). (1994). “Sharing the challenge: floodplain management into the 21st century,”Rep., Admin. Floodplain Mgmt. Task Force, U.S. Govt. Printing Ofc., Washington, D.C.
26.
James, L. D., and Hall, B.(1986). “Risk information for floodplain management.”J. Water Resour. Plng. and Mgmt., 112(4), 485–499.
27.
Kuczera, G.(1982). “Combining site-specific and regional information, an emirical Bayes approach.”Water Resour. Res., 18(2), 306–314.
28.
Moran, P. A. P.(1957). “The statistical treatment of floods.”Trans. Am. Geophys. Union, 38(4), 519–523.
29.
Morgan, M. G., and Henrion, M. (1990). Uncertainty, a guide to dealing with uncertainty in quantitative risk and policy analysis. Cambridge University Press, New York, N.Y.
30.
National Research Council Task Force on Estimation of Peak Flows of the Panel on Flood Studies in Riverine Areas. (1978). “Estimation of peak flows.”Contract Number H-3569 with the Dept. of Housing and Urban Devel., Nat. Acad. of Sci., Washington, D.C.
31.
National Research Council. (NRC). (1995). “Flood risk management and the American river basin: an evaluation.”Rep., Nat. Acad. Press, Washington, D.C.
32.
Plate, E. (1993). “Some remarks on the use of reliability analysis in hydraulic engineering applications.”Reliability and uncertainty analyses in hydraulic design, B. C. Yen, and Y.-K. Tung, eds., ASCE, New York, N.Y., 5–15.
33.
Rasmussen, P. F., and Rosbjerg, D.(1991). “Evaluation of risk concepts in partial duration series.”Stochastic Hydro. and Hydr., 5(1), 1–16.
34.
Stedinger, J. R.(1983a). “Design events with specified flood risk.”Water Resour. Res., 19(2), 511–522.
35.
Stedinger, J. R.(1983b). “Confidence intervals for design events.”J. Hydr. Engrg., ASCE, 109(1), 13–27.
36.
Stedinger, J. R., and Lu, L.(1995). “Appraisal of regional and index flood quantile estimators.”Stochastic Hydro. and Hydr., 9(1), 49–75.
37.
Stedinger, J. R., Pei, D., and Cohn, T. A.(1985). “A disaggregation model for incorporating parameter uncertainty into monthly reservoir simulations.”Water Resour. Res., 21(5), 665–675.
38.
Stedinger, J. R., Vogel, R. M. and Foufoula-Georgiou, E. (1993). “Frequency analysis of extreme events.”Handbook of hydrology, D. Maidment, ed., McGraw-Hill Book Co., Inc., New York, N.Y.
39.
Thomas, D. M. (1976). “Flood frequency—expected and unexpected probabilities,”U.S. Geological Survey Open File Rep., 76–775.
40.
Tung, Y.-K.(1987). “Effects of uncertainties on optimal risk-based design of hydraulic structures.”J. Water Resour. Plng. and Mgmt., ASCE, 113(5), 709–722.
41.
Tung, Y.-K. (1993). “Confidence intervals of optimal risk-based hydraulic design parameters.”Reliability and uncertainty analyses in hydraulic design, B. C. Yen, and Y.-K. Tung, eds., ASCE, New York, N.Y., 81–96.
42.
U.S. Army Corps of Engineers (USACE). (1992). “Guidelines and procedures for risk and uncertainty analysis in CORPS' civil works planning.”Vol. II: Example cases, guidelines for risk and uncertainty analysis in water resources planning, Water Resour. Support Ctr., Inst. of Water Resour., Fort Belvoir, Va, Rep. 92-R-2.
43.
U.S. Army Corps of Engineers (USACE). (1994). “Risk based analysis for evaluation of hydrology/hydraulics and economics in flood damage reduction studies.”Circular EC 1105-2-205, Dept. of the Army, Washington D.C.
44.
U.S. Army Corps of Engineers (USACE). (1996a). “Risk-based analysis of flood damage reduction studies.”Draft Manual, EM 1110-2-1619, Washington, D.C.
45.
U.S. Army Corps of Engineers (USACE). (1996b). “Risk-based analysis for evaluation of hydrology/hydraulic, geotechnical stability, and economics in flood damage reduction studies.”ER1105-2-101, Washington, D.C.
46.
Vicens, G. J., Rodríquez-Iturbe, I., and Schaake Jr., J. C.(1975). “A Bayesian framework for the use of regional information in hydrology.”Water Resour. Res., 11(3), 405–414.
47.
Williamson, M. S. (1984). “Methodology for estimating uncertainties in net benefits for flood damage mitigation design,” MS thesis, Dept. of Civ. Engrg., Univ. of Washington, Seattle, Wash.
48.
Wood, E.(1978). “Analyzing hydrologic uncertainty and its impact upon decision making in water resources.”Adv. Water Resour., 1(5), 299–305.
49.
Zellner, A. (1971). An introduction to Bayesian inference in econometrics. J. Wiley & Sons, Inc., New York, N.Y.

Information & Authors

Information

Published In

Go to Journal of Water Resources Planning and Management
Journal of Water Resources Planning and Management
Volume 123Issue 2March 1997
Pages: 125 - 135

History

Published online: Mar 1, 1997
Published in print: Mar 1997

Permissions

Request permissions for this article.

Authors

Affiliations

Jery R. Stedinger, Member, ASCE
Prof., School of Civ. and Envir. Engrg., Cornell Univ., Ithaca, NY 14853-3501.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share