Safety of Dams Flood and Earthquake Criteria (1985) / Chapter Skim
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Appendix D: Concepts of Probability in Hydrology
Appendix D: Concepts of Probability in Hydrology
Pages 227-240
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From page 227... ...
. To quantify or parameterize the probability of occurrence of a continuous random variable, one can use a standard probability density function (pdf)
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From page 228... ...
In broad outline, Bulletin 17 characterizes flood occurrence at any location as a sequence of annual events or trials. The occurrence of multiple trials (floods)
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From page 229... ...
Given these annual exceedance probabilities, the probabilities of multiyear events, such as the occurrence of no exceedances during a specified design period, can be calculated as explained below. By considering only annual events, Bulletin 17 reduces the flood-frequency problem to the classical statistical problem of estimating the log-Pearson probability curve using a random sample consisting of the record of annual peak flows at a site.
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From page 230... ...
These two sample moments, along with a weighted average of the sample skewness coefficient and a regional estimate of the skewness coefficient, generally serve to define the estimated frequency distribution of the floods at a site. Several of the steps above pertain to special techniques and adjustments employed to deal with special cases, unusual flood values, and historical information.
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From page 231... ...
The approximate probabilities that various planning periods will be without exceedances of the 100-year flood are listed in Table D-1. Thus, there is only a 15 percent chance that a 200-year period will be free of exceedances of the 100-year flood.
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From page 232... ...
The following section considers whether statistical approaches are able to provide reliable and credible estimates of flood-frequency curves out into the 10,000- to 1,000,000-year event range. It would be useful if a reliable and credible estimate of the return period or, equivalently, the exceedance probability of a PMF could be obtained by analysis of rainfall-runoff processes.
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These considerations demonstrate the issues that must be addressed by an analysis that wouIc] assign return periods to extreme flood events.
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From page 234... ...
FREQUENCY ANALYSES FOR RARE FLOODS Bulletin 17 provides uniform procedures for estimation of floods with modest return periods, generally 100 years or less. Extrapolation much beyond the 100-year flood using flood-frequency relationships based on available 30- to 80-year systematic records is often unwise.
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From page 235... ...
On balance, statistical analysis of available records of annual flood peaks is unlikely to provide reliable and credible estimates of floods with return periods of the order of 104-106 years. 235 Use of Historical Flood Data Physical evidence and written records of large floods that have occurred in the recent and distant past provide objective evidence of the likelihood and frequency of larger floods beyond that provided by gaged flow records.
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From page 236... ...
is used to interpolate the damages associated with various flood flows between the flood flow values for which the corresponding damages have been estimated by flood routing and actual damage estimates. Once these two functions have been constructed, one can numerically integrate their product D(q jf~q)
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From page 237... ...
This can be done as described above. A Simple Example of Expected Damages In Appendix E, simple flood frequency and damage estimation models are presented along with the results of five cases that showed the expected annual damages depending on the characteristics of the project and the parameters of the models.
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From page 238... ...
] The probable maximum flood is assumed to be 120,000 cfs with a return period T of 104 or 106 years, and the 100-year flood (F = 0.99)
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From page 239... ...
In our example, if the flow ever exceeds the PMF, the damage will not depend on the particular dam and spillway design selected. Thus, the expected damages of interest are +~ 120,000 D— 10,000 [qc 10,000 120,~0 11 qc D(q)
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From page 240... ...
] The average annual damages depend on the damage function parameters M, L, and s;` the parameters of the flood flow frequency distribution r and qO (which in turn depend on the return period assigned to the PMF, T)
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