FEASIBILITY OF ASSIGNING A PROBABILITY TO THE PROBABLE MAXIMUM FLOOD Prepared by the U.S. Geological Survey in cooperation with U.S. Army Corps of Engineers National Weather Serivce, Bureau of Land Management, Bureau of Reclamation, National Park Service, Federal Energy Regulatory Commission, Nuclear Regulatory Commission, Tennessee Valley Authority, University of Maryland (consultant to Soil Conservation Service) 1986 TABLE OF CONTENTS Executive summary I. Introduction     A. Purpose and authority     B. Background     C. Evolution of flood hydrology methods     D. Statistical considerations in flood hydrology     E. Comparison of computed PMF's with extreme observed floods II. Review of proposed methods     A. Extrapolation of the frequency curve         1. Description of methodology         2. Variations among papers         3. Verification of methodology         4. Evaluation     B. Joint probability         1. Description of methodology         2. Variations among papers         3. Verification of methodology         4. Evaluation     C. Regional data methods         1. Description of methodology         2. Variations among papers         3. Verification of methodology         4. Evaluation     D. Paleohydrology methods         1. Description of methodology         2. Variations among papers         3. Verification of methodology         4. Evaluation     E. Bayesian techniques         1. Description of methodology         2. Variations among papers         3. Verification of methodology         4. Evaluation III. Conclusions     A. Probability assignment to PMF     B. Probability to rare floods less than the PMF IV. References Appendix A. Deterministic approach     A. PMF estimates         1. Probable maximum precipitation         2. Infiltration and other losses         3. Conversion of rainfall to runoff Appendix B. Statistical approach     A. Probability, frequency, and recurrence interval     B. Annual frequency analysis     C. Problems in application         1. Data availability and adequacy         2. Random-sampling fluctuations         3. Distributional uncertainty Appendix C. Comparison of PMF with envelope curves Appendix D. Glossary of terms ABSTRACT A Work Group was formed in mid-1984 by the Hydrology Subcommittee of the Interagency Advisory Committee on Water Data to investigate two specific questions: 1. Is it within the state of the art to calculate the probability of the probable maximum flood (PMF) within definable confidence or error bounds? 2. If the probability of the PMF cannot be defined, how far out on the probability scale can flood probability be determined within definable confidence or error bounds? In addressing these two questins, the Work Group further defined their charge as follows: Estimation of the probability of the PMF was interpreted as estimation of the probability of a flood of specified magnitude of the same order of magnitude as the PMF, regardless of how determined. State of the art was interpreted to mean methods documented in articles dealing directly and explicity with probabilities of extreme floods that had been published in a form reasonably accessible to the hydrologic and/or engineering professions. Definable confidence or error bounds was interpreted to mean there must be an objective observational or experiential basis upon which the assignment of bounds is based. No recommendation on methods to use would be provided unless reliable, consistent, and credible methods are identified that have been systematically tested. The Work Group conducted a survey of over 230 papers and reports from both technical journals and project reports of engineering studies pertaining to the broad topic of large flood events. The statistical literature and this study emphasize the peak discharge of floods, however, volume and duration estimates are sometimes of interest, and the same considerations that prevent assessment of the accuracy of peak flow frequency estimates also apply to volume and duration estimates. The methods found in the literature were separated into five categories: (1) extrapolation of a frequency curve based on gaged records; (2) regional analyses; (3) joint probability analyses; (4) paleohydrologic analyses; and (5) Bayesian analyses. In effect, the regional, joint probability, and paleohydrologic analyses are part of extension of the frequency curve in that they provide additional information to extend the frequency curve. Extrapolation of the frequency curve is limited to developing a frequency curve from gaging station data and extending it without benefit of additional information to define the probability of the PMF. Two types of errors affect the accuracy of such an extrapolation: (1) random-sampling errors and (2) distributional errors. Although random-sampling errors may be large for rare hydrologic events, error or confidence bounds for these errors can be defined. Distribution errors which affect the right tail of the frequency curve can also result in large errors. However, these errors have not been described in terms of definable error or confidence bounds. Because this error source cannot be evaluated, it is not possible to define the overall accuracy of extrapolated flood estimates. The joint probability method recognizes that floods result from interactions among assumed independent probabilistic causative factors. The probability of a flood is the sum of the joint probabilities associated with all the possible combinations of factors which result in that flood. The reliability of these methods depends on the accuracy or validity of the probabilities of the causative factors. None of the papers reviewed claimed to be capable of estimating the probability of the PMF. Regional methods attempt to counteract the sampling fluctuations in individual station records by combining records at several sties in a homogeneous region in order to establish a common flood-frequency relation applicable to all sites in the region. The regional data methods reviewed here are all severely limited in their application to PMF risk assessment by the quantity of data available. The station-year method can furnish information about recurrence intervals greater than the length of individual records but because of dependence among stations, effective station-year record lengths are limited to a few hundred to 1,000 station-years. The paleohydrology method involves the study of sediment deposits and other geomorphic features to define flood levels from which flow estimates can be made. Radiocarbon dating of matter in the deposits is used to define the flood date. Therefore, this method allows for an evaluation of major flood events over the past hundred to thousands of years, and may provide guidance on extending the frequency curve beyond the range of the gage record. Bayesian analysis is a method for combining different sources of flood information. For longer record stations (>20 years), use of a secondary data source (regional flood information, subjective judgment, or expert opinion) does not substantially improve the overall accuracy of flood estimates. Bayesian analysis by inself does not generate any information about assigning probabilities to extreme events and does not make significant contributions to defining confidence intervals on flood probabilities. The Work Group's conclusions about defining the probability of the PMF as based on a review of the literature are summarized as follows: It is not within the state of the art to calculate the probability of PMF-scale floods within definable confidence or error bounds. There is no definable point on the probability scale at which it becomes impossible to define error bounds on flood magnitude and probability estimates. Rather, an analysis displays a gradual transition from common place events, whose estimation errors can be defined by statistical random-sampling theory, to unprecedented events, whose errors cannot be defined. Many professionals believe this transition begins at recurrence intervals of about twice the record length and is complete by recurrence intervals in the general area of about 1,000 years. The Work Group finds on reason to contradict these general perceptions. LizardTech's Djvu plug-in is needed to view these reports. CLICK HERE TO VIEW THE ENTIRE REPORT For questions or comments, contact K. Van Wilson.