Application of Frequency and Risk in Water Resources

Flood risk is nature related. Flood uncertainty is investigation related. The former can be changed only by changing the characteristics of floods. The latter can be changed only by more observation and investigation. The question to be answered yet is whether or not there is a physical upper bound to flood magnitude. The concept of probable maximum precipitation (PMP) seems to imply that there is an upper bound to flood magnitude. Flood characteristics are estimated by one or more methods: frequency curves, transfer of information (joint probability), regional data, paleohydrology, Bayesian and PMF groups of methods. The contemporaneous aspects of analysis of flood characteristics are related to reliability of estimation of floods of small exceedence probabilities in the range 10-2 to 10-7, whether there is an upper bound to floods and whether it is feasible to attach a probability value to probable maximum flood (PMF). To eventually answer these basic questions, three investigations are needed: (1) study of properties of the upper tail of probability distributions of floods; (2) use of regional data for drawing either the envelopes of largest floods or the curves of average largest flood characteristics for given sample sizes in the region, with probabilities attached to these envelopes or average curves; and (3) finding of the composite probability of PMF by studying the aggregated probabilities of random variables which are “maximized” in the process of computing PMP and PMF. Flood characteristics change with time due to changes in river basins. The need exists for methods of estimation of flood characteristics over periods of time of 25–100 years, particularly for planning flood mitigation measures over an extended future.

Designs of most major dams and spillways are based on probable maximum floods (PMF). When properly estimated, PMFs provide the basis for confident sizing of spillway. There are, however, many factors which affect the estimation of a PMF. In analyzing each of these factors, certain assumptions have to be made and subjective judgements exercised. Depending on these assumptions and judgements, resulting PMF estimates may be quite different. This paper provides a brief summary of current practices in PMF estimation and application, and offers some guidelines for such practices. It also includes a comparison and discussion of PMF and risk-based analysis for spillway design.

Four heavy rainstorm systems resulted in extraordinary floods in China are presented. Each has its synoptic feature which are different from those of ordinary heavy rainstorms. There is a reason to believe that extraordinary floods and frequent and minor floods do not come from the same parent population. In addition to this, it is difficult to estimate the recurrence interval of historic floods. And therefore the outliers could hardly match the ordinary floods even if the historic floods are involved. Closely scrutinizing the features of the heavy rain storms, we find that Probable Maximum Precipitation and Flood (PMP/PMF) estimation is favorable compared with that of frequency analysis.

One of the major problems facing flood frequency analysis is that predictions typically require extrapolation beyond observed flood experience. Such extrapolations are very much affected by model and parameter uncertainty. This review reflects on the contributions that Bayesian theory has made, and can possibly make, in managing this uncertainty. Some of the issues examined from a Bayesian perspective include the choice of a flood distribution, the exploitation of gauged and historic site information possibly affected by measurement error, development of regional models and the pooling of site and regional information.

Two procedures are described that have been developed for the estimation of floods of very low probability as part of the revision of “Australian Rainfall and Runoff”, the guide to flood estimation in Australia published by The Institution of Engineers, Australia. A relatively simple procedure for interpolation of floods between the 1 in 100 flood and the PMF was developed after other procedures were shown to be unsatisfactory over a wide range of Australian data. Choice between flood estimates based on design rainfalls and flood frequency analyses is an important design decision. Guidelines for this choice were developed from the statistical characteristics of Australian flood and design rainfall data.

This paper presents the process of estimating the design flood for a large dam located in the equatorial region. The method applied was to estimate an exceptional synthetic storm and consequently, the corresponding hydrograph. Advantage was taken of techniques for evaluating storm potential, developed for temperate latitudes. The peak flow was computed as 28.500 m3/s. Because of limitations in the applied procedure it was not possible to assign probability level to this event.

This paper is based on the experiences accumulated from the actual design flood of more than eighty thousand reservoirs on main channel of medium and small basins. Most of these dams are earth dam, so that it is not permissible the water to flow over the dam. In China, the dam break is rarely due to the deviation error of design flood. Therefore, as a reference these experiences may be useful in actual design work. China is a developing country, most of the gaging stations were established from fifties, but, part of the raingage stations were established in early thirties, this is the reason why we like to use the design storm and then to transformed it into design flood.This paper will introduce the method of design storm (including it’s spatial and temporal distribution) and the method of transformation of design storm into design flood hydrograph. The conclusion of this paper is to introduce the crystalized experiences from many and many actual flood design works in medium and small basins. I’d very happy if something might be useful to the designers in other developing countries.

A new class of methods such as Smemax (Bethlahmy, 1977), Power Transformation (Chander et al., 1978), and Modified Smemax (Rasheed et al., 1982), has recently been developed for estimation of design flood using the approach of transforming the skewed distribution of observed data into normal distribution. It has been demonstrated that by these methods skewness practically in all cases reduces to a value very near to zero, but in many cases Kurtosis does not reduce to 3. To account for the effect of this residual Kurtosis,Chander et al. (1978) have recommended the use of a correction factor. These methods thus do not truly transform the skewed data into normal distribution. The complete transformation can be achieved by the proposed transformation called Two Step Power Transformation (TSPT), described in detail in the paper and it is demonstrated through its application in large number of cases that it is capable of converting flood data of any degrees, of skewness and kurtosis to a normal distribution. A comparison of the results of TSPT with those obtained by other methods has been made.

This paper highlights details of a study for estimation of flood magnitudes of different return periods for Narmada Sagar dam(India) using the partial duration series. The comparison of the efficiencies of annual and partial flood series has been given on the basis of exact theoretical approach and approximate theoretical approach. On the basis of exact theoretical approach it is seen that the partial flood series estimate of T year flood Q(T) (for any value of λ) always has a smaller sampling variance than that of the annual flood series for a return period T less than 11 years. For any return period the partial flood series estimate of Q(T) has a smaller sampling variance than annual flood series if the average number of peaks per year(λ) is at least 1.65. On the basis of approximate theoretical approach, it is observed that in the range of λ studied (1.0 to 2.437) the sampling variance of annual flood series is smaller than that of partial flood series.

The paper deals with the various approaches, methods, techniques and steps adopted in estimating the design flood or design floods for a reservoir project having limitations of data in respect of length, reliability and instrumentation. Two approaches of defining design floods, the physical or genetic approach and the statistical approach have been indicated. The various steps in PMF estimation, the deviations from standard techniques, the need for making the deviations and their rationale have been described in some detail in the paper. The exercise, carried out with respect to a World Bank assisted project in eastern India, serves to demonstrate practically suitable and theoretically justifiable procedures to be adopted in applying standard techniques in design flood computation in a case where the available data and information have various limitations. This case is typical in developing countries and hence the study may be of interest to project planners and designers in these countries.

In many engineering activities relating to floods one has to use a sample x₁… x_n of flood data along with a statistical distribution f(x) that approximately fits this sample, in order to estimate a particular extreme flood event x corresponding to a small probability of exceedance 1-p (return period T = l/(l-p)). Although one can never tell with certainty what is the true form of f(x) that represents the flood population, it is common practice to assume that one specific form applies, and to estimate its unknown parameters θ, …, θ_k from the sample values x₁,…, x_n. The precision with which the event (or “quantile”) x_p is estimated, depends on the accuracy with which the parameters of f(x) have been obtained. This precision can be quantified by constructing confidence intervals for x_p. Since these confidence intervals can contain valuable information, they should be calculated with as much accuracy as possible. In hydrology, however, practitioners have often used simple but inaccurate methods for calculating confidence intervals for x_p. The purpose of the present study is to draw attention to some relatively simple techniques found in the mathematical literature for calculating confidence intervals for x_p that give more accurate and better informative results than those commonly used in hydrology at present. We present in particular some useful techniques for obtaining confidence intervals for the quantiles of the normal (log Normal), Pearson (log Pearson), Weibull (Gumbel), and Exponential distributions. We also discuss the problem of constructing confidence intervals for x_p when x_p is estimated via the partial-duration-series approach, under the assumption that the distribution of the number of flood events arriving in an arbitrary time interval [0, t], is Poissonian, and that of the magnitude of flood events, is exponential.

For a more reliable estimation of design floods, it is necessary to take in account sampling and model uncertainties. A better control of the involved errors requires the use of all available informations, and especially we emphasize the importance of additional historical data. These data are essentially the more or less precise estimations of the few extreme events observed in the past before the regular observation of the river.In the first part of the paper we recall the way this information is integrated in the estimation process of classical parametric model such as partial duration curves. The results are associated with their approximate confidence intervals especially in the case of design flood discharges estimation. The involved approximations are now in progress and will be discussed. Moreover these confidence intervals constitute a first element for judging the quality of the fits of the models.In a more developped second part, we emphasize the importance of the non parametric estimation of probabilities (sometimes called empirical frequencies) taking in account additional historical information for the graphical validation of the model.The confidence intervals of these non parametric estimations are as important as the previous ones calculated with the parametric models. Both intervals constitutes the basis of a better tool for choosing the adequate probability distribution for floods on one hand, and a better appraisal of sampling and model uncertainties on the other hand.For illustration the described methods are applicated at two rivers.

The frequency analysis of annual peak flood data is considered to be one of the widely used methods for estimating frequency floods. The extra-apolation of frequency floods is generally avoided due to indadequate data available for such studies. In the present paper, an attempt has been made to study the amount of errors involved in extrapolation over sufficiently long periods by using short period series. In order to achive this aim, flood data available for six gauging stations with varying catchment areas and spread over different regions of the country (India) have been selected for studies and analysed by the most commonly used Gumbel’s extreme value distribution using Least Square Method and by Method of Maximum Likelihood. It has been found that the extent of error in exrapolation does not increase appreciably with the extent of extrapolation but corresponds to the error in selection of sample series. In order to estimate the frequency floods within an error of ±10%, about 50 years flood record may be essential.

A mathematical model of the discharge measurement error was proposed, verified and calibrated. On the basis of the model, theoretical effect of the error on the population parameters was analysed by analytic method and the sample effect of error on the results of frequency analysis was studied by Monte Carlo simulation. Results obtained show that in the absence of historical outlier, error effects are small and may be neglected if the magnitude of the error is of ordinary order. When a historical outlier is considered, the results of flood flow frequency analysis can be improved if the error parameter of the outlier is less than 0.3.

This paper emphasizes the important effect of historical flood on flood frequency analysis and points out that the considerable swayed range of the exceedance frequency of high extraordinary floods may bring about some difficulties for the upper fitting. The authors suggest that the representativity of computing series including observed and historical data be demonstrated through analysing the magnitude and frequency of high extraordinary flood which has occurred from further years to the present and the plotting position for the first terms in computing series calculated by use of the average return period so as to strengthen the stability of sample.

Limitations of uncertainty in estimating flood frequencies and means of minimizing the uncertainty are discussed. The value of reducing uncertainty by improved use of data is discussed in relation to risk of future flooding that cannot be eliminated or reduced except by structural measures. The value and uses of reliability criteria are much misunderstood. An arbitrary safety factor is infeasible, whereas the concept of expected probability is a logical result of considering uncertainties. This concept has been used to assess impacts of uncertainties in mean and variance of flood values. When it can be extended to include uncertainties in higher order moments, such as the skew coefficient, light might be shed on the reason why extreme events occur that are far beyond any reasonable expectation. Applications of flood frequency estimates in the flood insurance program and in general flood mitigation projects are discussed. Most important, stress is placed on the most fundamental use of flood frequency information — assessment of expected damages and benefits of all kinds for various alternative programs of flood management under all possible flood conditions.

This paper discusses the regulatory requirement of flood analysis as part of the licensing procedure of nuclear power plants. Flood analyses for three nuclear power stations which are representative of the coastal, estuarine, and inland sites are presented. The flood analyses include combinations of events, methodology, and results. Finally, the paper discusses the need for further research to balance the safety and economic goals of nuclear power plants.

Floods have been responsible for the damage or destruction of numerous forest road, channel, and water diversion structures. Some of the losses are to be expected because it is too costly to design for all circumstances. Other losses occur because of little or no flood design, debris accumulations, slope instability, and poor awareness and understanding of the problem. Presented are some applications of flood frequency and risk information in forest land management. Some of the problems of application are discussed. A simple approach to refine water resource records to meet local needs is included as a tool to check other flood analyses or provide design assistance.

Recently, considerable emphasis has been given to the problem of the state of decay in the nation’s infrastructure because of its importance to the needs of society and industrial growth. Large capital expenditures will be needed to bring the concerned systems to higher levels of serviceability. These systems include many types of hydraulic structures found in urban areas such as storm sewer systems, flood levees, water distribution systems, culverts, bridges, flood bypass tunnels, detention systems, etc. Conventional design methods for hydraulic structures basically fail to recognize and to systematically analyze and account for the effect of the various uncertainties that prevail in the design. Because of the existence of uncertainties, the hydraulic structure has an associated risk or probability of failure and an associated reliability or probability of not failing. There is much confusion among engineers in using the concepts and terms of uncertainties, risk, and reliability as applied to the design of hydraulic structures. For hydraulic structures subjected to the conveyance of flood waters, many engineers only think of the uncertainty of hydrologic events as being attributable to risk. For hydraulic structures such as water distribution systems, there is no universally accepted definition for risk or reliability. A great deal of work related to risk and reliability has been reported in the electronics, mechanical engineering, chemical engineering, and operations research literature; however, only a limited amount of work has been reported in the water resources literature. Several works have been reported dealing with hydrologic uncertainties and only a few works have been reported on the risk and reliability evaluation of hydraulic structures. The purpose of this paper is to review the work that has been done in the risk and reliability evaluation of hydraulic structures and to identify research areas that need to be explored.

The authors have presented the equi-risk line theory for storage facilities with the constant release rule. It is extended to be applicable to those with the following general storage-release relation: g = az′p, where g is the release discharge, and Z’ the volume of stored water. The release rule is characterized by the value of p. The shape parameter of the equi-risk line is expressed in terms of p. A standard equi-risk line for urban flood control systems is proposed, which can be applicable in common within a basin to calculate the necessary and sufficient capacities of any kind of flood control facilities, regardless of their location.

Risk in hydrological design is often based on the return period of the design flood. This measures the average interval between events and hence presents only a partial picture. A method of assessing financial risk is presented which recognises the potentially greater impact of flooding which occurs near the start of a project’s life or in proximity to a preceding flood. The fundamental concept is that of a flood-fighting fund. The fund starts with an initial capital which in time accrues interest. In years when flooding occurs the fund is depleted to pay for agricultural losses caused by the inundation. Attention focuses on the size of the capital sum which will reduce the risk of extinction of the fund to an acceptable level within some specified design horizon. The practical utility of the method will be illustrated using a recent UK case where floodplain storage was to be provided to alleviate downstream urban flooding. The financial risk concept was used to arrive at a fair level of compensation for occupants of the area to be flooded. Parallels are drawn with insurance risk and the further applicability of the technique to conventional flood protection schemes is discussed.

Two of the sources of uncertainty associated with the delineation of floodplains, those of estimation of design discharge and channel capacity, are examined via the joint probability distribution. The uncertainty of the channel capacity is determined using first-order uncertainty analysis of Manning’s equation. The variations of the flow area, wetted perimeter, and the friction slope, are expressed in terms of the variances of vertical, lateral, and longitudinal measurements. The variation of Manning’s n is characterized by a triangular distribution. The uncertainty information is used to derive confidence limits for the water surface elevation of a flood of a given return period for a channel. In a case study application to the Grand River, Ontario, the standard deviation due to the two sources of error was estimated as 0.50 meter.

The risk or probability of failure associated with a flood control project is a random variable, even if perfect information, rather than sample estimates of flood frequency are used for the design process. This paper presents procedures for the estimation of the expected value of this risk and its distribution where die flood control project has a finite operation period. Of interest are both the variability of the flood process during project operation and uncertainties inherent in the flood frequency estimation process. The traditional design procedure for flood control projects considers a finite project operation period, as far as the amortization of economic values is concerned. No analysis on the likely exceedance of the design magnitude during an actual run of events in a finite duration, is however considered. As far as the likelihoods of project failure are concerned, the project operation period is thus implicitly considered to be infinite. Design choices are likely to be quite different where the likelihood of project failure during a specified period (over a certain random set of future events) is considered. Where a finite operation period is considered and flood frequency relationships are estimated from annual maximum flow records, the probability of one or more exceedances of the design level is a function of the sample size for estimation and the length of the project operation period. General procedures in a Bayesian framework for the estimation of this probability are presented. Possible design implications are discussed.

The aim of this study is to establish the optimal flood control system accounted for the comprehensive criteria on the whole river basin. Especially, for the system consisted of multi-sub basins and multi-defense or reference points, we will examine the effects of the flood control projects on the flood inundation probability in time and space. Project planning is divided into two parts, such as the site and scale problems and the scheduling problem. They are formulated through the screening model, the simulation model and the sequential model in order to be optimized by using Experimental Planning Method, and Dynamic Programming, Branch-bound Method.

The decision making process regarding the issuance of flood watches and warnings often relies on the use of real-time flood forecasting models for watersheds. The floods predicted by these models are subject to uncertainties which may be significant for efficient operation of flood warning and preparedness systems. System reliability analysis offers a means to account for the uncertainties in the flood forecast in the form of occurrence probabilities for any flood level of interest. In this paper the advanced first-order second moment (AFOSM) reliability analysis method is used to analyze the uncertainties in a rainfall-runoff flood frequency model proposed by Eagleson (1972) and extended by Wood (1976) for an analytical derivation of the expected flood exceedance probability considering parameter uncertainty. Comparison of the results shows that the AFOSM method is a viable, reasonable, and practical method useful for hydrologic problems subject to uncertainties.

Effective flood plain management requires estimation of the costs and benefits of all contemplated projects. In this study the focus is on estimatig the benefits of such schemes. Starting from the similarity between flood flow and flood damage time series, the authors take a probabilistic approach to flood damage estimation. They first develop a hydroeconomic model to asses flood-related damages and then derive a damage distribution function by applying the theory of extreme values and the sum of the random variables to the estimated damage series. It is assumed that the values of extreme damages are independent and identically distributed over the time interval (0,t] of one year and one season simultaneously. The distribution function can then be used to estimate the benefits of flood plain management projects. The Richelieu River basin has been used for a numerical application because of its combined rural and urban characteristics and the fairly large amount of information acquired through previous studies.

The recognition and assessment of the hazard that flash floods can pose to structures located on alluvial fans is seriously deficient relative to the ability of the engineer to assess flood risk to structures located in the vicinity of perennial rivers. With the development of major urban areas and hazardous, radioactive, and mixed waste sites on alluvial fans in the southwestern United States, there is both an increasing need and interest in developing rational and reliable techniques for assessing the hazards floods pose to these developments and facilities.In this discussion, the three primary assumptions on which the assessment of flood hazard on alluvial fans are usually based are critically examined. Of these three assumptions, two are demonstrated to be reasonable based on a survey of the pertinent geologic and engineering literature and available field data while the third assumption which quantifies alluvial channel geometry during extreme flow events is shown to be invalid. A number of methods which may be used to predict alluvial channel geometry are discussed along with critical research needs.

The impact of urbanization resulted in serious flooding problems in the Beargrass Creek basin, which lies principally in the City of Louisville, Kentucky. The watershed is 60.9 square miles in size with the South Fork and Middle Fork as the two principal streams draining into the Ohio River. In order to mitigate the damage due to flooding, the U.S. Army Corps of Engineers, Louisville District undertook a study in 1973 to evaluate the existing and future flood damage potential in the watershed. Using the Clarks Instantaneous Unit Hydrograph approach and the rainfall events associated with the maximum annual flood events over the period of record (1941–1973), a flood-frequency analysis was carried out for both the present (1973) and future conditions (1990). Future flood conditions were simulated using projected Unit Hydrograph parameters and the historical rainfall record. The year 1990 was selected since the watershed is expected to be completely urbanized by that time. Backwater profiles were developed using Army Corps of Engineers HEC-2 program in order to establish flood elevation-frequency curves in selected reaches. Using this information, flood damage-frequency curves, both under existing and projected conditions, were derived.In order to provide flood protection in the Beargrass Creek basin, several structural and non-structural measures of flood control were examined in the study. A dry-bed reservoir located upstream on the South Fork, was recommended as the best alternative using a combination of economic, environmental, technical and social criteria. A comparison of the flood damage-frequency curves under modified conditions along the South Fork due to the dry-bed reservoir with similar curves under pre-development conditions is presented.

Flood risk bias introduced through the traditional method of flood frequency analysis can distort the assessment of flood insurance premium, the fair actuarial rate of flood insurance, even though the insurance payout is maintained the same. The extent of this statistical bias is examined through the concept of expected probability analysis.To assist in the analysis of flood risk bias, a multi-state: insurance is developed, based on some of the basic assumptions of the two-state insurance model developed by Lippman and McCall.

It is the Corps practice to design dams above populated areas to safely accommodate the largest flood considered physically possible. This magnitude of flood is refered to as the Probable Maximum Flood (PMF). The Corps existing dams are being evaluated to determine how safely they could accommodate inflow floods up to a PMF developed in accordance with todays standards. If it is found that failure of a dam could endanger peoples lives, a modification of the dam will be developed that would remove the threat to human life. Alternatives will be studied to determine the least costly modification that will meet the requirement, to not endanger lives. Economic analysis, that is comparing average annual benefits to average annual cost, will not be used as a basis for selecting the dam modification. Why economics is not considered to be an appropriate decision criteria is explained in some detail.

This paper briefly presents the Bureau of Reclamation’s philosophy and methodology in using risk-based analysis to select appropriate actions in its safety of dams program.

The Tennessee Valley Authority (TVA) is a government corporation established in 1933 with broad regional resource development responsibilities. In carrying out its responsibilities TVA has constructed dams and fossil and nuclear power plants, operates and maintains its dams including their safety evaluation, and maintains a program of floodplain management activities with communities, industries, and individuals. This paper describes the flood frequency and risk analysis procedures used by TVA in these activities. Discussed are (1) TVA’s conclusions about the most accurate methods to compute flood frequency at ungaged locations including use of limited site historic flood data obtained through TVA’s flood documenting activities, (2) the procedures and data used by TVA to estimate the PMF to ensure estimates are realistic and compatible with meteorological experience, (3) approaches TVA has used to define flood frequencies of extreme events up to and including the PMF, and (4) risk analysis as applied by TVA in community planning and dam safety evaluations. Recommendations as to additional procedures needed to enhance the engineer’s capability for improved flood frequency and risk analysis are made.

The Nuclear Regulatory Commission (NRC) (formerly the Atomic Energy Commission) has recognized the potential hazards resulting from the flooding of a commercial nuclear power plant. Indeed, the siting regulation (10 CFR 100) recognized floods as a natural hazard. Flooding of a great enough magnitude in some cases could cause loss of electrical controls, emergency cooling water pumps, diesel generators and other safety systems through mechanisms of inundation, impact forces, and erosion. In order to independently evaluate the potential for flooding at proposed reactor sites, the Atomic Energy Commission in 1968 contracted the U.S. Army Corps of Engineers and the U.S. Geological Survey to evaluate flooding potential at coastal sites and river sites, respectively. For river sites, the USGS often used statistical.

Flood frequency and risk analysis play a fundamental role in the insurance, floodplain management and hazard mapping aspects of the National Flood Insurance Program. This paper describes the analytic procedures commonly utilized in flood insurance studies of riverine and coastal floodplains in the United States. Consistency in flood frequency estimates over both time and space is needed to effectively administer the Program at national and local levels. Enhanced capability in risk analysis for flood-related hazards such as ice jams, erosion, levee failure, shifting channels, long term lake level fluctuations, and mudflows is also needed to support Program operations in these specialized hazard environments.

The National Weather Service does not have a direct role in studies concerning flood-flow frequency and risk analysis; however, it does take part in a number of areas that are of interest to such studies. NWS publications, as the primary source of probable maximum precipitation estimates and precipitation frequency studies in the United States, have long been recognized throughout the world. A brief summary of these subjects and NWS involvement in work groups assembled to resolve aspects of the flood frequency problem is presented here.

The U.S. Geological Survey is involved in several flood-related activities as part of its mission to monitor the Nation’s water resources. This paper describes techniques and approaches utilized in (1) archiving flood data, (2) analyzing flood data at gaging stations, (3) documenting extreme floods, (4) estimating flood-peak discharges at ungaged sites, (5) estimating flood-peak depths at ungaged sites, and (6) developing flood-hazard maps. A brief description of the future direction of flood-frequency analysis within the U.S. Geological Survey is also given.

The Federal Energy Regulatory Commission, formerly the Federal Power Commission, has been in dam safety regulation since 1920. As of October 1, 1985, there were about 2,050 dams under our jurisdiction. Almost all of our spillway inflow design floods creep higher and higher with passing years. Mathematical probability methods provide no guidance to the shape and magnitude of the hydrographs of rare floods which would be substantially above the measured data. Risk analysis should include the probability of engineering, administrative, or other human error. Therefore, we require that the adequacy of both new and existing dams be evaluated by considering the hazard potential which would result from failure of the project works during flood flows. If structural failure would present a hazard to human life or cause significant property damage, the dam must withstand the loading or overtopping which may occur from a flood up to the probable maximum (risk analysis that involves loss of life is not permitted). We do in most cases, allow the dam owner to use risk analysis, if the failure will not cause loss of life or significant property damage.