Flood Frequency Estimation Research Articles

Split sampling technique for selecting a flood frequency analysis procedure

The use of a split sampling technique for selecting a flood frequency analysis procedure is discussed in detail with the aid of simulation experiment results. Although this technique is unable to identify the most likely statistical distribution which generated given flood data, it is demonstrated that it provides useful results with which to compare the relative merits of different flood frequency estimation procedures.

A hierarchical approach to regional flood frequency analysis

A hierarchical approach to regional flood frequency estimation is described, where higher‐order parameters controlling the skewness of annual maximum floods are determined from larger regions than are used for determining parameters controlling the coefficient of variation. Procedures based on two‐component extreme value and generalized extreme value distributions are developed, and it is shown that dividing a region into subregions to estimate some parameters can lead to more precise quantile estimates. The practical problem of defining the optimum number of subregions is discussed.

Maps of flood statistics for regional flood frequency analysis in New Zealand

Abstract The two-parameter EV1 distribution adequately describes New Zealand's flood series. Contour maps of [Qbar]/A0.8 and Q100[Qbar] are presented, where [Qbar] is the mean annual flood, A is the basin area and Q100 is the 1% annual exceedance probability flood. The maps are based directly on measured discharge series from a large sample of river recording stations. Thus when basins are ungauged, or have just a short record, an estimate of a design flood QT with specified annual exceedance probability (1/T) can be obtained using map estimates of [Qbar]/A0.8 and Q100[Qbar], without having first to estimate rainfall statistics for the basin, a particularly difficult task in sparsely instrumented mountainous areas. These maps succinctly summarize a great deal of hydrological information and permit improved flood frequency estimates.

Discussion of “ Expected Annual Damages and Uncertainties in Flood Frequency Estimation ” by Nigel W. Arnell (January, 1989, Vol. 115, No. 1)

Discussion of “ <i>Expected Annual Damages and Uncertainties in Flood Frequency Estimation</i> ” by Nigel W. Arnell (January, 1989, Vol. 115, No. 1)

Bias in log-transformed frequency distributions

Estimates of the parameters of frequency distributions are often derived from the logarithms of a series of measured data rather than from the original series itself. This is common practice, for example, in estimating flood frequencies from measured streamflow data, extreme wave frequencies from wave height data, as well as in many other contexts. This procedure leads to biased estimates of the moments and quantiles of the frequency distribution in arithmetic space. This bias is the result of the non-linear inverse transformation process. The case of the two parameter lognormal distribution is examined in detail and analytical expressions for the bias are derived. The bias introduced by the logarithmic transformation is dependent on the sample size and the population parameters. The derived analytical expressions for bias agree with the results of a series of Monte Carlo simulations.

Paleohydrologic techniques used to define the spatial occurrence of floods

Defining the cause and spatial characteristics of floods may be difficult because of limited streamflow and precipitation data. New paleohydrologic techniques that incorporate information from geomorphic, sedimentologic, and botanic studies provide important supplemental information to define homogeneous hydrologic regions. These techniques also help to define the spatial structure of rainstorms and floods and improve regional flood-frequency estimates. The occurrence and the non-occurrence of paleohydrologic evidence of floods, such as flood bars, alluvial fans, and tree scars, provide valuable hydrologic information. The paleohydrologic research to define the spatial characteristics of floods improves the understanding of flood hydrometeorology. This research was used to define the areal extent and contributing drainage area of flash floods in Colorado. Also, paleohydrologic evidence was used to define the spatial boundaries for the Colorado foothills region in terms of the meteorologic cause of flooding and elevation. In general, above 2300 m, peak flows are caused by snowmelt. Below 2300 m, peak flows primarily are caused by rainfall. The foothills region has an upper elevation limit of about 2300 m and a lower elevation limit of about 1500 m. Regional flood-frequency estimates that incorporate the paleohydrologic information indicate that the Big Thompson River flash flood of 1976 had a recurrence interval of approximately 10,000 years. This contrasts markedly with 100 to 300 years determined by using conventional hydrologic analyses. Flood-discharge estimates based on rainfall-runoff methods in the foothills of Colorado result in larger values than those estimated with regional flood-frequency relations, which are based on long-term streamflow data. Preliminary hydrologic and paleohydrologic research indicates that intense rainfall does not occur at higher elevations in other Rocky Mountain states and that the highest elevations for rainfall-producing floods vary by latitude. The study results have implications for floodplain management and design of hydraulic structures in the mountains of Colorado and other Rocky Mountain States.

A comparison of regional flood frequency estimation methods using a resampling method

Most comparisons of flood frequency estimation methods have been based on Monte Carlo simulation. An alternative method which does not require the choice of a parent distribution is to resample from the historical record. The relative performance of 10 flood frequency estimation methods, including four at‐site methods, four regional index flood methods, and two variations of the U.S. Water Resources Council regional method, was evaluated using a resampling method. Performance measures were based on two statistics. The first was a flood damage surrogate, which was defined as a power of the excess of the flood peak over a fixed threshold approximately equal to the median annual flood; the second was the estimator of the 100‐year flood. For each subsampling of the historical record, the expected flood loss and 100‐year flood quantile conditioned on the estimated parameters were computed. From the remainder of the record, an empirical estimate of the mean damage was computed. The performance of the methods is summarized in terms of the mean and variance of the difference between the conditional expectation and the empirical damages, and the variance of the 100‐year flood estimates. The results are qualitatively similar to those reported in earlier Monte Carlo studies. The U.S. Water Resources Council method, in particular, produced variability in the damage estimates that was much greater than that for any of the index flood methods tested. Estimates of the 100‐year flood were about twice as variable on average as 100‐year flood estimates obtained using any of the regional index flood methods. For the Wisconsin and New England flood records tested, the regional Generalized Extreme Value estimators yielded 100‐year flood estimates with lower variability at virtually all sites than the U.S. Water Resources Council method.

Flood Frequency Analysis for the 1988 Truro Floods

ABSTRACTIn January 1988 the city of Truro experienced a severe flood from the River Kenwyn. The return period of this event was initially estimated at 350 years using the methodology recommended in the Flood Studies Report1. In October of the same year a second flood, of even greater magnitude, occurred. The subsequent investigations employed a variety of flood frequency estimation techniques including one which uses descriptive information on the history of flooding, obtained from local newspapers and journals, in addition to recent flow records. The return periods of the two events were reassessed to be 50 and 100 years respectively. This flood frequency behaviour was found to be markedly different from the regional average for the South West of England.

Expected Annual Damages and Uncertainties in Flood Frequency Estimation

The expected annual damge is the most frequently used index of the impact of flooding at a site. However, estimates of expected annual damages are very uncertain as a result of uncertainties in both the estimation of the flood frequency relationship from limited data and the relationships between magnitude and damage. Computer simulation experiments using synthetic flood peak data and fixed magnitude‐damage functions have shown that the sampling distribution of estimates of expected annual damages is highly skewed to a degree depending on the form of the damage function, and most importantly, that bias in the estimates is most closely related to error in the estimated probability at which damage begins. The use of expected probability leads to a very significant increase in bias in the estimation of expected annual damages.

Reply [to “Comment on “Nonparametric Kernel Estimation of flood frequencies” by Kaz Adamowski”

Reply [to “Comment on “Nonparametric Kernel Estimation of flood frequencies” by Kaz Adamowski”

Comment on “Nonparametric Kernel Estimation of flood frequencies” by Kaz Adamowski

Comment on “Nonparametric Kernel Estimation of flood frequencies” by Kaz Adamowski

Problems in statistical treatment of flood series

This paper discusses some common hydrologic problems in the statistical treatment of flood series associated with the calculation of flood frequency. These problems are: (1) the assumptions used in flood frequency estimation; (2) the moment method and the moment-calculation error; (3) the application of the empirical frequency formula to extraordinary floods; (4) individual curve fitting method; (5) sampling error; (6) computation of combined frequencies; and (7) frequency estimation in the presence of zeros in the series. In addition, other problems, such as the accuracy of statistical calculations, the combination of hydrologic events and the reasonableness of derived results, are discussed.

Probability plotting position formulas for flood records with historical information

For purposes of evaluating fitted flood frequency distributions or for purposes of estimating distributions directly from plots of flood peaks versus exceedance probabilities (either by subjective or objective techniques), one needs a probability plotting position formula which can be applied to all of the flood data available: both systematic and historic floods. Some of the formulas in use are simply extensions of existing formulas (such as Hazen and Weibull) used on systematic flood records. New plotting position formulas proposed by Hirsch and Stedinger (1986) and in this paper are based on a recognition that the flood data arises from partially censored sampling of the flood record. The theoretical appropriateness, bias in probability and bias in discharge of the various plotting position formulas are considered. The methods are compared in terms of their effects on flood frequency estimation when an objective curve-fitting method of estimation is employed. Consideration is also given to the correct interpretation of the historical record length and the effect of incorrectly assuming that record length equals the time since the first known historical flood. This assumption is employed in many flood frequency studies and may result in a substantial bias in estimated design flood magnitudes.

Paleoflood hydrology and extraordinary flood events

Paleoflood hydrology is the study of past or ancient flood events. The most accurate technique involves the analysis of slackwater deposits and paleostage indicators (SWD-PSI). Slackwater deposits are sand and silt emplaced from suspension in exceptionally deep, high-velocity floods that characterize narrow, deep canyons in resistant geologic materials. These and other paleostage indicators are used to establish hydraulic grade lines for the generating flow events. Favorable sites for slackwater deposition include channel-margin areas where stresses and velocities are reduced below critical values necessary to maintain fine-grained bedload material (sand and silt) in suspension. Computerized procedures for hydraulic flow modeling are used to tie the elevations of the highest slackwater deposits to surveyed river cross sections. The flood discharges calculated by this method can be calibrated through the study of modern floods on gaged rivers. Correlation of multiple SWD-PSI sites along a river reach is used to identify the maximum paleostage achieved by a given flood. Advances in the dating of flood deposits permit estimates of flood frequency to be made extending over a data base of thousands of years. The major geochronologic tool is radiocarbon dating of various kinds of organic matter intercalated with the slackwater deposits. An important development is the use of the tandem accelerator mass spectrometer for direct measurement of 14C. Tiny blebs of charcoal, seeds and other organics can be analyzed in order to date ancient flood deposits of hydrologic significance. Since SWD-PSI studies yield very accurate determinations of paleoflood ages and magnitudes, there is a pressing need for new statistical procedures that make optimum use of the information content in paleoflood records for flood-frequency analysis. Nevertheless, SWD-PSI paleoflood hydrology has moved beyond the research phase; its use should be encouraged in evaluating past experience of extraordinary floods at appropriate hazardous sites.

Flood Frequency Estimates in Southeastern Arizona

The effect of the October 1983 floods in southeastern Arizona, on a previously established generalized envelope for floods expected once in 100 years (Q100), is studied. The design envelope is found to produce more conservative estimates of Q100 than individual data sets find. The design envelope for Q100 is revised to correct for some longer periods of record now available, and to be consistent with floods on a wider range of drainage area than previously considered. Additional design envelopes for floods expected once in 2 years (Q2) and once in 10 years (Q10) are prepared, and the three envelopes are used to provide conservative estimates of flood frequencies on ungaged watersheds in southeastern Arizona with drainage areas between 0.01km2 and 10,000km2. A procedure is presented for developing regional flood frequency estimates that could be used in geographically and climatically homogeneous areas.

Estimation of flood frequency: An evaluation of two derived distribution procedures

The derived distribution approach for predicting flood frequency distributions provides a potentially attractive way to analyze flood hazards in ungaged watersheds. This paper examines the performance of two typical derived distribution techniques (Hebson and Wood, 1982; Diaz‐Granados et al., 1984). Flood frequency distributions obtained with each technique are compared to sample distributions estimated from measured discharge records. The comparison is based on over 40 years of discharge data from each of three different watersheds. Input parameters required by the derived distribution methods are estimated from limited data sets to simulate conditions encountered in watersheds where rainfall and discharge records are available for only a few years. Both of the derived flood frequency methods performed poorly in every watershed when compared to sample distributions. The results of the comparison suggest that fundamental improvements are needed before the derived distribution approach can be applied with any confidence.

The generalized method of moments as applied to problems of flood frequency analysis: Some practical results for the log-Pearson type 3 distribution

The log-Pearson type 3 distribution is widely used in North America and Australia for fitting annual flood series. Four different versions of the method of moments used in fitting this distribution are compared using Monte Carlo simulated samples which reflect some of the characteristics of annual flood series observed at some Canadian rivers. The bias, standard error, root mean square error, and skew, of the parameter estimates, and of estimates of events associated with different probabilities of occurrence are examined. Also examined are the correlation coefficients between probabilities of occurrence are examined. Also examined are the correlation coefficients between the parameter estimates and between the sample moments that are used in each of the four methods of estimation. It is observed that variances, covariances and correlation coefficients calculated using the usual first-order asymptotic approximation might have considerable error and therefore should be used with caution. On the basis of mean square error of events with return period above the range covered by the sample it is observed that a method proposed earlier ★ ★ Bobée (1975). which uses moments of order 1, 2 and 3 in real space performs better than the other three methods although certain of the other methods follow the recommendation put forward by some investigators that higher order moments (moments of order 3 or more) should be avoided in flood frequency estimation. It is argued in the present study that the use of higher order moments should not be avoided simply because they have high variability because it is not only the variability of the moments which determines the degree of variability of the estimated design flood events but also the correlation that exists between these moments. Some recommendations are given at the end of the study aimed at achieving better efficiency in flood frequency research at a period where more and more distributions and methods of estimation are being proposed.

Effect of regional heterogeneity on flood frequency estimation

Recent work on regional flood frequency estimation has shown that accurate flood quantile estimates are possible when the underlying flood frequency distributions are identical at all sites in the region except for a scaling factor, particularly when the underlying distribution has a two‐parameter form. The class of regional probability‐weighted moment (PWM) estimators is investigated for robustness to mis‐specification of the assumed distributional form and to regional heterogeneity in moments of order higher than one. Whereas two‐parameter distributions belonging to the extreme value family perform quite well when the form of the underlying distribution is close to that of the fitted distribution, large biases can result when the distribution is misspecified. The three‐parameter generalized extreme value distribution (GEV), when fitted using the regional PWM method, has been shown to be relatively insensitive to violations of the distributional assumption, and to have low variability and bias. In this paper it is shown that regional estimation methods using the three‐parameter GEV distribution are relatively insensitive to modest regional heterogeneity in the coefficient of variation and quite insensitive to regional variation in the skew coefficient. The key determinant of the performance of the regional estimators is shown to be the regional mean coefficient of variation. For high values of the mean coefficient of variation, such as might be encountered in arid regions, an alternate PWM estimation method based on the GEV distribution that accommodates the regional heterogeneity in the higher order moments is preferred. The trade‐off between this alternate method and the approach that assumes regional homogeneity in moments higher than order one is sensitive to the record lengths.

Flood frequency estimation in Scotland using index floods and regional growth curves

ABSTRACTThe index flood/regional growth curve method is the most commonly used procedure for estimating a design flood at an ungauged site in the United Kingdom when only the instantaneous peak discharge is required. This paper summarises recent work in Scotland in which the authors have refined the equations for estimating the index flood from the physical characteristics of the drainage basin and have proposed new methods for classifying basins to increase the hydrological homogeneity of the regions on which the growth curves are based. A new algorithm for estimating regional growth curves is reported which allows for correlation between flood magnitude at different sites. Simulation experiments are described which highlight the consequences of the data failing to meet the assumptions of the models used.

Flood Frequency Analysis Using the Cox Regression Model

Procedures for incorporating time‐varying exogenous information into flood frequency analyses are developed using the Cox regression model for counting processes. In this statistical model the probability of occurrence of a flood peak in a short interval [t, t + dt) depends in an explicit manner on the values at t of k “covariate” processes Z1, …, Zk. Specifically, letting dN(t) be 1 if a flood peak occurs in [t, t + dt) and 0 otherwise, dN(t) = a(t) exp {∑j=1kbjZj(t)} + dM(t) where a, the “baseline intensity,” is an unknown function, b is a vector of unknown “regression” parameters, and the error dM(t) is (conditionally) orthogonal to the past history. Two applications, assessment of relative importance of physical processes such as snow melt or soil moisture storage on flood frequency at a site and derivation of time‐varying flood frequency estimates, are considered.