Flood Frequency Studies Research Articles

Proposal of the ‘extreme rank plot’ for extreme value analysis: with an emphasis on flood frequency studies

AbstractTo assess model ‘fit’ for flood frequency studies, the annual maximum flow sample is often plotted alongside the frequency curve in an extreme value plot. The comparison is ill advised because a value is speculatively assigned for each rank, in the form of a frequency (the plotting positions); in which case a model of the frequencies is being used to assess a frequency model. The modelled and observed, with attributed plotting positions, are incommensurable. The proposed method in this paper does not attempt to provide a frequency attributed to the ranks and instead attributes ranks to the model under investigation. If the model is used to simulate thousands of samples of the same size as the observed, a distribution of possible peak flow values for each rank can be obtained. For each simulated sample, descriptive statistics can be derived. In this way, statistical testing can be undertaken to compare the observed with the modelled. Using such methods, two or more models can also be compared. Examples are provided for Flood Estimation Handbook pooling and continuous simulation models along with a comparison of the two.

Robust flood frequency analysis: Performance of EMA with multiple Grubbs‐Beck outlier tests

AbstractFlood frequency analysis generally involves the use of simple parametric probability distributions to smooth and extrapolate the information provided by short flood records to estimate extreme flood flow quantiles. Parametric probability distributions can have difficulty simultaneously fitting both the largest and smallest floods. A danger is that the smallest observations in a record can distort the exceedance probabilities assigned to the large floods of interest. The identification and treatment of such Potentially Influential Low Floods (PILFs) frees a fitting algorithm to describe the distribution of the larger observations. This can allow parametric flood frequency analysis to be both efficient, and also robust to deviations from the proposed probability model's lower tail. Historically, PILF identification involved subjective judgement. We propose a new multiple Grubbs‐Beck outlier test (MGBT) for objective PILF identification. MGBT PILF identification rates (akin to Type I errors) are reported for the lognormal (LN) distribution and the log‐Pearson Type III (LP3) distribution with a variety of skew coefficients. MGBT PILF identification generally matched subjective identification from a recent California flood frequency study. Monte Carlo results show that censoring of PILFs identified by the MGBT algorithm improves the extreme quantile estimator efficiency of the expected moments algorithm (EMA) for negatively skewed LP3 distributions and has little effect for zero or positive skews; simultaneously it protects against deviations from the LP3 in the lower tail, as illustrated by distorted LN examples. Thus, MGBT generally makes flood frequency analysis based on the LP3 distribution with EMA both more accurate and more robust.

Reducing uncertainty in flood frequency analyses: A comparison of local and regional approaches involving information on extreme historical floods

Summary This paper proposes a detailed comparison of local and regional approaches for flood frequency analyses, with a special emphasis on the effects of (a) the information on extreme floods used in the analysis (historical data or recent extreme floods observed at ungauged sites), and (b) the assumptions associated with regional approaches (statistical homogeneity of considered series, independence of observations). The results presented are based on two case studies: the Ard e che and Argens rivers regions in south-east of France. Four approaches are compared: 1 – local analysis based on continuous measured series, 2 – local analysis with historical information, 3 – regional index-flood analysis based on continuous series, 4 – regional analysis involving information on extremes (including both historical floods and recent floods observed at ungauged sites). The inference approach used is based on a GEV distribution and a Bayesian Monte Carlo Markov Chain approach for parameters estimation. The comparison relies both on (1) available observed datasets and (2) Monte Carlo simulations in order to evaluate the effects of sampling variability and to analyze the possible influence of regional heterogeneities. The results indicate that a relatively limited level of regional heterogeneity, which may not be detected through homogeneity tests, may significantly affect the performances of regional approaches. These results also illustrate the added value of information on extreme floods, historical floods or recent floods observed at ungauged sites, in both local and regional approaches. As far as possible, gathering such information and incorporating it into flood frequency studies should be promoted. Finally, the presented Monte Carlo simulations appear as an interesting analysis tool for adapting the estimation strategy to the available data for each specific case study.

Usefulness of historical information for flood frequency analyses: Developments based on a case study

This paper illustrates how historical information on floods can be retrieved in the a priori unfavourable case of small and sparsely populated catchments, and how this information can improve the estimation of flood discharge quantiles. It is based on the analysis of four small gauged rivers located in the south of France. Using various sources of archives, the flood discharges were estimated for past historical periods ranging from 100 to 200 years. The corresponding historical discharge series were then used in combination with the available systematic measurement series to evaluate peak discharge quantiles. The selected Bayesian Monte Carlo Markov Chain statistical inference approach provides credibility intervals for the estimated quantiles, the width of which reflects the information content of the data set used for the inference. The use of the historical data in the inference procedure leads to significant reductions of these credibility intervals, even if limitations in the content of historical inventories are introduced. A sensitivity analysis is conducted in the second part of the paper to evaluate to what extent these positive conclusions on the added value of historical data for flood frequency analysis can be extrapolated to other case studies. The influence of the number of historical floods documented (perception threshold) and of the level of knowledge of historical flood peak discharges is studied. The results are consistent with the previous works on the same issue and explain why these works led to apparently contradictory conclusions concerning the possible usefulness of historical data in flood frequency studies.

Bayesian MCMC approach to regional flood frequency analyses involving extraordinary flood events at ungauged sites

summary This paper proposes a method for using major flash flood events occurred at ungauged catchments to reduce the uncertainties in estimating regional flood quantiles. The approach is based on standard regionalization methods assuming that the flood peak distribution rescaled by a site-dependent index flood is uniform within a homogeneous region. A likelihood formulation and a Bayesian Markov Chain Monte Carlo (MCMC) algorithm are used to infer the parameter values of the regional distributions. This statistical inference technique has been selected for its rigorousness – various hypotheses are explicitly formulated in the likelihood function, its flexibility as for the type of data that can be treated, and its ability to compute accurate estimates of the confidence intervals for the adjusted parameters and for the corresponding flood quantiles. The proposed method is applied to two data sets from Slovakia and the South of France that consist of series of annual peak discharges at gauged sites and estimated peak discharges of extreme flash flood events that have occurred at ungauged sites. The results suggest that the confidence intervals of the quantiles can be significantly narrowed down provided that the set of ungauged extremes is the result of a comprehensive sampling over the selected region. This remains valid, even if the uncertainties in the estimated ungauged extreme discharges are considered. The flood quantiles estimated by the proposed method are also consistent with the results of site specific flood frequency studies based on historic and paleoflood information.

A comparative flood frequency study of Ganga and Brahmaputra river systems of north India — a brief appraisal

An attempt has been made to study the occurrence of floods in the two important river systems of north India, viz. Brahmaputra and Ganga. Both these river systems are located north of Lat. 22°N and lie in the longitudinal belt of north India from Long. 73°E to 97°E. Both these river systems are affected by floods during monsoon months of June–September. It has been seen after examining rainfall and floods of the period 1986–1999 that although variation of monsoon rainfall magnitudes received by these two basins differ considerably in each monsoon season, but by and large, the frequency of floods at their terminal gauge/discharge (G/D) sites at Dhubri and Farakka do not differ very much from each other.

An algorithm for computing moments‐based flood quantile estimates when historical flood information is available

This paper presents the expected moments algorithm (EMA), a simple and efficient method for incorporating historical and paleoflood information into flood frequency studies. EMA can utilize three types of at‐site flood information: systematic stream gage record; information about the magnitude of historical floods; and knowledge of the number of years in the historical period when no large flood occurred. EMA employs an iterative procedure to compute method‐of‐moments parameter estimates. Initial parameter estimates are calculated from systematic stream gage data. These moments are then updated by including the measured historical peaks and the expected moments, given the previously estimated parameters, of the below‐threshold floods from the historical period. The updated moments result in new parameter estimates, and the last two steps are repeated until the algorithm converges. Monte Carlo simulations compare EMA, Bulletin 17B's [United States Water Resources Council, 1982] historically weighted moments adjustment, and maximum likelihood estimators when fitting the three parameters of the log‐Pearson type III distribution. These simulations demonstrate that EMA is more efficient than the Bulletin 17B method, and that it is nearly as efficient as maximum likelihood estimation (MLE). The experiments also suggest that EMA has two advantages over MLE when dealing with the log‐Pearson type III distribution: It appears that EMA estimates always exist and that they are unique, although neither result has been proven. EMA can be used with binomial or interval‐censored data and with any distributional family amenable to method‐of‐moments estimation.

A technique for selecting the Box–Cox transformation in flood frequency analysis

In hydrology, the Box–Cox power normal transformation has been found to perform well in a number of at-site and regional flood frequency studies. In this paper, an alternative to the maximum likelihood method of finding the Box–Cox transformation parameter, λ, is suggested. The proposed method is based on finding the λ that maximizes the correlation coefficient in the probability plot correlation coefficient test for normality. The proposed method of finding λ was tested on maximum daily discharge data from all over Canada and was found to give almost identical results to that obtained by the method of maximum likelihood. The main advantage of the proposed method is that finding the appropriate transformation and objectively testing whether the transformed data are normally distributed can be done in one step. In other methods, at least two steps are required. In addition, the proposed method makes use of techniques that are familiar to the hydrologist, namely, the probability plot and correlation analysis. Key words: flood frequency analysis, Box–Cox transformation, probability plotting, maximum likelihood method, Blom's plotting position, probability plot correlation coefficient test, correlation analysis, normal distribution.

On the transposition of areal reduction factors for rainfall frequency estimation

The meaning and significance of areal reduction factors in the estimation of areal rainfall for flood frequency studies are examined. It is common for areal reduction factors calculated for one region to be transposed to another but little testing of this practice has been reported. The present study suggests that the United States 1 day reduction factors are generally higher than the Australian values but that they may be satisfactorily transposed to Australian capital city sites for areas of between 200 and 500 km 2.

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.

FLOOD FREQUENCY CHARACTERISTICS OF SOME ARIZONA WATERSHEDS1

ABSTRACTThe flood frequency characteristics of 18 watersheds in southeastern Arizona were studied using the log‐Boughton and the log‐Pearson Type 3 distribution. From the flood frequency study, a generalized envelope for Q100 for watersheds 0.01 to 4000 mi2 in area has been produced for southeastern Arizona. The generalized envelope allows comparisons to be made among the relative flood characteristics of the watersheds used in the study and provides a conservative estimate of Q100 for ungaged watersheds in the region.

Impact of Hydrologic Uncertainties on Flood Insurance

Traditional techniques of flood frequency estimation produce a bias in estimated frequencies such that, on the average in a great many applications, floods will occur far more frequently than estimated. This is particularly critical in flood insurance studies. It appears to be imperative that the principle of expected probability be used in flood frequency studies in order to remove or minimize this bias, both for application in actuarial studies and for flood-plain zoning.

Streamflow and Flood-Frequency Studies

Streamflow and Flood-Frequency Studies

Streamflow and Flood-Frequency Studies

Streamflow and Flood-Frequency Studies

Streamflow and Flood-Frequency Studies

Streamflow and Flood-Frequency Studies

Discussion of “Flood frequencies and sedimentation from forest watersheds”

The history of flood studies might be said to consist of seeking answers to: “How big can floods get?”, then “How often will floods come?”, and now “What causes floods?” ‐ or design flood studies, flood frequency studies, and flood cause studies. Hydrologists have lately devoted more and more time to the last. Peak discharges and sedimentation from watersheds as related to storm and watershed variables are one part of these flood cause studies.Schiff's discussion [Trans., v . 30, pp. 584–586, 1949] of our report on such a study brings out some important points. In the present primitive state of development of the relationship of peak discharges to meteorological and watershed variables such suggestions are sure to be helpful. He suggests and presents data to show that for two Ohio watersheds the effects on discharges of increasing forest cover varied considerably between two areas, one of .001 and one of .068 sq mi. In the smaller of these (his Watershed 134) he reports significant reductions in peak discharges occurred when forest cover was changed from a density of ten to 95 per cent. This was due to a reduction in surface runoff. Of the larger (his Watershed 172) he makes the statement that, “Had the actual peak discharges been used to establish an equation for Watershed 172, increases in cover would seem to have little influence. Better cover increased permeability rates and consequently infiltration rates so that most of the flow of Watershed 172 is now subsurface flow which reappears above the measuring flume. Peak discharges have not materially reduced and reflect the particular soil and geologic conditions of Watershed 172.” This is an interesting interpretation, and the factors which he talks of are probably operating; however, the results on peak discharges seem to be not at all what he hypothesizes. First, we would expect a reduction in peak discharges when surface runoff is changed to subsurface flow. And second, that such a reduction occurs and is of large magnitude may be shown when Schiff's data are actually “used to establish an equation.] Taking the data from his Table 1 and testing the relation of Q172, the peak discharges in inches depth per hour to the associated per cent cover density (C), with the maximum hourly precipitation (P1) in inches per hour as the meteorological control we find thatequation imageThe regression coefficient for cover density is found to be highly significant and the magnitude of the effect indicated is such that associated with the increase in cover from ten to 95 per cent there was a reduction of 61 per cent in the peak discharges. This is certainly not an insignificant decrease. With more storm data it would be possible to test other meteorological parameters and improve the equation but probably the cover density effect would remain about the same, since no obvious correlation appears between cover density and any of the meteorological characteristics listed in his Table 1.