STATISTICAL TERMINOLOGY: DEFINITIONS AND INTERPRETATION FOR FLOOD PEAK ESTIMATION1

ABSTRACT: Considerable effort is expended each year in making flood peak estimates at both gaged and ungaged sites. Many methods, both simplistic and complex, have been proposed for making such estimates. The hydrologist that must make an estimate at a particular site is interested in the accuracy of the estimate. Most methods are developed using either statistical analyses or analytical optimization schemes. While publications describing these methods often include some statistical measure of goodness-of-flt, the terminology often does not provide the potential user with an answer to the question,‘How accurate is the estimate?’ That is, statistical terminology often are not used properly, which may lead to a false sense of security. The use of the correct terminology will help potential users evaluate the usefulness of a proposed method and provide a means of comparing different methods. This study provides definitions for terms often used in literature on flood peak estimation and provides an interpretation for these terms. Specific problems discussed include the use of arbitrary levels of significance in statistical tests of hypotheses, the identification of both random and systematic variation in estimates from hydrologic methods, and the difference between accuracy of model calibration and accuracy of prediction.     

REGION OF INFLUENCE REGRESSION FOR ESTIMATING THE 50-YEAR FLOOD AT UNGAGED SITES1

ABSTRACT: Five methods of developing regional regression models to estimate flood characteristics at ungaged sites in Arkansas are examined. The methods differ in the manner in which the State is divided into subregions. Each successive method (A to E) is computationally more complex than the previous method. Method A makes no subdivision. Methods B and C define two and four geographic subregions, respectively. Method D uses cluster/discriminant analysis to define subregions on the basis of similarities in watershed characteristics. Method E, the new region of influence method, defines a unique subregion for each ungaged site. Split-sample results indicate that, in terms of root-mean-square error, method E (38 percent error) is best. Methods C and D (42 and 41 percent error) were in a virtual tie for second, and methods B (44 percent error) and A (49 percent error) were fourth and fifth best.     

COUPLING OF NONPARAMETRIC FREQUENCY AND L-MOMENT ANALYSES FOR MIXED DISTRIBUTION IDENTIFICATION 1

ABSTRACT: Both L-moment and nonparametric frequency analyses were performed on a series of annual maximum floods from New Brunswick, Canada. The L-moment analysis concluded that the data were generated from a unimodal Generalized Extreme Value (GEV) distribution. However, the nonparametric frequency analysis indicated that a majority of stations followed nonunimodal mixed distributions since peak flows occur during different seasons and are the result of different generating mechanisms. The coupling of L-moment and nonparametric analyses facilitates mixed distribution identification. Thus, the nonparametric method helps in identifying underlying probability distribution, especially when samples arise from mixed distributions.     

COMPARISON OF METHODS FOR ESTIMATING FLOOD MAGNITUDES ON SMALL STREAMS IN GEORGIA1

ABSTRACT: The U.S. Geological Survey has collected flood data for small, natural streams at many sites throughout Georgia during the past 20 years. Flood-frequency relations were developed for these data using four methods: (1) observed (log-Pearson Type HI analysis) data, (2) rainfall-runoff model, (3) regional regression equations, and (4) map-model combination. The results of the latter three methods were compared to the analyses of the observed data in order to quantify the differences in the methods and determine if the differences are statistically significant. Comparison of regression-estimates with observed discharges for sites having 20 years (1966 to 1985) and 10 years (1976 to 1985) of record at different sites of annual peak record indicate that the regression-estimates are not significantly different from the observed data. Comparison of rainfall-runoff-model simulated estimates with observed discharges for sites having 10 years and 20 years of annual peak record indicated that the model-simulated estimates are significantly and not significantly different, respectively. The biasedness probably is due to a “loss of variance” in the averaging procedures used within the model and the short length of record as indicated in the 10 and 20 years of record. The comparison of map-model simulated estimates with observed discharges for sites having 20 years of annual-peak runoff indicate that the simulated estimates are not significantly different. Comparison of “improved” map-model simulated estimates with observed discharges for sites having 20 years of annual-peak runoff data indicate that the simulated estimates are different. The average adjustment factor suggested by Lichty and Liscum to calculate the “improved” map-model overestimates in Georgia by an average of 20 percent for three recurrence intervals analyzed.     

FLOOD WARNINGS AND FLOOD RESPONSES FOR THE RED RIVER OF THE NORTH1

ABSTRACT The flooding conditions in the basin of the Red River of the North are reviewed in terms of the accuracy of the flood forecasts and the response of both the floodplain occupants and government agencies to these forecasts. The flood prediction methods in Canada and the United States are compared. The accuracy of these prediction measures for the major floods in recent history is reviewed. The differences between the way in which the American and Canadian authorities approach the flood emergencies are outlined. The accuracy of the forecasts are plotted against a number of parameters which reflect the efficiency of the flood fighting measures initiated by those flood forecasts. The significant features of these plots are discussed.     

PLOTTING FORMULA FOR FLOOD FREQUENCY1

ABSTRACT: In flood frequency analysis it is required to estimate the values of probabilities based on plotting formula. All of the many existing formula provide different results, particularly at the tails of the distribution. The existing practice in selection of a particular formula is rather arbitrary; and often Weibull's formula is recommended, which provided biased and conservative results. Based on the mean square criterion, a new plotting formula is developed, and it is given by F_m= (m - 0.24)/(N + 0.5).     

USE OF HISTORIC FLOOD INFORMATION IN ESTIMATING FLOOD PEAKS ON UNGAGED WATERSHEDS1

Regional procedures to estimate flood magnitudes for ungaged watersheds typically ignore available site-specific historic flood information such as high water marks and the corresponding flow estimates, otherwise referred to as limited site-specific historic (LSSH) flood data. A procedure to construct flood frequency curves on the basis of LSSH flood observations is presented. Simple inverse variance weighting is employed to systematically combine flood estimates obtained from the LSSH data base with those from a regional procedure to obtain improved estimtes of flood peaks on the ungaged watershed. For the region studied, the variance weighted estimates of flow had a lower logarithmic standard error than either the regional or the LSSH flow estimates, when compared to the estimates determined by three standard distributions for gaged watersheds investigated in the development of the methodology. Use of the simple inverse variance weighting procedure is recommended when “reliable” estimates of LSSH floods for the ungaged site are available.     

A FLOOD DAMAGE MODEL FOR FLOOD PLAIN STUDIES1

ABSTRACT: Hydrologic and economic information must be integrated in flood plain management. This study describes an integrated approach which includes consideration of the hydrologic, hydrodynamic, physical, and economic components of the total system. On the basis of these components, a theoretical model is proposed which provides a rational procedure for estimating flood damages from projections of economic development within an area. The utility of the model is demonstrated by applying it to a flood-prone region in Southern Quebec, Canada.     

COMPARISON OF MODELS FOR ESTIMATING FLOOD QUANTILES IN NEW HAMPSHIRE AND VERMONT1

We develop and compare three regression models for estimating flood quantiles at ungaged stream reaches in New Hampshire and Vermont. These models emerge from systematic analysis and validation of relations between flood magnitude and six candidate predictors reflecting basin size, topography, and climate and channel size at 36 gaging stations with record lengths exceeding 20 years. Of the candidate predictors, bank full width is most highly correlated with flood magnitude and the best prediction equation is based on width. Thus channel geometry is closely related to the current hydrologic regime in spite of geologically recent glaciation and apparently non-alluvial bank materials. We also develop models that use information obtainable from maps or GIS. The best of these uses drainage area and drainage-basin elevation as predictors, but it is substantially less precise than the width-based relation. A third relation using only drainage area as a predictor is even less precise but may be useful for some purposes. No other single predictors or combinations yielded useful predictions, although some had been included in previously-established models for the region. Model comparison included examination of residuals generated by regression using one-at-a-time suppression of data points and comparison with precision obtainable with gaging records of varying lengths.     

AN ANALYSIS OF REGION‐OF‐INFLUENCE METHODS FOR FLOOD REGIONALIZATION IN THE GULF‐ATLANTIC ROLLING PLAINS1

ABSTRACT: Region‐of‐influence (RoI) approaches for estimating stream flow characteristics at ungaged sites were applied and evaluated in a case study of the 50‐year peak discharge in the Gulf‐Atlantic Rolling Plains of the southeastern United States. Linear regression against basin characteristics was performed for each ungaged site considered based on data from a region of influence containing the n closest gages in predictor variable (PRoI) or geographic (GRoI) space. Augmentation of this count based cutoff by a distance based cutoff also was considered. Prediction errors were evaluated for an independent (split‐sampled) dataset. For the dataset and metrics considered here: (1) for either PRoI or GRoI, optimal results were found when the simpler count based cutoff, rather than the distance augmented cutoff, was used; (2) GRoI produced lower error than PRoI when applied indiscriminately over the entire study region; (3) PRoI performance improved considerably when Rol was restricted to predefined geographic subregions.     

AN EVALUATION OF FLOOD FREQUENCY ESTIMATES BASED ON RAINFALL/RUNOFF MODELING1

ABSTRACT: An evaluation of flood frequency estimates simulated from a rainfall/runoff model is based on (1) computation of the equivalent years of record for regional estimating equations based on 50 small stream sites in Oklahoma and (2) computation of the bias for synthetic flood estimates as compared to observed estimates at 97 small stream sites with at least 20 years of record in eight eastern states. Because of the high intercorrelation of synthetic flood estimates between watersheds, little or no regional (spatial) information may be added to the network as a result of the modeling activity. The equivalent years of record for the regional estimating equations based totally on synthetic flood discharges is shown to be considerably less than the length of rainfall record used to simulate the runoff. Furthermore, the flood estimates from the rainfall/runoff model consistently underestimate the flood discharges based on observed record, particularly for the larger floods. Depending on the way bias is computed, the synthetic estimate of the 100-year flood discharge varies from 11 to 29 percent less than the value based on observed record. In addition, the correlation between observed and synthetic flood frequency estimates at the same site is also investigated. The degree of correlation between these estimates appears to vary with recurrence interval. Unless the correlation between these two estimates is known, it is not possible to compute a weighted estimate with minimum variance.     

CLIMATE FACTOR FOR SMALL-BASIN FLOOD FREQUENCY1

ABSTRACT: A climate factor, C_T, (T = 2–, 25-, and 100-year recurrence intervals) that delineates regional trends in small-basin flood frequency was derived using data from 71 long-term rainfall record sites. Values of C_T at these sites were developed by a regression analysis that related rainfall-runoff model estimates of T-year floods to a sample set of 50 model calibrations. C_T was regionalized via kriging to develop maps depicting its geographic variation for a large part of the United States east of the 105th meridian. Kriged estimates of C_T and basin-runoff characteristics were used to compute regionalized T-year floods for 200 small drainage basins. Observed T-year flood estimates also were developed for these sites. Regionalized floods are shown to account for a large percentage of the variability in observed flood estimates with coefficients of determination ranging from 0.89 for 2-year floods to 0.82 for 100-year floods. The relative importance of the factors comprising regionalized flood estimates is evaluated in terms of scale (size of drainage area), basin-runoff characteristics (rainfall. runoff model parameters), and climate (C_T).     

ESTIMATING PROBABLE MAXIMUM FLOOD PROBABILITIES1

ABSTRACT: Methods of computing probabilities of extreme events that affect the design of major engineering structures have been developed for most failure causes, but not for design floods such as the probable maximum flood (PMF). Probabilities for PMF estimates would be useful for economic studies and risk assessments. Reasons for the reluctance of some hydrologists to assign a probability to a PMF are discussed, and alternative methods of assigning a probability are reviewed. Currently, the extrapolation of a frequency curve appears to be the most practical alternative. Using 46 stations in the Mid-Atlantic region, the log-gamma, log-normal, and log-Gumbel distributions were used to estimate PMF probabilities. A 600,000-year return period appears to be a reasonable probability to use for PMFs in the Mid-Atlantic region. The coefficient of skew accounts for much of the variation in computed probabilities.     

SOME TECHNIQUES FOR USING FREQUENCY ANALYSIS AND REALTIME DATA TO INTERPRET FLOOD POTENTIAL DATA1

ABSTRACT: Flood potential data can be effectively interpreted if simple frequency analysis concepts are used to explain the significance of flood potential. Instead of simply presenting data as a quantitative amount or as a percentage of the average condition, predictions can be discussed in terms of their probabilities of exceedance, or return periods. Criteria are presented for evaluating the significance of various return periods. Frequency interpretations are applied to snow course data, peak flow forecasts, and streamflow volume forecasts in northern Utah to illustrate these concepts. In addition, access to realtime data allows tracking of snowmelt progression and identification of any deviations from the forecast flood potential situation. Several data elements, including snowpack, streamfiow volume and peak, and realtime data are jointly evaluated to assess potential hazard and probable risk.     

GENERALIZED SKEW COEFFICIENTS FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: In order to promote a uniform and consistent approach for floodflow frequency studies, the U.S. Water Resources Council has recommended the use of the log-Pearson type III distribution with a generalized skew coefficient. This paper investigates various methods of determining generalized skew coefficients. A new method is introduced that determines generalized skew coefficients using a weighting procedure based upon the variance of regional (map) skew coefficients and the variance of sample skew coefficients. The variance of skew derived from sample data is determined using either of two non-parametric methods called the jackknife or bootstrap. Applications of the new weighting procedure are presented along with an experimental study to test various weighting procedures to derive generalized skew coefficients.     

HYDROLOGIC EFFECTS OF THE TONKAWA CREEK FLOOD ABATEMENT PROGRAM1

ABSTRACT: Floodwater-retarding impoundments, controlling 68 percent of the drainage area of Tonkawa Creek, a Washita River tributary in southwestern Oklahoma, have reduced the total flow volume about 36 percent over a 5-year period. Analyses showed the reduction occurred primarily in the less-than-2.5-cfs flow range, indicating the base flow regime has been altered. However, channelizing the downstream, mild-sloped, 3.6 miles of Tonkawa Creek that flows across a Washita River terrace increased the flow volume fourfold at the outlet. A double-masscurve analysis of water yield from a 1,127-square-mile Washita basin segment versus an untreated tributary showed the yield has not changed after 25 percent of the tributary area had been treated. Therefore, the flow reduction caused by structures is being offset by increased yields from channelization.     

PARAMETER DETERMINATION FOR THE MUSKINGUM-CUNGE FLOOD ROUTING METHOD1

ABSTRACT: The proportionality coefficient, K, and the weighing parameter, X, required for the Muskingum-Cunge Flood Routing Method are dependent on the hydraulic characteristics of the channel and the dynamic characteristic of the flood wave. This work focuses on the determination of the Muskingum-Cunge Flood Routing Method parameters for streams where measured hydrographs are not available (i.e., ungaged streams) with floods that stay within the channel banks. In the present work, a gaged creek was used and a dynamic wave was routed to test the reliability of the parameters determined through the Schaefer and Stevens technique (Schaefer and Stevens, 1978). The predicted outflow hydrographs are compared to the hydrographs obtained for the same stream determined with the Muskingum Routing option of the HEC-1 program. Cypress Creek in Harris County, Texas, was the model for this work; and the corresponding data were extracted from the Grant Road and Westfield, Texas, USGS gaging stations.     

THE USE OF FLOOD POTENTIAL INDICES FOR FLOOD PEAK ESTIMATION ON UNGAGED WATERSHEDS1

: The construction of a flood peak index map was attempted for use by hydrologists in the simple format of rainfall maps. Since flood peaks are highly dependent on watershed area, the effect of area was removed. By regression analysis flood peaks of 2.33 and 100-year return periods were found to be proportional to watershed area to the 0.8 and 0.7 powers, respectively. Therefore, indices C_{2 33}= Q_{2 33}/_A0.7 were completed at each gage and plotted on a Pennsylvania map. It was attempted to further remove some of the scatter by regression of C with several other watershed parameters like slope, percent forest cover, and watershed shape, but no significant correlation could be found. The index maps, drawn without attenuation of the scatter, can be used by hydrologists to compute flood peaks as Q = CAⁿ (with n = 0.8 and 0.7 for the 2.33 and 100-year flood peaks, respectively). Flood peak safety factors can be based on visual observation of the index variation in the vicinity of the location for which the flood peak estimate is needed.     

VERIFICATION AND APPLICATION OF REGIONAL EQUATIONS FOR THE STORAGE FUNCTION RUNOFF MODEL1

The storage function model is a nonlinear rainfall-runoff model that has been developed for and applied to flood runoff analysis in Japan. This paper extends the model applicability by developing practical equations for estimating model parameters which are appropriate on a regional basis, i.e., so-called regional equations. Previously, the parameters were computed from historical data for a specific basin or from relationships that do not account for land use and topography. To develop the regionalized equations, model parameters were identified for 91 flood events from 22 watersheds in Japan by applying a mathematical optimization technique. Results from 39 of these events were statistically compared and regional relationships were determined as a function of land use, basin area and rainfall intensity. The utility of the estimated equations were tested by computing runoff hydrographs for lumped basins. The estimated parameters were also applied in a distributed watershed model formulation. Both applications showed acceptable results that validate the use of the regionalized relationships.     

THE MEASUREMENT OF IMPACTS IN SMALL WATERSHEDS FOR FLOOD CONTROL1

ABSTRACT: An analogue method of ex post evaluation is proposed as a method of measuring the effectiveness of small watershed projects in obtaining flood control and economic benefits. Two watersheds were compared on a “with vs. without” project basis by both direct and indirect measurement of economic benefits. Direct measurements indicated that small watershed flood control projects did not generate the expected economic benefits. However, the indirect measurements of the same watersheds using land value enhancement as a surrogate suggested that the expected economic benefits were reflected in differential land values. The economic efficiency of small watershed projects should be measured ex ante and ex post on a “with vs. without” project basis rather than on a “before vs. after” basis whether using direct or surrogate variables.