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.     

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.     

APPLICATION OF ADVANCES IN FLOOD FREQUENCY ANALYSIS1

ABSTRACT: Flood frequency analyses are frequently being made using widely available computer programs. Serious errors can result from blind acceptance of such results. Visual interpretation of observed flood series can be used for evaluation on frequency paper with compatible scales. Such frequency papers are presented in the paper. In ephemeral streams, more infrequent floods may constitute a separate set from the more frequent floods because (a) runoff producing storms cover only a portion of the contributing area, (b) transmission losses in the normally dry streambed may reduce the peak flow, and (c) some runoff may be stored in stock water ponds which therefore leads to partial area runoff. The Cunnane plotting position used in this paper is superior to the more widely used Weibull equation, having a mathematically sound basis for locating observed floods on an assumed probability.     

ANALYZING URBANIZATION IMPACTS ON PENNSYLVANIA FLOOD PEAKS1

ABSTRACT: The impact of man made change on the hydrology of developing watersheds is frequently measured in terms of the ratio: flood peak after development to flood peak before development over a range of return periods. However, the analysis of urbanization effects on flood frequency presents a vexing problem because of a general lack of flood data in urban areas and also because of nonstationarity in the development process. Clearly, the flood peak ratio depends on the impervious fraction and percent of basin sewered and these factors have been taken into account in recent urban flood peak models. In genral, these models are developed either by: (1) split sample analysis of available annual flood data, or (2) by computer simulation using mathematical watershed models capable of representing man made changes. The present paper discusses the results of work in progress to characterize the impact of urbanization on small developing watersheds in Pennsylvania.     

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).     

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.     

ADAPTATION OF FLOOD PEAKS AND DESIGN HYDROGRAPHS FROM GAGED TO NEARBY UNGAGED WATERSHEDS1

ABSTRACT: Equations were developed to transform peak flows and to adapt design hydrographs and unit hydrographs from gaged watersheds to ungaged watersheds with similar hydrologic characteristics. Dimensional analysis was used to develop adjustment equations for peak flow and time base, and these equations were reinforced with results from regional flood frequency research. The authors believe that the use of these transformation equations should yield more reliable flood peak values and hydrogrphs than the common use of empirical flood estimating curves or equations.     

FLOOD FREQUENCY ANALYSIS FOR EVALUATING WATERSHED CONDITIONS WITh RAINFALL-RUNOFF MODELS1

ABSTRACT: Many rainfall-runoff modeling studies compare flood quantiles for different land-use and/or flood mitigation scenarios. However, when flood quantiles are estimated using conventional statistical methods, comparisons may be misleading because the estimates often misrepresent the quantile relationship between scenarios. An alternate statistical procedure is proposed, in which rainfall-runoff modeling is used to evaluate an approximate relationship between flood quantiles for different scenarios. Monte Carlo experiments show that the proposed method produces flood quantile estimates that better reflect the differences between scenarios. The ratio between quantiles for different scenarios is more accurate, so comparisons of the scenarios using flood quantiles are more reliable.     

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.     

PARAMETER ESTIMATION FOR TPLN DISTRIBUTION FOR FLOOD FREQUENCY ANALYSIS1

ABSTRACT: The principle of maximum entropy (POME) was used to derive an alternative method for parameter estimation for the three parameter lognormal (TPLN) distribution. Six sets of annual peak discharge data were used to evaluate this method and compare it with the methods of moments and maximum likelihood estimation.     

CATCHMENT RESPONSE TIME AS A PREDICTOR OF FLOOD QUANTILES1

ABSTRACT: A regression analysis using a generalized least squares approach on flow data from the driftless area of Wisconsin indicates that the ratio of drainage area to time-to-peak is a good predictor of flood quantiles. The estimation of time-to-peak (or some other measure of basin response time) requires direct measurement of river stage and possibly rainfall at the site of which the quantiles are to be estimated. The cost-effectiveness of such an approach must yet be determined.     

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).     

FLOOD FREQUENCY CHARACTERISTICS OF SOME ARIZONA WATERSHEDS1

The 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.     

INSTANTANEOUS PEAK FLOW ESTIMATION PROCEDURES FOR NEWFOUNDLAND STREAMS1

ABSTRACT: A procedure of estimating instantaneous flood flows for various return periods on the Island of Newfoundland is presented. The procedure is based on annual maximum instantaneous flows rather than annual maximum daily-mean flows, as the latter requires the conversion of estimated daily-mean flows into instantaneous flows. Regression equations were developed for each of three homogeneous regions for the desired return periods. The flood flow estimation capability of the presented procedure is demonstrated to be better than any other currently available procedure on the Island.     

FLOOD FREQUENCY ANALYSIS FOR SMALL WATERSHEDS IN SOUTHERN ILLINOIS1

ABSTRACT: Twenty-two gaging stations were selected for developing a regional flood frequency curve for small (area less than 2 square miles) watersheds in southern Illinois. Five probability functions were compared, and the extreme value type I function was selected to develop the regional flood curve. The curve was generated with the index flood method and also another empirical method that related the function parameters to the watershed area. Estimated peak discharges with various return periods were compared with the results obtained from multiple regression analysis.     

ROLE OF CARBONATE ROCKS IN MODIFYING FLOOD FLOW BEHAVIOR1

ABSTRACT. The interrelationships between the runoff characteristics of watersheds (expressed as the mean annual flood), standard basin parameters (area, drainage properties, and relief), and the parameters which describe the solutional modification of the basins (carbonate rock fractions, sinkhole development, and measures of internal drainage) were used to group 62 carbonate watersheds. Simple binary correlations were obtained by direct plotting of the data. This was followed by multivariate analyses: factor and cluster analyses. Following the cluster analysis, which separated the basins into three groups, the variance within each group was examined again by binary correlations and by factor analysis. Prediction equations for those basins underlain by dolomite rock [QBAR = 12.4 TOT^1.01] and for those basins underlain by carbonate rock with very little surface expression [QBAR = 43.5 TOT^0.87] were proposed. Basins underlain by karstic limestone had a large amount of variance within the data set; therefore no prediction equation could be obtained. (QBAR = mean annual flood, cfs; TOT = total length of all blue lines shown on topographic maps, miles.)     

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.     

COMPREHENSIVE FLOOD PLAIN STUDIES USING SPATIAL DATA MANAGEMENT TECHNIQUES1

ABSTRACT: A pilot study undertaken to develop and test analytical methodologies for application in comprehensive flood plain information studies is described. The methodology permits and encourages comprehensive, systematic, practical assessments of present and alternative future basin-wide development patterns as reflected by alternative land use patterns and physical works in terms of flood hazard, economic damage potential and selected environmental consequences. The analysis methodologies are centered about integrated use of computerized spatial, gridded geographic and resource data files. A family of special purpose utility computer programs access the data file and extract appropriate variables and interpret and format the data into specific analytical parameters that are subsequently formatted for input to traditional modeling computer programs. An example application to Trail Creek in Clarke County, Georgia, is described.