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).     

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.     

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.     

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.     

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.     

WATER QUALITY FROM TWO SMALL FORESTED WATERSHEDS IN SOUTHERN ILLINOIS1

Two intermittent streams on oak-hickory watersheds in southern Illinois were gaged with a V-notched weir and sampled with an automatic water sampler. For three years data were collected on flow volume and water quality. Flow volumes show large variations between years and watersheds. Samples were analyzed for Na⁺, K⁺, Ca⁺⁺, Mg⁺⁺, P, and NO^-₃. Water quality was consistently high, although there were significant differences between watersheds. A baseline for water quality has been established for comparison after one of the watersheds is clearcut at a later date.     

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.     

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.     

MODIFIED SMEMAX TRANSFORMATION FOR FREQUENCY ANALYSIS1

ABSTRACT: SMEMAX is a transformation technique suggested by Bethalmy to transform random hydrological series to a near normal series. This paper puts forward an alternative simpler form of the SMEMAX transformation. The modified SMEMAX transformation avoids use of trigonometric functions and the transformed variables range from 0 to 100.     

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.     

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.     

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.     

PREDICTION OF PEAK FLOWS ON SMALL WATERSHEDS IN OREGON FOR USE IN CULVERT DESIGN1

ABSTRACT: Using data from 80 Oregon watersheds that ranged in size from 0.54 km² to 27.45 km², equations were developed to predict peak flows for use in culvert design on forest roads. Oregon was divided into six physiographic regions based on previous studies of flood frequency. In each region, data on annual peak flow from gaging stations with more than 20 years of record were analyzed using four flood frequency distributions: type 1 extremal, two parameter-log normal, three parameter-log normal, and log-Pearson type III. The log-Pearson type III distribution was found to be suitable for use in all regions of the State, based on the chi-square goodness-of-fit-test. Flood magnitudes having recurrence intervals of 10, 25, 50, and 100 years were related to physical and climatic characteristics of drainage basins by multiple regression. Drainage basin size was the most important variable in explaining the variation of flood peaks in all regions. Mean basin elevation and mean annual precipitation were also significantly related to flood peaks in two regions of western Oregon. The standard error of the estimate for the regression relationships ranged from 26 to 84 percent.     

URBANIZATION IMPACT ON WATER QUALITY DURING A FLOOD IN SMALL WATERSHEDS1

ABSTRACT: The impact of various urban land uses on water flow and quality in streams is being studied by monitoring small streams in the Milwaukee urban area. This paper compares the responses of an urban watershed and an agricultural watershed to an autumn rainfall of 2.2 cm. Flow from the urban basin showed a substantially greater response to the rain than that from the rural. Dilution, resulting from the greater quantities of surface runoff in the urban watershed, caused lower concentrations of sodium, chloride, calcium, magnesium, bicarbonate and total dissolved solids in the urban stream. The total quantity of these materials removed per unit drainage area of the urban basin was much greater, however. Road salt was still among the dominant dissolved materials in the urban water chemistry seven months after the last road salting. Sodium was apparently being released from adsorption by clays in the urban basin. Suspended sediment concentrations and total loads were higher in the urban stream.     

CLASSIFICATION OF EVALUATION OF FLOOD FLOW FREQUENCY ESTIMATION TECHNIQUES1

ABSTRACT: The literature abounds with procedures for estimating the magnitude and frequency of floods at ungaged locations. Unfortunately, the large number of available procedures creates an awesome task for potential users of sorting and selecting a method for immediate use. The objectives of this paper are to present (1) criteria that are necessary to evaluate the usefulness of hydrologic procedures, (2) to present a classification system for categorizing the multitude of procedures that are available, (3) to summarize the findings of the literature review, and (4) to make recommendations on reporting of flood frequency estimation procedures on ungaged watersheds.     

ANALYSIS OF UNCERTAINTY IN FLOOD PLAIN MAPPING1

ABSTRACT: Components contributing to uncertainty in the location of the flood plain fringe of a mapped flood plain are identified and examined to determine their relative importance. First-order uncertainty analysis is used to provide a procedure for quantifying the magnitude of uncertainty in the location of the flood plain fringe. Application of the procedure indicated that one standard deviation of uncertainty in flood plain inundation width was about one third of the mean computed inundation width for several flood population-flood geometry combinations. Suggested mapping criteria, which directly incorporate uncertainty estimates, are given. While these criteria are more suitable for use in developing areas than in flood plains that have had extensive development, the analysis procedure can be used to accommodate property owners who challenge the validity of estimated flood fringe boundaries. Use of uncertainty analysis in flood plain mapping should enhance the credibility of the final plan.     

A PROBABILISTIC BENEFIT-COST ANALYSIS OF A ZONING PROGRAM FOR FLOOD PLAINS1

ABSTRACT: Various techniques, one of which is zoning, are used to control the extent of flood damage. The benefit-cost analysis of zoning programs must take into account the random nature of flooding. This paper outlines a method for determining not only the expected value of the benefit-cost ratio, but also the probability of such a zoning program being profitable. It also presents an application of the method to the assessment of the Outaouais Regional Community zoning program.     

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.     

UNIT HYDROGRAPHS FOR DEVELOPING DESIGN FLOOD HYDROGRAPHS1

ABSTRACT: In Illinois, a procedure has been developed to derive unit hydrographs for generating 100-year and probable maximum flood hydrographs, on the basis of 11 parameters that define the hydrograph shape very well. Regional regressions of these parameters with basin factors show very high correlation. Thus satisfactory values of parameters can be determined for ungaged areas or those with a few years' record. The nonlinearity in unit hydrographs derived from usual floods is largely attributed to mixing within-channel and overbank-flow flood events. To minimize the effects of nonlinearity and to derive unit hydrographa suitable for calculating spillway design floods, use of the proposed method of developing such hydrographs is recommended.