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.     

MAPPING REGIONAL PRECIPITATION INTENSITY DURATION FREQUENCY ESTIMATES1

ABSTRACT: For regional precipitation frequency analyses, methods are needed to spatially interpolate or smooth point intensity duration frequency (IDF) estimates at gage sites for the purposes of visualization and estimation at ungaged sites. In this study to update IDF estimates for Michigan, the assumption is made that for practical purposes, the entire state may be treated as a homogeneous region in which annual maximum precipitation is identically distributed at each site apart from a site‐specific scaling factor, commonly known as the index flood. Several interpolation and smoothing techniques are evaluated for IDF estimation at ungaged sites, including trend surface analysis, thin plate splines, inverse distance weighting, and several kriging algorithms. Ordinary block kriging is recommended as a practical and objective method for smoothing the variability in the index flood values and developing isopluvial maps.     

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.     

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.     

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.     

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.     

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.)     

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.     

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.     

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.     

UNCERTAINTY OF EXTREME FLOOD ESTIMATES INCORPRATING HISTORICAL DATA1

ABSTRACT: The ability to predict extreme floods is an important part of the planning process for any water project for which failure will be very costly. The length of a gage record available for use in estimating extreme flows is generally much shorter than the recurrence interval of the desired flows, resulting in estimates having a high degree of uncertainty. Maximum likelihood estimators of the parameters of the three parameter lognormal (3PLN) distribution, which make use of historical data, are presented. A Monte Carlo study of extreme flows estimated from samples drawn from three hypothetical 3PLN populations showed that inclusion of historical flows with the gage record reduced the bias and variance of extreme flow estimates. Asymptotic theory approximations of parameter variances and covariances calculated using the second and mixed partial derivatives of the log likelihood function agreed well with Monte Carlo results. First order approximations of the standard deviations of the extreme flow estimates did not agree with the Monte Carlo results. An alternative method for calculating those standard deviations, the “asymptotic simulation” method, is described. The standard deviations calculated by asymptotic simulation agree well with the Monte Carlo results.     

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.     

Use of Streamflow Data to Estimate Base Flow/Ground‐Water Recharge For Wisconsin1

Abstract: The average annual base flow/recharge was determined for streamflow‐gaging stations throughout Wisconsin by base‐flow separation. A map of the State was prepared that shows the average annual base flow for the period 1970‐99 for watersheds at 118 gaging stations. Trend analysis was performed on 22 of the 118 streamflow‐gaging stations that had long‐term records, unregulated flow, and provided aerial coverage of the State. The analysis found that a statistically significant increasing trend was occurring for watersheds where the primary land use was agriculture. Most gaging stations where the land cover was forest had no significant trend. A method to estimate the average annual base flow at ungaged sites was developed by multiple‐regression analysis using basin characteristics. The equation with the lowest standard error of estimate, 9.5%, has drainage area, soil infiltration and base flow factor as independent variables. To determine the average annual base flow for smaller watersheds, estimates were made at low‐flow partial‐record stations in 3 of the 12 major river basins in Wisconsin. Regression equations were developed for each of the three major river basins using basin characteristics. Drainage area, soil infiltration, basin storage and base‐flow factor were the independent variables in the regression equations with the lowest standard error of estimate. The standard error of estimate ranged from 17% to 52% for the three river basins.     

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 NEW LOOK AT FLOOD RISK DETERMINATION1

ABSTRACT: The probability distributions of annual peak flows used in flood risk analysis quantify the risk that a design flood will be exceeded. But the parameters of these distributions are themselves to a degree uncertain and this uncertainty increases the risk that the flood protection provided will in fact prove to be inadequate. The increase in flood risk due to parameter uncertainty is small when a fairly long record of data is available and the annual flood peaks are serially independent, which is the standard assumption in flood frequency analysis. But standard tests for serial independence are insensitive to the type of grouping of high and low values in a time series, which is measured by the Hurst coefficient. This grouping increases the parameter uncertainty considerably. A study of 49 annual peak flow series for Canadian rivers shows that many have a high Hurst coefficient. The corresponding increase in flood risk due to parameter uncertainty is shown to be substantial even for rivers with a long record, and therefore should not be neglected. The paper presents a method of rationally combining parameter uncertainty due to serial correlation, and the stochastic variability of peak flows in a single risk assessment. In addition, a relatively simple time series model that is capable of reproducing the observed serial correlation of flood peaks is presented.     

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.     

Streamflow Hydrology Estimate Using Machine Learning (SHEM)

Continuity and accuracy of near real‐time streamflow gauge (streamgage) data are critical for flood forecasting, assessing imminent risk, and implementing flood mitigation activities. Without these data, decision makers and first responders are limited in their ability to effectively allocate resources, implement evacuations to save lives, and reduce property losses. The Streamflow Hydrology Estimate using Machine Learning (SHEM) is a new predictive model for providing accurate and timely proxy streamflow data for inoperative streamgages. SHEM relies on machine learning (“training”) to process and interpret large volumes (“big data”) of historic complex hydrologic information. Continually updated with real‐time streamflow data, the model constructs a virtual dataset index of correlations and groups (clusters) of relationship correlations between selected streamgages in a watershed and under differing flow conditions. Using these datasets, SHEM interpolates estimated discharge and time data for any indexed streamgage that stops transmitting data. These estimates are continuously tested, scored, and revised using multiple regression analysis processes and methodologies. The SHEM model was tested in Idaho and Washington in four diverse watersheds, and the model's estimates were then compared to the actual recorded data for the same time period. Results from all watersheds revealed a high correlation, validating both the degree of accuracy and reliability of the model.     

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 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.     

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.