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.     

A NONTRADITIONAL METHODOLOGY FOR FLOOD STAGE-DAMAGE CALCULATIONS1

ABSTRACT: This paper presents a new methodology to calculate economic losses from hypothetical, extreme flood events, such as the Probable Maximum Flood. The methodology uses economic data compiled from already-available secondary sources, such as U.S. Census data on magnetic tapes, utilizing microcomputer and other electronic media. Estimates of land elevations are obtained from topographic maps, and flood elevations axe estimated using, for example, a dam breach and flood routing (DAMBRK) model (Fread, 1984). The calculations are performed at a disaggregate spatial scale, by various land use and industrial classification categories. The basic areal units are city blocks (for urbanized areas), enumeration districts, and Census tracts. Depth-damage functions, which provide an estimate of damages as a proportion of the existing value of the structure, are estimated statistically. Computer software (called DAMAGE) is used to combine the economic, flood elevation, and depth-damage information to compute economic losses for different possible flood stages and for different inflow events. Two case studies are presented as illustrations of the method.     

UNIT HYDROGRAPHS – A COMPARATIVE STUDY1

ABSTRACT. Unit hydrographs derived by using two methods, linear programming and least squares, are compared. Test data comprise rainfall and runoff information from four storms over the North Branch Potomac River near Cumberland, Maryland. The mathematical bases of these methods for unit-hydrograph derivation are explained. The linear programming method minimizes the sum of absolute deviations, and the least squares method minimizes the sum of the squares of deviations. Computer subroutines are readily available for application of these methods. The unit hydrographs derived with the two methods are practically the same for storms 2 and 3, but differ somewhat for storms 1 and 4. However, the reconstituted direct surface runoff hydrographs are similar to those observed with the exception of the hydrograph for storm 4 which had a relatively more non-uniform rainfall excess of a considerably larger duration.     

A MODIFIED RATIONAL FORMULA FOR FLOOD DESIGN IN SMALL BASINS1

ABSTRACT: New formulas and procedures under the framework of the Rational Formula are presented that are applicable to flood design problems for a small basin if the geometry of the basin can be approximated as an ellipse or a rhombus. Instead of making the assumption in the traditional rational formula that the rainfall is uniformly distributed in the whole duration (D_w) of a design storm, the new method modifies that assumption as: the rainfall is uniformly distributed only in each time interval CD) of the design storm hyetograph, thus extending the rational formula applicable to the case that the rainfall duration is less than the basin concentration time (T_c). The new method can be applied to estimate the flood design peak discharge, and to generate the flood hydrograph simultaneously. The derivation of the formulas is provided in detail in this paper, and an example is also included to illustrate how to apply the new formulas to the flood design problems in small basins.     

AN ANALOG COMPUTER DEMONSTRATION OF DOUBLE-PEAKED INSTANTANEOUS UNIT HYDROGRAPHS1

The properties of an instantaneous unit hydrograph model consisting of two cascades of linear reservoirs in parallel were explored with the aid of an analog computer. By proper choice of the model parameters it is possible to produce two-peaked instantaneous unit hydrographs. The relative magnitudes and locations of the two peaks can be varied by changing the values of the parameters. An example of the use of the analog computer to select the parameters of the model giving the best fit to an observed runoff hydrograph is also included. The analog computer used in the study was the ASTRAC II developed at the University of Arizona.     

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.     

FLOOD EVENT MODELING - A STUDY OF TWO METHODS1

: Despite the advances in catchment modeling in recent years, engineers still face major problems in estimating flood flows. Application of unit hydrograph and runoff routing models to five United Kingdom catchments shows that either can be tuned to predict, on a test event, the routing effects of a catchment with equal accuracy. The larger remaining problem is the prediction of losses from rainfall and this study shows how alternative ways of describing the within event distribution of these losses can be an important factor controlling the success of the overall model. Other problems include the risks of extrapolation to larger events, baseflow separation methods, rainfall patterns, and inevitable errors in the data.     

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.     

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.     

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.     

A COMPUTERIZED DATA BASE FOR FLOOD PREDICTION MODELING1

ABSTRACT: A computerized geographic information system (GIS) was created in support of data requirements by a hydrologic model designed to predict the runoff hydrograph from ungaged basins. Some geomorphologic characteristics (i.e., channel lengths) were manually measured from topographic maps, while other parameters such as drainage area and number of channels of a specified order, land use, and soil type were digitized and manipulated through use of the GIS. The model required the generation of an integrated Soil Conservation Service (SCS) curve number for the entire basin. To this end, soil associations and land use (generated from analysis of Landsat satellite data) were merged in the GIS to acquire a map representing SCS runoff curve numbers. The volume of runoff obtained from the Watershed Hydrology Simulation (WAHS) Model using this map was compared to the volume computed by hydrograph separation and found to be accurate within 19 percent error. To quantify the effect of changing land use on basin hydrology, the GIS was used to vary percentages from the drainage area from forest to bare soil. By changing the basin runoff curve numbers, significant changes in peak discharge were noted; however, the time to peak discharge remained essentially independent of change in area of land use. The GIS capability eliminated many of the more traditional manual phases of data input arid manipulation, thereby allowing researchers to concentrate on the development and calibration of the model and the interpretation of presumably more accurate results.     

REGIONAL FLOOD EQUATIONS FOR THE PROVINCES OF ONTARIO AND QUEBEC1

ABSTRACT: When nonparametric frequency analysis was performed on 183 stations from Ontario and Quebec, unimodal and multimodal maximum annual flood density functions were discovered. In order to determine generating mechanisms, a monthly partitioning of the annual maximum floods was undertaken. The timing of the floods revealed that the unimodal distributions reflected a single flood generating mechanism while the multi-modal densities reflected two or more mechanisms. Based on the division of the flood series by mechanisms, nine homogeneous regions were delineated. L-moment distributional homogeneity tests along with smaller standard errors for the regional equations supported the delineation.     

ECONOMIC FRAMEWORK FOR FLOOD AND SEDIMENT CONTROL WITH DETENTION BASINS1

ABSTRACT: A framework for combining economic factors and the hydrolo of detention basins is provided. The general development of economic production functions for water quality (sediment) and flood control is discussed. Example production functions are generated to compare water quality (sediment control only) and flood control. For the given example, the design of a detention basin for downstream sediment control is economically unwarranted. When compared to on-site detention facilities, regional detention structures appear to be more practical from an economic standpoint for water quality control. Since sediment was the only water quality parameter assessed, it is entirely possible that the design of a detention basin for water quality control would be justified if the effects of all pollutants of concern could be quantified. Policy aspects of detention facilities that relate to the economics of water quality control are also discussed.     

HICKORY CREEK DRY RESERVOIR: A COMPRAOMISE DESIGN FOR BOTH FLOOD CONTROL AND NATURAL AREA PROTECTION1

Abstract: The proposed Hickory and Spring Creeks Flood Control and Recreation Project of the Illinois State Division of Water Resources and the Will County Forest Preserve District is desinged to provide flood control for Joliet, Illinos, and areas of the watershed to the east of the city and to provide open-space recreational land upstream from the Hickory Breek Dry Reservoir embankement. A viable forest ecosytem in the reservoir flood pool following construction is of major importance to the project. Factors of the environment influencing tree distribution and flood tolerance and a process for determining the best operational design to provide both flood control and the maintenance of a natural streamside forest ecosystem are described.     

WILLINGNESS TO PAY FOR FLOOD RISK REDUCTION AND ITS DETERMINANTS IN JAPAN1

ABSTRACT: This study aimed to clarify public preferences for flood control measures in Japan, willingness to pay (WTP), and the main factors involved in WTP by applying the contingent valuation method. Findings showed that most residents surveyed expected some flood control measures, and revealed a diversity of interest in river management. WTP levels for different measures ranged from a mean of ¥2,887 to ¥4,861 and from a median of ¥1,000 to ¥2,000. However, WTP for additional flood risk reduction beyond initial levels was found to be zero. This was considered to be because WTP for flood risk reduction must be determined within a multi‐risk context. WTP for flood control measures may increase with per capita income, individual preparedness, and/or experience with flooding, but may decrease with distance from a river, acceptability of flood risk, and provision of environmental information. Furthermore, perception of flood risk may increase WTP, while perception of other risks may decrease it. Methods of dealing with environmental risk that were proposed in the survey may have affected WTP levels.     

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.     

HYDRAULIC GEOMETRY RELATIONSHIPS FOR URBAN STREAMS THROUGHOUT THE PIEDMONT OF NORTH CAROLINA1

ABSTRACT: Hydraulic geometry relationships, or regional curves, relate bankfull stream channel dimensions to watershed drainage area. Hydraulic geometry relationships for streams throughout North Carolina vary with hydrology, soils, and extent of development within a watershed. An urban curve that is the focus of this study shows the bankfull features of streams in urban and suburban watersheds throughout the North Carolina Piedmont. Seventeen streams were surveyed in watersheds that had greater than 10 percent impervious cover. The watersheds had been developed long enough for the streams to redevelop bankfull features, and they had no major impoundments. The drainage areas for the streams ranged from 0.4 to 110.3 square kilometers. Cross‐sectional and longitudinal surveys were conducted to determine the channel dimension, pattern, and profile of each stream and power functions were fitted to the data. Comparisons were made with regional curves developed previously for the rural Piedmont, and enlargement ratios were produced. These enlargement ratios indicated a substantial increase in the hydraulic geometry for the urban streams in comparison to the rural streams. A comparison of flood frequency indicates a slight decrease in the bankfull discharge return interval for the gaged urban streams as compared to the gaged rural streams. The study data were collected by North Carolina State University (NCSU), the University of North Carolina at Charlotte (UNC), and Charlotte Storm Water Services. Urban regional curves are useful tools for applying natural channel design in developed watersheds. They do not, however, replace the need for field calibration and verification of bankfull stream channel dimensions.