DEVELOPMENT AND EVALUATION OF A DIMENSIONLESS UNIT HYDROGRAPH1

ABSTRACT: A generalized unit hydrograph method is developed and evaluated for ungaged watersheds. A key component in this method is the value of a dimensionless storage coefficient. Procedures to estimate this coefficient are given using calibrated values from 142 rainfall-runoff events gaged in watershed located mainly in the Eastern US. Only limited success was obtained in predicting this storage coefficient. Thirty-seven, independent rainfall-runoff events were used to test the proposed technique. The generalized unit hydrograph predicted the observed runoff hydrographs fairly well with considerable improvement in accuracy over the SCS dimensionless unit hydrograph. Approximately one-half of test storms had percent errors in predicted peak flow rates that were less than 34 percent compared to percent error of 88 percent with the SCS method.     

THE APPLICATION OF HYDROLOGIC MODELS TO SMALL WATERSHEDS HAVING MILD TOPOGRAPHY1

ABSTRACT: The application of hydrologic models to small watersheds of mild topography is not well documented. This study evaluates the applicability of hydrologic models described by Huggins and the Soil Conservation Service to small watersheds by comparing the simulated and actual hydrograph for both gaged and ungaged situations. The annual maximum rainfall events plus storms exceeding 2.5 inches from 25 years of rainfall and runoff data for two small watersheds were selected for the model evaluations. These storms had a variety of patterns and occurred on many different watershed conditions. Simulated and actual hydrographs were compared using a parameter which contained volume, peak, and shape factors. One-half of the selected storms were used to calibrate the models. For both models, there were no significant differences between the simulated and actual runoff volumes and peak runoff rates. Parameters obtained during the calibration process and relationships developed to estimate antecedent moisture and to modify tabulated runoff curve numbers were used to simulate the runoff hydrograph from the remaining storms. These remaining storms or test storms were simulated only once in order to imitate an ungaged situation. In general, both the Huggins and SCS model performed similarly on the test storms, but the level of model performance was lower than that for the calibration storms. For both models, the two-day antecedent rainfall was more important than the five-day in determining antecedent moisture and modifying tabulated curve numbers. The time of concentration which resulted in good hydrograph simulations was about three times larger than that estimated using published empirical relationships.     

THE RATIONAL METHOD FOR PEAK FLOW RATE ESTIMATION1

ABSTRACT: The Rational Method continues to be the most widely used approach for estimating P-year return frequency peak flow rates for small catchments of about one square mile or less in area. The Balanced Design Storm unit hydrograph method is perhaps the second most widely used technique for estimating peak flow rates (and is the most widely used method for developing runoff hydrographs) but is generally considered to be more accurate than the Rational Method. In this paper, both of these T-year return frequency peak flow rate estimators are shown to be mathematically comparable. The close similarity between these two approximators may help explain why the Rational Method continues to be widely used even though other more computationally sophisticated techniques are readily available due to widespread computer software.     

CALIBRATION OF SNYDER COEFFICIENTS FOR PENNSYLVANIA1

ABSTRACT Unit hydrograph theory is one of the most widely used techniques to predict surface runoff. The present study is concerned with the Snyder unit hydrograph and the calibration of the Snyder coefficients for Pennsylvania. Twenty-seven study basins were selected, located randomly across the state. With the rainfall and runoff recorded for several events for each basin (more than 500 events were analyzed) unit hydrographs were calculated and the Snyder coefficients determined. A map of the coefficients was drawn to illustrate the variability in the coefficients and two equations using multiple regression theory were developed. The unexplained variability of the coefficients suggests that upper and lower bounds on the peak flow might be placed on storm hydrographs developed for ungaged watersheds.     

SIMULATION OF RUNOFF FROM URBAN WATERSHEDS1

ABSTRACT. .A mathematical model for urban watersheds is being developed in stages at the Utah Water Research Laboratory, Utah State University at Logan. In verifying the watershed as a unit, watershed coefficients are determined on the computer, and related to the urbanization characteristics. The second stage of verification consists of dividing the watershed into subzones, and determining the urban parameters within each subzone. Each subzone is then individually modeled, and outflow hydrographs are routed through succeeding downstream subzones to the gaging point. The model thus makes it possible to: (a) develop runoff models for subzone hydrographs within the urban watershed, and (b) account for spatial variations of storm and watershed characteristics. An attempt was also made to analytically model the outflow hydrograph based on storm and watershed characteristics.     

MODELING RAINFALL-RUNOFF PROCESS INCLUDING LOSSES1

ABSTRACT: Existing discrete, linear rainfall-runoff models generally require the effective rainfall of a given storm as the input for computing the runoff hydrograph. This paper proposes a method for estimating, simultaneously, the optimal values of model parameters and the rainfall losses frem the measured rainfall hyetograph and the runoff hydrograph. The method involves an ARMA model for the rainfall-runoff process and a nonlinear iterative technique. The number of model parameters to be estimated for the ARMA model is much less than the unit hydrograph model. Applications of the model to three different watersheds show that the computed runoff hydrographs agree well with the measurements.     

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.     

UNIT HYDROGRAPHS DERWED FROM THE NASH MODEL1

ABSTRACT: Unit hydrograph ordinates are often estimated by deconvoluting excess rainfall pulses and corresponding direct runoff. The resulting ordinates are given at discrete times spaced evenly at intervals equal to the duration of the rainfall pulse. If the new duration is not a multiple of the parent duration, hydrograph interpolation is required. Linear interpolation, piece-wise nonlinear interpolation and graphical smoothing have been used. These interpolation schemes are expedient but they lack theoretical basis and can lead to undesirable results. Interpolation can be avoided if the instantaneous unit hydrograph (IUH) for the watershed is known. Here two issues connected with the classic Nash IUH are examined: (1) how should the Nash parameters be estimated? and (2) under what conditions is the resulting hydrograph able to reasonably represent watershed response? In the first case, nonlinear constrained optimization provides better estimates of the IUH parameters than does the method of moments. In the second case, the Nash IUH gives good results on watersheds with mild shape unit hydrographs, but performs poorly on watersheds having sharply peaked unit hydrographs. Overall, in comparison to empirical interpolation alternatives, the Nash IUH offers a theoretically sound and practical approach to estimate unit hydrographs for a wide variety of watersheds.     

GENERATING DESIGN HYDROGRAPHS BY DEM ASSISTED GEOMORPHIC RUNOFF SIMULATION: A CASE STUDY1

ABSTRACT: The geomorphic instantaneous unit hydrograph (GIUH) may be one of the most successful methodologies for predicting flow characteristics in ungauged watersheds. However, one difficulty in applying the GIUH model is determination of travel time, and the other difficulty is the large amount of geomorphologic information required in the study watershed. Recently, using the kinematic-wave theory Lee and Yen (1997) have analytically determined the travel times for overland and channel flows in watersheds. The limitation of using an empirical velocity equation to estimate the runoff travel time for a specified watershed is then relaxed. To simplify the time-consuming work involved in geomorphic parameter measurement on topographic maps, the GIUH model is linked with geographic information systems to obtain geomorphic parameters from digital elevation models. In this paper, a case study performed for peak flow analysis in an ungauged watershed is presented. The geomorphic characteristics of the study watershed were analyzed using a digital elevation model and were used to construct the runoff simulation model. The design storm was then applied to the geomorphic runoff simulation model to obtain the design hydrograph. The analytical procedures proposed in this study can provide a convenient way for hydrologists to estimate hydrograph characteristics based on limited hydrologic information.     

Comparison of Stormwater Lag Times for Low Impact and Traditional Residential Development1

Abstract: This study compared lag time characteristics of low impact residential development with traditional residential development. Also compared were runoff volume, peak discharge, hydrograph kurtosis, runoff coefficient, and runoff threshold. Low impact development (LID) had a significantly greater centroid lag‐to‐peak, centroid lag, lag‐to‐peak, and peak lag‐to‐peak times than traditional development. Traditional development had a significantly greater depth of discharge and runoff coefficient than LID. The peak discharge in runoff from the traditional development was 1,100% greater than from the LID. The runoff threshold of the LID (6.0 mm) was 100% greater than the traditional development (3.0 mm). The hydrograph shape for the LID watershed had a negative value of kurtosis indicating a leptokurtic distribution, while traditional development had a positive value of kurtosis indicating a platykurtic distribution. The lag times of the LID were significantly greater than the traditional watershed for small (<25.4 mm) but not large (≥25.4 mm) storms; short duration (<4 h) but not long duration (≥4 h) storms; and low antecedent moisture condition (AMC; <25.4 mm) storms but not high AMC (≥25.4 mm) storms. This study indicates that LID resulted in lowered peak discharge depth, runoff coefficient, and discharge volume and increased lag times and runoff threshold compared with traditional residential development.     

Fitting a Gamma Distribution Over a Synthetic Unit Hydrograph1

ABSTRACT: Several methods for synthetic unit hydrographs are available in the literature. Most of these methods involve the hand fitting of a curve over a set of a few hydrograph points, which can sometimes be a subjective task. Besides, the user often finds it difficult or simply neglects to adjust the generated unit graph to a runoff volume of one unit (inch, cm, or mm). It is the purpose of this paper to present to the design hydrologist a simple method to fit a smooth gamma distribution over a single point specified by the unit hydrograph peak and the time to peak with a guaranteed unit depth of runoff.     

Inferring Hydrograph Components from Rainfall and Streamflow Records Using a Kriging Method-Based Linear Cascade Reservoir Model1

Cheng, Shin-jen, 2010. Inferring Hydrograph Components From Rainfall and Streamflow Records Using a Kriging Method-Based Linear Cascade Reservoir Model. Journal of the American Water Resources Association (JAWRA) 46(6):1171–1191. DOI: 10.1111/j.1752-1688.2010.00484.x Abstract: This study investigates the characteristics of hydrograph components in a Taiwan watershed to determine their shapes based on observations. Hydrographs were modeled by a conceptual model of three linear cascade reservoirs. Mean rainfall was calculated using the block Kriging method. The optimal parameters for 42 events from 1966-2008 were calibrated using an optimal algorithm. Rationality of generated runoffs was well compared with a trusty model. Model efficacy was verified using seven averaged parameters with 25 other events. Hydrograph components were characterized based on 42 calibration results. The following conclusions were obtained: (1) except for multipeak storms, a correlation between base time of the surface runoff and soil antecedent moisture is a decreasing power relationship; (2) a correlation between time lag of the surface flow and soil antecedent moisture for single-peak storms is an increasing power relationship; (3) for single-peak events, times to peak of hydrograph components are an increasing power correlation corresponding to the peak time of rainfall; (4) the peak flows of hydrograph components are linearly proportional to that of total runoff, and the peak ratio for the surface runoff to total runoff is approximately 78 and 13% for subsurface runoff to total runoff; and (5) the relationships of total discharges have direct ratios between hydrograph components and observations of total runoffs, and a surface runoff is 60 and 32% for a subsurface runoff.     

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.     

COMPOSITE VS. DISTRIBUTED CURVE NUMBERS: EFFECTS ON ESTIMATES OF STORM RUNOFF DEPTHS1

ABSTRACT: The U.S. Department of Agriculture Curve Number (CN) method is one of the most common and widely used techniques for estimating surface runoff and has been incorporated into a number of popular hydrologic models. The CN method has traditionally been applied using compositing techniques in which the area weighted average of all curve numbers is calculated for a watershed or a small number of sub-watersheds. CN compositing was originally developed as a time saving procedure, reducing the number of runoff calculations required. However, with the proliferation of high speed computers and geographic information systems, it is now feasible to use distributed CNs when applying the CN method. To determine the effect of using composited versus distributed CNs on runoff estimates, two simulations of idealized watersheds were developed to compare runoff depths using composite and distributed CNs. The results of these simulations were compared to the results of similar analyses performed on an urbanizing watershed located in central Indiana and show that runoff depth estimates using distributed CNs are as much as 100 percent higher than when composited CNs are used. Underestimation of runoff due to CN compositing is a result of the curvilinear relationship between CN and runoff depth and is most severe for wide CN ranges, low CN values, and low precipitation depths. For larger design storms, however, the difference in runoff computed using composite and distributed CNs is minimal.     

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.     

STORM RUNOFF PREDICTION BASED ON A SPATIALLY DISTRIBUTED TRAVEL TIME METHOD UTILIZING REMOTE SENSING AND GIS1

ABSTRACT: In this study, remotely sensed data and geographic information system (GIS) tools were used to estimate storm runoff response for Simms Creek watershed in the Etonia basin in northeast Florida. Land cover information from digital orthophoto quarter quadrangles (DOQQ), and enhanced thematic mapper plus (ETM+) were analyzed for the years 1990, 1995, and 2000. The corresponding infiltration excess runoff response of the study area was estimated using the U.S. Department of Agriculture (USDA), Natural Resources Conservation Service Curve Number (NRCS‐CN) method. A digital elevation model (DEM)/GIS technique was developed to predict stream response to runoff events based on the travel time from each grid cell to the watershed outlet. A comparison of predicted to observed stream response shows that the model predicts the total runoff volume with an efficiency of 0.98, the peak flow rate at an efficiency of 0.85, and the full direct runoff hydrograph with an average efficiency of 0.65. The DEM/GIS travel time model can be used to predict the runoff response of ungaged watersheds and is useful for predicting runoff hydrographs resulting from proposed large scale changes in the land use.     

PARAMETER UNCERTAINTY IN RAINFALL-RUNOFF MODELING FOR POLDER SYSTEM DESIGN1

ABSTRACT: An approach is developed for incorporating the uncertainty of parameters for estimating runoff in the design of polder systems in ungaged watersheds. Monte Carlo Simulation is used to derive a set of realizations of streamflow hydrographs for a given design rainstorm using the U. S. Soil Conservation Service (SCS) unit hydrograph model. The inverse of the SCS curve number, which is a function of the antecedent runoff condition in the SCS model, is the random input in the Monte Carlo Simulation. Monte Carlo realizations of streamfiow hydrographs are used to simulate the performance of a polder flood protection system. From this simulation the probability of occurrence of flood levels for a particular hydraulic design may be used to evaluate its effectiveness. This approach is demonstrated for the Pluit Polder flood protection system for the City of Jakarta, Indonesia. While the results of the application indicate that uncertainty in the antecedent runoff condition is important, the effects of uncertainty in rainfall data, in additional runoff parameters, such as time to peak, in the hydraulic design, and in the rainfall-runoff model selected should also be considered. Although, the SCS model is limited to agricultural conditions, the approach presented herein may be applied to other flood control systems if appropriate storm runoff models are selected.     

A DISTRIBUTED DYNAMIC WATERSHED MODEL1

ABSTRACT: A distributed watershed model was developed to mathematically simulate overland and channel flow for a single-event storm. The modeled watersheds in the study were subdivided into rectangular grid elements. All hydrologically significant parameters, such as land slope, rainfall and precipitation excess, were assumed to be uniform within each element. The Green-Ampt method was adopted to generate precipitation excess for each element during the simulation period. A two-dimensional diffusion wave model was used for overland flow routing and an iterative Alternative Direction Implicit scheme was used to solve the simultaneous overland flow equations. Once the overland flow became inflow to the channel, a one-dimensional dynamic wave flood routing technique, based on a four-point, implicit, non-linear finite difference solution of the St. Venant equation of unsteady flow, was applied. A limited number of comparisons were made between simulated and observed hydrographs for areas of about one square mile. Given the appropriate parameters, the model was able to accurately simulate runoff for single-event storms. This paper describes a distributed watershed model developed to simulate overland and channel flow. Comparisons were made between simulated and observed hydrographs for three watersheds. The model was able to accurately simulate the runoff for single-event storms using 61-m by 61-m (200 ft by 200 ft) watershed grid elements.     

ESTIMATING PEAK RUNOFF FROM FIELD-SIZE WATERSHEDS1

ABSTRACT: A simple nonlinear runoff model was developed and tested for use on field-size agricultural watersheds. A Wooding idealization of the watershed topography was used. Kinematic wave equations were used with an assumed, instead of computed, overland flow, watersurface profile in order to simplify the numerical computations. The approach was used to synthesize runoff hydrographs for an agricultural watershed in Iowa. The accuracy of the synthesized hydro-graphs was judged by comparing the estimated and observed peak discharges and by comparing estimated and observed stages at the measuring weir. The mean errors were 0.01 in/hr and 0.05 ft, respectively. A qualitative comparison was also made with a detailed kinematic wave study. The largest variability occurred during the seedbed period for both models, which was attributed to changes in surface roughness. The roughness was more constant and the results more consistent for the canopy and ground residue periods.     

EFFECTS OF STORM PATTERNS ON RUNOFF HYDROGRAPHS1

ABSTRACT: As an alternative to the conventional single-peak design storms commonly used in hydrologic practice, a large number of Southeastern Pennsylvania storm events were selected from hourly U.S. National Oceanographic and Atmospheric Administration (NOAA) records, and their temporal distributions were analyzed. From these recorded events, design storms of a typical distribution were developed for storm durations between 6 and 18 hours. All of these generated design storms have two or more peaks. The conventional single peak as well as the “typical” multi-peak storms were then applied to a simulated watershed. It was found that the multi-peak storms consistently produced more dispersed hydrographs with lower runoff peaks than the conventional single peak storms.