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.     

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.     

NORMALIZED UNIT HYDROGRAPH AGGREGATION1

ABSTRACT: The unit hydrograph is a common tool in hydraulic design. Used correctly, it allows a design engineer to estimate a runoff hydrograph from a drainage basin given a rainfall event. The typical method for estimating a unit hydrograph for a gaged watershed is by deconvolution. However, distinct storms produce different unit hydrographs for a single watershed. Consequently, a design engineer usually develops a composite, or average, unit hydrograph based on several recorded storm events. Common methods for estimating this composite unit hydrograph include curve fitting, simple aggregation, and multistorm optimization techniques. This paper introduces a new method to perform aggregation of unit hydrographs. The method is an extension to the simple averaging technique, in which prior to averaging, the individual unit hydrograph time ordinates are normalized with respect to the average time to peak. The normalization method is compared to a simple averaging technique and two multistorm aggregation techniques at six rural watersheds in Alabama. The results indicate that on average the normalization method predicts runoff nearly as accurately as the multistorm techniques, and displays improvement for 60 percent of the storms tested when compared with the simple averaging technique.     

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.     

EFFECT OF RAINFALL EXCESS CALCULATIONS ON MODELED HYDROGRAPH ACCURACY AND UNIT-HYDROGRAPH PARAMETERS1

ABSTRACT: Two methods of computing rainfall excess in the U.S. Army Corps of Engineers’flood hydrograph package (HEC-1), the Initial and Uniform method and the Exponential method, are compared to evaluate the effects on modeled hydrograph accuracy. Two computed unit-hydrograph parameters, time of concentration and storage coefficient, were also compared. Rainfall and runoff data from 209 storms in 32 gaged basins in Illinois were used to calibrate the HEC-1 model. Three hydrograph characteristics - sum of incremental flows, peak discharge, and time of peak discharge - were used to evaluate modeled hydrograph accuracy. Mean percent error for each basin and hydrograph characteristic was computed. An evaluation of the mean errors indicates that, although some bias in modeled hydrograph accuracy is evident, rainfall excess computed using either method results in a computed hydrograph accuracy that is within generally accepted limits. Application of a linear-regression model shows no significant differences in computed values of unit-hydrograph parameters.     

A SEMI-DISTRIBUTED ADAPTIVE MODEL FOR REAL-TIME FLOOD FORECASTING1

ABSTRACT: A semi-distributed deterministic model for real-time flood forecasting in large basins is proposed. Variability of rainfall and losses in space is preserved and the effective rainfall-direct runoff model segment based on the Clark procedure is incorporated. The distribution of losses in space is assumed proportional to rainfall intensity and their evolution in time is represented by the φ-index; furthermore, an initial period without production of effective rainfall is considered. The first estimation of losses and the associated forecasts of flow are performed at the time corresponding to the first rise observed in the hydrograph. Then the forecasts of flow are corrected at each subsequent time step through the updating of the φ-index. The model was tested by using rainfall-runoff events observed on two Italian basins and the predictions of flow for lead times up to six hours agree reasonably well with the observations in each event. For example, for the coefficient of persistence, which compares the model forecasts with those generated by the no-model assumption, appreciable positive values were computed. In particular, for the larger basin with an area of 4,147 km², the mean values were 0.4, 0.4 and 0.5 for forecast lead times of two hours, four hours and six hours, respectively. Good performance of the model is also shown by a comparison of its flow predictions with those derived from a unit hydrograph based model     

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.     

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 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.     

PREDICTING TEMPORAL AND SPATIAL FLOOD DYNAMICS USING A PRECALIBRATED MODEL1

ABSTRACT: A large storm in December 1990 allowed the evaluation of flood predictions from a hydrologic model (TOPMODEL) that had been previously calibrated on the West Fork of Walker Branch Watershed, a gauged 37.5 ha catchment near Oak Ridge, Tennessee. The model predicts both hydrograph dynamics and the spatial distribution of overland flow using an index based on topography. Maximum extent of overland flow during the storm was determined from patterns of leaf litter removal from valley bottoms. Both the flood hydrograph and the extent of overland flow were accurately predicted using model parameters obtained from a three-month period of normal flow conditions during 1983.     

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.     

THE EFFECT OF DATA INDEPENDENCE IN MODEL CALIBRATION AND MODEL TESTING1

ABSTRACT: With the increased use of models in hydrologic design, there is an immediate need for a comprehensive comparison of hydrologic models, especially those intended for use at ungaged locations (i.e., where measured data are either not available or inadequate for model calibration). But some past comparisons of hydrologic models have used the same data base for both calibration and testing of the different models or implied that the results of model calibration are indicative of the accuracy at ungaged locations. This practice was examined using both the regression equation approach to peak discharge estimation and a unit hydrograph model that was intended for use in urban areas. The results suggested that the lack of data independence in the calibration and testing of regression equations may lead to both biased results and misleading statements about prediction accuracy. Additionally, although split-sample testing is recognized as desirable, the split-samples should be selected using a systematic-random sampling scheme, rather than random sampling, because random sampling with small samples may lead to a testing sample that is not representative of the population. A systematic-random sampling technique should lead to more valid conclusions about model reliability. For models like a unit hydrograph model, which are more complex and for which calibration is a more involved process, data independence is not as critical because the data fitting error variation is not as dominant as the error variation due to the calibration process and the inability of the model structure to conform with data variability.     

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.     

THE UNIT HYDROGRAPH: A SATISFACTORY MODEL OF WATERSHED RESPONSE?1

ABSTRACT: Some 96 flood events larger than the mean annual flood from 16 watersheds in the Commonwealth of Pennsylvania were used to derive unit hydrographs by the least-squares method. Analyses of the unit hydrographs were conducted to ascertain their response to watershed parameters, climatic and storm variables and locations within different hydrologic regions. Significant differences both within and among watersheds led to the formulation and testing of hypotheses stating that differences among watersheds are caused by physiographic differences while differences within watersheds result from climatic and storm differences. The analysis showed, that while many watersheds parameters strongly influence the shape of the unit hydrograph, only the storm variables duration and volume of precipitation excess produce significant differences. Seasonal differences were apparent but not proven statistically significant.     

History and Development of the NRCS Lag Time Equation1

Abstract: Many of the hydrologic methods that are used in engineering practice today resulted from the Spring Flood of 1936, which blanketed the Northeastern portion of the United States. Because of the flood damage that was caused by this rainfall‐snowmelt event, many federal agencies including the U.S. Army Corp of Engineers and the Soil Conservation Service (SCS) implemented the hydrologic theories that were available in the literature at this time and developed hydrologic procedures for design flow estimation. Sherman had recently published his unit hydrograph theory in 1932, and later in 1938 Snyder, who had been charged by the Water Resource Council to develop a synthetic unit hydrograph, published his famous paper. The SCS unit hydrograph theory was developed by Victor Mockus in the late 1950s. Most if not all of the theories at that time reported the rainfall‐runoff process for floods as a surface phenomenon, and as such those theories all required some type of a timing parameter to estimate watershed response time. This article documents the development of the SCS lag equation.     

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.     

CHANGES IN HYDROLOGIC RESPONSE DUE TO STREAM NETWORK EXTENSION VIA LAND DRAINAGE ACTIVITIES1

ABSTRACT: The objective of this work is to determine the effects of extension of a stream network through land drainage activities during the late 1800s on the hydrologic response of a watershed. The Mackinaw River Basin in Central Illinois was chosen as the focus and the pre‐land and post‐land drainage activity hydrologic responses were obtained through convolution of the hill slope and channel responses and compared. The hill slope response was computed using the kinematic wave model and the channel response was determined using the geomorphologic instantaneous unit hydrograph method. Our hypothesis was that the hydrologic response of the basin would exhibit the characteristic effects of settlement (i.e., increases in peak discharges and decreases in times to peak). This, indeed, is what occurred; however, the increase in peak discharges diminishes as scale increases, leaving only the decrease in times to peak. At larger scales, the dispersive effects of the longer hill slope lengths in the pre‐settlement scenario seem to balance the depressive effects of the longer path lengths in the post‐settlement scenario, thus the pre‐settlement and post‐settlement peak discharges are approximately equivalent. At small scales, the dispersion caused by the hill slope is larger in the pre‐settlement case; thus, the post‐settlement peak discharges are greater than the pre‐settlement.