Direct Runoff Hydrograph Research Articles

Optimal design of unit hydrographs using probability distribution and genetic algorithms

A nonlinear optimization model is developed to transmute a unit hydrograph into a probability distribution function (PDF). The objective function is to minimize the sum of the square of the deviation between predicted and actual direct runoff hydrograph of a watershed. The predicted runoff hydrograph is estimated by using a PDF. In a unit hydrograph, the depth of rainfall excess must be unity and the ordinates must be positive. Incorporation of a PDF ensures that the depth of rainfall excess for the unit hydrograph is unity, and the ordinates are also positive. Unit hydrograph ordinates are in terms of intensity of rainfall excess on a discharge per unit catchment area basis, the unit area thus representing the unit rainfall excess. The proposed method does not have any constraint. The nonlinear optimization formulation is solved using binary-coded genetic algorithms. The number of variables to be estimated by optimization is the same as the number of probability distribution parameters; gamma and log-normal probability distributions are used. The existing nonlinear programming model for obtaining optimal unit hydrograph has also been solved using genetic algorithms, where the constrained nonlinear optimization problem is converted to an unconstrained problem using penalty parameter approach. The results obtained are compared with those obtained by the earlier LP model and are fairly similar.

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.

Simplified Use of Gamma-Distribution/Nash Model for Runoff Modeling

A simple method is suggested for computing the direct runoff hydrograph resulting from a complex storm using a two-parameter gamma distribution as the instantaneous unit hydrograph. The computation of the incomplete gamma function is accomplished indirectly, which requires evaluations of only simple functions that can be performed on a scientific calculator. In place of “unit hydrograph,” a “unit kernel” approach is suggested, which reduces the computational effort when dealing with any selected sampling interval because it implicitly accounts for the sampling interval. The use of the unit kernel renders the S-curve invariant with the sampling interval, as opposed to the conventional procedure. The new procedure enhances the applicability of the two-parameter gamma distribution or the Nash model for rainfall-runoff modeling, as the calculations can be performed using a spreadsheet, such as an Excel spreadsheet. Application of the new procedure on published data sets shows that the direct runoff obtained is almost the same as computed using either tabulated or computer-obtained values of the incomplete gamma function.

Regional dimensionless hydrograph for Alberta foothills

AbstractThe majority of hydrologic engineering applications deal with ungauged watersheds. Various empirical methods are available for synthesizing unit hydrographs for ungauged watersheds from information obtained from maps or field inspection of the watershed. An alternative to the employment of generalized synthetic unit hydrographs is to develop a regional dimensionless hydrograph to characterize the local rainfall‐runoff processes better. The derivation of such a dimensionless hydrograph is described for Alberta foothills, based on the analysis of 31 basins and 61 rainfall‐runoff events. The analysis shows that it is possible to derive a representative dimensionless hydrograph for the region with reasonable accuracy by averaging the observed direct runoff hydrographs converted into a dimensionless form. However, considerable uncertainty is associated with the estimation of the excess rainfall duration and the lag time of the events analysed. The lag time is the key parameter needed to convert the regional dimensionless hydrograph into an ungauged watershed unit hydrograph. Possible reasons for unexplained lag time variations are discussed. The regional dimensionless hydrograph developed and lag time curve were used to regenerate the original 61 hydrographs. Results were compared with the generalized Soil Conservation Service dimensionless unit hydrograph which tended to produce larger errors in predicted peak flows. Error analysis indicates the limits of accuracy that may be expected from the method. Copyright © 2003 John Wiley & Sons, Ltd.

Input output models for estimating suspended sediment flow

Linear discrete input-output models were developed for estimating sediment discharge hydrographs from the Chaukhutia watershed comprising an area of 452.25 km2 of the Ramganga reservoir catchment. The causative factors such as sediment mobilized, direct runoff and excess rainfall water was used as input to the models and sediment discharge as the output. The parameters of these models were estimated from rainfall hyetographs, direct runoff hydrographs and direct sediment flow graphs by Lagrangian's method. The generation and prediction performance of these models were assessed based on pattern recognition technique and using the criteria of accuracy. The computed sediment graphs were in closer agreement with measured sediment flow graphs. The average values of coefficient of efficiency and relative error in estimated peak for sediment mobilized-sediment discharge model were more than 96.0% and less than 7.6 %, respectively whereas for direct runoff-sediment discharge model the values were more than 79.0% and less than 18.8%, respectively. For rainfall excess-sediment discharge model these values were more than 57.0% and less than 29.0, respectively.

Simulation of the direct runoff hydrograph at basin outlet

A simple model describing the transformation of effective rainfall to direct runoff through the overland flow mechanism is presented. The model is based on the classical representation of a watershed by a combination of planes and channels. The dynamics of overland flow in each plane is simulated by the non-linear kinematic wave, but the outflow from a given plane is concentrated in the middle of the corresponding drainage channel. The water routing in the channels is carried out by a piece-wise linearized formulation in space of the kinematic wave approximation. Using synthetic events on 10 watersheds, the model was tested by comparing it with results obtained by applying the non-linear kinematic wave to all the elements of the watershed. The model was found to be adequate, even in a form that simplifies the geometric features of the planes through an averaging procedure based on the Horton–Strahler ordering scheme of the watershed. © 1998 John Wiley & Sons, Ltd.

Reliability analysis of hydraulic structures considering unit hydrograph uncertainty

Unit hydrographs (UHs), along with design rainfalls, are frequently used to determine the discharge hydrograph for design and evaluation of hydraulic structures. Due to the presence of various uncertainties in its derivation, the resulting UH is inevitably subject to uncertainty. Consequently, the performance of hydraulic structures under the design storm condition is uncertain. This paper integrates the linearly constrained Monte-Carlo simulation with the UH theory and routing techniques to evaluate the reliability of hydraulic structures. The linear constraint is considered because the water volume of each generated design direct runoff hydrograph should be equal to that of the design effective rainfall hyetograph or the water volume of each generated UH must be equal to one inch (or cm) over the watershed. For illustration, the proposed methodology is applied to evaluate the overtopping risk of a hypothetical flood detention reservoir downstream of Tong-Tou watershed in Taiwan.

Predicting Sedimentgraphs for a Small Agricultural Catchment

The key components of a sedimentgraph prediction procedure for small agricultural catchments are outlined in the paper. An instantaneous unit sedimentgraph (IUSG) based on the IUH and on a dimensionless sediment concentration distribution is developed, and used for transforming the sediment produced during a specified rainfall duration into a sedimentgraph. Rainfall-runoff-suspended sediment transport data from the River Dart basin, in Devon, UK, are used to evaluate several relationships for sediment yield estimation. The relationship between the lag time of the direct runoff hydrograph and the sedimentgraph is analysed, and the use of these lag times for estimating an IUSG (sediment routing) parameter is examined. The effectiveness of the proposed sedimentgraph prediction procedure is demonstrated by the successful regeneration of a measured sedimentgraph.

A dynamic hillslope response model in a geomorphology based rainfall-runoff model

This paper presents a technique for the determination of a dynamic hillslope instantaneous unit hydrograph (IUH) in concert with a variable saturation excess runoff production model using a grid-based digital elevation model (DEM). The total channel network responsible for routing the runoff produced on the catchment is divided into two parts: the main channel network and the hillslope channel network. The hillslope IUH, which routes water from the hillslopes to the main channel network, is essentially the solution of the linear advection-dispersion routing model weighted by the hillslope travel distance distribution of saturated pixels to the main channel network. The shape of the hillslope travel distance is found to consist of an initial spike, representing saturated pixels on the main channel network, and an exponential decay function for those pixels on the hillslope. However, the proportion of saturated pixels on the main channel network varies with total saturated pixels, causing an inverse change of scale of the spike and the exponential decay part. As the number of saturated pixels changes during a storm event, the hillslope IUH is dynamic. The main channel network IUH is also modelled by the linear advection-dispersion model weighted by the normalized width function of the main channel network. Convolution of the hillslope and main channel network IUHs gives the catchment IUH, which is also dynamically changing with the degree of saturation. It is demonstrated that the direct runoff hydrograph is sensitive to the variation of the degree of saturation within and between storm events.

Estimation of Unit Hydrograph by Ridge Least-Squares Method

Least squares (LS) methods are frequently used to determine an optimal unit hydrograph (UH) for a watershed. However, the conventionally used ordinary LS method could potentially produce a UH with unwanted fluctuation among hydrograph ordinates. When that occurs, the ridge LS method can be used to reduce noise fluctuation in a derived UH. In the framework of the ridge LS method, a UH can be obtained by minimizing the mean-squared error (MSE) of the estimated UH or direct runoff hydrograph (DRH). Therefore, the ridge LS method theoretically would enhance the predictability of the derived UH. This paper describes methodologies of obtaining the optimal ridge parameter for use in the ridge LS method to estimate a UH. Furthermore, the unit volume constraint is considered in the determination of the optimal ridge parameter. A statistical validation study is also conducted to show that a UH obtained by the ridge LS method has a better predictive capability than the one derived by the ordinary LS method.

Determination of optimal unit hydrographs by linear programming

A unit hydrograph (UH) obtained from past storms can be used to predict a direct runoff hydrograph (DRH) based on the effective rainfall hyetograph (ERH) of a new storm. The objective functions in commonly used linear programming (LP) formulations for obtaining an optimal UH are (1) minimizing the sum of absolute deviations (MSAD) and (2) minimizing the largest absolute deviation (MLAD). This paper proposes two alternative LP formulations for obtaining an optimal UH, namely, (1) minimizing the weighted sum of absolute deviations (MWSAD) and (2) minimizing the range of deviations (MRNG). In this paper the predicted DRHs as well as the regenerated DRHs by using the UHs obtained from different LP formulations were compared using a statistical cross-validation technique. The golden section search method was used to determine the optimal weights for the model of MWSAD. The numerical results show that the UH by MRNG is better than that by MLAD in regenerating and predicting DRHs. It is also found that the model MWSAD with a properly selected weighing function would produce a UH that is better in predicting the DRHs than the commonly used MSAD.

Finite Element Watershed Modeling: One‐Dimensional Elements

A procedure for calculating the spatial and temporal distribution of a direct runoff hydrograph from an ungauged watershed is presented. Nodal values of hydraulic roughness and slope are used to avoid kinematic shock. This formulation allows the simulation of overland flow over spatially variable surfaces typical of natural watersheds. The procedure is compared to an analytic solution for a simple case of a watershed composed of two planes. Broader application to watersheds with spatially variable parameters is possible because of the flexibility of the finite element. The Galerkin formulation of the finite element method is used to solve the kinematic wave equations. The method of characteristic and the finite element method were compared on a two‐plane system with an abrupt change in slope. The numerical and analytical considerations are presented to enable practicing engineers to adopt this method for the calculation of flow depth and discharge rate in a distributed manner throughout a watershed domina...

Forecasting of a nonlinear cascade for watershed runoff

Forecasting of a nonlinear cascade was developed for modeling watershed runoff, and was tested by computing the direct runoff hydrograph for two rainfall-runoff events on a small watershed in China. The forecasting model was superior to Dings variable unit hydrograph method and the method of limited differences for these two events.

Application of a Cell Model to the Bellebeek Watershed

A new version of a semi-distributed routing model has been applied to the Bellebeek watershed in Belgium, where runoff data were available for a number of internal gauging stations in addition to the outlet runoff data. The new version has provisions for separately routing the rainfall excess input and the channel inflow input to each unit of area represented in the model by a cell. The cells are interconnected in a tree-like structure reflecting the main drainage pattern of the watershed. The semi-distributed nature of the model makes it possible to simulate spatially variable rainfalls or moving storms. The cell model was calibrated by adjusting its three parameters to reproduce, as nearly as possible, the outflow at the main gauging station of the watershed. The direct surface runoff hydrographs for internal points of the model were then compared to the measured runoff at the internal gauging stations.

Meixner functions for derivation of the unit hydrograph

The Meixner functions are utilized to relate the effective rainfall, the direct runoff and the unit hydrograph through linkage equations. The linkage equations are then employed to derive the unit hydrograph for given rainfall-runoff data on a small agricultural watershed. These functions are tested with regard to their ability to reproduce and predict the direct runoff hydrograph. The Meixner functions are found to be an effective analytical tool for hydrograph synthesis. Further, they compare well with the least squares and linear programming methods of the unit hydrograph derivation.

Flood hydrograph simulation model

A model with a minimum number of parameters has been conceived and developed to simulate direct runoff hydrographs when given3the required input data. Rainfall and runoff data from 39 storms over four watersheds were used for this purpose. The model takes into account both the basin and rainstorm characteristics. A computer model was developed for the computations.The physical aspects of the model are expressed by division of the drainage area into isochronal sub-areas.Formulae were developed which permit computations of water loss parameters as variables dependent on antecedent precipitation. These formulae, together with a watershed lag, obtained by optimization or by the measurement of basin parameters, were used to simulate the runoff hydrograph for a watershed.The model was applied to Runnets watershed which has not been used for the development of the model. Good agreement was found between the simulated and observed hydrographs.

A representation of an instantaneous unit hydrograph from geomorphology

The channel network and the overland flow regions in a river basin satisfy Horton's empirical geo‐morphologic laws when ordered according to the Strahler ordering scheme. This setting is presently employed in a kinetic theoretic framework for obtaining an explicit mathematical representation for the instantaneous unit hydrograph (iuh) at the basin outlet. Two examples are developed which lead to explicit formulae for the iuh. These examples are formally analogous to the solutions that would result if a basin is represented in terms of linear reservoirs and channels, respectively, in series and in parallel. However, this analogy is only formal, and it does not carry through physically. All but one of the parameters appearing in the iuh formulae are obtained in terms of Horton's bifurcation ratio, stream length ratio, and stream area ratio. The one unknown parameter is obtained through specifying the basin mean lag time independently. Three basins from Illinois are selected to check the theoretical results with the observed direct surface runoff hydrographs. The theory provided excellent agreement for two basins with areas of the order of 1100 mi2 (1770 km2) but underestimates the peak flow for the smaller basin with 300‐mi2 (483‐km2) area. This relative lack of agreement for the smaller basin may be used to question the validity of the linearity assumption in the rainfall runoff transformation which is embedded in the above development.

Parallel Cascades Model for Urban Watersheds

The conversion of rainfall to surface runoff in urbanized watersheds is represented by a model composed of three main elements. The first element receives the total rainfall hyetograph as input and produces two rainfall excess hyetographs as output. These are used as inputs to the other two elements which are in parallel. The two elements, representing the impervious and the pervious portions of the watershed, were taken to be composed of cascades of linear reservoirs. The elements produce as their outputs two hydrographs that are added to produce the direct surface runoff hydrograph of the watershed. The first element of the model is nonlinear but the other two are linear. The model, viewed as one unit converting total rainfall to runoff, is thus nonlinear. Data from a semi-arid urban watershed in Arizona were used to demonstrate the use of the model.

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.

The Kernel function of linear nonstationary surface runoff systems

Adopting a linear nonstationary model for the surface runoff system gives a better fit to a set of observed direct surface runoff hydrographs than adopting a stationary linear model. The kernel of this model, which is a function of two time variables, can be considered to be an assembly of impulse response functions for unit pulses acting at various time intervals after the beginning of the storm. Each of these impulse response functions must have the properties of an ordinary instantaneous unit hydrograph. The kernel function is evaluated by an optimization procedure that seeks to minimize the sum of squared deviations between the observed and computed hydrographs for a number of independent storms, subject to given constraints. The procedure is based on a discretization scheme for the functions involved. The set of equations for the unknown kernel values can be partitioned into independent subsets, each of which is solved individually. The complete equation set need be considered only when area constraints of the kernel function are imposed.