Nash Instantaneous Unit Hydrograph Research Articles

Developing an Empirical Relations between Nash Model Parameters and Watersheds Topographical Characteristics for Predicting Direct Runoff Hydrograph

The limited availability of the recorded rainfall-runoff data for many watersheds restricts the development and management of different activities of water resources. To overcome this limitation, the Natural Resources Conservation Service (NRCS) for estimating storm excess rainfall and momentum and optimization methods were combined in a mathematical model to estimate the optimal parameters of Nash Instantaneous unit hydrograph (IUH) and resulting direct runoff hydrograph (DRH), using a developed computer program in MATLAB. The available recorded data of 14 storms (out of 18) of four watersheds in northern Iraq have been applied in the calibration stage. An empirical relationship was developed between the average of each IUH optimal parameter (obtained by optimization as an optimal method according to the applied tests) and the effective watershed topographical characteristics. The developed empirical relations were used in the verification stage to estimate the IUH parameters and DRH for the verification storms and compare with that resulted from Haan’s empirical relations and optimization method. The statistical tests showed that the developed empirical relations efficiency was better than that of Haan’s method and close to that of the recorded storm by optimization method, where the average value of the Nash-Sutcliffe Efficiency for the four watersheds resulted from applying the optimization method, Haan’s method and the developed empirical relations were 0.925, 0.587, 0.883 respectively. The results indicated the developed model’s ability to estimate the IUH and direct runoff hydrograph for ungauged watersheds in northern Iraq.

Parameter estimation of Nash IUH for multiple storm events using particle swarm optimization method

In present study, we proposed to optimize the parameters of Nash Instantaneous Unit Hydrograph using particle swarm optimization method. The application of particle swarm optimization method made the optimal parameter estimation for multiple storm events possible. The effectiveness of the proposed method was tested by published data sets. Compared with the reported results, the simulation accuracy in terms of peak magnitude and peak time is all improved, and the convergence rate is significantly improved, which demonstrates that the superiority of particle swarm method in parameter optimization of Nash IUH model.

Development of the Nash instantaneous unit hydrograph to predict subsurface flow in catchments

Development of the Nash instantaneous unit hydrograph to predict subsurface flow in catchments

Evaluation of geomorphological approaches combined with digital elevation models for the Nash's instantaneous unit hydrograph

Methodologies for estimation of direct surface runoff (DSR) hydrographs have been proposed, especially for the Unit Hydrograph (UH) and Instantaneous Unit Hydrograph (IUH). The widely used IUH developed by Nash (NIUH) has two main parameters: number of reservoirs (n) and storage coefficient (k), which by definition are determined based on observed rainfall-runoff events. In order to overcome the need for hydrological data for application of NIUH, geomorphological approaches (GAs) have been developed to provide the aforementioned parameters for ungauged watersheds, thus allowing for the estimation of DSR hydrographs using only relief information. The aim of this study was to evaluate the performance of 4 GAs (GA1 - Nash, 1960; GA2 - Wu, 1963; GA3 - Rosso, 1984; GA4 - Bhaskar et al., 1997). Moreover, this study sought to investigate the influence of different digital elevation models (DEMs) (TOPO, ASTER, SRTM-30 and SRTM-90) on the determination of geomorphological attributes necessary for the application of the above-mentioned GAs. Twenty rainfall-runoff events observed in a small Brazilian watershed were used to evaluate the performance of NIUH combined with different GAs and DEMs for estimation of DSR hydrographs. In view of the results found in this study, the main conclusions are: i) the GAs exert more influence on the parameters n and k than the DEMs; ii) GA1 and GA2 outperformed GA3 and GA4; and iii) GA2 coupled with the ASTER DEM results in the best estimates of DSR hydrographs.

An Integrated Modelling Approach for Flood Simulation in the Urbanized Qinhuai River Basin, China

The accurate simulation and prediction of flood response in urbanized basins remains a great challenge due to the spatial and temporal heterogeneities in land surface properties. We hereby propose an integrated modelling approach that consists of a semi-distributed conceptual hydrological model and a novel parameterization strategy. The modelling approach integrates the Xinanjiang (XAJ) model, Taihu Basin (TB) model, and Nash instantaneous unit hydrograph (IUH) into a framework. Model parameters are calibrated by optimizing their relationships with corresponding physical factors. The proposed modelling approach is applied in the Qinhuai River basin (QRB), China. The modelling approach shows satisfactory performance in flood simulation both for calibration and validation of flood events in the QRB. The approach has temporal and spatial prediction capability by using the established relationships between parameter values and physical factors. Robustness analysis reveals that the different sets of flood events used for parameter relationship calibration led to similar model performance. Numerical experiments show that impervious coverage poses strong influences on the model performance and needs to be considered in flood routing simulations for small- or medium-intensity flood events.

Investigating Parameters of Geomorphic Direct Runoff Hydrograph Models

Formulation of rainfall runoff models and identification of their parameters is difficult step especially for catchments having scanty or no data. Parameters of geomorphic instantaneous unit hydrograph (GIUH) models have been investigated in this research. Recorded data of Shahpur Dam Catchment, Pakistan was used for developing direct runoff hydrograph model. Satellite imageries of the catchment were processed using ArcGIS 10.1 to estimate geomorphologic parameters. The rainfall and runoff data for 10 events was collected from Meteorological Department Lahore and from Small Dam Organization, Rawalpindi, Pakistan. Rainfall data was analyzed and excess rainfall was estimated using Percent Runoff Method. Using estimated geomorphologic parameters the ordinates of GIUH- Nash Model were obtained by standard equations of Nash instantaneous unit hydrograph (IUH). These ordinates of Nash-IUH, were converted into the ordinates of direct runoff hydrographs through their convolution with the excess rainfall. The results of model were evaluated on the basis of their deviation from the observed runoff data. Statistical parameter Nash-Sutcliffe Coefficient and percent error between observed and simulated direct runoff were used for this purpose. The impact of using digital elevation models (DEM) of two different resolutions; 30 and 90 m, was then investigated. It is observed that the geomorphic parameters are affected due to DEM’s resolution. Hence the resolution of DEM impacts the direct runoff as well.

Runoff prediction in ungauged catchments using the gamma dimensionless time-area method

Time-area (TA), which constitutes the basis for rainfall-runoff transformation in the Clark model, is conventionally derived from the tedious procedure of delineating isochrones. In the present study, by combining the Nash instantaneous unit hydrograph (IUH), in terms of the gamma function, and the Clark model, a new TA relationship (TAR) is introduced. This equation involves the Nash models’ parameters (i.e., the number of reservoirs, n, and the storage coefficient, k). Considering that n = 5 for ungauged catchments, the following equation for estimating k was obtained: k = t c /4.24, with t c being the time of concentration of the catchment. Finally, a gamma time-area (GTA) function was derived for estimating the time-area diagram (TAD) of catchments. The TADs derived from the GTA function were compared to the GIS-based TADs and those derived from the US Army Corps of Engineers (USACE) method and the kinematic wave (KW) model in four catchments, namely, Kasilian, Ajay, Jafarabad, and Shourandika. In the Kasilian catchment, the direct runoff hydrograph (DRH) was simulated using the Clark model based on the GTA and USACE methods and compared with the observed hydrographs. Results indicate that the coefficient of efficiency (CE) in the Kasilian catchment for the two methods is approximately 0.8, while the errors in the peak discharge prediction are 9 and 11.2% in the GTA and USACE methods, respectively.

A generalized concentration curve (GCC) method for storm flow hydrograph prediction in a conceptual linear reservoir-channel cascade

The unit hydrograph (UH) is a hydrological tool that represents the unit response of a watershed to a unit input of rainfall. UH models based on lumped reservoir and channel conceptual cascade assume that rainfall is evenly distributed, thus limiting the use of UHs to relatively small watersheds of less than around 500 km2 in area. In this paper, a new hydrograph prediction method, named the generalized concentration curve (GCC), was derived that can be applied to large heterogeneous watersheds. The GCC method divides the watershed into subareas by isochrones. In each subarea, an independent linear reservoir-channel cascade model that considers both attenuation and translation is established. Comparative application of the GCC and the traditional Nash instantaneous unit hydrograph to 18 storm events from three medium-sized watersheds (727, 1,800 and 5,253 km2 in area) revealed superior performance of the GCC, with the average Nash–Sutcliffe efficiency coefficient higher by 7.66%, and the average peak discharge error lower by 4.14%. This study advances the theory of UH and expands the scope of application of UH to larger watersheds.

Derived flood frequency distribution and sensitivity analysis to variations in model parameters

In this paper we propose a new derived flood frequency distribution approach using the Nash instantaneous unit hydrograph (IUH) as the catchment's response model and analyze the sensitivity of flood frequency distributions to variations in the model parameters. We analyzed the effect of applying the Nash IUH to estimate peak flows in two basins in the province of Buenos Aires (Argentina). For the new flood frequency distribution, the Nash IUH parameters were estimated using the method of moments and a technique that relates the IUH parameters to the basin geomorphologic and hydraulic features. After applying the proposed derived flood frequency distributions to the basins, it is concluded that the new model (which includes the Nash IUH) yields similar results to those attained with a model developed by Raines and Valdés; the new model parameters can be estimated using a technique for ungauged basins. Also observed is a change in the shape of the flood frequency curves according to the IUH parameter estimation technique and to the set of infiltration parameters used.

A comparative study for prediction of direct runoff for a river basin using geomorphological approach and artificial neural networks

Traditional techniques for estimation of flood using historical rainfall–runoff data are restricted in application for small basins due to poor stream gauging network. To overcome such difficulties, various techniques including those involving the morphologic details of the ungauged basin have been evolved. The geomorphologic instantaneous unit hydrograph method belongs to the latter approach. In this study, a gamma geomorphologic instantaneous unit hydrograph (GGIUH) model (based on geomorphologic characteristics of the basin and the Nash instantaneous unit hydrograph model) was calibrated and validated for prediction of direct runoff (flood) from the catchment of the Dulung-Nala (a tributary of the Subarnarekha River System) at Phekoghat station in the state of West Bengal in the eastern part of India. Sensitivity analysis revealed that a change in the model parameters viz., n, RA and RB by 1–20% resulted in the peak discharge to vary from 1.1 to 27.2%, 3.4 to 21.2% and 3.4 to 21.6%, respectively, and the runoff volume to vary from 0.3 to 12.5%, 2.1 to 2.6% and 2.2 to 2.7%, respectively. The Nash–Sutcliffe model efficiency criterion, percentage error in volume, the percentage error in peak, and net difference of observed and simulated time to peak which were used for performance evaluation, have been found to range from 74.2 to 95.1%, 2.9 to 20.9%, 0.1 to 20.8% and −1 to 3 h, respectively, indicating a good performance of the GGIUH model for prediction of runoff hydrograph. Again, an artificial neural network (ANN) model was prepared to predict ordinates of discharge hydrograph using calibrative approach. Both the ANN and GGIUH models were found to have predicted the hydrograph characteristics in a satisfactory manner. Further, direct surface runoff hydrographs computed using the GGIUH model at two map scales (viz. 1:50,000 and 1:250,000) were found to yield comparable results for the two map scales. For a final clarification, the probability density function of the actual and predicted data from the two models was prepared to compare the pattern identification ability of both the models. The GGIUH model was found to identify the distribution pattern better than the ANN model, although both the models were found to be ably replicating the data patterns of the observed dataset.

Nash 모형을 이용한 유역 저류상수 및 집중시간의 이론적 검토

본 연구에서는 간단한 단위도 이론인 Nash 모형을 이용하여 유역 저류상수 및 집중시간의 문제를 이론적으로 고찰해 보았다. 먼저, Nash 순간단위도의 저류상수 및 집중시간을 그 정의에 따라 유도하고, 각각의 특성은 물론 둘 사이의 관계를 검토하였다. 추가로, 국내에서 많이 사용되고 있는 저류상수 및 집중시간의 경험공식들을 유도된 Nash 모형의 저류상수 및 집중시간 특성과 비교 검토하였다. 이 과정을 통해 얻은 주요 결과는 다음과 같다. (1) Nash 순간단위도의 집중시간은 선형저수지의 개수에 거의 선형적으로 비례하는 형태를 가지나 저류상수는 비선형적으로 제곱근에 비례하는 형태를 가진다. 즉, 선형저수지의 수를 4배로 증가시키면 집중시간은 약 4배 증가하게 되나 저류상수는 약 2배 증가하는데 그치게 된다. 이러한 결과는 특히 유역분할에 따른 집중시간과 저류상수의 변화를 이해하는데 중요하다. (2) Nash 순간단위도의 집중시간과 저류상수의 관계는 서로 독립적이 아니며, 따라서 두 매개변수가 서로 독립적으로 결정되는 것은 물리적으로 타당하지 않다. 두 매개변수 중 집중시간이 선형저수지의 개수에 보다 민감하므로 이를 먼저 결정하고 저류상수의 경우는 기 결정된 집중시간을 반영하여 결정하는 것이 보다 바람직한 방법으로 이해할 수 있다. (3) 유역의 집중시간과 관련한 경험공식은 크게 선형하천의 개념에 충실한 경우와 그렇지 않은 것으로 나눌 수 있었으며, 각각의 경우에 포함된 식의 형태는 매우 유사한 것으로 나타났다. 이는 집중시간을 결정하는 유역의 특성인자가 대체로 유사함을 의미하며, 또한 유역 전반에 걸쳐 일관된 식의 형태를 적용하는 지역화가 가능함을 의미한다. (4) 유역의 저류상수와 관련해서 검토한 Russell 공식 등의 경우 그 적용범위 설정에 유역의 물리적인 특성을 충분히 고려할 수 있어, 비합리적인 적용은 충분히 배제될 수 있음을 확인할 수 있었다. This study theoretically reviews the basin storage coefficient and concentration time using the Nash model, a simple unit hydrograph theory. First, the storage coefficient and concentration time of Nash instantaneous unit hydrograph (IUH) are derived based on their definitions, whose characteristics as well as their relationship are also reviewed. Additionally, several empirical equations of storage coefficient and concentration time commonly used in Korea are evaluated by comparing them with those for the Nash IUH. Major results of this study are summarized as follows. (1) The concentration time of Nash IUH is approximately linearly proportional to the number of linear reservoirs, but the storage coefficient non-linearly to the square root. That is, if increasing the number of linear reservoirs by four times, the concentration time becomes also increased by about four times, but the storage coefficient only about two times. This result has a special meaning to understand the effect of basin subdivision on the concentration time and storage coefficient. (2) The storage coefficient and concentration time of Nash IUH are not independent each other, so their independent estimation does not make any physical sense. As the concentration time among the two is more sensitive to the number of linear reservoirs, which should be estimated first, then the storage coefficient considering the concentration time estimated. (3) Empirical equations of concentration time can be divided into two groups, one following the linear channel theory and the other not, whose equation forms are also found to be very similar. This result indicates that the characteristic factors dominating the concentration time are very similar, indicating the possibility of its regionalization over a basin with consistent equation forms. (4) Those for storage coefficient like the Russell formulae are found to consider the physical characteristics of a basin, so their unreasonable applications could sufficiently be excluded.

평활화된 무차원 단위핵함수를 이용한 단위도의 유도

본 연구에서는 복합 강우사상으로부터 단위도와 S-곡선을 도출하는 실용적인 방법을 강구하였다. 이 연구에서 이용된 단위핵함수는 단위도와 S-곡선을 유도하는데 있어서 기존의 방법보다 편리하다. 그러나 실제 자료를 분석할 때 단위핵함수는 진동을 보이고 불안정하기 때문에 단위도와 S-곡선 도출에 있어서 장애가 있다. 그런데 단위핵함수의 요소인 Nash 의 순간단위도를 추정함에 있어서 Laplacian 행렬을 이용한 능형회귀분석을 이용하면 사상에 대한 평균적인 단위핵함수를 구하는데 유익함을 발견하였다. 또한 이를 이용하여 단위도의 지속기간 변경도 가능하였다. 이 연구에서 제시된 방법론은 단위도 제작에 적지 않은 도움이 될 것으로 기대한다. A practical method is derived for determining the unit hydrograph and S-curve from complex storm events by using a smoothed unit kernel approach. The using a unit kernel yields more convenient way of constructing a unit hydrograph and its S-curve than a conventional method. However, with use of real data, the unit kernel oscillates and is unstable so that a unit hydrograph and S-curve cannot easily obtained. The use of non-parametric ridge regression with a Laplacian matrix is suggested for deriving an event averaged unit kernel which reduces the computational efforts when dealing with the Nash instantaneous unit hydrograph as a basis of the kernel. A method changing the unit hydrograph duration is also presented. The procedure shown in this work will play an efficient role when any unit hydrograph works is involved.

Use of Nash's IUH and DEMs to identify the parameters of an unequal‐reservoir cascade IUH model

AbstractUnder the assumption that hydrograph generation was affected by n linear reservoirs with the same value of storage coefficient k, Nash proposed the formulation of the Instantaneous Unit Hydrograph (IUH), which has been widely used in rainfall–runoff simulation and flood forecasting. However, the assumption of the parameter k having the same value in all reservoirs is obviously unphysical as it results in the estimated value of n not being integral. In this study, for parameter n integral, the different k value for each reservoir was derived using the Laplace transform and developing a general rule for the equation of the IUH of any order. The relationship between parameter k and the slope of the river channel estimated using digital elevation model (DEM) data is established, the parameter estimation procedures are given. As in most unit hydrograph studies, only isolated storm events are considered here. Seventeen flood events in three catchments were selected for the case studies. Application results show that the proposed method is slightly better than Nash's IUH with higher model efficiency and smaller absolute relative errors. This work provides a new methodology for the formulation of the IUH. Copyright © 2008 John Wiley & Sons, Ltd.

Estimation of Nash's IUH parameters using stochastic search algorithms

AbstractIn rainfall–runoff studies, it is often necessary to change the duration of a given unit hydrograph. Nash's Instantaneous Unit Hydrograph (IUH) is an ideal method that eliminates the hydrograph duration. This paper presents the results of the application of search algorithms, namely a genetic algorithm and hill climbing, to develop the IUH that minimizes the error between the observed and generated hydrographs. Also the performance of these methods has been compared with that of the classical method used for estimation of IUH, namely the method of moments. The genetic algorithm is a popular search procedure for function optimization that applies the mechanics of natural genetics and natural selection to explore a given search space. Hill climbing is an optimization technique that belongs to the family of local search and algorithms can be used to solve problems that have many solutions, with some solutions better than others. The results obtained from both the genetic algorithm and hill climbing algorithm for estimation of Nash's IUH parameters were compared with the results obtained by the method of moments for storms from two river basins that are located in different climatic regions. It was found that both the genetic algorithm and hill climbing provided improved and consistent results. Copyright © 2008 John Wiley & Sons, Ltd.

Runoff estimation for an ungauged catchment using geomorphological instantaneous unit hydrograph (GIUH) models

AbstractA geomorphological instantaneous unit hydrograph (GIUH) is derived from the geomorphological characteristics of a catchment and it is related to the parameters of the Clark instantaneous unit hydrograph (IUH) model as well as the Nash IUH model for deriving its complete shape. The developed GIUH based Clark and Nash models are applied for simulation of the direct surface run‐off (DSRO) hydrographs for ten rainfall‐runoff events of the Ajay catchment up to the Sarath gauging site of eastern India. The geomorphological characteristics of the Ajay catchment are evaluated using the GIS package, Integrated Land and Water Information System (ILWIS). The performances of the GIUH based Clark and Nash models in simulating the DSRO hydrographs are compared with the Clark IUH model option of HEC‐1 package and the Nash IUH model, using some commonly used objective functions. The DSRO hydrographs are computed with reasonable accuracy by the GIUH based Clark and Nash models, which simulate the DSRO hydrographs of the catchment considering it to be ungauged. Inter comparison of the performances of the GIUH based Clark and Nash models shows that the DSRO hydrographs are estimated with comparable accuracy by both the models. Copyright © 2007 John Wiley & Sons, Ltd.

Application of a unit hydrograph based on subwatershed division and comparison with Nash's instantaneous unit hydrograph

The Unit Hydrograph (UH) technique is widely used for runoff estimation, especially for determining peak discharges. In this paper, a geomorphologically based UH has been applied. Its most remarkable characteristic is that it includes the watershed structure in its formulation. This is defined from the drainage network, each subwatershed being considered as a linear reservoir. In this method, the fact of considering this reservoir sequence according to the drainage network leads to the formulation of the model only depending on a single parameter. The Geomorphological Unit Hydrograph of Reservoirs (GUHR), proposed in this paper, is compared with Nash's Instantaneous Unit Hydrograph (Nash's IUH), by applying the two methods to the Aixola watershed. This 4.7-km 2 watershed is located in Gipuzkoa (Northern Spain). It is characteristic of the headwaters watersheds of the area. Most of them are forested and have steep slopes. Annual rainfall is over 1500 mm and many intense rainfall events are observed, among which 18 were selected for this study. Both UH techniques were applied to the rainstorms. The resulting hydrographs were plotted against registered data and the best fits were determined. According to these results, the GUHR model behaved similarly to Nash's IUH. However, the GUHR method seemed able to reproduce a wider range of rainstorms than Nash's IUH. While analyzing the UHs calculated, seasonal behavior was observed in runoff generation, and different average UHs were proposed for two different periods. This variability was also observed in values adopted by the GUHR model parameter, providing some information about the watershed time response. The dynamic character of the only uncertain parameter, and the model formulation, in which the watershed morphology is reflected, together with the model's simplicity, leads us to consider GUHR as being a promising UH model.

GIUH based Clark and Nash models for runoff estimation for an ungauged basin and their uncertainty analysis

Runoff estimation is an important aspect of river basin planning, development and management. Geomorphological instantaneous unit hydrograph (GIUH) approach holds a great potential for estimation of runoff from ungauged basins because of its direct application to ungauged basins, without going for cumbersome procedure of regionalization. In this study, GIUH is derived from the geomorphological characteristics of a basin and it is related to the parameters of the Clark instantaneous unit hydrograph (IUH) model as well as Nash IUH model for deriving its complete shape. The developed GIUH based Clark and Nash models are applied for simulation of the direct surface runoff (DSRO) hydrographs for ten rainfall‐runoff events of the Ajay basin upto Sarath gauging site of eastern India. The geomorphological characteristics of the Ajay basin are evaluated using the GIS package, Integrated Land and Water Information System (ILWIS). A comparison of the performances of the GIUH based Clark and Nash models in simulating the DSRO hydrographs by employing some of the commonly used error functions reveals that the DSRO hydrographs are computed with reasonable accuracy by both the models, which simulate the DSRO hydrographs of the basin considering it to be ungauged. The relative sensitivity and the degree of uncertainty associated with each of the input parameters of the GIUH based Clark and Nash models have been quantified. The uncertainty analysis reveals that apart from the velocity (V) parameter, the length of the highest order stream (LO) is the only geomorphological parameter which results in higher degree of uncertainty in derivation of unit hydrograph using the GIUH based Clark and Nash models, and hence, it is to be evaluated with greater precision for accurate runoff estimation from ungauged basins.

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.

Flood Estimation for Ungauged Catchments Using the GIUH

Traditional techniques for design flood estimation use historical rainfall-runoff data and unit hydrographs derived from them. Such procedures are questioned for their reliability due to the climatic and physical changes in the watershed and their application to ungauged areas. To overcome such difficulties, the use of physically based rainfall-runoff estimation methods such as the geomorphological instantaneous unit hydrograph (GIUH) have evolved. In this study, the GIUH is derived from watershed geomorphological characteristics and is then related to the parameters of the Nash instantaneous unit hydrograph (IUH) model for deriving its complete shape. The model parameters of the GIUH and the Nash IUH model are derived using two different approaches. In the first approach (referred to as GIUH-I) the rainfall intensity during each time interval is allowed to vary, whereas in the second approach (referred to as GIUH-II) rainfall intensity is averaged over the entire storm period. This methodology has been applied to the Jira river subcatchment in eastern India to simulate floods from 12 storm events. Results from both the GIUH approaches and those obtained by using Nash IUH are comparable with observed events.

Derivation of a new variable instantaneous unit hydrograph

A new variable instantaneous unit hydrograph (NVIUH) was derived by employing a second-order representation of the convolution integral and a nonlinear storage-discharge relation. This derivation removed a conceptual inconsistency in Ding's variable instantaneous unit hydrograph (DVIUH), and led to an analytical expression for second-order kernel. An alternative procedure for derivation of DVIUH was also formulated. The NVIUH was verified on two watersheds in China, and was found to be superior to both Nash's instantaneous unit hydrograph (NIUH) and DVIUH.