Application of a regionalized Clark IUH model with limited hydrologic data availability

To aid prediction of the flow hydrograph in a basin with limited data, a practical approach to determining a regionalized Clark instantaneous unit hydrograph (IUH) model is presented. The proposed model is described in terms of the synthetic time–area concentration curve, the concentration time, and a special regional similarity value that is valid in the whole basin. The latter was estimated from a Monte Carlo testing procedure based on the normal probability distribution of transformed regional similarity values composed of the time of concentration and the storage coefficient in gauged basins. The time–area concentration curve and the concentration time were calculated from a rational equation as in conventional methods. The method of transformation adopted was the Box–Cox power transformation, which is known to make non‐normal values resemble normal data. By introducing the regional similarity value into a Clark IUH, a statistically best estimate of IUH for given data conditions and its quantified degree of uncertainty were realized. The Wi River basin in Korea was used to test the applicability of the regionalized Clark IUH. The performance of the suggested methodology was evaluated by assuming an ungauged sub‐basin at the site. The results showed that the IUH model developed in this work was an effective tool, predicting a reliable hydrograph within the study area even though only limited data were available. Copyright © 2008 John Wiley & Sons, Ltd.     

A practical estimation of Clark IUH parameters using root selection and linear programming

The values of the parameters of the Clark instantaneous unit hydrograph (IUH) are often relying on the subjective decision of the researcher, which leads to large variations of their values. Therefore, an objective method minimizing the subjective judgement in the IUH modelling procedure while providing a reduced range of acceptable values is proposed. The proposed method uses a basin average IUH to mitigate the robustness problem of the Clark IUH parameters. Using linear system theory, the z‐transform is applied to the average IUH and then the IUH polynomial is factored into the recession and time‐area curve (TAC) components based on a convolution relation between the Clark IUH parameters. During this calculation, the root selection method was adopted to verify the storage coefficient R from the recession component and a linear programming technique was applied for determining the TAC for the basin of interest. The Wi River basin was used to test the applicability of the proposed method. The results showed that the components of a single reservoir and the TAC for Clark IUH were separated effectively, and acceptable values for the parameters were obtained. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimation of Nash's IUH parameters using stochastic search algorithms

In 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.     

Reservoir attenuation of floods from ungauged basins

Abstract

In a typical reservoir routing problem, the givens are the inflow hydrograph and reservoir characteristic functions. Flood attenuation investigations can be easily accomplished using a hydrological or hydraulic routing of the inflow hydrograph to obtain the reservoir outflow hydrograph, unless the inflow hydrograph is unavailable. Although attempts for runoff simulation have been made in ungauged basins, there is only a limited degree of success in special cases. Those approaches are, in general, not suitable for basins with a reservoir. The objective of this study is to propose a procedure for flood attenuation estimation in ungauged reservoir basins. In this study, a kinematic-wave based geomorphic IUH model was adopted. The reservoir inflow hydrograph was generated through convolution integration using the rainfall excess and basin geomorphic information. Consequently, a fourth-order Runge-Kutta method was used to route the inflow hydrograph to obtain the reservoir outflow hydrograph without the aid of recorded flow data. Flood attenuation was estimated through the analysis of the inflow and outflow hydrographs of the reservoir. An ungauged reservoir basin in southern Taiwan is presented as an example to show the applicability of the proposed analytical procedure. The analytical results provide valuable information for downstream flood control work for different return periods.     

Book Review

Abstract

The instantaneous unit hydrograph (IUH) of a watershed is the result of one instantaneous unit of rainfall excess distributed uniformly over the watershed. Although the geomorphological characteristics of the basin remain relatively constant, the variable characteristics of storms cause variations in the shape of the resulting hydrographs. It is, therefore, inadequate to use one typical IUH to represent the hydrological response generated from any specific storm. In this study, a variable IUH was derived that directly reflects the time-varying rainfall intensity during storms. The rainfall intensity used to generate the variable IUH at time t is the mean rainfall intensity occurring from the time t—T _c to t in which T _c is the watershed time of concentration. Hydrological records from three watersheds in Taiwan were used to demonstrate the applicability of the proposed model. The results show that better simulations can be obtained by using the proposed model than by using the conventional unit hydrograph method, especially for concentrated rainstorm cases.     

Salinograph trends as indicators of the recession characteristics of stream components

Compared to hydrograph recession analysis, which is widely applied in engineering hydrology, the quantitative assessment of stream salinity with time (i.e. the salinograph) has received significantly less attention. In particular, while in many previous hydrological studies an inverse relationship between hydrograph and salinograph responses is apparent, the concept of salinity accession (the inversely related salinity counterpart to hydrograph recession) has not been introduced nor quantitatively evaluated in previous literature. In this study, we conduct a mathematical analysis of salinograph accession, and determine new quantitative relationships between salinity accession and hydrograph recession parameters. An equation is formulated that reproduces the general trend in salinity accession. A salinity accession parameter k_c is then introduced and is shown to be the ratio of direct runoff to total stream flow recession parameters: k_r/k. The groundwater recession parameter k_g was estimated using a simple and rapid method that uses both salinograph and hydrograph data. Salinity accession type‐curves illustrate that under certain conditions, the relative steepness of individual salinographs is dependent upon the ratio of groundwater salinity to direct runoff salinity: C_g/C_r. The salinity accession algorithms are applied to two contrasting field settings: Scott Creek, South Australia and Sandy Creek, northern Queensland, Australia. It was found that k_g > k during periods of obvious stream flow recession, for the events analysed. Salinograph accession behaviour was fairly similar for both sites, despite contrasting environments. Using assumed end‐member salinities for groundwater and direct runoff based upon field observations, the behaviour of k_c from the Scott Creek site was approximately reproduced by varying the initial groundwater to runoff flow ratio: Q_g0/Q_r0, within reasonable parameter ranges. The use of salinograph information when used in addition to standard hydrograph analyses provided useful information on recession characteristics of stream components. Copyright © 2008 John Wiley & Sons, Ltd.     

A semi‐distributed parallel‐type linear reservoir rainfall‐runoff model and its application in Taiwan

The main purpose of this paper is to introduce a semi‐distributed parallel surface rainfall‐runoff conceptual model. In this paper, a general solution of the instantaneous unit hydrograph (IUH) has been derived successfully for N linearly connected reservoirs, each having a different storage constant. The solution is a function of geomorphologic parameters, meteorologic factors and roughness coefficients. The model also takes into account the hydrologic response which is influenced by outflow downstream of a reservoir. For calibration, the shuffled complex evolution (SCE) algorithm is used to search for the global optimal parameters of the model. Because of the parallel structure, the mean roughness parameter of the channel becomes a “conceptual” parameter without a real physical meaning. To evaluate the adaptability of the model adopted, three watersheds around the city of Taipei in Taiwan were chosen to test the effectiveness of the model. The study provides an appropriate rainfall‐runoff model for planning flood mitigation in Taiwan. Copyright © 1999 John Wiley & Sons, Ltd.     

The meaning of oscillations in unit hydrograph S-curves

ABSTRACT

The Duhamel superposition integral is used to obtain some exact solutions for unit hydrograph applications. These equations and numerical examples are used to show that oscillations will occur in an S-curve when the time step is less than the excess rainfall duration if the measured hydrograph differs from a hydrograph that would be obtained by solving a linear differential equation with time-independent coefficients. The implications of this result with regard to the calculation of the instantaneous unit hydrograph (IUH) are discussed.     

Bivariate flood frequency analysis using the copula function: a case study of the Litija station on the Sava River

As an alternative to the commonly used univariate flood frequency analysis, copula frequency analysis can be used. In this study, 58 flood events at the Litija gauging station on the Sava River in Slovenia were analysed, selected based on annual maximum discharge values. Corresponding hydrograph volumes and durations were considered. Different bivariate copulas from three families were applied and compared using different statistical, graphical and upper tail dependence tests. The parameters of the copulas were estimated using the method of moments with the inversion of Kendall's tau. The Gumbel–Hougaard copula was selected as the most appropriate for the pair of peak discharge and hydrograph volume (Q‐V). The same copula was also selected for the pair hydrograph volume and duration (V‐D), and the Student‐t copula was selected for the pair of peak discharge and hydrograph duration (Q‐D). The differences among most of the applied copulas were not significant. Different primary, secondary and conditional return periods were calculated and compared, and some relationships among them were obtained. Copyright © 2014 John Wiley & Sons, Ltd.     

Comparative analysis of a geomorphology‐based instantaneous unit hydrograph in small mountainous watersheds

A conceptual insytnataneous unit hydrograph (IUH) based on geomorphologival association of linear reservoirs (GR) previously developed by the authors has been compared with other IUH models: a distributed GR variation (GR(v)), the Nash IUH, the Chutha and Dooge IUH, and the Troutman and Karlinger IUH for the analysis of direct runoff hydrographs recorded in three experimental watershed of the north of Spain. The comparison was made through a calibration‐validation process in which a leave‐one‐out cross‐validation method was applied. The results indicate the satisfactory performance of all the models, with the advantage for the GR model of the dependence on only one parameter, which can be identified from the watershed and event characteristics. This property makes its use easier than that of other models. Copyright © 2011 John Wiley & Sons, Ltd.     

Assessment of river flow with significant lateral inflow through reverse routing modeling

The discharge hydrograph estimation in rivers based on reverse routing modeling and using only water level data at two gauged sections is here extended to the most general case of significant lateral flow contribution, without needing to deploy rainfall–runoff procedures. The proposed methodology solves the Saint‐Venant equations in diffusive form also involving the lateral contribution using a “head‐driven” modeling approach where lateral inflow is assumed to be function of the water level at the tributary junction. The procedure allows to assess the discharge hydrograph at ends of a selected river reach with significant lateral inflow, starting from the stage recorded there and without needing rainfall data. Specifically, the MAST 1D hydraulic model is applied to solve the diffusive wave equation using the observed stage hydrograph at the upstream section as upstream boundary condition. The other required data are (a) the observed stage hydrograph at the downstream section, as benchmark for the parameter calibration, and (b) the bathymetry of the river reach, from the upstream section to a short distance after the downstream gauged section. The method is validated with different flood events observed in two river reaches with a significant intermediate basin, where reliable rating curves were available, selected along the Tiber River, in central Italy, and the Alzette River, in Luxembourg. Very good performance indices are found for the computed discharge hydrographs at both the channel ends and along the tributaries. The mean Nash‐Sutcliffe value (NS_q) at the channel ends of two rivers is found equal to 0.99 and 0.86 for the upstream and downstream sites, respectively. The procedure is also validated on a longer stretch of the Tiber River including three tributaries for which appreciable results are obtained in terms of NS_q for the computed discharge hydrographs at both the channel ends for three investigated flood events.     

An investigation of lag times for rainfall–runoff–sediment yield events in small river basins / Une analyse des temps de réponse d'événements pluie–débit–transport solide au sein de petits bassins versants

Abstract

River basin lag time (LAG), defined as the elapsed time between the occurrence of the centroids of the effective rainfall intensity pattern and the storm runoff hydrograph, is an important factor in determining the time to peak and the peak value of the instantaneous unit hydrograph, IUH. In the procedure of predicting a sedimentgraph (suspended sediment load as a function of time), the equivalent parameter is the lag time for the sedimentgraph (LAG_s ), which is defined as the elapsed time between the occurrence of the centroids of sediment production during a storm event and the observed sedimentgraph at the gauging station. Results of analyses of rainfall, runoff and suspended sediment concentration event data collected from five small Carpathian basins in Poland and from a 2.31-ha agricultural basin, in central Illinois, USA have shown that LAG_s was, in the majority of cases, smaller than LAG, and that a significant linear relationship exists between LAG_s and LAG.     

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

A 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 the Kalman filter to the Nash model

The Nash model was used for application of the Kalman filter. The state vector of the rainfall–runoff system was constituted by the IUH (instantaneous unit hydrograph) estimated by the Nash model and the runoff estimated by the Nash model using the Kalman filter. The initial values of the state vector were assumed as the average of 10% of the IUH peak values and the initial runoff estimated from the average IUH. The Nash model using the Kalman filter with a recursive algorithm accurately predicted runoff from a basin in Korea. The filter allowed the IUH to vary in time, increased the accuracy of the Nash model and reduced physical uncertainty of the rainfall–runoff process in the river basin. © 1998 John Wiley & Sons, Ltd.     

Regionalization of floods in New Brunswick (Canada)

This study uses the method of peaks over threshold (P.O.T.) to estimate the flood flow quantiles for a number of hydrometric stations in the province of New Brunswick, Canada. The peak values exceeding the base level (threshold), or `exceedances', are fitted by a generalized Pareto distribution. It is known that under the assumption of Poisson process arrival for flood exceedances, the P.O.T. model leads to a generalized extreme value distribution (GEV) for yearly maximum discharge values. The P.O.T. model can then be applied to calculate the quantiles X <sub>T</sub> corresponding to different return periods T, in years. A regionalization of floods in New Brunswick, which consists of dividing the province into `homogeneous regions', is performed using the method of the `region of influence'. The 100-year flood is subsequently estimated using a regionally estimated value of the shape parameter of the generalized Pareto distribution and a regression of the 100-year flood on the drainage area. The jackknife sampling method is then used to contrast the regional results with the values estimated at site. The variability of these results is presented in box-plot form. Received: June 1, 1997     

Regionalization of floods in New Brunswick (Canada)

This study uses the method of peaks over threshold (P.O.T.) to estimate the flood flow quantiles for a number of hydrometric stations in the province of New Brunswick, Canada. The peak values exceeding the base level (threshold), or `exceedances', are fitted by a generalized Pareto distribution. It is known that under the assumption of Poisson process arrival for flood exceedances, the P.O.T. model leads to a generalized extreme value distribution (GEV) for yearly maximum discharge values. The P.O.T. model can then be applied to calculate the quantiles X <sub>T</sub> corresponding to different return periods T, in years. A regionalization of floods in New Brunswick, which consists of dividing the province into `homogeneous regions', is performed using the method of the `region of influence'. The 100-year flood is subsequently estimated using a regionally estimated value of the shape parameter of the generalized Pareto distribution and a regression of the 100-year flood on the drainage area. The jackknife sampling method is then used to contrast the regional results with the values estimated at site. The variability of these results is presented in box-plot form. Received: June 1, 1997     

Safety assessment for dams of the cascade reservoirs system of Lancang River in extreme situations

Numerous dams have been constructed in the midstream and downstream regions of Lancang River, which form a complex cascade reservoirs system. The safety of dams is critical for water resource management of the whole system. To check the safety of dams, this study used the MIKE 11 model to simulate flood routing along the Lancang River from Xiaowan dam to Jinghong dam under extreme situations of 100-, 500-, 1000-, 5000-, and 10,000-year design floods throughout the whole cascade reservoirs system. The design flood events used as the input for the MIKE 11 model contains the design flood hydrograph of the upstream reservoirs and corresponding flood hydrographs of the intermediate areas. The design flood hydrograph of the upstream reservoirs was obtained using the Equal Frequency Factor Method, and the corresponding flood hydrograph of the intermediate areas was obtained using the Equivalent Frequency Regional Composition Method. The results show that all dams are safe for the 100-, 500-, 1000-, and 5000-year design flood situations throughout the whole cascade reservoirs system, whereas the Manwan and Jinghong dams have a risk of overtopping under a 10,000-year design flood. The curves showing the relationship between the highest water level and return period for the dams are also presented.     

Identifying hydrograph parameters and their relationships to urbanization variables

Abstract

This study examines relationships between model parameters and urbanization variables for evaluating urbanization effects in a watershed. Rainfall–runoff simulation using the Nash model is the main basis of the study. Mean rainfall and excesses resulting from time-variant losses were completed using the kriging and nonlinear programming methods, respectively. Calibrated parameters of 47 events were related to urbanized variables, change of shape parameter responds more sensitively than that of scale parameter based on comparisons between annual average and optimal interval methods. Regression equations were used to obtain four continuous correlations for linking shape parameter with urbanization variables. Verification of 10 events demonstrates that shape parameter responds more strongly to imperviousness than to population, and a power relationship is suitable. Therefore, an imperviousness variable is a major reference for analysing urbanization changes to a watershed. This study found that time to peak of IUH was reduced from 11.76 to 3.97 h, whereas peak discharge increased from 44.79 to 74.92 m³/s.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi

Citation Huang, S.-Y., Cheng, S.-J., Wen, J.-C. and Lee, J.-H., 2012. Identifying hydrograph parameters and their relationships to urbanization variables. Hydrological Sciences Journal, 57 (1), 144–161.     

Hydraulic model calibration for extreme floods in bedrock‐confined channels: case study from northern Thailand

Palaeoflood reconstructions based on stage evidence are typically conducted in data‐poor field settings. Few opportunities exist to calibrate the hydraulic models used to estimate discharge from this evidence. Consequently, an important hydraulic model parameter, the roughness coefficient (e.g. Manning's n), is typically estimated by a range of approximate techniques, such as ‘visual estimation’ and semi‐empirical equations. These techniques contribute uncertainty to resulting discharge estimates, especially where the study reach exhibits sensitivity in the discharge–Manning's n relation. We study this uncertainty within a hydraulic model for a large flood of known discharge on the Mae Chaem River, northern Thailand. Comparison of the ‘calibrated’ Manning's n with that obtained from semi‐empirical equations indicates that these underestimate roughness. Substantial roughness elements in the extra‐channel zone, inundated during large events, contribute significant additional sources of flow resistance that are captured neither by the semi‐empirical equations, nor by existing models predicting stage–roughness variations. This bedrock channel exhibits a complex discharge–Manning's n relation, and reliable estimates of the former are dependent upon realistic assignment of the latter. Our study demonstrates that a large recent flood can provide a valuable opportunity to constrain this parameter, and this is illustrated when we model a palaeoflood event in the same reach, and subsequently examine the magnitude–return period consequences of discharge uncertainty within a flood frequency analysis, which contributes its own source of uncertainty. Copyright © 2005 John Wiley & Sons, Ltd.     

Development of the instantaneous unit hydrograph using stochastic differential equations

Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement.