On-line estimation of unit hydrographs using the wavelet-based LMS algorithm / Estimation en ligne des hydrogrammes unitaires grâce à l'algorithme des moindres carrés moyens à base d'ondelettes

Abstract

This study applies the discrete wavelet transform (DWT) to decompose the unit hydrograph, thereby generating parsimonious reparameterizations of the unit hydrograph. A model compression method is then employed to significantly compress the unit hydrograph requiring that fewer coefficients be estimated. Moreover, a wavelet-based linearly constrained least mean squares (WLCLMS) algorithm is also used to estimate on-line the wavelet coefficients of the unit hydrograph. The updated wavelet coefficients of the unit hydrograph, convoluted with effective rainfall input in the wavelet domain, allow for accurate prediction of one-step-ahead runoff in the time domain. The proposed approach allows the unit hydrographs to vary in time and accurately predicts runoff from a basin in Taiwan, thus making it highly promising for flood forecasting.     

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.     

Unit hydrograph estimation with multiple events and prior information: I. Theory and a computer program

Abstract

The method of regularization for estimating unit hydrographs is expanded to allow the inclusion of prior information about the unit hydrograph shape. This may give smooth estimates without any loss in volume. The method is illustrated with prior information from a regression on catchment characteristics and with catchment lag determined from the data. A computer program to implement the method is given together with a sample calculation.     

A spatially distributed Clark’s unit hydrograph based hybrid hydrologic model (Distributed-Clark)

ABSTRACT

A hybrid hydrologic model (Distributed-Clark), which is a lumped conceptual and distributed feature model, was developed based on the combined concept of Clark’s unit hydrograph and its spatial decomposition methods, incorporating refined spatially variable flow dynamics to implement hydrological simulation for spatially distributed rainfall–runoff flow. In Distributed-Clark, the Soil Conservation Service (SCS) curve number method is utilized to estimate spatially distributed runoff depth and a set of separated unit hydrographs is used for runoff routing to obtain a direct runoff flow hydrograph. Case studies (four watersheds in the central part of the USA) using spatially distributed (Thiessen polygon-based) rainfall data of storm events were used to evaluate the model performance. Results demonstrate relatively good fit to observed streamflow, with a Nash-Sutcliffe efficiency (E_NS) of 0.84 and coefficient of determination (R²) of 0.86, as well as a better fit in comparison with outputs of spatially averaged rainfall data simulations for two models including HEC-HMS.     

Reliability assessment of water structures subject to data scarcity using the SCS-CN model

ABSTRACT

When discharge measurements are not available, design of water structures relies on using frequency analysis of rainfall data and applying a rainfall–runoff model to estimate a hydrograph. The Soil Conservation Service (SCS) method estimates the design hydrograph first through a rainfall–runoff transformation and next by propagating runoff to the basin outlet via the SCS unit hydrograph (UH) method. The method uses two parameters, the Curve Number (CN) and the time of concentration (T_c). However, in data-scarce areas, the calibration of CN and T_c from nearby gauged watersheds is limited and subject to high uncertainties. Therefore, the inherent uncertainty/variability of the SCS parameters may have considerable ramifications on the safety of design. In this research, a reliability approach is used to evaluate the impact of incorporating the uncertainty of CN and T_c in flood design. The sensitivity of the probabilistic outcome against the uncertainty of input parameters is calculated using the First Order Reliability Method (FORM). The results of FORM are compared with the conventional SCS results, taking solely the uncertainty of the rainfall event. The relative importance of the uncertainty of the SCS parameters is also estimated. It is found that the conventional approach, used by many practitioners, might grossly underestimate the risk of failure of water structures, due to neglecting the probabilistic nature of the SCS parameters and especially the Curve Number. The most predominant factors against which the SCS-CN method is highly uncertain are when the average rainfall value is low (less than 20 mm) or its coefficient of variation is not significant (less than 0.5), i.e. when the resulting rainfall at the design return period is low. A case study is presented for Egypt using rainfall data and CN values driven from satellite information, to determine the regions of acceptance of the SCS-CN method.

EDITOR D. Koutsoyiannis; ASSOCIATE EDITOR A. Efstratiadis     

A review of the synthetic unit hydrograph: from the empirical UH to advanced geomorphological methods

Abstract

This review paper critically examines one of the most popular flood hydrograph modelling techniques for ungauged basins, the synthetic unit hydrograph (SUH), and its recent developments and advances. For this purpose, the SUH models were first grouped into four main classes, as follows: (a) traditional or empirical models; (b) conceptual models; (c) probabilistic models; and (d) geomorphological models. It was found that the geomorphological class is the most useful and interesting, since it is able to employ topographic information, so limiting the role of the calibration parameters. This review is expected to be helpful to hydrologists, water managers and decision-makers searching for models to study the flood hydrograph, modelling techniques and related processes in ungauged basins. It was completed as the International Association of Hydrological Sciences (IAHS) Decade (2003–2012) on predictions in ungauged basins (PUB), drew to a close.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi

Citation Singh, P.K., Mishra, S.K., and Jain, M.K., 2013. A review of the Synthetic Unit Hydrograph: from the empirical UH to advanced geomorphological methods. Hydrological Sciences Journal, 59 (2), 239–261.     

Accounting for sparsely observed rainfall space—time variability in a rainfall—runoff model of a semiarid Tunisian basin/Prise en compte d'observations peu denses de la variabilité spatiotemporelle de la pluie dans une modélisation pluie—débit d'un bassin semi-aride Tunisien

Abstract

The management of water excesses and deficits is a major task in semiarid Mediterranean regions, where the variability of rainfall inputs is high at different time and space scales. Thus intense hydrometeorological events, which generate both potential resource and hazards, are of major interest. A simple method is proposed, with the example of the Skhira basin (192 km²) in central Tunisia, to account for the event space–time variability of rainfall in a rainfall–runoff model, in order to check its influence on the shape, magnitude and timing of resulting hydrographs. The transfer function used is a geomorphology-based unit hydrograph with an explicit territorial significance. Simulations made for highly variable events show the relevance of this method, seen as the first step of a downward approach, and its robustness with respect to the quality and the density of rainfall data.     

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.     

Coding random self-similar river networks and calculating geometric distances: 2. Application to runoff simulations / Codage de réseaux hydrographiques auto-similaires aléatoires et calcul de distances géométriques: 2. Application à la simulation de l'écoulement

Abstract

A preliminary method for coding random self-similar river networks and the corresponding distance calculations are proposed in a companion paper. The coding method is applied to generate random self-similar river networks, and the corresponding algorithm for calculating the geometric distances of the links is employed to determine the width function of the river networks, and thus evaluates the adaptability of the process. The width function-based geomorphological instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results imply that the separately random self-similar generating algorithm can be used to simulate river networks during the rainfall–runoff process. It can also help analyse the variations of the river network when rainfall locations change and study the influence on hydrological responses (IUH) when the shape of river network changes.     

Relating hydrograph components to rainfall and streamflow: a case study from northern Taiwan

Abstract

This study investigates the characteristics of hydrograph components from a watershed in Taiwan. Hydrograph components were modelled by using a model of three serial reservoirs with one parallel reservoir. Mean rainfall was calculated by using the block kriging method. The model parameters for 38 events were calibrated by using the shuffled complex evolution optimization algorithm. The model verification was made using 18 events. Based on the study results, the following findings were obtained: (1) for single-peak events, times to peak of hydrograph components are an increasing power function of the peak time of rainfall; (2) peak discharges of hydrograph components are linearly proportional to that of total runoff, and the ratios of quick and slow runoff are approximately 83% and 17% of total runoff, respectively; and (3) the total volume of quick runoff component is 52% of total runoff and that of slow runoff is 27%.

Editor D. Koutsoyiannis

Citation Li, Y.-J., Cheng, S.-J. Pao, T.-L. and Bi, Y.-J., 2012. Relating hydrograph components to rainfall and streamflow: a case study from northern Taiwan. Hydrological Sciences Journal, 57 (5), 861–877.     

Application of the geomorphological instantaneous unit hydrograph theory to development of forecasting models in Poland

ABSTRACT

Geomorphological instantaneous unit hydrograph (GIUH) theory has been applied for the estimation of the parameters of two conceptual models: a linear cascade model and a Laurenson-type model. Conceptual models, especially the linear cascade model, are more convenient for operational forecasting than the original GIUH model. A single linear reservoir model is suggested, with limited storage to represent the subsurface flow component. Subsurface flow is significant in Polish mountainous river catchments. Preliminary results of applying the model to operational flood forecasting are described.     

FLOOD MODELLING WITH GIS-DERIVED DISTRIBUTED UNIT HYDROGRAPHS

The concept of a spatially distributed unit hydrograph is based on the fact that the unit hydrograph can be derived from the time–area curve of a watershed by the S-curve method. The time–area diagram is a graph of cumulative drainage area contributing to discharge at the watershed outlet within a specified time of travel. Accurate determination of the time–area diagram is made possible by using a GIS. The GIS is used to describe the connectivity of the links in the watershed flow network and to calculate distances and travel times to the watershed outlet for various points within the watershed. Overland flow travel times are calculated by the kinematic wave equation for time to equilibrium; channel flow times are based on the Manning and continuity equations. To account for channel storage, travel times for channel reaches are increased by a percentage depending on the channel reach length and geometry. With GIS capability for rainfall mapping, the assumption of a uniform spatial rainfall distribution is no longer necessary; hence the term, spatially distributed unit hydrograph. An example of the application for the Waiparous Creek in the Alberta Foothills is given. IDRISI is used to develop a simple digital elevation model of the 229 km² watershed, using 1 km × 1 km grid cells. A grid of flow directions is developed and used to create an equivalent channel network. Excess rainfall for each 1 km × 1 km cell is individually computed by the Soil Conservation Service (SCS) runoff curve method and routed through the equivalent channel network to obtain the time–area curve. The derived unit hydrograph gave excellent results in simulating an observed flood hydrograph. The distributed unit hydrograph is no longer a lumped model, since it accounts for internal distribution of rainfall and runoff. It is derived for a watershed without the need for observed rainfall and discharge data, because it is essentially a geomorphoclimatic approach. As such, it allows the derivation of watershed responses (hydrographs) to inputs of various magnitudes, thus eliminating the assumption of proportionality of input and output if needed. The superposition of outputs is retained in simulating flood hydrographs by convolution, since it has been shown that some non-linear systems satisfy the principle of superposition. The distributed unit hydrograph appears to be a very promising rainfall runoff model based on GIS technology.     

Characterization of a cavern conduit system in Vietnam by time series correlation,cross-spectrum and wavelet analyses / Caractérisation du système du conduit d’une grotte au Vietnam par des analyses corrélatoires,spectrales-croisées et en ondelettes de séries temporelles

Abstract

Abstract Time series analyses are applied to characterize the transient flow regimes of the Nam La cavern conduit, northwest Vietnam. The conduit transforms the input signal to an output signal, and the degree of transformation provides information on the nature of the flow system. The input for the analysis is net precipitation and the flow hydrograph at the cave entrance, while the output series is the flow hydrograph at the resurgence. Cross-correlation and cross-spectrum analysis are used to investigate the stationarity and linearity of the input–output transformation of the system, resulting in hydrodynamic properties such as system memory, response time, and mean delay between input and output. It is shown that during high flow periods, the flow in the conduit is pressurized. Consequently, the linear input–output assumption holds only for low flows. To highlight the hydrodynamics of the cavern conduit for the high flow periods, wavelet spectrum and wavelet cross-spectrum analyses are applied.     

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.     

Hydrodynamic derivation of a variable parameter Muskingum method: 2. Verification

Abstract

The hydrodynamic derivation of a variable parameter Muskingum method and its solution procedure for estimating a routed hydrograph were presented in Part I of this series (Perumal, 1994a). In this paper, the limitations of the method, the criterion for its applicability and its accuracy are discussed based on the assumptions used. The method is verified by routing a given hypothetical inflow hydrograph through uniform rectangular cross-section channels and comparing the results with the corresponding numerical solutions of the St. Venant equations. The stage hydrographs as computed by the method are also compared with the corresponding St. Venant solutions. It is demonstrated that the method closely reproduces the St. Venant solutions for the discharge and stage hydrographs subject to the compliance of the assumptions of the method by the routing process.     

SYMPOSIUM ON EVAPORATION / SYMPOSIUM SUR L'ÉVAPORATION

SUMMARY

The geographical transposition of the results obtained from representative and experimental watersheds is a matter of regressions based upon geomorphological caracteristics of these watersheds. Therefore, the lumped model for the transformation of precipitations into runoff, generally used for small sized basins, must be simplified and standardized in order to be defined, in any case, by the same parameters. Moreover, the elements of the hydrograph, especially the base time, are to be determined by a very strict processus providing with “consistent” estimates. These new necessary conditions lead to see again the methods used till now for scientific purposes in operating the data from small watersheds, to the so-called “standard hydrograph”.     

Automatic calibration of the tank model / L'étalonnage automatique d'un modèle à cisterne

Abstract

The automatic calibration is done not by a hill-top climbing method but by a trial and error method carried out automatically by a computer program. The feedback procedure is made by comparing some criteria obtained from the observed hydrograph and the calculated hydrograph output from the working tank model. The two criteria are discharge volume and the shape of the hydrograph. The feedbacks of these two criteria correspond to dispacement feedback and velocity feedback in automatic control. The output of the working tank model is composed of components, the outputs from each of the tanks. Correspondingly, the whole period is divided into subperiods, in each of which each of the components plays the main part. The volume and shape are calculated in each subperiod and are used for the adjustment of the respective tanks. The feedback procedure starts from some initial model and converges very quickly after several (usually less than 15) iterations, and the result obtained is very good.     

Secretary Generals notes

Abstract

The influence of suburbanization upon runoff response to snowmelt and rain-on-snow inputs was examined for a small drainage basin in south-central Ontario. Modification of more than 50% of the basin area over a 14 year period led to a six-fold increase in the spring quickflow response ratio and an increase in the number of snowmelt events that generate appreciable quickflow. Anticipated changes in mean peak discharge, time of rise and quickflow response ratio did not emerge, and the influence of development upon these streamflow characteristics may have been overshadowed by annual changes in basin antecedent conditions. The distinction between hydrograph properties associated with snowmelt and rain-on-snow events has become more pronounced with suburbanization. Rain-on-snow generated higher maximum peak flows and lower average peak discharge per unit input compared with snowmelt, and these differences were accentuated by development of the basin. Rain-on-snow also produced more variable time of rise values, while the reduction in hydrograph recession coefficients that accompanied suburban development was most apparent for snowmelt events. The results suggest that suburbanization can have a subtle, yet real, influence upon basin runoff regime during spring snowmelt.     

An approach for the determination of precipitation input for worst-case flood modelling

ABSTRACT

There is a lack of suitable methods for creating precipitation scenarios that can be used to realistically estimate peak discharges with very low probabilities. On the one hand, existing methods are methodically questionable when it comes to physical system boundaries. On the other hand, the spatio-temporal representativeness of precipitation patterns as system input is limited. In response, this paper proposes a method of deriving spatio-temporal precipitation patterns and presents a step towards making methodically correct estimations of infrequent floods by using a worst-case approach. A Monte Carlo approach allows for the generation of a wide range of different spatio-temporal distributions of an extreme precipitation event that can be tested with a rainfall–runoff model that generates a hydrograph for each of these distributions. Out of these numerous hydrographs and their corresponding peak discharges, the physically plausible spatio-temporal distributions that lead to the highest peak discharges are identified and can eventually be used for further investigations.

Editor A. Castellarin; Associate editor E. Volpi