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.     

A multilinear discrete Nash-cascade model for stage-hydrograph routing in compound river channels

ABSTRACT

Stream gauge-based information is the foundation for many hydrological applications in a river basin including the aquatic-habitat conservation. A simple two-parameter model for routing streamflow depth (alternatively, stream–stage) hydrographs and estimating corresponding discharge hydrographs in river channels is proposed using the multilinear approach, based on Nash-type discrete-cascade model. The applicability of this model is investigated by extending its framework to the realm of compound cross-section trapezoidal channels for both in-bank and overbank flows by using 20 flood events of the Tiber River in the Umbria region of Central Italy, and subsequently comparing the simulated results with the corresponding simulations of the HEC-RAS (Hydrologic Engineering Center – River Analysis System) hydrodynamic model and observed flow depth hydrographs. The field application, comparative study, and uncertainty and sensitivity analysis of the results demonstrate that the proposed multilinear discrete Nash-cascade stage-hydrograph (MDNS) routing model has the potential for routing floods in real-world rivers and canal irrigation systems, especially in operational mode.     

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.     

Two‐dimensional continuous simulation of spatiotemporally varied hydrological processes using the time‐area method

Distributed, continuous hydrologic models promote better understanding of hydrology and enable integrated hydrologic analyses by providing a more detailed picture of water transport processes across the varying landscape. However, such models are not widely used in routine modelling practices, due in part to the extensive data input requirements, computational demands, and complexity of routing algorithms. We developed a two‐dimensional continuous hydrologic model, HYSTAR, using a time‐area method within a grid‐based spatial data model with the goal of providing an alternative way to simulate spatiotemporally varied watershed‐scale hydrologic processes. The model calculates the direct runoff hydrograph by coupling a time‐area routing scheme with a dynamic rainfall excess sub‐model implemented here using a modified curve number method with an hourly time step, explicitly considering downstream ‘reinfiltration’ of routed surface runoff. Soil moisture content is determined at each time interval based on a water balance equation, and overland and channel runoff is routed on time‐area maps, representing spatial variation in hydraulic characteristics for each time interval in a storm event. Simulating runoff hydrographs does not depend on unit hydrograph theory or on solution of the Saint Venant equation, yet retains the simplicity of a unit hydrograph approach and the capability of explicitly simulating two‐dimensional flow routing. The model provided acceptable performance in predicting daily and monthly runoff for a 6‐year period for a watershed in Virginia (USA) using readily available geographic information about the watershed landscape. Spatial and temporal variability in simulated effective runoff depth and time area maps dynamically show the areas of the watershed contributing to the direct runoff hydrograph at the outlet over time, consistent with the variable source area overland flow generation mechanism. The model offers a way to simulate watershed processes and runoff hydrographs using the time‐area method, providing a simple, efficient, and sound framework that explicitly represents mechanisms of spatially and temporally varied hydrologic processes. Copyright © 2015 John Wiley & Sons, Ltd.     

Genetic programming approach for flood routing in natural channels

In recognition of the non‐linear relationship between storage and discharge existing in most river systems, non‐linear forms of the Muskingum model have been proposed, together with methods to calibrate the model parameters. However, most studies have focused only on routing a typical hypothetical flood hydrograph characterized by a single peak. In this study, we demonstrate that the storage–discharge relationship adopted for the non‐linear Muskingum model is not adequate for routing flood hydrographs in natural channels, which are often characterized by multiple peaks. As an alternative, an evolutionary algorithm‐based modelling approach, i.e. genetic programming (GP), is proposed, which is found to route complex flood hydrographs accurately. The proposed method is applied for constructing a routing model for a channel reach along the Walla Walla River, USA. The GP model performs extremely well with a root‐mean‐square error (RMSE) of 0·73 m³ s^?1 as against an RMSE of 3·26 m³ s^?1 for routing the multi‐peaked hydrograph. The advantage of GP lies in the fact that, unlike other models, it establishes the routing relationship in an easy and simple mathematical form. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

Hybrid method to update the design flood shape for spillway operation in a dam: case study of the Huites Dam,Mexico

To design and review the operation of spillways, it is necessary to estimate design hydrographs, considering their peak flow, shape and volume. A hybrid method is proposed that combines the shape of the design hydrograph obtained with the UNAM Institute of Engineering Method (UNAMIIM) with the peak flow and volume calculated from a bivariate method. This hybrid method is applied to historical data of the Huites Dam, Sinaloa, Mexico. The goal is to estimate return periods for the maximum discharge flows (that account for the damage caused downstream) and the maximum levels reached in the dam (measure of the hydrological dam safety) corresponding to a given spillway and its management policy. Therefore, to validate the method, the results obtained by the flood routing of the 50-year hydrograph are compared with those obtained by the flood routing of the three largest historical floods. Both maximum flow and elevation were in the range of values observed within 37.5–75 years corresponding to the length of the historical record.     

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.     

Effectiveness of BIOECODS for peak flow attenuation: an appraisal using InfoWorks SD

The Bio-Ecological Drainage System (BIOECODS) is a sustainable drainage system, which adopts a “control at source” approach for urban storm water management in Malaysia. This study attempts to model a small-scale BIOECODS using InfoWorks SD. New modelling techniques are used to fully integrate the surface and on-line subsurface conveyance system, in which overland flow routing is described by a storm water management model that uses a nonlinear reservoir method and the kinematic wave approximation of the St Venant equation, and subsurface flow is described by the Horton method in conjunction with the Soil Conservation Service (SCS) curve number (CN) method. The observed water levels at primary outlets are compared with those obtained from model simulation. The modelling approach has been proven successful as the hydrographs (predicted and observed) match each other closely, with a mean error in the range of 4.58–7.32%. Results from the model showed that the BIOECODS is able to attenuate peak flow by 60–75%, and increase the lag time by 20 min within an area of <28?300 m² when compared with a traditional drainage system.     

Synthetic hydrograph generation by hydrological donors

A method to build synthetic hydrographs is introduced, based on 1300 gauging stations in France and Switzerland, covering a wide range of size and climatology. For each station, an average of two floods per year are selected by a peak-over-threshold method, providing about 69?000 hydrographs. For a given catchment, some “donor stations” are selected with criteria of proximity in space, size and runoff production. These donors provide hundreds of hydrographs which can complement the ones recorded locally, or replace them if no hydrograph is available. With this subset of hydrographs, one can estimate the catchment’s average peak-to-volume ratio of floods, and build the corresponding median hydrograph. Another application is, for a given daily discharge sequence (being observed or simulated), to generate a relevant synthetic hydrograph by combining appropriate hydrographs of the subset. These methods are assessed by performing a jack-knife validation on a wide dataset of stations.     

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.     

MÉTHODE D'ÉTUDE DES NAPPES LIBRES DANS LES AQUIFÈRES ANISOTROPES

Abstract

The necessary and sufficient conditions for non-zero phase shift and non-zero attenuation in linear flood routing can be derived from the continuity equation alone and are found to depend on the existence of an imaginary part in the expression for frequency or in the expression for wave number. It is shown that in linear flood routing the phase lag between flow rate and area of flow is directly related to the attenuation per unit wave length. The effects of using various forms of the momentum equation, in addition to the continuity equation, are exemplified by deriving analytical expressions in terms of the frequency, both for attenuation per unit channel length and for phase shift, for the kinematic wave, the general diffusion analogy, and the complete St. Venant equation.     

Using stochastic state‐space modelling to specify and reduce hydrograph error

A Bayesian post‐processor is used to generate a representation of the likely hydrograph forecast flow error distribution using raingauge and radar input to a stochastic catchment model and its deterministic equivalent. A hydrograph ensemble is so constructed. Experiments are analysed using the model applied to the River Croal in north‐west England. It is found that for rainfall input to the model having errors less than 3mm h^?1, corresponding to about a 15% error in peak flow, the stochastic model outperforms the deterministic model. The range of hydrographs associated with the different model simulations and the measured hydrographs are compared. The significant improvement possible using a stochastic approach is demonstrated for a specific case study, although the mean hydrograph derived using the stochastic model has an error range associated with it. Copyright © 2007 John Wiley & Sons, Ltd.     

Nonlinear transformation of unit hydrograph

Unit hydrograph (UH) and its numerous derivatives have been popular for estimation of flood hydrographs. Two major assumptions still overshadow UH applications. One is the linearity and the other is time invariance. In theory, only peak discharge of an equilibrium hydrograph follows linear proportionality to excess rainfall intensity. In trying to relax the linearity constraint, this paper aims to propose a nonlinear way of transforming a given UH to other general hydrographs. The transformation or mapping technique relies on a simple rainfall ratio raised to a power less than unity. The case of nonlinear transformation is illustrated for a number of watershed geometries with either known kinematic wave analytic solutions or observed data. The nonlinear UH approach also relaxes the assumption of constant time base of the UH. The proposed nonlinear UH transformation may thus be viewed as a major step in closing the gap between physically based and traditional UH-based surface runoff simulation approaches.     

Time-dependent shear velocities in channel routing

Abstract

The main aim of this study is the experimental investigation of friction velocities and shear stresses in rivers under unsteady flow conditions. Special measurements of mean velocities and other hydraulic parameters were made in two small lowland rivers in central Poland. Four controlled flood waves were released and analysed in the selected reaches. The main hydrometric characteristics and the relationship between water level and discharge were established. Friction velocities were obtained directly from the full St Venant equations of motion, as well as from only the steady momentum equation, and their time-dependent forms were established. Both these approaches provided similar results when the unsteadiness parameter was relatively low. It appeared that real friction velocities were much larger than those obtained from the common uniform flow formula. The passing hydrograph influenced the value of the shear velocity significantly.     

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     

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.     

Updating Real-Time Flood Forecasting Using a Fuzzy Rule-Based Model/Mise à Jour de Prévision de Crue en Temps Réel Grâce à un Modèle à Base de Règles Floues

Abstract

An updating technique is a tool to update the forecasts of mathematical flood forecasting model based on data observed in real time, and is an important element in a flood forecasting model. An error prediction model based on a fuzzy rule-based method was proposed as the updating technique in this work to improve one- to four-hour-ahead flood forecasts by a model that is composed of the grey rainfall model, the grey rainfall—runoff model and the modified Muskingum flow routing model. The coefficient of efficiency with respect to a benchmark is applied to test the applicability of the proposed fuzzy rule-based method. The analysis reveals that the fuzzy rule-based method can improve flood forecasts one to four hours ahead. The proposed updating technique can mitigate the problem of the phase lag in forecast hydrographs, and especially in forecast hydrographs with longer lead times.     

Analytical solutions of a routing problem for storm water in a detention basin

Abstract

Analytical solutions of a routing problem for storm water flowing through a linear reservoir are presented for the assumption of trapezoidal-shaped inflow hydrograph. The maximum ponded (water) depth in the detention basin is chosen as a main design criterion. Calculations are carried out for a given rain recurrence interval but for various rain durations and sand filter surface areas to reach the maximum permitted ponded depth. A design example is also provided.