Inverse flood routing using simplified flow equations

For determining of Muskingum model coefficients, requires to an output hydrograph. Such hydrograph is not available in most rivers. In this research, the Muskingum's new coefficients are determined by the method that which is not require to output hydrograph and its accuracy is high. This coefficient is determined based on kinematic wave model with suitable scheme. The comparison between results of Muskingum model with new coefficients and dynamic wave model, showed that the new coefficients, are valid at special conditions. The new coefficients were adjusted by optimization technique for all conditions. The new adjusted coefficients are function of bed slop, bottom width and Manning's roughness coefficient for the river. The results of these coefficients were validated by dynamic wave model.

6th International Conference on Flood Management (ICFM6), 2014

An effective water resources management is important to meet multiple objectives such as water supply, navigation, hydroelectricity generation, environmental obligations and flood protection. By implementing a predictive control approach over a short-term forecast horizon, it is possible to foresee stress conditions or peak flow events and support decision-makers to take actions before these events happen for minimizing their impacts. In the case of flood events, this technique enables the operators to pre-release water from a reservoir for allocating additional storage before the flood event occurs for mitigating flood damage along downstream river reaches. A robust and fast routing model is required in order to obtain quick and reliable estimates of downstream flow conditions related to release changes of the reservoir. In this paper, four different models are assessed concerning their implementation in a predictive control of the Três Marias Reservoir located at the Upper River São Francisco in Brazil: i) a fully dynamic model using the software package SOBEK; ii) a semi-distributed rainfall-runoff model with Muskingum-Cunge routing for the flow reaches of interest, the MGB-IPH (Modelo Hidrológico de Grandes Bacias-Instituto de Pesquisas Hidráulicas); iii) a simplified reservoir routing and iv) a diffusive wave model. The last two models are implemented in the RTC-Tool toolbox.In general, we find comparable results between the simplified models in RTC-Tools and the more sophisticated SOBEK model and a lower performance of the MGB model. However, both hydraulic modeling approaches, i.e. the SOBEK model as well as the diffusive wave model in RTC-Tools, suffer from too much numerical diffusion in case of courser grids. In the reservoir routing approach, the introduction of pure advection by time lags offers an efficient cure for excessive numerical diffusion even on courser grids. From the predictive control point of view, this approach shows the best compromise in terms of robustness, computational efficiency and accuracy.

Hydrological Sciences Journal, 1983

The effect of the downstream boundary condition on the flow in a channel reach as predicted by the linear diffusion analogy model is analysed by both Laplace transformation and by modal analysis. In each case the solution takes the form of an infinite series. It is shown that the series based on Laplace transformation is highly convergent for small times and the series based on modal analysis is highly convergent for medium and longer times. Sur les effets de remous dans le calcul de propagation des crues par la diffusion linéaire RESUME L'effet des conditions aux limites aval sur le débit d'un bief de rivière, tel q'il est prévu par le modèle analogique de diffusion linéaire, est analysé ici par la transformation de Laplace et aussi par l'analyse modale. Dans ces deux cas, la solution prend la forme d'une série infinie. On montre aussi que la série basée sur la transformation de Laplace converge rapidement pour des temps courts et que la série basée sur l'analyse modale converge rapidement pour des temps moyens et longs.

Water Practice and Technology, 2021

Flood impact assessment in a river system is done with the help of flood routing and this process helps to determine the status of sensitive points of the route in terms of flood entry and the resulting risks for urban and rural areas. For flood routing, a hydrodynamic numerical model should be implemented and this model needs upstream and downstream boundaries. In some cases, the upstream boundary, which is usually a hydrograph, is not available due to the lack of facilities and it is necessary to be generated for numerical model implementation. The purpose of this study is to present an integrated method comprising an optimization model and a hydrodynamic numerical model for flood modeling in order to determine the upstream hydrograph using the measured downstream hydrograph along a river. The routing procedure consists of three steps: (1) generating a hypothetical upstream hydrograph using the genetic algorithm method; (2) hydrodynamic modeling using a numerical simulation model ...

Water Resources Management, 2012

In this paper attention is first focused on a comparative analysis of three hydraulic models for overland flow simulations. In particular, the overland flow was considered as a 2D unsteady flow and was mathematically described using three approaches (fully dynamic, diffusive and kinematic waves). Numerical results highlighted that the differences among the simulations were not very important when the simulations referred to commonly used ideal tests found in the literature in which the topography is reduced to plane surface. Significant differences were observed in more complicated tests for which only the fully dynamic model was able to provide a good prediction of the observed discharges and water depths. Then, attention is focused on the fully dynamic model and in particular on the analysis of two numerical schemes (TVD-MacCormack and HLL) and the influence of the grid size. Numerical tests carried out on irregular topography show that, as the grid size decreases, the performance of the HLL scheme becomes closer to that of the TVD-MacCormack scheme in shorter computational times at least for high rainfall intensity.

Journal of Hydro-environment Research, 2011

Routing of floods is essential to control the flood flow at the flood control station such that it is within the specified safe limit. In this paper, the applicability of the extended Muskingum method is examined for routing of floods for a case study of Hirakud reservoir, Mahanadi river basin, India. The inflows to the flood control station are of two types e one controllable which comprises of reservoir releases for power and spill and the other is uncontrollable which comprises of inflow from lower tributaries and intermediate catchment between the reservoir and the flood control station. Muskingum model is improved to incorporate multiple sources of inflows and single outflow to route the flood in the reach. Instead of time lag and prismoidal flow parameters, suitable coefficients for various types of inflows were derived using Linear Programming. Presently, the decisions about operation of gates of Hirakud dam are being taken once in 12 h during floods. However, four time intervals of 24, 18, 12 and 6 h are examined to test the sensitivity of the routing time interval on the computed flood flow at the flood control station. It is observed that mean relative error decreases with decrease in routing interval both for calibration and testing phase. It is concluded that the extended Muskingum method can be explored for similar reservoir configurations such as Hirakud reservoir with suitable modifications.

Water Resources Research, 2015

Simplified flood propagation models are often employed in practical applications for hydraulic and hydrologic analyses. In this paper, we present a new numerical method for the solution of the Linear Parabolic Approximation (LPA) of the De Saint Venant equations (DSVEs), accounting for the space variation of model parameters and the imposition of appropriate downstream boundary conditions. The new model is based on the analytical solution of a cascade of linear diffusive channels in the Laplace Transform domain. The time domain solutions are obtained using a Fourier series approximation of the Laplace Inversion formula. The new Inverse Laplace Transform Diffusive Flood Routing model (ILTDFR) can be used as a building block for the construction of real-time flood forecasting models or in optimization models, because it is unconditionally stable and allows fast and fairly precise computation.

Water Resources Research, 1993

A simple and efficient method for flow routing, combining the kinematic wave equation with a statistical procedure, is introduced. It accounts for the nonlinearity and the dispersion of the flood wave propagation phenomenon and for lateral flow. The method is flexible, because it can be used to simulate a variety of flow variables, for example, water stage or discharge. Its calibration is based on historical records at both ends of the reach, and does not require geometric cross-section or longitudinal data. An application to the White Nile in Sudan demonstrates the practicality and accuracy of the method. INTRODUCTION The theory for flow routing in open channels is based on the de St. Venant's equations which describe unsteady nonuniform gradually varied flow. Although the de St. Venant's equations already involve approximations to simplify the mathematical formulation of the problem, flow muting still remains a difficult problem in open channel hydraulics. The flow-routing methods described in the literature range from linear conceptual models, which replace the momentum equation by an empirical storage equation [McCarthy, 1938; Meyer, 1941; Kalinin and Mi•/ukov, 1958], to highly complicated numerical techniques, which solve the complete nonlinear hydrodynamic equations [Preissmann, 1961; Amein, 1966; Cooley and Moin, 1976]. Both the accuracy of the simple conceptual models and the suitability of the numerical techniques are in doubt, at least for some situations. An important category of flow-routing models developed to fill the gap between the two extremes is that of the multilinear models [Keefer and McQuivey, 1974; Becker, 1976]. These models are based on the linearization of the flow equations and rely on the unit hydrograph theory. Although the multilinear models have the advantage of simplicity typical of the conceptual linear models and, in addition, take into account the nonlinearity of the flood wave phenomenon, the present multilinear models do not account for lateral flow and cannot route water depths or stages. The general objective of this study was to develop a mathematical flow-routing model which is flexible and practical in both calibration and simulation modes and at the same time preserves the nonlinear character of the flow wave propagation phenomenon. This flexibility means that

2012

Network of reservoirs has become a standard hydraulic construct for multipurpose use. In this work, we present a formulation based on nonlinear reservoir method and coupled tank approach to model the reservoir network for flood control. The network of reservoirs consists of both detention and retention pond which give rise to nonlinear system of ODE for the m reservoirs in the network. The inflow consists of rainfall runoff in each sub catchment and discharges from the adjacent reservoirs. On the other hands, the outflow consists of infiltration and discharges. The nonlinear system obtained is linearized about the normal operating height of each reservoir in the network. The discharge term on the last equation is dropped in order to allow all the runoff captured into it. The establishment of relationship between the area of catchment and area of reservoir give room for the estimation of the forcing function in terms time of concentration rather than in terms of area of the reservoir which is difficult to obtain in an existing network. Two sets of solutions are presented, one at the convergent point and the other the best solution in respect of the lowest point in the reservoirs.

Flood Routing is a mathematical procedure for predicting the changing magnitude, Speed and shape of a flood wave as a function of time at one or more points along a Watercourse. When a flood wave moves downstream a river, the wave configuration will be modified due to channel irregularities and roughness. Flood routing is important in the design of flood protection measures, to estimate how the proposed measures will affect the behavior of flood waves in rivers, so that adequate protection and economic solutions may be found. Flood routing procedures may be classified as either hydrological or hydraulics. Hydrological methods use the principle of continuity and a relationship between discharge and the temporary storage of excess volumes of water during the flood period. Hydraulic methods of routing involve the numerical solutions of the convective diffusion equations, the one dimensional Saint Venant equations of gradually varied unsteady flow in open channels. In present research, the examination of the several hydraulic, hydrologic methods, have been proceeded for several rivers data, compared with a written hand program in MATLAB software analysis. Also, a comparison was made between the results of various methods, using statistical analysis for river data employed. Furthermore, several hydraulic methods are compared through a series of numerical experiments that covered varied channel bed slopes, varied roughness coefficient and varied unsteady flow with different hydrograph geometric shapes. The results indicated that the developed methods generally provided reasonable output compared with the observed measured hydrologic data provided.