Mass and momentum conservation in the simplified flood routing models

Hydrologic flood routing models have been, and continue to be, the primary tool of the flood forecaster. However, any advancement in our ability to model a wider variety of flow scenarios, including extreme flood events (for which no calibration may be available), dam break floods, or ice-related events, necessitates the use of deterministic (hydraulic) models. A more fundamental advantage of hydraulic flood routing models over hydrologic models, in terms of less dynamic events, is that output describing flood hydrographs between gauge sites is produced. Such output is valuable in flow forecasting, and as input to the hydraulic analyses required for floodplain delineation. To date, hydraulic flood routing models have not gained widespread use for two key reasons. First, they present a particularly challenging numerical problem. Second, they are seen to be data intensive, requiring geometric data over the entire modelled reach. The former problem is no longer the primary concern, as recent research has led to the development of numerous robust computational schemes. The intensive data requirements of hydraulic models are much more limiting from a practical perspective, as flood routing typically involves very long reaches and the cost of obtaining sufficient cross section data is generally prohibitive. In this investigation, the reliability of a hydraulic flood routing model based on limited cross section survey data is evaluated for the case of the Peace River in British Columbia and Alberta. Based on the successful results of these investigations, it is concluded that a reliable hydraulic flood routing model can be developed with limited field data supplemented with topographic map data. Key words: flood routing, St. Venant equations, Peace River, characteristic-dissipative Galerkin scheme, finite element method.

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Flood routing models in confluent and dividing channels

Applied Mathematics and Mechanics ◽

10.1007/bf02438290 ◽

2004 ◽

Vol 25 (12) ◽

pp. 1333-1343 ◽

Cited By ~ 1

Author(s):

Fan Ping ◽

Li Jia-chun ◽

Liu Qing-quan

Keyword(s):

Flood Routing ◽

Routing Models

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A new partitioning approach for nonlinear Muskingum flood routing models with lateral flow contribution

Journal of Hydrology ◽

10.1016/j.jhydrol.2017.07.050 ◽

2017 ◽

Vol 553 ◽

pp. 142-159 ◽

Cited By ~ 6

Author(s):

M. Tamer Ayvaz ◽

Gurhan Gurarslan

Keyword(s):

Lateral Flow ◽

Flood Routing ◽

Routing Models

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Development of a New 8-Parameter Muskingum Flood Routing Model with Modified Inflows

Water ◽

10.3390/w13223170 ◽

2021 ◽

Vol 13 (22) ◽

pp. 3170

Author(s):

Eui Hoon Lee

Keyword(s):

Flood Routing ◽

The Self ◽

Correction Algorithm ◽

New Model ◽

Vision Correction ◽

Proposed Model ◽

Calculation Process ◽

Different Types ◽

And Storage ◽

Routing Models

Flood routing can be subclassified into hydraulic and hydrologic flood routing; the former yields accurate values but requires a large amount of data and complex calculations. The latter, in contrast, requires only inflow and outflow data, and has a simpler calculation process than the hydraulic one. The Muskingum model is a representative hydrologic flood routing model, and various versions of Muskingum flood routing models have been studied. The new Muskingum flood routing model considers inflows at previous and next time during the calculation of the inflow and storage. The self-adaptive vision correction algorithm is used to calculate the parameters of the proposed model. The new model leads to a smaller error compared to the existing Muskingum flood routing models in various flood data. The sum of squares obtained by applying the new model to Wilson’s flood data, Wang’s flood data, the flood data of River Wye from December 1960, Sutculer flood data, and the flood data of River Wyre from October 1982 were 4.11, 759.79, 18,816.99, 217.73, 38.81 (m3/s)2, respectively. The magnitude of error for different types of flood data may be different, but the error may be large if the flow rate of the flood data is large.

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Evaluation of the Simplified Dynamic Wave, Diffusion Wave and the Full Dynamic Wave Flood Routing Models

Earth Science Research ◽

10.5539/esr.v7n2p14 ◽

2018 ◽

Vol 7 (2) ◽

pp. 14 ◽

Cited By ~ 4

Author(s):

John Perdikaris ◽

Bahram Gharabaghi ◽

Ramesh Rudra

Keyword(s):

Wave Model ◽

Ease Of Use ◽

Flood Routing ◽

Diffusion Wave ◽

Event Simulation ◽

Wave Diffusion ◽

Wave Models ◽

Accuracy Of Prediction ◽

Routing Models ◽

Dynamic Wave

The accuracy of prediction and ease of use of the three popular flood routing models; simplified dynamic Wave, diffusion wave, and full dynamic wave were evaluated. The models were evaluated along a reach of the Credit River Watershed, in Southern Ontario, Canada. The simplified dynamic wave model showed better accuracy and easier formulation when compared against the diffusion wave and the full dynamic wave models. Indicating that the simplified dynamic wave model can be applied to reaches where the diffusion wave and the full dynamic wave models may not be applicable. The principle novel contributions of the paper are (a) the extension of the flood routing formulations by Keskin and Agiralioglu, (b) the use of a prismatic channel and floodplain with varying top-widths, (c) the validation of the methodology through the application of an event simulation to an actual river reach, and (d) comparison of the modeling results to those obtained using the full dynamic wave model and the diffusion wave models.

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Addressing Spatial Heterogeneity in the Discrete Generalized Nash Model for Flood Routing

Water ◽

10.3390/w13213133 ◽

2021 ◽

Vol 13 (21) ◽

pp. 3133

Author(s):

Bao-Wei Yan ◽

Yi-Xuan Zou ◽

Yu Liu ◽

Ran Mu ◽

Hao Wang ◽

...

Keyword(s):

Spatial Heterogeneity ◽

Cross Sections ◽

Model Performance ◽

Flood Routing ◽

Ungauged Basins ◽

Nash Model ◽

Model Efficiency ◽

S Curve ◽

Relative Errors ◽

Routing Models

River flood routing is one of the key components of hydrologic modeling and the topographic heterogeneity of rivers has great effects on it. It is beneficial to take into consideration such spatial heterogeneity, especially for hydrologic routing models. The discrete generalized Nash model (DGNM) based on the Nash cascade model has the potential to address spatial heterogeneity by replacing the equal linear reservoirs into unequal ones. However, it seems impossible to obtain the solution of this complex high order differential equation directly. Alternatively, the strict mathematical derivation is combined with the deeper conceptual interpretation of the DGNM to obtain the heterogeneous DGNM (HDGNM). In this work, the HDGNM is explicitly expressed as a linear combination of the inflows and outflows, whose weight coefficients are calculated by the heterogeneous S curve. Parameters in HDGNM can be obtained in two different ways: optimization by intelligent algorithm or estimation based on physical characteristics, thus available to perform well in both gauged and ungauged basins. The HDGNM expands the application scope, and becomes more applicable, especially in river reaches where the river slopes and cross-sections change greatly. Moreover, most traditional routing models are lumped, whereas the HDGNM can be developed to be semidistributed. The middle Hanjiang River in China is selected as a case study to test the model performance. The results show that the HDGNM outperforms the DGNM in terms of model efficiency and smaller relative errors and can be used also for ungauged basins.

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Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

Annals of Glaciology ◽

10.3189/s026030550000567x ◽

1983 ◽

Vol 4 ◽

pp. 297-297

Author(s):

G. Brugnot

Keyword(s):

Finite Difference Method ◽

Transverse Velocity ◽

Longitudinal Velocity ◽

Momentum Conservation ◽

Dimensional Model ◽

One Dimensional ◽

Modelling Techniques ◽

Reference Grid ◽

The One ◽

Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

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Conservation laws

10.1093/oso/9780198786399.003.0007 ◽

2018 ◽

Author(s):

Nathalie Deruelle ◽

Jean-Philippe Uzan

Keyword(s):

Dynamical System ◽

Angular Momentum ◽

Conservation Laws ◽

Total Energy ◽

Superposition Principle ◽

Momentum Conservation ◽

Conserved Quantities ◽

Angular Momentum Conservation ◽

Third Law ◽

The Law

This chapter defines the conserved quantities associated with an isolated dynamical system, that is, the quantities which remain constant during the motion of the system. The law of momentum conservation follows directly from Newton’s third law. The superposition principle for forces allows Newton’s law of motion for a body Pa acted on by other bodies Pa′ in an inertial Cartesian frame S. The law of angular momentum conservation holds if the forces acting on the elements of the system depend only on the separation of the elements. Finally, the conservation of total energy requires in addition that the forces be derivable from a potential.

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