8.2 Channel routing methods

Channel routing methods are crucial for predicting flood wave movement in rivers. They help determine downstream hydrographs from upstream data, essential for flood forecasting and water management. Understanding these methods is key to grasping streamflow routing concepts.

There are two main types: hydraulic (distributed) and hydrologic (lumped) methods. Hydraulic methods use complex equations for detailed flow dynamics, while hydrologic methods simplify calculations. The choice depends on factors like channel characteristics, data availability, and modeling goals.

Channel routing concepts

Importance and purpose of channel routing

Top images from around the web for Importance and purpose of channel routing

• 

  GMD - Development of the Community Water Model (CWatM v1.04) – a high-resolution hydrological ... View original

  Is this image relevant?

• 

  HESS - Relations - Improving flood forecasting capability of physically based distributed ... View original

  Is this image relevant?

• 

  HESS - On the representation of water reservoir storage and operations in large-scale ... View original

  Is this image relevant?

• 

  GMD - Development of the Community Water Model (CWatM v1.04) – a high-resolution hydrological ... View original

  Is this image relevant?

• 

  HESS - Relations - Improving flood forecasting capability of physically based distributed ... View original

  Is this image relevant?

1 of 3

Top images from around the web for Importance and purpose of channel routing

• 

  GMD - Development of the Community Water Model (CWatM v1.04) – a high-resolution hydrological ... View original

  Is this image relevant?

• 

  HESS - Relations - Improving flood forecasting capability of physically based distributed ... View original

  Is this image relevant?

• 

  HESS - On the representation of water reservoir storage and operations in large-scale ... View original

  Is this image relevant?

• 

  GMD - Development of the Community Water Model (CWatM v1.04) – a high-resolution hydrological ... View original

  Is this image relevant?

• 

  HESS - Relations - Improving flood forecasting capability of physically based distributed ... View original

  Is this image relevant?

1 of 3

• Channel routing is the process of predicting the temporal and spatial variations of a flood wave as it moves through a river channel or reservoir
• The main purpose of channel routing is to determine the downstream hydrograph given an upstream hydrograph as a boundary condition
• Accurate channel routing is essential for flood forecasting, flood control, and water resources management

Factors affecting flood wave propagation

• Channel routing considers the effects of channel storage, flow resistance, and channel geometry on the shape and timing of the flood wave
• Channel storage influences the attenuation and dispersion of the flood wave as it moves downstream
• Flow resistance, determined by factors such as channel roughness and vegetation, affects the velocity and diffusion of the flood wave
• Channel geometry, including cross-sectional shape, slope, and sinuosity, impacts the speed and characteristics of the flood wave propagation

Categories of channel routing methods

• The two main categories of channel routing methods are hydraulic (or distributed) methods and hydrologic (or lumped) methods
• Hydraulic methods are based on the Saint-Venant equations, which describe one-dimensional unsteady open-channel flow
  • Examples of hydraulic methods include the dynamic wave model and the diffusion wave model
• Hydrologic methods use simplified equations based on the continuity equation and an empirical relationship between storage and discharge
  • Examples of hydrologic methods include the Muskingum method and the linear reservoir model

Muskingum method application

Muskingum method principles

• The Muskingum method is a widely used hydrologic channel routing method that accounts for the effects of channel storage and flow resistance on the flood wave propagation
• The method is based on the continuity equation and a linear relationship between storage, inflow, and outflow in a channel reach
• The storage-discharge relationship in the Muskingum method is represented by the equation: $S = K[XI + (1-X)Q]$, where S is the storage, I is the inflow, Q is the outflow, K is the travel time, and X is the weighting factor

Muskingum method parameters

• The Muskingum method uses two parameters: K (travel time) and X (weighting factor)
• The parameter K is related to the travel time of the flood wave through the reach and is influenced by factors such as channel length, slope, and roughness
• The weighting factor X ranges from 0 to 0.5 and determines the shape of the outflow hydrograph
  • A value of X = 0 indicates a pure translation of the inflow hydrograph, while X = 0.5 represents a pure storage effect with maximum attenuation
• The parameters K and X can be estimated using optimization techniques, such as the least-squares method, by minimizing the difference between the observed and simulated outflow hydrographs

Muskingum method implementation and limitations

• The Muskingum method can be applied using a finite difference scheme, where the outflow at each time step is calculated based on the inflow and the previous outflow values
• The finite difference equations for the Muskingum method are:
  • $Q_{j+1} = C_0 I_{j+1} + C_1 I_j + C_2 Q_j$
  • $C_0 = (-KX + 0.5\Delta t) / (K - KX + 0.5\Delta t)$
  • $C_1 = (KX + 0.5\Delta t) / (K - KX + 0.5\Delta t)$
  • $C_2 = (K - KX - 0.5\Delta t) / (K - KX + 0.5\Delta t)$
• The Muskingum method has limitations, such as the assumption of a linear storage-discharge relationship and the inability to account for backwater effects or flow reversal
• The method may not be suitable for channels with significant lateral inflows or outflows, as it assumes a constant discharge along the reach

Kinematic wave model implementation

Kinematic wave model assumptions

• The kinematic wave model is a simplified hydraulic channel routing method that assumes a balance between the gravitational and frictional forces in the flow
• The model neglects the pressure and inertial terms in the Saint-Venant equations, assuming that the flow is primarily controlled by the channel bed slope and roughness
• The kinematic wave model is suitable for steep channels with supercritical flow, where the backwater effects are negligible

Governing equations and relationships

• The kinematic wave model is based on the continuity equation and a power-law relationship between the discharge and the cross-sectional area
• The continuity equation for the kinematic wave model is: $\frac{\partial A}{\partial t} + \frac{\partial Q}{\partial x} = q$, where A is the cross-sectional area, Q is the discharge, q is the lateral inflow or outflow per unit length, t is time, and x is the distance along the channel
• The power-law relationship between discharge and cross-sectional area is given by the Manning's equation or the Chezy's equation:
  • Manning's equation: $Q = \frac{1}{n} A R^{2/3} S_0^{1/2}$
  • Chezy's equation: $Q = C A R^{1/2} S_0^{1/2}$
  • where n is the Manning's roughness coefficient, C is the Chezy's coefficient, R is the hydraulic radius, and S_0 is the channel bed slope

Numerical solution and result interpretation

• The kinematic wave model can be solved using various numerical methods, such as the finite difference, finite volume, or finite element methods
• The choice of the numerical method depends on the spatial and temporal discretization of the domain, the boundary conditions, and the desired accuracy and stability of the solution
• The results of the kinematic wave model include the discharge and water depth profiles along the channel reach at different time steps
• These results can be used to assess the flood wave propagation and attenuation, estimate the travel time and peak discharge, and evaluate the impact of channel modifications or flow control measures
• The accuracy of the kinematic wave model depends on the quality of the input data, such as the channel geometry, roughness, and boundary conditions, as well as the numerical scheme and the spatial and temporal resolution used in the simulation

Channel routing methods vs applicability

Comparison of hydraulic and hydrologic methods

• Channel routing methods can be classified into hydraulic (or distributed) methods and hydrologic (or lumped) methods, based on their level of complexity and the governing equations used
• Hydraulic methods, such as the dynamic wave model and the diffusion wave model, are based on the Saint-Venant equations and provide a more accurate representation of the flow dynamics
  • These methods can capture the effects of backwater, flow reversal, and hydraulic jumps, making them suitable for complex flow situations
  • However, hydraulic methods require detailed input data, such as the channel geometry and roughness, and are computationally intensive, limiting their applicability to short reaches or simple channel networks
• Hydrologic methods, such as the Muskingum method and the linear reservoir model, use simplified equations based on the continuity equation and an empirical relationship between storage and discharge
  • These methods assume a linear or nonlinear reservoir behavior and are computationally efficient, requiring fewer input data
  • Hydrologic methods are suitable for long reaches or complex channel networks, but they may not capture the detailed flow dynamics and the backwater effects

Kinematic wave model as a compromise

• The kinematic wave model is a compromise between the hydraulic and hydrologic methods, as it assumes a balance between the gravitational and frictional forces, neglecting the pressure and inertial terms in the Saint-Venant equations
• The kinematic wave model is suitable for steep channels with supercritical flow, where the backwater effects are negligible
• However, the model may not be appropriate for mild-sloped channels or in the presence of downstream controls, as it cannot capture the backwater effects or flow reversal

Factors influencing the choice of channel routing method

• The choice of the appropriate channel routing method depends on various factors, such as:
  • Channel characteristics (e.g., slope, roughness, and geometry)
  • Flow regime (e.g., subcritical or supercritical)
  • Data availability and quality
  • Computational resources
  • Modeling objectives (e.g., flood forecasting, flood control, or water resources management)
• In practice, it is often necessary to use multiple channel routing methods and compare their results to assess the uncertainty and the sensitivity of the model predictions to the underlying assumptions and the input parameters
• The selection of the channel routing method should be based on a thorough understanding of the model assumptions, limitations, and applicability to the specific case study, as well as a sensitivity analysis and a validation against observed data, when available