Flood Routing Methods: Dynamic Wave, Characteristic, Kinematic Wave, Muskingum-Cunge, and UBC Flow

 

FLOOD ROUTING

Flood routing is a part of hydraulics and hydrology that involves tracking the movement of a flood wave as it travels down a channel or river. It's not only interesting but also crucial for predicting and mitigating the effects of floods on downstream areas. By understanding how flood waves behave, engineers can anticipate water levels, enabling them to take timely actions to protect lives and properties.

 

Significance of Flood Routing

The ability to predict water levels in a channel is vital for making informed decisions during flood events. This information helps authorities implement measures such as channel improvements, early warning systems, and reservoir operations to control flooding and minimize its impact. Moreover, the insights gained from studying flood wave movement can have broader applications, such as designing irrigation systems based on tidal patterns.

 

Mathematical Models of Flood Routing

Flood routing relies on mathematical models, which can be broadly categorized into hydraulic and hydrological models. Hydraulic models focus on the physical processes of water movement in channels, streams, or overland areas. These models apply principles of mass and momentum conservation to simulate flood wave dynamics accurately.

 

Comparison of Different Models

Several models exist for flood routing, each with its own approach and features. Five common models include dynamic wave, characteristic, and kinematic wave methods (hydraulic-based), a hydrological-based model, and a hybrid model derived from the UBC Flow model. These models vary in their input requirements and computational methods, but they all aim to predict flood wave behavior.

 

Input Parameters and Data Requirements

The input parameters for flood routing models differ based on their approach. Hydraulic models often require data related to channel geometry, roughness coefficients, and boundary conditions. In contrast, hydrological models may focus more on rainfall patterns, soil characteristics, and land use. Some models need data from both upstream and downstream boundaries, while others rely solely on upstream data. However, with suitable adjustments, these models can be compared using standardized input parameters for research purposes.

 

Applications

Understanding flood wave movement has implications beyond flood control. For example, the insights gained from flood routing can be applied to design tidal irrigation systems, leveraging natural water fluctuations for agricultural purposes. By accurately predicting water level fluctuations, these systems can optimize water usage in rice fields and manage river resources effectively.

 METHODS OF FLOOD ROUTING

Dynamic Wave Method

The dynamic wave method for flood routing has a rich history of development, with significant contributions from various researchers over the years. It was pioneered by Preissmann, Abbot & Ionesscu, Blatzer & Lai, Dronkers, Amien & Fang, and Fread. The method gained traction after Amien & Fang introduced the Newton Raphson iteration method for solving the Saint Venant equations rapidly and accurately. Subsequent improvements by Fread and Amien & Chu expanded the method's applicability to forecasting flash floods, dam failures, and floods in rivers with floodplains and meanders.

Various studies have been conducted to assess the numerical stability and accuracy of the dynamic wave method. It has been found to be stable with small, medium, and large time steps, but instability may occur with excessively large time steps or insufficient weighting factors. The method's performance depends on factors such as wave shape, Courant condition, distance step, and the type of implicit scheme used. Irregular channel cross-sections that vary rapidly in the x-direction can also lead to numerical instability. Overall, the dynamic wave method remains a valuable tool for flood forecasting and management.

 

Characteristic Method

The characteristic method for flood routing is based on the assumption that a flood wave is a disturbance in the free water surface of a channel. This method considers that any disturbance occurring at a specific point in open channel flow propagates both downstream and upstream along the channel. The method utilizes characteristic lines, represented by C1 and C2, which depict the paths of disturbances moving downstream and upstream from a given point at time t = 0. These characteristic lines define the range of influence of the disturbance at that point.

To solve the equations of unsteady flow using the characteristic method, characteristic forms of the equations are employed. These equations can be solved using finite difference approximations on either a rectangular grid mesh or a characteristic grid mesh. Studies by Blatzer, Cunge et al., and Abbott have shown that flows computed using the characteristic method generally agree well with field-measured flows. Liggett even regarded the method of characteristics as the most suitable general method due to its good results across a wide range of parameters. Additionally, Cunge et al. noted that the method could be considered a standard approach and its solutions can closely approximate those of the basic equations. Overall, the characteristic method is a valuable tool for flood routing and hydrological analysis.

 

KINEMATIC WAVE METHOD

The kinematic wave method is widely utilized in flood routing models, with programs like HEC-1 employing this approach for both overland flow and stream flow within a watershed. This method is favored for its simplicity and its ability to approximate natural flood flow conditions without requiring downstream boundary conditions. The kinematic wave method operates under the assumption that the effects of inertia and depth slope in natural flood flow are minimal compared to the bed slope term, allowing them to be neglected. This simplifies the momentum equation, where the friction term primarily depends on the bed slope, leading to a simplified equation: Sf = So. Overall, the kinematic wave method offers an efficient and effective means of simulating flood flow dynamics in various hydrological applications.

 

MUSKINGUM-CUNGE METHOD

The Muskingum-Cunge method is a widely used hydrological flood routing technique known for its simplicity. Despite its straightforward approach, determining accurate values for K and x poses a challenge. Traditionally, these values are determined graphically or through methods like the least squares method, requiring extensive historical data on storage, inflow, and outflow within a specific reach. Additionally, variations in bed slope (So) and Manning's roughness coefficient (n) necessitate different historical data sets for each condition.

Alternative approaches proposed by Cunge, Dooge, and Koussis offer methods to determine K and x based on diffusive wave analogy, with improvements suggested by Ponce, Gill, and others. The Muskingum-Cunge method with variable parameters, allowing K and x to vary over time and space, is considered more physically accurate. However, challenges persist in accommodating changes in So and Manning's n, requiring the determination of K and x from extensive historical datasets.

Further enhancements proposed by Tung and Singh introduce non-linearity to the method but still require historical data for determining K and x. Overall, while the Muskingum-Cunge method offers simplicity, ensuring accurate parameter values remains a critical aspect of its application in hydrological flood routing models.

 

UBC FLOW

The UBC Flow model, developed by the University of British Columbia, was initially created to address specific challenges encountered in the Fraser River, British Columbia, Canada. Over the years, it has undergone testing on various river systems, including the Fraser River, the North Saskatchewan River, and the upper reaches of the Columbia River. Results from these tests have shown that the model is adaptable, easy to calibrate, and suitable for both large and small rivers.

One notable feature of the UBC Flow model is its flexibility in handling local issues such as ungauged lateral inflow, steep bed slopes, and short travel times. It has proven effective in incorporating lateral inflow into downstream boundaries, simplifying routing calculations within the reach. Additionally, routing coefficients are directly determined from velocity-discharge and area-discharge relationships, streamlining the modeling process. Overall, the UBC Flow model offers a versatile and reliable tool for analyzing river flow dynamics and hydrological processes.

 

FAQs:

 

What is flood routing, and why is it important?

   Flood routing is the process of tracking the movement of flood waves through channels or rivers. It's crucial for predicting downstream water levels, which helps in protecting lives and properties from flood damage.

 

What is the dynamic wave method in flood routing?

   The dynamic wave method is a technique used to simulate flood waves by solving the complete Saint Venant equations. It's effective for forecasting flash floods and river floods, considering factors like channel geometry and flow velocity.

 

How does the characteristic method work in flood routing?

   The characteristic method treats flood waves as disturbances in the water surface, propagating both downstream and upstream along the channel. By analyzing characteristic lines and domains, it predicts flood behavior accurately.

 

What is the kinematic wave method in flood routing?

   The kinematic wave method simplifies flood flow equations by neglecting inertia and depth slope terms. It assumes that bed slope mainly influences flow, making it suitable for overland flow and stream flow predictions.

 

What is the Muskingum-Cunge method used for in flood routing?

   The Muskingum-Cunge method is a standard approach for hydrological flood routing. It involves determining parameters like K and x to accurately predict flood wave propagation based on historical data sets of inflows and outflows.

 

How does the UBC Flow model contribute to flood routing?

   The UBC Flow model, developed by the University of British Columbia, is versatile and easy to calibrate. It effectively handles local challenges in river systems and provides reliable predictions for both large and small rivers.

 

Which flood routing method is best for predicting flash floods?

   The dynamic wave method is often preferred for forecasting flash floods due to its ability to account for rapid changes in water levels and flow velocities.

 

Can flood routing methods be applied to urban drainage systems?

   Yes, flood routing methods like the dynamic wave and kinematic wave methods can be adapted for use in urban drainage pipe networks, helping to manage storm water runoff and prevent flooding in urban areas.