Kinematic wave

Kinematic wave

This refers to a method of calculating the characteristics of flows across planes and in channels, based on a simplified or cut-down part of the St. Venant Equations for conservation of mass and momentum in open channel flow.

Kinematic wave procedures are used in some hydrological models that represent a catchment as a plane or series of planes. They are also applied in channel and pipe hydraulics.

One of the simplest applications is in determining times of concentration, assuming that flows caused by rain falling onto a plane surface reach an equilibrium in a time that is five-eighths of the time of concentration.


The formula used to calculate times of travel or of concentration, is:


If the rational method is used with intensity-frequency-duration rainfall data, the intensity 'I' is the average intensity for the selected duration. If the Horton (ILSAX) or IL - CL model is used with ARR87 or ARR 2019 rainfall patterns, or other rainfall data, the average rainfall is used also.

This steady-state 'kinematic-wave' equation can be adjusted to apply to a series of overland flow planes, as described on page 301 of Australian Rainfall and Runoff, 1987. This feature is not yet available in DRAINS.

Surface roughnesses recommended by Australian Rainfall and Runoff for use in the formula are:

  Surface Type  

Roughness Coefficient n*

  Concrete or Asphalt

0.01 - 0.013

 Bare Sand

0.01 - 0.016

 Graveled Surface

0.012 - 0.03

 Bare Clay-Loam Soil (eroded)

0.012 - 0.033

 Sparse Vegetation0.053 - 0.130

 Short Grass Prairie
 (Veldt or Scrub)

0.10 - 0.20

 Lawns

0.17 - 0.48

[Source: Woolhiser (1975)]

The roughness or retardance coefficient n* is based on Manning's equation, but is applied to a shallow flow over a plane, rather than a channel flow. Different flow situations are shown below:

For smooth surfaces, planes and channels have similar roughness values. For vegetated or stony surfaces, planes are likely to have higher n values because the obstructions are larger compared to the depth of flow. In general, the deeper the flow, the lower the roughness.

The ‘Lawns’ category has caused problems because of the large range of roughnesses and because earlier design methods gave results that corresponded to roughnesses outside this range. The range reflects the different types of grassed surface that can be encountered, ranging from lawn bowling greens to 'jungles' of unmown grass. Sensitivity analysis can be applied to test the effects of assumptions and to select suitable values.            

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