Lighthill and Whitham developed the kinematic wave theory but Iwagaki also independently conceived the kinematic wave concept. Over a decade later, the theory started to receive wide acceptance. By the 1980s, the theory became an accepted tool for modeling not only surface runoff but also for subsurface flow, soil moisture movement, macropore flow, snowmelt runoff, and soil erosion. Many watershed models began incorporating the kinematic wave method for modeling overland flow. The decade of the 1990s also witnessed applications of the theory to a variety of other hydrologic processes. This study provides a historical perspective of the kinematic wave theory-based models in hydrology.

Kinematic Wave Modeling in Hydrology

In almost all of the present mathematical models, the upstream subbasins, with overland flow as the dominant type of flow, are simulated as a rectangular plane. However, the converging plane is the closest shape to an actual upstream subbasin. The intricate nature of the governing equations of the overland flow on a converging plane is the cause of prolonged absence of an analytical or semi analytical solution to define the rising limb of the resulted hydrograph. In the present research, a new geomorphologic semi analytical method was developed that tries to establish a relationship between the parallel and converging flows to reduce the complexity of the equations. The proposed method uses the principals of the Time Area method modified to apply the kinematic wave theory and then by applying a correction factor finds the actual discharge. The correction factor, which is based on the proportion of the effective drained area to the analytically calculated one, introduces the convergence effect of the flow in reducing the potentially available discharge in a parallel flow. The proposed method was applied to a case study and the result was compared with that of Woolhiser's numerical method that showed the reliability of the new method.

/pdf/a-semi-analytical-solution-for-rising-limb-of-hydrograph-in-54o3n928aq.pdf

A semi analytical solution for rising limb of hydrograph in 2d overland flow

Urban Hydrology (Paper 3R00063)

The history of the kinematic wave theory and its applications in water resources are traced. It is shown that the theory has found its niche in water resources and its applications are so widespread that they may well constitute what may be termed ‘kinematic wave hydrology’. Few theories have been applied in hydrology and water resources as extensively as the kinematic wave theory. This theory, however, is not without limitations and when it is applied they must be so recognized. Copyright © 2001 John Wiley & Sons, Ltd.

Kinematic wave modelling in water resources: a historical perspective

A converging kinematic wave overland flow model was applied to an urban catchment, Rock Creek Watershed in Maryland. The 2-parameter model was easily calibrated and gave reasonable predictions for hydrograph shape as well as peak flow. Two methods for estimating abstractions from gross precipitation were applied. The first was a generalization of a standard infiltration equation and the second used a linear regression between direct runoff and gross precipitation. The fairly accurate results suggest that the converging flow model is ideal for a variety of uses in urban hydrology.

Converging Flow Model Applied to Urban Catchment

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Converging Flow Model Applied to Urban Catchment