Kinematic wave modelling in water resources: a historical perspective

Since its development by Lighthill and Whitham (1955a,b), the kinematic wave theory has found widespread application in environmental and water sciences, It took nearly 15 years before the theory was accepted as a sound scientific concept for modelling of a variety of hydrological processes. The debate as to its validity, however, still continues in some quarters and is not likely to end any time soon. Irrespective of the merits of the argument for or against the theory, new areas of its application continue to unfold and its scope is expanding considerably. These days the kinematic wave theory is being applied to a variety of hydrological processes (Singh, 1996a, 1997a,b). Examples of its application span overland and channel flow, baseflow, unsaturated flow, macropore flow, flow in furrows and borders, river hydraulics, movement of glaciers, erosion and sediment transport, sedimentation, solute transport, microbial. transport and chromatographic transport, to name but a few. These and other applications of the kinematic wave theory can be pooled together under different branches of hydrology, including surface water hydrology, vadose zone hydrology, river and coastal hydrology, irrigation hydrology, subsurface hydrology, snow and glacier hydrology, and water quality hydlology. The discussion in what follows is organized according to these areas of application. The objective of this paper is to trace the history of evolution of the kinematic wave theory and its application in hydrology and water resources. This historical essay attempts to put the theory in I,roper perspective and should serve as a guide to decide when and where to use the theory. The essay points to areas where further advances in applying the theory can be made.