A theory developed by Lighthill and Whitham (1995) Procs Royal Soc., London, Series A 229 which has applications in geomorphology. See Howes and Abrahams (2003) Geomorph. 53, 1–2 for a kinematic wave equation for overland flow, and Van de Wal and Oerlemans (1995) J. Glaciol. 41 on high-velocity kinematic waves in glaciers, generated by a major accumulation of snow above the firn line, and causing a glacial surge when the wave reaches the snout.