WATER RESOURCES RESEARCH, VOL. 38, NO. 2, 10.1029/2001WR000482, 2002
Linearity and nonlinearity of basin response as a function of scale: Discussion of alternative definitions
Centre for Water Research, Department of Environmental Engineering,
University of Western Australia,
Crawley, Australia
Abstract
[1] Two uses of the terms “linearity” and “nonlinearity” appear in recent literature. The first definition of nonlinearity is with respect to the dynamical property such as the rainfall-runoff response of a catchment, and nonlinearity in this sense refers to a nonlinear dependence of the storm response on the magnitude of the rainfall inputs [Minshall, 1960; Wang et al., 1981]. The second definition of nonlinearity [Huang and Willgoose, 1993; Goodrich et al., 1997] is with respect to the dependence of a catchment statistical property, such as the mean annual flood, on the area of the catchment. They are both linked to important and interconnected hydrologic concepts, and furthermore, the change of nonlinearity with area (scale) has been an important motivation for hydrologic research. While both definitions are correct mathematically, they refer to hydrologically different concepts. In this paper we show that nonlinearity in the dynamical sense and that in the statistical sense can exist independently of each other (i.e., can be unrelated). If not carefully distinguished, the existence of these two definitions can lead to a catchment's response being described as being both linear and nonlinear at the same time. We therefore recommend separating these definitions by reserving the term “nonlinearity” for the classical, dynamical definition with respect to rainfall inputs, while adopting the term “scaling relationship” for the dependence of a catchment hydrological property on catchment area.
Received 12 May 2001; revised 16 October 2001; accepted 16 October 2001; published 16 February 2002.
Keywords: Scaling, Nonlinearity, Floods, Unit Hydrographs, Geomorphology.
Index Terms: 1821 Hydrology: Floods; 1824 Hydrology: Geomorphology (1625); 1860 Hydrology: Runoff and streamflow; 1869 Hydrology: Stochastic processes.
Citation: Linearity and nonlinearity of basin response as a function of scale: Discussion of alternative definitions, Water Resour. Res., 38(2), 10.1029/2001WR000482, 2002.