A combined power-law and exponential model for streamflow recessions

This paper proposes a non-linear model to describe streamflow recessions. A model of combining power-law and exponential functions is derived from a non-linear differential equation associating outflow change rate and flow itself with a time-dependent decreasing decay rate. The decay rate is approximated by the first three terms in a Taylor series expansion. The solution of the resulting differential equation includes three components of the expansion determining two exponential functions and a power-law function, respectively. It is demonstrated analytically and empirically that the introduction of a non-linear differential equation comprising a mixture of power-law and exponential forms is superior to using an ordinary differential equation with exponential solution, or a non-linear equation with power-law solution, for modeling the decay patterns of flow in river systems. Analytical properties of the mixing model are discussed and the model is subsequently validated by characterizing the relationships between decay of peak flow as a function of time after the initial occurrence of flow peak in 10 datasets of flow events chosen from five gauging stations in the Oak Ridges Moraine (ORM) area, Canada.