ABSTRACT Linear models in recession analysis have been widely used, particularly at larger scales and longer times, to make accurate predictions of streamflow recession. However, their derivation has been somewhat impenetrable until now, since water flowing out of the soil of a catchment and into streams flows out of an area, but water stored in the soil is stored in a volume. This mismatch in units, as given in Euclidean geometry, requires a relationship that has a length scale included and which makes the flow a non‐linear function of the volume. However, in percolation theory, the surface area has two terms: one that is proportional to the volume V as well as the customary Euclidean term proportional to V 1−1/ d . Here, d = 2 or 3 is used as a generalisation of 3, in case the vertical dimension of the flow in the catchment can be considered negligibly thin in comparison with the scale of the catchment heterogeneity. Then, the Euclidean term is proportional to V 1−1/2 = V 1/2 . The term linear in V must dominate at large volumes or areas in either case, since its dependence on length is to a larger power than the Euclidean surface area. Thus, identification of the principal flow paths as near the percolation threshold automatically concentrates flow across a boundary as having the same units as the interior, making Q proportional to S and d Q /d t proportional to d S /d t . The mass conservation constraint then makes d S /d t proportional to − Q in low flow regimes without P or ET, generating the ‘linear’ model, d Q /d t proportional to − Q . Results are tested against known recession constants for Iowa streams.
Mohan et al. (Sun,) studied this question.