COMPARATIVE HYDRAULIC DIFFUSIVITIES OF CHEMICAL AND PHYSICAL PARAMETERS IN WATERSHEDS WITH HIERARCHIES OF FLOW PATHS

The theoretical hydrograph developed by Criss and Winston (GRL 2003) to model the sharp perturbation of hydrologic systems following storms provides a means to compare the time constants of different water quality parameters, which individually represent x2/D, the square of the transport length scale divided by the effective diffusivity for the parameter in question. Examination of several thousand hydrographs of diffuse springs as well as creeks and small rivers provides abundant examples, ranging from desert gulches to swampy rivers, where the theoretical curve closely matches natural discharge data determined at gauging stations. New mathematical results show how watersheds can be theoretically modeled, through integration, as assemblages of elementary hydrographs, each representing a different flow path with an individual time constant that connects a surface element with a common discharge point. The integrated sum of all the elemental hydrographs is shown to be accurately reproduced by the curve for a single theoretical hydrograph, using an appropriate average time constant. The documentation of different time constants for different parameters (e.g., discharge, temperature, electrical conductivity, Ca++, oxygen-18, etc.) measured at a single site following a single storm illustrates disparities among their various transport path lengths and/or effective diffusivities (Winston and Criss, WRR 2004). The theoretical model provides two independent ways to quantify the time scales that embody these transport impedances, first, in the lag time between the causal perturbation and the peak (maximum) or minimum for the given parameter, and second, in the rate of recessional recovery of the parameter to pre-perturbation conditions.