Travel Time for Catchment Flow in a Small Watershed: An Approach Based on Fractal Persistence of Stream Tracer Concentrations

Christopher C. Barton U.S. Geological Survey

Jorge Gomez-Moreno U.S. Geological Survey

We calculate the time it takes for precipitation to move through the catchment to the stream in the Watershed-6 at Hubbard Brook, New Hampshire. The catchment travel time is a fundamental hydrologic parameter that affects the retention of soluble contaminants in the watershed. Our tracer is Cl, which is conservative. Spectral analysis of the 35 year Cl concentration time series shows that the fluctuations over three orders of magnitude are fractal with a scaling exponent of 0.5 for precipitation and 0.7 for stream water measured at the weir. Therefore, the Cl fluctuations in the catchment are necessarily fractal, as are flow paths. A fractal distribution of catchment travel times means that after a contaminant pulse, concentration will initially drop rapidly, but then decline much more gradually and will persist for very long times.This “fat tailed” decay is characteristic of fractal distributions. Flow through the catchment dampens the chloride signal and increases the persistence of the signal, which permits calculation of the average flow time through the catchment. We fit the catchment spectrum with a power form of the Gamma distribution and calculate the average travel time through the catchment. The average flow time through the catchment is 3.7 months.