Fractal stream chemistry and its implications for contaminant transport in catchments

The time it takes for rainfall to travel through a catchment and reach the stream is a fundamental hydraulic parameter that controls the retention of soluble contaminants and thus the downstream consequences of pollution episodes. Catchments with short flushing times will deliver brief, intense contaminant pulses to downstream waters, whereas catchments with longer flushing times will deliver less intense but more sustained contaminant fluxes. Here we analyse detailed time series of chloride, a natural tracer, in both rainfall and runoff from headwater catchments at Plynlimon, Wales. We show that, although the chloride concentrations in rainfall have a white noise spectrum, the chloride concentrations in streamflow exhibit fractal 1/f scaling over three orders of magnitude. The fractal fluctuations in tracer concentrations indicate that these catchments do not have characteristic flushing times. Instead, their travel times follow an approximate power-law distribution implying that they will retain a long chemical memory of past inputs. Contaminants will initially be flushed rapidly, but then low-level contamination will be delivered to streams for a surprisingly long time.