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Time series of chemical tracers in rainfall and streamflow can be used to probe the internal workings of catchments. We have recently proposed that catchments act as fractal filters for inert chemical tracers like chloride, converting ‘white noise’ rainfall chemistry inputs into fractal ‘1/f noise ’ chemical time series in runoff [Nature 403 (2000) 524]. This implies that catchments have long-tailed travel-time distributions, and thus retain soluble contaminants for unexpectedly long timespans. Here we show that these long-tailed travel-time distributions, and the fractal tracer time series that they imply, can be generated by advection and dispersion of spatially distributed rainfall inputs as they travel toward a channel. Tracer pulses that land close to the stream reach it promptly, with relatively little dispersion. Tracer pulses that land farther upslope must travel farther to reach the stream, and undergo more dispersion. The tracer …