Catchment residence and travel time distributions: The master equation

The probability density functions (pdf's) of travel and residence times are key descriptors of the mechanisms through which catchments retain and release old and event water, transporting solutes to receiving water bodies. In this paper we analyze theoretically such pdf's, whose proper characterization reveals important conceptual and practical differences. A general stochastic framework applicable to arbitrary catchment control volumes is adopted, where time-variable precipitation, evapotranspiration and discharge are assumed to be the major hydrological drivers. The master equation for the residence time pdf is derived and solved analytically, providing expressions for travel and residence time pdf's as a function of input/output fluxes and of the relevant mixing. Our solutions suggest intrinsically time-variant travel and residence time pdf's through a direct dependence on hydrological forcings and soil-vegetation dynamics. The proposed framework integrates age-dating and tracer hydrology techniques, and provides a coherent framework for catchment transport models based on travel times. Citation: Botter, G., E. Bertuzzo, and A. Rinaldo (2011), Catchment residence and travel time distributions: The master equation, Geophys. Res. Lett., 38, L11403, doi:10.1029/2011GL047666.