B2. The Isotopic Age of Runoff in Natural Flow Systems

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This paper outlines a theory describing fundamental controls on the isotopic “age” of runoff from watersheds. In this context “age” is defined as the time since the water and environmental tracer entered the system as precipitation. The paper first examines the theoretical basis for directly modeling “age” of environmental tracers, and explains how subsurface flow (Boussinesq equation) and transport processes affect age dynamics. Solutions for the age of watershed runoff are presented for storm events, seasonal and stochastic tracer inputs. Through a simple analogy to boundary layer theory and potential flow, a strategy to estimate the effective depth and corresponding age of groundwater circulation is presented. The approach reveals an important relationship for flow-depth and age, which can be used to define the practical mixing layer for environmental tracers contributing to runoff. Extension of the model to the unsaturated zone and the effects of mobile-immobile on flow and transport on the age of runoff are briefly outlined. Preliminary results from a field experiment for stable isotopes at the Shale Hills Critical Zone Observatory provides some initial validation and estimates for the “dynamic” age of runoff.
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