| Abstract: |
This research is developing a dynamical systems model for estimating recharge and the age of recharge across in watersheds. An extensive literature has developed around the problem of direct simulation of tracer age distributions to diagnose transport in environmental systems. Theories have also been developed for estimation of tracer or isotope age in local and regional steady groundwater flow systems, and these approaches have been useful for making estimates of flow paths, flow rates, recharge, and time of travel for water resource assessment. The present paper explores theoretical and practical questions of how to interpret transient concentration-flow signals in terms of short term precipitation events and long term climate-time scale oscillations. The paper extends some earlier work (Duffy and Cusumano, WRR, 1998), where concentration-discharge phase-plane plots were shown to carry important time scales of both the flow and the environmental tracer inputs, in terms of direct simulation of “age” of water in a watershed setting. The dynamical model simulates the qualitative characteristics of climate, vegetation and hydrogeologic conditions. Discretization of the model is accomplished using the natural coordinates of the terrain (hypsometry). Explicit expressions are developed for transient mean age in the soil zone and recharge, and for groundwater flow across the mountain-front. Although the nonlinear dynamical model results are qualitative, the theory is easily extended to fully distributed models of concentration, age, and flow under transient conditions. The model is demonstrated at the Shale Hills/Susquehanna Critical Zone Observatory using a new stable isotope network deployed in 2009-10. |
