The rate at which water and carbon move through lake catchments strongly influences the extent to which carbon is metabolized, stored, or transported to down-stream ecosystems. However, lake catchments can have complex hydrologic flow paths and multiple sources of carbon, and representing that complexity in spatially explicit dynamical models presents great challenges. A conceptually simpler approach to characterizing combined hydrologic and carbon transport through the full catchment would provide for a synthetic measure of the hydrologic and chemical residence times that has lower data requirements and is more easily applied to a variety of catchments. This research focuses on a conceptual-mathematical modeling of the “age” of isotopes of water and carbon in lake-catchment systems, in which the storage and fluxes of water and tracer are both dynamic. Will climate change affect the level of lakes or the flow in rivers and what are the time scales of change? What is the role of ecological disturbance on the water cycle? How long does it take for nutrient pulses in the watershed to reach and pass through the lake? We address these questions with simulations of the Yahara watershed of Lake Mendota, Wisconsin.
By coupling the lake and the catchment and including both fast and slow water/solute reservoirs, the combined effects of age and residence time are simulated, which lead to a better understanding of how changes in mean flow path, initial conditions and disturbances alter the system. The mean flow path of the catchment contributing to the lake is affected by the depth and area contributing to the lake as well as soil properties, such as conductivity and porosity, and the level of forcing for both water and solutes. The mean flow path is a general scaling concept for the size and “age” of the system and indicates the time required to build a stable carbon pool. The initial age of the system indicates the time required for the system to adapt to change. When a large (very old) initial carbon pool is assumed, it can take decades to adapt to changes in climate forcing, and the model explains both the time to steady state and the dynamics of how it gets there. The model shows the time to recovery from events, such as floods, drought, and carbon input from changing land use and highlights contrasting age dynamics of solutes and water.