The Boussinesq equation offers a powerful approach forunderstanding the flow dynamics of unconfined aquifers. Though this nonlinear equation allows for concise representation of both soil and geomorphological controls on groundwater flow, it has only been solved exactly for a limited number of initial and boundary conditions. These solutions do not include source/sink terms (evapotranspiration, recharge, and seepage to bedrock) and are typically limited to horizontal aquifers. Here we present a class of exact solutions that are general to sloping aquifers and a time varying source/sink term. By incorporating the source/sink term, they may describe aquifers with both time varying recharge over seasonal or weekly time scales, as well as a loss of water from seepage to the bedrock interface, which is a common feature in hillslopes. These new solutions shed light on the hysteretic relationship between streamflow and groundwater and the behavior of the hydrograph recession curves, thus providing a robust basis for deriving a runoff curves for the partition of rainfall into infiltration and runoff.
Bartlett, M. S., Jr.; Porporato, A. M. (2017): Rainfall-runoff response informed by exact solutions of Boussinesq equation on hillslopes. American Geophysical Union 2017 Fall Meeting, 11-15 Dec. 2017, New Orleans, LA.
This Paper/Book acknowledges NSF CZO grant support.