[1] Many physical-based models of surface and groundwater hydrology are constructed without the possibility of multiple stable states for the same parameter set. For such a conceptualization, at the cessation of a transient hydrological disturbance of any magnitude the model will return to the same stable state and thus show an infinite resilience. To highlight and falsify this assumption, a numerical distributed ecohydrological model (coupled hillslope Boussinesq-vertically lumped vadose zone) is presented, in which qualitatively different steady state water table elevations exist for the same parameter set. The multiple steady states are shown to emerge from a positive feedback arising from a reduction in leaf area index (LAI) and thus transpiration, as a saline water table approaches the surface. Limit cycle continuation is also undertaken to quantify the state-space location of the threshold (repellor) between the steady states (attractors) and quantify the resilience. While the model is biophysically simple, it is sufficiently complex to challenge this potentially significant assumption within water resource planning.
.[1] In recent years a number of papers have quantitatively explored multiple steady states and resilience within a wide range of hydrological systems. Many have identified multiple steady states by conducting simulations from different initial state variables and a few have used the more advanced technique of equilibrium or limit cycle continuation analysis to quantify how the number of steady states may change with a single model parameter. However, like resilience investigations into other natural systems, these studies often omit explanation of these fundamental resilience science techniques; rely on complex numerical methods rather than analytical methods; and overlook use of more advanced techniques from nonlinear systems mathematics. In the interests of wider adoption of advanced resilience techniques within hydrology, and advancing resilience science more broadly, this paper details fundamental methods for quantitative resilience investigations. Using a simple model of a spatially lumped unconfined aquifer, one and two parameter continuation analysis was undertaken algebraically. The shape of each steady state attractor basin was then quantified using Lyapunov stability curves derived at a range of precipitation rates, but was found to be inconsistent with the resilience behavior demonstrated by stochastic simulations. Most notably, and contrary to standard resilience concepts, the switching between steady states from wet or dry periods (and vice versa) did not occur by crossing of the threshold between the steady states. It occurred by exceedance of the two steady-state domain, producing a counterclockwise hysteresis loop. Additionally, temporary steady states were identified that could not have been detected using equilibrium continuation with a constant forcing rate. By combining these findings with the Lyapunov stability curves, new measures of resilience were developed for endogenous disturbances to the model and for the recovery from disturbances exogenous to the model.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.