Multiple Stable Hydrological States in Models: Implications for Water Resource Management

Many models of surface and groundwater hydrology are constructed without thought given to the possibility of multiple stable states for the same parameter set. If a single stable state is assumed, a transient hydrological disturbance of any magnitude will result in a return of the model to the same stable state, and thus show an infinite resilience. In an attempt to make this assumption less implicit, a plausible numerical hydrological model is presented in which this assumption is violated. The model is developed from the assumption that multiple coexistent hydrological states do not exist. Its aim is not to prove such multiple equilibria exist but rather demonstrate that minor, defensible and plausible changes to groundwater-vadose zone interaction equations give rise to multiple equilibria. The impetus for the model derives from the concept of ecosystem resilience. It is based upon the hillslope Boussinesq partial differential equation (PDE) coupled to a vertically integrated unsaturated zone ordinary differential equation (ODE) and solved numerically. The only significant change from traditional coupled models is the reduction in leaf area index (LAI) and thus transpiration as the watertable, which is assumed highly saline, approaches the surface. This is demonstrated to produce a positive feedback and two coexistent equilibrium watertable depths. If a watertable has only one equilibria, then irrespective of the initial head it will eventually come to the same equilibrium. To investigate the potential for two equilibria the model was solved with an initial head of 5% and 92.5% of the maximum saturated thickness. Figure 1 show results for a saturated lateral hydraulic conductivity, k(sat), of 0.16 m/day. Clearly the model has both a deep and shallow watertable equilibria. To highlight that all dryland catchments are unlikely to have two such equilibria, the simulation is repeated for a high and low k(sat). For the low k(sat) the system has only a shallow equilibria, while for the high k(sat) only deep equilibria. The water resource impacts from climate change may be significantly amplified for catchments having two equilibria. For a catchment currently at the shallow equilibria, more extended periods of reduced infiltration may increase the probability of a shift to the deep equilibria. Upon a shift, streams hydrologically connected to the aquifer may shift from gaining to losing. The stream baseflow would reduce, suffer ecologically and, regionally, yields would further decline under climate change. If one attractor instead existed, changes would likely be more proportional to the change in recharge and thus less significant. While somewhat alarmist, and the model developed thus far omits the interaction with streams, it highlights the change in natural resource outcomes assuming two attractors as opposed to one. [GRAPHICS] .