Multiple stable states and thresholds within the Goulburn catchment

T. J. Peterson, R. M. Argent, F. H.S. Chiew

Research output: Chapter in Book/Report/Conference proceedingConference PaperOther

3 Citations (Scopus)


Over the last decade, ecosystem management has been tending toward understanding ecosystems as having multiple stable states. Often such states are characterised as socially desirable and undesirable, with for instance high/low fish stocks or oligotrophic/eutrophic lake states. Their significance is that small stochastic forces may force the system over a threshold toward an alternative, potentially undesirable, state. Until recently no investigation of similar behaviour in regional agricultural catchments has been made. This paper further develops the only published model of a regional agricultural catchment system predicted to have such multiple states. Simple analytical models have been developed to numerically predict the existence of such multiple stable states. They are models of physical behaviour, comprised of a set of ordinary differential equations (ODE), with each equation defining the evolution of a state variable. Bifurcations of the ODE models provide a means of identifying the set of stable states and the thresholds between them, and thus quantifying the resilience of current state of the system to shocks. The resilience of agricultural catchments has recently begun to be qualitatively addressed. The only catchment-resilience model is a salt and water groundwater-unsaturated zone model of the Goulburn catchment (Anderies 2005). The catchment is modelled at two connected lumped regions; one for the lowland plains and the other for the uplands. It predicts the catchment to have only two stable states; one of deep water table depth and low stream salt loads and the other of a water table approaching the surface and high salt loads. It predicts that beyond 15.4% of land clearing in the upper Goulburn, the system has only the latter state. This paper expands upon this model to test these predictions. The predicted two states are the result of a positive feedback loop emerging as the depth to the water table becomes very shallow. It results in high soil salinity which reduces transpiration, and in turn increases groundwater recharge, thus closing the feedback. Lumping of the Goulburn catchment into only two regions treats the landscape salinity processes as uniform across the catchment, rather than varying locally and realistically. This inconsistency was investigated by subdividing the upland region of the model. This tests its predictions with greater spatial resolution and more realistic representation of critical processes. The multiple stable states predicted by the original model do not appear to be an artefact of the degree of spatial lumping. Expanding the model from two lumped regions to three and four regions still produces the predicted multiple states. Significantly more complex stability structures did emerge but the general properties of a cluster of stable states at only a deep water table and another at an approximately zero water table depth persisted. Included in these sets, and in the 2-region model, were previously unpublished stable states produced by non-uniform shocks applied across the regions. The phenomena predicted by these models have major implications for stream and landscape salinity management. These predictions are, however, based upon a very simple and highly spatially lumped model. Future work will apply a greater spatial resolution in order to allow more rigorous calibration against stream and groundwater hydrographs, and thus more valid identification of stable states and thresholds. If the predictions of multiple stale states for the Goulburn catchment are correct, then based upon the very high percentage of cleared land, the entire catchment should have only the shallow water table stable state. As the percentage of land cleared has significantly increased throughout the last century within the catchment, it should also have switched from having at least two stable states to the current single stable state. If this is correct, it should be observable in the catchment data. An investigation of whether it is will be undertaken following refinement of the model.

Original languageEnglish
Title of host publicationMODSIM05 - International Congress on Modelling and Simulation
Subtitle of host publicationAdvances and Applications for Management and Decision Making, Proceedings
Number of pages7
Publication statusPublished - 1 Dec 2005
Externally publishedYes
EventInternational Congress on Modelling and Simulation 2005: Advances and Applications for Management and Decision Making - Melbourne, Australia
Duration: 12 Dec 200515 Dec 2005

Publication series

NameMODSIM05 - International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, Proceedings


ConferenceInternational Congress on Modelling and Simulation 2005
Abbreviated titleMODSIM 2005


  • Bifurcation
  • Goulburn catchment
  • Multiple states
  • Resilience
  • Salinity

Cite this

Peterson, T. J., Argent, R. M., & Chiew, F. H. S. (2005). Multiple stable states and thresholds within the Goulburn catchment. In MODSIM05 - International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, Proceedings (pp. 2526-2532). (MODSIM05 - International Congress on Modelling and Simulation: Advances and Applications for Management and Decision Making, Proceedings).