Tim J' Peterson

1
Multiple Stable States, Resilience and Shocks
within the Goulburn Catchment

• Tim J. Peterson
• PhD Candidate
• Supervisors
• Rob Argent, Francis Chiew

2
An Outline

• Background
• Multiple stable states of natural resource
  systems
• Resilience models
• Bifurcation.
• An existing catchment resilience model
• Expansion to tests its predictions of 2 states
• Further work.

3
BackgroundMultiple stable states of natural
resource systems

• Ecosystem thought to have multiple stable states
• States defined by different sets of feedbacks
• Shock (contagious or exogenous) may force the
  system over a threshold into an alternative
  state
• Resilience is a measure of the vulnerability to
  such shocks
• Operational definition of sustainability.
• Hydrology of saline catchments suggested to also
  have such stable states
• Why does it matter
• Optimised system thought to be at the cusp of a
  threshold
• Non-linear recovery
• Major water quality and yield changes.

4
BackgroundResilience Models

• Multiple stable states exist when positive
  feedbacks are switched on when a threshold is
  crossed
• Shocks (e.g. climatic extremes) may push the
  system over a threshold into an undesirable
  state
• Management actions (e.g. land clearing) change
  the size of the shock required for a state
  change
• Resilience to shocks is quantified using
  bifurcation of an ODE model.

5
BackgroundBifurcation

• Resilience models predominantly use Ordinary
  Differential Equations (ODE) for each state
  variable
• Bifurcation locates attractors (stable states)
  and repellors (thresholds) as a function of a
  parameter change in state space
• Parameter is often a management lever, e.g.
  percentage land clearing.

6
Existing regional catchment salinity
modelsOverview

• Few published models
• Anderies (2005) resilience model of the Goulburn
  catchment (north eastern Victoria)
• annual time step
• 2 bucket lumped
• physical salt water
  ordinary differential equation model (ODE).
• No soil moisture store
• Parametric partitioning similar to Zhang curves.

7
Existing regional catchment salinity modelsSome
Equations

• 3 state variables characterise each region
• Their evolution defined by a set of differential
  equations
• Depth to the unconfined groundwater
• Unsaturated zone salt store
• Groundwater (unconfined) soil salt store

8
Existing regional catchment salinity
modelsRevised Bifurcation Results

• Bifurcation identified two stable states
• High stream salt load and shallow water table
• Low steam salt load and deep water table.
• At 1 M/EC at Morgan S.A. this has major costs
• Additional states identified to that of Anderies
  (2005)
• Suggests hydrology of saline catchments ALSO have
  multiple state states.

9
Expanding the Existing ModelOverview

• Anderies (2005) model assumes DBNS is uniform
  within each region
• BUT only a fraction of a region become saline,
  not the whole region.
• As the multiple states are heavily influenced by
  the DBNS
• Are the predicted multiple states an artefact of
  the model lumping or a phenomena of the region?
• To investigate
• Implemented within MatLab Simulink
• Numerical bifurcation using the Broyden updating
  Newton chord pseudo-arc length predictor
  corrector algorithm plus local minima recursive
  algotithm
• Upland region subdivided into 2 and 3 sequential
  subregions
• Bifurcation with equal land clearing within
  each region undertaken.

10
Expanding the Existing ModelBifurcation Results
Stable state set gt 0m DBNS
0m DBNS beyond threshold
Stable state set 0m DBNS
Region Subdivided
Region Subdivided
11
Expanding the Existing ModelConclusions

• Simulating more realistic landscape salinity
  processes produced
• More complex sets of stable states
• Maintained two stable sets of i) 0m DBNS
  watertable and ii) gtgt0m watertable
• Critical landscape clearing threshold no longer
  constant b/w regions.
• Therefore
• Multiple stable states do not appear to be an
  artefact of the model(s)
• Goulburn hydrologic system appears to have
  multiple stable states.

12
Further Development

• Spatial bifurcation / resilience map for the
  upper Goulburn with
• Heterogeneity of hydrogeology, landuse and
  climate
• Probability of state change.
• Detection of historic state changes using
  recursive predictive error algorithm
• Reflexive management to End-Of-Valley salinity
  targets within a multi-stable system using
  multi-agent modelling of decision making.

13
Acknowledgements

• Assoc. Prof. Marty Anderies for provision of the
  Linux XPPAUT format Anderies of (2005) model
• Prof. John P. Norton for review of the paper (in
  press)
• Funding from
• Australian Research Council (ARC)
• Murray-Darling Basin Commission
• S. Australia Dept. of Wildlife, Land
  Biodiversity Conservation.
• ARC Linkage project partners at
• The Universities of Adelaide
• The Australian National University.