Multiple Stable States within Dryland
Catchments:
Validity of theories, prevalence and impacts of
climate variability.
Tim Peterson, Rob Argent, Andrew Western,
Francis Chiew
18/11/2008
Tim J. Peterson
Slide 1 / 26
System State
Some assumptions of water resource models…
Disturbance
Disturbance
Removed
Time
Time
18/11/2008
Tim J. Peterson
Slide 2 / 26
Disturbance
Disturbance
Removed
Background to PhD ...
• Validity of Anderies 2005?
–
Spatial discretisation;
–
Shorter time-steps;
• Testing against observed data via calibration
and evaluation.
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Tim J. Peterson
Slide 3 / 26
An Existing catchment resilience model for Goulburn
Catchment, Victoria (Anderies 2005)
Depth to watertable (m)
Uplands
Fraction of Landscape Cleared
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Tim J. Peterson
Slide 4 / 26
Depth to watertable (m)
Lowland
Plains
Fraction of Landscape Cleared
Validity of Lumped Model?
Water table remains
deep in a large % of
the area
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Tim J. Peterson
Slide 5 / 26
Expanding the Existing Model:
Bifurcation Results
Region Subdivided
Depth to watertable (m)
Region Subdivided
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Tim J. Peterson
Fraction
Slideof6 Landscape
/ 26
Cleared
A distributed model for validation:
Sunday Creek-SWG implementation.
depth to
water table (m)
0
2
4
6
8
10
12
14
16
18
20
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Tim J. Peterson
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But, 2 states only at extreme parameter values.
depth to
water table (m)
0
2
4
6
8
10
12
14
16
18
20
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Tim J. Peterson
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Back to Basics:
A simple lumped model…
Observation
Bore
Surface
Elevation
Area
Depth to
water
table
Δh
(constant)
Qin = 0
Basement
Qout
Qbasement = 0
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Tim J. Peterson
Slide 9 / 26
Back to Basics:
Simple unsat. zone processes…
Flux (m/yr)
Discharge
-0.4
-0.2
0
0.2
Depth to water table (m)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Gross Capillary
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Tim J. Peterson
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Recharge
Gross Recharge
0.4
+ Feedback
Net Flux
Two states still emerge...
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Tim J. Peterson
Slide 11 / 26
Fraction Landscape Cleared of Woody Veg.
Back to Basics:
Some trials and calibrations …
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Tim J. Peterson
Slide 12 / 26
Away from Basics:
Adding Lateral Flow Processes …
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Tim J. Peterson
Slide 13 / 26
Source: Peterson, et al., in-press, Water Resources Research.
An exploration of the model ...
• Supplied limited climate (P/PET = 0.5);
• Clay loam and pastures (LAImean = 2.0);
• Homogeneous isotropic unconfined aquifer;
• Geometry: convergent and sloping:
18/11/2008
Tim J. Peterson
Slide 14 / 26
Hilberts et al.
2003
Transient solutions:
Saturated lateral conductivity = 0.5 m/day
Shallow
Initial
Head
Shallow
Equilibria
Deep
Initial
Head
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Tim J. Peterson
Slide 15 / 26
Deep
Equilibria
Transient solutions:
High saturated lateral conductivity (ksat = 1.3 m/day)
Shallow
Initial
Head
Deep
Equilibria
Deep
Initial
Head
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Tim J. Peterson
Slide 16 / 26
Not all catchments have two attractors:
Low saturated lateral conductivity (ksat = 0.01 m/day)
Shallow
Initial
Head
Shallow
Equilibria
Deep
Initial
Head
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Tim J. Peterson
Slide 17 / 26
Positive feedbacks and model changes
• Transpiration declines as water table approaches
the surface*:
− klight LAI  θ − θ wp

T = PET1 − e


 θ − θwp
 Pt 

LAI = LAIavg 
P 
 avg 
β


d vα
 α α 
 d v + d LAI / 2 
• Logistic Function (0->1)
• LAI α 1 / Depth to water table
• Simulations repeated without logistic function.
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Tim J. Peterson
Slide 18 / 26
* adapted form: Johnson, I. R. and Thornley, J. H. M., Vegetative crop growth model incorporating leaf
area expansion and senescence, and applied to grass. Plant, Cell and Environment. 1983, 6 p721-729
Transient solutions without transpiration feedback
Saturated lateral conductivity = 0.5 m/day
Shallow
Initial
Head
Only
Deep
Equilibria
Deep
Initial
Head
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Tim J. Peterson
Slide 19 / 26
Some Findings…
• Only some catchments have two states;
–
Saturated conductivity, Areal convergence /
outlet constriction, slope, …
• Parameters independently observable.
• Climate time step significantly affects estimated
range of two states.
• Transparent and tractable processes for two
states.
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Limit Cycle Continuation (i.e. stability analysis):
General head boundary condition.
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Tim J. Peterson
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Limit Cycle Continuation 2-D View:
General head boundary condition.
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Tim J. Peterson
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Some Findings…
• Boundary conditions are very significant in
defining which catchments have 2 states;
• 72% reduction in streamflow!
• But, recharge is very event driven.
–
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Tim J. Peterson
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Do two states occur with observed data?
Climate Variability:
Do two states still emerge?
Shallow watertable initially
Deep watertable initially
Probability of switching state.
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Tim J. Peterson
Slide 24 / 26
: Saturated lateral conductivity (ksat) range of 2
stable states.
Some Implications …
•
•
Identify catchments >1 stable state:
–
where existing models are applicable;
–
prioritising actions to >1 catchments.
Major hysteresis when state change occurs:
–
asymmetric vulnerability of the 2 states;
–
existing measures of resilience are incomplete.
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Tim J. Peterson
Slide 25 / 26
What's Next?
•
Repeat with probability simulations with daily
data.
•
Implementation to paired catchments in
Wimmera.
•
Post-Doctorate at Uni Melb with DPI (Cheng),
DSE (McAuley), BoM (Frost-Daamen).
–
18/11/2008
Tim J. Peterson
Slide 26 / 26
Mid-2009 to mid-2011.