CSC2720H:% Systems%Thinking%for%% Global%Problems%sme/SystemsThinking/2016/slides/07...Complex Systems Complex Adaptive Systems (e.g. Levin) !Sustained diversity & individuality of

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© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license.

Prof Steve Easterbrook Dept of Computer Science

h8p://www.cs.toronto.edu/~sme/SystemsThinking

CSC2720H: Systems Thinking for Global Problems

University of Toronto Department of Computer Science

© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 2

Week 7

Week 7 ➜ Chaos Theory

Ä Game: The Chaos Game Ä Case Study: Chaos in Weather Forecasting

➜ Complexity Science

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Calculating the weather…

Zonal (East-West) Wind:

Meridional (North-South) Wind:

Temperature:

Precipitable Water:

Air pressure:

1904: Vilhelm Bjerknes identified the “primitive equations”

These capture the flow of mass and energy in the atmosphere;

Sets out a manifesto for practical forecasting



Towards Numerical Forecasts 1910s: Lewis Fry Richardson performs the first numerical weather

forecast, imagines a giant computer to do this regularly;

First plan for massively parallel computation

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First Computer Model of Weather 1950s: John Von Neumann develops a killer app for the first programmable electronic computer ENIAC: weather forecasting

Imagines uses in weather control, geo-engineering, etc.


© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 6 Image Source: Lynch, P. (2008). The ENIAC Forecasts: A Recreation. Bulletin of the American Meteorological Society

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© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 7 Bauer, P., Thorpe, A., & Brunet, G. (2015). The quiet revolution of numerical weather prediction. Nature, 525(7567), 47–55.


© 2014 Steve Easterbrook. This presentation is available free for non-commercial use with attribution under a creative commons license. 8 Source: http://www.vets.ucar.edu/vg/T341/index.shtml

Global Precipitation in CCSM CAM3

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The discovery of Chaos 1950s: Edward Lorenz discovers non-linear effects in weather

forecasting, develops Chaos Theory;

Basis for understanding what is predictable and what isn’t



Chaos Theory - Key concepts ➜ Non-linear Dynamical Systems

Ä Inputs are not proportional to outputs Ä Determinism: Can you work out future states?

➜ Sensitivity to Initial Conditions Ä The “butterfly effect” Ä E.g. The Lorenz Attractor

➜ Denseness ➜ Attractors (Simple and Strange) ➜ Criticality and Tipping Points ➜ Self-similarity and Fractals

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Example of the butterfly effect

Source: https://www.youtube.com/watch?v=FYE4JKAXSfY



Forecasting Weather and Climate

Analysis

Initial condition uncertainty

Climatology

Forecast uncertainty

Deterministic forecast

Time

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Deterministic Complexity Pattern of population

for x' = rx(1-x)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

Iteration

Po

pu

latio

n



Bifurcation Diagram for x’ = rx(1-x)

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Example: population growth

Source: Sterman, J. D. (2012). Sustaining Sustainability



Finding Equilibria

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Eckmann Recurrence Plots

White Noise:HarmonicOscillation

Chaotic dataw. linear trend

Auto-regressiveprocess



Example: The ice ages

➜ Milankovitch cycles: Ä 26,000yr cycle in the earth’s precession (axis rotation) Ä 41,000yr cycle in the earth’s obliquity (axis tilt) Ä 100,000yr cycle in the earth’s orbital inclination & eccentricity

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Aggregate Complexity ➜ Learning and Memory

Ä …through persistence of internal structure Ä A system “learns” by reconfiguring internal structure

➜ Emergence

➜ Change & Evolution Ä Self-organization Ä Dissipation (push towards a disorganized state) Ä Self-organized criticality (re-structuring on the edge of chaos)



Complex Systems ➜ Complex Adaptive Systems (e.g. Levin)

Ä Sustained diversity & individuality of components Ä Localized interactions among those components Ä Autonomous process that selects subsets for replication or

enhancement

➜ Adaptive Non-Linear Networks (e.g. Brian Arthur) Ä Dispersed Interaction Ä No Global Controller (no privileged agent) Ä Cross-Cutting Hierarchical Organization (much tangling across levels) Ä Continual Adaptation (the system learns and adapts) Ä Perpetual Novelty (new niches created & filled) Ä Out-of-equilibrium dynamics (system can never reach an optimum)

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Study via Simple models?

The Abelian Sandpile ModelConway’s Game of Lifehttp://www.bitstorm.org/gameoflife/ https://www.youtube.com/watch?v=-d7_OGn22d4



Self-Organized Criticality

Simple model of how avalanches work:Bak, Tang, and Wiesenfeld’s Sandpile model

https://www.youtube.com/watch?v=h737qbQRPME&feature=youtu.be&t=4m

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CSC2720H:% Systems%Thinking%for%% Global%Problems%sme/SystemsThinking/2016/slides/07...Complex Systems Complex Adaptive Systems (e.g. Levin) !Sustained diversity & individuality of