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An Introduction to Systems

Daisyworld

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What are systems?What are feedback loops?What are equilibrium states?Does viewing Earth as a system allow for

deeper insight into the interrelationships among the physical and biological worlds?

Can Earth’s climate be self-regulating?

Chapter focus – the fundamentals of systems theory needed to study Earth

Key Questions

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Human physiologySystems interrelated, function together to

maintain the body in a healthy state

Systems Approach

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System – composed of diverse but interrelated components that function as a complex wholeComponents can be:

reservoir of matterreservoir of energysystem attributesubsystem

Introduction to Systems

System Essentials

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Set of important attributes that characterize the system at a particular timeComponents interact so that a change in state

is sensed by the whole systemThis linkage allows for the control of important

attributes

State of a System

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Links between systems that allow the flow of information from one component to the nextElectric blanket example

Couplings

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Keep track of couplings within a system

Systems Diagrams

Positive Coupling – a change ( or ) in one component leads to a change in the same direction in the linked component - represented by

Negative Coupling - a change in one component leads to a change in the opposite direction in the linked component - represented by

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Feedback LoopsPositive Feedback Loops – amplify the effects of the disturbance

Negative Feedback Loops – diminish the effects of the disturbance

“Sign” of the Loop –• odd number of negative couplings – negative• even number of negative or all positive couplings- positive

Feedback is a self-perpetuating mechanism of change and response to that change

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Condition will not change unless the system is disturbedStable

Created by negative feedback loopsModest disturbances will be followed

by return to equilibrium stateUnstable

Slight disturbance carry the system further and further away from the state

Equilibrium State

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Stable State

• Small disturbances followed by return to equilibrium state• Large disturbances can lead to a new different equilibrium state• There are limits to the stability of stable equilibrium states

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Unstable States

• No region of stability•Will not return to original state on its own• Slightest disturbance pushes system to a new stable equilibrium

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For natural systems with a single feedback loop it is usually true that Stable systems result from negative

feedback loopsUnstable systems result from positive

feedback loops

Equilibrium State

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Perturbation – temporary disturbance of a systemVolcanic eruption example – average climatic

response to the 5 largest eruptions in the last 100 years

Perturbations and Forcings

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Forcing – more persistent disturbance of a systemSolar Luminosity example

Increase in temperature countered by decrease in CO2

Perturbations and Forcings

LLGHG = Long Lived Greenhouse Gases

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Hypothetical planet with a simpler climate systemOnly life forms are daisiesCreation of Lovelock & WatsonDemonstrates that natural systems can

be self-regulating on a global scale without the need for intelligent intervention

Daisyworld

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A two component systemArea of white daisy coverageAverage surface temperature

Daisy coverage affects temperatureTemperature affects daisy coverage

Daisyworld Climate System

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Albedo – reflectivity of a surfaceExpressed as a decimal fraction of the total

incoming energy reflected from the surface

Daisyworld Couplings

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Su

rface

Tem

pera

ture

vs

Dais

y C

ove

rag

e

• Negative Coupling• Negative slope

• Daisy Coverage - Surface Temp

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Coupling:Daisy Coverage – Albedo - Temperature

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Daisy Coverage in response to Temp

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Equilibrium States• Put the two together• Intersection shows• Effect of daisies

on temperature AND• Effect of temp on

daisies• EQUILIBRIUM STATES•Two Feedback loops• One above

optimum• One below

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Feedback Loops

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TH

E D

AIS

Y W

OR

LD

CL

IMA

TE

SY

TE

MResponse of Daisy world to perturbations depends on the temperature

-Below optimum has negative feedback loop and is stable-Above optimum has positive feedback loop and is unstable

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Increased solar luminosityDaisies would increase (immediately) and

albedo increase and warming would be slowed

Persistent increasing solar luminosity would eventually lead to a new higher equilibrium temperature, but it would happen at a much slower rate (daisies & environment feedback loops)

Response to External Forcing

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Assumption – daisies respond to temperature change only

So – no change to

More Accurate Response to External Forcing

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However, change in surface temperature and daisy coverage expected

Temperature will be higher for any amount of daisy coverage

So – change to

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P1' stable

P2' unstableBoth temperature

and daisy coverage higher at new stable equilibrium

Stability limit for P1' is lower

New equilibrium state less resistant to perturbations

Combine the two Graphs

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Comparing equilibrium temperature with and without feedback

∆Teq = ∆T0 + ∆Tf

The overall temperature change resulting from increase solar luminosity is the sum of the temperature change with no feedback and the temperature change due to feedback

Mathematically Speaking . . .

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The change in state of a system as it moves from one equilibrium to the next is the sum of the state change that would result without feedback and the effect of the feedback itself

To qualify the strength of the feedback effect . . .

For Any Stable Equilibrium in a System Involving Feedback Loops

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The ratio of the equilibrium response to forcing (the response with feedback) to the response without feedback

= temperature change with feedback = ∆Teq

temperature change w/out feedback ∆T0

Negative feedback loop if 0 < < 1Positive feedback loop if 1 < Feedback factor defined only for stable systems

The Feedback Factor

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Daisyworld Climate History

History of Daisy Coverage

Temperature History-Initially temp rises quickly-Once min temp for daisies met, daisies increase-Growth of daisies cools planet-Eventually, when optimal temp is met, daisy coverage at max-Increasing solar luminosity not countered by daisy growth and daisies die, causing increasing temp-Feedback loop positive & unstable-Surface temp rises, daisies extinct

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A planetary climate system is not passive in the face of internal or external forcesNegative feedback loops counter external forcings

Non-human systems that self-regulate seem intelligent, yet no foresight or planning is involved

In a natural self-regulating system, there is no preset state that the system is programmed to “seek-out”

Thresholds often exist in systems that when surpassed can lead to rapid changes in system stateAbrupt changes can have no forewarning

Earth is like DaisyworldStrong negative feedback loops lead to long-term

stabilityAre we approaching a climate threshold that will

result in a much warmer state?

The Lessons of Daisyworld

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