An Introduction to Systems 1

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 Earths climate be self-regulating? Chapter focus – the fundamentals of systems theory needed to study Earth 2

Human physiology Systems interrelated, function together to maintain the body in a healthy state 3

System – composed of diverse but interrelated components that function as a complex whole Components can be: reservoir of matter reservoir of energy system attribute subsystem Introduction to Systems 4

Set of important attributes that characterize the system at a particular time Components interact so that a change in state is sensed by the whole system This linkage allows for the control of important attributes 5

Links between systems that allow the flow of information from one component to the next Electric blanket example 6

Keep track of couplings within a system 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 7

Positive 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 8

Condition will not change unless the system is disturbed Stable Created by negative feedback loops Modest disturbances will be followed by return to equilibrium state Unstable Slight disturbance carry the system further and further away from the state 9

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 10

No region of stability Will not return to original state on its own Slightest disturbance pushes system to a new stable equilibrium 11

For natural systems with a single feedback loop it is usually true that Stable systems result from negative feedback loops Unstable systems result from positive feedback loops 12

Perturbation – temporary disturbance of a system Volcanic eruption example – average climatic response to the 5 largest eruptions in the last 100 years 13

Forcing – more persistent disturbance of a system Solar Luminosity example Increase in temperature countered by decrease in CO 2 LLGHG = Long Lived Greenhouse Gases 14

Hypothetical planet with a simpler climate system Only life forms are daisies Creation of Lovelock & Watson Demonstrates that natural systems can be self- regulating on a global scale without the need for intelligent intervention 15

A two component system Area of white daisy coverage Average surface temperature Daisy coverage affects temperature Temperature affects daisy coverage 16

Albedo – reflectivity of a surface Expressed as a decimal fraction of the total incoming energy reflected from the surface 17

Surface Temperature vs Daisy Coverage Negative Coupling Negative slope Daisy Coverage - Surface Temp 18

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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 21

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THE DAISY WORLD CLIMATE SYTEM Response 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 23

Increased solar luminosity Daisies 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) 24

Assumption – daisies respond to temperature change only So – no change to 25

However, change in surface temperature and daisy coverage expected Temperature will be higher for any amount of daisy coverage So – change to 26

P 1 ' stable P 2 ' unstable Both temperature and daisy coverage higher at new stable equilibrium Stability limit for P 1 ' is lower New equilibrium state less resistant to perturbations 27

Comparing equilibrium temperature with and without feedback T eq = T 0 + T f 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 28

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... 29

The ratio of the equilibrium response to forcing (the response with feedback) to the response without feedback = temperature change with feedback = T eq temperature change w/out feedback T 0 Negative feedback loop if 0 < < 1 Positive feedback loop if 1 < Feedback factor defined only for stable systems 30

31 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

A planetary climate system is not passive in the face of internal or external forces Negative 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 state Abrupt changes can have no forewarning Earth is like Daisyworld Strong negative feedback loops lead to long-term stability Are we approaching a climate threshold that will result in a much warmer state? 32

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