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Earth Systems Science Chapter 2 SYSTEMS

- Systems Analysis some basic concepts /

definitions - Daisyworld a heuristic model to demonstrate

the potential for negative feedbacks on a planet

to stabilize the climate - Equilibrium vs Dynamical models

- Systems Analysis some basic concepts /

definitions - System a set of interrelated parts, or

components - State of a system a set of attributes that

characterize the system (depth of water in the

tub temperature of earth) - Coupling a link between 2 components
- coupling component 1 increases, component 2

increases - coupling - component 1 increases,

component 2 decreases - Feedback loops positive and negative
- Equilibrium States stable and unstable
- Perturbations Forcings

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Each person controlling their own blanket

temperature (negative feedback, stable

equilibrium)

Jimmy Rosalynn Carter Each was inadvertently

controlling the temperature of the others

blanket Positive feedback, unstable equilibrium

STABLE / UNSTABLE EQUILIBRIUM

Stable Equilibrium If the system is perturbed by

a small amount, it will return to the same

equilibrium state Unstable Equilibrium If the

system is perturbed by a small amount, it will

NOT return to the same equilibrium

state Example a thermostat

Perturbation sudden / temporary disturbance to a

system The disturbance is temporary, but the

system might take a while to recover

Impact of asteroid injects massive amount of

particulates into the atmosphere

a volcanic eruption injects SO2 into the

atmosphere, which is washed out of the atmosphere

in a few years

Forcing a persistent disturbance to a system e.g.

a gradual change in solar radiation over long

time, the faint young sun paradox

DAISYWORLD A HEURISTIC MODEL

- Heuristic (dictionary.reference.com)
- Of or relating to a usually speculative

formulation serving as a guide in the

investigation or solution of a problem The

historian discovers the past by the judicious use

of such a heuristic device as the ideal type

(Karl J. Weintraub). - Of or constituting an educational method in which

learning takes place through discoveries that

result from investigations made by the student.

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Response of average surface temperature to daisy

coverage

(c) Equation Temp adaisy b

Graph

Systems Diagram

Systems Diagram explicitly including albedo

Response of daisy coverage to average surface

temperature

(c) Equation Daisy 100 (T-22)2/4

- Equilibrium States Graphical Determination
- Overlay the two graphs (this is the graphical way

of setting them equal to each other). - The points where they meet are equilibrium

points. - Draw a systems diagram to determine whether each

one is stable or unstable.

- Equilibrium States Algebraic Determination
- Response of Temp to daisies Temp adaisy

b daisy (Temp b)/a - Response of daisies to Temp daisy 100

(Temp-22)2/4 - Set the equal to each other (Temp b)/a 100

(Temp-22)2/4 - Do some algebraic manipulation, you get a

quadratic equation T2 (44-4/a)T (84-4b/a) 0 - solution to a quadratic (aT2 bT c 0) is T

-b sqrt(b2 4ac) / 2a - This will give 2 solutions, corresponding to P1

and P2

External Forcing the response of Daisy World

- Assume that the external forcing is an increase

in solar luminosity - The effect of temperature on daisy coverage

should not change (this depends on the physiology

of daisies) - The effect of daisy coverage on temperature

should change for the same daisy coverage,

higher temperature

Algebraic Temp adaisy bDT0

Response of the Equilibrium State to the Forcing

- Use the new line for the effect of daisy coverage

on temperature - Notice that the new equilibrium points have

changed P1, the stable point, is at a higher

temperature - Notice that P1 is not as high a temperature as it

would have been without the daisies responding - Feedback factor DTeq DTo - DTf

Climate history of Daisyworld solar luminosity

increasing

- As solar luminosity increases, with no feedback

(or no daisies) the average temperature will

increase close to linearly - With the daisy feedback, the temperatures on

Daisyworld are kept much more stable compared to

the case without feedback - No intention is required on the part of the

daisies to stabilize the climate. All this is

required is a negative feedback

EQUILIBRIUM MODELS The model of Daisyworld in the

text is an equilibrium model, just like the

models of the bathtub and the earths radiation

balance from lab 1. These models do not allow one

to determine if it ever actually reaches

equilibrium, or how long it takes to get

there. In these equilibrium models, the the STATE

of one variable (daisy coverage, water level in

the tub, or earths temperature) is a function of

the state of a second variable (planetary

temperature, rate of water coming out of faucet,

solar luminosity). DYNAMICAL MODELS In dynamical

models, the CHANGE of one variable (daisy growth

rate, water level rate of increase, rate of

earths temperature change) is a function of the

state of the second variable.