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Earth Systems Science Chapter 2: SYSTEMS

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Use the new line for the effect of daisy coverage on temperature ... With the daisy feedback, the temperatures on Daisyworld are kept much more ... – PowerPoint PPT presentation

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Title: Earth Systems Science Chapter 2: SYSTEMS


1
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

2
  • 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

3
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4
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
5
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
6
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
7
Forcing a persistent disturbance to a system e.g.
a gradual change in solar radiation over long
time, the faint young sun paradox
8
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.

9
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10
Response of average surface temperature to daisy
coverage
(c) Equation Temp adaisy b
Graph
Systems Diagram
11
Systems Diagram explicitly including albedo
12
Response of daisy coverage to average surface
temperature
(c) Equation Daisy 100 (T-22)2/4
13
  • 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.

14
  • 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

15
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
16
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

17
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

18
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.
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