Daisyworld. What is a System? Definition: A system is a group of different components that interact...
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![Page 1: Daisyworld. What is a System? Definition: A system is a group of different components that interact with each other Example: The climate system includes.](https://reader036.fdocuments.in/reader036/viewer/2022062518/56649e4a5503460f94b3e500/html5/thumbnails/1.jpg)
Daisyworld
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What is a System?
Definition: A system is a group of different components that interact with each other
Example: The climate system includes the atmosphere, oceans, polar caps, clouds, vegetation…and lots of other things
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How do we study systems?
• Identify the components
• Determine the nature of the interactions between components
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Systems Notation
= system component
= positive coupling
= negative coupling
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Positive Coupling
AtmosphericCO2
Greenhouseeffect
• An increase in atmospheric CO2 causes a corresponding increase in the greenhouse effect, and thus in Earth’s surface temperature• Conversely, a decrease in atmospheric CO2
causes a decrease in the greenhouse effect
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Negative Coupling
Earth’s albedo(reflectivity)
Earth’ssurface
temperature
• An increase in Earth’s albedo causes a corresponding decrease in the Earth’s surface temperature by reflecting more sunlight back to space• Or, a decrease in albedo causes an increase in surface temperature
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Equilibrium State:
Conditions under which the system will remain indefinitely
--If left unperturbed
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An Unstable Equilibrium State
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An Unstable Equilibrium State
Perturbation
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When pushed by a perturbation, an unstable equilibrium state shifts to a new, stable state.
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A Stable Equilibrium State
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A Stable Equilibrium State
Perturbation
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When pushed by a perturbation, a stable equilibrium state, returns to (or near) the original state.
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Daisy World
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Gaia hypothesis
Earth as a single living superorganism (James Lovelock)
Gaia - a new look at life on Earth, Oxford University Press, 1979.
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James Lovelock: NASA atmospheric chemist analyzing distant Martian atmosphere.
Why has temp of earth’s surface remained in narrow range for last 3.6 billion years when heat of sun has increased by 25%?
Lovelock’s Questions
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Why has oxygen remained near 21%?Martian atmosphere in chemical equilibrium, whereas
Earth’s atmosphere in unnatural low-entropy state.
Lovelock’s Questions
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Runaway greenhouse ::
No water cycle to remove carbon from atmosphereEarth is unique in our solar system in its capacity to sustain highly diversified life
Our Earth is a Unique Planet in the Solar System
Loss of carbon ::
No lithosphere motion on Mars to release carbon
Earth
Harbor of Life
from Guy Brasseur (NCAR)
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Lovelock´s answers
Earth can’t be understood without considering role of life
Abiotic factors(physical, geological
and chemical)determine biological
possibilities
Biotic factors feed back to
control abiotic factors
Increased Planetary
Temperature
Sparser Vegetation, More Desertification
Increased Planetary
Albedo
Reduced Temperature
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Gaia Hypothesis
Organisms have a significant influence on their environment
Species of organisms that affect environment in a way to optimize their fitness leave more of the same – compare with natural selection.
Life and environment evolve as a single system – not only the species evolve, but the environment that favors the dominant species is sustained
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White daisies
Black daisies
Available fertile land
Daisy world
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About Daisyworld…About Daisyworld…
Daisyworld: a mythical planet Daisyworld: a mythical planet with dark soil, white daisies, with dark soil, white daisies, and a sun shining on it.and a sun shining on it. The dark soil have low albedo – they The dark soil have low albedo – they
absorb solar energy, warming the absorb solar energy, warming the planet.planet.
The white daisies have high albedo – The white daisies have high albedo – they reflect solar energy, cooling the they reflect solar energy, cooling the planet.planet.
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The number of daisies affects temperature
The number of daisies The number of daisies influences temperature influences temperature of Daisyworld. of Daisyworld.
More white daisies means More white daisies means a cooler planet.a cooler planet.
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Temperature affects the number of daisiesTemperature affects the number of daisies
At 25° C many daisies At 25° C many daisies cover the planet.cover the planet.
Daisies canDaisies can’’t survive t survive below 5° C or above below 5° C or above 40° C. 40° C.
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White Daisy Response to Increasing Solar Luminosity
Relative solar luminosity
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26
Daisies can live between a min.T & a max. T
T
Dai
sy c
over
age
min. max.
optimum
T daisycoverage
T daisycoverage
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ENSC 425/625 Chapter 3UNBC
27
Intersection of 2 curves means the 2 effects are balanced => equilibrium points P1 & P2.
T
Dai
sy c
over
age
Effects of T ondaisy coverage
P1
Effects of daisy coverage on T
P2
T daisycoverage
T daisycoverage
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Feedback loops
ENSC 425/625 Chapter 3UNBC
28
P1
Effects of daisy coverage on T
P2T
Da
isy
cove
rag
e
Effects of T ondaisy coverage
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Perturb daisy coverage at P1 => sys. returns to P1 (stable equil. pt.)
29
T
Dai
sy c
over
age P1
P2
A large perturb. => daisies all die from extreme T
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Large incr. in daisy cover => very low T => decr. in daisy cov. => very high T => lifeless.
P1
T
Dai
sy c
over
age
P2
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ENSC 425/625 Chapter 3UNBC
31
From P2, incr. daisy cov. => decr. T => further incr. in daisy cov. => converge to P1
P1
T
Dai
sy c
over
age
P2
unstable equilib. pt.
T daisycoverage
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ENSC 425/625 Chapter 3UNBC
33
Gradual incr. in solar luminosity
T
Dai
sy c
over
age
P1
P2Teq
To Tf
P1
P2
The effect of T on Daisy unchanged
For any particular value of daisy cov., T incr.
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The key variables
b: Fraction of planet covered in black daisies
w: Fraction covered in white daisies
Tb: Temperature where the black daisies areTw: Temperature where the white daisies are
L: Solar luminosity
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An equation for the black daisies
dαb/dt = αb ( 1 – αb – αw) β(Tb) - γαb
= αb (αg β(Tb) – γ)
(T) is a function that is zero at 5C, rises to a maximum ofone at 22.5C and then falls to zero again at 40C
A simple and convenient choice is ( )( . )
.T
T
1
22 5
17 5
2
2
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An equation for the white daisies
We use a similar equation for the white daisies:
We don’t have to use the same and but itkeeps things simple. We can use different oneslater if we want to.
dαw/dt = αw (αg β(Tw) – γ)
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Heat Flow
Because different regions of Daisyworld are at differenttemperatures, there will be heat flow. We include this in the model using the equations
Tb4 = T4 + q(A-Ab) Tw
4=T4 + q(A-Aw)
Note that if q=0 the whole planet is at the same temperature,i.e., the heat flow is very rapid indeed. As q increases, so dothe temperature differences. Don’t worry about the 4th powers; they’re only there to makethe calculations easier and don’t make any real difference.
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The Daisyworld Equations
db/dt = b(g
(Tb) - ) d
w/dt=w(g
(Tw) - ) (T+273)4 = SL(1-A) A = gAg + bAb + wAw
Tb4 = T4 + q(A-Ab) Tw
4 = T4 + q(A-Aw)
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No daisies
TSL
2273
1 4
/
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Black daisies only
0 11
b b b bb
T a T( ( )( ) ) ( )
( )( . )
.T
Tb
b
122 5
17 5
2
2
Tbb
b
22 5 17 5
1
1. .
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Gaia Hypothesis
• Proposed by James Lovelock • Developed in 1960s• First published in 1975
• Definition of Gaia: • a complex entity involving the Earth's biosphere,
atmosphere, oceans, and soil; the totality constituting a feedback or cybernetic system which seeks an optimal physical and chemical environment for life on this planet. (Lovelock)
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Daisyworld Model
• Daisyworld is a hypothetical planet orbiting a sun that increases in intensity
• The planet is inhabited by 2 species• Black daisies• White daisies
• Original Daisyworld model consisted of a system of differential equations
• This project uses these equations to build a 2D cellular automata representation of Daisyworld
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Daisyworld Model (2)
• Temperature of Daisyworld is based on the assumption that the planet is in radiative equilibrium (i.e. energy emitted = energy absorbed)
• Albedo of the planet is computed based on the albedos of each type of daisy and the area covered by them
4)1(
SB
pp
LST
bbbbununp aaa
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Daisyworld Model (3)
• Area of daisies is modified according to the following equations
pspHAs
ss
sunss
TFT
Tg
deathrategaadt
da
)(
)5.22()540(
41
001.0)(
22
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Daisyworld Model (4)
• 2D CA rules:• If da/dt > 0
– If neighbors with no daisies < spreading threshold » Bare neighbors grow daisy with probability:
p = c*da/dt– Else if neighbors with no daisies >= spreading threshold
» Start new patch of daisies
• If da/dt <= 0– Daisies die with probability p = -da/dt
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Example of Daisy Crowding
• Spreading-threshold = 6
=> Start new patch of daisies
=> Don’t start new patch
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Parameter Settings
• Two different temperature models• Automatic linear increase of solar luminosity• Manual adjustment of solar luminosity
• Death-rate: 0.3• Albedo of white daisies: 0.75• Albedo of black daisies: 0.25• Albedo of bare land: 0.50• Spreading threshold: 8• Optimal daisy growth temperature: 22.5 C
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Spatial Daisyworld vs. Mathematical Daisyworld
(Mathematical Model)
Area Occupied by Daisies
(Spatial Model)
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Spatial Daisyworld vs. Mathematical Daisyworld (2)
(Mathematical Model)
Temperature of Daisyworld
(Spatial Model)
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Effects of Solar Luminosity on Daisyworld0.80.7 0.9 1.0
1.1 1.2 1.3 1.4
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The Effects of Death Rate on Daisyworld
death-rate = 0.1
death-rate = 0.3
death-rate = 0.5
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Daisyworld with Four Species of Daisies
Area covered by daisies Temperature of Daisyworld
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Effects of Solar Luminosity on Daisyworld with Four Species
0.80.7 0.9 1.0
1.1 1.2 1.3 1.4