Daisyworld
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Daisyworld. 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. How do we study systems? Identify the components

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Daisyworld

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Daisyworld

Daisyworld


What is a system

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


Daisyworld

  • How do we study systems?

  • Identify the components

  • Determine the nature of the

  • interactions between components


Systems notation

Systems Notation

= system component

= positive coupling

= negative coupling


Positive coupling

Positive Coupling

Atmospheric

CO2

Greenhouse

effect

  • 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


Negative coupling

Negative Coupling

Earth’s albedo

(reflectivity)

Earth’s

surface

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


Daisyworld

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.


Daisyworld

Daisy World


Gaia hypothesis

Earth as a single living superorganism (James Lovelock)

Gaia - a new look at life on Earth, Oxford University Press, 1979.

Gaia hypothesis


Lovelock s questions

Lovelock’s Questions

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 questions1

Lovelock’s Questions

Why has oxygen remained near 21%?

Martian atmosphere in chemical equilibrium, whereas Earth’s atmosphere in unnatural low-entropy state.


Our earth is a u nique planet in the solar system

Our Earth is a Unique Planet in the Solar System

Loss of carbon ::

No lithosphere motion on Mars to release carbon

Runaway greenhouse ::

No water cycle to remove carbon from atmosphere

Earth

Harbor of Life

Earth is unique in our solar system in its capacity to sustain highly diversified life

from Guy Brasseur (NCAR)


Lovelock s answers

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

Increased Planetary Albedo

Sparser Vegetation, More Desertification

Reduced Temperature


Gaia hypothesis1

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


Daisy world

Daisy world

White daisies

Black daisies

Available fertile land


About daisyworld

About Daisyworld…

  • Daisyworld: a mythical planet with dark soil, white daisies, and a sun shining on it.

    • The dark soil have low albedo – they absorb solar energy, warming the planet.

    • The white daisies have high albedo – they reflect solar energy, cooling the planet.


The number of daisies affects temperature

The number of daisies influences temperature of Daisyworld.

More white daisies means a cooler planet.

The number of daisies affects temperature


Temperature affects the number of daisies

Temperature affects the number of daisies

  • At 25° C many daisies cover the planet.

  • Daisies can’t survive below 5° C or above 40° C.


White daisy response to increasing solar luminosity

White Daisy Response to Increasing Solar Luminosity

Relative solar luminosity


Daisies can live between a min t a max t

daisy

coverage

daisy

coverage

T

T

optimum

Daisy coverage

T

min.

max.

Daisies can live between a min.T & a max. T


Daisyworld

ENSC 425/625 Chapter 3UNBC

Effects of daisy coverage on T

daisy

coverage

daisy

coverage

T

T

P1

Effects of T on

daisy coverage

Daisy coverage

P2

T

  • Intersection of 2 curves means the 2 effects are balanced => equilibrium points P1 & P2.


Feedback loops

ENSC 425/625 Chapter 3UNBC

Effects of daisy coverage on T

P1

Effects of T on

daisy coverage

Daisy coverage

P2

T

Feedback loops


Perturb daisy coverage at p 1 sys returns to p 1 stable equil pt

P1

Daisy coverage

P2

T

Perturb daisy coverage at P1 => sys. returns to P1 (stable equil. pt.)

A large perturb.

=> daisies all die

from extreme T


Daisyworld

Daisy coverage

P1

P2

T

Large incr. in daisy cover => very low T =>

decr. in daisy cov. => very high T => lifeless.


Daisyworld

ENSC 425/625 Chapter 3UNBC

daisy

coverage

T

Daisy coverage

P1

P2

T

  • From P2, incr. daisy cov. => decr. T =>

    further incr. in daisy cov. => converge to P1

unstable

equilib. pt.


Gradual incr in solar luminosity

ENSC 425/625 Chapter 3UNBC

P1

P1

P2

Daisy coverage

To

Tf

Teq

P2

T

Gradual incr. in solar luminosity

For any particular value

of daisy cov., T incr.

The effect of T on

Daisy unchanged


The key variables

The key variables


An equation for the black daisies

An equation for the black daisies

αb

( 1 – αb – αw)

β(Tb)

- γαb

dαb/dt =

= αb (αg β(Tb) – γ)

b(T) is a function that is zero at 5C, rises to a maximum of

one at 22.5C and then falls to zero again at 40C

A simple and convenient choice is


An equation for the white daisies

An equation for the white daisies

We use a similar equation for the white daisies:

dαw/dt = αw (αg β(Tw) – γ)

We don’t have to use the same b(T) and g but it

keeps things simple. We can use different ones

later if we want to.


Heat flow

Heat Flow

Because different regions of Daisyworld are at different

temperatures, there will be heat flow. We include this in

the model using the equations

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 do

the temperature differences.

Don’t worry about the 4th powers; they’re only there to make

the calculations easier and don’t make any real difference.


The daisyworld equations

The Daisyworld Equations


No daisies

No daisies


Black daisies only

Black daisies only


Gaia hypothesis2

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)


  • Daisyworld model

    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


  • Daisyworld model 2

    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


    Daisyworld model 3

    Daisyworld Model (3)

    • Area of daisies is modified according to the following equations


    Daisyworld model 4

    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


    Example of daisy crowding

    Example of Daisy Crowding

    • Spreading-threshold = 6

      => Start new patch of daisies

      => Don’t start new patch


    Parameter settings

    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


  • Spatial daisyworld vs mathematical daisyworld

    Spatial Daisyworld vs. Mathematical Daisyworld

    Area Occupied by Daisies

    (Mathematical Model)

    (Spatial Model)


    Spatial daisyworld vs mathematical daisyworld 2

    Spatial Daisyworld vs. Mathematical Daisyworld (2)

    Temperature of Daisyworld

    (Mathematical Model)

    (Spatial Model)


    Effects of solar luminosity on daisyworld

    Effects of Solar Luminosity on Daisyworld

    0.7

    0.8

    0.9

    1.0

    1.1

    1.2

    1.3

    1.4


    The effects of death rate on daisyworld

    The Effects of Death Rate on Daisyworld

    death-rate = 0.3

    death-rate = 0.1

    death-rate = 0.5


    Daisyworld with four species of daisies

    Daisyworld with Four Species of Daisies

    Area covered by daisies

    Temperature of Daisyworld


    Effects of solar luminosity on daisyworld with four species

    Effects of Solar Luminosity on Daisyworld with Four Species

    0.7

    0.8

    0.9

    1.0

    1.1

    1.2

    1.3

    1.4


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