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Daisyworld

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Daisyworld

- 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
- Determine the nature of the
- interactions between components

= system component

= positive coupling

= negative 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

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

Equilibrium State:

Conditions under which the system will remain indefinitely

--If left unperturbed

An Unstable Equilibrium State

An Unstable Equilibrium State

Perturbation

When pushed by a perturbation, an unstable equilibrium state shifts to a new, stable state.

A Stable Equilibrium State

A Stable Equilibrium State

Perturbation

When pushed by a perturbation, a stable equilibrium state, returns to (or near) the original state.

Daisy World

Earth as a single living superorganism (James Lovelock)

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

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%?

Why has oxygen remained near 21%?

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

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)

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

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

White daisies

Black daisies

Available fertile land

- 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 influences temperature of Daisyworld.

More white daisies means a cooler planet.

- At 25° C many daisies cover the planet.
- Daisies can’t survive below 5° C or above 40° C.

Relative solar luminosity

daisy

coverage

daisy

coverage

T

T

optimum

Daisy coverage

T

min.

max.

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.

ENSC 425/625 Chapter 3UNBC

Effects of daisy coverage on T

P1

Effects of T on

daisy coverage

Daisy coverage

P2

T

P1

Daisy coverage

P2

T

A large perturb.

=> daisies all die

from extreme T

Daisy coverage

P1

P2

T

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

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

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.

ENSC 425/625 Chapter 3UNBC

P1

P1

P2

Daisy coverage

To

Tf

Teq

P2

T

For any particular value

of daisy cov., T incr.

The effect of T on

Daisy unchanged

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

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.

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.

- Proposed by James Lovelock
- Developed in 1960s
- First published in 1975

- 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 is a hypothetical planet orbiting a sun that increases in intensity
- The planet is inhabited by 2 species
- Black daisies
- White daisies

- This project uses these equations to build a 2D cellular automata representation of Daisyworld

- 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

- Area of daisies is modified according to the following equations

- 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 neighbors with no daisies < spreading threshold
- If da/dt <= 0
- Daisies die with probability p = -da/dt

- If da/dt > 0

- Spreading-threshold = 6
=> Start new patch of daisies

=> Don’t start new patch

- Two different temperature models
- Automatic linear increase of solar luminosity
- Manual adjustment of solar luminosity

Area Occupied by Daisies

(Mathematical Model)

(Spatial Model)

Temperature of Daisyworld

(Mathematical Model)

(Spatial Model)

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

death-rate = 0.3

death-rate = 0.1

death-rate = 0.5

Area covered by daisies

Temperature of Daisyworld

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4