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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= system component
= positive coupling
= negative coupling
Conditions under which the system will remain indefinitely
--If left unperturbed
When pushed by a perturbation, an unstable equilibrium state shifts to a new, stable state.
When pushed by a perturbation, a stable equilibrium state, returns to (or near) the original state.
Gaia - a new look at life on Earth, Oxford University Press, 1979.Gaia hypothesis
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
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
(physical, geological and chemical)
determine biological possibilities
Biotic factors feed back to control abiotic factors
Increased Planetary Albedo
Sparser Vegetation, More Desertification
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
Available fertile land
More white daisies means a cooler planet.The number of daisies affects temperature
Relative solar luminosity
Effects of daisy coverage on T
Effects of T on
TPerturb daisy coverage at P1 => sys. returns to P1 (stable equil. pt.)
A large perturb.
=> daisies all die
from extreme T
Large incr. in daisy cover => very low T =>
decr. in daisy cov. => very high T => lifeless.
further incr. in daisy cov. => converge to P1
( 1 – αb – αw)
= 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.
=> Start new patch of daisies
=> Don’t start new patch
Area Occupied by Daisies
Temperature of Daisyworld
death-rate = 0.3
death-rate = 0.1
death-rate = 0.5
Area covered by daisies
Temperature of Daisyworld