Daisyworld

1. Daisyworld

2. 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

3. How do we study systems? • Identify the components • Determine the nature of the • interactions between components

4. Systems Notation = system component = positive coupling = negative coupling

5. 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

6. 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

7. Equilibrium State: Conditions under which the system will remain indefinitely --If left unperturbed

8. An Unstable Equilibrium State

9. An Unstable Equilibrium State Perturbation

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

11. A Stable Equilibrium State

12. A Stable Equilibrium State Perturbation

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

14. Daisy World

15. Earth as a single living superorganism (James Lovelock) Gaia - a new look at life on Earth, Oxford University Press, 1979. Gaia hypothesis

16. 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%?

17. Lovelock’s Questions Why has oxygen remained near 21%? Martian atmosphere in chemical equilibrium, whereas Earth’s atmosphere in unnatural low-entropy state.

18. 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)

19. 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

20. 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

21. Daisy world White daisies Black daisies Available fertile land

22. 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.

23. The number of daisies influences temperature of Daisyworld. More white daisies means a cooler planet. The number of daisies affects temperature

24. 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.

25. White Daisy Response to Increasing Solar Luminosity Relative solar luminosity

26. daisy coverage daisy coverage T T optimum Daisy coverage T min. max. Daisies can live between a min.T & a max. T

27. 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.

28. ENSC 425/625 Chapter 3UNBC Effects of daisy coverage on T P1 Effects of T on daisy coverage Daisy coverage P2 T Feedback loops

29. 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

30. Daisy coverage P1 P2 T Large incr. in daisy cover => very low T => decr. in daisy cov. => very high T => lifeless.

31. 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.

33. 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

34. The key variables

35. 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

36. 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.

37. 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.

38. The Daisyworld Equations

39. No daisies

40. Black daisies only

41. 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)

42. 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

43. 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

44. Daisyworld Model (3) • Area of daisies is modified according to the following equations

45. 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

46. Example of Daisy Crowding • Spreading-threshold = 6 => Start new patch of daisies => Don’t start new patch

47. 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

48. Spatial Daisyworld vs. Mathematical Daisyworld Area Occupied by Daisies (Mathematical Model) (Spatial Model)

49. Spatial Daisyworld vs. Mathematical Daisyworld (2) Temperature of Daisyworld (Mathematical Model) (Spatial Model)

50. Effects of Solar Luminosity on Daisyworld 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4