DaisyBall, the Math
DaisyBall uses the same math described in DaisyWorld - the Math, except:
- DaisyBall has 92 locations, to DaisyWorld's one. Each location has a separate multi-species DaisyWorld calculation running. Each of the 92 locations is drawn with one daisy on the ball.
- Since the base deathrate is 0.3, the petals of a daisy are colored based only on the 0.7 (70%) of daisies which could ever be alive. For example, if a 6-petaled daisy represents a population of 30% barren, 45% black, and 25% white, it is drawn with 4 black petals and 2 white petals.
- The luminosity at each DaisyBall location depends on its latitude. The planet is tilted at 23.5 degrees, which gives even the poles some light density.
- In order to use the same luminosity plot limits as DaisyWorld, the base albedos of black and white daisies are 0.2 and 0.8, compared to DaisyWorld's 0.25 and 0.75.
- There are two kinds of insulation in DaisyBall - instrasite insulation between one color population versus the multispecies location temperature, and planetary insulation between the location and the world temperature. DaisyWorld uses insulation of 0.12 between one-color population and the planet (which is the single multi-color site). DaisyBall uses 0.12 for intrasite insulation, and 0.3 for planetary insulation.
- Since DaisyBall has 2 orders of magnitude more work to do with all those parallel DaisyWorlds running, it uses 2 orders of magnitude fewer convergence steps per luminosity step - 25, compared to DaisyWorld's 1000.
I don't believe typesetting the math here would help anyone understand it.
Please don't take the color names seriously - that's pure creative license. They don't match the albedos of ground cover on Earth. Here are some actual terrestrial albedo values:
| Ground cover | Albedo |
|---|---|
| deep water | .05 - .20 |
| desert | .20 - .35 |
| short greenery | .10 - .20 |
| dry vegetation | .20 - .30 |
| summer conifers | .10 - .15 |
| deciduous forest | .15 - .25 |
| snowy forest | .20 - .35 |
| dry snow | .60 - .90 |
Cloud cover probably also varies up to 0.90 albedo.
Further Information
Other help files: