Equations for Daisyworld Model
Reservoirs: (make sure these are all non-negative by clicking the
appropriate box)
INIT Uncovered_Area = 1.0 {portion of surface that daisies can occupy}
INIT Black_Area = 0
INIT White_Area = 0
Flows:
black_growth = Black_Area*(Uncovered_Area*Black_Growth_fact-death_rate)+.001
{the .001 is needed to give the system a bit of a nudge; without it the daisies
never get going}
white_growth = White_Area*(Uncovered_Area*White_Growth_fact-death_rate)+.001
{the .001 is needed to give the system a bit of a nudge; without it the daisies
never get going}
Converters:
Avg_Planet_Temp = ((Solar_Luminosity*Solar_Flux_Constant*(1-planetary_albedo)/SB_constant)^.25)-273
{energy balance to calculate temperature in °C}
black_albedo = .25
Black_Growth_fact = 1-.003265*((22.5-Temp_Black_Land)^2) {this is the equation
for a parabola like that shown in Figure 8.03}
death_rate = 0.3
heat_absorp_fact = 20 {this controls how the local temperatures of the daisies
differ from the average planetary temperature}
planetary_albedo = (Uncovered_Area*uncovered_albedo)+(Black_Area*black_albedo)+(White_Area*white_albedo)
SB_constant = 5.669E-8 {Stefan-Boltzmann constant W/°K^4}
Solar_Flux_Constant = 917 {W/m2 -- for reference, our Sun cranks out 1370
W/m2 }
Temp_Black_Land = heat_absorp_fact*(planetary_albedo-black_albedo)+Avg_Planet_Temp
Temp_White_Land = heat_absorp_fact*(planetary_albedo-white_albedo)+Avg_Planet_Temp
T_Dead_Planet = ((Solar_Luminosity*Solar_Flux_Constant*(1-.5)/SB_constant)^.25)-273
{energy balance to calculate temperature in °C of a planet with no dasisies}
uncovered_albedo = .5
white_albedo = .75
White_Growth_fact = 1-.003265*((22.5-Temp_White_Land)^2)
Solar_Luminosity = 0.6+(time*(1.2/200))
Be careful in assembling this model - there is no steady state that we can use as a test of whether or not the model is properly constructed.
11/12