Unit 4_Daisyworld_model 455f3608-bd57-4010-8556-bd5e9c7258ea isee systems, inc. Stella Professional
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m meter yr year degc degree C w watt The area of the planet covered by black daisies, measured as a fraction of the total planetary area (units = fractional area). Initial value = 0.001 0.001 BD_growth BD_death fractional area Growth of black daisies per year is dependent on the population size of black daisies, the fraction of ground remaining to be colonized (X), and a growth function that is dependent on temperature (BD_beta). Units of BD_growth are fractional area of daisies/year. black_daisies*BD_beta*X fractional area/yr Death of black daisies is dependent on the population of black daisies and their death rate (gamma). If the population falls below a threshold value of 0.001 the death flow is set to zero to ensure that a small stock of daisies persists to allow colonization if temperatures again become favorable. Units (fraction/year) IF (black_daisies>0.001) THEN (black_daisies*gamma_1) ELSE 0 fractional area/yr The area of the planet covered by white daisies, measured as a fraction of the total planetary area (units = fractional area). Initial value = 0.001 0.001 WD_growth WD_death fractional area Growth of white daisies per year is dependent on the population size of white daisies, the fraction of ground remaining to be colonized (X), and a growth function that is dependent on temperature (WD_beta). Units of WD_growth are fractional area of daisies/year. white_daisies*WD_beta*X fractional area/yr Death of white daisies is dependent on the population of white daisies and their death rate (gamma). If the population falls below a threshold value of 0.001 the death flow is set to zero to ensure that a small stock of daisies persists to allow colonization if temperatures again become favorable. Units are fractional area of daisies/year IF (white_daisies>0.001) THEN (white_daisies*gamma_1) ELSE 0 fractional area/yr Gamma is the death rate of daisies (fraction dying per year). 0.3 fraction The area of available fertile ground, not covered by either species, measured as a fraction of the total planetary area (units = fractional area). X=P-white_daisies-black_daisies P-white_daisies-black_daisies fractional area BD_beta is the growth rate of black daisies, which is a function of BD_temp. In this model, the daisies, like most Earth species, have very specific ecological tolerances. Daisies cannot grow at temperatures colder than 5 degrees C or warmer than 40 degrees C. Their growth is maximized at 22.5 degrees. BD_beta=if(BD_temp>5)and(BD_temp<40)then(1-0.003265*((22.5-BD_temp)^2))else(0) IF(BD_temp>5)AND(BD_temp<40)THEN(1-0.003265*((22.5-BD_temp)^2))ELSE(0) WD_beta is the growth rate of white daisies, which is a function of WD_temp. In this model, the daisies, like most Earth species, have very specific ecological tolerances. Daisies cannot grow at temperatures colder than 5 degrees C or warmer than 40 degrees C. Their growth is maximized at 22.5 degrees. WD_beta=if(WD_temp>5)and(WD_temp<40)then(1-0.003265*((22.5-WD_temp)^2))else(0) IF(WD_temp>5)AND(WD_temp<40)THEN(1-0.003265*((22.5-WD_temp)^2))ELSE(0) The proportion of the planet's area which is fertile ground (fractional area). P=1.0 1 fractional area Temperature of the black daisy population in degrees Celsius. BD_temp=((q*(planetary_albedo-BD_albedo)+((earth_temp+273)^4))^(0.25))-273 ((q*(planetary_albedo-BD_albedo)+((daisyworld_temp+273)^4))^(0.25))-273 degrees C Temperature of the white daisy population in degrees Celsius. WD_temp=((q*(planetary_albedo-WD_albedo)+((earth_temp+273)^4))^(0.25))-273 ((q*(planetary_albedo-WD_albedo)+((daisyworld_temp+273)^4))^(0.25))-273 degrees C Temperature of the entire planet in degrees Celsius. daisyworld_temp=((solar_flux*(1-planetary_albedo)/stefboltz)^(0.25))-273 ((solar_flux*(1-planetary_albedo)/stefboltz)^(0.25))-273 Degrees C Q is a positive constant that expresses the degree to which absorbed solar energy is redistributed to the three types of surfaces on the planet (dimensionless). A q value of 0 represents a planet that is a perfect conductor. Highs and lows in energy absorption are immediately smoothed out to make a uniform surface energy content and surface temperature. A q value of 1*solar_constant/stefboltz represents a planet that is a perfect insulator. Highs and lows in energy absorption are completely maintained - no energy flows from high absorbing to low absorbing areas. Units of q are K^4. 1.*solar_flux/stefboltz Kelvin^4 The percentage of incoming solar radiation that is reflected back into space (dimensionless). The planetary albedo is taken as the area weighted average of the white daisy, black daisy, and bare ground albedos. planetary_albedo=(white_daisies*WD_albedo)+(black_daisies*BD_albedo)+(X*bare_ground_albedo) (white_daisies*WD_albedo)+(black_daisies*BD_albedo)+(X*bare_ground_albedo) The percentage of incoming solar radiation that is reflected back into space by the black daisies (dimensionless). BD_albedo = 0.25 0.25 The percentage of incoming solar radiation that is reflected back into space by the white daisies (dimensionless). WD_albedo = 0.75 0.75 The percentage of incoming solar radiation that is reflected back into space by bare ground (dimensionless). bare_ground_albedo = 0.5 0.5 stefboltz = The Stefan Boltzmann constant {5.67e-8 (W/(m^2*K^4))} The S-B constant relates the energy contained in a black body to its temperature. 5.67e-8 Solar flux is the change in the amount of insolation reaching Daisyworld over time. solar_flux=luminosity(dimensionless)*solar_constant(W/m^2) luminosity*solar_constant watts/meters^2 The solar constant is the amount of solar energy reaching the surface of Daisyworld. For the solar constant, Watson and Lovelock (1983) use a value of 9.17*105 ergs/cm2s, or 917 W/m^2. solar_constant=917.0 917 watts/meters^2 Luminosity takes into account an increase in the amount of solar energy given off by the sun over time (dimensionless). This equation begins with the sun at half its current brightness and ramps up the insolation by 2% a year. luminosity=0.5+(0.02*time) 0.5+(0.02*TIME) Temperature of the bare ground areas on the planet in degrees Celsius. ground_temp=((q*(planetary_albedo-bare_ground_albedo)+((earth_temp+273)^4))^(0.25))-273 ((q*(planetary_albedo-bare_ground_albedo)+((daisyworld_temp+273)^4))^(0.25))-273 degrees C gamma_1 BD_death black_daisies BD_death WD_death white_daisies WD_death black_daisies BD_growth white_daisies WD_growth BD_growth WD_growth BD_beta BD_growth WD_beta WD_growth X X P X BD_beta WD_beta BD_temp BD_temp BD_temp BD_temp WD_temp WD_temp WD_temp WD_temp BD_albedo planetary_albedo planetary_albedo WD_albedo planetary_albedo planetary_albedo bare_ground_albedo planetary_albedo planetary_albedo daisyworld_temp stefboltz daisyworld_temp solar_flux daisyworld_temp solar_constant solar_flux luminosity solar_flux stefboltz q solar_flux q ground_temp ground_temp ground_temp ground_temp Based on the following reading: Watson, A.J., and Lovelock, J.E., 1983, Biological homeostasis of the global environment: the parable of Daisyworld, Tellus, v. 35B, p. 284-289. James Lovelock's Daisyworld This model explores the idea that self-regulating systems of organisms can exist and can optimize the environment to themselves simply by responding to external conditions that cause increases or decreases in birth and death rates. gamma_1 X X black_daisies white_daisies BD_temp WD_temp BD_albedo planetary_albedo q daisyworld_temp q daisyworld_temp planetary_albedo WD_albedo black_daisies white_daisies X planetary_albedo bare_ground_albedo planetary_albedo daisyworld_temp q