{UTF-8} absorbed luminosity= solar luminosity*(1-planet's average albedo) ~ ~ | actual black growth rate= indicated black growth rate*growth reduction multiplier ~ ~ | actual white growth rate= indicated white growth rate*growth reduction multiplier ~ ~ | black albedo= 0.25 ~ ~ | black albedo difference= planet's average albedo-black albedo ~ ~ | black daisy area= INTEG ( black growth-black decay, 250) ~ ~ | black decay= black daisy area*decay rate ~ ~ | black growth= black daisy area*actual black growth rate ~ ~ | black growth rate multiplier from temperature deviation= MAX(0,1-0.003265*black temperature deviation^2) ~ ~ This is the parabolic relationship shown in eqt. 3 on page 285 of Watson \ and Lovelock | black temperature deviation= temperature near black area-optimum temperature ~ ~ | black warming effect= 20*black albedo difference ~ ~ | decay rate= 0.3 ~ ~ 30%/yr is the value in Watson and Lovelock | empty area= INTEG ( black decay+white decay-black growth-white growth, 500) ~ ~ | empty area albedo= 0.5 ~ ~ | fr black= black daisy area/1000 ~ ~ | fr empty= empty area/1000 ~ ~ | fr white= white daisy area/1000 ~ ~ | "growth rate @ optimum temperature"= 1 ~ ~ 100%/yr is the growth rate if the flowers experience the optimum \ temperature. This is the peak of parabolic curve in Fig 11.1 | growth reduction multiplier= empty area/total area ~ ~ this creates a linear reduction in the growth rate. | indicated black growth rate= "growth rate @ optimum temperature"*black growth rate multiplier from temperature deviation ~ ~ | indicated white growth rate= "growth rate @ optimum temperature"*white growth rate multiplier from temperature deviation ~ ~ | new luminosity= 1.25 ~ ~ 1.25 is used in the book; this variable is a slider on the 2nd view | optimum temperature= 22.5 ~ ~ Lovelock's daisies grow best when they experience 22.5 degrees C. | planet's average albedo= black albedo*fr black+white albedo*fr white+empty area albedo*fr empty ~ ~ | planet's average temperature= (((917000*absorbed luminosity)/5.67e-005)^0.25)-273 ~ ~ This formula taken from Eldon's implementation, and it looks like the \ 1/4th root less 273 degrees comes from eqt 4 on page 285 of the Watson and \ Lovelock paper. | solar luminosity= IF THEN ELSE(Time>year of jump , new luminosity , 1 ) ~ ~ this is the exogenous input. It jumps from 1.0 to 1.25 in the year 2010. \ We can play with the year of the jump on the 2nd view | temperature near black area= planet's average temperature+black warming effect ~ ~ | temperature near white area= planet's average temperature-white cooling effect ~ ~ | total area= 1000 ~ ~ the total is 1,000 acres. notice that the iniital values of the three \ stocks adds to 1,000 acres | white albedo= 0.75 ~ ~ | white albedo difference= white albedo-planet's average albedo ~ ~ | white cooling effect= 20*white albedo difference ~ ~ If white albedo is 0.75 and the planet's average albedo is 0.50, then the \ difference is 0.25. Multiply by 20 degrees, and the cooling effect would \ be 5 degrees C. | white daisy area= INTEG ( white growth-white decay, 250) ~ ~ | white decay= white daisy area*decay rate ~ ~ | white growth= white daisy area*actual white growth rate ~ ~ | white growth rate multiplier from temperature deviation= MAX(0,1-0.003265*white temperature deviation^2) ~ ~ This is the parabolic relationship shown in eqt. 3 on page 285 of Watson \ and Lovelock | white temperature deviation= temperature near white area-optimum temperature ~ ~ | year of jump= 2010 ~ ~ | ******************************************************** .Control ********************************************************~ Simulation Control Parameters | FINAL TIME = 2040 ~ Year ~ The final time for the simulation. | INITIAL TIME = 2000 ~ Year ~ The initial time for the simulation. | SAVEPER = TIME STEP ~ Year [0,?] ~ The frequency with which output is stored. | TIME STEP = 0.25 ~ Year [0,?] ~ The time step for the simulation. | \\\---/// Sketch information - do not modify anything except names V300 Do not put anything below this section - it will be ignored *View of the model \$192-192-192,0,Times New Roman|12||0-0-0|0-0-0|0-0-255|-1--1--1|-1--1--1|96,96,5 10,1,white daisy area,429,94,44,53,3,131,0,24,0,2,0,0,0-0-0,0-0-0,|16|B|0-0-0 10,2,empty area,730,87,87,42,3,131,0,24,0,2,0,0,0-0-0,0-0-0,|16|B|0-0-0 10,3,black daisy area,1057,91,44,50,3,131,0,24,0,2,0,0,0-0-0,0-0-0,|16|B|0-0-0 1,4,6,2,4,0,0,22,0,0,0,-1--1--1,,1|(610,56)| 1,5,6,1,100,0,0,22,0,0,0,-1--1--1,,1|(519,56)| 11,6,380,572,56,6,8,34,3,0,0,1,0,0,0 10,7,white decay,572,75,38,11,40,3,0,0,-1,0,0,0 1,8,10,2,4,0,0,22,0,0,0,-1--1--1,,1|(871,64)| 1,9,10,3,100,0,0,22,0,0,0,-1--1--1,,1|(975,64)| 11,10,556,931,64,6,8,34,3,0,0,1,0,0,0 10,11,black decay,931,83,39,11,40,3,0,0,-1,0,0,0 10,12,decay rate,714,16,34,11,8,3,0,0,0,0,0,0 1,13,12,7,1,0,0,0,0,64,0,-1--1--1,,1|(640,26)| 1,14,12,11,1,0,0,0,0,64,0,-1--1--1,,1|(826,26)| 1,15,1,7,1,0,0,0,0,64,0,-1--1--1,,1|(481,35)| 1,16,3,11,1,0,0,0,0,64,0,-1--1--1,,1|(991,49)| 10,17,growth reduction multiplier,730,193,47,23,8,131,0,0,0,0,0,0 1,18,2,17,1,0,0,0,0,64,0,-1--1--1,,1|(697,181)| 10,19,total area,868,174,30,11,8,3,0,0,0,0,0,0 1,20,19,17,1,0,0,0,0,64,0,-1--1--1,,1|(792,149)| 1,21,23,1,4,0,0,22,0,0,0,-1--1--1,,1|(515,105)| 1,22,23,2,100,0,0,22,0,0,0,-1--1--1,,1|(606,105)| 11,23,684,564,105,6,8,34,3,0,0,1,0,0,0 10,24,white growth,564,124,41,11,40,3,0,0,-1,0,0,0 1,25,27,3,4,0,0,22,0,0,0,-1--1--1,,1|(967,106)| 1,26,27,2,100,0,0,22,0,0,0,-1--1--1,,1|(863,106)| 11,27,572,916,106,6,8,34,3,0,0,1,0,0,0 10,28,black growth,916,125,42,11,40,3,0,0,-1,0,0,0 10,29,actual white growth rate,517,211,38,19,8,3,0,0,0,0,0,0 10,30,actual black growth rate,953,195,39,19,8,3,0,0,0,0,0,0 1,31,29,24,1,0,0,0,0,64,0,-1--1--1,,1|(538,181)| 1,32,30,28,1,0,0,0,0,64,0,-1--1--1,,1|(932,162)| 1,33,1,24,1,0,0,0,0,64,0,-1--1--1,,1|(504,150)| 1,34,3,28,1,0,0,0,0,64,0,-1--1--1,,1|(966,145)| 10,35,indicated white growth rate,502,275,48,19,8,3,0,0,0,0,0,0 10,36,indicated black growth rate,968,269,48,19,8,3,0,0,0,0,0,0 1,37,35,29,1,0,0,0,0,64,0,-1--1--1,,1|(524,245)| 1,38,36,30,1,0,0,0,0,64,0,-1--1--1,,1|(977,235)| 1,39,17,29,1,0,0,0,0,64,0,-1--1--1,,1|(658,225)| 1,40,17,30,1,0,0,0,0,64,0,-1--1--1,,1|(807,222)| 10,41,"growth rate @ optimum temperature",748,283,68,19,8,3,0,0,0,0,0,0 10,42,white growth rate multiplier from temperature deviation,505,369,86,19,8,3,0,0,0,0,0,0 10,43,black growth rate multiplier from temperature deviation,965,350,86,19,8,3,0,0,0,0,0,0 1,44,42,35,1,0,0,0,0,64,0,-1--1--1,,1|(521,341)| 1,45,43,36,1,0,0,0,0,64,0,-1--1--1,,1|(977,319)| 1,46,41,35,1,0,0,0,0,64,0,-1--1--1,,1|(681,257)| 1,47,41,36,1,0,0,0,0,64,0,-1--1--1,,1|(824,262)| 10,48,white temperature deviation,449,438,57,19,8,3,0,0,0,0,0,0 10,49,black temperature deviation,858,420,58,19,8,3,0,0,0,0,0,0 1,50,48,42,1,0,0,0,0,64,0,-1--1--1,,1|(492,439)| 1,51,49,43,1,0,0,0,0,64,0,-1--1--1,,1|(871,386)| 10,52,optimum temperature,695,384,39,19,8,3,0,0,0,0,0,0 10,53,temperature near white area,552,513,54,19,8,3,0,0,0,0,0,0 10,54,temperature near black area,898,491,54,19,8,3,0,0,0,0,0,0 1,55,53,48,1,0,0,0,0,64,0,-1--1--1,,1|(466,485)| 1,56,52,48,1,0,0,0,0,64,0,-1--1--1,,1|(617,442)| 1,57,52,49,1,0,0,0,0,64,0,-1--1--1,,1|(743,421)| 1,58,54,49,1,0,0,0,0,64,0,-1--1--1,,1|(893,453)| 10,59,planet's average temperature,714,483,51,19,8,3,0,0,0,0,0,0 10,60,absorbed luminosity,710,588,32,19,8,3,0,0,0,0,0,0 10,61,solar luminosity,848,610,48,25,8,131,0,24,0,0,0,0,0-0-0,0-0-0,|14|BI|0-0-0 10,62,Time,746,636,26,11,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-128-128 1,63,62,61,1,0,0,0,0,64,0,-1--1--1,,1|(788,644)| 1,64,61,60,1,0,0,0,0,64,0,-1--1--1,,1|(812,593)| 1,65,60,59,1,0,0,0,0,64,0,-1--1--1,,1|(647,556)| 1,66,59,53,1,0,0,0,0,64,0,-1--1--1,,1|(621,464)| 1,67,59,54,1,0,0,0,0,64,0,-1--1--1,,1|(811,463)| 10,68,white cooling effect,390,551,42,19,8,3,0,0,0,0,0,0 10,69,black warming effect,1038,544,47,19,8,3,0,0,0,0,0,0 1,70,68,53,1,0,0,0,0,64,0,-1--1--1,,1|(438,525)| 1,71,69,54,1,0,0,0,0,64,0,-1--1--1,,1|(998,502)| 10,72,white albedo difference,483,664,41,19,8,3,0,0,0,0,0,0 10,73,black albedo difference,982,634,42,19,8,3,0,0,0,0,0,0 1,74,72,68,1,0,0,0,0,64,0,-1--1--1,,1|(409,639)| 1,75,73,69,1,0,0,0,0,64,0,-1--1--1,,1|(1053,602)| 10,76,planet's average albedo,698,677,51,19,8,3,0,0,0,0,0,0 1,77,76,60,1,0,0,0,0,64,0,-1--1--1,,1|(681,640)| 10,78,white albedo,461,748,41,11,8,3,0,0,0,0,0,0 1,79,78,72,1,0,0,0,0,64,0,-1--1--1,,1|(474,695)| 1,80,76,72,1,0,0,0,0,64,0,-1--1--1,,1|(631,642)| 10,81,black albedo,1010,738,41,11,8,3,0,0,0,0,0,0 1,82,76,73,1,0,0,0,0,64,0,-1--1--1,,1|(817,684)| 1,83,81,73,1,0,0,0,0,64,0,-1--1--1,,1|(1024,723)| 10,84,empty area albedo,896,698,58,11,8,3,0,0,0,0,0,0 10,85,white daisy area,500,808,60,11,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-128-128 10,86,black daisy area,1028,805,41,19,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-128-128 10,87,empty area,762,812,45,11,8,2,0,3,-1,0,0,0,128-128-128,0-0-0,|12||128-128-128 1,88,84,76,1,0,0,0,0,64,0,-1--1--1,,1|(802,698)| 1,89,78,76,1,0,0,0,0,64,0,-1--1--1,,1|(562,705)| 10,90,fr white,638,769,25,11,8,3,0,0,0,0,0,0 10,91,fr black,904,765,25,11,8,3,0,0,0,0,0,0 10,92,fr empty,718,757,27,11,8,3,0,0,0,0,0,0 1,93,85,90,0,0,0,0,0,64,0,-1--1--1,,1|(568,788)| 1,94,86,91,1,0,0,0,0,64,0,-1--1--1,,1|(967,812)| 1,95,87,92,1,0,0,0,0,64,0,-1--1--1,,1|(733,793)| 1,96,90,76,1,0,0,0,0,64,0,-1--1--1,,1|(661,732)| 1,97,91,76,1,0,0,0,0,64,0,-1--1--1,,1|(821,775)| 1,98,92,76,1,0,0,0,0,64,0,-1--1--1,,1|(703,715)| 1,99,81,76,1,0,0,0,0,64,0,-1--1--1,,1|(857,735)| 12,100,0,759,859,335,19,3,132,0,0,-1,2,0,0 this View of Vensim Daisyworld: Set up for Scenario #1: Solar Luminosity jumps to 1.25 in 2010; 10,101,year of jump,960,589,60,11,8,131,0,0,0,0,0,0 1,102,101,61,1,0,0,0,0,64,0,-1--1--1,,1|(915,570)| 10,103,new luminosity,769,531,46,11,8,3,0,0,0,0,0,0 1,104,103,61,1,0,0,0,0,64,0,-1--1--1,,1|(823,559)| 12,105,0,758,912,335,19,3,132,0,0,-1,2,0,0 go to next view to experiment with the different years when the solar luminosity increases. \\\---/// Sketch information - do not modify anything except names V300 Do not put anything below this section - it will be ignored *Experiment with the model \$192-192-192,0,Times New Roman|12||0-0-0|0-0-0|0-0-255|-1--1--1|-1--1--1|96,96,5 12,1,0,459,354,430,350,3,188,0,0,1,0,0,0 temperatures 12,2,0,1020,192,118,48,3,252,0,0,0,0,0,0 year of jump,2005,2025,1 12,3,0,1026,327,115,46,3,252,0,0,0,0,0,0 new luminosity,1.05,1.4,0.01 12,4,0,1026,440,125,38,3,132,0,24,-1,3,0,0,0-0-0,0-0-0,|16|B|0-0-0 This view can be used to test for the span of control. 12,6,0,1023,83,114,47,3,4,0,24,-1,4,0,0,0-0-0,0-0-0,|24|B|0-0-0 Daisyworld in Vensim 12,7,0,1027,584,107,91,3,4,0,0,0,1,0,0 Note: The results will not be an identical match to Fig 11.7 because the model in the book includes a lagged effect of temperature. I left the lag out of this model since we do not cover lags until chapter 14. ///---\\\ :GRAPH temperatures :TITLE Graph Similar to Fig 11.6 in Book :SCALE :VAR solar luminosity :Y-MIN 0 :Y-MAX 4 :LINE-WIDTH 2 :SCALE :VAR planet's average temperature :Y-MIN 0 :Y-MAX 50 :LINE-WIDTH 4 :VAR temperature near white area :LINE-WIDTH 2 :VAR temperature near black area :LINE-WIDTH 2 :L<%^E!@ 1:Current.vdf 1:C:\Andy's Documents\Book 2nd Ed\AA Chapters\Ch 11 Daisyworld\Current.vdf 9:Current 23:0 15:0,0,0,0,0,0 19:5,1 27:2, 4:Time 5:black albedo difference 24:2000 25:2040 26:2040