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					Daisy World Model
Initial Values                                                                                                                        28.500




                                                                                                     Average Global Temperature (C)
Initial area covered by daisies                        0.8                                                                            28.000
Albedo bare ground                                   0.25
                                                                                                                                      27.500
Albedo daisies                                       0.75
Solar luminosity (arbitrary units!!)             1289.500                                                                             27.000
Stefan Boltzmann constant                        5.67E-08
                                                                                                                                      26.500
Daisy growth parameters
                                                                                                                                      26.000
Topt                                                  22.5
dT                                                    17.5                                                                            25.500
death rate                                             0.2



Final temperature                                  28.062         Stable:             yes
Final % daisies                                     0.778         Stable:             yes




                                            The Model:

                                            % bare ground    avg. Albedo    planet. Temp.    growth rate
initial conditions:                                  0.200          0.650           25.694        0.967
                                        1            0.205          0.647           26.261        0.954
                                        2            0.209          0.646           26.611        0.945
                                        3            0.211          0.645           26.851        0.938
                                        4            0.213          0.644           27.028        0.933
                                        5            0.214          0.643           27.164        0.929
                                        6            0.215          0.643           27.272        0.926
                                        7            0.216          0.642           27.361        0.923
                                        8            0.216          0.642           27.434        0.921
                                        9            0.217          0.641           27.496        0.919
                                       10            0.218          0.641           27.549        0.917
                                       11            0.218          0.641           27.594        0.915
                                       12            0.218          0.641           27.634        0.914
                                       13            0.219          0.641           27.669        0.913
                                       14            0.219          0.640           27.701        0.912
                                       15            0.219          0.640           27.728        0.911
                                       16            0.220          0.640           27.753        0.910
                                       17            0.220          0.640           27.776        0.909
                                       18            0.220          0.640           27.796        0.908
                                       19            0.220          0.640           27.815        0.908
                                       20            0.220          0.640           27.832        0.907
                                       21            0.220          0.640           27.847        0.907
                                       22            0.221          0.640           27.861        0.906
                                       23            0.221          0.640           27.874        0.906
                                       24            0.221          0.640           27.887        0.905
25   0.221   0.640   27.898   0.905
26   0.221   0.640   27.908   0.905
27   0.221   0.639   27.918   0.904
28   0.221   0.639   27.927   0.904
29   0.221   0.639   27.935   0.904
30   0.221   0.639   27.943   0.903
31   0.221   0.639   27.950   0.903
32   0.221   0.639   27.957   0.903
33   0.222   0.639   27.963   0.903
34   0.222   0.639   27.969   0.902
35   0.222   0.639   27.975   0.902
36   0.222   0.639   27.980   0.902
37   0.222   0.639   27.985   0.902
38   0.222   0.639   27.990   0.902
39   0.222   0.639   27.994   0.901
40   0.222   0.639   27.998   0.901
41   0.222   0.639   28.002   0.901
42   0.222   0.639   28.006   0.901
43   0.222   0.639   28.009   0.901
44   0.222   0.639   28.013   0.901
45   0.222   0.639   28.016   0.901
46   0.222   0.639   28.019   0.901
47   0.222   0.639   28.022   0.900
48   0.222   0.639   28.024   0.900
49   0.222   0.639   28.027   0.900
50   0.222   0.639   28.029   0.900
51   0.222   0.639   28.032   0.900
52   0.222   0.639   28.034   0.900
53   0.222   0.639   28.036   0.900
54   0.222   0.639   28.038   0.900
55   0.222   0.639   28.040   0.900
56   0.222   0.639   28.041   0.900
57   0.222   0.639   28.043   0.900
58   0.222   0.639   28.045   0.900
59   0.222   0.639   28.046   0.900
60   0.222   0.639   28.048   0.899
61   0.222   0.639   28.049   0.899
62   0.222   0.639   28.051   0.899
63   0.222   0.639   28.052   0.899
64   0.222   0.639   28.053   0.899
65   0.222   0.639   28.054   0.899
66   0.222   0.639   28.055   0.899
67   0.222   0.639   28.056   0.899
68   0.222   0.639   28.057   0.899
69   0.222   0.639   28.058   0.899
70   0.222   0.639   28.059   0.899
71   0.222   0.639   28.060   0.899
72   0.222   0.639   28.061   0.899
73   0.222   0.639   28.062   0.899
74   0.222   0.639   28.063   0.899
75   0.222   0.639   28.063   0.899
28.500

28.000

27.500

27.000

26.500

26.000

25.500
         0       20                40   60

                 Model Time Step




 daisy change         % daisies
        -0.005            0.795
        -0.003            0.791
        -0.002            0.789
        -0.002            0.787
        -0.001            0.786
        -0.001            0.785
        -0.001            0.784
        -0.001            0.784
        -0.001            0.783
        -0.001            0.782
         0.000            0.782
         0.000            0.782
         0.000            0.781
         0.000            0.781
         0.000            0.781
         0.000            0.780
         0.000            0.780
         0.000            0.780
         0.000            0.780
         0.000            0.780
         0.000            0.780
         0.000            0.779
         0.000            0.779
         0.000            0.779
         0.000            0.779
0.000   0.779
0.000   0.779
0.000   0.779
0.000   0.779
0.000   0.779
0.000   0.779
0.000   0.779
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
0.000   0.778
                          Exercise A:   Exercise B:             Exercise C:
                          no daisies    initial daisies = 0.2   initial daisies = final daisiy abund. from previou
luminosity (arb. units)   avg. temp.    avg. temp.              avg. temp.

                    600
                    650
                    700
                    750
                    800
                    850
                    900
                    950
                   1000
                   1050
                   1100
                   1150
                   1200
                   1250
                   1300
                   1350
                   1400
aisiy abund. from previous run
Daisy World Model:
Amount of bare ground available for            x = (1 - D)
daisy growth.
D = area covered by daisies
x = area of bare ground

Average planetary albedo Ap                    Ap = x*Ag + D*Ad
Ag = albedo of bare ground                     Ag = 0.25
Ad = albedo of daisies                         Ad = 0.75

Average planetary temperature                  Te = ((S/sig *(1 - Ap))^0.25 - 273
Te = avg. planetary temperature
S = solar luminosity                           S = 1370
sig = Stefan-Boltzmann constant                sig = 5.67E-8

Growth rate of daisies                         G = 1 - (1/dT)^2 * (Te - Topt)^2
G = growth rate of daisies
Topt = optimal growth temperature              Topt = 22.5 C
dT = temperature interval where growth is
possible                                       dT = 17.5 C

Change in area covered by daisies per          dD/dt = D*(x*G - y)
timestep
y = death rate of daisies                      y = 0.2

New area covered by daisies                    ND = dD/dt + D

                                               It then uses these parameters as
The model reads the initial parameters         input for the next modelling step and
specified and calculates the amount of bare    iterates the model through 70 steps,
ground, planetary albedo, daisy growth rate,   the first 60 of which are displayed in
and new area covered by daisies.               the graph.

				
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posted:7/31/2012
language:English
pages:7