Forward euler with multiple changing variables (Daisyworld model)
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Jake Lloyd Newman
on 12 Feb 2021
Commented: Jake Lloyd Newman
on 12 Feb 2021
I am currently trying to run a numerical model of Daisyworld (which should in theory be quite a simple model). I am using the values from the original Lovelock paper.
I am trying to solve it using the forward euler method upon the following equations:
(dαW)/dt=αw (αg β(Tw )-γ)
(dαb)/dt=αb (αg β(Tb )-γ)
I am unsure if I have set out my equations correctly and I am receiving the error :
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/517882/image.png)
Here is my code:
clear% clear the workspace
%set initial conditions and constants
q = 2.06e9; %heat flux coefficient k-4
white_albedo = 0.75; %set white albedo
black_albedo = 0.25; %set black albedo
Albedo_bare = 0.5; %set bare albedo
SB = 5.67e-8; % Stefann Boltzmann constant
Solar_lumin = 917; %solar luminosity (W m-2)
TempOpt = 295.65 ; %this is the optimum temperature for daisy growth in celsius 22.5/ 298
B = 0.25; %constant used in analytical solution
k = 17.5^-2; %width parametetr of daisy temperature growth 290.65K/17.5 celsius
qt= 79.79; % rescaled q
DRate = 0.3; %death rate (gamma)
initial_coverage = 0.01; %set initial coverage of B/W daises as 1%
black_area = initial_coverage; %initial coverage of black daisies = 0.01
white_area = initial_coverage; %initial coverage of white daisies = 0.01
bare_area = 0.98; %initial coverage of bare ground = 0.98
L = 1;%set luminosity
t_start = 0
t_end = 10
tstep = 1
t=t_start:tstep:t_end; %time series of 0-100
P = 1; %proportion of fertile ground set to unity
%preallocate arrays for changing variables
dfw_dt= zeros(1,length(t)) %preallocate array
white_area=zeros(1,length(t)) %preallocate array
black_area=zeros(1,length(t)) %preallocate array
bare_area = zeros(1,length(t)) %preallocate array
T4w = zeros(1,length(t)) %preallocate array
BrW = zeros(1,length(t)) %preallocate array
T4e = zeros(length(t)) %preallocate array
Albedo_planetary = zeros(1,length(t)) %preallocate array
%set initial valies of changing variables
dfw_dt(1) = 0
white_area(1) = 0.01
black_area(1) = 0.01
bare_area(1) = 0.98
T4w(1) = 0
BrW(1) = 0
T4e(1) = 0
Albedo_planetary(1) = 0.98*0.5
for i = 2:length(t)
white_area(i+1) = white_area(i) + dfw_dt(i) * tstep
dfw_dt(i) = white_area(i) * bare_area(i) * BrW(i) * T4w(i) - DRate
BrW(i) = 1 - k * (T4w(i) - TempOpt)^2
if (T4w < Topt) BrW = 0
end
T4w(i) = (q * (Albedo_planetary(i) - white_albedo) + T4e(i)^4)
T4e(i) = Solar_lumin * L * (1-Albedo_planetary(i))
Albedo_planetary(i) = (white_area(i)*white_albedo) + (black_area(i) * black_albedo) + (bare_area(i) * Albedo_bare)
bare_area(i) = P - black_area(i) - white_area(i)
end
Any help would be much appreciated!
Thanks
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Accepted Answer
Kevin Barkett
on 12 Feb 2021
Hi there,
I believe the error you are seeing is has to do with how the variable 'BrW' is being set. While 'BrW' has been initially set as an array, in the following line within the for-loop:
if (T4w < Topt) BrW = 0
the entire of 'BrW' is being updated as a double variable. Then on subsequent iterations of the for-loop, when function call attempts to access 'BrW' as if it were an array of elements, the call fails with the error message you are seeing.
Try replacing the above line with:
if (T4w < TempOpt) BrW(i) = 0
which tells the loops to only update the specific entry in 'BrW', rather than the entire variable.
Cheers,
Kevin
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