Climate model Debug matrix size issues

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Theodore Anderson on 24 Oct 2020
Edited: Landen Alexander on 28 Oct 2021
Hey all! I have a really complex model that runs, but does not run very well. I get some errors where my matrix values exceed 1 one where it cant exceed one. It took a long time to get this to run, I was hoping you guys could give me some general feed back on how to clean up my code :) let me know if you have suggestions or can fix errors in my equations.
% function columnmodel =
PLOTSON = 1; % change this to 0 to hide debugging plots
% physical constants
sigma = 5.67e-8;
Cp_air = 1e3; %j/kgK
Cp_water = 4060e3; % j/kgK
rho_water = 1000; %kg/m3
% set up the model space
N_levels = 25; % how many levels of atmosphere
Z_atm = [ logspace(-2, log10(30), N_levels-2) 50 100];
% in kilometers, vertical spacing of layers: logarithmic between 10m and
% 30km, then two extra at 50 and 100km
% temperature and emissivity of the atmosphere
T_atm(Z_atm < 12) = 288 - Z_atm(Z_atm < 12)*6.5; %Kelvin, starting with a 6.5°C/km lapse rate
T_atm(Z_atm >= 12) = 210; % set constant above 12km
T_surf = 288; % Kelvin
rho_air = 1.225*exp(-9.81*.029*Z_atm*1000/(8.31*288)); %kg/m^3 density of air (approximate)
% Constant conditions
I_toa = 1361; % W/m^2, solar radiation at the top of the atmosphere total radiation
%five times globe average = daytime-ish
I_SW_toa = .9*I_toa; % 90% shortwave
I_LW_toa = .1*I_toa; %10% long wave
Emissivity_LW_atmos = .5*ones(N_levels, 1);% emissivity of the atmosphere, LW
absorptionsw = 5e-4*ones(N_levels, 1); %absorption in SW
absorptionlw = 4e-1*ones(N_levels, 1); % absorption in LW
scattering = 2e-4*ones(N_levels, 1); % layer by layer reflectivity (scattering) of the atmosphere
%(if you want to add clouds, change this)
Ka = absorptionsw;
Ks = scattering;
% shortcuts for the
ksw = (scattering+absorptionsw);
klw = absorptionlw;
%surface conditions
surface_albedo = .2;
E_surf = 1;
% time and vertical space step settings
dt = 15*60; % time step in seconds = 15 minutes
dz = [.01 diff(Z_atm) ]*1e3; % vertical layer thickness in m, starting with a 10m surface layer
% thiq = ((Ka+Ks)*rho_air*dz);% optical thickness
% thiqlw = (Ka*rho_air*dz);
% step through time steps
for t = 1:30
% EM radiation moves faster than a time step.
% Model all of this as if it happens instantaneously
% using v for the atmosphere level counter
v = N_levels; % very top of the atmosphere
% initiate some variables as column vectors
SWd = zeros(N_levels, 1); % downwelling SW
SWu = zeros(N_levels, 1); % upwelling SW
SWa = zeros(N_levels, 1); % absorbed SW
SWe = zeros(N_levels, 1); % emitted SW
LWd = zeros(N_levels, 1); % downwelling LW
LWu = zeros(N_levels, 1); % upwelling LW
LWa = zeros(N_levels, 1); % absorbed LW
LWe = zeros(N_levels, 1); % emitted LW
% very top of the atmosphere
SWd(v) = I_SW_toa*exp(-ksw(v)*rho_air(v)*dz(v));
SWa(v) = I_SW_toa*((Ka(v)*rho_air(v)*dz(v)));
% SWe(v) = %atmalbedo?
%lw
LWe(v) = Emissivity_LW_atmos(v)*sigma*T_atm(v)^4;
LWd(v) = I_LW_toa*exp(-klw(v)*rho_air(v)*dz(v));
LWa(v) = I_LW_toa*(1-exp(-(Ka(v)*rho_air(v)*dz(v))));
% downwelling
for v = (N_levels-1):-1:1 % start one level down from the top, increment by -1
SWd(v) = SWd(v+1)*exp(-ksw(v)*rho_air(v)*dz(v));%energy going down
SWa(v) = SWd(v+1)*(-ksw(v)*rho_air(v)*dz(v));%energy down * thiqness (essentially trasmitted thru a layer?)
SWe(v) = 0;
SWu(v) = 0; % how much is reflected back up??? why do we need this?
% LWe(v) =
LWd(v) = I_LW_toa*exp(-klw(v)*rho_air(v)*dz(v));
LWa(v) = I_LW_toa*1-exp(-(Ka(v)*rho_air(v)*dz(v)));
% nothing is reflected back up in the LW
end
% at the surface level
v = 1;
% surface reflection, absorption, emission
SWu(1) = SWu(1)+surface_albedo*SWd(1)*exp(-ksw(v)*rho_air(v)*dz(v));
SWa(1) = surface_albedo*SWd(1)*(ksw(v)*rho_air(v)*dz(v))+SWa(1);
SWe(1) = 0; % no short wave emission
SurfSWa = SWd(1)*(ksw(v)*rho_air(v)*dz(v))*(1-surface_albedo); % absorbed at the surface
SurfSWe = SWd(1)*(ksw(v)*rho_air(v)*dz(v))*surface_albedo; % emitted at the surface
LWe(1) = LWe(1)+Emissivity_LW_atmos(1)*sigma*T_atm(t,v)^4;
SurfLWe = LWd(1)*(klw(v)*rho_air(v)*dz(v))%E_surf(1)*sigma*T_surf(1)^4 + LWe(1)*exp(-(Ka*rho_air*dz));
LWu(1) =Emissivity_LW_atmos(v)*sigma*T_atm(t,v)^4 + (SurfLWe(v)*exp(-(Ka(v)*rho_air(v)*dz(v)))); % just the part emitted that is going up
LWa(1) = LWd(v+1)*(klw(v)*rho_air(v)*dz(v));
SurfLWa = LWd(v+1)*(klw(v)*rho_air(v)*dz(v));
% upwelling
for v = 2:N_levels
% upwelling short wave
SWu(v) = SWu(v-1)*exp(-((Ka(v)+Ks(v))*rho_air(v-1)*dz(v-1)))+SWu(v-1); % how much gets passed up
SWa(v) = SWu(v-1)*Ka(v)*rho_air(v-1)*dz(v-1)+SWa(v-1); % how much gets absorbed here
% make sure to add it to what you absorbed on the way down
% upwelling long wave
LWe(v) = LWe(v)+Emissivity_LW_atmos(v)*sigma*T_atm(t,v)^4; % how much is emitted here pointed up
LWu(v) = Emissivity_LW_atmos(v)*sigma*T_atm(t,v)^4 + LWu(v-1)*exp(-(Ka(v-1)*rho_air(v-1)*dz(v-1))); % how much gets passed up
LWa(v) = LWd(v-1)*(klw(v)*rho_air(v)*dz(v)); % how much gets absorbed here
% nothing gets reflected down in the LW
end
Rnet = LWa + SWa - LWe - SWe; % add up the components of the net radiative balance
Rnet_surf = SurfLWa - SurfLWe + SurfSWa - SurfSWe;
%% calculate the temperature at the next time step from the current
% update temperatures
T_atmos(t+1, :) = Rnet;
T_atmos(t+1, N_levels) = 210; % fix the top two because
% numerical instabilities add up at the edge of space.
T_atmos(t+1, N_levels-1) = 210;
% surface temp
T_surf(t+1) = Rnet_surf;
%% show results for debugging
if PLOTSON
figure(1)
clf;
subplot(1,4,1)
semilogy(LWa, Z_atm, 'r')
hold on
semilogy(LWe, Z_atm, 'b')
semilogy(LWu, Z_atm, 'g')
semilogy(LWd, Z_atm, 'k')
hold off
xlabel('LW ')
legend('absorbed', 'emitted', 'upwelling', 'downwelling')
subplot(1,4,2)
semilogy(SWa, Z_atm, 'r')
hold on
semilogy(SWe, Z_atm, 'b')
semilogy(SWu, Z_atm, 'g')
semilogy(SWd, Z_atm, 'k')
hold off
xlabel('SW ')
legend('absorbed', 'emitted', 'upwelling', 'downwelling')
subplot(1,4,3)
semilogy(Rnet, Z_atm)
xlabel('Rnet')
subplot(1,4,4)
semilogy(T_atm(t, :), Z_atm)
xlabel('Temp')
end
end
%% plot the end results
figure(3)
subplot(3,4,[1 2 3 5 6 7])
pcolor(1:t+1, Z_atm, (T_atm)' - repmat(T_atm(:,1)',length(kl), 1 ))
%set(gca, 'Ydir', 'normal');
ylim([0 30])
colorbar;
caxis([-50 50])
subplot(3,4,[4 8])
plot(T_atm(end, 1:end-3)-273, Z_atm(1:end-3))
ylim([0 30])
xlabel('Temp, C')
subplot(3,4,[9:12])
plot((1:length(T_surf))*dt/(60*60), T_surf - 273)
xlabel('Hour of simulation')
ylabel('Surface temp')
% for making this a function:
% tsurf = T_surf(end);
% tatmos = T_atmos(end,:);
% zatmos = Z_atmos;
%end
Mathieu NOE on 26 Oct 2020
hi
for such a complex code , it would be good if you could put some explanations at the beginning of your file about variables and their size.
next, you should do preallocation for variables that grow inside a loop like T_atmos and T_surf

Saurav Chaudhary on 27 Oct 2020
Identify bottlenecks by using the Profiler tool within MATLAB.
To know more about profiling refer below points:
• Profiling is a way to measure the time it takes to run your code and identify where MATLAB spends the most time.
• After you identify which functions are consuming the most time, you can evaluate them for possible performance improvements.
• You also can profile your code to determine which lines of code do not run.
You can refer this documentation link to see how to run profiler on your code-
You can also refer to this documentation page for better techniques that can be followed for MATLAB programming-

Landen Alexander on 18 Oct 2021
Edited: Landen Alexander on 28 Oct 2021
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