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idealizedLifetimes.m
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load('forward_model_test.mat')
concentration_structs = {out_large, out_small, out_large_noninteractive, out_small_noninteractive};
for i=1:length(concentration_structs)
lifetimes = calculateLifetimes(concentration_structs{i}, params);
disp(max(lifetimes.ch4_global_lifetime))
end
function result = calculateLifetimes(con_struct, params)
day2sec = 60*60*24; % convert days to seconds
year2sec = 365.25*day2sec;
n_air = params.n_air; % molec/cm^3 for dry atmosphere
conversion = day2sec * n_air/1d9; % conversion factor rom ppb/day to molec/cm^3 / s;
ppb2con = n_air / 1e9;
ppt2con = n_air / 1e12;
k_ch4 = params.k_12ch4; % ppb/day
k_co = params.k_co; % ppb/day
k_ch4 = k_ch4 / conversion % molec/cm^3 / s
k_co = k_co / conversion % molec/ cm^3 / s
kX_NH = 1.885 ; % molec/cm^3/s
kX_SH = 2.07 ; % molec/cm^3/s
kx_global = 0.5 * (kX_NH + kX_SH); % molec/cm^3 / s
%%% Read in concentrations
nh_ch4 = ppb2con * con_struct.nh_ch4; % molec/cm^3
sh_ch4 = ppb2con * con_struct.sh_ch4; % molec/cm^3
global_ch4 = 0.5* (nh_ch4 + sh_ch4); % molec/ cm^3
nh_co = ppb2con * con_struct.nh_co; % molec/ cm^3
sh_co = ppb2con * con_struct.sh_co; % molec/ cm^3
global_co = 0.5* (nh_co + sh_co); % molec/ cm^3
nh_oh = con_struct.nh_oh; % molec/ cm^3
sh_oh = con_struct.sh_oh; % molec/ cm^3
global_oh = 0.5* (nh_oh + sh_oh); % molec/ cm^3
[time_index, p] = size(con_struct.nh_ch4);
nh_e_folds = zeros(size(con_struct.nh_ch4));
sh_e_folds = zeros(size(con_struct.nh_ch4));
global_e_folds = zeros(size(con_struct.nh_ch4));
for t = 1:time_index
nh_jacobian = zeros(3,3);
sh_jacobian = zeros(3,3);
global_jacobian = zeros(3,3);
%%% Construct the jacobians according to Prather 1994
nh_jacobian(1,1) = -k_ch4 * nh_oh(t);
sh_jacobian(1,1) = -k_ch4 * sh_oh(t);
global_jacobian(1,1) = -k_ch4 * global_oh(t);
%%% the [2,1] element is 0
nh_jacobian(3,1) = -k_ch4 * nh_ch4(t);
sh_jacobian(3,1) = -k_ch4 * sh_ch4(t);
global_jacobian(3,1) = -k_ch4 * global_ch4(t);
% 2. Now for the CO equation
nh_jacobian(1,2) = k_ch4 * nh_oh(t);
sh_jacobian(1,2) = k_ch4 * sh_oh(t);
global_jacobian(1,2) = k_ch4 * global_oh(t);
nh_jacobian(2,2) = -k_co * nh_oh(t);
sh_jacobian(2,2) = -k_co * sh_oh(t);
global_jacobian(2,2) = -k_co * global_oh(t);
nh_jacobian(3,2) = k_ch4 * nh_ch4(t) - k_co * nh_co(t);
sh_jacobian(3,2) = k_ch4 * sh_ch4(t) - k_co * sh_co(t);
global_jacobian(3,2) = k_ch4 * global_ch4(t) - k_co * global_co(t);
% 3. The Oh reaactions, d OH / dt
nh_jacobian(1,3) = -k_ch4 * nh_oh(t);
sh_jacobian(1,3) = -k_ch4 * sh_oh(t);
global_jacobian(1,3) = -k_ch4 * global_oh(t);
nh_jacobian(2,3) = -k_co * nh_oh(t);
sh_jacobian(2,3) = -k_co * sh_oh(t);
global_jacobian(2,3) = -k_co * global_oh(t);
nh_jacobian(3,3) = -k_ch4 * nh_ch4(t) - k_co * nh_co(t) - kX_NH;
sh_jacobian(3,3) = -k_ch4 * sh_ch4(t) - k_co * sh_co(t) - kX_SH;
global_jacobian(3,3) = -k_ch4 * global_ch4(t) - k_co * global_co(t) - kx_global;
nh_jacobian = nh_jacobian';
sh_jacobian = sh_jacobian';
global_jacobian = global_jacobian';
%%% Take the eigenvalues
D_nh = eig(nh_jacobian);
D_sh = eig(sh_jacobian);
D_global = eig(global_jacobian);
% CH4 lifetimes
result.ch4_nh_lifetime(t) = -1/D_nh(2)/year2sec;
result.ch4_sh_lifetime(t) = -1/D_sh(2)/year2sec;
result.ch4_global_lifetime(t) = -1/D_global(2)/year2sec;
result.ch4_ss(t) = -1 ./(global_jacobian(1,1)*year2sec);
% CO lifetimes
result.co_nh_lifetime(t) = -1/D_nh(3)/day2sec;
result.co_sh_lifetime(t) = -1/D_sh(3)/day2sec;
result.co_global_lifetime(t) = -1/D_global(3)/day2sec;
result.co_ss(t) = -1 ./(global_jacobian(2,2)*day2sec);
% OH lifetimes
result.oh_nh_lifetime(t) = -1/D_nh(1);
result.oh_sh_lifetime(t) = -1/D_sh(1);
result.oh_global_lifetime(t) = -1/D_global(1);
result.oh_ss(t) = -1 ./global_jacobian(3,3);
% End of loop
end
end
%%% End of function