Why does my ode45 return a solution with the first values as zero despite I supplying non-zero initial conditions?
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In the following code to simulate Pond volume and water temperature changes the code returns the solution (Y) with the first values of pondvolume and water temperature as 0,0. What could be the problem and ho can I solve it?
% Solar constant [MJ m-2 min-1]
Gsc = 0.08;
lat = 0; % Latitude
% Define simulation period
startdate = datetime(2023, 01, 01, 'Format', 'uuuu-MM-dd');
finishdate = datetime(2023, 06, 30, 'Format', 'uuuu-MM-dd');
tspans = (1:1:days(finishdate - startdate) + 1);
% Initialize arrays to store MM, doy, and dd values
MM_array_s = zeros(1, days(finishdate - startdate) + 1);
doy_array_s = zeros(1, days(finishdate - startdate) + 1);
dd_array_s = zeros(1, days(finishdate - startdate) + 1);
% Convert date to datetime object
for idx = 1:days(finishdate - startdate) + 1
current_date = startdate + days(idx - 1);
MM = month(current_date);
dd = day(current_date);
doy = days(current_date - datetime(year(current_date), 1, 1)) + 1;
% Store values in arrays
MM_array_s(idx) = MM;
doy_array_s(idx) = doy;
dd_array_s(idx) = dd;
end
CWR = 20; % To be read from Aquacrop
A_Irr = 200;
Irr_data = A_Irr * CWR / 1000*ones(length(tspans),1);
T_a_data = 25 *ones(length(tspans),1); % Later read from file/ it should be a data series
U2_data = 1.3*ones(length(tspans),1); % Read from file
RH_data = 0.75*ones(length(tspans),1); % Read from file
Y= zeros(length(tspans), 2);
Rho_net_values =zeros(length(tspans), 1);
for t=1:length(tspans)-1
T_a =T_a_data(t);
U2 = U2_data(t);
RH = RH_data(t);
Irr = Irr_data(t);
doy_array = doy_array_s(t);
% Convert latitude to radians
phi = deg2rad(lat);
% Calculate inverse relative distance Earth-Sun (dr)
dr = 1 + 0.033 * cos(2 .* pi .* doy_array ./ 365);
% Calculate solar declination (delta)
delta = 0.409 * sin(((2 * pi ./ 365)* doy_array) - 1.39);
% Calculate sunset hour angle (ws)
ws = acos(-tan(phi) * tan(delta));
% Calculate extraterrestrial radiation (Ra)
Ra = 1000*extraterrestrialRadiation(Gsc, dr, pi, phi, ws, delta);
% Display the result
% Constants and parameters
As = 0.06;
as = 0.25;
bs = 0.5;
%N = (2 / 15) .* acos(-tand(lat) .* tand(rad2deg(delta)));
N = (24/pi)*ws;
n = 11; %to be provided as a data series
Rs = (as + (bs .* (n ./ N))) .* Ra;
% Calculate net shortwave solar radiation (and photoperiod/24(phi_Light))
pi_light = N / 24;
Rho_SWR = Rs * (1 - As);
% Calculate rho_an (the difference between the incident and reflected components of long-wave radiation)
sigma = 4.896 * 10^(-6);
r = 0.36; % Change the value as necessary
C_c = 0.5; % Read from file/enter
epslon_a = 0.937 * 10^-5 * (273+T_a).^2 * (1 + 0.17 * C_c^2);
Rho_an = (1 - r) * epslon_a * sigma .* (273+T_a).^4;
% Calculate Water Surface Radiation (HO2_heat_Emm)
Initial_T_w = 27;
T_w = Initial_T_w; % To be simulated first
epslon_w = 0.97;
Rho_HO2_heat_Emm = epslon_w * sigma * (273+T_w).^4;
% Calculate Evaporative Heat Loss (Evap_HLoss)
bo = 368.61;
lambda = 311.02;
es = 25.37 * exp(17.62 - 5271 ./ (273+T_w));
ea = RH .* 25.37 .* exp(17.62 - 5271 ./ (273+T_a));
z = 1000; % Entered in the app
P = 760 / (10^(z / 19748.2));
T_wv = ((273+T_w) / (1.0 - (0.378 * es / P)));
T_av = ((273+T_a) / (1.0 - (0.378 * ea / P)));
Rho_Evap_HLoss = (es - ea) * (lambda * ((T_wv - T_av))^(1 / 3) + bo * U2);
% Calculate Conductive Heat Loss or Gain (Heat_cond)
Rho_Heat_cond = Rho_Evap_HLoss * 0.61 * 10^-3 * P * (((273+T_w) - (273+T_a)) / (es - ea));
Rho_net= Rho_SWR + Rho_an - Rho_HO2_heat_Emm - Rho_Evap_HLoss + Rho_Heat_cond;
% Define Rho_net as an anonymous function of time
%Computation of water balance components
A = 100;
pond_depth = 1;
V = A * pond_depth;
dmin = 0.8;
dcurr = 0.6;
dmax = pond_depth;
Ir = 12.923;
if Ir == 0
Qi = A * (dmin - dcurr) / tspans(2);
else
Qi = Ir / 100 * V;
end
Er = 10;
if Er == 0
Qe = A * (dcurr - dmax) / tspans(2);
else
Qe = Er / 100 * V;
end
pd = 10; % To be read from a file
PCP = A * pd / 1000;
Density_w = 1000;
Latent_vapw = 2260;
Evap = A * Rho_Evap_HLoss / (Density_w * Latent_vapw);
Sr = 5;
Seep = A * Sr / 1000;
% Initial conditions for the ODEs
T_win = 27; % Initial water temperature
T_wout = 27;
Cpw = 4.18;
% Define your ODEs
dVdt = @(t, Y) Qi + PCP - Qe + Evap + Seep - Irr;
dTdt = @(t, Y) Qi * T_win / Y(1) - Qe * T_wout / Y(1) + Rho_net / (Density_w * Cpw * pond_depth) - Y(2) / Y(1) * dVdt(t,Y);
% Combine the ODEs into a single function
dYdt = @(t, Y) [dVdt(t, Y); dTdt(t, Y)];
% Set initial conditions
Initial_conditions10 = [V; Initial_T_w]; % Ensure that this is a column vector
% Solve the system of ODEs using ode45
options = odeset('AbsTol', 1e-6, 'RelTol', 1e-6);
[t_integrated10,Y_integrated]=ode45(@(t,Y) dYdt(t,Y),tspans(t:t+1),Initial_conditions10);
Y(t+1,:) = Y_integrated(end,:);
Initial_conditions10=Y(t+1,:);
Rho_net_values(t+1) = Rho_net;
end
disp(['Extraterrestrial Radiation (Ra): ' num2str(Ra(1)) ' kJ/m^2/day']); % Displaying only the first value
figure
plot(tspans(1):tspans(end), Rho_net_values(tspans(1):tspans(end)), '.', 'markersize', 3), grid on,
title('\rho_{net}')
% Extract results
V_solution = Y(:, 1);
T_w_solution = Y(:, 2);
% Display or use the solutions as needed
disp('Volume (V) solution:');
disp(V_solution);
disp('Water Temperature (T_w) solution:');
disp(T_w_solution);
% Plot the results
figure;
subplot(2, 1, 1);
plot(tspans, V_solution); grid on
title('Volume (V) vs Time');
xlabel('Time');
ylabel('Volume (V)');
subplot(2, 1, 2);
plot(tspans, T_w_solution); grid on
title('Water Temperature (T_w) vs Time');
xlabel('Time');
ylabel('Water Temperature (T_w)');
function Ra = extraterrestrialRadiation(Gsc, dr, pi, phi, ws, delta)
% Calculate extraterrestrial radiation (Ra)
Ra = (24 * 60 / pi) * Gsc * dr .* (ws .* sin(phi) .* sin(delta) + cos(phi) .* cos(delta) .* sin(ws));
end
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Risposta accettata
Dyuman Joshi
il 27 Mar 2024
Modificato: Dyuman Joshi
il 27 Mar 2024
"Why does my ode45 return a solution with the first values as zero despite I supplying non-zero initial conditions?"
Because you loop variable t is set from 1 to length(tspans)-1, but the indexing (for variables Y and Rho_net_values) and is done using t+1. And as you have preallocated the array using zeros(), the 1st value is not modified and remains as it is.
To resolve this issue change the index from t+1 to t -
% Solar constant [MJ m-2 min-1]
Gsc = 0.08;
lat = 0; % Latitude
% Define simulation period
startdate = datetime(2023, 01, 01, 'Format', 'uuuu-MM-dd');
finishdate = datetime(2023, 06, 30, 'Format', 'uuuu-MM-dd');
tspans = (1:1:days(finishdate - startdate) + 1);
% Initialize arrays to store MM, doy, and dd values
MM_array_s = zeros(1, days(finishdate - startdate) + 1);
doy_array_s = zeros(1, days(finishdate - startdate) + 1);
dd_array_s = zeros(1, days(finishdate - startdate) + 1);
% Convert date to datetime object
for idx = 1:days(finishdate - startdate) + 1
current_date = startdate + days(idx - 1);
MM = month(current_date);
dd = day(current_date);
doy = days(current_date - datetime(year(current_date), 1, 1)) + 1;
% Store values in arrays
MM_array_s(idx) = MM;
doy_array_s(idx) = doy;
dd_array_s(idx) = dd;
end
CWR = 20; % To be read from Aquacrop
A_Irr = 200;
Irr_data = A_Irr * CWR / 1000*ones(length(tspans),1);
T_a_data = 25 *ones(length(tspans),1); % Later read from file/ it should be a data series
U2_data = 1.3*ones(length(tspans),1); % Read from file
RH_data = 0.75*ones(length(tspans),1); % Read from file
Y= zeros(length(tspans), 2);
Rho_net_values =zeros(length(tspans), 1);
for t=1:length(tspans)-1
T_a =T_a_data(t);
U2 = U2_data(t);
RH = RH_data(t);
Irr = Irr_data(t);
doy_array = doy_array_s(t);
% Convert latitude to radians
phi = deg2rad(lat);
% Calculate inverse relative distance Earth-Sun (dr)
dr = 1 + 0.033 * cos(2 .* pi .* doy_array ./ 365);
% Calculate solar declination (delta)
delta = 0.409 * sin(((2 * pi ./ 365)* doy_array) - 1.39);
% Calculate sunset hour angle (ws)
ws = acos(-tan(phi) * tan(delta));
% Calculate extraterrestrial radiation (Ra)
Ra = 1000*extraterrestrialRadiation(Gsc, dr, pi, phi, ws, delta);
% Display the result
% Constants and parameters
As = 0.06;
as = 0.25;
bs = 0.5;
%N = (2 / 15) .* acos(-tand(lat) .* tand(rad2deg(delta)));
N = (24/pi)*ws;
n = 11; %to be provided as a data series
Rs = (as + (bs .* (n ./ N))) .* Ra;
% Calculate net shortwave solar radiation (and photoperiod/24(phi_Light))
pi_light = N / 24;
Rho_SWR = Rs * (1 - As);
% Calculate rho_an (the difference between the incident and reflected components of long-wave radiation)
sigma = 4.896 * 10^(-6);
r = 0.36; % Change the value as necessary
C_c = 0.5; % Read from file/enter
epslon_a = 0.937 * 10^-5 * (273+T_a).^2 * (1 + 0.17 * C_c^2);
Rho_an = (1 - r) * epslon_a * sigma .* (273+T_a).^4;
% Calculate Water Surface Radiation (HO2_heat_Emm)
Initial_T_w = 27;
T_w = Initial_T_w; % To be simulated first
epslon_w = 0.97;
Rho_HO2_heat_Emm = epslon_w * sigma * (273+T_w).^4;
% Calculate Evaporative Heat Loss (Evap_HLoss)
bo = 368.61;
lambda = 311.02;
es = 25.37 * exp(17.62 - 5271 ./ (273+T_w));
ea = RH .* 25.37 .* exp(17.62 - 5271 ./ (273+T_a));
z = 1000; % Entered in the app
P = 760 / (10^(z / 19748.2));
T_wv = ((273+T_w) / (1.0 - (0.378 * es / P)));
T_av = ((273+T_a) / (1.0 - (0.378 * ea / P)));
Rho_Evap_HLoss = (es - ea) * (lambda * ((T_wv - T_av))^(1 / 3) + bo * U2);
% Calculate Conductive Heat Loss or Gain (Heat_cond)
Rho_Heat_cond = Rho_Evap_HLoss * 0.61 * 10^-3 * P * (((273+T_w) - (273+T_a)) / (es - ea));
Rho_net= Rho_SWR + Rho_an - Rho_HO2_heat_Emm - Rho_Evap_HLoss + Rho_Heat_cond;
% Define Rho_net as an anonymous function of time
%Computation of water balance components
A = 100;
pond_depth = 1;
V = A * pond_depth;
dmin = 0.8;
dcurr = 0.6;
dmax = pond_depth;
Ir = 12.923;
if Ir == 0
Qi = A * (dmin - dcurr) / tspans(2);
else
Qi = Ir / 100 * V;
end
Er = 10;
if Er == 0
Qe = A * (dcurr - dmax) / tspans(2);
else
Qe = Er / 100 * V;
end
pd = 10; % To be read from a file
PCP = A * pd / 1000;
Density_w = 1000;
Latent_vapw = 2260;
Evap = A * Rho_Evap_HLoss / (Density_w * Latent_vapw);
Sr = 5;
Seep = A * Sr / 1000;
% Initial conditions for the ODEs
T_win = 27; % Initial water temperature
T_wout = 27;
Cpw = 4.18;
% Define your ODEs
dVdt = @(t, Y) Qi + PCP - Qe + Evap + Seep - Irr;
dTdt = @(t, Y) Qi * T_win / Y(1) - Qe * T_wout / Y(1) + Rho_net / (Density_w * Cpw * pond_depth) - Y(2) / Y(1) * dVdt(t,Y);
% Combine the ODEs into a single function
dYdt = @(t, Y) [dVdt(t, Y); dTdt(t, Y)];
% Set initial conditions
Initial_conditions10 = [V; Initial_T_w]; % Ensure that this is a column vector
% Solve the system of ODEs using ode45
options = odeset('AbsTol', 1e-6, 'RelTol', 1e-6);
[t_integrated10,Y_integrated]=ode45(@(t,Y) dYdt(t,Y),tspans(t:t+1),Initial_conditions10);
%%v
Y(t,:) = Y_integrated(end,:);
Initial_conditions10=Y(t+1,:);
%% v
Rho_net_values(t) = Rho_net;
end
disp(['Extraterrestrial Radiation (Ra): ' num2str(Ra(1)) ' kJ/m^2/day']); % Displaying only the first value
figure
plot(tspans(1):tspans(end), Rho_net_values(tspans(1):tspans(end)), '.', 'markersize', 3), grid on,
title('\rho_{net}')
% Extract results
V_solution = Y(:, 1);
T_w_solution = Y(:, 2);
% Display or use the solutions as needed
disp('Volume (V) solution:');
disp(V_solution);
disp('Water Temperature (T_w) solution:');
disp(T_w_solution);
% Plot the results
figure;
subplot(2, 1, 1);
plot(tspans, V_solution); grid on
title('Volume (V) vs Time');
xlabel('Time');
ylabel('Volume (V)');
subplot(2, 1, 2);
plot(tspans, T_w_solution); grid on
title('Water Temperature (T_w) vs Time');
xlabel('Time');
ylabel('Water Temperature (T_w)');
function Ra = extraterrestrialRadiation(Gsc, dr, pi, phi, ws, delta)
% Calculate extraterrestrial radiation (Ra)
Ra = (24 * 60 / pi) * Gsc * dr .* (ws .* sin(phi) .* sin(delta) + cos(phi) .* cos(delta) .* sin(ws));
end
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Più risposte (2)
Saurabh
il 27 Mar 2024
Modificato: Saurabh
il 27 Mar 2024
Hi Daniel,
It seems like you were expecting to have a non-zero initial value, but it appears you received a zero initial value instead.
Upon very closely analyzing your code, I find that the value of ‘tspans’ is 181 and the size of matrix ‘Y’ is also 181.
In the looping part, the variable ‘t’ is ranging from 1 to 180. So, the maximum time matrix ‘Y’ is getting updated is only 180 times.
If you change this part of the code,
Y (t+1, :) = Y_integrated(end, :);
Initial_conditions10=Y (t+1, :);
Rho_net_values(t+1) = Rho_net;
With this:
Y (t, :) = Y_integrated(end, :);
Initial_conditions10=Y (t, :);
Rho_net_values(t) = Rho_net;
The last value of the vector will hold a zero value.
I hope this was helpful.
2 Commenti
Saurabh
il 28 Mar 2024
In that case, simply reduce the size of the matrix 'Y' by 1. This will exclude the possibility of zero in the code.
Thomas Males
il 16 Mag 2024
Hi Daniel,
I would suggest looking into timetables for processing of timeseries data. This would likely allow you to get rid of the for loops and calulate the new variables with dot notation like this:
myTable.NewVar = mytable.OldVar1 .* myTable.Oldvar2 + Const1.
This also opens up a lot of funtionality through the retime function and simplifies plotting of multiple variables through the stacked plot function.
You've probably got everything working with your loop by now but it could be a consideration for the future.
Cheers,
Tom
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