I want to know if my code is well written based on a set of criteria.

To estimate DIP_s, it is necessary to approximate the expected DIP concentration within the current time step used in the integration(i.e DIP_interm . If the time step is one day, this concentration (DIP_interm) is the sum of the present DIP and the result of Equation 1 with DIP_fert= 0. The difference between DIP_interm and DIP_O is an estimate of DIP_s.

dDIPdt = DIP_Fert + DIP_resp_phy - DIP_grow_phy - (0.1 * DIP) ...............................................................EQN(1)

DIP_req = DIP_grow_phy-(DIP_resp_phy + DIP_msc);

DIP_fert can then be calculated by applying the following rules:

if DIP_interm < DIP_O

DIP_Fert = DIP_req + (DIP_O - DIP_interm);

elseif 0 <= DIP_s <= DIP_req

DIP_Fert = DIP_req - DIP_s;

elseif DIP_s > DIP_req

DIP_Fert = 0;

end

Finally, Equation 1 is re-evaluated by inserting the value of DIP_fert obtained based on the above rules so as to obtain the rate change of DIP. The sum of DIP_fert calculated at each time step over the entire integration period is a rough estimate of the overall fertilizer N requirements for that period

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% 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);

%Dissolved inorganic phosphorous (DIP)
T_w = 20;
T_min = 18;
T_max = 27;
T_opt = 33;
if T_w < T_opt
    Tau = exp(-4.6 * ((T_opt - T_w) / (T_opt - T_min)).^4);
else
    Tau = exp(-4.6 * ((T_w - T_opt) / (T_max - T_opt)).^4);
end
V_n = 1;
GPP_lambda = 7.0; % assumed as & in g m^-3 d^-1
GPP = GPP_lambda * Tau * V_n;
DIP_IN = 0.2;
DIP_Fert = 0;
Redfield_ratio_p = 0.025;
DIP_grow_phy = GPP*Redfield_ratio_p;
DIP_resp_phy = 0.5 *DIP_grow_phy;

% Initialize DIP
DIP = zeros(length(tspans), 1); % Initialize DIP vector

% Initialize arrays to store DIP_Fert
DIP_Fert_values = zeros(length(tspans), 1);

for t = 1:length(tspans)-1
    dDIPdt = @(t, DIP) calculate_dDIPdt(t, DIP, DIP_Fert, DIP_resp_phy, DIP_grow_phy);
    [t_integrated, DIP_integrated] = ode45(@(t, DIP) dDIPdt(t, DIP), tspans(t:t+1), DIP_IN);
    
    DIP(t+1) = DIP_integrated(end);
    
    % Recalculate DIP_Fert based on conditions
    DIP_O       = 0.1;
    DIP_msc     = 0.1*DIP(t);
    DIP_req     = DIP_grow_phy-(DIP_resp_phy + DIP_msc);
    DIP_interm  = DIP(t) + (DIP_resp_phy + DIP_msc - DIP_grow_phy);
    DIP_s       =max(0,(DIP_interm - DIP_O));
    
    if DIP_interm < DIP_O
        DIP_Fert = DIP_req + (DIP_O - DIP_interm);
    elseif all((0 <= DIP_s) & (DIP_s <= DIP_req))
        DIP_Fert = DIP_req - DIP_s;
    elseif DIP_s > DIP_req
        DIP_Fert = 0;
    end
    % Check if DIP_Fert is negative and set it to zero
    if DIP_Fert < 0
        DIP_Fert = 0;
    end
    % Update DIP_Fert array
    DIP_Fert_values(t+1) = DIP_Fert;
    
    % Update initial condition for the next iteration
    DIP_IN = DIP(t+1);
end
% Output DIP_Fert values at different time steps
disp('DIP_Fert values:');

DIP_Fert values:

disp(DIP_Fert_values);

         0
    0.1131
         0
         0
         0
         0
         0
         0
         0
         0
         0
    0.0163
    0.0330
    0.0294
    0.0072
         0
    0.0020
    0.0200
    0.0341
    0.0262
    0.0030
         0
    0.0066
    0.0242
    0.0326
    0.0200
         0
         0
    0.0133
    0.0303
    0.0304
    0.0112
         0
         0
    0.0179
    0.0344
    0.0289
    0.0050
         0
    0.0032
    0.0211
    0.0337
    0.0246
    0.0020
         0
    0.0087
    0.0261
    0.0319
    0.0173
         0
         0
    0.0147
    0.0315
    0.0299
    0.0093
         0
    0.0008
    0.0189
    0.0345
    0.0278
    0.0040
         0
    0.0047
    0.0224
    0.0332
    0.0226
    0.0008
         0
    0.0111
    0.0282
    0.0311
    0.0141
         0
         0
    0.0164
    0.0330
    0.0294
    0.0071
         0
    0.0020
    0.0201
    0.0340
    0.0261
    0.0030
         0
    0.0067
    0.0243
    0.0325
    0.0199
         0
         0
    0.0134
    0.0303
    0.0304
    0.0110
         0
         0
    0.0180
    0.0345
    0.0289
    0.0050
         0
    0.0033
    0.0212
    0.0336
    0.0245
    0.0020
         0
    0.0087
    0.0261
    0.0319
    0.0172
         0
         0
    0.0148
    0.0316
    0.0299
    0.0092
         0
    0.0008
    0.0189
    0.0344
    0.0277
    0.0040
         0
    0.0047
    0.0225
    0.0332
    0.0225
    0.0007
         0
    0.0112
    0.0283
    0.0311
    0.0140
         0
         0
    0.0165
    0.0331
    0.0294
    0.0070
         0
    0.0021
    0.0201
    0.0340
    0.0260
    0.0029
         0
    0.0068
    0.0244
    0.0325
    0.0197
         0
         0
    0.0135
    0.0304
    0.0303
    0.0110
         0
         0
    0.0180
    0.0345
    0.0289
    0.0049
         0
    0.0033
    0.0212
    0.0336
    0.0245
    0.0019
         0
    0.0088
    0.0262
    0.0319
    0.0171
         0
         0
    0.0148
    0.0316
    0.0299
    0.0092

% Plot DIP
plot(DIP);
xlabel('Time');
ylabel('Concentration');
legend('DIP',Location='northwest');

function dDIPdt = calculate_dDIPdt(~, DIP, DIP_Fert, DIP_resp_phy, DIP_grow_phy)
dDIPdt = DIP_Fert + DIP_resp_phy - DIP_grow_phy +- (0.1 * DIP);
end

[Dyuman Joshi]

Looks good.

[Daniel]

Thank you for checking my code @Dyuman Joshi and for your response. i will consider.