PyStan-CO2-Modeling-Forecasting

Modeling and forecasting atmospheric CO₂ from 1958 into the future

Data file: "weekly_in_situ_co2_mlo.csv" via Mauna Loa Observatory Dataset from Scripps CO₂ program

Quadratic Model

• N; // number of observations
• level[N]; // CO2 PPM measured values
• total; // total days
• t[total]; // days since first measurement
• c0; // intercept
• c1; // linear trend
• c2; // quadratic trend
• phi_x; // seasonal variation
• phi_y; // seasonal variation
• c4; // amplitude
• noise; // noise
• c3 = atan2(phi_x, phi_y); //phi

Likelihood

• level[i] ~ normal(c0+ c1* t[i]+ (c2* (t[i]^2)) + (c4)* cos(((2* pi* t[i])/ 365.25)+ c3), noise)

Linear Model

• n; //number of observations
• x_t[n]; //CO2 ppm measured values
• t[n]; //number of days since measurements started in 1958
• c0; //intercept
• c1; //linear trend
• c2; //seasonal variation
• c3; //seasonal variation
• c4; //gaussian noise

Likelihood

• x_t[i] ~ normal(c0 + c1* t[i] + c2* cos((2* pi* t[i])/ 365.25 + c3), c4);

function 1, y = mx + c

• f1 = c0 + c1*t

function 2, with seasonal variation

• f2 = c0 + c1* t + c2* cos((2* pi* t)/ 365.25 + c3