Temperature formulas (Heat Overlay)

Two temperature formulas are used in the calculation of the PET value:

The atmospheric temperature T_a
The wet-bulb temperatur T_w

Atmospheric Temperature formula

$T_{a,t}=T_{station,t}+UHI_{max,t}\cdot f_{sun,t}$

where

$T_{a,t}$ is the calculated atmospheric temperature at time t;
$T_{station,t}$ is the temperature measured at a weather station at time t;
$UHI_{max,t}$ is the calculated Urban Heat Island effect at time t;
$f_{sun,t}$ is the sun daily motion factor at time t;

Wet-bulb Temperature formula

Failed to parse (syntax error): {\displaystyle T_{w,t} = T_{a,t} \cdot \arctan{ 0.151977 \cdot \sqrt{\phi + 8.313659}} + \arctan {T_{a} + \phi} - \arctan{\phi - 1.676331} + 0.00391838 · \phi^{\frac{3}{2}} \arctan{0.023101 \cdot \phi} - 4.686935} where: