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} $T_{w,t}=T_{a,t}\cdot \arctan(0.151977\cdot {\sqrt {\phi +8.313659}})+\arctan(T_{a}+\phi )-\arctan(\phi -1.676331)+0.00391838\cdot \phi ^{\frac {3}{2}}\arctan(0.023101\cdot \phi )-4.686935$