# Temperature formulas (Heat Overlay)

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

• The atmospheric temperature Ta
• The wet-bulb temperature[1] Tw

## Atmospheric Temperature formula

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

where

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

## Wet-bulb Temperature formula

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

where:

• ${\displaystyle T_{w,t}}$ is the calculated wet-bulb temperature;
• ${\displaystyle T_{a,t}}$ is the calculated atmospheric temperature;
• ${\displaystyle \phi }$ is the sun altitude angle;
• Constant values are sourced from the DPRA Heat stress report;