# PET formulas (Heat Overlay)

The physiological equivalent temperature PET is calculated for two possible options based on the situation:

• A cell is in the shade or it is night at time t: PETshade, night;
• A cell is in the sun during the day: PETsun;

## PET Sun formula

The PET sun formula is as followed:

${\displaystyle PET_{sun}=-13.26+1.25\cdot T_{a,t}+0.011\cdot Q_{gl,t}-3.37\cdot ln(u_{t})+0.078\cdot T_{w,t}+0.0055\cdot Q_{gl,t}\cdot ln(u)+5.56\cdot sin(\phi _{t})-0.0103\cdot Q_{gl,t}\cdot ln(u_{t})\cdot sin(\phi _{t})+0.546\cdot B_{b,t}+1.94\cdot S_{vf}}$

where,

• ${\displaystyle T_{a,t}}$ is the calculated atmospheric temperature at time t;
• ${\displaystyle Q_{gl,t}}$ is the hourly radiation at time t;
• ${\displaystyle u_{t}}$ is the calculated wind speed at 1.2 meters above ground time t;
• ${\displaystyle T_{w,t}}$ is the calculated wet-bulb temperature at time t;
• ${\displaystyle \phi _{t}}$ is the sun altitude at time t;
• ${\displaystyle B_{b,t}}$ is the bowen ratio at time t;
• ${\displaystyle S_{vf}}$ is the calculated sky view factor.
• Constant values are sourced from the DPRA Heat stress report;

## PET Shade and Night formula

The PET shade and night formula is as followed:
${\displaystyle PET_{shade,night}=-12.14+1.25\cdot T_{a,t}-1.47\cdot ln(u_{t})+0.060\cdot T_{w,t}+0.015\cdot S_{vf}\cdot Q_{d,t}+0.0060\cdot (1-S_{vf})\cdot \sigma \cdot (T_{a,t}+273.15)^{4}}$

where,

• ${\displaystyle T_{a,t}}$ is the calculated atmospheric temperature at time t;
• ${\displaystyle u_{t}}$ is the calculated wind speed at 1.2 meters above ground time t;
• ${\displaystyle T_{w,t}}$ is the calculated wet-bulb temperature at time t;
• ${\displaystyle S_{v,f}}$ is the calculated sky view factor;
• ${\displaystyle Q_{d,t}}$ is the calculated diffusive radiation at time t;
• ${\displaystyle \sigma }$ is the Stefan Boltzmann constant, which is ${\displaystyle 5.670374419...\times 10^{-8}W\cdot m^{-2}\cdot K^{-4}}$.
• Constant values are sourced from the DPRA Heat stress report;