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: PET_{shade, night};
A cell is in the sun during the day: PET_sun;

PET Sun formula

The PET sun formula is as followed:

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

where,

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

PET Shade and Night formula

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

where,

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