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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_{a,t}} is the calculated atmospheric temperature at time t;
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q_{gl,t}} is the hourly radiation at time t;
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u_{t}} is the calculated wind speed at 1.2 meters above ground time t;
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_{w,t}} is the calculated wet-bulb temperature at time t;
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi_{t}} is the sun altitude at time t;
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B_{b,t}} is the bowen ratio at time t;
$S_{vf}$ 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:
$PET_{shade,night}=-12.14+1.25\cdot T_{a,t}-1.47\cdot ln(u_{t})+0.060\cdot T_{w,t}+0.015\cdot S_{vf}\cdot Q_{d,t}+0.0060\cdot (1-S_{vf})\cdot \sigma \cdot (T_{a,t}+273.15)^{4}$

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;
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} is the Stefan Boltzmann constant, which is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5.670374419...\times 10^{-8} W \cdot m^{-2} \cdot K^{-4}} .
Constant values are sourced from the DPRA Heat stress report;