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:

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

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;
• ${\varphi }_t$ 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:
$PE{T}_{shade,night}=-12.14+1.25\cdot T_{a,t}-1.47\cdot ln(u_t)+0.060\cdot T_{w,t}+0.015\cdot S_{vf}\cdot Q_{d,t}+0.0060\cdot (1-S_{vf})\cdot \sigma \cdot (T_{a,t}+273.15{)}^4$

where,

• $T_{a,t}$ is the calculated atmospheric temperature at time t;
• $u_t$ is the calculated wind speed at 1.2m 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 $5.670374419...\times 10^{-8}W\cdot m^{-2}\cdot K^{-4}$.

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