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 · T_a,t + 0.011 · Q_gl,t - 3.37 · ln(u_t) + 0.078 · T_w,t + 0.0055 · Q_gl,t · ln(u) + 5.56 · sin(ϕ_t) - 0.0103 · Q_gl,t · ln(u) · sin(ϕ_t) + 0.546 · B_b,t + 1.94 · 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 1.2m above ground time t;
• T_w,t is the calculated wet-bulb temperature at time t;
• ϕ_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 sun formula is as followed:
PET_{shade,night,t} = -12.14 + 1.25 · T_a,t - 1.47 · ln(u_t) + 0.060 · T_w,t + 0.015 · S_vfQ_d,t + 0.0060 · (1-S_vf) · σ · (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;
• Q_d,t is the calculated diffusive radiation at time t;
• σ is the Stefan Boltzmann constant, which is 5.670374419...×10−8 W⋅m⁻²⋅K⁻⁴;
• B_b,t is the bowen ratio at time t;
• S_vf is the calculated sky view factor;

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