PET formulas (Heat Overlay): Difference between revisions
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* u<sub>t</sub> is the calculated [[Wind_speed_formula_(Heat_Overlay)|wind speed]] at 1.2m above ground time t; | * u<sub>t</sub> is the calculated [[Wind_speed_formula_(Heat_Overlay)|wind speed]] at 1.2m above ground time t; | ||
* T<sub>w,t</sub> is the calculated [[Temperature_formulas_(Heat_Overlay)#Wet-bulb_Temperature_formula | wet-bulb temperature]] at time t; | * T<sub>w,t</sub> is the calculated [[Temperature_formulas_(Heat_Overlay)#Wet-bulb_Temperature_formula | wet-bulb temperature]] at time t; | ||
* ϕ<sub>t</sub> is the [[Sun_altitude_(Heat_Overlay)|sun altitude]] at time t; | * ϕ<sub>t</sub> is the [[Sun_altitude_(Heat_Overlay)|sun altitude]] at time t; | ||
* B<sub>b,t</sub> is the [[Bowen_ratio_(Heat_Overlay)|bowen ratio]] at time t; | * B<sub>b,t</sub> is the [[Bowen_ratio_(Heat_Overlay)|bowen ratio]] at time t; | ||
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==PET Shade and Night formula== | ==PET Shade and Night formula== | ||
The PET sun formula is as followed:<br> | The PET sun formula is as followed:<br> | ||
PET<sub>shade,night,t</sub> = -12.14 + 1.25 · T<sub>a</sub> - 1.47 · ln(u<sub>t</sub>) + 0.060 · T<sub>w</sub> + 0.015 · S<sub>vf</sub>Q<sub>d</sub> + 0.0060 · (1-S<sub>vf</sub>) · σ · (T<sub>a</sub>+273.15)<sup>4</sup> | PET<sub>shade,night,t</sub> = -12.14 + 1.25 · T<sub>a,t</sub> - 1.47 · ln(u<sub>t</sub>) + 0.060 · T<sub>w,t</sub> + 0.015 · S<sub>vf</sub>Q<sub>d,t</sub> + 0.0060 · (1-S<sub>vf</sub>) · σ · (T<sub>a,t</sub>+273.15)<sup>4</sup> | ||
where, | where, | ||
* T<sub>a,t</sub> is the calculated [[Temperature_formulas_(Heat_Overlay)#Atmospheric_Temperature_formula |atmospheric temperature]] at time t; | * T<sub>a,t</sub> is the calculated [[Temperature_formulas_(Heat_Overlay)#Atmospheric_Temperature_formula |atmospheric temperature]] at time t; | ||
* u<sub>t</sub> is the calculated [[Wind_speed_formula_(Heat_Overlay)|wind speed]] at 1.2m above ground time t; | * u<sub>t</sub> is the calculated [[Wind_speed_formula_(Heat_Overlay)|wind speed]] at 1.2m above ground time t; | ||
* T<sub>w,t</sub> is the calculated [[Temperature_formulas_(Heat_Overlay)#Wet-bulb_Temperature_formula | wet-bulb temperature]] at time t; | * T<sub>w,t</sub> is the calculated [[Temperature_formulas_(Heat_Overlay)#Wet-bulb_Temperature_formula | wet-bulb temperature]] at time t; | ||
* Q<sub> | * Q<sub>d,t</sub> is the calculated [[diffusive radiation (Heat Overlay)|diffusive radiation]] at time t; | ||
* | * σ is the Stefan Boltzmann constant, which is 5.670374419...×10−8 W⋅m<sup>−2</sup>⋅K<sup>−4</sup>; | ||
* B<sub>b,t</sub> is the [[Bowen_ratio_(Heat_Overlay)|bowen ratio]] at time t; | * B<sub>b,t</sub> is the [[Bowen_ratio_(Heat_Overlay)|bowen ratio]] at time t; | ||
* S<sub>vf</sub> is the calculated [[Sky_view_factor_formula_(Heat_Overlay)|sky view factor]]; | * S<sub>vf</sub> is the calculated [[Sky_view_factor_formula_(Heat_Overlay)|sky view factor]]; | ||
{{Template:HeatOverlay_formula_nav}} | {{Template:HeatOverlay_formula_nav}} | ||
Revision as of 12:02, 12 September 2019
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:
PETsun = -13.26 + 1.25 · Ta,t + 0.011 · Qgl,t - 3.37 · ln(ut) + 0.078 · Tw,t + 0.0055 · Qgl,t · ln(u) + 5.56 · sin(ϕt) - 0.0103 · Qgl,t · ln(u) · sin(ϕt) + 0.546 · Bb,t + 1.94 · Svf
where,
- Ta,t is the calculated atmospheric temperature at time t;
- Qgl,t is the hourly radiation at time t;
- ut is the calculated wind speed at 1.2m above ground time t;
- Tw,t is the calculated wet-bulb temperature at time t;
- ϕt is the sun altitude at time t;
- Bb,t is the bowen ratio at time t;
- Svf is the calculated sky view factor;
PET Shade and Night formula
The PET sun formula is as followed:
PETshade,night,t = -12.14 + 1.25 · Ta,t - 1.47 · ln(ut) + 0.060 · Tw,t + 0.015 · SvfQd,t + 0.0060 · (1-Svf) · σ · (Ta,t+273.15)4
where,
- Ta,t is the calculated atmospheric temperature at time t;
- ut is the calculated wind speed at 1.2m above ground time t;
- Tw,t is the calculated wet-bulb temperature at time t;
- Qd,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;
- Bb,t is the bowen ratio at time t;
- Svf is the calculated sky view factor;
