PET formulas (Heat Overlay): Difference between revisions

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==PET Sun formula==
==PET Sun formula==
The PET sun formula is as followed:<br>
The PET sun formula is as followed:
<math>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 · 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}</math>
 
<math>PET_{sun} = -13.26</math>
<math>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} </math>


where,
where,
* T<sub>a,t</sub> is the calculated [[Temperature_formulas_(Heat_Overlay)#Atmospheric_Temperature_formula |atmospheric temperature]] at time t;
* <math>T_{a,t}</math> is the calculated [[Temperature_formulas_(Heat_Overlay)#Atmospheric_Temperature_formula |atmospheric temperature]] at time t;
* Q<sub>gl,t</sub> is the [[Hourly_radiation_(Heat_Overlay)|hourly radiation]] at time t;
* <math>Q_{gl,t}</math> is the [[Hourly_radiation_(Heat_Overlay)|hourly radiation]] at time t;
* u<sub>t</sub> is the calculated [[Wind_speed_formula_(Heat_Overlay)|wind speed]] at 1.2m above ground time t;
* <math>u_{t}</math> is the calculated [[Wind_calculation_model_(Heat_Overlay)|wind speed]] at 1.2 meters 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;
* <math>T_{w,t}</math> 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;
* <math>\phi_{t}</math> 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;
* <math>B_{b,t}</math> 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]].
* <math>S_{vf}</math> is the calculated [[Sky_view_factor_calculation_model_(Heat_Overlay)|sky view factor]].
* Constant values are sourced from the {{Heat DPRA Report}};


==PET Shade and Night formula==
==PET Shade and Night formula==
The PET shade and night formula is as followed:<br>
The PET shade and night formula is as followed:<br>
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>
<math>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</math>
 
where,
where,
* T<sub>a,t</sub> is the calculated [[Temperature_formulas_(Heat_Overlay)#Atmospheric_Temperature_formula |atmospheric temperature]] at time t;
* <math>T_{a,t}</math> 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;
* <math>u_{t}</math> is the calculated [[Wind_calculation_model_(Heat_Overlay)|wind speed]] at 1.2 meters 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;
* <math>T_{w,t}</math> is the calculated [[Temperature_formulas_(Heat_Overlay)#Wet-bulb_Temperature_formula | wet-bulb temperature]] at time t;
* S<sub>vf</sub> is the calculated [[Sky_view_factor_formula_(Heat_Overlay)|sky view factor]];
* <math>S_{v,f}</math> is the calculated [[Sky_view_factor_calculation_model_(Heat_Overlay)|sky view factor]];
* Q<sub>d,t</sub> is the calculated [[Diffuse_radiation_formula_(Heat_Overlay)|diffusive radiation]] at time t;
* <math>Q_{d,t}</math> is the calculated [[Diffuse_radiation_formula_(Heat_Overlay)|diffusive radiation]] at time t;
* σ is the Stefan Boltzmann constant, which is 5.670374419...×10<sup>-8</sup> W⋅m<sup>-2</sup>⋅K<sup>-4</sup>.
* <math>\sigma</math> is the Stefan Boltzmann constant, which is <math>5.670374419...\times 10^{-8} W \cdot m^{-2} \cdot K^{-4}</math>.
* Constant values are sourced from the {{Heat DPRA Report}};


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Latest revision as of 11:52, 13 September 2021

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:

where,

PET Shade and Night formula

The PET shade and night formula is as followed:

where,

  • is the calculated atmospheric temperature at time t;
  • is the calculated wind speed at 1.2 meters above ground time t;
  • is the calculated wet-bulb temperature at time t;
  • is the calculated sky view factor;
  • is the calculated diffusive radiation at time t;
  • is the Stefan Boltzmann constant, which is .
  • Constant values are sourced from the DPRA Heat stress report;