PET formulas (Heat Overlay): Difference between revisions

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: PET_{shade, night};
A cell is in the sun during the day: PET_sun;

PET Sun formula

The PET sun formula is as followed:

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

where,

$T_{a,t}$ 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;
$\phi _{t}$ 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.
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;
$\sigma$ is the Stefan Boltzmann constant, which is $5.670374419...\times 10^{-8}W\cdot m^{-2}\cdot K^{-4}$ .
Constant values are sourced from the DPRA Heat stress report;

Group: Calculation models and formulas
Formulas

UHI • Temperatures • Diffuse radiation • PET
Calculation models

Foliage height • Sky view factor • Shade • Average vegetation and sky view factor

Related

Calculation models and formulas • Feature attributes • Model attributes • Result types

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 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<sub>shade, night</sub>;
+* A cell is in the shade or it is night at time t: [[#PET Shade and Night formula|PET<sub>shade, night</sub>]];
 * A cell is in the sun during the day: [[#PET Sun formula|PET<sub>sun</sub>]];
 ==PET Sun formula==
-The PET sun formula is as followed:<br>
+The PET sun formula is as followed:
-PET<sub>sun</sub> = -13.26 + 1.25 · T<sub>a,t</sub> + 0.011 · Q<sub>gl,t</sub> - 3.37 · ln(u<sub>t</sub>) + 0.078 · T<sub>w,t</sub> + 0.0055 · Q<sub>gl,t</sub> · ln(u) + 5.56 · sin(ϕ<sub>t</sub>) - 0.0103 · Q<sub>gl,t</sub> · ln(u) · sin(ϕ<sub>t</sub>) + 0.546 · B<sub>b,t</sub> + 1.94 · S<sub>vf</sub><br>
+<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,
-* 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;
-* Q<sub>gl,t</sub> is the [[Hourly_radiation_(Heat_Overlay)|hourly radiation]] at time t;
+* <math>\phi_{t}</math> 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;
+* <math>B_{b,t}</math> 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;
+* <math>S_{vf}</math> is the calculated [[Sky_view_factor_calculation_model_(Heat_Overlay)|sky view factor]].
-* S<sub>vf</sub> is the calculated [[Sky_view_factor_formula_(Heat_Overlay)|sky view factor]];
+* Constant values are sourced from the {{Heat DPRA Report}};
 ==PET Shade and Night formula==
-The PET sun formula is as followed:<br>
+The PET shade and night formula is as followed:<br>
-PET<sub>sun</sub> = -13.26 + 1.25 · T<sub>a,t</sub> + 0.011 · Q<sub>gl,t</sub> - 3.37 · ln(u<sub>t</sub>) + 0.078 · T<sub>w,t</sub> + 0.0055 · Q<sub>gl,t</sub> · ln(u) + 5.56 · sin(ϕ<sub>t</sub>) - 0.0103 · Q<sub>gl,t</sub> · ln(u) · sin(ϕ<sub>t</sub>) + 0.546 · B<sub>b,t</sub> + 1.94 · S<sub>vf</sub><br>
+<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,
-* 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>u_{t}</math> is the calculated [[Wind_calculation_model_(Heat_Overlay)|wind speed]] at 1.2 meters 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;
+* <math>T_{w,t}</math> 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;
+* <math>S_{v,f}</math> is the calculated [[Sky_view_factor_calculation_model_(Heat_Overlay)|sky view factor]];
-* Q<sub>gl,t</sub> is the [[Hourly_radiation_(Heat_Overlay)|hourly radiation]] at time t;
+* <math>Q_{d,t}</math> is the calculated [[Diffuse_radiation_formula_(Heat_Overlay)|diffusive radiation]] at time t;
-* ϕ<sub>t</sub> is the [[Sun_altitude_(Heat_Overlay)|sun altitude]] at time t;
+* <math>\sigma</math> is the Stefan Boltzmann constant, which is <math>5.670374419...\times 10^{-8} W \cdot m^{-2} \cdot K^{-4}</math>.
-* B<sub>b,t</sub> is the [[Bowen_ratio_(Heat_Overlay)|bowen ratio]] at time t;
+* Constant values are sourced from the {{Heat DPRA Report}};
-* S<sub>vf</sub> is the calculated [[Sky_view_factor_formula_(Heat_Overlay)|sky view factor]];
 {{Template:HeatOverlay_formula_nav}}

PET formulas (Heat Overlay): Difference between revisions

Latest revision as of 11:52, 13 September 2021

PET Sun formula

PET Shade and Night formula

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