PET formulas (Heat Overlay): Difference between revisions
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* <math>B_{b,t}</math> 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; | ||
* <math>S_{vf}</math> is the calculated [[Sky_view_factor_calculation_model_(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== | ||
Revision as of 15:34, 13 February 2020
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:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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,
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_{a,t}} is the calculated atmospheric temperature at time t;
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q_{gl,t}} is the hourly radiation at time t;
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u_{t}} is the calculated wind speed at 1.2 meters above ground time t;
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_{w,t}} is the calculated wet-bulb temperature at time t;
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi_{t}} is the sun altitude at time t;
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B_{b,t}} is the bowen ratio at time t;
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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,
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_{a,t}} is the calculated atmospheric temperature at time t;
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle u_{t}} is the calculated wind speed at 1.2 meters above ground time t;
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T_{w,t}} is the calculated wet-bulb temperature at time t;
- is the calculated sky view factor;
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Q_{d,t}} is the calculated diffusive radiation at time t;
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma} is the Stefan Boltzmann constant, which is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 5.670374419...\times 10^{-8} W \cdot m^{-2} \cdot K^{-4}} .
