UHI formula (Heat Stress Overlay)

The Urban heat island effect is calculated using the following formula:

$UH{I}_{max}=(2-S_{vf}-F_{veg})\cdot \sqrt[4]{\frac{S\cdot (T_{max}-T_{min}{)}^3}{U}}$

where:

• $S_{vf}$ is the calculated average sky view factor;
• $F_{veg}$ is the calculated average vegetation fraction;
• $S$ is the calculated daily average global radiation in K m/s
• $T_{max}$ is the maximum temperature measured at a weather station between 8 AM and 7 AM the next day.
• $T_{min}$ is the minimum temperature measured at a weather station between 8 AM and 7 AM the next day.
• $U$ is the daily average wind speed measured at 10 meters above ground at a weather station.

Formula Decomposition

The formula has two parts, the factor and the temperature effect:
$UH{I}_{max}=factor\cdot effec{t}_{temperature}$

Factor

The factor is influenced by the sky view factor and the vegetation fraction, both ranging from 0 to 1. When both are low, i.e. barely any sky and no vegetation, the factor is near 2. When both are high, i.e. no surrounding buildings and a lot of vegetation, the factor is near 0. In that case, the resulting heat island effect will be low as well.

Temperature effect

The Urban heat island temperature effect is calculated as:

• the daily average global radiation S,
• the maximum-minimum temperature difference ΔT
• the daily average wind speed, measured at 10m above ground.

Daily average global radiation

The S is calculated as follows:

${\rho }_{air}=\frac{p}{R_{specific}\cdot (T_{station}+273.15)}$

$S=\frac{Q_{ql-avg}}{C_{air}\cdot {\rho }_{air}}$

where,

• $p$ is the atmospheric pressure, also known as air pressure, with a value of 101325 Pa.
• $Q_{ql-avg}$ is the daily average global radiation in W/m².
• $C_{air}$ is the air heat capacity in J/(kg·K). We use a value of 1007 J/(kg·K).
• $T_{station}$ is the hourly temperature measured at the station.
• ${\rho }_{air}$ is the calculated air density in kg/m³.
• $R_{specific}$ is the specific gas constant for dry air. We use a value of 287.058 J/(kg·K).
• $273.15$ converts the used temperature from degrees Celsius (°C) to Kelvin (K).

See also

• Atmospheric temperature formula

References

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UHI • Temperatures • Diffuse radiation • PET

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

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