UHI formula (Heat Overlay)

The Urban heat island effect is calculated using the following formula:
$UHI_{max}=(2-S_{vf}-F_{veg})\cdot {\sqrt[{4}]{\frac {S\cdot (T_{max}-T_{min})^{3}}{U}}}$ 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:
UHI_max = factor · temperature_effect

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.

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 followed:
$\rho _{air}=p/R_{specific}\cdot (T_{station}+273.15)$ 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 = \frac{Q_{ql-avg}}C_{air} \cdot \rho_{air}}} where,