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:
$UHI_{max}=factor\cdot effect_{temperature}$

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. The resulting heat island effect will be low then 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 followed:
$\rho _{air}=p/R_{specific}\cdot (T_{station}+273.15)$

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

where,

$Q_{ql-avg}$ is the daily average global radiation in W/m²/hr
$C_{air}$ is the air heat capacity in J. We use a value of 1007 J.
$T_{station}$ is the hourly temperature measured at the station
$\rho _{air}$ is the calculated air density in kg/m³;
$R_{specific}$ is the gas constant for dry air. We use a value of 287.058 J/(kg·K)