UHI formula (Heat Overlay)

The Urban heat island effect is calculated using the following formula:
UHI_max = ( 2 - S_vf - F_veg ) * ( S * (T_max-T_min)³ / U )^-4
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

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:
ρ_air = p / R_specific * (T_station + 273.15)
S = Q_ql-avg / (C_air * ρ_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 1007.0.
• T_station is the temperature measured at the station
• ρ_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)