UHI formula (Heat Overlay): Difference between revisions

Latest revision as of 11:53, 13 September 2021

The Urban heat island effect is calculated^[1] 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. 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 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)
$273.15$ converts the used temperature from celcius (°C) to kelvin (K)

References

↑ A diagnostic equation for the daily maximum urban heat island effect for cities in northwestern Europe • N.E. Theeuwes et al. • http://www.meteo.wur.nl/medewerkers/steeneveld/Theeuwes_JOC_2016.pdf • last visited 13-02-2020

[rmets-1] A diagnostic equation for the daily maximum urban heat island effect for cities in northwestern Europe • N.E. Theeuwes et al. • http://www.meteo.wur.nl/medewerkers/steeneveld/Theeuwes_JOC_2016.pdf • last visited 13-02-2020

[1]

@@ Line 1: / Line 1: @@
 __NOTOC__
-The Urban heat island effect is calculated using the following formula:<br>
+The Urban heat island effect is calculated<ref name='rmets'/> using the following formula:<br>
-<math>UHI_{max} = ( 2 - S_{vf} - F_{veg} ) \cdot \root{\frac{ (S \cdot (T_{max}-T_{min})^3}{U}}{-4}</math>
+<math>UHI_{max} = ( 2 - S_{vf} - F_{veg} ) \cdot \sqrt[4]{\frac{ S \cdot (T_{max}-T_{min})^3}{U}}</math>
 where:
 * S<sub>vf</sub> is the calculated [[Sky_view_avg_result_type_(Heat_Overlay)|average sky view factor]];
@@ Line 12: / Line 12: @@
 ==Formula Decomposition==
 The formula has two parts, the factor and the temperature effect:<br>
-UHI<sub>max</sub> = [[#Factor|factor]] · [[#Temperature effect|temperature_effect]] <br>
+<math>UHI_{max} = factor \cdot effect_{temperature}</math>
 ====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 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:
@@ Line 23: / Line 24: @@
 =====Daily average global radiation=====
 The S is calculated as followed:<br>
-ρ<sub>air</sub> = p / R<sub>specific</sub> · (T<sub>station</sub> + 273.15)<br>
+<math>\rho_{air} = p / R_{specific} \cdot (T_{station} + 273.15)</math>
-S = Q<sub>ql-avg</sub> / (C<sub>air</sub> · ρ<sub>air</sub>)<br>
+<math>S = \frac{Q_{ql-avg}}{C_{air} \cdot \rho_{air}}</math>
 where,
-* Q<sub>ql-avg</sub> is the [[Daily_avg_radiation_(Heat_Overlay)|daily average global radiation]] in W/m<sup>2</sup>/hr
+* <math>Q_{ql-avg}</math> is the [[Daily_avg_radiation_(Heat_Overlay)|daily average global radiation]] in W/m<sup>2</sup>/hr
-* C<sub>air</sub> is the air heat capacity in J. We use a value of 1007 J.
+* <math>C_{air}</math> is the air heat capacity in J. We use a value of 1007 J.
-* T<sub>station</sub> is the hourly [[Hourly_temperature_(Heat_Overlay)|temperature]] measured at the station
+* <math>T_{station}</math> is the hourly [[Hourly_temperature_(Heat_Overlay)|temperature]] measured at the station
-* ρ<sub>air</sub> is the calculated air density in kg/m<sup>3</sup>;
+* <math>\rho_{air}</math> is the calculated air density in kg/m<sup>3</sup>;
-* R<sub>specific</sub> is the [https://en.wikipedia.org/wiki/Specific_gas_constant|specific gas constant] for dry air. We use a value of 287.058 J/(kg·K)
+* <math>R_{specific}</math> is the [https://en.wikipedia.org/wiki/Specific_gas_constant|specific gas constant] for dry air. We use a value of 287.058 J/(kg·K)
+* <math>273.15</math> converts the used temperature from celcius (°C) to kelvin (K)
 ==See also==
 * [[Temperature_formulas_(Heat_Overlay)#Atmospheric Temperature formula|Atmospheric temperature formula]]
 {{Template:HeatOverlay_formula_nav}}
+==References==
+<references>
+<ref name='rmets'>A diagnostic equation for the daily maximum urban heat island effect for cities in northwestern Europe • N.E. Theeuwes et al. • http://www.meteo.wur.nl/medewerkers/steeneveld/Theeuwes_JOC_2016.pdf • last visited 13-02-2020</ref>
+</references>