What the weather feels like

apparent temperaturewind chill and humidexfeels like

Wind chill, humidex, heat index and dew point — the four numbers that explain why the thermometer lies.

Wind Chill (2001 North American Formula)

T_{wc} = 13.12 + 0.6215\,T - 11.37\,V^{0.16} + 0.3965\,T\,V^{0.16}

The wind chill index adopted by Canada and the United States in 2001, from air temperature and wind speed at 10 m.

Humidex (Canadian Humidity Index)

H = T + 0.5555\,(e - 10), \quad e = 6.11\,e^{5417.753\left(\frac{1}{273.16} - \frac{1}{T_d}\right)}

Environment Canada's humidex: air temperature raised by the excess vapour pressure computed from the dew point.

Heat Index (Rothfusz Regression)

\mathrm{HI} = c_1 + c_2 T + c_3 R + c_4 T R + c_5 T^2 + c_6 R^2 + c_7 T^2 R + c_8 T R^2 + c_9 T^2 R^2

The US National Weather Service heat index, Rothfusz's nine-term regression through Steadman's apparent-temperature table (T in °F, R in percent).

Dew Point (Magnus Approximation)

T_d = \frac{c\,\gamma}{b - \gamma}, \quad \gamma = \ln\!\frac{\mathrm{RH}}{100} + \frac{b\,T}{c + T}

Dew point from air temperature and relative humidity by the Magnus formula with the WMO's Sonntag coefficients (b = 17.62, c = 243.12 °C).

How they fit together

Air temperature alone is a poor guide to how weather feels, because a body loses heat to moving air faster and sheds it to humid air slower. These four formulas correct for that in opposite directions, and each has a range in which it is defined.

Wind chill is the cold-weather correction and applies at or below 10 °C with wind above 4.8 km/h. Humidex and the heat index are the warm-weather corrections and disagree by design: humidex is Canadian, dimensionless, and built from vapour pressure, while the heat index is American, reported as an apparent temperature in degrees, and regressed in Fahrenheit. Neither is more correct; they are different conventions, which is why a summer day carries a humidex of 40 on one side of the border and a heat index of 105 °F on the other.

Dew point underlies both warm-weather indices and is the most useful of the four for a building operator, because it names the surface temperature at which condensation begins. A dew point above 20 °C is what makes a night feel oppressive, and a pipe below the dew point is what makes a ceiling drip.