Heat index - WorldWeatherAttribution/wwa-wiki GitHub Wiki

Notes on attributing changes in the heat index

The Heat Index (HI) is a measure of humid heat that combines temperature and humidity into a measure reflecting the human body's comfort. Based on the envisaged risk of heat-related disorders in people, HI values are categorised into low risk (< 27 °C, < 80 °F), caution (27–32 °C, 80–90 °F), extreme caution (32–41 °C, 90–105 °F), danger (41–54 °C, 105–130 °F) and extreme danger ( > 54 °C, > 130 °F) ((Blazejczyk et al., 2012; Debnath et al., 2023). These HI categories were originally defined for a North American context, and may not be directly transferable to typical weather conditions prevailing in regions with different climates; however, they are still a useful indicator of likely risk thresholds.

The Heat Index (HI) equation was introduced by Rothfusz (1990) by fitting a multiple regression model to pairs of temperature (in Fahrenheit) and relative humidity (in %) values which were initially calculated by Steadman (1979). Steadman's calculations were based on functional relationships that account for the impact of these variables on human thermal comfort. The HI equation is expressed as

$$ \displaylines{HI=-42.379+2.04901523T+10.14333127R-0.22475541TR -0.00683783 {T} ^ {2} -0.05481717 {R} ^ {2} +\ 0.00122874 {T} ^ {2} R +0.00085282T {R} ^ {2} -0.00000199 {T} ^ {2} {R} ^ {2}} $$

where $T$ is the daily maximum temperature $\color{red}\text{in }^\circ F$ and $R$ is the daily mean relative humidity, expressed as a percentage from 0 to 100. The heat index has units of $\color{red}^\circ F$.

The NOAA Weather Prediction Center uses a modified version of this equation in their outlook, by making adjustments for extreme temperature and relative humidity conditions that are outside of the range of data considered by Steadman (1979) as follows:

$$ HI = \left\lbrace \begin{matrix} \ HI - A_1 & \text{if }R < 13 &\text{ and }& 80 < T < 112 \ HI + A_2 & \text{if }R > 85 &\text{ and }& 80 < T < 87 \ HI & \text{otherwise} \end{matrix}\right. $$ where $$ \begin{matrix} A_1 = \frac{13-R}{4}\sqrt{\frac{17-|T-95|}{17}} && \text{and} && A_2 = \frac{R-85}{10}\frac{87-T}{5} \end{matrix} $$

If, after this adjustment, the heat index is less than 80F, then

$$ HI = 0.5 \left(T+61+1.2(T-68)+0.094R \right). $$

Where the relative humidity is not directly available, it is calculated from the daily mean dew point temperature $T_{dew}$ and daily maximum temperature $T_{max}$, $\color{red}\text{both in }°C$, using the improved Magnus approximation proposed by Alduchov and Eskridge (1996):

$$ R = 100\exp{\left(\frac{17.625 T_{dew}}{243.04+T_{dew}} - \frac{17.625 T_{max}}{243.04+T_{max}}\right)}. $$

Previous WWA studies that used the Heat Index to characterise humid heatwaves can be found here: South Asia Humid Heatwave, 2023 and West Africa Humid Heatwave, 2024.