Table 1 Equations of the 12 thermal indices.

AT_in

Apparent Temperature (indoors)

\(A{T}_{in}=-1.3+0.92\times T+2.2\times {E}_{a}\)

Steadman⁷¹

AT_out

Apparent Temperature (outdoors, in the shade)

\(A{T}_{out}=-2.7+1.04\times T+2\times {E}_{a}-0.65\times V\)

Steadman⁷²

DI

Discomfort Index

\(DI=0.5\times WBT+0.5\times T\)

Epstein and Moran⁷³

ET

Effective Temperature

\(ET=T-0.4\times \left(T-10\right)\times \left(1-0.001\times RH\right)\)

Gagge et al.⁷⁴

HI

Heat Index

\(\begin{array}{c}{HI}^{\ast }=-8.784695+1.61139411\times T-2.338549\times RH-0.14611605\times T\times RH-1.2308094\,\times \\ 1{0}^{-2}\times {T}^{2}-1.6424828\times 1{0}^{-2}\times R{H}^{2}+2.211732\times 1{0}^{-3}\times {T}^{2}\times RH+7.2546\times 1{0}^{-4}\times T\times R{H}^{2}\,+\\ 3.582\times 1{0}^{-6}\times {T}^{2}\times R{H}^{2}\end{array}\)

Rothfusz and Headquarters⁷⁵

HMI

Humidex

\(HMI=T+0.5555\times \left(0.1\times {E}_{a}-10\right)\)

Masterton and Richardson⁷⁶

MDI

Modified Discomfort Index

\(MDI=0.75\times WBT+0.38\times T\)

Moran et al.⁷⁷

SAT

Surface Air Temperature

Air temperature at 2-meter height

/

sWBGT

Simplified Wet-bulb Temperature

\(sWBGT=0.567\times T+0.0393\times {E}_{a}+3.94\)

Willett and Sherwood⁷⁸

WBT

Wet-bulb Temperature

\(WBT=T\times {\rm{atan}}\left(0.151977\times {\left(RH+8.313659\right)}^{0.5}\right)+{\rm{atan}}\left(T+RH\right)-{\rm{atan}}\left(RH-1.676331\right)+0.00391838\times R{H}^{1.5}\times {\rm{atan}}\left(0.02301\times RH\right)-4.686035\)

Stull⁷⁹

NET

Net Effective Temperature

\(NET=37-\frac{37-T}{0.68-0.0014\times RH+\frac{1}{1.76+1.4\times {V}^{0.75}}}-0.29\times T\times \left(1-0.01\times RH\right)\)

Houghton et al.⁸⁰

WCT

Wind Chill Temperature

\(WCT=13.12+0.6215\times T-11.37\times {\left(V\times 3.6\right)}^{0.16}+0.3965\times T\times {\left(V\times 3.6\right)}^{0.16}\)

Osczevski and Bluestein⁸¹