Apparent Temperature (Steadman, as the Bureau of Meteorology Prints It)

Air temperature alone does not say how a day feels. Humid air feels warmer and wind cools, and apparent temperature folds temperature, humidity and wind into one number: the temperature, at a reference humidity, that would give the same discomfort to a person walking in the shade. This version is the fit by Robert Steadman (1994) to his model of a walking adult, in the form the Australian Bureau of Meteorology prints for its observations. The answer reads as a feels-like temperature in degrees Celsius.

Each term has a plain job. $T_a$ is the dry-bulb air temperature in the shade, in degrees Celsius. $e$ is the water vapour pressure in hectopascals, the partial pressure of the vapour, and each hectopascal adds 0.33 degrees. $v$ is the wind speed at 10 metres in metres per second, and each metre per second takes off 0.70 degrees. The constant 4.00 is a fixed offset, so in dry, still air the apparent temperature is the air temperature less 4. If you start from relative humidity, the Bureau gives the vapour pressure as $e=\frac{rh}{100}\times6.105\,\exp\frac{17.27\,T_a}{237.7+T_a}$, with $rh$ in percent; find $e$ first and enter it here.

The page can be checked against the Bureau's own table, after Steadman. At 30 C with 0 percent humidity (so $e=0$) in still air the table reads 26, and the equation gives 30 less 4, exactly 26. At 30 C and 50 percent the Bureau's vapour pressure is 21.144 hPa; the table reads 33 and the equation gives 32.98. At 25 C and 50 percent (15.791 hPa) the table reads 26 and the equation gives 26.21. The table is rounded to whole degrees, so a half-degree allowance is fair. With wind, 25 C, 20 hPa and 3 m/s give 25.5 C, and the page also works backwards from that result to the wind, the vapour pressure or the air temperature.

The limits matter. This version leaves out the sun; the Bureau's second form adds net radiation. It is a comfort index for adults in the shade, not a heat-stress limit for work in the sun, and the wind term uses the wind speed measured at 10 metres.