Pressure calculations (QNH-QFE-QFF)

QNH : hPa
QFE : hPa
QFF : hPa
QFE: Standard reduction calculation based on a rearrangement of the hypsometric equation; Ps is the measured pressure, Hs is the height of the barometer above station reference level, g = 9.81 ms-1

$$QFE = P_s \left (1 + \frac{gH_s}{RT} \right)$$
QNH: There are a number of QNH calculation methods in use around the world by different organisations. The method used here is taken from the International Meteorological tables (International Meteorological Committee 1890) and is the method in use by the UK Meteorological Office. It is suitable for when the barometer is not more than 350 m above mean sea level.

The correction M in hPa, to be added to the observed pressure (corrected for instrument error) is given by: $$M = p(10^m-1)$$ where: $$m=\frac{h}{18429.1 + 67.53 t + 0.003 h}$$ p = barometer level pressure in hPa.
t = the observed temperature at station level in degrees Celsius.
h = the height of the barometer, in metres, above the level at which the corrected pressure is required i.e. mean sea level for QFF, official aerodrome elevation for QFE and touch-down zone elevation for runway QFE.
If the barometer is below the level for which corrected pressure is required h will be negative.

The correction to be added to the observed (barometer level) pressure to obtain QNH is QNHCOR and is given by: $$QNHCOR = AA + (BB-1) \times p + BB \times QFECOR$$ where: $$AA = 0.022857 \times H$$ $$BB = 1 + (9.6 \times {10}^{-5} \times H) + (6 \times {10}^{-9} \times {H}^{2})$$ H = official aerodrome elevation, in metres, above mean sea level.
p = barometer level (observed) pressure
QFECOR = correction applied to the barometer level pressure to obtain QFE

QFF: Calculated using the Swedish Meteorological and Hydrological Institute method:
$$QFF = QFE * e^{\frac{H * 0.034163 (1 - 0.0026373 cos\phi)}{T_1}}$$
Φ is the station latitude, H the elevation. T1 is a way of taking account of winter inversions: If t is the air temperature:
$$t<-7^\circ C \Rightarrow T_1 = 0.5 * t + 275$$ $$-7^\circ C < t < + 2^\circ C \Rightarrow T_1 = 0.535 * t + 275.6$$ $$t > + 2^\circ \Rightarrow T_1 = 1.07 * t + 274.5$$