The German Weather Service DWD provides a formula in their operating 
documents:

DWD VuB2 BUFR 
<https://www.dwd.de/DE/leistungen/pbfb_verlag_vub/pdf_einzelbaende/vub_2_binaer_barrierefrei.pdf?__blob=publicationFile&v=4>
 page 
28

SP * exp (g / R * H / (TT + VP * Ch + a * H / 2))


   - SP  measured pressure
   - g  earth acceleration 9.80665 m/s^2
   - R  gas constant 287,05 J/kgK
   - TT  air temperature in K
   - VP  actual vapor pressure
   - a  vertical temperature gradient 0.0065 K/m
   - H  altitude of the pressure gauge *above NN*
   - Ch  average vapor pressure gradient 0.12 K/hPa
   
The formulae of the vapor pressure and saturation vapor pressure are found 
in that document as well.

Wikipedia says about NN:

"*Normalnull* ("standard zero") or *Normal-Null* (short *N. N.* or *NN* ) 
is an outdated official vertical datum 
<https://en.wikipedia.org/wiki/Vertical_datum> used in Germany. Elevations 
using this reference system were to be marked *Meter über Normal-Null* (“meters 
above standard zero”). *Normalnull* has been replaced by *Normalhöhennull 
<https://en.wikipedia.org/wiki/Normalh%C3%B6hennull>* (NHN)."

The same DWD document says about the station data to send within synoptic 
messages according to the WMO BUFR standard:


   - 0 07 030 station elevation *above NN*
   - 0 07 031 pressure gauge altitude *above NN*
   
The WMO specifies BUFR in Manual on Codes, volume I.2 
<https://library.wmo.int/doc_num.php?explnum_id=11283>. They say there:

"Geometric altitude. Vertical distance (Z) of a level, a point or an object 
considered as a point, measured from mean sea level."

"Height of station ground above mean sea level is defined as the height 
above mean sea level of the ground on which the raingauge stands or, if 
there is no raingauge, the ground beneath the thermometer screen. If there 
is neither raingauge nor screen, it is the average level of terrain in the 
vicinity of the station (Reference: Guide to Meteorological Instruments and 
Methods of Observation (WMO-No. 8), 1996)."

"Height of barometer above mean sea level, referring to the location of 
barometer of a station, does not redefine the descriptor 0 07 030."


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