tl;dr: What elevation is barometric reduced to?  0 meters in NAVD88?
Some other height datum?   What about other countries, WMO, etc?

I'm going down the rabbit-hole of barometer calibration.   I'm trying to
address it in two parts: calibrating station pressure, and then using
the correct altitude.  This is part trip report and part question.

I realize that my question has close to zero practical value.  But nerds
like to measure things correctly anyway.

For station pressure, I have a VP2, a Brunton "Atmospheric Data Center"
that measures pressure (also T/H), a BME280, and a BME680.
Provisionally treating the Brunton as a correct reference (because it's
portable, so I can move it to my various sensors and at some point take
it to visit other people's stations), I find the following offsets:

  VP2           +0.1 hPa
  BME680        +2.5 hPa
  BME280        +1.5 hPa

It's encouraging that the Brunton and VP2 are so close (resolution 0.1
and 0.01 hPa respectively), but of course they could be off the same
amount.  It is clear that that BME280 family isn't that accurate, but
that's no surprise given the cost and intent.  However the offsets are
pretty stable.

For reference

  - a height change of 1 meter corresponds to 0.12 hPa. (That's 0.09
    mils of Hg per foot :-)

  - WMO seems to specify 0.1 hPa as the required uncertainty for field
    instruments.

For altitude, I borrowed some 25-year old survey-grade GPS equipment,
and am in the process of measuring from that mark to where my console
is.  The data is natively in "NAD83(2011) epoch 2010.0 Height above
Ellipsoid", but I can transform to NAVD88 or to "WGS84 Orthometric
Height".  I expect to end up with a height value that is accurate to
about 10 cm in HAE and not too much more in orthometric heights.

My questions are:

  - When people talk about reducing a station pressure reading to "sea
    level", what do they mean?

  - Specifically, what does NWS mean?  Given the overall US government
    approach, I would guess they mean "0m elevation in NAVD88".

  - What is the situation with other countries' national weather
    organizations?

  - What is the situation with the WMO?  It seems there is an idea that
    each country might specify a height reference more precisely and is
    to report it.  There is a hint of EGM96 in CWOP-WM08 -- but EGM96
    has long since been superceded.  Hence mentioning "WGS84 Orthometric
    Height" above.

I would appreciate not only an answer but a pointer to where NWS, other
national agencies, and WMO specify this.

(As a side note for people who find my question boggling, "sea level" is
a concept that really only applies to a particular tide gauge station,
and the elevations of different stations' zero points are different.
Referring to "sea level" in a general way introduces fuzz of around a
meter.)

Greg

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