Geoid height is defined value of a geoid model. There is not much of assume or experimental behind that. It is here for all location. Variables are the position on that particular geoid, which is defined by x,y,z.
All other things are simply values of fast movable things like water and air or other liquids and gases. Those values do not contribute to any value of geoidal height.
'Height above sea level' ? This might have been used hundreds year ago, when all was based on some observed natural phenomena.
As there is nothing like sea level, it can not be used for any practical purpose.
Where average value, not referenced to any particular point, is needed, standard value (in fact rather meaningless) is used. Also called average sea level not telling any particular geographical location, nothing to do with any assumptions or variables. Simply pure theoretical value, just so all use approximately the same reference where ever they are.
Maps can use what ever they like, as long as it is defined and thus known to the user. Many regions or even countries use some kind of local reference height point to which the entries in maps are referenced, as pure geoid height definition might not be very useful for local map use.
There are for example in Europe some very old maps having a mark on the edge: heights displayed are above the average sea level of the mediteran sea.
OK, such maps might be 150 years old, when such reference was sufficient.
what the standard is means difference to 1013.25 hpascal
it has nothing to do with sea level any more as this is valid universally in any place in the world.
And yes, maps are created to a chart datum and this is based on a x,y,z shift , diameter of the elipsoid and flattening.
Positions and also all elevations are based on that, unless there is some regional or national fixed correction applied to all the elevation
There is no sea level involved.
Yes, in my village, the railway station has a height mark and there it is described as height above mean sea surface of Mediterranean sea. But this building stands there since 1898. And stands under national heritage protection.
Using barometric pressure for some cartography in 2024 would be quite a disaster, as heights of building, bridges and what ever would depend entirely on weather.
In addition, even relaying on measured air pressure as in indication of altitude has its own natural limits. Air density varies not in a linear matter with rising height, the temperature makes such measurement non linear and further corrections are needed.
So using air pressure as indication of elevation needs frequent calibration to a known value, obtained otherwise, and the increments can be used for some reasonable time as indication.
