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No, a standard barometer does not stop working at sea level.
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Sea level reference is used to define the height of specific land as compared to the sea, taken as a standard. Karachi is about 150 meters above sea level.
The height of a landform on Earth is DEFINED as its height above sea level since sea level is the closest thing on Earth to a constant or standard starting point. Sea level itself changes with the tides and wind and weather, so we use what is called "mean sea level" which is an average of measured levels at a given place over an extended time.
Sea level is a standard 'height' from which you can measure the relative height of objects (ie. cities) as such, high above sea level would refer to something 1,000+ metres above sea level... or whatever definition you think appropriate.
We call this "elevation".
Sea Level
The height of a place from sea level can be calculated using a device called an altimeter, which measures the atmospheric pressure. By comparing the atmospheric pressure at the location with the standard atmospheric pressure at sea level, the height above sea level can be determined. GPS receivers can also provide accurate altitude information by using satellite signals.
800mb (now hectoPascals) is approx. 6500ft or 2000m above sea level. It is not a well-used Standard Level, as 850hPa is close and the next one is 700hPa.
Height from sea level.
The Wave Height measuring Network.
atmospheric pressure ... the diff. in the two pressure in which it will find the height from the level of sea