the climbing rate gauge should have HUGE variations caused by atmosphere

[nadasero]

Because of this I am using altimeters on my bike since about 20 years. They are very precise if it goes for altitude changes. They measure in steps of one Meter and if you hold them over your head, you get usually two meters more than on the ground.

Today I'm using a GPS-System (Garmin Edge 705). It has a barometric altimeter in addition to the GPS because this is more precise for small altitude changes. It gives precise readings for the steepness of a climb and the climbing speed.

The absolute precision is not that good. Over a day, the error can grow up to 100 meters if the weather changes. Typically it is less than 20 meters. A plane, flying from one weather system to the next can see changes of more than 50 mbar which can add up to an error of 500 meters at see level.