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What is the definition of the tropopause.
tropopause altitude varies with latitude.
The tropophere is 55 to 65 thousand feet at the equator and 25 to 30 thousand feet at the poles.
That is a variation of 16.7 to 19.8 km at the equator and 7.6 to 9.1 km at the poles.
That is a variation of 10.1 to 12.3 miles at the equator and 4.7 to 5.6 miles at the poles.

Density decreases with altitude.
The first figure show on the right how the molecules of air get spaced out as the pressure decreases. However the curves showing the red and blue line decrease of density and pressure with no scale on the X axis except the subjective low to high is dumb. The next chart showing quantification pressure in millibars is far more informative.
99.9% of the Atmosphere is below 48km
99.0% of the Atmosphere is below 32km
90.0% of the Atmosphere is below 17km
50.0% of the Atmosphere is below 5.5km

but but but... Is 50% or 500 millibar defined as the tropopause?

Does latitude change the mean tropopause height?

Does a high pressure area and low pressure area effect the mean tropopause height?

Temperature relapse rate.
The relapse rate is the cooling of the atmosphere with altitude. Constants for this vary for the atmosphere below the tropopause.

REF: atmospheric_structure.html The troposphere is the layer closest to the Earth's surface. The graph of temperature change indicates that air temperature decreases with an increase in altitude through this layer. Air temperature normally decreases with height above the surface because the primary source of heating for the air is the Earth. The rate of change in temperature with altitude is called the environmental lapse rate of temperature (ELR) The ELR varies from day-to-day at a place, and from place to place on any given day. The normal lapse rate of temperature is the average value of the ELR, .65o C /100 meters. That is, at any particular place and on any given day the actual ELR may be larger or smaller, but on average has a value of .65o C /100 m. So if I went outside today it could be .62o C /100 m and then tomorrow it might be .68o C /100 m. The ELR also varies from place - to - place on a given day. That is, at Chicago, Illinois it might be .65o C /100 m and on the same day it could be .62o C /100 m over London, England .

info in this html found originally from google image search troposphere temperature latitude

http://cimss.ssec.wisc.edu/goes/sndprf/sndprf.htm W. Paul Menzel APPLICATION OF GOES-8/9 SOUNDINGS TO WEATHER FORECASTING AND NOWCASTING
Explanation of the geostationary sounders measuring atmospheric radiances in eighteen infrared spectral bands.