The apparent position of the Sun is shifted from its true position by atmospheric refraction so any measurement of its altitude needs to be corrected. The Earth's atmosphere varies in composition, pressure and temperature with height and models such as the standard atmosphere have been created for it.
With these models one can one can compute the curved path of light through the atmosphere by dividing it vertically into thin shells. Bessel's tables were among the most accurate but changes in standards have resulted in their discontinued use. These tables contained the refractions for the standard reference values of pressure and temperature as a function of zenith distance as well as corrections for changes in pressure and temperature near the ground. The relative humidity of the air also contributes some reftaction. These parameters should be recorded at the time of the measurements if later corrections are to be made.
For the altitudes of the Sun at the Solstices in the tropics and middle latitudes the correction for refraction is small and should be less than 3 minutes of arc. One minute of arc along a meridian is a nautical mile.