  Calculations of atmospheric refraction are generally based on a simplified
model of atmospheric density in the troposphere which assumes that the
temperature decreases at a constant lapse rate from sea level up to a height
equal to eleven km, and that afterwards it remains constant. In this model, the
temperature divided by the lapse rate determines the length scale in the
calculations for altitudes less than this height. But daily balloon
measurements across the U.S.A. reveal that in some cases the air temperature
actually increases from sea level up to a height of about one km, and only
after reaching a plateau, it decreases at an approximately constant lapse rate.
Moreover, in three examples considered here, the temperature does not remain
constant at eleven km , but continues to decreases to a minimum at about
sixteen kilometers , and then increases at higher altitudes at a lower rate.
Calculations of atmospheric refraction based on this atmospheric data is
compared with the results of simplified models.
