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 L from sea level up to a height h _ { t } \approx 11 km , and that afterwards it remains constant .
In this model , the ratio T _ { o } / L , where T _ { o } is the temperature at the observer ’ s location , determines the length scale in the calculations for altitudes h \leq h _ { t } .
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 h _ { p } of about one km , and only after reaching a plateau with temperature T _ { o } ^ { \prime } at this height , it decreases at an approximately constant lapse rate.Hence , in such cases , the relevant length scale for atmospheric refraction calculations in the altitude range h _ { p } \leq h < h _ { t } is T _ { o } ^ { \prime } / L , and the contribution for h \leq h _ { p } has to be calculated from actual measurements of air density in this range .
Moreover , in three examples considered here , the temperature does not remain constant for h _ { t } \leq h , but continues to decreases to a minimum at h _ { m } \approx 16 km , 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 .