Analytical Expressions for Temperature Profiles in Model Atmospheres

The altitudinal variation of temperature is traditionally given in tabular form in most neutral atmospheric models. In the homosphere (troposphere, stratosphere and mesosphere), only one table is employed, which is indicative of the average conditions over the entire globe (latitude and longitude; land and water), day (hours) and year (seasons). In the thermosphere, on the other hand, many tables are used corresponding to different exospheric temperatures ranging from 600K to 2000K. It is assumed that the average temperature represents a steady-state condition governed by the time-independent thermal diffusion equation in the vertical dimension, which is nothing but a form of Fick's law in that dimension. It is found that: (1) In the troposphere, the temperature profile is best described by an exponential profile; (2) In the stratosphere-mesosphere region, a Normal distribution adequately fits the temperature profile; and (3) In the thermosphere-exosphere region, a modified inverted exponential profile best describes the observed temperature variation with altitude. By employing a least-squares fit between a simple exponential model and the observed temperature profiles above 120 km, the average exospheric temperature is estimated to be 1350K.