Why temperature drops with altitude?

The temperature of the troposphere generally decreases as altitude increases. The rate at which the temperature decreases, is called the environmental lapse rate (ELR). The ELR is nothing more the difference in temperature between the surface and the tropopause divided by the height. The reason for this temperature difference is the absorption of the sun's energy occurs at the ground which heats the lower levels of the atmosphere, and the radiation of heat occurs at the top of the atmosphere cooling the earth, this process maintaining the overall heat balance of the earth. The temperature drop with height  is 6.5 degrees Celsius per 1000 meters/ the temperature drop with height is 0.0065 degree Celsius per 1 meter.

Another interesting information about the increase in the altitude is that:-

Montane Wet temperate forests- the adoption of the term temperate in respect of montane conditions in the tropics was originally put forward by Humboldt in 1817 who generalized that the successive altitudinal zones of vegetation correspond to the latitudinal zones from equator to the poles. An increase of elevation, according to him, about 1,000m. On a tropical mountain would correspond to an increase of about 9⁰ 30’ of latitude, or roughly a difference of 100 m. in altitude could be equivalent to a difference of 1⁰  latitude. According to this, an altitude of about 8000 m. correspond phytogeographycally to the poles!!

Inspite of the obvious general similarity between the physiognomy (in ecology = The apparent characteristics) of the vegetaion at different altitudes and that at latitudes of corresponding mean temperature, this concept has been held to be inappropriate as being far too simple to be general application; for, on closer scrutiny, this similarity will be found to be far from exact. The climate of the equivalent altitudinal and latitudinal zones is never the same, since in a given altitudinal zone at the equator the length of day and the seasonal changes are greatly different.

(Ref:-Nilgiris District Gazatteer)