# [Physics] What’s the altitude of the flat base of Cumulus clouds

atmospheric sciencemeteorologyweather

Is there a formula that describes the altitude of clouds with respect to the local temperature? I think of the flat bases of Cumulus clouds.

Thanks…

According to Ahrens R.

The bases of cumulus cloud can be estimated quite easily when the surface air temperature and dew point are known. If the air is not too windy, we can assume that entrainment of air will not change the characteristics of a rising thermal. Since the rising air cools at the dry adiabatic rate of about 10°C per 1000 m, and the dew point drops at about 2°C per 1000 m, the air temperature and dew point approach each other at the rate of 8°C for every 1000 m of rise. Rising surface air with an air temperature and dew point spread of 8°C would produce saturation and a cloud at an elevation of 1000 m. Put another way, a 1°C difference between the surface air temperature and the dew point produces a cloud base at 125 m. Therefore, by finding the difference between surface air temperature (T) and dew point ($T_{d}$), and multiplying this value by 125, we can estimate the base of the convective cloud forming overhead, as $H_{meter}=  125 (T-T_{d})$ .