Relating Static Energy to Potential Temperature: A Caution

Abstract

The relationship between dry static energy and potential temperature, cp? = cpT + gz, is exact for an adiabatic temperature profile, and extremely close to exact for an isothermal profile. Even though it is extremely accurate, its use in atmospheres with nonadiabatic temperature profiles can lead to significant errors when comparing the entropies of isolated atmospheric layers. Use of the relation in this context leads to the incorrect conclusion that an adiabatic temperature profile has greater entropy than an isothermal profile for the same static energy. The relation fails in this application because of the extreme sensitivity of the column-integrated entropy to temperature.