Open AccessRelating Static Energy to Potential Temperature: A Caution
Author(s) -
Alex J. DeCaria
Publication year - 2007
Publication title -
journal of the atmospheric sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.853
H-Index - 173
eISSN - 1520-0469
pISSN - 0022-4928
DOI - 10.1175/jas3906.1
Subject(s) - adiabatic process , isothermal process , potential temperature , thermodynamics , context (archaeology) , potential energy , entropy (arrow of time) , physics , statistical physics , mechanics , materials science , atmospheric sciences , classical mechanics , geology , paleontology
The relationship between dry static energy and potential temperature, cpθ = 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.