Reconciling the Discrepancies of Equivalent Potential Temperatures in Atmosphere: A General Pathway Rooted in Entropy Conservation

Equivalent potential temperature is a widely used thermodynamic variable in atmospheric science. However, various formulations have been proposed in the literature over the last one and half-century but their differences and connections are not straightforward to be understood. In this study, a general pathway is proposed to understand the differences and consistency between equivalent potential temperatures in the atmosphere. It is found that previous formulations of equivalent potential temperature can be explained in a mathematically and physically consistent way, and can be easily derived from the general pathway. In addition, new formulations of equivalent potential temperature under certain processes can be defined under the general pathway, without sophisticated mathematical derivation and inconsistent thermodynamic approximations. Our study provides insights to define new thermodynamic variables that can be applied to a wide range of physical conditions and advance our understanding of weather and climate systems.