A Reevaluation of Ice–Liquid Water Potential Temperature

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Abstract
A synthesis of previous studies suggests the need for new, more accurate approximations for ice–liquid water potential temperature (θil), a thermodynamic variable utilized in some numerical models. Starting from equations presented in a previous study, two new approximate formulations of θil are derived, along with their governing equations. The new formulations are significant improvements over previous ones because no terms are dropped during their derivation and no Taylor series approximations are utilized. The governing equations for the new formulations reveal conditions under which θil can be considered a conserved variable. Potential temperature lapse rates determined from a reference thermodynamic equation are compared numerically against lapse rates determined from several approximations of θil. Many of the findings agree with previous studies. However, the results show that a commonly used formulation does not account for the specific heats of water, and thus has an inherent cold bias. ... Abstract A synthesis of previous studies suggests the need for new, more accurate approximations for ice–liquid water potential temperature (θil), a thermodynamic variable utilized in some numerical models. Starting from equations presented in a previous study, two new approximate formulations of θil are derived, along with their governing equations. The new formulations are significant improvements over previous ones because no terms are dropped during their derivation and no Taylor series approximations are utilized. The governing equations for the new formulations reveal conditions under which θil can be considered a conserved variable. Potential temperature lapse rates determined from a reference thermodynamic equation are compared numerically against lapse rates determined from several approximations of θil. Many of the findings agree with previous studies. However, the results show that a commonly used formulation does not account for the specific heats of water, and thus has an inherent cold bias. ...

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