Technical note: A noniterative approach to modelling moist thermodynamics

Abstract

Formulation of noniterative mathematical expressions for moist thermodynamics presents a challenge for both numerical and theoretical modellers. This technical note offers a simple and efficient tool for approximating two common thermodynamic relationships: temperature, T , at a given pressure, P, along a saturated adiabat, T .P; w/, as well as its corresponding inverse form w.P;T /, where w is wet-bulb potential temperature. Our method allows direct calculation of T .P; w/ and w.P;T / on a thermodynamic domain bounded by 70 w < 40 C, P > 1 kPa and 100 T < 40 C, P > 1 kPa, respectively. The proposed parameterizations offer high accuracy (mean absolute errors of 0.016 and 0.002 C for T .P; w/ and w.P;T /, respectively) on a notably larger thermodynamic region than previously studied. The paper includes a method summary and a ready-to-use tool to aid atmospheric physicists in their practical applications.