A noniteratiave 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,θw), as well as its corresponding inverse form θw(P,T), where θw is wet-bulb potential temperature. Our method allows direct calculation of T(P,θw) and θw(P,T) on a thermodynamic domain bounded by −70 ≤ θw < 40°C, P > 1 kPa and −100 ≤ T < 40°C, P > 1 kPa, respectively. The proposed parameterizations offer high accuracy (mean absolute errors of 0.017°C and 0.002°C for T(P,θw) and θw(P,T), respectively) on a notably larger thermodynamic region than previously studied. The paper includes a method summary, as well as a ready-to-use tool to aid atmospheric physicists in their practical applications.