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 0.016 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 and a ready-to-use tool to aid atmospheric physicists in their practical applications.
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