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, θ_w), as well as its corresponding inverse form θ_w(P, T), where θ_w is wet-bulb potential temperature. Our method allows direct calculation of T(P, θ_w) and θ_w(P, T) on a thermodynamic domain bounded by −70 ≤ θ_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, θ_w) and θ_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.