Articles | Volume 17, issue 24
Technical note
19 Dec 2017
Technical note |  | 19 Dec 2017

Technical note: A noniterative approach to modelling moist thermodynamics

Nadya Moisseeva and Roland Stull

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 0.016 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.

Short summary
This technical note presents simple noniterative approximations for two common thermodynamic relationships used for moist convection. The method offers roughly 2 orders of magnitude improvement in accuracy over the only existing noniterative solution. The proposed approach alleviates the need for costly numerical integration of saturated thermodynamic equations within numerical weather prediction models and in theoretical studies.
Final-revised paper