This study presents the development of a so-called Turbulent Kinetic Energy (TKE)-l, or TKE-l, parameterization of the diffusion coefficients for the representation of turbulent diffusion in neutral and stable conditions in large-scale atmospheric models. The parameterization has been carefully designed to be completely tunable in the sense that all adjustable parameters have been clearly identified and the number of parameters has been minimized as much as possible to help the calibration and to thoroughly assess the parametric sensitivity. We choose a mixing length formulation that depends on both static stability and wind shear to cover the different regimes of stable boundary layers. We follow a heuristic approach for expressing the stability functions and turbulent Prandlt number in order to guarantee the versatility of the scheme and its applicability for planetary atmospheres composed of an ideal and perfect gas such as that of Earth and Mars. Particular attention has been paid to the numerical stability and convergence of the TKE equation at large time steps, an essential prerequisite for capturing stable boundary layers in General Circulation Models (GCMs). Tests, parametric sensitivity assessments and preliminary tuning are performed on single-column idealized simulations of the weakly stable boundary layer. The robustness and versatility of the scheme are assessed through its implementation in the Laboratoire de Météorologie Dynamique Zoom GCM and the Mars Planetary Climate Model and by running simulations of the Antarctic and Martian nocturnal boundary layers.

In planetary atmospheres, turbulent motions actively contribute to the mixing of quantities such as heat, momentum, and chemical species. Such motions are not resolved in coarsegrid atmospheric models and have to be parameterized. The parameterization of turbulent mixing should ideally be based on physical laws and sufficiently sophisticated to realistically represent the full spectrum of motions over the full range of stability encountered in the atmospheres. However, it also necessarily contains a number of closure parameters not always well identified and whose values are determined empirically-thereby questioning the universality of the parameterization and its potential application over the full globe or even to other planets-or adjusted to guarantee the numerical stability of the model. This study presents the design of a turbulent mixing parameterization that can be fully calibrated and applied in planetary atmospheres such as that of Mars. We then calibrate the parameterization on an idealized simulation set-up and test its robustness and performance by running simulations of the Antarctic and Martian atmospheres.