A prognostic TKE scheme in the IFS model

The global IFS model currently utilizes a first-order closure scheme for turbulence parameterization. While this approach is reliable and sufficiently accurate at coarser resolutions, a higher-order scheme is expected to improve the representation of turbulent processes at higher resolutions. A prognostic turbulence kinetic energy (TKE) scheme is a natural candidate for such an upgrade, as it introduces a higher-order closure while maintaining numerical stability and keeping the computational cost feasible. Its main advantage over first-order closure lies in its ability to introduce a "memory" effect, by retaining information about turbulence intensity over time and space. This enables a more realistic representation of flow and turbulence evolution.

Although prognostic TKE schemes are well established in limited-area models, their implementation in global modeling frameworks presents additional challenges due to the wide range of regimes that must be represented in a global context. To address this, a prognostic TKE scheme has been implemented in the IFS model, based on the formulation used in the global ARPEGE model. However, several extensions and model-specific calibrations have been applied to adapt it to the IFS framework.

These modifications include an expanded formulation of the turbulence length scale, revised stability dependency functions, and the integration of prognostic cloud fraction into the stability parameter calculation. Furthermore, the TKE source terms are partially computed using an equilibrium assumption, and the advection of TKE is explicitly included in the solver. Particular attention has also been paid to the improved identification and treatment of stratocumulus regions.

The performance of the new prognostic TKE scheme in the IFS is evaluated globally against observations and analysis and for selected case studies.