Regime-Dependent Turbulence Length-Scale Formulation for NWP Models Based on Turbulence Kinetic Energy, Shear, and Stratification

Abstract This paper presents a new turbulence length scale (TLS) formulation based on turbulence kinetic energy, shear, and stratification. Starting from the well-known parcel-based method, several updates are introduced to obtain (i) a smooth and stability-dependent near-surface transition toward the similarity theory-based TLS, (ii) a regime-dependent TLS decrease near the planetary boundary layer (PBL) top, and (iii) a nonvanishing (constant) upper-air TLS to support the jet stream-related turbulence. The new formulation’s TLS profile better matches its LES-diagnosed counterpart in idealized stratocumulus and very stable PBL cases, thus improving the PBL structure and decay rate of turbulence in aloft layers. Simultaneously, the performance in convective cases is nearly neutral to the reference formulation. Aiming its implementation in the 3D operational numerical weather prediction model, the new TLS formulation is evaluated in inversion and mesoscale convective system cases. Thereby, a spatial distribution of cloudiness and precipitation better corresponds to products derived from meteorological satellites and radars. Furthermore, the comparison with atmospheric soundings and tower measurements points to improved wind speed and temperature profiles within the PBL and turbulent fluxes in the surface layer. The preliminary objective verification suggests (i) the essential role of so-called κ scaling, (ii) a nearly neutral upper-air performance with the reference formulation, (iii) a decrease in the RMSE of cloudiness and random error of 2-m temperature (1.5%–2.0%), and (iv) a potential to improve the 10-m wind speed prediction for categories above the 90th percentile (3.0%–6.5%). Finally, we discuss possible further upgrades of the turbulence scheme used in our model. Significance Statement The length scale is an empirical component closing the turbulence parameterization in most of today’s weather prediction and climate models. It represents a dimension of the most energetic turbulence eddies and is typically defined using algebraic formulations or simple physical concepts. We address the impact of turbulence length scale on the forecast and elaborate on the necessary adjustments of a frequently utilized parcel-based formulation preceding its implementation into the 3D operational numerical weather prediction model. Thereby, we show its added value in predicting high-impact weather situations, e.g., inversion-related clouds and fog, convective storms, and extreme wind, while maintaining a nearly neutral statistical performance compared to the reference formulation over an extended period.