Sensitivity of the QBO to the turbulent diffusion scheme in an idealized model

Vertical diffusion in the free atmosphere due to turbulence has received limited attention in the literature, but its parameterization has significant effects on the models' general circulation. In the new cycle 50r1 of the ECMWF Integrated Forecasting System (IFS), scheduled to become operational in February and already used in the ERA6 reanalysis currently in production, the turbulence scheme was updated to reduce vertical momentum and heat diffusivities in the lower stratosphere. This change is motivated by persistent biases in IFS seasonal forecasts in that region, including biases in the amplitude and vertical descent of the simulated Quasi-Biennial Oscillation (QBO) (ECMWF Newsletter No.185, Autumn 2025). 

In this study, we use a recently developed idealized two-dimensional (longitude–altitude) tropical channel model to investigate, in a controlled framework, the impact of these recent changes in the vertical diffusion scheme on the QBO. The model is based on the Weather Research and Forecasting (WRF) model and reproduces, in two dimensions, the canonical wave–mean-flow interaction regime of the QBO following Holton, Lindzen, and Plumb: two monochromatic, planetary-scale gravity waves diabatically forced in the lower model layer propagate upward and force the mean flow as they dissipate. We compare a cycle-49–like long-tail Richardson-number closure (Viterbo, 1999, fLTG) with a cycle-50–like blended stability function that reduces vertical mixing over a finite layer in the lower stratosphere and relies on a cycle-38–like short-tail Richardson-number closure (Beljaars and Holtslag, 1991, fMO). 

The new reduced diffusion formulation substantially modifies the simulated QBO, with larger amplitudes in the lower stratosphere and a longer period. This shows how an idealized framework can help identify key sensitivities in a global forecasting system.