Perspectives towards stochastic and learned-by-data turbulence in Numerical Weather Prediction

The increased social need for more precise and reliable weather forecasts, especially when focusing on extreme weather events, pushes forward research and development in meteorology towards novel numerical weather prediction (NWP) systems that can provide simulations that resolve atmospheric processes on hectometric scales on demand. Such high-resolution NWP systems require a more detailed representation of the non-resolved processes, i.e. usage of scale-aware schemes for convection and three-dimensional turbulence (and radiation), which would additionally increase the computation needs. Therefore, developing and applying comprehensive, reliable, and computationally acceptable parametrizations in NWP systems is of urgent importance. All operationally used NWP systems are based on averaged Navier-Stokes equations, and thus require an approximation for the small-scale turbulent fluxes of momentum, energy, and matter in the system. The availability of high-fidelity data from turbulence experiments and direct numerical simulations has helped scientists in the past to construct and calibrate a range of turbulence closure approximations (from the relatively simple to more complex), some of which have been adopted and are in use in the current operational NWP systems. The significant development of learned-by-data (LBD) algorithms over the past decade (e.g. artificial intelligence) motivates engineers and researchers in fluid dynamics to explore alternatives for modeling turbulence by directly using turbulence data to quantify and reduce model uncertainties systematically. This review elaborates on the LBD approaches and their use in NWP currently, and also searches for novel data-informed turbulence models that can potentially be used and applied in NWP. Based on this literature analysis, the challenges and perspectives to do so are discussed.