Development of stable boundary layer parameterizations in numerical weather prediction models: a scale dependent dynamic LES modeling approach

Numerical weather prediction (NWP) modeling always involves boundary layer (BL) parameterization schemes to represent: (i) turbulent transfer of heat, momentum and moisture between the surface and the lowest computational level, and also (ii) turbulent transport of the same quantities across model levels inside the BL. Typically, a turbulence K-closure model specifies the turbulent flux of a given quantity at a given level proportional to the vertical gradient of that quantity using the concept of eddy-diffusivity. The eddy-diffusion coefficients strongly depend on prescribed stability correction functions, and in turn, play crucial roles in BL parameterization schemes. Unfortunately, performances of the field-observations-based correction functions – like Monin-Obukhov stability correction functions and their variants – in operational forecasting under very stable conditions were found to be extremely poor (Beljaars and Viterbo, Clear and Cloudy Boundary Layers, 1998; Viterbo et al., Q. J. R. Meteorol. Soc., 1999; King et al., Q. J. R. Meteorol. Soc., 2001). This prompted ECMWF among others to propose artificial stability correction functions (e.g., Louis-Tiedtke-Geleyn – LTG scheme and its revised version), which are not physically based but “inspired by model performance” (Beljaars and Viterbo, Clear and Cloudy Boundary Layers, 1998; Viterbo et al., Q. J. R. Meteorol. Soc., 1999).

Stability correction functions are integral parts of every present-day NWP model and from a scientific perspective, specifying them in an ad-hoc manner is not satisfactory. It has to be emphasized that the shapes of the field-observations-based correction functions in the very stable regime are quite uncertain and a subject of ongoing debate. This ambiguity arises from the fact that stable boundary layer (SBL) measurements are rarely free from nonstationarities (e.g., bursting, mesoscale disturbances, wave activities) and the observations become increasingly uncertain with increasing stability. This inevitable limitation highlights the need for high-resolution spatio-temporal simulated information about these flows to supplement the observations. With the recent developments in computing resources, three dimensional numerical simulations (particularly large-eddy simulation – LES, at present the most efficient technique available for high Reynolds number flow simulations, in which the larger scales of motion are resolved explicitly and the smaller ones are modeled) of turbulent flow in the atmospheric boundary layer can provide this kind of information. Unlike NWP models, a few state-of-the-art LES models – for example, the Scale Dependent Dynamic models (Porté-Agel et al., J. Fluid Mech., 2000; Porté-Agel, Boundary-Layer Meteorology, 2004) – are even capable of dynamically adjusting (i.e., without tuning) model coefficients to account for atmospheric stability. In other words, these specific LES models do not require any ad-hoc prescription of stability correction functions for turbulent flux parameterizations inside the BL. Therefore, these LES models have the potential to evaluate existing stability correction functions and also come up with revised and improved yet physically-based stability formulations for SBL parameterization.

In this work, we propose a new form of SBL parameterization for large-scale models based on a suite of idealized large-eddy simulations of varying atmospheric stabilities utilizing the scale dependent dynamic approach.