Towards Grid-independent Dynamics in High-resolution Numerical Weather Prediction Models

Since the beginning of numerical weather prediction (NWP), which was performed on O(700 km) grids, advances in computing technology have driven corresponding advances in model resolution. In recent years, operational NWP efforts have reached O(1 km) horizontal resolutions, leading to the use of large-eddy simulation (LES) to simulate the atmospheric boundary layer (ABL). However, the available turbulence closure models for atmospheric LES were designed to model the smallest scales of atmospheric turbulence, leaving operational forecasters and researches in many diverse fields alike without a turbulence model fit for the computing power available to them. This range of resolutions is known as the "gray zone" or "terra incognita" in the atmospheric turbulence literature, and will be the focus of much discussion in this dissertation. Further, the results will be presented in a way that is visual and digestible to a user of LES whose expertise is not necessarily in theoretical turbulence.Here, the Weather Research and Forecasting (WRF) model is used to give a thorough and visual demonstration of the inadequacies of the more popular LES turbulence closure models, the Smagorinsky-Lilly and TKE-1.5 models, at gray-zone resolutions, and an explanation of the behavior is offered. Two alternatives, both with multiple flavors, the dynamic reconstruction model (DRM) and an alternative-anisotropic formulation of the classical eddy-viscosity models, are presented as potential remedies to the gray-zone issue. Studies are conducted first for an idealized free-convection case with constant surface heat flux and zero mean wind. A more realistic initial profile with an initial wind and geostrophic forcing is then considered. Finally, three more cases are considered with various surface heat flux values and initial wind profiles. Both the DRM and alternative-anisotropic eddy-viscosity models are able to deliver much more consistent results at coarse resolutions when considering planar-averaged profiles of potential temperature and velocity, resolved velocity fields and resolved turbulent kinetic energy, and their performance inspires interesting topics of future work regarding the representation of scales of energy in the atmosphere. The implementation of the anisotropic eddy-viscosity model in general, as well as the anisotropic Smagorinsky-Lilly model specifically, in the WRF model is also considered, resulting in a change in the WRF turbulent diffusion routines and a demonstration of improvement seen at coarse resolutions by reformulating the anisotropic Smagorinsky-Lilly model to partition stress terms into horizontal and vertical components. An additional chapter presents the gray zone problem as it relates to complex terrain