Improving Spectral Resolution of Finite Difference Schemes for Multiscale Modeling Applications Using Numerical Weather Prediction Model

Advances in high performance computing make possible simulations of atmospheric flows simultaneously resolving large synoptic scales and turbulent eddies in boundary layers. These multiscale simulations bridge numerical weather prediction (NWP) and large eddy simulations (LES). Such numerical simulations represent a number of challenges including development of scale aware parameterizations of physical processes, numerical effects of variable spatial resolution or grid nesting, stability of advection schemes vs. spectral resolution, etc. Here, we focus on the need for better spectral resolution of numerical schemes for multiscale simulations that include resolving turbulent eddies. Idealized simulations of canonical, horizontally homogeneous atmospheric boundary layers are usually carried out with periodic lateral boundary conditions that enable effective utilization of pseudospectral methods. Pseudospectra simulations achieve maximum possible spectral resolution on a given grid. Good spectral resolution can also be achieved with high even order finite difference schemes. However, in the presence of strong gradients such schemes can result in spurious high frequency oscillations. Such numerical artifacts can be avoided if upwind differencing is utilized. Upwind schemes are numerically dissipative and result in inferior spectral resolution. We therefore propose a hybrid scheme developed by Fang et al. (2013) that combines high order upwind and centered schemes. We implemented the hybrid scheme in the Weather Research and Forecasting model and HIGRAD model. We then carried out a series of LES of convective boundary layers characterized by different stability parameters zi/L. The results of these LES were compared to pseudospectral LES. The results show that the hybrid scheme provides optimal performance with enhanced spectral resolution compared to upwind schemes and no undesired numerical artifacts associated with centered schemes of similar order.