Verification of the Time-Split Method for Higher-Order Diffusion in the Spectral Element Method Model on a Cubed-Sphere Grid

Abstract

This study used the time-split method for higher-order diffusion in a global numerical weather prediction model of the spectral element method on a cubed-sphere grid, and verified its performance compared to those of the explicit and implicit timestep diffusion schemes. Because the spectral element method on a cubed-sphere grid involves intrinsic characteristics of eigenvalues of the Laplacian operator, allowable timestep sizes are more restricted for stable time integration in higher-order diffusion. For example, the 6th-order diffusion significantly limits the timestep size for adequate filtering of small-scale numerical noise during simulation. The time-split scheme can be an alternative to overcome the severe constraints on the timestep size and allow the model a timestep size as large as is potentially acceptable even in higher-order diffusion, while maintaining atmospheric kinetic energy compared to that of the explicit and implicit schemes. During analysis of the amplification factor and numerical simulation of the schemes, it was shown that the time-split scheme has a theoretical response comparable to that of the explicit and implicit schemes. The numerical simulations were conducted using the Korean Integrated Model (KIM) with a 6th-order diffusion operator of three different diffusion schemes at resolutions of 0.25- or 0.125-degree grid spacing. The time-split scheme yields a forecast performance similar to both the explicit and implicit timestep schemes while greatly reducing the computational time.