Improving the Efficiency of Non-hydrostatic Models using a Explicit-Implicit Vertical Advection Scheme
Simulation of clouds and convection is a computationally intensive problem and requires numerical methods that are efficient and flexible over a large range of grid spacings and atmospheric flow regimes. Computational power has now increased sufficiently to enable the use of the fully compressible equations with convection-permitting resolutions within global models of the deep atmosphere. These models, referred to as Convective Allowing Models (hereafter, CAMs), often employ grids having large aspect ratios where dx >> dz. The model’s time step is then often constrained by the vertical Courant number in small regions where strong convective updrafts and downdrafts are occurring. To use a bigger time step and increase efficiency, some operational CAMs employ damping methods to reduce the vertical velocity to maintain numerical stability for the prescribed time step. This is a form of filtering the solution, which can have significant impacts on the updraft speeds, and potentially significantly alter the transport of water substance and other tracers into the upper troposphere. A first attempt to work around this problem used a semi-Lagrangian discretization in the vertical thus enabling a stable larger Courant number – but this method has been shown to be formally unstable when combined with split-explicit time-splitting methods. A second approach employed a 5-step Runge-Kutta scheme with a larger stability region, enabling a larger time step. Experiments show that the increase in time step is not large enough to “pay” for the extra computation, even in a full physics model. The talk will focus on a third method which was first proposed by Shchepetkin in 2015 for the ROMs ocean model. This method breaks the vertical advection into explicit and an implicit components resulting in a scheme that appears stable for vertical Courant numbers as large as 3 or more. The method has been implemented in the WRF model. Examples of stable integrations will be shown for several applications.