CMAQv5.0.2 Vertical advection time step
Under Courant-Friedrichs-Lewy (CFL) numbers greater than 10 the time step and vertical velocity re-diagnosis in CMAQ could become unstable. These were typically encountered under the following conditions: large CTM_MAX_SYNC environment variable, climate downscaling, and/or 4km and finer grid resolution. To improve the stability and model run time, a dynamic vertical advection sub-time step algorithm was implemented. This was done in two steps: First, the selection of a sub time step that satisfied a 0.9 CFL number using the initial vertical velocity. This resulted in a larger time step for CFL < 9 and a smaller time step for CFL > 9. Second, The ppm scheme in vpp.F parameterizes the vertical velocity as a 3rd order polynomial of the flux between grid cells.
Prior to this update, a new vertical velocity was estimated using a linear approximating of the flux during the sub-time step. This could result in an overestimate of the vertical velocity and instability in the ppm scheme. This was addressed by interpolating the vertical velocity using a linear approximation of the square root of the flux. The square root of the flux was chosen because the 3rd order coefficient in the ppm scheme is typically small and this approximation was found to be stable and faster than one based on the cube root.
Significance and Impact
The vertical advection sub time step is now dynamic and CTM_MAX_SYNC can be set to an arbitrarily large number, e.g. 720. This allows the model to find an optimally large time step and less iteration of model processes resulting in up to a 20% reduction model run time. The model concentration fields are numerically different due to the selection of different time steps. However, these differences are orders of magnitude smaller than typical model concentrations and do not impact the model evaluation against observations.
Jesse Bash, Atmospheric Modeling and Analysis Division, U.S. EPA