Impact of Time Integration Scheme on Supercell Development ATMS-597R Alexandra Jones, Samantha Chiu, David Plummer 8 October 2010

Control vs. Test Simulation Both used Thompson microphysics Control run used 3rd-order Runge-Kutta differentiation in time Test run used 2nd-order Runge-Kutta scheme Larger amplification/phase error with lower-order scheme (Durran 69)

Mesocyclone track (Control run)

Mesocyclone track (Test run)

Low-level reflectivity field at t=60 minutes, when difference in vorticity advective term was most significant

Conclusions Lower-order time differentiation resulted in noisier simulation, but general development was similar In both cases, advection and stretching/divergent terms contributed most to relative vorticity tendency Differences in tendency terms between runs generally small Advection term larger for test run at 60 minutes, but difficult to identify persistent differences visually

Reference Durran, D. R., 1999: Numerical Methods for Wave Equations in Geophysical Fluid Dynamics. Springer, 465 pp.