Modifications to WRF's dynamical core to improve the treatment of moisture for large-eddy simulations

In this study, we reproduce and analyze this sensitivity issue using two stratocumulus cases, one marine and one continental. Results show that (1) the sensitivity is associated with spurious motions near the moisture jump between the boundary layer and the free atmosphere, and (2) these spurious motions appear to arise from neglecting small variations in water vapor mixing ratio (qv) in the pressure gradient calculation in the acoustic substepping portion of the integration procedure.

We show that this issue is remedied in the WRF dynamical core by replacing the prognostic equation for the potential temperature θ with one for the moist potential temperature θm=θ(1 + 1.61qv), which allows consistent treatment of moisture in the calculation of pressure during the acoustic substeps. With this modification, the spurious motions and the sensitivity to the time stepping settings (i.e., the dynamic time step length and number of acoustic sub-steps) are eliminated in both of the example stratocumulus cases.