Supra-domain-scale parameterizations provide a way to represent the behavior of large-scale circulations in a model domain that is too small to resolve them explicitly. (See the description given here). In this study, the WTG and WPG approximations are compared numerically against a benchmark simulation in a bowling-alley domain. The premise of the relaxed form of WTG -- that vertical velocity is equal to buoyancy times a positive timescale -- is found to be violated by thick layers of negative buoyancy in steady-state ascent. The premise of WPG -- that horizontal divergence and pressure anomalies are colocated -- is validated by these simulations. WPG is also found to out-perform WTG in the representation of both transient and steady-state motions. This evidence suggests that WPG is a relatively accurate method for parameterizing supra-domain-scale (SDS) dynamics.
Net vertical displacements (integrals over time of vertical velocity) for a benchmark bowling-alley simulation (top row), WPG (middle row), and WTG (bottom row). The left column shows the net displacements generated during the first and second hours to give a sense of the temporal evolution of the column. The right column gives the net displacement during the entire day. Dashed curves are from dry simulations and solid curves are from simulations containing lower-tropospheric humidity.