Parameterizing Large-Scale Dynamics: A Comparison of WTG and WPG

The weak temperature gradient (WTG) approximation and an alternative, the weak pressure gradient (WPG) approximation, are evaluated using analytical solutions and cloud-resolving simulations. Analytically, WPG reproduces key features of the 3D solutions that WTG is unable to generate, including ascending regions of negative buoyancy and adiabatic lifting below a transient buoyancy anomaly. Numerically, the assumptions of WPG are found to be approximately satisfied by large 3D cloud-resolving simulations, while the assumptions of WTG are clearly violated. When implemented in a cloud-resolving model, it is found that WPG correctly reproduces the behavior of the 3D simulations, including vertical velocities and convective triggering by buoyancy anomalies aloft. WTG, on the other hand, is unable to reproduce the vertical velocity profiles or the convective triggering.