The Spectral Weak Temperature Gradient Approximation

The weak temperature gradient (WTG) approximation is a tool used to parameterize the effects of the large-scale environment upon modeled convection. When implemented within a single-column model or within a limited domain cloud-resolving model, WTG admits insight into the behavior of tropical convection under a broad range of environmental conditions, and has been used to develop convective parameterizations. In strict WTG, the horizontal mean temperature profile in the model domain is held constant in order to maintain the small horizontal temperature gradients observed in the tropics over long time averages. Since the local temperature must change over short time scales due to convective heating, a relaxed form of the approximation is used. Such a scheme nudges the temperature back to a reference value according to the action of a vertical velocity derived from the temperature anomaly. The velocity incorporates an assumed time scale based on the overturning effects of gravity waves associated with convection.

Previous implementations of relaxed WTG use a time scale derived from a single gravity wave mode corresponding to a temperature anomaly extending through the depth of the troposphere. Since anomalies exhibit a range of depths, we modify the conventional scheme to include a complete set of depths, i. e., a spectrum of vertical wavenumbers. This improves the accuracy of relaxed WTG with minimal extra computation. The resulting spectral WTG scheme produces vertical mass flux profiles that are smoother and less top-heavy than those of conventional WTG. In addition, spectral WTG is shown to drive appreciably greater convergence in the lower troposphere, leading to greater precipitation and column water anomalies than those of conventional WTG.