Vertical-Mode and Cloud Decomposition of Large-Scale Convectively Coupled Gravity Waves in a Two-Dimensional Cloud-Resolving Model

This paper describes an analysis of large-scale [O(1000 km)] convectively coupled gravity waves simulated using a two-dimensional cloud-resolving model. The waves develop spontaneously under uniform radiative cooling and approximately zero-mean-flow conditions, with wavenumber 2 of the domain appearing most prominently and right-moving components dominating over left-moving components for random reasons. The analysis discretizes the model output in two ways. First, a vertical-mode transform projects profiles of winds, temperature, and heating onto the vertical modes of the model’s base-state atmosphere. Second, a cloud-partitioning algorithm sorts sufficiently cloudy grid columns into three categories: shallow convective, deep convective, and stratiform anvil. Results show that much of the tilted structures of the waves can be captured by just two main vertical spectral “bands,” each consisting of a pair of vertical modes. The “slow” modes have propagation speeds of 16 and 18 m s−1 (and roughly a full-wavelength vertical structure through the troposphere), while the “fast” modes have speeds of 35 and 45 m s−1 (and roughly a half-wavelength structure). Deep convection anomalies in the waves are more or less in phase with the low-level cold temperature anomalies of the slow modes and in quadrature with those of the fast modes. Owing to the characteristic life cycle of deep convective cloud systems, shallow convective heating peaks ∼2 h prior to maximum deep convective heating, while stratiform heating peaks ∼3 h after. The onset of deep convection in the waves is preceded by a gradual deepening of shallow convection lasting a period of many hours. Results of this study are in broad agreement with simple two-mode models of unstable large-scale wave growth, under the name “stratiform instability.” Differences here are that 1) the key dynamical modes have speeds in the range 16–18 m s−1, rather than 23–25 m s−1 (owing to a shallower depth of imposed radiative cooling), and 2) deep convective heating, as well as stratiform heating, is essential for the generation and maintenance of the slow modes.