Two univariate indices of the Madden–Julian oscillation (MJO) based on outgoing longwave radiation (OLR) are developed to track the convective component of the MJO while taking into account the seasonal cycle. These are compared with the all-season Real-time Multivariate MJO (RMM) index of Wheeler and Hendon derived from a multivariate EOF of circulation and OLR. The gross features of the OLR and circulation of composite MJOs are similar regardless of the index, although RMM is characterized by stronger circulation. Diversity in the amplitude and phase of individual MJO events between the indices is much more evident; this is demonstrated using examples from the Dynamics of the Madden–Julian Oscillation (DYNAMO) field campaign and the Year of Tropical Convection (YOTC) virtual campaign. The use of different indices can lead to quite disparate conclusions concerning MJO timing and strength, and even as to whether or not an MJO has occurred. A disadvantage of using daily OLR as an EOF basis is that it is a much noisier field than the large-scale circulation, and filtering is necessary to obtain stable results through the annual cycle. While a drawback of filtering is that it cannot be done in real time, a reasonable approximation to the original fully filtered index can be obtained by following an endpoint smoothing method. When the convective signal is of primary interest, the authors advocate the use of satellite-based metrics for retrospective analysis of the MJO for individual cases, as well as for the analysis of model skill in initiating and evolving the MJO.

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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 Ϫ1 (and roughly a full-wavelength vertical structure through the troposphere), while the "fast" modes have speeds of 35 and 45 m s Ϫ1 (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 ϳ2 h prior to maximum deep convective heating, while stratiform heating peaks ϳ3 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 Ϫ1, rather than 23-25 m s Ϫ1 (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.