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Andrew J. Majda of Courant Institute, New York University (NYU), or Andy as his friends called him--his wife, Gerta Keller, most affectionately called him Majda--died in Princeton, New Jersey, on [...]

A linear stability analysis, about a radiative-convective equilibrium in a sheared environment, on an equatorial beta plane, for a simple multicloud model for organized tropical convection is presented here. Both vertical/baroclinic and meridional/barotropic zonal wind shears are considered separately in a parameter regime for which the shear-free multicloud model exhibits synoptic-scale instability of Kelvin and n = 0 eastward inertio-gravity [eastward mixed Rossby--gravity (MRG)] waves only, with moderate growth rates. The maximum growth rates appear to increase significantly with the strength of the background wind shear, and new wave instabilities appear and/or disappear depending on the strength and type of the wind shear. It is found here that both high- and low-level vertical shears have a strong impact on the stability of convectively coupled waves (CCWs), consistent with the fact that the multicloud instability mechanism is controlled by both stratiform heating and low-level moisture and congestus heating. Typically, vertical shears with high-level easterly wind destabilize westward moving waves and stabilize eastward waves, whereas westerly winds aloft and on bottom tend to destabilize eastward moving and stabilize westward moving waves. In the mixed situation of high-level easterlies and low-level westerlies both eastward and westward waves are unstable, while in the case of high-level westerlies and low-level easterlies only eastward waves are unstable. In the presence of a barotropic/meridional shear, synoptic-scale convectively coupled westward MRG and Rossby waves emerge, when the shear strength is large enough, due essentially to pure shear instability of the dry dynamics. The meridional shear has also an important impact on the horizontal structure of the waves. Owing to the meridional shear, the Kelvin wave displays a nonzero meridional velocity that induces a significant contribution toward the horizontal convergence. The two-day waves adopt a crescentlike shape while the westward MRG, and somewhat the Rossby waves, become less trapped in the vicinity of the equator. DOI: 10.1175/2010JAS3335.1

The role of environmental moisture in the deepening of cumulus convection is investigated by means of cloud-resolving numerical experiments. Under idealized conditions of uniform SST and specified radiative cooling, the evolution of trade wind cumulus into congestus clouds, and ultimately deep convection, is simulated and analyzed. The results exhibit a tight coupling between environmental moisture and cloud depth, both of which increase over the course of the simulations. Moistening in the lower troposphere is shown to result from the detrainment of water vapor from congestus clouds, and the strength of this tendency is quantified. Moistening of the lower troposphere reduces the dilution of cloud buoyancy by dry-air entrainment, and the relationship between this effect and increasing cloud depth is examined. The authors confirm that the mixing of water vapor by subgrid-scale turbulence has a significant impact on cloud depth, while the mixing of sensible heat has a negligible effect. By contrast, the dependence of cloud depth on CAPE appears to be of secondary importance. However, the deepening trend observed in these simulations is not solely determined by the evolving mean vapor profile. While enhancing the horizontally averaged humidity does result in deeper clouds, this occurs only after an adjustment period of several hours, presumably because of the buildup of CAPE. The implications of these findings for large-scale simulations in which resolved mixing is reduced--for example, by coarser spatial resolution or 2D experiments--are also discussed. DOI: 10.1175/2010JAS3357.1

A simplified model of intermediate complexity for convectively coupled gravity waves that incorporates the bulk dynamics of the atmospheric boundary layer is developed and analyzed. The model comprises equations for velocity, potential temperature, and moist entropy in the boundary layer as well as equations for the free tropospheric barotropic (vertically uniform) velocity and first two baroclinic modes of vertical structure. It is based on the multicloud model of Khouider and Majda coupled to the bulk boundary layer-shallow cumulus model of Stevens. The original multicloud model has a purely thermodynamic boundary layer and no barotropic velocity mode. Here, boundary layer horizontal velocity divergence is matched with barotropic convergence in the free troposphere and yields environmental downdrafts. Both environmental and convective downdrafts act to transport dry midtropospheric air into the boundary layer. Basic states in radiative--convective equilibrium are found and are shown to be consistent with observations of boundary layer and free troposphere climatology. The linear stability of these basic states, in the case without rotation, is then analyzed for a variety of tropospheric regimes. The inclusion of boundary layer dynamics--specifically, environmental downdrafts and entrainment of free tropospheric air--enhances the instability of both the synoptic-scale moist gravity waves and nonpropagating congestus modes in the multicloud model. The congestus mode has a preferred synoptic-scale wavelength, which is absent when a purely thermodynamic boundary layer is employed. The weak destabilization of a fast mesoscale wave, with a phase speed of 26 m [s.sup.-1] and coupling to deep convection, is also discussed.

Linear stability results for the multicloud model recently developed by the authors on an equatorial beta plane are presented here. The linearized equations, about a realistic radiative--convective equilibrium (RCE) are projected in the meridional direction via a Galerkin truncation procedure based on the parabolic cylinder functions. In a suitable parameter regime, the multicloud model exhibits convectively coupled Kelvin, M = 0 eastward (Yanai), and M = 1 westward inertia--gravity waves, unstable at the synoptic scales in agreement with the outgoing longwave radiation (OLR) spectral peaks observed by Wheeler and Kiladis. The horizontal wave structure and vertical wavenumber of the unstable waves qualitatively match those of the rotating equatorial shallow water waves but with a reduced phase speed, as in the observations. More importantly, they exhibit the same self-similar front-to-rear vertical tilt in the zonal winds, temperature, and heating fields as observed by Kiladis and colleagues. Similar to the case without rotation (from earlier work) a wave life cycle is identified, once again demonstrating the crucial role, played by congestus clouds and moisture, of preconditioning and moistening prior to deep convection and of triggering and maintaining the instability. When the troposphere is excessively dry, the convective wave instability fades out and an instability of low-frequency modes moving in both eastward and westward directions takes place. The eigenstructure of the low-frequency modes projects heavily on the congestus and moisture components and exhibits a quadruple vortex configuration reminiscent of Rossby waves with strong meridional convergence of warm and moist air toward the equatorial belt, suggesting a moistening and preconditioning role resembling the congestus standing mode seen in the case without rotation.

Despite the recent advances in supercomputing, the current general circulation models (GCMs) poorly represent the large-scale variability associated with tropical convection. Multicloud model convective parameterizations based on three cloud types (congestus, deep, and stratiform), introduced recently by the authors, have been revealed to be very useful in representing key features of organized convection and convectively coupled waves. Here a new systematic version of the multicloud models is developed with separate upper- and lower-troposphere basis functions for the congestus and stratiform clouds. It naturally leads to a new convective closure for the multicloud models enhancing the congestus heating in order to better pinpoint the congestus preconditioning and moistening mechanisms. The models are studied here for flows above the equator without rotation effects. First, the new model results consist of the usual synopticscale convectively coupled moist gravity wave packets moving at 15-20 m [s.sup.-1] but, in addition, these packets have planetary-scale envelopes moving in the opposite direction at about 6 m [s.sup.-1] and have many of the self-similar features of convectively coupled waves, reminiscent of the Madden-Julian oscillation. Second, when a warm pool forcing is imposed, dry regions of roughly 250 km in extent form 'convective barriers' surrounding the warm pool region where only congestus heating survives. Deep convection and moist gravity waves are thus confined within the warm pool region. Finally, linear analysis reveals that, for sufficiently dry mean states, in addition to the inherent synoptic-scale moist gravity waves, the new model supports a planetary (wavenumber 1) standing congestus mode that provides, within its congestus active phase, a region where moist gravity waves evolve and propagate, which results in a Walker-like circulation over a uniform SST background.

The Madden-Julian Oscillation (MJO) is the dominant component of tropical intraseasonal variability, and a theory explaining its structure and successful numerical simulation remains a major challenge. A successful model for the MJO should have a propagation speed of 4-7 m/s predicted by theory; a wavenumber-2 or -3 structure for the planetary-scale, low-frequency envelope with distinct active and inactive phases of deep convection; an intermittent turbulent chaotic multiscale structure within the planetary envelope involving embedded westward- and eastward-propagating deep convection events; and qualitative features of the low-frequency envelope from the observational record regarding, e.g., its zonal flow structure and heating. Here, such an MJO analog is produced by using the recent multicloud model of Khouider and Majda in an appropriate intraseasonal parameter regime for flows above the equator so that rotation is ignored. Key features of the multicloud model are (i) systematic low-level moisture convergence with retained conservation of vertically integrated moist static energy, and (ii) the use of three cumulus cloud types (congestus, stratiform, and deep convective) together with their differing vertical heating structures. Besides all of the above structure in the MJO analog waves, there are accurate predictions of the phase speed from linear theory and transitions from weak, regular MJO analog waves to strong, multiscale MJO analog waves as climatological parameters vary. With all of this structure in a simplified context, these models should be useful for MJO predictability studies in a fashion akin to the Lorenz 96 model for the mid-latitude atmosphere. coherent planetary intraseasonal variability | multiscale structure | intermittency in convection | nonlinear analog model

Observations in the Tropics point to the important role of three cloud types, congestus, stratiform, and deep convective clouds, besides ubiquitous shallow boundary layer clouds for both the climatology and large-scale organized anomalies such as convectively coupled Kelvin waves, two-day waves, and the Madden-Julian oscillation. Recently, the authors have developed a systematic model convective parameterization highlighting the dynamic role of the three cloud types through two baroclinic modes of vertical structure: a deep convective heating mode and a second mode with lower troposphere heating and cooling corresponding respectively to congestus and stratiform clouds. The model includes both a systematic moisture equation where the lower troposphere moisture increases through detrainment of shallow cumulus clouds, evaporation of stratiform rain, and moisture convergence and decreases through deep convective precipitation and also a nonlinear switch that favors either deep or congestus convection depending on whether the lower middle troposphere is moist or dry. Here these model convective parameterizations are applied to a 40 000-km periodic equatorial ring without rotation, with a background sea surface temperature (SST) gradient and realistic radiative cooling mimicking a tropical warm pool. Both the emerging 'Walker cell' climatology and the convectively coupled wave fluctuations are analyzed here while various parameters in the model are varied. The model exhibits weak congestus moisture coupled waves outside the warm pool in a turbulent bath that intermittently amplify in the warm pool generating convectively coupled moist gravity wave trains propagating at speeds ranging from 15 to 20 [ms.sup.-1] over the warm pool, while retaining a classical Walker cell in the mean climatology. The envelope of the deep convective events in these convectively coupled wave trains often exhibits large-scale organization with a slower propagation speed of 3-5 [ms.sup.-1] over the warm pool and adjacent region. Occasional much rarer intermittent deep convection also occurs outside the warm pool. The realistic parameter regimes in the multicloud model are identified as those with linearized growth rates for large scale instabilities roughly in the range of 0.5 K [day.sup.-1].

Recent observational analysis of both individual realizations and statistical ensembles identifies moist convectively coupled Kelvin waves in the Tropics with supercluster envelopes of convection. This observational analysis elucidates several key features of these waves including their propagation speed of roughly 15 m [s.sup.-1] and many aspects of their dynamical structure. This structure includes anomalously cold temperatures in the lower troposphere and warm temperatures in the upper troposphere (below 250 hPa) within and sometimes leading the heating region and strong updrafts in the wave, and an upward and westward tilting structure with height below roughly 250 hPa. Other key features in the wave are that anomalous increases in convective available potential energy (CAPE) and surface precipitation lead the wave while the trailing part of the supercluster is dominated by stratiform precipitation. The main result in this paper is the development of a simple model convective parameterization with nonlinear convectively coupled moist gravity waves, which reproduce many of the features of the observational record listed above in a qualitative fashion. One key feature of the model convective parameterization is the systematic use of two vertical modes with one representing deep convective heating and the other stratiform heating. The other key feature in the model is the explicit parameterization of the separate deep convective and stratiform contribution to the downdrafts, which change equivalent potential temperature in the boundary layer. The effects of rotation on convectively coupled equatorial waves are also included through a suitable linear stability theory for the model convective parameterization about radiative convective equilibrium.

Prototype coarse-grained stochastic parametrizations for the interaction with unresolved features of tropical convection are developed here. These coarse-grained stochastic parametrizations involve systematically derived birth/death processes with low computational overhead that allow for direct interaction of the coarse-grained dynamical variables with the smaller-scale unresolved fluctuations. It is established here for an idealized prototype climate scenario that, in suitable regimes, these coarse-grained stochastic parametrizations can significantly impact the climatology as well as strongly increase the wave fluctuations about an idealized climatology.

A new way to parametrize certain aspects of tropical convection through stochastic and mesoscopic models is developed here. The technical idea is to adapt tools from statistical physics and materials science to model important unresolved features of tropical convection. This new strategy consists of modeling the unresolved effects of convective inhibition in a coarse mesh mesoscopic parametrization through a 'heat bath' model involving a stochastic spin flip model with very natural interaction rules for convective inhibition combined with a suitable external potential defined by the coarse mesh values. In turn, the values of the order parameter from this heat bath alter the vertical mass flux in regions of deep convection. Both stochastic and systematic deterministic mesoscopic parametrizations are developed here. The deterministic mesoscopic models derived in this fashion exhibit new phenomena such as multiple radiative equilibria in suitable parameter regimes. The simplest first numerical experiments reported here with the mesoscopic deterministic parametrization qualitatively reproduce several key features of the observational record regarding convectively coupled tropical waves. The systematic stochastic modeling strategy proposed here could also be very useful for capturing other features of tropical convection such as those involving cloud radiation feedbacks.

Convection in the tropics is observed to involve a wide-ranging hierarchy of scales from a few kilometers to the planetary scales and also has a profound impact on short-term climate. The mechanisms responsible for this behavior present a major unsolved problem. A promising emerging approach to address these issues is cloud-resolving modeling. Here a family of numerical models is introduced specifically to model the feedback of small-scale deep convection on tropical planetary waves and tropical circulation in a highly efficient manner compatible with the approach through cloud-resolving modeling. Such a procedure is also useful for theoretical purposes. The basic idea in the approach is to use low-order truncation in the meriodonal direction through Gauss-Hermite quadrature projected onto a simple discrete radiation condition. In this fashion, the cloud-resolving modeling of equatorially trapped planetary waves reduces to the solution of a small number of purely zonal two-dimensional wave systems along a few judiciously chosen meriodonal layers that are coupled only by some additional source terms. The approach is analyzed in detail with full mathematical rigor for linearized equatorial primitive equations with source terms.