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Ying Han
and
Boualem Khouider

Abstract

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.

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Boualem Khouider
and
Andrew J. Majda

Abstract

In this chapter, a model parameterization for organized tropical convection and convectively coupled tropical waves is presented. The model is based on the main three cloud types, congestus, deep, and stratiform, that are observed to play an important role in the dynamics and morphology of tropical convective systems. The model is based on the self-similarity across scales of tropical convective systems and uses physically sound theory about the mutual interactions between the three cloud types and the environment. Both linear analysis and numerical simulations of convectively coupled waves and the Madden–Julian oscillation are discussed.

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Boualem Khouider
and
Andrew J. Majda

Abstract

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.

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Michael L. Waite
and
Boualem Khouider

Abstract

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.

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Boualem Khouider
and
Andrew J. Majda

Abstract

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 m s−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 m s−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−1.

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Boualem Khouider
and
Andrew J. Majda

Abstract

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 synoptic-scale convectively coupled moist gravity wave packets moving at 15–20 m s−1 but, in addition, these packets have planetary-scale envelopes moving in the opposite direction at about 6 m s−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.

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Michael L. Waite
and
Boualem Khouider

Abstract

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−1 and coupling to deep convection, is also discussed.

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Boualem Khouider
and
Andrew J. Majda

Abstract

Recent observational analysis reveals the central role of three multicloud types, congestus, stratiform, and deep convective cumulus clouds, in the dynamics of large-scale convectively coupled Kelvin waves, westward-propagating two-day waves, and the Madden–Julian oscillation. A systematic model convective parameterization highlighting the dynamic role of the three cloud types is developed here through two baroclinic modes of vertical structure: a deep convective heating mode and a second mode with low-level heating and cooling corresponding respectively to congestus and stratiform clouds. A systematic moisture equation is developed 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. A nonlinear switch is developed that favors either deep or congestus convection depending on the relative dryness of the troposphere; in particular, a dry troposphere with large convective available potential energy (CAPE) has no deep convection and only congestus clouds. The properties of the multicloud model parameterization are tested by linearized analysis in a two-dimensional setup with no rotation with constant sea surface temperature. In particular, the present study reveals new mechanisms for the large-scale instability of moist gravity waves with features resembling observed convectively coupled Kelvin waves in realistic parameter regimes without any effect of wind-induced surface heat exchange (WISHE). A detailed dynamical analysis for the linear waves is given herein and idealized nonlinear numerical simulations are reported in a companion paper. A maximum congestus heating leads during the dry phase of the wave. It is followed by an increase of the boundary layer θe , that is, CAPE, and lower troposphere moistening that precondition the upper troposphere for the next deep convective episode. In turn, deep convection consumes CAPE and removes moisture, thus yielding the dry episode.

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Boualem Khouider
and
Mitchell W. Moncrieff

Abstract

Mesoscale convective systems (MCSs) are of fundamental importance in the dynamics of the atmospheric circulation and the climate system. They are often observed to develop over significant terrain in ambient shear flows in midlatitudes and embedded within the Madden–Julian oscillation (MJO) and convectively coupled equatorial wave (CCEW) envelopes, as well as in the intertropical convergence zone (ITCZ). Yet general circulation models (GCMs) fail to resolve these systems, and their underlying convective parameterizations are not directed to represent organized circulations. Shear-parallel MCSs, which are common in the ITCZ, have a three-dimensional structure and, as such, present a serious modeling challenge. Here, a previously developed multicloud model (MCM) is modified to parameterize MCSs. One of the main modifications is the parameterization of stratiform condensation to capture extended stratiform outflows, which characterize MCSs, resulting from strong upper-level jets. Linear analysis shows that, under the influence of a typical double African and equatorial jet shear flow, this modification results in an additional new scale-selective instability peaking at the mesoalpha scale of roughly 400 km. Nonlinear simulations conducted with the modified MCM on a 400 km × 400 km doubly periodic domain, without rotation, resulted in the spontaneous transition from a quasi-two-dimensional shear-perpendicular convective system, consistent with linear theory, to a fully three-dimensional flow structure. The simulation is characterized by shear-parallel bands of convection, moving slowly eastward, embedded in stratiform systems that expand perpendicularly and propagate westward with the upper-level jet. The mean circulation and the implications for the domain-averaged vertical transport of momentum and potential temperature are discussed.

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Qiang Deng
,
Boualem Khouider
, and
Andrew J. Majda

Abstract

The representation of the Madden–Julian oscillation (MJO) is still a challenge for numerical weather prediction and general circulation models (GCMs) because of the inadequate treatment of convection and the associated interactions across scales by the underlying cumulus parameterizations. One new promising direction is the use of the stochastic multicloud model (SMCM) that has been designed specifically to capture the missing variability due to unresolved processes of convection and their impact on the large-scale flow. The SMCM specifically models the area fractions of the three cloud types (congestus, deep, and stratiform) that characterize organized convective systems on all scales. The SMCM captures the stochastic behavior of these three cloud types via a judiciously constructed Markov birth–death process using a particle interacting lattice model. The SMCM has been successfully applied for convectively coupled waves in a simplified primitive equation model and validated against radar data of tropical precipitation. In this work, the authors use for the first time the SMCM in a GCM. The authors build on previous work of coupling the High-Order Methods Modeling Environment (HOMME) NCAR GCM to a simple multicloud model. The authors tested the new SMCM-HOMME model in the parameter regime considered previously and found that the stochastic model drastically improves the results of the deterministic model. Clear MJO-like structures with many realistic features from nature are reproduced by SMCM-HOMME in the physically relevant parameter regime including wave trains of MJOs that organize intermittently in time. Also one of the caveats of the deterministic simulation of requiring a doubling of the moisture background is not required anymore.

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