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.

Systematic strategies from applied mathematics for stochastic modelling in climate are reviewed here. One of the topics discussed is the stochastic modelling of mid-latitude low-frequency variability through a few teleconnection patterns, including the central role and physical mechanisms responsible for multiplicative noise. A new lowdimensional stochastic model is developed here, which mimics key features of atmospheric general circulation models, to test the fidelity of stochastic mode reduction procedures. The second topic discussed here is the systematic design of stochastic lattice models to capture irregular and highly intermittent features that are not resolved by a deterministic parametrization. A recent applied mathematics design principle for stochastic column modelling with intermittency is illustrated in an idealized setting for deep tropical convection; the practical effect of this stochastic model in both slowing down convectively coupled waves and increasing their fluctuations is presented here.

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 birth͞death 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. The current practical models for prediction of both weather and climate involve general circulation models (GCMs) where the physical equations for these extremely complex f lows are discretized in space and time and the effects of unresolved processes are parametrized according to various recipes. With the current generation of supercomputers, the smallest possible mesh spacings are Ϸ50 -100 km for shortterm weather simulations and of order 200 -300 km for shortterm climate simulations. There are many important physical processes that are unresolved in such simulations such as the mesoscale sea-ice cover, the cloud cover in subtropical boundary layers, and deep convective clouds in the tropics. An appealing way to represent these unresolved features is through a suitable coarse-grained stochastic model that simultaneously retains crucial physical features of the interaction between the unresolved and resolved scales in a GCM. In recent work in two different contexts, the authors have developed both a systematic stochastic strategy (1) to parametrize key features of deep convection in the tropics involving suitable stochastic spin-f lip models and also a systematic mathematical strategy to coarse-grain such microscopic stochastic models (2) to practical mesoscopic meshes in a computationally efficient manner while retaining crucial physical properties of the interaction. This last work (2) is general with potential applications in material sciences, sea-ice modeling, etc. Crucial new scientific issues involve the fashion in which a stochastic model effects the climate mean state and the strength and nature of f luctuations about the climate mean. The main topic of this article is to discuss development of a family of coarse-grained stochastic models for tropical deep convection by combining the systematic strategies from refs. 1 and 2 and to explore their effect on both the climate mean and f luctuations for an idealized prototype model parametrization in the simplest scenario for tropical climate involving the Walker circulation, the east-west climatological state that arises from local region of enhanced surface heat f lux, mimicking the Indonesian marine continent.

The aim for a more accurate representation of tropical convection in global circulation models is a longstanding issue. Here, the relationships between large and convective scales in observations and a stochastic multicloud model (SMCM) to ultimately support the design of a novel convection parameterization with stochastic elements are investigated. Observations of tropical convection obtained at Darwin and Kwajalein are used here. It is found that the variability of observed tropical convection generally decreases with increasing large-scale forcing, implying a transition from stochastic to more deterministic behavior with increasing forcing. Convection shows a more systematic relationship with measures related to large-scale convergence compared to measures related to energetics (e.g., CAPE). Using the observations, the parameters in the SMCM are adjusted. Then, the SMCM is forced with the time series of the observed large-scale state and the simulated convective behavior is compared to that observed. It is found that the SMCM cloud fields compare better with observations when using predictors related to convergence rather than energetics. Furthermore, the underlying framework of the SMCM is able to reproduce the observed functional dependencies of convective variability on the imposed large-scale state-an encouraging result on the road toward a novel convection parameterization approach. However, establishing sound cause-and-effect relationships between tropical convection and the large-scale environment remains problematic and warrants further research.

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.C onvection in the tropics has a profound impact on short-term climate. Tropical convection is roughly organized into two types of cloud structures. The first type is ubiquitous and involves shallow cumulus convection over heights of roughly 1 km above the surface, and the second type involves deep penetrative convection to heights of 5-10 km with associated anvil towers of clouds. Observational data indicate that tropical deep convection is organized on a hierarchy of scales ranging from hundreds of kilometers due to mesoscale organized squall lines to intraseasonal oscillations over planetary scales of order 40,000 km (1-3). The present practical models for prediction of both weather and climate involve general circulation models (GCM) where the physical equations for these extremely complex flows are discretized in space and time and the effects of unresolved processes are parametrized according to various recipes (4, 5). With the current generation of supercomputers, the smallest possible mesh spacings are roughly 50-100 km for short-term tropical weather simulations and of 200-300 km for short-term climate simulations. With such coarse mesh spacing, despite much progress in the parametrization of tropical convection, the current generation of GCMs (4, 5) still fails to reproduce most of the significant features of the observational record (1-3) regarding tropical convection (4, 5). Thus, given the importance of the tropics for short-term climate, new strategies for parametrizing the unresolved effects of tropical convection are very important.The main topic of this paper is to introduce a different approach for parametrizing certain features of...

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.

Despite recent advances in supercomputing, current general circulation models (GCMs) poorly represent the variability associated with organized tropical convection. A stochastic multicloud convective parameterization based on three cloud types (congestus, deep, and stratiform), introduced recently by Khouider, Biello, and Majda in the context of a single column model, is used here to study flows above the equator without rotation effects. The stochastic model dramatically improves the variability of tropical convection compared to the conventional moderate-and coarse-resolution paradigm GCM parameterizations. This increase in variability comes from intermittent coherent structures such as synoptic and mesoscale convective systems, analogs of squall lines and convectively coupled waves seen in nature whose representation is improved by the stochastic parameterization. Furthermore, simulations with a sea surface temperature (SST) gradient yield realistic mean Walker cell circulation with plausible high variability. An additional feature of the present stochastic parameterization is a natural scaling of the model from moderate to coarse grids that preserves the variability and statistical structure of the coherent features. These results systematically illustrate, in a paradigm model, the benefits of using the stochastic multicloud framework to improve deterministic parameterizations with clear deficiencies.

The adequate representation of the dominant intraseasonal and synoptic-scale variability in the tropics, characterized by the Madden-Julian oscillation (MJO) and convectively coupled waves, is still problematic in current operational general circulation models (GCMs). Here results are presented using the next-generation NCAR GCM-the High-Order Methods Modeling Environment (HOMME)-as a dry dynamical core at a coarse resolution of about 167 km, coupled to a simple multicloud parameterization. The coupling is performed through a judicious choice of heating vertical profiles for the three cloud types-congestus, deep, and stratiform-that characterize organized tropical convection.Important control parameters that affect the types of waves that emerge are the background vertical gradient of the moisture and the stratiform fraction in the multicloud parameterization, which set the strength of largescale moisture convergence and unsaturated downdrafts in the wake of deep convection, respectively. Three numerical simulations using different moisture gradients and different stratiform fractions are considered. The first experiment uses a large moisture gradient and a small stratiform fraction and provides an MJO-like example. It results in an intraseasonal oscillation of zonal wavenumber 2, moving eastward at a constant speed of roughly 5 m s 21 . The second uses a weaker background moisture gradient and a large stratiform fraction and yields convectively coupled Rossby, Kelvin, and two-day waves, embedded in and interacting with each other; and the third experiment combines the small stratiform fraction and the weak background moisture gradient to yield a planetary-scale (wavenumber 1) second baroclinic Kelvin wave. While the first two experiments provide two benchmark examples that reproduce several key features of the observational record, the third is more of a demonstration of a bad MJO model solution that exhibits very unrealistic features.