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.