Clouds play an important role in regulating weather and climate in the tropical ocean-atmosphere system through convective-radiative-mixing processes. The incoming solar radiative flux and the internal climate oscillations provide the environment with a large amount of unstable energy, which initiates the formation of cloud clusters. The development of convection, in turn, significantly modifies the environment by redistributing momentum, temperature, moisture, and salinity vertically through radiative, microphysical, and dynamic mixing processes. These processes are fundamentally important in maintaining tropical oscillations and the climate state.

To improve our knowledge of the convective-radiative-mixing processes, appropriate models like cloud-resolving models are powerful tools. Soong and Ogura (1980a) performed a pioneering study using their two-dimensional slab-symmetric numerical cloud model to examine the statistical properties of cumulus clouds that respond to the given large-scale forcing, which is mainly a vertical velocity. Their nonhydrostatic model with an anelas-tic approximation includes prognostic equations for momentum, temperature, specific humidity, and cloud species. This model was greatly improved later at the NASA Goddard Space Flight Center (GSFC), and named the Goddard cumulus ensemble (GCE) model (Tao and Simpson, 1993; Tao, 2003; Tao et al., 2003). The GCE model includes detailed solar and infrared parametrization schemes (Chou et al., 1991, 1997; Chou and Suarez, 1994a), cloud-microphysical parametrization schemes for cloud water, raindrops, cloud ice, snow, and graupel (Rutledge and Hobbs, 1983, 1984; Lin et al., 1983; Tao et al., 1989; Krueger et al., 1995), and subgrid-scale turbulence closure (Klemp and Wilhelmson, 1978).

The GCE model was originally designed to study the cumulus response to large-scale forcing (a prospective from a grid box of general circulation models), which can be imposed in the model in two ways: one with a vertical velocity and the other with heat and moisture source/sink. The model has been applied to case-oriented short-term simulations such as deep tropical cumulus clouds (Soong and Tao, 1980b), tropical squall line (Tao and Simpson, 1989), cloud interaction and merging (Tao and Simpson, 1984), and three-dimensional tropical clouds (Tao and Soong, 1986; Tao and Simpson, 1989).

In addition to the one-way response to large-scale forcing, convective-radiative processes may interact with climate change to form a feedback loop, like the feedback mechanisms of water vapor-cloud radiative forcing and surface evaporative cooling to climate warming (e.g. Newell, 1979; Fu et al., 1992; Hartmann and Michelsen, 1993; Lau et al., 1994a; Prabhakara et al., 1993; Ramanathan and Collins, 1991; Lindzen, 2001). Some of these climate feedback mechanisms may be investigated using a cloud resolving model. Lau et al. (1993, 1994a) and Sui et al. (1994) integrated the two-dimensional GCE model imposed with the large-scale vertical velocity to reach quasi-equilibrium states, applying the cloud-resolving model as a new tool for studying the effects of the convective-radiative interaction on tropical climate.

Based on extensive knowledge acquired through previous studies, longer simulations were performed to study the cumulus ensemble response of the model to the vertical velocity derived from observational data such as Marshall Island data (Yanai et al., 1973; Sui et al., 1994). Other research groups employed different cloud-resolving models, and successfully simulated the deep convective response to large-scale forcing observed in the Global Atmosphere Research Programme Atlantic Tropical Experiment (GATE) (e.g. Xu and Randall, 1996; Grabowski et al., 1996) and the TOGA COARE (e.g. Wu et al., 1998; Li et al., 1999; Johnson et al., 2002).

In addition to the studies just mentioned, the GCE model has been further extended to study various convective-radiative processes related to cumulus ensemble responses to large-scale forcing (Li et al., 1999, 2002b, 2005), diurnal cycle (Sui et al., 1998a), microphysical processes and cloud clusters (Peng et al., 2001; Li et al., 2002c; Sui and Li, 2005), and precipitation efficiency (Li et al., 2002a; Sui et al., 2005, 2007b). Similarly, an ocean mixed layer model has been used to study air-sea exchange and ocean mixing at diurnal to intraseasonal scales (Sui et al., 1997b; Lau and Sui, 1997; Li et al., 1998; Sui et al., 1998b).

This article will highlight major scientific findings made by the authors during the past 15 years at NASA/GSFC, USA, and the National Central University, Taiwan. In the next section, the roles of convective-radiative processes in climate equilibrium states, cumulus ensemble responses, the diurnal cycle, microphysical processes and the development of cloud clusters, and precipitation efficiency will be reviewed. Air-sea exchange and ocean mixing at diurnal-to-intraseasonal scales will be discussed in Sec. 3. The coupled boundary layer at the atmosphere-ocean interface and forced oceanic responses will be addressed in Sec. 4. Representation of convective-radiative processes in climate models will be discussed in Sec. 5. A summary and a discussion are given in Sec. 6.

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