In most atmospheric circulation models used for climate projections, cloud and convective processes are not explicitly resolved but parameterized. Such models are known to produce a diurnal cycle of continental thunderstorms in phase with insolation, while observed precipitation peaks in late afternoon. We propose a new approach which corrects this long standing bias of parameterized convection. In this approach, deep convection triggering and intensity are controlled by sub-cloud processes: here boundary layer thermals and gust fronts, and potentially orography or surface heterogeneities. The representation of the diurnal cycle of deep convection is greatly improved in 1D mode, with rainfall maximum delayed from midday to late afternoon, provided parameterizations account for the key role played by shallow cumulus in preconditioning deep convection and by gust fronts in the self-sustaining of thunderstorms in the afternoon.
 In current climate models, with typical resolution of 30 to 300 km, convective and cloud processes are subgrid-scale and must be “parameterized”, i.e. represented through a set of approximate equations describing their ensemble behaviour and their effect on the large-scale variables. Models with parameterized convection are known to produce a diurnal cycle of continental thunderstorms in phase with insolation [Betts and Jakob, 2002; Guichard et al., 2004], while observed precipitation peaks in late afternoon [Yang and Slingo, 2001]. This erroneous response to the strong diurnal forcing as well as the huge dispersion in simulations of present day climatology and trends of tropical rainfall [Intergovernmental Panel on Climate Change (IPCC), 2007] have brought into question the use of parameterized convection in climate change simulations. Given the foreseen computer evolution, running series of long climate change simulations with a resolution fine enough to explicitly resolve the largest convective structures (1–2 km) will however not be feasible within a couple of decades. To increase confidence in climate change simulations, it is worth improving further the physical content of climate models and in particular the representation of convective clouds.
 Atmospheric convection can be either shallow or deep depending on dominant physical processes and dynamical regimes. Shallow convection is associated with organized boundary layer structures (cells, rolls, …) and is driven by surface heat flux and entrainment at boundary layer top. Shallow cumulus, with a vertical extension of a few kilometres, may be seen as the saturated part of plumes of warm air, called thermals, originating from the surface and driven by buoyancy [LeMone and Pennell, 1976]. They contribute to the preconditioning of deeper convection, through a gradual deepening of the boundary layer and moistening of the inversion layer [Chaboureau et al., 2004; Stevens, 2006]. Deep cumulonimbus convection bursts locally overcoming an inhibition barrier located at the boundary layer top and is mainly driven by water phase changes. Evaporation of rainfall under deep convective clouds generates pools of cold air, also called density currents or wakes, the spreading edges of which form gust fronts which lift the air and initiate new convection [Lima and Wilson, 2008].
 While some recent studies encourage the development of unified convection schemes [Kuang and Bretherton, 2006], we present here a new approach based on a distinct treatment of shallow and deep convection. This choice allows us to represent the control of deep convection initiation and maintenance by sub-cloud processes – here thermals and wakes (see illustration in Figure 1).
2. Deep Convection Controlled by Sub-cloud Processes
 To capture the diurnal cycle of convection, it is essential to represent the succession of three regimes of convection: dry, moist non-precipitating, precipitating.
 For boundary layer turbulence and shallow convection, we combine a diffusive approach for small-scale turbulence based on a prognostic equation for the turbulent kinetic energy [Yamada, 1983] with a mass-flux scheme that represents the vertical transport by thermals within the convective boundary layer [Hourdin et al., 2002; Coindreau et al., 2007; Rio and Hourdin, 2008]. Coherent structures within a horizontal grid cell of a large-scale model are idealized by considering a mean ascending dry or cumulus toped thermal of mass-flux f, surrounded by subsidence in the environment of mass-flux −f. The fractional area αu covered by the plume, the plume vertical velocity wu and the mass-flux f = αuρwu, ρ being the air density, are computed from mass conservation:
(e and d being the entrainment and detrainment rates respectively), and from the equation of vertical momentum in stationary and frictionless conditions:
where θvu (respectively ) is the plume (respectively large-scale) virtual potential temperature. The closure of the scheme relates the mass-flux at the base of the thermal plume to the instability of the surface layer (see details given by Rio and Hourdin  and auxiliary material). Boundary layer convection and shallow clouds are represented in a unified way, with no discontinuity at cloud base. The so-called “thermal plume model” used here and similar approaches [Soares et al., 2004; Siebesma et al., 2007] were shown to effectively reproduce the diurnal cycle of the continental boundary layer on fair-weather cumulus days.
 The transition from shallow to deep convection is handled by coupling the thermal plume model with a deep convection scheme derived from Emanuel , which triggering function and closure have been modified in order to relate them to sub-cloud processes. Deep convection is initiated as soon as the kinetic energy of parcels inside thermals, called the Available Lifting Energy (ALE = ALEth = w*2/2 in J kg−1) overcomes the Convective INhibition (CIN), so that deep convection is active when:
Considering an air parcel rising adiabatically from the surface; the CIN is defined as the work of buoyancy forces in the region of negative buoyancy, around cloud base. The work of positive buoyancy forces above is called the Convective Available Potential Energy (CAPE). Here, w* is the maximal of wu on the vertical, which corresponds at transition time to the vertical velocity near the top of shallow clouds. A similar criteria was used by Bretherton et al.  for shallow convection triggering using a typical vertical velocity at cloud base.
 The flux of kinetic energy associated with thermals defines the Available Lifting Power (ALP, in W m−2) which is used to determine the convective intensity through a new ALP-closure. The convective power above inhibition Mbwb2 – where Mb is the deep convective mass-flux and wb the vertical velocity at level of free convection taken as a constant of 1 m s−1 at this stage – is computed as:
where Mb ∣CIN∣ is the power consumed to overcome inhibition and the last term is the power lost by dissipation (assumed to scale with Mbwb2). The power provided by thermals is taken as ALPth = kthρ3/2 where the third order moment of the vertical velocity reads 3 = and kth is an adjustable parameter.
 After deep convection initiation, evaporation of precipitation generates cold pools represented here by the wake parameterization described in the auxiliary material. Each atmospheric column is divided into a mean wake and its environment. The wake fractional cover within the grid cell evolves according to the wake spread rate C* which depends on the Wake Available Potential Energy, C* = k*, with
where hw is the height of wakes and k* is an adjustable parameter. The difference of virtual potential temperature between the wake and its environment, δθv, is driven to first order by reevaporation of convective rainfall in the unsaturated downdraughts of the Emanuel's scheme, supposed to take place inside wakes. Gust fronts associated with wakes provide an additional lifting energy ALEwk ≃ C*2 which maintains convection active even after thermals extinction (as long as max(ALEth, ALEwk) > ∣CIN∣), and an additional lifting power ALPwk ≃ C*3, ALP = ALPth + ALPwk being used in the ALP-closure (see details and parameters values in the auxiliary material).
3.1. Diurnal Cycle of Convection on the EUROCS Case
 We use, for evaluation purposes, the idealized EUROCS case [Guichard et al., 2004], built from observations collected over the Southern Great Plains (USA) at the Atmospheric Radiation Measurement site between the 27th and 30th of June 1997. The case is defined by initial conditions, large-scale forcings and sensible and latent heat fluxes having a maximum around midday of 120 W m−2 and 400 W m−2 respectively.
Guichard et al.  compare large-scale models in single-column mode with Cloud Resolving Models (CRMs) run on a horizontal domain corresponding to a typical grid cell of global models. CRMs succeed in simulating the observed transition from shallow cumulus in the morning to deep convection in the afternoon on that case despite a too coarse resolution (250 m to 2 km) to resolve explicitly boundary layer circulations. Parameterized convective precipitation starts around 09:00LT instead of 12:00LT, illustrating that the bias of full 3D large-scale models is reproduced when models are used in a single-column mode.
 Following the same approach, CRMs are used here to evaluate various combinations of the parameterizations presented above in the 1-dimensional version of the LMDz model (the atmospheric component of one of the IPCC global climate models [Hourdin, 2006; IPCC, 2007]) run with a vertical resolution of 31 layers for the entire atmospheric column and a 5-minute time-step starting from 5:30LT. Figure 2a displays the diurnal evolution of precipitation obtained with the various simulations and CRMs from Guichard et al. . With a classical diffusive approach for boundary layer turbulence and the original CAPE closure version of the Emanuel scheme (simulation E), rain starts too early by about 2 hours and peaks 4 hours too early compared with CRMs. Activation of the Thermal plume model (simulation ET) does not change the onset time but delays the maximum rainfall by one hour. When controlling convection by the thermal plume model with the new ALE and ALP concepts (simulation AT), the onset of precipitation is delayed from 11:00LT to 13:00LT, in much better agreement with CRMs, but precipitation is much too weak. Activation of the wake parameterization (simulation ATW) allows a gradual reinforcement of precipitation in the afternoon, resulting in both good phasing and intensity when compared with CRMs.
 How can we explain this phase shift?
3.2. Deep Convection Preconditioning
 Compared with the original simulation (simulation E), activation of the thermal plume model (simulation ET) results in a faster deepening boundary layer in the morning, with stronger heating in the mixed layer and cooling at the inversion as seen from the comparison of the convective (shallow plus deep) apparent heat source Q1 (Figure 3). As a consequence, the air is warmer and drier near surface (Figures 2b and 2c), due to a stronger mixing with tropospheric air via the compensating subsidence. Around midday, at a time close to deep convection initiation, the air is consequently moister and colder in the inversion layer (Figures 2d and 2e).
 The thermal plume model, by a better representation of boundary layer processes, thus allows a better preconditioning for deep convection: a larger inhibition, and a gradual moistening of the inversion layer by cumulus clouds. This is not enough however to delay convection with the old convection scheme. With the new scheme (simulations AT and ATW), deep convection is delayed until CIN is overcome by the thermals kinetic energy, ALEth (Figure 4a), deduced from w* (Figure 4c), which increases suddenly around midday, when the latent heat release associated with condensation in thermals is strong enough to make the vertical velocity increase from cloud base to cloud top. Convection then suddenly switches from shallow to deep.
3.3. Deep Convection Continuation
 The further evolution of convection in the afternoon is governed by several feedbacks. On the one hand, precipitating downdraughts cool the boundary layer and dry the inversion, inhibiting the formation of thermals and cumulus clouds, in turn weakening deep convection which vanishes after thermal extinction in simulation AT (Figure 3b). On the other hand, gust fronts associated with wakes reinforce convection. The additional lifting energy provided by wakes (simulation ATW; Figure 4a), deduced from C* (Figure 4c), keeps deep convection active until 20:00LT, while the additional lifting power (Figure 4b) intensifies deep convection, with an apparent heat source Q1 comparable with CRM results (Figures 3c and 3d). This yields colder air at the surface in the evening, in better agreement with CRMs (Figure 2b).
 We have shown with a single-column version of the general circulation model LMDz that it is finally possible to simulate a realistic diurnal cycle of convective rainfall with parameterized convection. In the present approach, thermals drive shallow convection in the morning and play a key role in the preconditioning and triggering of deep convection while wakes reinforce thunderstorms in late afternoon. The control of deep convection by boundary layer processes relies on the new ALE and ALP concepts, at first designed to couple the wake and deep convection parameterizations. Those concepts may also be used to account for other factors such as thermal breezes along orography slopes or land-sea contrasts.
 The set of parameterizations presented here is at the heart of the future version of LMDz, the atmospheric component of the IPSLCM4 climate model [Braconnot et al., 2007] used for climate change projections in the frame of IPCC. Hopefully it will help obtain realistic present climatology and variability of tropical rainfall and improve confidence in its evolution in climate projections, a key issue for impact studies of global warming on human societies.
 The authors want to thank Françoise Guichard for providing CRMs results on the EUROCS case and Pascal Marquet and Marie-Pierre Lefèbvre for providing the case set up. We also thank Laurent Fairhead and Jean-Louis Dufresne for useful comments on the manuscript, as well as Praveen Kumar and two anonymous reviewers. Figures and graphs were made using grads and xmgrace free softwares.