In this work, deep moist convective processes, observed during the Tropical Composition, Cloud and Climate Coupling Experiment (TC4) over the East Pacific Intertropical Convergence Zone, were modeled by means of high-resolution numerical simulations with the Weather Research and Forecasting model. Three different turbulence parameterizations and two microphysical parameterizations are used. Their impact on the spatio-temporal structure of predicted convective fields is compared to TC4 observations from a geostationary imager, airborne precipitation radar, and dropsondes. It is found that the large-eddy simulation turbulence closure “upscaled” to the terra incognita range of grid spacings (i.e., 0.1–1 km) is best suited to model the deep convective processes under examination.
 Atmospheric modeling of deep moist convective processes benefited in recent years from the growing use of high-resolution meteorological models, as well as from the increased availability of multisensor meteorological observations from spaceborne, airborne and ground-based instruments. However, combination of modeling tools and observational data is complicated by the convective nature of the events and the associated small spatio-temporal scales. In fact, while the quantity, quality, and resolution of available observational data are promoting the use (and validation) of increasingly more sophisticated and computationally demanding atmospheric models, compromises are still needed to simulate observed deep convection. Among them, the first is the choice of horizontal resolution, or grid spacing, and the associated choices of parameterizations for unresolved subgrid processes.
 A long record of atmospheric simulations seems to suggest that a 1–4 km grid spacing is sufficient to simulate deep moist convective processes, since the typical scale of a convective cell is of the order of 10 km in all three directions. In fact, the 1–4 km resolution range is generally referred to as cloud permitting and is often adopted to resolve the basic thunderstorm structure [Klemp and Wilhelmson, 1978; Redelsperger and Sommeria, 1986; Weisman et al., 1997].
Grabowski et al.  performed two- and three-dimensional simulations of cloud observed during the Global Atmospheric Research Programme Atlantic Tropical Experiment. They showed that model resolution had an effect on the upper tropospheric cloud cover and, consequently, on the upper tropospheric temperature tendency because of radiative flux divergence.
Petch et al.  focused on the development of convection in simulations of both shallow and deep convection over land and discussed the sensitivity to horizontal resolution. In both cases, they found it necessary to provide adequate resolution of the subcloud layer to obtain a satisfactory representation of the transport of moisture from the subcloud layer into the free troposphere. Typically, this required the horizontal grid spacings to be no coarser than about one-quarter of the subcloud layer depth. Poorer resolution led to significant delays in the development of convection.
Done et al.  showed how the Weather Research and Forecasting (WRF) model [Skamarock et al., 2005] at 4 km grid spacing can provide insight into the benefits of explicitly treating convection in numerical weather prediction (NWP) models, through an object-based verification of the prediction of mesoscale convective systems (MCSs) observed during the BAMEX project (Bow echo and MCV Experiment [Davis et al., 2004]). The results are encouraging and confirm the better performances of WRF at 4 km in capturing the morphology of MCSs, when compared with runs at 10 km.
Adlerman and Droegemeier , in an effort to approach the CRM range, found that simulations of supercell thunderstorms are very sensitive to horizontal resolution. They found, for example, that a simulated supercell undergoing repeated mesocyclone formation cycles simulated at a grid spacing of 1 km and smaller becomes, instead, a nearly steady state, unicellular storm when simulated at a grid spacing of 2 km.
Lang et al.  used the 3-D Goddard Cumulus Ensemble model to simulate two convective events observed during the Tropical Rainfall Measuring Mission Large-Scale Biosphere-Atmosphere experiment in Brazil: lowering the horizontal grid spacing from 1000 to 250 m and adopting microphysics parameterizations more suitable at fine resolution produced better simulations compared to observations.
 Along the same lines, Bryan et al.  studied the spatial resolution appropriate for the simulation of deep moist convection from a turbulence perspective. Numerical simulations of squall lines were conducted with grid spacing between 125 and 1000 m. The results reveal that simulations with 1 km grid spacing do not produce equivalent squall line structures and evolution compared to the higher-resolution simulations. Details of the simulated squall lines that change as resolution is increased include precipitation amount, system phase speed, cloud depth, static stability values, thunderstorm cell size, and organizational mode of convective overturning (e.g., upright towers versus sloped plumes).
 Recently, Fiori et al.  tackled the problem of understanding how the uncertainty in the NWP of extreme events is affected by the adoption of smaller grid spacing and by the choice of turbulence parameterization used to represent subgrid scale mixing processes.
 The studies by Bryan et al.  and Fiori et al.  addressed a novel crucial issue in the modeling of deep convective processes at very fine resolution: the joint choice of turbulence parameterization (or closure) and of grid spacing.
 In current meteorological applications, two main classes of modeling philosophies can be identified [Wyngaard, 2004]: mesoscale modeling on larger domains and large-eddy simulation (LES) on the small ones. Their fundamental difference is the value of L/Δ, the ratio of the energy-containing turbulent scale L over the scale Δ of the spatial filter used in the equations of motion, which can be interpreted, to some extent, as the model horizontal resolution.
 By assuming ΔMESO = O (10 km), as in traditional mesoscale modeling, no turbulence is resolved since L/ΔMESO < 1; in traditional LES, ΔLES = O (0.1 km), both energy and flux-containing turbulent eddies are resolved, albeit crudely in some cases, since L/ΔLES ≫ 1. Until recently, the L/Δ values and domain sizes for mesoscale modeling and LES were nonoverlapping.
 The introduction and rapid evolution of the CRM concept, supported by continued increases in computing power [Xue et al., 2007], allows today use of very fine grid spacings over domains typical of mesoscale modeling. Consequently, the ratio L/Δ for CRM is approaching the values traditionally used in relatively coarse-resolution LES of severe storms (i.e., L/Δ ≈ 1 [Wyngaard, 2004]).
 Since neither LES nor mesoscale modeling is designed to operate in this L/Δ range, Wyngaard  proposed to term it the terra incognita. In this scale interval, 0.1 < Δ < 1 km, a new issue emerges: since the subgrid parameterization carries significant fluxes, it is not clear whether it is more appropriate to “downscale” the turbulence parameterizations used in mesoscale models or to “upscale” LES turbulent closures (Figure 1).
 This issue can be easily translated in an important question challenging the numerical modeling in the terra incognita range: It is necessary to establish whether the performances of these two turbulent closures are satisfactory in the terra incognita range.
 To address this question, we selected a deep moist convection scenario, observed during the Tropical Composition, Cloud and Climate Coupling Experiment (TC4) in July 2007 in the East Pacific Intertropical Convergence Zone (ITCZ). In this scenario, several favorable characteristics are encountered: a large number of convective cells were triggered and evolved within a domain of manageable size (i.e., a few hundred square kilometers); the convective cells developed in kinematic and thermodynamic conditions that are good representation of a quasi-equilibrium convective situation [Emanuel, 1994]; and numerous in situ and remote sensing observations are available from airborne and spaceborne instruments to assess the modeled results.
 This scenario was modeled with a version of WRF customized to allow use of three different turbulent closures and two microphysical parameterizations. The microphysical parameterizations are two six-class single-moment schemes (water vapor, cloud water, rain, cloud ice, snow, and graupel) included in the standard WRF package and recommended for use at these resolutions. One of the three turbulence parameterizations is representative of the mesoscale modeling approach, and two are representative of the LES approach.
 Their impact on the spatio-temporal structure of convective fields is analyzed by comparing simulated observations to actual observations. The scope is similar to that of Otkin and Greenwald , who used Moderate Resolution Imaging Spectroradiometer-derived cloud data to study WRF model sensitivities to different turbulence parameterizations and microphysics, but they were interested in the cloud-permitting range instead of the terra incognita range.
 This paper is organized as follows. In section 2, the customized nonhydrostatic WRF model is presented, and particular attention is paid to the presentation of the turbulence parameterizations adopted here. The experimental settings adopted in this work also are discussed. Section 3 describes the observations from TC4 with a special focus on the deep moist convection scenario under examination. Section 4 presents and discusses the results of the numerical experiments with the WRF model and their comparison with available observations. In section 5, conclusions are drawn.
2. Turbulence Parameterizations
 We use a customized version 2.2 of the WRF modeling system [Skamarock et al., 2005], a fully compressible, nonhydrostatic, scalar variable-conserving mesoscale model. Created in 2000 by the National Center for Atmospheric Research and developed continuously, the WRF model is used for operational forecasting and research purposes. The physics of the model is based on a wide range of radiative, turbulence, surface, and microphysical parameterizations. In this section, we describe and analyze the turbulence parameterization chosen as representative paradigms of the subgrid scale (SGS) turbulent schemes in the mesoscale and LES limits, respectively. We also introduce the different experimental settings adopted for the simulation of the deep moist convective scenario under examination.
 The Yonsei University (YSU) planetary boundary layer (PBL) scheme [Hong et al., 2006] is a vertical turbulent diffusion package with a nonlocal turbulent mixing coefficient in the PBL. This scheme is based on the studies by Hong and Pan  and Noh et al. ; it is suitable for mesoscale weather forecasting and climate prediction models. The major strength of the YSU scheme is the inclusion of an explicit treatment of entrainment processes at the top of the PBL and the use of the countergradient terms to represent fluxes caused by nonlocal gradients.
 PBL height h is defined as the level where minimum flux exists inside the inversion layer; according to Hong et al. , in the mixed layer region (z ≤ h), the turbulence diffusion equation for a generic prognostic variable C is
where Kc is the turbulent diffusion coefficient, γc is a correction factor to the local gradient that incorporates the contribution of the large-scale eddies to the total flux, and the second term on the right represents the asymptotic entrainment flux in the inversion layer. The term is the flux at the inversion layer, w′ is the vertical velocity perturbation, and c′ is the perturbation term for C.
 Above the mixed layer (z > h), a local diffusion approach is adopted to account for free atmospheric diffusion. For a more comprehensive description of the YSU model, the reader is referred to the study by Hong et al. .
 In this work, the YSU PBL scheme is used in combination with a Smagorinsky first-order closure approach (S1) [Smagorinsky, 1963], which independently handles the horizontal turbulent mixing as a function of the horizontal deformation tensor.
2.2. LES-Type SGS Turbulence Parameterization: Turbulent Kinetic Energy Equation for the 1.5 Order Turbulence Closure
 The 1.5 order LES turbulence parameterization [Deardorff, 1980; Moeng, 1984] adopted in this study is based on the following prognostic equation governing the evolution of the turbulent kinetic energy e:
where μdis the dry hydrostatic pressure difference between the surface and top of the model; V is the velocity vector; the shear production term is a function of the deformation tensor D, where Kh and Kv are the horizontal and vertical turbulent diffusion coefficients and (x,y,η) are the coordinates:
the buoyancy term is provided by the following formula, where the Brunt-Vaisala frequency N is computed with either the formula for a moist saturated or unsaturated environment:
and the dissipation term is provided by
The vertical and horizontal turbulent diffusion coefficients are computed according to the following expression:
where CK is a constant, ranging between 0.15 and 0.25, and lh,v is the horizontal and vertical mixing length.
 Two possible formulations exist for the LES-based turbulence parameterization: anisotropic and isotropic.
 The isotropic formulation (hereafter LES_iso) holds if the horizontal resolution Δx is less than a critical length scale lcr (here lcr = 500 m), then
Both the horizontal and vertical turbulent diffusion coefficients are multiplied by the inverse turbulent Prandtl number calculated as Pr−1 = 1+2l/(ΔxΔyΔz)1/3.
 The anisotropic formulation (hereafter LES_ani) holds if the horizontal resolution Δx > lcr, then:
The turbulent diffusion coefficient used for mixing scalars is divided by the turbulent Prandtl number Pr, calculated as Pr = 1/3 for the horizontal turbulent diffusion coefficient Kh and as Pr = (1+2l/Δz)−1 for the vertical turbulent diffusion coefficient Kv.
2.3. Design of the Numerical Experiments
 A system of four two-way nested domains is adopted: the corresponding horizontal resolutions are 9, 3, 1, and 0.333 km, respectively (Table 1), ranging from the mesoscale to the CRM limits. The finest horizontal resolution is consistent with the grid spacing recommended by Craig and Dörnbrack  for the numerical simulations of the mixing processes in cumulus clouds. They identified two possible candidates for cloud-resolving resolution: the size of cloud D0 [Morton et al., 1956] and the buoyancy scale Lbuoy = [Stiller and Craig, 2001]. The smaller of these two scales should be resolved for LES of cumulus clouds, which is D0≈ 3–4 km, Lbuoy≈ 300–400 m in this study.
Table 1. Domain Parameters and SGS Turbulent Schemes Adopted for Each Member of the WRF Numerical Experiments
Min, minimum; Lat, latitude; Max, maximum; Lon, longitude.
 The outermost domain (d01), whose size is consistent with the recommendation of Johnson et al.  for modeling of tropical convective systems, adopts the Kain-Fritsch convective parameterization [Kain and Fritsch, 1990, 1993]. Convective parameterization is switched off for the remaining domains, in agreement with recent studies that provided skillful guidance for convective system morphology when convection is assumed to be resolved explicitly, albeit crudely, at horizontal grid spacing below 4–5 km [Done et al., 2004; Kain et al., 2008; Weisman et al., 2008]. Atmospheric radiation is parameterized for all domains with the Eta Geophysical Fluid Dynamics Laboratory longwave and shortwave schemes [Fels and Schwarzkopf, 1975; Lacis and Hansen, 1974]. The surface layer is parameterized according to the Monin-Obukhov similarity theory scheme derived from the MM5 model [Monin and Obukhov, 1954]; it allows computation of friction velocities and exchange coefficients that enable the calculation of surface heat and moisture fluxes.
 To investigate the performance of downscaled mesoscale turbulence parameterizations versus upscaled LES turbulence parameterizations in the terra incognita range, a set of six numerical experiments is designed: the three SGS turbulent closures (YSU/S1, LES_ani, LES_iso) are combined with two different microphysical parameterizations. The two microphysical parameterizations are the WRF Single Moment 6-class scheme (WSM6) [Hong et al., 1998] and the Thompson microphysical scheme (TM) [Thompson et al., 2004]. WSM6 and TM are the recommended microphysical parameterizations for WRF (version 2.2) applications at these grid sizes. They were selected to analyze the model sensitivity to changes in thermodynamical atmospheric structure induced by different microphysical assumptions, under three different turbulence parameterizations.
Table 1 summarizes the parameters and turbulent schemes adopted for each numerical experiment: the first character of each member ID indicates the turbulence parameterization (Y = YSU/S1, A = LES_ani, I = LES_iso), and the second character indicates the microphysics (W = WSM6, T = Thompson).
 All experiments were initialized at 1200 Z on 23 July 2007, with input from the National Centers for Environmental Prediction (NCEP) Global Reanalysis product at 1° × 1° resolution. All experiments lasted 36 h.
3. Observation of an ITCZ Convective System During TC4
 Many facets of the chemical, dynamic, and physical processes occurring in the tropical upper troposphere and tropopause transitional layer are not well understood. Identifying the key processes in this region is essential for progress on issues involving global climate change, stratospheric ozone depletion, and global tropospheric chemistry. Along these lines, the TC4 experiment investigated the structure, properties, and processes in the tropical eastern Pacific [Toon et al., 2010].
 One of the TC4 aircraft sorties collected a number of observations for an ITCZ event on 24 July in the eastern Pacific area, around 400 km to the south of Costa Rica (local time = UTC + 6 h). The scenario considered here is associated with a system of deep moist convective cells initiated in the early morning, nearly stationary in terms of location, and persisting until the late evening of 24 July because of highly favorable thermodynamical and kinematical environmental conditions.
Figure 2 provides a comprehensive overview of this convective scenario as depicted by the GOES infrared brightness temperature (from Langley Cloud and Radiation Group home page http://angler.larc.nasa.gov/tc4/) (P. Minnis et al., Cloud properties determined from GOES and MODIS data during TC4, submitted to Journal of Geophysical Research, 2009). In the early stage of the event (before 1100 Z), the level of convective activity in the study region (indicated by the black box) is low and characterized by the presence of shallow convection with limited vertical development (<2500–3000 m); a more mature convective system is present in the area to the northwest (labeled with A). The area of shallow convection intensifies in the early morning. Of particular interest for this investigation is the small, isolated region with infrared brightness temperature TIR < 240 K that appears in the 1115 Z image and evolves in a system of intense convective cells characterized by a well-defined anvil (AN) by 1300 Z (labeled with B). System B further intensifies and deepens, and at around 1515 Z it merges with system A. In the next half-hour, the merged system grows in spatial extension, vertical development, and intensity. One important characteristic of this convective activity is that from the instant of initial trigger at 1115 Z until the late afternoon, it exhibited steady and sustained activity with no significant contraction of the AN at any intermediate point.
 This case study is of interest for this investigation because it is representative of common deep moist convective scenarios in the ITCZ developed in quasi-equilibrium conditions. The quasi-equilibrium conditions occur when the production of convective available potential energy (CAPE) by large-scale processes is nearly balanced by its consumption by convective phenomena; therefore, the CAPE values remain relatively small [Arakawa and Schubert, 1974]. In quasi-equilibrium conditions, the convection is dependent on and responds to thermodynamical destabilization induced by boundary conditions and physical processes as such radiative cooling, adiabatic cooling by large-scale ascent, and surface fluxes. Then convective time scales can be assumed small compared to time scales of forcing changes, and, consequently, the convection may be considered to be in a state of statistical equilibrium with the forcing itself [Emanuel, 1994, 2000]. The quasi-equilibrium conditions rarely generate dramatic overshootings of the troposphere (e.g., beyond 15 km altitude), but they often penetrate the tropical tropopause layer (TTL) through its lower boundary (at around 200 hPa). As such, their role in the moistening of the TTL is considered to be of critical importance, but their role is not as well understood as that of other cloud types [Toon et al., 2010, and references therein].
 The NASA DC-8 approached this region of convective activity at 1340 Z from the north and collected in situ and remotely sensed data until about 1600 Z. Two penetrations in convectively active regions occurred at about 1340 and 1520 Z, respectively, and observations of the resulting anvil were obtained throughout the ∼2 h interval.
 The case study of primary interest is the penetration around 1520 Z of a convective region including aged outflow, four convective cells at various stages of maturity, and a rather extensive transitional region around said convective cells (Figure 2). A detailed discussion of the microphysical characteristics of this system is provided by Jensen et al. . In this study, we focus on the thermodynamical information provided by the DC-8 dropsondes and the data collected by the Airborne Precipitation Radar 2nd Generation (APR-2) [Sadowy et al., 2003], combined with the GOES images.
Figure 3 shows three soundings at 1459, 1504, and 1528 Z. The release points are depicted in Figure 2 superimposed to the TIR scene at 1528 Z.
 Dropsonde 1459 Z was dropped at the interface between systems A and B during their merging phase. The atmospheric column can be divided in three portions: an almost perfectly saturated region in the layer at 1000–600 hPa representing intense moist convection processes in the lower and middle troposphere; a subsequent dry layer over 600–400 hPa; and a further saturated region straddling the 400 hPa level and suggesting the presence of an anvil in its mature stage. The corresponding APR-2 radar imagery confirms this subdivision by showing a region of shallow warm rain processes topped by a mature anvil composed of larger crystals advected from the convective area of interest to the northeast and embedding a younger convective cell topping at 9 km and beginning to generate its own small anvil.
 Dropsonde 1504 Z was dropped in the southern portion of the main convective system resulting from the merging process: the corresponding thermodynamical structure is quite similar to the one reported by dropsonde 1459 Z, with less pronounced saturation features suggesting a more marginal penetration in the active region. Radar imagery shows only a sporadic warm rain process topped by a thin cirrus shield.
 Similar thermodynamical profiles were measured (albeit partially) by dropsonde 1528 Z dropped to the south of the mature convective activity observed by APR-2 between 1520 and 1526 Z.
 The CAPE calculated from these profiles is in the 1200–1400 J kg−1 range, with negligible convective inhibition values, confirming the quasi-equilibrium character of these events. Consistent with observations, CAPE values calculated from the WRF experiments are in the 1200–1600 J kg−1 range.
Figure 4 shows the APR-2 observations of the convective area. As discussed by Jensen et al. , four distinct convective cores (only the first three are included in Figure 4) are surrounded by an extensive transitional area and flanked to the west by a portion of stratiform rain generated by aged outflow. The vertical velocity profiles of the four convective cells vary in maximum intensity (around 10–15 m/s) as well as vertical development, possibly reflecting different stages of maturity. Two measured quantities suggest that the subfreezing portion of the transitional area is mainly composed of small (i.e., mean particle size <0.9 mm), high-density (i.e., ≫ 0.1 g/m3) ice particles: the dual wavelength ratio (DWR) between the observed reflectivity at Ku band and that at Ka band assumes values close to 0 dB throughout the cloud layer (indicating that the scattering properties of the dominant particles are in Rayleigh regime at both frequencies and therefore small with respect to the wavelengths [e.g., Rose and Chandrasekar, 2005, and references therein]); and the mean Doppler velocity does not show a sharp increase in correspondence to the zero-isotherm (characteristic of low-density aggregates melting into raindrops). In fact, the contrast with the portion of cloud associated with the aged outflow is evident in these measurements. It allows us to identify immediately the two distinct portions of this system: in the aged outflow portion, the rapid increase in DWR just above the melting layer is typical of the aggregation processes, and the sharp increase in terminal velocity is typical of melting low-density ice particles (where also the DWR drops back to near-zero decibel values reflecting the reduction in size from snowflakes to raindrops).
 The bottom panel of Figure 4 shows in color the retrieval of mean particle diameter (mass weighted) obtained by the APR-2 Bayesian retrieval algorithm. The iso-Doppler curves in red and blue mark the location of the updrafts (UDs) and downdrafts, respectively, whereas the thin and thick black curves are positioned at the 0.1 and 1 g/m3 total hydrometeor density contours.
4. Results and Discussion
 Here we analyze the influence of the different turbulence parameterizations on the WRF model's predictive ability in the terra incognita range by comparing actual observations to observations simulated from the model output (i.e., predicted versus observed thermodynamical, kinematical, and microphysical features and spectral characteristics).
 GOES imagery is compared to assess performance in capturing the main qualitative aspects of the triggering and spatio-temporal evolution of the convective scenario. Radar measurements are compared to assess performance in reproducing vertical profiles of microphysical and dynamical quantities in convective areas. Soundings are compared to assess performance in reproducing vertical profiles of thermodynamical quantities. Power spectral analysis is also undertaken to evaluate performance in representing the turbulent energy cascade. This part of the investigation allows us to determine how accurately the model resolves features of various wavelength and to find the resolution limits and the effectiveness of the dissipation mechanisms [Bryan et al., 2003; Skamarock, 2004].
4.1. GOES Imagery
 The frequent updates of GOES imagery allows us to assess whether a given experiment setup is able to properly trigger and sustain the convective structures. This allows us to evaluate the model efficiency in reproducing the cold pool/shear interaction and mixing processes inside the PBL.
 WRF outputs were sampled every 5 min and were used to obtain rough simulations of TIR images as described by Rossow and Schiffer  and references therein. Hereafter, we will indicate the GOES observations with TIR,G and the simulated ones with TIR,##, where ## is the member ID from Table 1.
 To provide more insight into the simulated TIR images, Figure 5 includes the corresponding map of profile classification where nine classes are identified: clear air, updraft, downdraft, transition (defined as the region with moderate vertical air motion and significant graupel loading surrounding convective cores), stratiform (defined as the portion of a cirrus shield with precipitation reaching the surface), anvil (defined as the portion of a cirrus shield without precipitation reaching the surface), warm rain, warm cloud, and other. The specific criteria adopted to classify profiles in this work are summarized in Table 2.
 For the sake of clarity, the results are presented separately for WSM6 and TM.
Table 2. Criteria Used to Classify Modeled Profilesa
Condition on Cgb + Cs
Condition on Cl
Condition on W
The table should be read by first applying the discrimination in the first row to determine the side of the table to be used and then intersecting with the appropriate conditions for that side. All profiles not satisfying any of the conditions are classified as other (OT).
Figure 5 shows TIR,YW and TIR,IW maps for the time window 1100–1600 Z, covering the spatio-temporal evolution of the observed convective scenario from its triggering (see Figure 3 at 1100 Z), through the deepening phase (1100–1400 Z), up to the mature stage (1400 Z onward).
 At 1100 Z, experiment YW does not show any clear evidence of convective initiation. Until 1200 Z, it is dominated by the presence of large cirrus areas and shallow convection; a few isolated updrafts hardly can be detected at 1200 Z in the western portion of the domain. By 1300 Z, a few scattered updrafts have generated a small anvil in the western portion of the domain, while new more intense activity has just initiated in the eastern portion. Over the time interval 1300–1600 Z, while the observations show the ongoing merging between convective systems A and B, experiment YW shows that the convective structures initiated at 1200 Z are already completely dissipated, and also that the few new entities initiated around 1300 Z have begun dissipating. Thus, experiment YW, driven by YSU turbulent closure, does not seem to be able to properly trigger and sustain the convective activity compared to observations.
 Experiment IW predicts a convective area in the northwest corner of the domain, which intensifies progressively until 1600 Z. The isolated convective cell evolves in a deep moist convective system that is highly persistent, towering in nature (achieving a considerable vertical development as testified by TIR values around 210–220 K around 1600 Z), and dominated by the presence of two intense updraft areas. Around 1500 Z, convective activity is initiated also in the eastern sector. Thus, the predictive ability of WRF improves significantly when the LES turbulent closure, in isotropic mode, is applied over the innermost domain (d04).
 It is noted that both convective systems (A and B) in the simulations appear offset about 60 km to the west with respect to observations as shown in the example in Figure 6. This discrepancy is not critical for this study, nor surprising, since the resolution of the NCEP initialization data set is 1° × 1°. The goal of this study is not to capture the exact location of observed convective cells but to reproduce properly the corresponding physical processes and related statistical properties.
 Experiment AW represents the intermediate SGS parameterization step between the pure mesoscale turbulent closure (YW) and the isotropic LES (IW). It provides results (not shown here for sake of conciseness) that are qualitatively between those discussed for YW and IW.
4.1.2. Thompson Microphysics
 The YSU-driven experiment YT shows poor behavior in terms of predictive ability, being unable to trigger and sustain adequately the deep moist convective processes compared with those observed through GOES images (compare Figure 7 with Figure 2). This is especially true over the time period 1100–1300 Z, where the atmospheric scenario is dominated by large anvils and transition zones, while convective updrafts are nearly absent. The situation improves at 1400 Z, when some convective cores develop over the southwestern part of the domain. In fact, a small convective region developed very deep convection, comparable in vertical extent to the strongest among those generated by experiment IW, with updraft velocity reaching 12 m/s at 13 km altitude, but, once again, this area is not persistent neither in time nor in space, and it collapses shortly after 1600 Z, contrary to those developed in IW.
 Experiment IT shows a convective system in deepening phase around 1100 Z that migrates to the west while maintaining its intensity and spatial coherence. A new convective tower appears around 1500 Z in the southern portion of the domain. The systems of convective cells produced by experiment IT are less extended spatially and more intermittent in time than those provided by the IW case. This difference can be due to the different behavior induced by TM compared with WSM6: TM produces a large amount of snow at all levels in the atmosphere because of enhanced cloud ice content in the upper troposphere [Otkin et al., 2006]. This results in the formation of smaller droplets with a slower fall speed than WSM6. In that study, TM was deemed not suitable for the modeling of intense and persistent convective processes. Indeed, TM was designed to represent the major physical processes characteristics of precipitation development in wintertime midlatitude storms with the particular emphasis on the problem of predicting freezing drizzle events [Thompson et al., 2004]. Our comparison between TIR,G and TIR,#b sustains such a conclusion that intense convection was generated in YT and IT but did not persist as long as in IW.
4.2. Airborne Radar Measurements
 As is often the case, high-resolution airborne observations of convection during this case study are too sparse in time to allow the reconstruction of the life cycle of a single convective cell. However, comparison between a model run and such snapshots is of high interest for two main reasons. First, in cases such as this one in areas void of land- or ship-based instrumentation, airborne snapshots are often all that it is available. Second, there is a need to develop methods to maximize the usefulness of low Earth orbit-based observations that are, in most cases, affected by the same exact weakness.
 In general, we aim to address the following question: Given a set of alternate model runs, each providing a time-lapse representation of the convective activity inside the region of interest, what kind of metrics can be extracted from the comparison with observed radar snapshots? And how can the alternate model runs be ranked in this sense?
 One classical method is that of assuming stationarity and therefore time-space equivalence: a 3-D snapshot is considered a representative sample of the characteristics of the system, both in time and space.
 We chose not to adopt the time-space equivalence approach for one main reason: the aircraft trajectory was not randomly chosen with respect to the storm dynamics and location (as it is for a spaceborne observation). In fact, the occurrence of convective activity in the observed data set is mainly determined by conscious decisions taken onboard the aircraft, decisions based on a plethora of scientific and safety considerations and not by the true statistics of occurrence.
 Instead, we extracted from the model runs a large number of “convective cell histories,” and we constructed a database of complete cell lifetimes (see Appendix A for details). In this context, we refer simply to convective cell history as the evolution of a sequence of convective cells evolving from a common convective environment. For each convective cell and for each instant of its history, a set of simulated APR-2 measurements was obtained by applying a Doppler radar simulator (adapted from the one used by Tanelli et al. ) with the APR-2 parameters. A total of about 400,000 profiles of the radar equivalent reflectivity factor at Ku and Ka bands (ZKu and ZKa), and of mean Doppler velocity at Ku band (VKu), was generated this way to represent the six experiment members.
 The properties of vertical profiles can be analyzed by means of contoured frequency by altitude diagrams (CFAD). Figure 8 shows the CFAD of radar reflectivity at Ku band (ZKu), dual wavelength ratio, and mean Doppler velocity (VKu) for the 167 observed APR-2 profiles of the two mature convective areas included in system B (cell B1 is shown also in Figure 4 between 4.5 and 5 min from the start of the file). The corresponding CFAD from simulated APR-2 measurements obtained from experiments YW, IW, YT, and IT are shown in the bottom rows. A few general considerations can be drawn from the comparison of modeled and observed profiles: (1) the observed variability of the vertical velocities is significantly larger than the modeled ones; visual inspection of the observed profiles revealed profiles with double-peaked updrafts and other features that were at a scale smaller than the model vertical resolution (about 750 m above the zero isotherm); (2) the loading of liquid water below the zero isotherm is larger in the observations than in the modeled profiles (reflected by the larger DWR values present between 3 and 5 km altitude); and (3) the size of particles and the amounts of cloud liquid water lifted up to the 10 km altitude are, in general, slightly larger in the observations than in the modeled profiles (reflected by the larger values of DWR at 10 km altitude), with the LES_iso-driven experiments being more capable in approaching the observed DWR. Comparison among the four experiments indicates that YW was the least capable to produce vertically developed convection, and while YT produced somewhat larger values of negative vertical velocity (upward), IW was the most efficient in lifting significant quantities of large condensate in the upper troposphere (reflected by the larger values of ZKu and DWR above 10 km altitude). Indeed, although the comparison of revealing features provides some insight into the skills of each experiment in reproducing the observed profiles, the general differences between the observed and modeled CFAD indicate that the WRF model with these settings is only marginally capable to resolve the high-resolution features of the convective processes at hand. A finer resolution or more sophisticated microphysics schemes are expected to provide more accurate representation of convective cores, to the expenses of computational time.
 In an attempt to further quantify the model performance under the different settings, the best match in mean least square sense was searched in the set of profiles simulated from the convective cell histories for each observed profile of ZKu, ZKa, and VKu (VKu expressed in m s−1 was weighted by a factor of 2 to equalize dynamic ranges with respect to the reflectivities expressed in dBZ). In other words, one-third of the observed profiles was not reproduced well by any of the model experiments, at any time and any position, reflecting once again the stronger variability of the observed profiles with respect to the modeled ones. For the other two-thirds, visual inspection confirmed that the best matching profile was capturing satisfactorily well the major characteristics of the profile. In general, the performance of the six experiments was comparable; however, a subtle but persistent difference emerged when we ranked how many times each experiment had produced the “best match” for each APR-2 profile. The results of this ranking are reported in Table 3. In 63% of cases, the best match was found among those generated from members IW; 20% were found among those generated by YW; and 9% were from AW. We note that the same comparison performed with the metric for VKu weighted with a factor of 1 (i.e., one m/s error equating to a 1 dB error in reflectivity) yielded significantly better performance for experiment YT mainly to the expenses of YW. This indicates that YW may statistically outperform YT in terms of modeled vertical profiles of vertical velocity, but the opposite is true when the resulting vertical distribution of hydrometeors is concerned. In both cases, a majority of profiles found their best match in experiment IW.
Table 3. Number of APR-2 Profiles Observed in and Around the Two Mature Convective Cores That Were Best Matched by Each Experiment
 In all, APR-2 observations are in better agreement with the adoption of WSM6 than TM in this specific case study. Furthermore, a majority of profiles found their best representation in the profiles driven by the LES_iso turbulence parameterization.
 The advantage in using WSM6 for this case study can be attributed mainly to the fact that WSM6 is known to produce more graupel than snow aggregates, while the opposite is true for TM (see, for example, the two cells depicted in Figure A1). As discussed in section 3, APR-2-based retrievals of microphysical properties indicated that a very large transition region dominated by small graupel particles was surrounding the convective cores. These conditions are quite peculiar to this specific scenario observed during TC4 in the ITCZ.
 The advantage in using IW (LES_iso + WSM6) appears to be linked to the generation of updrafts that are perhaps even slightly weaker in maximum intensity than those generated with YSU/S1, but they are also more vertically developed and sustain a more efficient uplifting of large condensate to the upper troposphere, as discussed in detail in section 4.3.
4.3. Thermodynamic and Kinematic Considerations
 An explanation for the better performances of experiment IW is provided by the analysis of thermodynamical profiles, vertical velocity spectra, and water vapor fluxes at the surface.
 The predicted mean thermodynamical profiles were computed over the nine regions classified in section 4.1. The mean profiles for the updraft and anvil regions for experiments YW and IW at 1500 Z are shown in Figure 9. Profiles in the AN region are shown for comparison to the dropsonde observations: a well-defined saturated region is visible in the 1000–600 hPa layer with a drier zone above it and a moistening inside the anvil. Indeed, the relative humidity inside the modeled anvil in all experiments is not as high as in the observations; however, experiment IW achieves values slightly closer to observations with respect to the others.
 What is perhaps more interesting is that experiment IW, driven by LES closure in isotropic mode, is characterized by more vertically developed updrafts (Figure 9, UD IW) as reflected by the atmospheric column almost fully saturated up to 250 hPa. The same statement does not hold for YW, where the updrafts top at about 10 km and are less sustained over time, as reflected in the air column saturated only up to 400 hPa. The simulated profile for UD YT (not shown) was the only other one comparable to UD IW, the main difference being the fact that the occurrence of updrafts in YT was more sporadic than IW, as discussed in section 4.1.
 Vertical velocity spectra (not shown) were calculated at 1000, 2500, 5000, and 7500 m altitude, respectively. All experimental settings properly describe the turbulent kinetic energy cascade from large scales to small ones [Bryan et al., 2003; Skamarock, 2004]. All spectra show a well-defined inertial subrange with a power spectral slope around −5/3, and they do not show the typical artifact indicative of shorter wavelengths being aliased over longer wavelengths (i.e., a slope inversion at the high-end end of the spectra). However, experiment IW slightly outperforms the remaining experiments when the width of the inertial subrange is examined: IW produces an inertial subrange between about 1 and 3 km wavelength, indicating a better representation of the turbulent energy cascade with respect to YW (where the inertial subrange ends at about 1.5 km) and resulting in a more realistic representation of the vertical velocity field. Experiment IW produces also a vertical velocity field more turbulent with a total variance from all wavelengths 2–3 times larger than YW.
 Water vapor surface fluxes, QFX, shown at time step 1500 Z in Figure 10, indicate that experiment IW is characterized by a better defined interface between a low QFX region and a high QFX region resulting in a higher efficiency in triggering and supporting deep moist convective structures, as discussed also by Johnson et al. .
 All these results are consistent with the outcomes of sections 4.1 and 4.2, where the experimental setting IW appears to be able to trigger a higher number of convective cells and sustain them for a longer time, as observed in the field.
 Six modeling experiments were implemented, in the terra incognita range of grid spacing (i.e., 0.1–1 km), to test the effectiveness of three different turbulence parameterizations and two microphysics parameterizations against observations collected during TC4 in 2007.
 Comparison of real and simulated infrared brightness temperature imagery, soundings, and airborne dual-frequency Doppler radar measurements indicates that an LES-type turbulence parameterization upscaled in isotropic mode combined with the WSM6 microphysical parameterization is best suited to reproduce the observed scenario of convective activity in the East Pacific ITCZ. In general, as expected, the choice of the microphysical parameterization does have a significant impact on the model performance in reproducing deep moist convection since it affects the characteristics of updraft profiles and persistence via its implications in regard to particle density, size, and terminal velocity, which drive all underlying processes and the associated energy release and absorption [e.g., Grabowski, 2003; Parodi and Emanuel, 2009]. In fact, while the WSM6/LES_iso combination appears to perform best for this specific case study, it is interesting to point out that, in many respects, the experiment that performed second best among the six was the one derived from the TM/YSU/S1 combination. Additional work, possibly involving an extensive experimentation with more recent and more complex microphysics parameterizations (e.g., explicitly binned), is necessary to extend the results of this work to other atmospheric scenarios.
 Given a sequence of 3-D WRF model outputs, sampled every 5 min and with 333 m grid spacing, convective cell histories were extracted in two steps.
 1. The hunter algorithm described by von Hardenberg et al.  to extract rainfall cells from ground-based weather radar CAPPI was modified to extract convective cells out of WRF model output fields. The quantity used to perform the extraction and identification of each convective cell is the cloud liquid water mass flux at 5 km altitude. The algorithm is based on the following procedure: a maximum in the cloud water mass flux field is defined as a pixel value that is larger than any of its 20 neighbors. Each maximum constitutes a cell. Around each cell center, gradually lower contour levels are traced, and the horizontal extent of each rain cell corresponds to the connected region that has a value larger than a chosen level. Here we retain only cells corresponding to maxima larger than 0.015 kg/kg m/s.
 2. For each experiment, the time steps richer in well-defined convective cells were used as initial time T0 for a tracker algorithm initialized with the results of the hunter algorithm (cell position and size). For each cell, a local 3-D grid was then constructed from position and size at T0, and the corresponding field of vertical velocity was calculated. Maximum correlation with the vertical velocity field at a previous time step was propagated backward and forward in time from the initial position to lock on the convective activity and advect the local 3-D grid according to the horizontal motion of the convective core. When the local vertical velocity field ceased to exhibit any significant signature, the local grid was stalled in place.
 Two examples of the history of convective cells are shown in Figure A1.
 This work was performed at Jet Propulsion Laboratory under contract with NASA, in collaboration with the CIMA Research Foundation with the support of the Italian Civil Protection Department. Support from the NASA Cloud and Radiation Program, Precipitation Measurement Missions Program, and Earth Sciences New Investigator Program is gratefully acknowledged. We are grateful to W.-K. Tao, F. Siccardi, R. Rotunno, Z. S. Haddad, K. A. Emanuel, S. L. Durden, and M. Antonelli for enlightening discussions and useful comments.