1. Introduction
A large percentage of convective precipitation stems from traveling mesoscale systems of scale ∼100 km consisting of heavily precipitating clusters of cumulonimbus embedded in stratiform regions usually associated with moderate precipitation. This manifestation of convective organization is evident as squall lines, mesoscale convective systems, and mesoscale convective complexes as well as multiscale precipitating systems embedded in the tropical intraseasonal oscillation. The mechanistic properties of organized convection have been investigated thoroughly by observational analysis, numerical simulation, and dynamical models. However, in addition to understanding the underlying mechanisms, there is the important practical problem of how to approximate convective organization in models that contain just a subset of atmospheric motion scales. This convective organization is conspicuously absent from contemporary parameterizations, reflecting difficulties in approximating dynamical properties such as propagation, coherence, and upscale transport.
The existence of convective organization and the role of environmental shear in the organization process has long been known (see Ludlam 1980) and has gradually been quantified in the interim. Over the tropical oceans, the ubiquity of convective organization was an unanticipated finding from the Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE) field campaign (Houze and Betts 1981). Studies in the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA-COARE) show interlocked scales of organization during the active phase of the tropical intraseasonal oscillation (WCRP 1999). Precipitation radar and passive microwave sensors on the Tropical Rainfall Measuring Mission (TRMM) satellite affirm the ubiquity of organized convection in the Tropics and subtropics (Nesbitt et al. 2000).
During summertime over North America and almost on a daily basis during strong episodes of convective precipitation, convective systems originate in the neighborhood of the Continental Divide fed by synoptic-scale upslope circulations. The systems continually regenerate and travel eastward for ∼1000 km steered by the prevailing westerly winds. Strong nocturnal storms having extensive stratiform regions travel over the Great Plains, stoked by moisture transported deep into the continent by the nocturnal jet from the Gulf of Mexico. The radiative effects of the extensive stratiform regions almost remove the diurnal variability of precipitation in the Midwest (Knievel et al. 2004).
The Carbone et al. (2002) analysis of Next-Generation Weather Radar (NEXRAD) data quantified the propagation characteristics of organized precipitating convection and provided datasets for model verification. Wavelet analysis of the radar data reveals variability on time scales ranging from semidiurnal to interannual (Hsu et al. 2006). Satellite observations show traveling systems of a similar kind over continents throughout the world (Laing and Fritsch 1997). This implies basic relationships among mountainous orography, traveling convective organization, and nonlocal dynamics that modulate the diurnal cycle of precipitation in ways not represented by contemporary convective parameterizations.
Traveling convective systems have been widely simulated (see review papers in Smith 1997). In particular, systems over the U.S. continent have been simulated by parameterized models (e.g., Zhang et al. 1988; Stensrud and Fritsch 1994), as well as by explicit models in two spatial dimensions (e.g., Tripoli and Cotton 1989) and in three spatial dimensions (e.g., Dudhia and Moncrieff 1989; Davis et al. 2003; Trier et al. 2006; among others). Resolution dependence was investigated by Weisman et al. (1997) and from a weather forecasting perspective by Gallus (1999) Gallus (2002), and Gallus and Segal (2001). Liu et al. (2001a, b) examined the effects of resolution on convective parameterization. Bukovsky et al. (2005) found that heating generated by convective adjustment improves the prediction of traveling organized convection, but spurious systems may get generated. Interestingly, the propagation and structure of the convective systems over the United States resemble West African squall lines simulated by Lafore and Moncrieff (1989) and Redelsperger and Lafore (1989).
Organized convection brings dynamical issues to the fore, which is a new aspect for convective parameterization. In the conceptualization shown in Fig. 1a, the mixing effects of ordinary convection represented by an entraining plume is the conceptual basis for contemporary parameterization. A separation of scale between the cumulus and the grid spacing of the numerical model is assumed. In contrast, for mesoscale convective systems (Fig. 1b), quasi-laminar transport dominates turbulent mixing. Organized convection involves singular events at the tail of cumulus population that statistical analysis shows may account for 90% of the total convective mass flux (Naveau and Moncrieff 2003). In view of the upscale nature of convective organization in models of intermediate resolution, the scale-separation assumption is questionable. Dynamical mechanisms such as shear, scale interaction, and quasi-laminar transport are strongly in play: the focus herein. The key question is: Can complex mesoscale dynamics be approximated in a simple way that is useful for convective parameterization?
The paper is organized as follows. In section 2 a framework for the hybrid parameterization and issues of resolution are introduced, followed by a description of the simulations in section 3. A dynamical analysis follows in section 4. In section 5 hybrid aspects of parameterization are described and a prototype mesoscale parameterization of stratiform heating and mesoscale downdrafts, called a predictor–corrector hybrid method, is introduced. The paper concludes in section 6, including discussion of next steps and broader issues.
2. Parameterization strategies
The physical resolution of a numerical model is LP = NΔ, where Δ is the grid spacing. Skamarock (2004) and Bryan et al. (2003) showed that 7 < N < 10 for models with nonhydrostatic dynamical cores. Mesoscale organization is represented explicitly by cloud-system-resolving models (CSRM: grid spacing a few kilometers) with reasonable accuracy because of the high aspect ratio (L/H ∼ 10) typical of convectively generated circulations, where L and H are the horizontal and vertical scales, respectively. However, turbulent towers embedded within the cumulonimbus, and cumulonimbus themselves, are not resolved unless the grid spacing is ∼100 m, which is impractical for large computational domains.
We distinguish three strategies for representing the effects of deep convection on the larger scales of motion: implicit, explicit, and hybrid. Until recently, only the implicit approach (i.e., contemporary parameterization: Fig. 2a) was available. Thermodynamic processes (heating and drying) have enjoyed much more attention than momentum transport in parameterizations. Contemporary parameterization is presently the only practical approach for long climate simulations.
The explicit approach (Fig. 2b) involves CSRMs whose methodology is based on nonhydrostatic cloud models inaugurated in the early 1970s. A prerequisite is that CSRMs simulate life cycles and transitions among convective regimes in evolving mean states (i.e., CAPE and shear). Grabowski et al. (1998) simulated nonsquall clusters, squall clusters, and scattered convection as the environment evolved from strong forcing/moderate shear, through moderate forcing/strong shear, to weak forcing/weak shear, respectively, during passage of an easterly wave. In global-scale two-dimensional CSRM, propagating mesoscale convective systems may develop from a motionless initial state (Grabowski and Moncrieff 2001). A recent explicit approach is to embed CSRMs in global models in place of convective parameterization, which is called cloud-resolving convection parameterization (Grabowski 2001) or superparameterization. Global CSRMs are the state of the art in the explicit representation of organized convection (Tomita et al. 2005).
Herein we provide a formal dynamical framework for a new hybrid approach in which convective parameterization and explicit circulations exist concurrently. This is targeted at models of intermediate grid spacing ∼10 km, that is, next-generation global weather prediction models. In the hybrid approach transient cumulonimbus is represented by convective parameterization and mesoscale organization by underresolved convectively driven circulations. Zhang et al. (1988) pointed out positive aspects of grid-scale circulations. In some regional models convective parameterizations do interact with the grid-scale physics. Kain and Fritsch (1993) permits ice generated by the convective parameterization to advect across neighboring grid cells.
A strong point of the explicit approach is that mesoscale dynamics (e.g., downdrafts, convective triggering by downdraft outflows, organized transport, and the scale interaction) occur spontaneously, even if the processes are represented incompletely by underresolved circulations. Underresolved circulations occur at remarkably coarse resolution in global models. Moncrieff and Klinker (1997) show that families of mesoscale convective systems (superclusters) in the Tropics occur explicitly at 80-km grid spacing. In other words, the hybrid approach is potentially relevant across a range of scales.
3. Numerical experiments
The fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5) is configured with 40 vertical levels with the model top at 50 hPa. The computational domain is 2400 km × 1800 km (Fig. 3). A 3-hourly 40-km operational Eta Model analysis provides initial conditions, lateral boundary conditions, and large-scale forcing. Cloud microphysics is represented by the NASA Goddard scheme (Tao et al. 1993). The radiative transfer parameterization activated every 15 minutes interacts with cloud, clear atmosphere, and the land surface (Dudhia 1996). Planetary boundary layer physics is represented by the scheme used in the National Centers for Environmental Prediction (NCEP) Medium-Range Forecast (MRF) model (Hong and Pan 1996). It is coupled with a five-layer soil model from which the surface temperature and surface fluxes are calculated.
We performed hierarchical simulations of three kinds: (i) explicit convection at 3-km grid spacing, the control simulation; (ii) underresolved convection at coarser resolution (i.e., 10-km grid spacing) with convective parameterization disabled; and (iii) simulations applying the Betts–Miller–Janjic convective parameterization (BMJ; Betts 1986; Janjic 1994) at coarser resolution. We simulated the 7-day period 0000 UTC 3 July–0000 UTC 10 July 2003 characterized by moderate-to-strong large-scale thermodynamic forcing. Reasonable convergence of the mesoscale organization simulations is demonstrated by comparing the 3-km grid-spacing results to a short 1.5-km-grid simulation (see appendix).
The Hovmöller diagrams in Fig. 4 show that the explicit simulations and the hybrid simulation capture the diurnal cycle of precipitation over the Continental Divide and eastward-traveling systems over the Great Plains. Traveling convection shows up as slanted precipitation in space–time coordinates. The diurnal composite in Fig. 5 indicates three kinds of temporal variability in precipitation: (i) the diurnal cycle over the Continental Divide shows the local variability associated with deep convection before organization mechanisms reach maturity; (ii) the early-morning maximum to the east shows the far-field effects of convection traveling from the west; and (iii) the semidiurnal variability in the central part of the domain represents the combined local and advective effects of eastward-traveling systems. The simulated temporal variability is in accordance with observations (e.g., Carbone et al. 2002). Figure 6 shows that the rainfall patterns at 10-km and 30-km grid spacing stem partly from (underresolved) explicit circulations and partly from convective parameterization, that is, hybrid behavior.
Figure 7 shows the arc-shaped rainfall distribution of length ∼500 km, manifesting flow organization of the squall-line kind. The heaviest precipitation occurs toward the southern end together with cold pools, surface mesohighs, strong convergence, and deep lifting at the cold-pool front. The along-line mesoscale structure is multicellular as is typical of observed systems.
Figure 8 shows the airflow organization in the vertical plane averaged along the length of the system shown in Fig. 7 in a frame of reference translating with the system. The key point is that the dynamical organization consists of three tightly coupled branches: (i) a propagating jumplike updraft, (ii) an overturning updraft, and (iii) a mesoscale downdraft. The propagating updraft that separates the overturning updraft from the mesoscale downdraft flows through the system without reversing direction; that is, it propagates in the strict sense. (For convenience, herein, the organized systems will be called “propagating” even though steering levels exist.) The backward-tilted propagating branch and the cross-system pressure gradient indicate hydraulic-jump-like properties that distinguish propagating systems from other regimes of convective organization (Moncrieff 1981, 1997).
The three-dimensional propagating branch overturns in the transverse plane as shown by the cellular precipitation ∼100 km in scale. The backward (up-shear) tilt of the propagating branch enables precipitation to fall into, evaporate, and maintain mesoscale downdrafts. The mesoscale pressure gradient, generated by latent heating by cumulonimbus in the leading part of the system, accelerates air from the rear deep into the convective system (Lafore and Moncrieff 1988). Hence, the pressure-gradient-driven inflow and evaporative cooling of the mesoscale downdraft is important to the longevity of propagating systems. It is necessary to represent these mechanisms in convective parameterizations.
Deep inflow to the propagating and overturning updrafts results in a high steering level (about 7 km), which in the westerly shear over the U.S. continent, is consistent with fast eastward propagation (about 17 m s−1). A similar three-branch morphology occurs in simulations by Trier et al. (2006) for the same period using the Weather Research and Forecasting (WRF) model and in many simulations cited in the introduction to this paper. The simulated propagation speed compares to the Carbone et al. (2002) radar estimates. It has long been known that fast-moving systems with deep mesoscale downdrafts occur widely over the United States (Houze et al. 1989).
4. Dynamical interpretation: The macrophysics of convective organization
The macrophysical and systemic properties of convective organization (i.e., propagation, mesoscale dynamics, and organized transport) are the mechanisms that we seek to represent in a mesoscale parameterization. Momentum transport is particularly interesting since it affects the large-scale circulation directly. The macrophysics of precipitating convection is well known to be strongly affected by wind shear, yet shear is conspicuously absent from contemporary convective parameterization.
a. Propagation, hydraulic dynamics, and the work–energy principle
Two points are of key importance in macrophysical terms. Firstly, in strong organized systems the rate of change of convective available potential energy (CAPE) by large-scale temperature and moisture advection primarily controls convective intensity (i.e., updraft kinetic energy). Second, mesoscale convective organization is a dynamical response of a sheared environment to vorticity generated (baroclinically) by horizontal gradients of latent heating/evaporative cooling (shear control). In regard to the transport module in convective parameterization, representing the macrophysics of organized flow is the supplanting aspect. Density currents enter into parameterization as a trigger mechanism. Strong forced ascent at density-current fronts overcomes convective inhibition (CIN), continually triggering cumulonimbus at the leading edge of propagating systems. Note that mesoscale organization, convective triggering, and interaction with the environment (“closure” in parameterizations) are explicit in CSRMs.
Since Ri and E are couched in terms of the kinetic energy of inflow, propagating systems are inherently self-organizing—inflow kinetic energy drives convective overturning even if CAPE is zero, if not modestly negative. Three-branch flow organization exists in subsets of {R, E} space determined by integral constraints on the mass, energy, and momentum equations (Moncrieff 1992).
b. Momentum transport
Since the convective momentum transport is strongly affected by the airflow organization, it is a rigorous way to evaluate the effects of horizontal resolution. Figure 10 shows the total momentum transport averaged along the length of the simulated convective system. For the 10-km grid simulation (Fig. 10b) the momentum transport compares favorably to the control (Fig. 10a), apart from being weaker. The negative momentum transport characteristic of westward-tilting, eastward-propagating systems is clearly evident. Since BMJ does not parameterize convective momentum transport, Figs. 10b and 10c are generated by explicit momentum transport and transport generated by the quasi-balanced response to diabatic heating.
Momentum transport for the 30-km grid simulation (Fig. 10c) is severely distorted compared to the higher-resolution simulations (cf. Figs. 8, 11 and 12). Instead of the characteristic backward tilt of the explicit simulations, two almost symmetric overturning updrafts overlie a low-level current that flows through the system with little vertical displacement (Fig. 12). Not only is the momentum transport weak, it has the wrong sign! The absence of a surface stagnation point means the horizontal convergence is too weak to lift boundary layer air to its level of free convection (i.e., overcome CIN). Nevertheless, this fortuitous propagation occurs without a density current, showing that a density current is not basically essential.
The similarity between the 10-km-grid results and the control simulation suggests a hybrid approach that utilizes the positive aspects of underresolved dynamics: the predictor–corrector hybrid approach. This new approach is physically based in the following way: Underresolved mesoscale dynamics is the predictor (it represents dynamics absent in the convective parameterization). Systematic errors arising as a consequence of underresolution (weak mesoscale downdraft) are corrected by a first-baroclinic heating couplet that bolsters the stratiform heating and/or the mesoscale downdraft (see section 5).
5. Convective parameterization
The heat budget calculated over the (1000 km × 800 km) region in Fig. 3 captures most of the heavy precipitation during the 7-day period. Following Yanai et al. (1973), the thermodynamic effect of precipitating convection on the environment is measured by the convective heat source (Q1 − QR) in which latent heating is the dominant process. The vertical gradient of the convective heating generates potential vorticity, which interacts directly with large-scale circulation.
Figure 13 compares the heating profiles at 3-km, 10-km, and 30-km grid spacing. All have an elevated maximum due to the high steering level. Compared to the 3-km grid-spacing result, the systematic warming in the mid-to-low troposphere gets progressively larger as resolution decreases because the mesoscale downdraft gets progressively weaker.
a. Betts–Miller convective parameterization
b. Implementation of the predictor–corrector hybrid: Mesoscale parameterization
There has been much effort in recent years to decompose latent heating into convective and stratiform components, such as retrieval algorithms for precipitation estimates from TRMM measurements. The predictor–corrector hybrid represents organized convection in a two-part way: cumulonimbus heating by the convective parameterization and mesoscale heating by explicit dynamics (appropriately corrected). This mesoscale parameterization represents observed relationships between convective and stratiform regions of mesoscale systems (Johnson 1984). Recall that the mesoscale downdraft inflow is driven by the horizontal pressure gradient generated by cumulonimbus heating in the leading region of the system.
Mesoscale momentum transport can be parameterized by the hybrid method, in a consistent way. The convective momentum tendency has a first-baroclinic structure in the vertical, except it has a cosinelike distribution in the vertical rather than the sinelike heating tendency. (See section 4b herein and Moncrieff 1992.)
We tested the heating prototype (presently, we have not tested the mesoscale momentum transport) in a 1-day simulation at 60-km grid spacing employing initial conditions at 0000 UTC 9 July 2003. In shear flow the heating/cooling couplet propagates at a speed consistent with the (hydraulic-like) pressure jump across the system. If the jump is too small, the convective system will travel too slowly, as in the standard BMJ (about 10 m s−1 instead of 17 m s−1).
Figure 14 shows that the heating couplet corrects the systematic low-to-mid-tropospheric warming error. Figure 15 shows the desired effect of increasing the travel speed of the three-part slanted precipitation distribution: parameterized convection, the predictor (the underresolved mesoscale circulation), and the corrector (the heating couplet).
6. Concluding discussion
At an intermediate grid spacing of about 10 km, the representation of organized convection differs significantly from contemporary parameterization. Primarily, dynamical structures in shear flow must be approximated. A mechanistic dynamical model of propagating convective systems is a rigorous basis for representing mesoscale convective organization (stratiform heating and mesoscale downdraft) by a predictor–corrector hybrid approach. Contemporary convective parameterization represents transient cumulonimbus convection, and explicit circulations (predictor) together with the first-baroclinic couplet (corrector) represent mesoscale convective organization. The predictor–corrector hybrid is appropriate for 10-km-grid models wherein underresolved explicit circulations (predictor) are reasonably accurate.
Mesoscale convective organization is primarily a product of dynamical interaction among latent heating, evaporative cooling, and environmental shear. Provided latent heating is approximated reasonably by the cloud-microphysics parameterization, interaction of the environmental shear with the baroclinically generated vorticity realizes mesoscale organization, coherent airflow, and propagation. However, at 10-km grid spacing the evaporatively driven mesoscale downdrafts are too systematically weak albeit correctable. That macrophysics dominates microphysical parameterization aspects during strong convective episodes is indicated by the low sensitivity of the simulated convective organization to the cloud-microphysical parameterizations (see discussion in the appendix herein).
The dynamical structure, heating, and momentum transport of propagating convection over the United States resembles those associated with superclusters over the tropical western Pacific predicted in a global NWP model (Moncrieff and Klinker 1997). In view of the scale invariance between mesoscale convective systems and superclusters demonstrated by Moncrieff (2004), we argue that the hybrid predictor–corrector strategy may have wider application.
Note that explicit approaches will be impractical for long climate simulations for the foreseeable future. In climate models mesoscale processes are poorly represented, if present at all. Hence, entire propagating mesoscale systems must be parameterized. The main difficulty here is getting precipitating organized systems to propagate because explicit circulations (predictor) likely do not exist or are badly distorted. Even without propagation, however, stratiform heating and mesoscale downdrafts will be represented by the first-baroclinic mode.
We formulated a formal framework for hybrid parameterization of propagating convection in terms of two processes involving two strongly interacting scales of motion: transient cumulonimbus, represented by contemporary parameterization, and explicit representation, represented by explicit circulations (suitably corrected). The first-baroclinic heating couplet applied within this framework is a prototype rather than a complete solution. Improvements could be made to the prototype, such as adding a consistent mesoscale momentum transport and a phase lag between the convective and mesoscale processes. On a broader note, we hope that by defining a framework and showing prototype results we will enliven interest in the hybrid approach to parameterization that, as we have noted, has long been implicit in regional models but has never realized its potential in regard to representing mesoscale convective processes in global models.
Acknowledgments
We thank Alan Betts and Martin Miller for discussions on convective parameterization, and George Bryan and Stan Trier for internal reviews of the draft manuscript. Changhai Liu acknowledges support from the Water-Cycle Program of The Institute for Integrative and Multidisciplinary Earth Studies (TIIMES) within NCAR.
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APPENDIX
Convergence and Sensitivity
Convergence of the simulations
The convergence of the cloud-system-resolving simulations was tested by comparing the 3-km-grid simulations against a 1.5-km-grid simulation for 9 July 2003. (Computational considerations dictated that only a 1-day-only experiment was practicable.) Figure A1 shows the accumulated rainfall. The simulations are generally similar, the main difference being that the 1.5-km-grid simulation gives more rainfall in the eastern part of the domain. This is in agreement with the radar measurements. Comparing the Hovmöller diagrams at 3-km and 1.5-km grid spacing (Fig. A2) explains this difference. At higher resolution the organized systems travel farther again in agreement with observations.
While detailed differences occur due to the different spatial resolution, the differences are no greater than would be expected of natural variability. The main aspects examined herein: mesoscale organization, propagation, and cloud distribution are remarkably similar. This shows a desirable convergence of the macrophysics of the problem, which is in agreement with other simulations of organized convection in shear reported in the literature. In particular, it agrees with Bryan et al. (2003), who argued that a significant leap in realism of simulated propagating mesoscale convective systems requires a grid spacing ∼100 m. At such resolution moist convective towers as well as convective boundary layer and moist convective turbulence within cumulonimbus get resolved. Presently, this degree of spatial resolution is impossible for the large computational domains required to simulate fields of cumulus along with the convective organization embedded in fields of cumulus.
Sensitivity to microphysics parameterizations
Our methodology implies that the macrophysics of convective organization dominate the effects of cloud microphysics in environments where thermodynamic forcing and shear are moderate to strong. Such conditions prevailed during the period examined herein. It was shown by Liu and Moncrieff (2006, manuscript submitted to Mon. Wea. Rev.) that variability due to different microphysics parameterizations is small compared to sensitivity to different convective parameterizations. This may not be the case for long simulations (e.g., climate models) and in conditions where the diurnal cycle is weaker (e.g., cloud fields over tropical oceans). In such circumstances the radiative effects of microphysics are likely to have a stronger impact, although this requires verification.
Distinction between (a) ordinary convection and (b) organized convection with attention to aspects pertinent to convective parameterization.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
(a) Contemporary convective parameterization, with grid spacing of the numerical model much coarser than the dynamical scale of convection; (b) fully explicit mesoscale dynamics as in a CRM; and (c) hybrid situation: underresolved mesoscale dynamics and parameterized cumulonimbus. Light/dark shading represents cumulonimbus convection/mesoscale convective system.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
Terrain heights in meters and the computational domain used for the numerical simulations. The dotted insert indicates the area over which the thermodynamic budget is calculated.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
Hovmöller diagrams of rain rate averaged in the meridional direction for (a) radar, (b) 3-km grid-spacing explicit simulation, (c) 10-km grid-spacing simulation applying the BMJ parameterization, (d) 10-km grid-spacing explicit simulation, (e) 30-km grid-spacing simulation applying the BMJ parameterization, and (f) 30-km grid-spacing explicit simulation.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
As in Fig. 4 but the diurnal cycle of precipitation composite for 3–9 Jul 2003.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
Hovmöller diagrams of rainfall rate averaged in the meridional direction: (a) total, (b) parameterized, and (c) grid-scale rainfall in the 10-km simulation applying the BMJ parameterization; (d) total, (e) parameterized, and (f) grid-scale rainfall for the 30-km simulation applying the BMJ parameterization.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
Fields at 0300 UTC 9 July for the 3-km explicit simulation: (a) hourly accumulated rainfall; (b) surface wind, temperature, and sea level pressure; (c) wind, temperature, and vertical velocity at 850 hPa; and (d) wind and condensate at 300 hPa. Contour interval is 2 hPa in (b) and 1 m s−1 for updrafts and 0.5 m s−1 for downdrafts in (c).
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
Vertical cross section averaged along the convective system shown in Fig. 7: (a) condensate and system-relative wind; (b) potential temperature perturbation relative to the values at the right-hand boundary. Light and heavy shading in (b) indicate front-to-rear flow and rear-to-front flow greater than 10 m s−1, respectively.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
The idealized steady propagating system consisting of three interlocked branches. The work done by the pressure field Δp/ρ represents hydraulic-jump-like properties. The flow structure is represented by solutions to the vorticity equation solved as a free-boundary problem, where G is the environmental shear, F(ψ, z, cmcs) is the buoyancy along trajectories, and the integrand the convectively generated vorticity. The convective system and density current travel at the same speed in the stationary frame of reference ccd = cmcs = 0.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
Total momentum transport relative to the convective system shown in Fig. 8: (a) 3-km grid-spacing explicit simulation, (b) 10-km grid-spacing simulation applying the BMJ parameterization, and (c) 30-km grid-spacing simulation applying BMJ parameterization. Contour interval is 2 kg m−1 s−2.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
As in Fig. 8 but for the 10-km grid-spacing simulation applying the BMJ parameterization.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
As in Fig. 8 but for the 30-km grid-spacing simulation applying the BMJ parameterization.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
Heat budget averaged over 7 days and the subdomain shown in Fig. 3: (a) 3-km explicit (solid), 10-km grid-spacing explicit (dashed), and 30-km grid-spacing explicit simulation (dotted); (b) 3-km grid-spacing explicit (solid), 10-km (dashed), and 30-km grid-spacing (dotted) simulation applying the BMJ parameterization.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
Effects of the heating couplet on the convective heat source. Full line: the profile for the standard BMJ; dotted line: BMJ and mesoscale downdraft only (α2 = 0); broken line: BMJ and antisymmetric stratiform heating and mesoscale downdraft cooling (α1 = α2 = 2.5).
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
Hovmöller diagrams of rainfall rate averaged in the meridional direction for the 60-km grid-spacing simulation: (a) Parameterized rainfall in the standard BMJ parameterization, (b) parameterized rainfall in BMJ with the mesoscale parameterization included, (c) total rainfall including the standard BMJ parameterization, the mesoscale parameterization, and the grid-scale rainfall.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
Fig. A1. Accumulated rainfall during 9 July 2003 for (a) 1.5-km grid-spacing simulation, (b) 3-km grid-spacing simulation, and (c) radar estimate.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
Fig. A2. Hovmöller diagrams of rainfall rate averaged in the meridional direction for (a) 1.5-km grid-spacing simulation, (b) 3-km grid-spacing simulation, and (c) radar estimate. The shading is in mm h−1.
Citation: Journal of the Atmospheric Sciences 63, 12; 10.1175/JAS3812.1
