1. Introduction and motivations

The “hot tower hypothesis” was proposed half a century ago by Riehl and Malkus (1958, hereafter RM58) to explain the mechanism of the vertical (equatorial) branch of the Hadley cell. The need for this radical theory arose because new incoming data collected during World War II showed a midtropospheric energy deficit. This deficit ruled out the previously theorized gradual widespread ascent to the upper troposphere of the warm, moist air within a latitudinal belt roughly 20° centered on the equatorial trough. To carry the warm moist air upward, RM58 proposed a population of buoyant cumulonimbus clouds transporting boundary layer (BL) air up to the top of the troposphere with little or no dilution by mixing with the lower energy in their surrounding environment.

In the RM58 calculations, the global energy budget required about 1500–2500 cumulonimbus hot towers to be simultaneously active, each containing nearly undilute updrafts of 2–4 m s⁻¹ to effectively carry out the function of the upward branch of the Hadley cell. These updraft cores were postulated to be 2–4 km in diameter and gathered in larger mesoscale groups or clusters. (The word “mesoscale” had not been invented prior to the satellite era.) By the 1970s, when satellite products and many other new datasets became available, Riehl and Simpson (1979) repeated their global energy budget. They found that the requirement for undiluted hot towers was essentially the same as in their previous study.

The Tropical Rainfall Measuring Mission (TRMM) satellite, launched in 1997 and related modeling research by Tao et al. (2001) and Johnson et al. (2002), showed how tropical precipitation processes may provide nearly all of the energy (latent heating) required to drive the Hadley cell. The largest contribution of this latent heat energy was found to be from condensation attributable to liquid precipitation, with an absolute maximum occurring near the 600-hPa level and a secondary maximum often observed near 300–200 hPa within stratiform anvil cloud layers embodying ice processes. The question remained, however, as to whether this infusion of energy was wholly accomplished by undiluted hot towers.

The hot tower hypothesis thus remained controversial. Undiluted hot towers were hard to find in tropical mesoscale convective systems (MCSs). Using Global Atmospheric Research Programme (GARP) Atlantic Tropical Experiment (GATE) data, LeMone and Zipser (1980) and Zipser and LeMone (1980) found that convective cores exhibited surprisingly weak vertical velocities. Similarly, data from the Equatorial Mesoscale Experiment (EMEX) revealed weak drafts (Lucas et al. 1994), with consistent evidence being offered by analysis of flight-level measurements obtained during the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE; Webster and Lukas 1992; Igau et al. 1999). However, the emphasis on airborne Doppler radar data collection in COARE—which required aircraft to fly abeam of rather than through the most intense convection—generally precluded penetrations of mesoscale systems until they were in their later, weakened stages. Moreover, owing to safety concerns, these data were mostly restricted to levels below the freezing level (5 km). Anderson et al. (2005) analyzed an extensive dataset of tropical oceanic updrafts from TRMM Large-Scale Biosphere–Atmosphere Experiment in Amazonia (LBA) and the Kwajalein Experiment [(KWAJEX)/tropical oceanic; Stith et al. 2004] and found stronger peak updrafts at 9 km, with maxima up to 16 m s⁻¹, although average velocities remained comparatively weak.

Evidence was accumulating for stronger updraft cores in other settings, however. In situ observations within eyewalls of mature hurricanes also revealed isolated strong updraft cores sometimes exceeding 15–20 m s⁻¹ (Jorgensen et al. 1985; Black et al. 1994, 1996). Model studies by Simpson et al. (1998) and Braun et al. (2006) provided further evidence of hot towers within hurricanes. As for MCSs, Zipser (1994) and Zipser and Lutz (1994) associated electrification with updrafts through the freezing level of the order of 5–6 m s⁻¹. An examination of satellite images showed such storms did exist over the ocean but were far more frequent over land (Orville and Henderson 1986; Williams and Stanfill 2002).

The TOGA COARE experiment, which took place in 1992–93 over the “warm pool” of the western equatorial Pacific Ocean, offered an additional opportunity to document convective cores. COARE employed a research ship array and, for the first time, a total of three Doppler radar–equipped aircraft that could be combined in multi-Doppler radar missions capable of documenting the three-dimensional air motions with unprecedented accuracy. Convective updraft profiles were generally bimodal, with a vertical velocity minimum around 3–5 km and stronger updrafts both above and below (e.g., Trier et al. 1996, 1997; Hildebrand et al. 1996; Hildebrand 1998; Fierro et al. 2008, hereafter F08). Cloud tops often protruded to near-tropopause heights of about 15 km.

As was the case during GATE (Barnes and Sieckman 1984) and EMEX (Alexander and Young 1992), the MCSs in TOGA COARE were typically organized into convective bands aligned parallel or normal to the environmental shear (LeMone et al. 1998); similar behavior was subsequently documented by Johnson et al. (2005) for the 1998 South China Sea Monsoon Experiment (SCSMEX). Although those convective bands oriented normal to the low-level shear tended to move rapidly and those parallel to the midlevel shear moving more slowly, both modes were able to “plow up” energy-rich surface and lower boundary layer air into buoyant updrafts that formed cumulus clouds based at about 600 m (Zipser 1977; Houze 1977; Zipser et al. 1981, among others). Estimated trajectories based upon limited available vertical motion observations showed that this low-level energy-rich air rose to and occasionally penetrated through the tropical tropopause. This effectively suggested that the towers could function as units in the Hadley cell, but this implication has until now received little attention.

The convective systems studied herein—namely, a pair of squall lines observed on 9 February 1993—were initially examined by Hildebrand et al. (1996), Smull et al. (1996), Roux (1998), and Petersen et al. (1999, hereafter P99). More recently, interest in these nocturnal TOGA COARE squall line cases was revived by the electrification model study of F08. By this time, three-dimensional convective cloud models had become more widely available, and some models possessed far more sophisticated cloud microphysics (i.e., Straka and Mansell 2005). The model employed in this study features 12 classes of hydrometeors, of which 10 are ice (refer to section 3). Sounding data from the R/V Vickers was used to specify their environments. The initial squall line passed over the ship array and was probed by shipborne Doppler radars. A slightly stronger squall line was observed a few hours later that same night to the southeast of the ship array by the three Doppler-equipped aircraft, which documented its internal air motion field in considerable detail over a ∼5-h period. P99 described the thermodynamic, kinematic, and electrification of those two systems and showed that the system occurring later in the night (referred to as the “aircraft case”) had slightly stronger updrafts due to stronger environmental low-level forcing than the weaker “ship case.” Despite these differences, both systems displayed remarkable similarities in their dynamical, kinematic, and thermodynamic environments (Fig. 1 in this study; also see P99, their Fig. 2) as well as their general morphology. As such, both MCSs can be classified as shear-parallel systems.

In this paper, observations of the “aircraft” system will be compared to a simulation initialized using the “ship case” sounding, for three reasons. First, the ship sounding used in F08 (Fig. 1a, thick gray line), modified slightly to enable the generation of a long-lived squall line, has previously been used with success in our model framework. Such modifications are common and are related to the artificial way the system was initialized, which is described in more detail in section 3. Second, the original aircraft sounding failed to produce a long-lived squall line unless changes comparable to the differences between the original ship and aircraft soundings (Figs. 1a,b; also refer to P99) were made. Finally, with combined data from three airborne Doppler-equipped platforms, the 9 February aircraft storm was perhaps the best-documented system during all of TOGA COARE. This affords us the opportunity to perform trajectory analyses for comparison with the model results.

Nevertheless, some differences between the two 9 February MCSs should be kept in mind. Indeed, given the limitations of the available observations (as will be described), one should not necessarily expect exact agreement with model depictions but should regard the observed and modeled events as complementary views of a representative cluster of hot towers in the TOGA COARE environment. The modified ship sounding has convective available potential energy (CAPE) and convective inhibition (CIN) values well within range of those from COARE soundings documented in LeMone et al. (1998, cf. their Table 4 and Fig. 1 in this study) and slightly smaller than those of the RM58 sounding, hence further supporting the results in this paper.

Derived values of equivalent potential temperatures (θ_e) near the surface in Fig. 1c are about 350.5 K, which is about 5 K lower than those computed by LeMone et al. (1998) for the 9 February ship sounding but consistent with typical tropical maritime values quoted in RM58. The Emanuel (1994) θ_e equation is used here, which allows the latent heat of vaporization to vary linearly with temperature. Also, the temperature at the lifting condensation level (LCL) used in the θ_e equation is computed iteratively. In contrast, LeMone et al. (1998) used the formulation in Bolton (1980), which does not account for heat retained by the condensed water process and can affect the value of θ_e by several degrees (Saunders 1957). The use of different θ_e equations in the tropics has long been a source of contention (Simpson 1978). Rather than favoring one estimate over the other, the differences will be highlighted when comparisons are discussed.

As detailed in section 3, the key aspect of this work involves the computation of θ_e along representative parcel trajectories. Indeed, the best variable to represent the thermodynamic energy of the atmosphere is θ_e, because dynamic energies are many orders of magnitude smaller, since the atmosphere is a very inefficient heat engine. The θ_e of an air parcel can only be changed by radiation, mixing, and ice-phase processes such as sublimation or freezing. Radiative effects are slow enough to be neglected in most cloud-scale studies. More precisely, the total energy H fueling the Hadley cell is related to θ_e and latent heating via the following approximation:

View Expanded

where c_p is the specific heat at constant pressure, L is latent heat, and the other symbols have their usual meanings. Because precipitation efficiency varies and is not known, we conventionally use L as the latent heat of condensation. The use of H by RM58 largely avoids the effects of release of latent heat, because H is conserved under conditions of evaporation or condensation. Moreover, in the model at least, accounting for the major transporting elements should capture most of the flux transport deduced from heat and moisture budgets. We chose to focus on trajectories because of their suitability for more direct comparison with RM58.

The next section will provide a brief description of the model used along with the simulation settings and methodology. In section 3 key results from past observational studies available only in conference reports by the coauthors as well as a new trajectory analysis of the aircraft case will be presented. Finally, in section 4, the modeling results are shown followed by the conclusions/discussion in section 5.

2. Model description and methodology

The model used in this study employs a sophisticated “10-ice bulk single-moment microphysics scheme” developed by Straka and Mansell (2005). This scheme features 12 discrete bulk hydrometeor categories following an inverse exponential distribution for precipitating particles and monodisperse distribution for cloud particles. The 12 categories are cloud droplets, rain, cloud ice (columns, plates, and rimed), snow particles, frozen drops, three graupel categories, and two hail sizes. The model predicts the mixing ratio of each category, while total concentration is diagnosed from evaluating mixing ratio in conjunction with assumed particle size. This refinement over conventional models with only two and three ice classes is desirable to test the effects of ice-phase particles on a given air parcel’s thermodynamic state.

This model solves the three-dimensional quasi-anelastic (Anderson et al. 1985) Navier–Stokes equations and uses a 1.5-order turbulence closure scheme, where diffusion of scalars is based on the prognostic equation for the square root of turbulent kinetic energy following Deardorff (1980). Including the electrification variables, which are set to zero for this study, 42 scalar variables are advected using a sixth-order flux conservative Crowley scheme (Tremback et al. 1987) with a monotonic limiter (Leonard 1991) on a forward time step.

As mentioned earlier, this approach extends F08 by using trajectories to examine the hot tower hypothesis put forth by RM58. The trajectories in this study were computed in a somewhat unique way. Instead of taking data that were spatially three-dimensional with 1- or 2-min temporal resolution and interpolating them in space and time using an iterative method, as is often done, we did the following: An array was created to store the positions of the trajectories and the velocity components and variables such as θ_e at the position of each trajectory. Trajectories were computed using a forward-upstream technique at each time step while the model was running. Each trajectory was started at a prescribed time within a prescribed volume. The array was written off to a file at each time step and then sorted out during post processing to make the plotted trajectories with the time resolution of the model time step (4 s). In this way the trajectories are nearly as accurate as they possibly can be, outside of using higher-order differencing for computing the trajectories.

The model setup to initialize the squall line is identical to that used in F08 and therefore will be summarized here only briefly. The initial thermodynamic environment and wind field were given by a slightly modified version of the sounding launched from the R/V Vickers (Figs. 1a,b). Minimal changes to the low-level water vapor mixing ratio and temperature were necessary to produce a well-developed squall line in the model. This was partly a consequence of initializing the model with an arbitrary ellipsoidal cold thermal anomaly. Small changes to the wind field at the first few model levels (below 1 km) were also made to increase the BL inflow relative to the storm. To preserve the orientation of the squall line relative to the environmental wind field, a 40° clockwise rotation of the winds at all levels was applied in order to initiate the line parallel to the edges of the model domain in a north–south direction (see F08 for details).

The only difference with respect to the simulation carried out in F08 lies in the horizontal and vertical grid spacing used: in the horizontal, dx = dy = 750 m, while the vertical grid was composed of 120 equally spaced levels at interval of dz = 200 m. The dimensions of the domain were kept identical to F08 with X, Y, and Z having the values of 132, 210, and 24 km, respectively. Such fine spatial resolution was necessary to ensure that most of the updraft cores (and hot towers) were resolved. Finer grid spacing would have been desirable (Bryan et al. 2003), but because the current version of the model is nonmessage passing interface (MPI), this prevented carrying out the present simulation at horizontal grid spacings smaller than 700 m without exceeding the physical memory limit of individual processors. It is planned, however, to test these results with an improved version of the model with MPI capabilities. Despite these aforementioned changes made in the spatial resolution, particularly in the vertical—which employed almost 3 times as many levels (120 versus 43) in the simulation considered here—the simulated squall line followed a similar evolution to that considered by F08.

Trajectories were computed at each time step starting at 2 h into the simulation and ending at 4 h 50 min. This guaranteed a good historical record of each trajectory. The trajectories, one per grid point, were all started at the lowest three model levels (in terms of horizontal wind points on the C grid), namely, at an altitude z = 100, 300 and 500 m, respectively (i.e., near and below cloud base) for points in a box with dimensions ΔX, ΔY, and ΔZ with values of 10, 30, and 0.4 km, respectively, centered at a distance of about 25 km ahead of the simulated gust front position. At a spatial resolution of 500 m horizontally and 200 m vertically, this resulted in 21 × 41 × 3 = 1968 trajectories. As mentioned in the introduction, a goal of this study is to determine qualitatively and quantitatively how many of these trajectories reach various layers of the convective clouds. In particular, what fraction of ascending trajectories reaches 10 km or higher and is associated with strong updrafts? For those meeting this test, how do the parcel thermodynamic properties, as determined using the tracer variable θ_e, change along the trajectories?

The statistics of vertical velocity (w) and θ_e along the trajectories were examined as follows: the first time each trajectory crossed a given height, it was flagged and the w and θ_e values were interpolated to that level. This method captures the parcel as it is ascending toward the top of the cloud and avoids counting later oscillatory crossings, including some that may occur outside of cloud. Each group was treated separately according to altitude of origin and maximum height reached. Similarly, the minimum θ_e value on the first upward trip was identified for each trajectory.

3. Observations

On 9 February 1993, a large maritime MCS developed over the western Pacific warm pool near 4°S, 158°E and was located immediately southeast of the TOGA COARE Intensive Flux Ship Array. This offered a unique opportunity for the scientists to sample this system through much of its lifetime. The storm was observed by three Doppler radar–equipped research aircraft consisting of two National Oceanic and Atmospheric Administration (NOAA) P-3s and the National Center for Atmospheric Research (NCAR) Electra [the latter carrying the Electra Doppler radar (ELDORA) system]. Details regarding the instrumentation and calibration are described in P99.

Because the availability of uninterrupted, repeated, and regularly spaced NOAA aircraft passes encompassing a ∼4-h interval (roughly 1600–2000 UTC), the corresponding dual-aircraft/quad-Doppler dataset shown here is ideally suited for comparison with our mesoscale simulation. Also available are dual-beam ELDORA observations described by Hildebrand et al. (1996), which benefit from ELDORA’s superior resolution in capturing finescale aspects of convective structure. The strategy for ELDORA, however, involved a survey pattern extending far to the west, while the NOAA P-3s focused on repeated sampling of evolving convective structure near the band’s eastern end. Moreover, as shown by Jorgensen et al. (1996, their Figs. 15 and 16), quad-Doppler scan geometry and solution techniques—which include explicit specification of an upper boundary condition for vertical air motion and allowance for hydrometeor fall speeds—provide a highly reliable representation of upper-level draft structures relevant to hot tower considerations emphasized in this study.

The 9 February aircraft-observed MCS consisted of an initially intense west-northwest–east-southeast-oriented convective line and a coexisting area of stratiform rain to its southwest (Fig. 2a). As mentioned previously, both convective bands were classified as “shear parallel” by LeMone et al. (1998), in reference to the deep-tropospheric shear. As indicated by Roux’s (1998) analysis, the large-scale environment for both the ship- and aircraft-observed cases was characterized by moderate low-level westerlies, reaching a maximum of ∼13 m s⁻¹ near 2 km (all heights MSL) overlain by easterly shear, with winds becoming easterly at 4–5 km (∼600 hPa; Figs. 1a,b). Wind speeds viewed in the absolute (i.e., earth relative) reference frame varied from ∼10 m s⁻¹ at the line’s eastern end, where new convective cells were forming, to about 15 m s⁻¹ (i.e., slightly stronger than undisturbed environmental values) beneath an arc-shaped mature convective segment to the west.

Overall, the squall line’s motion was directed toward 50° (i.e., nearly northeastward) at about 7.5 m s⁻¹. This reference frame motion was used to evaluate and display storm-relative winds in the quad-Doppler radar analysis discussed below. As the system weakened, its propagation speed decreased to about 4 m s⁻¹. Below 950 hPa, θ_e for both the ship and aircraft case soundings revealed values slightly above 350 K (Fig. 1c for the ship case), which agrees remarkably well with the composite value of Takayabu et al. (2006) over the equatorial Pacific warm-pool region (their Fig. 11a) and the mean surface value in the equatorial trough (RM58). As we shall discuss later, flight-level data during the MCS’s mature and intensifying stage showed peak θ_e values of ∼353 K (allowing for the previously mentioned 5-K discrepancy) immediately adjacent to the gust front, most likely denoting near-surface air being lifted above cooler outflow.

Between 1630 and 1730 UTC, the NOAA P-3s executed tightly coordinated tracks on either side of the eastern end of the intense convective band, while ELDORA was diverted to survey convection well to the west. Both NOAA aircraft subsequently continued quad-Doppler sampling of the central portion of the line along with a growing area of stratiform region to its south, while the Electra reoriented its tracks to be more orthogonal to the convective line’s axis (i.e., still cutting across the quad-Doppler analysis volume) at an altitude of 3.2 km.

Convection intensified between 1615 and 1705 UTC. Figures 2a,b show that during this time, the MCS contained a relatively solid line of heavy precipitation (delineated by the 40-dBZ contour) about 100 km in length, with reflectivity values exceeding 50 dBZ near 0.5 km. Some tendency toward multicellular structure was observed, with new cell development preferentially occurring along the line’s northern edge. Individual updrafts were transient, yet they occurred in sufficiently rapid succession that the surface precipitation structure remained relatively steady. At this early time, there was neither a clear bimodal updraft distribution with height nor a strong line-normal relative inflow (e.g., Fig. 2b). However, low-level convergence was strengthening, with accelerating inflow being detected in the flight-level data at later times (viz. between 1719 and 1739 UTC). Coincident with the line’s intensification, both the rear-to-front flow entering the system from the stratiform region to the south and the leading edge inflow from the north underwent a steady increase in strength.

At 1735 UTC, the quad-Doppler analysis revealed that the new, intensifying convection and associated heavy precipitation were confined to a ∼20-km zone to the east, with peak reflectivity values reaching 45 dBZ (Fig. 2c). Below about 4 km, the storm-relative flow was from the northwest and essentially directed along the squall line, with a superimposed cross-band vertical circulation feeding warm and moist BL air from the north side of the line into this developing convection. The analysis also revealed that resolved updraft vertical velocities exceeded 8–10 m s⁻¹ (not shown). Precipitation tended to be organized into mesoscale segments 40–50 km in length, with a particularly intense (and weakly electrified) arc-shaped convective entity drawing BL air from both its flanks located near the center of the analysis domain. The adjacent stratiform region exhibited relatively weak midlevel storm-relative flow. Upper-level northerly component flow forced by divergence atop deep convective cells helped stratiform echo to develop and expand west of this location later on.

Vertical cross sections cutting across the intense arc-shaped convective segment revealed a characteristic bimodal updraft distribution, with an initial maximum of about 2–4 m s⁻¹ below 4 km attributed to strong convergence along the gust front and a second more pronounced maximum above 12 km, with values ranging between 10 and 15 m s⁻¹. As noted by Hildebrand et al. (1996), resolution limitations inherent to the NOAA P-3 Doppler observations may have resulted in an underestimate of peak draft speeds, especially at lower levels. Relatively strong upper-tropospheric updrafts were associated with overshooting tops and adjacent upper-level downdrafts. By 1820 UTC, the convective band had begun to significantly weaken, with precipitation becoming progressively more stratiform. Nonetheless, a few localized updrafts were still observed reaching speeds of 5–7 m s⁻¹ at upper levels. In situ thermodynamic data collected by a NOAA P-3 between 1700 and 1840 UTC—that is, during the MCS’s mature-to-decaying stages—showed a lack of θ_e values exceeding 345 K (Fig. 3, allowing for the 5 K discrepancy) after about 1800 UTC (as compared to 353 K values encountered earlier on).

Because of an absence of precipitation-sized reflectors there, low-level convergence ahead (north) of the convective band largely escaped detection by the airborne radars but was quite evident in flight-level data. As the NOAA aircraft executed repeated reciprocal tracks paralleling the convective band, the P-3 on the band’s northern side crossed the undulating gust-front boundary several times, detecting an instantaneous wind change normal to the system of 6 m s⁻¹ about halfway through the subcloud layer (i.e., z = 324 m; Fig. 3).

To facilitate comparisons with the model, an analogous forward parcel trajectory analysis was carried out using the quad-Doppler kinematic data available during the time interval 1645–1850 UTC, which span horizontal dimensions of 142.5 km × 142.5 km and extend vertically to 17.5 km, with the lowest analysis level located at 500 m. The time separating successive realizations of radar-observed airflow is about 15 min (versus a 4-s time step for the model), with corresponding grid spacing of 1.5 km in the horizontal and 500 m in the vertical. It is also important to note that, owing to low-pass filtering of the radar data required to eliminate noise, the effective resolution of the quad-Doppler analysis is confined to circulations having horizontal wavelengths ≥5–6 km in horizontal scale. Hence only qualitative comparisons of the model and radar views are appropriate.

Trajectories were initiated during the mature stage (1645 UTC) along and across the band from z = 500 m to about 3 km in 500-m increments. It was not possible to initialize updrafts at the lowest levels (i.e., below cloud base) because the radar analysis did not extend below 500 m, owing to required editing to eliminate sea-clutter contamination. For convenience, trajectories were divided into four groups: 1) those reaching a maximum altitude less than or equal to 6 km; 2) those reaching a maximum altitudes between 6 and 10 km; 3) trajectories between 10 and 14 km; and 4) a small number of trajectories exceeding 14 km. Those levels were chosen for the following reasons: 6 km is a proxy for the lowest level of the mixed-phase region, 10 km is the mean height of the secondary updraft maximum, and 14 km corresponds to a height near-mean cloud top. Those distinct batches of trajectories are referred to as I, II, III, and IV, respectively.

It must be must kept in mind, however, that the observationally derived trajectories have important limitations in addition to their relatively coarse resolution. LeMone and Jorgensen (1991) found, for example, that low-level convergence was systematically underestimated because of the influence of the stationary surface. Furthermore, narrow/small-scale features typically cannot be fully resolved, hence the magnitudes of transport/peak updrafts associated with them are often underestimated. Indeed, preliminary results revealed that based upon mature stage observations between 1645 and 1705 UTC, only one point at 500 m possessed an analyzed updraft speed w exceeding 1 m s⁻¹ and only 60 points (again, out of a possible 9025 grid points) had w > 0.5 m s⁻¹. Analogous results were found at 1 km. It is important to recall that the gust front, which was well defined in the simulation as producing updraft speeds of 1–2 m s⁻¹ and also evident in the flight-level observations, was not fully captured by the radar analysis. In the simulation, the gust front forces nearly all (>99%) parcels ahead of the squall line to ascend (as discussed further in the next section). Finally, the radar fields in Fig. 2a depict a convective band embedded in a broader area of stratiform rain, implying much of the inflow air did not originate within an entirely pristine environment.

As such, very few observed trajectories initiated at z = 0.5 km reached higher levels. For this reason, and to be more consistent with our simulation, computation of forward trajectories based upon the observations was restricted to zones where w > 0.25 m s⁻¹ at z = 0.5 km. Among the 255 points meeting this criterion at 1645 UTC, about 74% fall into batch I, whereas 9.9%, 15.7%, and 0.4% of the points are in batches II, III, and IV, respectively. The same analysis carried out at 1705 UTC had 74.1%, 21%, 3.1%, and 1.8% among the 228 points in batches I–IV, respectively. As discussed below, the model output supported many more parcel trajectories reaching high levels (>60% exceeding 10 km). Nonetheless, the most relevant result is that observed parcels originating near cloud base were indeed able to exceed altitudes of 10 km, despite the limitations of the radar data. Examples of some of those trajectories are shown in Fig. 4. Because of these factors, resolved updraft speeds along observed trajectories rarely exceeded 10 m s⁻¹ (not shown), even though stronger drafts quite likely existed. Because flight-level thermodynamic observations are confined to widely separated flight paths at select levels, one cannot strictly determine if these parcels were undiluted based upon observed θ_e values. The idealized TOGA COARE simulation is, however, suitable for expressly addressing θ_e behavior along parcel trajectories, as discussed in the following section.

4. Model results

As mentioned earlier, the simulated squall line follows an evolution similar to that shown by F08—namely, a strong linear burst of convection initially near 20–30 min of model time—which is followed by a progressive collapse of these vigorous towers (some having updraft speeds exceeding 25 m s⁻¹, not shown). This collapse is coincident with the development of strong downdrafts below 4 km (all heights MSL), which are all coincident with the greater reflectivity values (exceeding 55 dBZ) found there. This sudden rush of rain-cooled, subsaturated air further reinforced the initial gust front/density current, allowing a mature squall line to develop near 1 h 30 min (not shown). Therefore, simulation-based trajectories are initiated at two hours of model time.

To remain consistent with the observational analysis, the 1968 model-generated trajectories are divided into the same four groups, which for clarity are referred to as batches A, B, C, and D, respectively. Of the trajectories, 17.25%, 20.125%, 60%, and 2.65% reached a maximum altitude within the layers A, B, C, and D, respectively; that is, more than 62% of these trajectories originating in the BL were able to exceed an altitude of 10 km. This result by itself demonstrates that most of the parcels originating within the boundary layer near and below cloud base ahead of the squall line are being transported to heights near the tropopause by buoyant convection.

Across-line vertical and horizontal cross sections shown in Fig. 5 at 3 h 35 min of model time offer a better perspective of trajectories originating within the BL at and below 300 m and exceeding 14-km altitude in their lifetime (i.e., from batch D). The three trajectories shown were selected because careful analysis of the data showed them to be representative of the great majority of the trajectories in batches C and D. Parcels originating at subcloud heights were lifted ahead of the gust front by an along-line averaged updraft exceeding 4 m s⁻¹ and quickly reached cloud top, near 15.5 km (Fig. 5a). Once these parcels reached heights above 10 km, they were advected into the stratiform region by the prevailing easterly ambient winds at those levels (Fig. 5b). Diagrams of batch C trajectories show similar behavior (not shown). The stratiform region expanded in areal coverage between 2 and 4 h, and the simulated squall line reached its maturity near 4 h 15 min of model time (Fig. 5a).

Figure 6 shows three representative trajectories experiencing a decrease in θ_e below 2 km as they ascended at speeds between 5 and 12 m s⁻¹ (Fig. 5a). Above 5.5 km—that is, just above the 0°C level—all trajectories subsequently underwent an increase in θ_e as they continued their ascent through stronger updraft ranging between 12 and 20 m s⁻¹. Analogous plots for trajectories in batches C and D gave similar results (discussed later in this section). This strongly suggests that parcels originating below cloud base initially experienced lateral mixing with lower θ_e environmental air between 1 and 5.5 km (Fig. 1c). Once the parcels were above the freezing level, they exhibited an increase in θ_e mainly due to ice processes, which were sufficiently strong to oppose the entrainment dilution (Zipser 2003) and negative buoyancy from condensate loading (Williams and Renno 1993). In the model, the ice processes causing a local increase in θ_e are enthalpy of freezing of drops/droplets, enthalpy of freezing by riming of supercooled liquid water onto any of the 10 species of ice particles, and enthalpy of deposition from nucleation of ice crystals. Future modeling studies of tropical convective systems are warranted to determine quantitatively which from the aforementioned microphysical processes is (are) key in generating buoyancy above the 0°C level. As updraft speeds began to decrease near 11 km, all trajectories maintained nearly constant θ_e during their rearward advection in the stratiform region until encountering weak downdrafts (>−2 m s⁻¹) originating above 14 km.

During their ascent, many trajectories exhibited two distinct maxima in updraft speed: one at or below 5 km and a stronger one between 10 and 12 km (Figs. 5b and 6b). This behavior is consistent with previous COARE squall line simulations (Trier et al. 1996, 1997; F08) and observations (Hildebrand et al. 1996; May and Rajopadhyaya 1996; Jorgensen et al. 1997; Hildebrand 1998; Roux 1998; Zipser 2003). Bimodal updraft profiles are evident in the along-line averaged vertical motions shown in Fig. 5a. To determine if this behavior was more broadly exhibited across the system, a probability density function of vertical velocity as a function of height (LeMone and Zipser 1980) was computed within a box surrounding only the heavy convection delineated by 40+ dBZ echoes in horizontal cross section similar to Fig. 6a but at 3 h 35 min of model time (Fig. 7). This plot indeed shows an indication of vertical bimodal distribution of 5 m s⁻¹ updraft speeds. This bimodal distribution also existed at earlier and later times (not shown). As suggested in F08 and shown by Trier et al. (1997), the lower-level updraft maximum is a persistent feature attributed to low-level forcing from the gust front (and associated upward buoyancy pressure gradient force), whereas the secondary maximum aloft is likely a consequence of water unloading and/or buoyancy from ice processes. Note that it would be warranted for future simulations of tropical systems exhibiting similar bimodal updraft speed structures to evaluate quantitatively how the loss of water substance by effective coalescence at low levels reduces the amount of latent heat released during freezing at upper levels.

In Fig. 8a, average θ_e profiles for each of the four trajectory batches are plotted along with the base state profile calculated from the initial environmental sounding in Fig. 1a. These profiles confirm the impression from the three selected individual trajectories that most parcels experienced a rapid decline of θ_e during their initial ascent below 2 km. This was not surprising because clouds rising below the melting level should be expected to encounter and mix with environmental air having lower θ_e.

There is a tendency for an increase in θ_e once parcels rise above 5 km, which is near the 0°C level. From Fig. 8a, parcels in batch D had a nearly constant θ_e profile above 11 km, while for batch C, θ_e continues to climb. The average for the 52 parcels of batch D, θ_e was generally higher than the average for the 1181 parcels in batch C. In fact, above about 5 km, the average θ_e at all levels systematically increased as the maximum altitude achieved by the parcel group increased.

Figure 8b shows that the trajectories making it higher in the cloud (batch D) had stronger updrafts at all levels on average, particularly above the melting level. Those stronger updrafts would leave less time for the parcels below the melting level to entrain the much lower θ_e environmental air (Fig. 8a, dotted line) and could explain why parcels in batches C and D have higher θ_e on average than batches A and B. This difference could also be explained by an increased role of ice processes in batches C and D.

To avoid potential sampling errors due to the relatively small number of trajectories in batch D (52), the 1181 trajectories in batch C were used to compute θ_e distributions at various altitudes, separated according to their level of origin (Fig. 9a). The distributions confirm nicely that θ_e decreases between 1 and 5 km, whereas θ_e increases above 5 km. This behavior appears to be consistent regardless of the altitude of origin of the parcel: All three subgroups of parcels are distributed similarly at all levels.

At and above the freezing level, near 5 km, ice processes tended to increase θ_e in all the parcels through the release of latent heat. Note that between 3 and 10 km, the environmental θ_e is significantly lower (335–340 K; Fig. 1b) than in the ascending air parcels, suggesting that lateral mixing and condensate loading is more than offset by ice processes.

These results agree remarkably well with Zipser (2003), who used parcel theory and observations of deep tropical cumulonimbus (diameter on the order of 2 km or more; LeMone and Zipser 1980) to conclude that updrafts were diluted rapidly, particularly below the freezing level. Stronger, wider, midlatitude storm clouds and hot towers in tropical cyclone eyewalls (Simpson et al. 1998; Molinari and Vollaro 2008), however, were shown to be often undiluted. Zipser (2003) suggested that before reaching the freezing level, tropical updrafts were strongly diluted; however, once air parcels rose above the freezing level, ice processes were primarily responsible for reinvigorating updrafts and for allowing them to reach the upper troposphere after a secondary maximum in updraft speed (Trier et al. 1996). Undoubtedly, water unloading further accelerates those parcels above the freezing level.

A parcel’s initial height influences its maximum altitude, with the lowest-origin trajectories reaching the highest peak altitudes. The 52 parcels reaching a maximum altitude greater than 14 km (batch D) tend to have more parcels originating at 100 m rather than at 300 or 500 m (not shown). Analysis of trajectories originating slightly above cloud base at 700 m confirmed this result: no trajectories originating from a slab of 300-plus trajectories at 700 m reached 14 km. Similarly, parcels in batches A and B had significantly more parcels originating from 500 m than at 100 and 300 m. This shows that in the selected volume of 1968 trajectories between 0 and 500 m, those parcels reaching a maximum altitude of 10 km and higher tended to originate at the lowest levels.

For batch C, the distribution of the number of trajectories as function of their minimum θ_e was determined and the height at which minimum θ_e occurred. Only time steps before any given parcel reached its maximum altitude were considered in order to concentrate our analysis on processes accompanying deep ascent. Figure 10a shows that the great majority of the trajectories in batch C had minimum θ_e values between 344 and 347 K. Because θ_e is near 349–350 K where the parcels originated (lowest three points in Fig. 8a), dilution below the melting level causes an estimated decrease in θ_e of about 4 K, which is not significant relative to much lower environmental θ_e values of about 335–340 K found between 1 and 5 km. Figure 10b shows a bimodal distribution of the height of minimum θ_e, which suggests that the height at which parcels reach their minimum θ_e is coincident in height with the environmental θ_e minima at z = 2 and 5 km in Fig. 8a.

As in the case of θ_e, distributions of updraft speed were created for each of the four trajectory batches. For batches A and B, most of the parcels with the largest updraft speeds originated at 500 m, while the opposite was true for the parcels originating at the surface. For batches C (Fig. 9b) and D (not shown), all three levels of origins were evenly distributed across various updraft speeds, indicating no particular preference in larger/weaker resulting drafts for parcels starting at 100, 300, or 500 m. Because air parcels initiated at 100 m tended to reach higher altitudes than those originating from 300 or 500 m, one suspects that the artificial increase in the lowest-level line-perpendicular shear invigorated the gust front and hence near-surface convergence. Above 5 km, the distribution quickly broadens with height toward larger updraft speeds, ultimately reaching extreme values near 25 m s⁻¹, consistent with water unloading and enhanced buoyancy as a result of the release of latent heat. It was also confirmed that at all levels, and particularly above 5 km, the maximum (not shown) and average (Fig. 8b) updraft speeds along the parcel trajectories were much greater for batches C and D than for batches B and A.

To determine how updraft speed w is related to θ_e values during ascent, joint probability distributions were computed relative to their means in Fig. 8 for different levels, as shown in Fig. 11. Below 2 km (near the first low-level updraft maximum), there was little correlation of w with θ_e. This strongly suggests that the air parcels are being forced upward by the pressure gradient force associated with the gust front and buoyant air above. However, by the time the air parcels get to 3 km, there was a stronger association of θ_e with w, with points roughly concentrated along the 45° diagonal, suggesting an emerging role of parcel buoyancy, even though dynamic pressure forces are important around 5 km (Trier et al. 1997). From 7 km on higher, the cloud of points rotates so that its long axis is ultimately almost parallel to the y axis, thus denoting negligible correlation of θ_e with w at 14 km. Again, there is little correlation between vertical velocity and θ_e, largely because the air parcels higher than 11 km decelerate (Fig. 5b) as they become negatively buoyant. Similar plots (not shown) showed correlations between θ_e and w near the middle of their altitude ranges, where one might expect buoyancy to play a role in driving the air parcels upward (2–3 km for batch A and 3–7 km for batch B). Near the top of their ranges, correlations became small.

5. Discussion and conclusions

The RM58 and Riehl and Simpson (1979) “hot tower” hypothesis consisted of two distinct parts: 1) taller convective clouds (i.e., those reaching near or above the tropopause) were viewed as transporting boundary layer air to the high troposphere, and 2) the protected cores within those stronger/deeper clouds were thought to remain nearly undiluted. Analysis of simulated behavior for a storm that developed over the TOGA COARE ship array on 9 February 1993 suggests considerable transport of high-energy air from the BL but by cores that were diluted by entrainment.

A forward trajectory analysis based upon quad-Doppler radar observations of a subsequent nearby (and very similar) MCS revealed that about 5% of the air parcels originating near cloud base did exceed 10 km in altitude. The modeled storm had, on the other hand, more than 60% of the air parcels originating near and below cloud base exceeding 10-km altitude. We speculate that this discrepancy arises partly from the characteristic inability of radar observations to completely capture convective-scale near-surface convergence rooted in the lowest levels, particularly in the subcloud layer, where the simulated storm exhibited a well-defined gust front along which nearly all air parcels were forced to rise. This impression is supported both by in situ flight-level observations on 9 February and previous comparisons of in situ radar observations by LeMone and Jorgensen (1991). The discrepancies between model and observations could also reflect the artificiality in our environmental sounding.

Our idealized simulation of a typical tropical maritime convective system from the TOGA COARE field program revealed that, during their ascent, warm, energy-rich subcloud parcels experienced nonnegligible mixing below the freezing level with lower ambient θ_e air as they were carried upward within gust-front-forced convective updrafts. However, once above the freezing level (∼5 km), these parcels underwent a significant increase in θ_e as updrafts further accelerated, possibly as a result of water unloading and/or additional buoyancy increase because of ice processes, thus displaying a secondary updraft maximum near 10–11 km.

The results in this paper support the assertion by Zipser (2003) that the hot tower hypothesis must be modified to allow for dilution of the tropical updrafts, particularly at levels lower than about 5 km. Latent heating by microphysical ice processes, which is sufficiently strong to offset the dilution by the lower θ_e of the environment, plays the key role in invigorating buoyant parcels and in providing the necessary energy in the upper troposphere for the Hadley cell circulation. On the basis of these collective results, hot towers should henceforth be redefined as any deep convective tower rooted on the BL and topping in the upper troposphere. The twentieth-century field programs GATE and TOGA COARE have shown that oceanic clouds organize into lines and squalls whereby they plough up surface energy-rich air. After low-level mixing and energy gain through ice processes, some of this air is lifted to high levels to fuel the poleward branch of the Hadley cell.

Future studies should investigate how heat fluxes vary with height and determine quantitatively to what degree ice processes and mixing account for the energy distribution within hot towers. To pursue further how they fuel the Hadley cell, it will be necessary to determine how many such cloud systems exist at any one time around the global tropics. This should ultimately help to determine whether or not updrafts occurring within more ubiquitous MCSs are sufficient to maintain the upward branch of the Hadley cell, or whether contributions by tropical cyclones are essential to its maintenance as well.