1. Introduction
The largest annual global precipitation and latent heat release occurs in the Pacific warm pool region, and mesoscale convective systems (MCSs) are the primary means by which precipitation systems are organized (Rickenbach et al. 1994; Rickenbach and Rutledge 1996, 1998). One of the objectives of the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE; Webster and Lukas 1992) was to investigate how MCSs influence the ocean and the atmosphere over the warm pool. Convective systems can influence the ocean by sensible and latent heat fluxes, momentum fluxes, and fallout of precipitation (Webster and Lukas 1992). Before global air–sea interactions can be modeled accurately over timescales of months to years, a better understanding of how convective systems impact the ocean and the larger-scale atmospheric structure is needed. The airborne observational platforms in TOGA COARE sampled a number of large convective events. These large systems, although relatively few in number, may have a significant impact on the climate of the Tropics.
This paper summarizes the kinematic evolution of one such system, a squall line observed on 20 February 1993. The focus of this paper is on vertical motions and mesoscale momentum transports and how they relate to storm structure and evolution. These interactions are important links between the tropical atmosphere and the ocean. Unfortunately, the fluxes in the lowest levels cannot be accurately observed using radar data, but knowledge of the mesoscale momentum fluxes helps us understand the importance of the mesoscale organization to fluxes at lower levels. Boundary layer modifications resulting from this system and the effects of the system on the larger scale will be discussed in a future paper.
Previous analyses of squall lines based on two-dimensional assumptions have taught us much about how they work. For example, the basic structure and evolution of squall lines has been outlined by Zipser (1977) and Houze (1977, 1989). Numerical modeling and theoretical work such as Rotunno et al. (1988) and Moncrieff (1992) have provided important insights into the dynamics of long-lived squall lines by focusing on locally two-dimensional dynamics.
More recent work indicates that a two-dimensional view might be overly simplistic. Hane and Jorgensen (1995) observed a complex three-dimensional structure. Several bands coexisted at various orientations to one another. The modeling work of Trier et al. (1997) shows three-dimensional structure in the 22 February TOGA COARE squall line system. Their simulations suggest transverse bands perpendicular to the squall line and vortices at the ends of the line. These simulations suggest that the complexity of tropical MCSs could play a role in the interaction of such systems with the ocean and surrounding atmosphere.
To understand the impact of a squall line on a global climate model, it is important to look closely at the complexity of such a line. The 20 February squall line evolved into a complex, three-dimensional MCS. Though it shows two-dimensional characteristics locally, these characteristics are not sharply defined because of the three-dimensional nature of the storm.
At the time of the aircraft flights into the 20 February system (Fig. 3), it was in a late stage of evolution. The convective echo was shaped like a horseshoe; the north–south squall line formed the center of the horseshoe and transverse bands to the west of the squall line formed the legs. We focus on the southern transverse band and a long-lived cell that formed 150 km to the rear of the system and traveled over 4 h before colliding with the northern band and dissipating.
The southern transverse band of 20 February was not solely a result of the squall line cold pool interacting with the environment. We will show that the southern transverse band did not form at the southern edge of the squall line–generated cold pool and draw updraft air from the south side, as one might expect (e.g., Geldmeier and Barnes 1997; Houze 1977; Zipser 1977). Rather, it drew most of its low-level updraft air from the north (cold pool) side. The vertical flux of horizontal momentum was in good agreement with the Moncrieff (1992) archetype model using air on the north side as inflow. At the highest levels, the transverse-band-averaged updrafts were considerably larger than can be accounted for in two dimensions. Evidence will be presented to show this upward motion was associated with the squall line’s mesoscale updraft, which transports warm, moist air from the environment ahead of the squall line. The transverse band resembles a similar band documented in an observational study by Jorgensen et al. (1997) and simulated by Trier et al. (1997), which also was fed by warm, moist air from the squall line inflow environment through the squall line updraft.
The long-lived cell that formed to the rear of the squall line on 20 February appeared to be a weak version of a supercell (Browning and Foote 1976). Its supercell characteristics include a 4-h lifetime, bulk Richardson number in the Weisman and Klemp (1982) supercell regime, and an updraft rotating in the sense predicted by the environmental hodograph, according to the work of Klemp and Wilhelmson (1978), and Rotunno and Klemp (1982, 1985). Little direct evidence exists of supercell-like features existing in the Tropics. McCaul (1991, 1993) has noted tornadoes in hurricanes, and WSR-57 radar data (McCaul 1987) suggested that some of the hurricane-spawned tornadoes have similar properties to those of supercells.
Other TOGA COARE case studies are documented by Jorgensen et al. (1995, 1996b, 1997), Smull et al. (1995, 1996), Roux and Moine (1996), and others. The individual nature of each case needs to be documented so that comparisons can be made, which may lead toward improved parameterization of the effects of MCSs on the global atmosphere and ocean.
2. Overview of the 20 February MCS
Figure 1 is the background flow field from the 2.5° × 2.5° gridded European Centre for Median-Range Weather Forecasts model data available for 0000 UTC on 21 February. The box at 5°S, 160°E is the area of the satellite image of Fig. 2. The satellite image shows the system at 2032 UTC, 20 February 1993 (all times will be UTC, for local time add 10 h), when the quad-Doppler observations with the two National Oceanic and Atmospheric Administration (NOAA) WP-3D aircraft began. The system studied by the aircraft is outlined on the figure. Satellite images showed clouds in the area of study as much as 4 h prior to the observation time.
The two NOAA P3 aircraft, designated N42 and N43, sampled the system between 1900 UTC on 20 February and 0300 UTC on 21 February with a combination of Doppler patterns and vertical soundings. The two P3s flew parallel tracks separated by 20–40 km using a“quad-Doppler” strategy (Jorgensen et al. 1996a). An early lower-fuselage (LF) radar display of the system (Fig. 3) shows convection, roughly in the shape of a horseshoe, composed of an eastward-moving north–south-oriented squall line and two east–west-oriented bands trailing from its north and south ends. The LF figures are composited images that have been corrected for aircraft motion but not for advection. The aircraft mission can be separated into three different quad-Doppler studies. The first focused on the convective east–west band to the south, the second was intended to be a stratiform study, and the third focused on a convective band that formed later.
When the aircraft began the Doppler studies, the squall line was in its later stages of evolution and demonstrated distinctly three-dimensional behavior. The southern east–west band was weakening, and had nearly dissipated by the completion of the pattern an hour after the image in Fig. 3 was taken. Neither the motion of the squall line nor that of the transverse bands was constant. Prior to the study time, the squall line was moving eastward at 13.0 m s−1, whereas at later times it slowed to 12.0 m s−1. The zonal motion of the southern east–west band was slower than the squall line, being eastward at 10.5 m s−1. The meridional motion showed the most variation. The northern east–west band initially had a southward component of 4 m s−1. The southern east–west band was moving northward at 5 m s−1 before the Doppler radar observations began; and, shortly after the Doppler analysis began, the band’s northward motion slowed to become imperceptible.
After the decay of the southern east–west band, the aircraft flew quad-Doppler patterns oriented north–south through what was expected to be stratiform precipitation in the cold pool region. Figures 4a and 4b show the LF reflectivity pattern for the first and second set of quad-Doppler legs through the squall line stratiform region. Within that stratiform precipitation area, the aircraft (flying at 30 m) encountered a strong outflow associated with a distinct arcus cloud. The cell associated with the arcus cloud appears in Fig. 4a as a >40 dBZ reflectivity region in the northern portion of the flight leg. Although this cell was not sampled with the Doppler radars prior to the time of Fig. 4a, it was observed earlier on the LF radar. As an example, the leading edge of the long-lived cell is marked with an × in Fig. 3. The long-lived cell was a separate phenomenon that was moving faster than the squall line and subsequently interacted with the northern east–west line, but was not part of that line. This cell had persisted for nearly 4-h prior to this analysis time and was in its final stages when it was sampled by two sets of quad-Doppler legs (notice the reduced reflectivity in Fig. 4b.) By the time the two aircraft returned to the area for a third leg (not shown), the cell was no longer visible on the radar and is assumed to have dissipated. During the time it was sampled by the Doppler radars, the cell was moving toward the east-northeast at 15.7 m s−1.
During the north–south flight legs, the LF radar observed a new east–west-oriented band to the west. This band was the focus of the final set of quad-Doppler patterns. This band moved eastward at 8 m s−1 and southward at 0.5 m s−1. Observations collected within this band will be analyzed and documented in a future paper.
3. Methods
a. Doppler analysis
Flight patterns in TOGA COARE were designed in part to maximize the opportunities for unique analysis of mesoscale systems made possible by the airborne Doppler radars on the turboprop aircraft. The Doppler radar is mounted on the tail of the aircraft, and is rotated about the aircraft axis so that the beams sample in a corkscrew pattern centered along the aircraft track. When the radar is operated using the fore-aft scanning technique, alternate beams scan forward and rearward of the aircraft at an angle of 22°N from a line normal to the heading of the aircraft. Thus, as a single aircraft flies along, the aft scans will overlap the previous fore scans, allowing for a pseudo-dual Doppler analysis. Jorgensen et al. (1996a) describe an innovative method to obtain quadruple-Doppler data by flying aircraft along coordinated, parallel tracks so that the resultant four beams intersect at a given point from different angles (the quad-Doppler pattern). With this overdetermined system, the vertical air velocity at the top of the echo can be obtained directly from measurements when a particle terminal fall speed is assumed. The accuracy of the vertical velocity measurement is increased with increasing angular distance above the aircraft (Jorgensen et al. 1996a). This result suggests that a low flight altitude (most of the flight paths on 20 February were flown below z = 1 km) yields vertical velocities at the top of the reflectivity region with unprecedented accuracy. Thus, assumptions about the vertical air velocity at the top of the echo can be avoided. This is desirable, since aircraft in situ measurements have indicated that vertical air velocities can be nonzero at the top of the radar reflectivity region.
Vertical motions throughout the depth of the cloud are obtained by using downward integration of horizontal divergences with an O’Brien (1970) correction to ensure zero vertical velocity at the surface. Quad-Doppler-estimated vertical velocities are used at the top of the domain as an upper boundary condition (Jorgensen et al. 1996a). A two-step Leise filter (Leise 1981) was also applied, which removes horizontal scales of motion less than about 8 km and resolves 80% of the signal for motions greater than 12 km. The resulting fields are thus best characterized as mesoscale rather than convective scale. The grid spacing used for the quad-Doppler analysis was 1.5 km for the horizontal dimensions and 1 km for the vertical dimension starting at z = 0.5 km up to 18 km.
b. Aircraft positions and velocities
Aircraft position is derived from an optimum combination of global positioning satellite (GPS) and inertial navigation system (INS) data using the variational technique discussed by Matejka and Lewis (1997). For quad-Doppler analysis, the absolute positions of both aircraft are critical for accurately combining observations. In addition, accurate aircraft ground speeds are required to remove the aircraft motion from the forward and rearward looking beams. The P3s each had three navigational systems: two INSs and one GPS. Both systems have problems that contribute to unacceptable error in the raw data. The INS signals are contaminated by unpredictable Schuler oscillations and drift error, whereas the GPS position and ground speed data not only contain gaps but they are inconsistent (e.g., the velocities cannot be derived by differentiating the positions). The variational technique exploits the best aspects of both datasets and handles gaps and small-amplitude noise in the GPS data—a step beyond simply combining the low-pass GPS signal with the high-pass INS signal. The variational technique also removes the inconsistencies between the position and velocity data.
c. Storm motion
Two techniques were used to determine storm motion, minimization of wind changes (e.g., Gal-Chen 1982), and subjective tracking of reflectivity features.
The minimization technique determines the most stationary reference frame. This is important for calculating vertical velocities. When working with radar data, the finite time necessary to collect a volume scan must be taken into account because during that time the storm will evolve. The preferred storm motion is the velocity that will minimize the errors in the wind analysis from multiple Doppler radar.
When the value Q is a minimum, the storm motion (Us, Vs) describes the most stationary frame. To find the minimum, Q is calculated for the initial (Us, Vs) estimate, and for nearby storm motions (i.e., at Us ± δ, Vs ± δ). If the original estimate is not the minimum Q value found, then the storm motion values are adjusted to be those that gave the minimum Q and the exercise is repeated with the motions near this new estimate. This technique determines the best winds from the data analysis.
The reflectivity-tracking technique used data collected from the P3’s LF scanning 6-cm radar. Using this reflectivity data, features can be tracked to a range of 370 km, and for periods of up to several hours. Since the aircraft is moving across a large area, cells between the aircraft and a distant feature of interest will frequently cause attenuation and make tracking reflectivity centroids difficult. However, features such as squall line or cell “leading edges” proved easier to track. An example of this technique is shown in Fig. 19 (section 5) with the long-lived cell storm motion discussion. The ability to obtain single scan information or composite images from the LF data alleviates the questions of whether the cell continuously propagates, if it “jumps,” or if a new cell forms in front of an old one. In this study, all cells were seen to propagate continuously.
The calculation of vertical velocities was done in the storm-relative coordinate system that was determined using the most stationary frame of reference (minimization technique). On occasion, however, we performed a Galilean transformation on these winds to a coordinate system moving with the speed of a reflectivity feature to make a point or to calculate momentum transports.
Tracking reflectivity features showed that the southern east–west band that was the focus of the first four sets of quad-Doppler flight patterns moved northward at 5 m s−1 prior to 2046 UTC, or the beginning of the first pattern. After that time, the reflectivity features in the western portion of the band ceased moving northward. This implies an average meridional speed of 2.5 m s−1 for the first pattern, and zero thereafter. However, the minimization technique applied to the entire quad-Doppler domain produced a meridional motion of 2.0 m s−1 over the course of the four sets of patterns. The flux calculations done on the east–west band focused on the first quad-Doppler pattern, so a value of 2.0–2.5 m s−1 seems appropriate. Acknowledging that there is uncertainty in determining storm motion, we use a northward translation speed of 2.0 m s−1. The zonal motion of the band was 10.5 m s−1.
The long-lived cell discussed in section 5 was also tracked. In this case the reflectivity tracking agreed well with the Doppler minimization technique at coincident times. This agreement indicates that the cell was the most dynamic feature in the Doppler range at the time of the north–south quad-Doppler legs. The velocity of the long-lived cell was (15.5, 2.5) m s−1 at that time.
d. Soundings
Two soundings were constructed, one to represent the environment of the squall line, and one to represent the environment of the long-lived cell. Both used upper-level (p < 300 mb) data from the ship Kexue #1 2300 UTC 19 February sounding, since the radiosonde-launching ships were no longer in the intensive flux array on 20 February. Data for p > 300 mb for the first sounding (Fig. 5) were derived from low-level aircraft and middle-level dropsonde data to the south of the southern east–west band. During data collection, this area was thought to be the inflow environment of the southern east–west band system. Although we will show that this is not the case, the sounding in Fig. 5 is still the only estimate available for the environment of the squall line. The convective available potential energy (CAPE) was low (700 J kg−1) in this region and the mixed layer was only 150 m deep at many locations, indicating that this air had been modified by convection. This result is consistent with the Doppler analysis, from which it was determined that the southern east–west band was not moving southward. At the end of the flight (0220 UTC on 21 February 1993), a second sounding was taken north of the extreme western portion of the MCS (Fig. 6), less than a degree from where the long-lived cell had formed 7 h earlier. Taking the squall line position as 160°E at 2050 (Fig. 3) and assuming a motion of 12 m s−1, we estimate the sounding (at 159.3°E, Fig. 2) was taken about 300 km behind the squall line. The data at the upper levels (p < 560 mb) were from the Kexue #1 sounding, and the data at lower levels (p > 560 mb) were from the aircraft at 0220 UTC 21 February. This second sounding yielded a CAPE of 1000 J kg−1.
A sounding is not available east of the squall line, which is presumed to be the inflow region for the squall line leading edge. The two soundings represented in this paper are distinct in their relationship to the squall line being studied. The first (Fig. 5) is the best available sounding of the inflow environment of the squall line. The western sounding (Fig. 6) is believed to represent the environment in which the long-lived cell formed.
4. Southern east–west band and squall line
a. Band structure
At the beginning of the Doppler investigation, the system consisted of three distinct bands forming a horseshoe (Fig. 3). Figure 7 is a low-level horizontal cross section showing the reflectivity and storm-relative winds for the southern east–west band for the first (roughly the same time as Fig. 3) and last quad-Doppler patterns. In the plots, the feature positions have been translated to a fixed time (2111 UTC) and the storm-relative wind vectors computed, using a constant storm motion of (us, υs) = (10.5, 2.0 m s−1). In this coordinate system, features moving at this speed should appear stationary. The southern east–west band is parallel to the environmental shear below 2 km as illustrated in Figs. 5 and 6 and the hodograph in Fig. 23 (section 5). Since both legs (Figs. 7a and 7b) were translated to the same time (2111 UTC), a form of leg identification other than the translated time was necessary. The identification of all legs in this paper was chosen to be the beginning time of N42 for that specific pair of coordinated quad-Doppler legs.
A comparison of the flight tracks between Fig. 7a and Fig. 3 indicates that the easternmost cell of the band was part of the squall line. The strong and persistent along-line winds at the eastern end are related to the squall line flow. Since the software that objectively determines the storm motion uses the most dynamically active features, the motion of the easternmost cell would drive that analysis. Hence, the easternmost cell (which is part of the squall line) remains stationary in the storm-relative frame (cf. Fig. 7a with Fig. 7b).
In contrast, Fig. 7 shows the western portion of the band clearly weakening with time. Flow is out of the north at the northern edge of the 30-dBZ reflectivity at y = 100 km in the first pattern (Fig. 7a), but this flow disappears at later times (Fig. 7b). The apparent southward drift in this storm-relative frame is because the western portion of the band stopped moving northward relative to the earth about halfway through the first quad-Doppler pattern. This was not “noticed” in the minimization technique when it was applied to the whole east–west line, because the western portion of the line was much weaker than the easternmost cell. The slowing and weakening of the western portion was probably related to its motion northward into the squall line cold pool.
The low-level cold air trailing a squall line has been frequently documented (e.g., Zipser 1977; Houze 1977). Their data suggests this colder air could extend 100–200 km behind the squall line. Geldmeier and Barnes (1997) show a cold pool in excess of 150 km across, for the dissipating TOGA COARE MCS sampled on 10 February 1993. Jorgensen et al.’s (1997) analysis of a TOGA COARE case that occurred on 22 February 1993 also shows colder air extending at least 150 km behind the squall line, partially due to continued infusion of downdraft air into the boundary layer. (There were some areas with air recovered to near environmental thermodynamic values less than 100 km behind the leading edge.)
The available thermodynamic data for 20 February is not complete enough to allow a full analysis of the cold pool and its extent. Figure 8 shows several shallow soundings, on a map that shows the major reflectivity features of Figs. 3 and 4a. In Fig. 8a, the profiles on both sides of the east–west band show vertical structure characteristic of modified air, with mixed layer tops at 300 m and less. The profile at 2143 UTC, just to the north of the east–west band, appears to be the most modified, with stable layers based at 30 m and 300 m. However, some of the structure could be associated with the outflow from the east–west band, since both Fig. 7 and in situ data show northward flow at lower levels.
Modification of air by the squall line is more clearly evident in Fig. 9, which shows the thermodynamic data collected by N43 along the eastern north–south leg in Fig. 8b. The east–west band is at 6.5°S. Just to the north of the band, θe drops off significantly, a result of both cooling and drying. The greater degree of modification of this air (compared to the air to the south of the east–west band) is presumably related to the relatively recent passage of the squall line over this area. The squall line passed over this area approximately 1–2 h before data were collected. There is also significant horizontal variation, as frequently observed in modified air (e.g., Jorgensen et al. 1997), with some pockets of surprisingly high θe. The pockets of high θe air may have been a factor in keeping the east–west band going.
1) East–west band flow
Figure 10 shows the airflow in a vertical plane perpendicular to the band at x = 120 km (see Fig. 7a for location) for the first set of quad-Doppler legs. Notice the similarity to a two-dimensional convective band structure, with a southward-flowing updraft surmounting a northward-flowing downdraft, similar to that documented repeatedly in the literature (e.g., Newton 1950;Houze and Betts 1981; Zipser et al. 1981). The source of inflow air is primarily to the north, near to or in the stratiform region of the north–south squall line, but from altitudes above 2 km. At the very lowest levels, the figure reveals divergent meridional flow, which is also documented in the aircraft flight-level data (not shown). Lack of indicated vertical motion at the edges of the figure does not necessarily mean that there was no vertical motion. Rather, these vectors are outside the area for which quad-Doppler analysis could be performed.
We can only speculate about the thermodynamics of the air entering the east–west band from the north. The radar cannot resolve the winds at the lowest levels, so it is possible that low-θe air from below 2 km could be entering the updraft. Since the aircraft was flying at 150 m MSL, the thermodynamics in the echo-free region above 2 km is unknown. The analysis in the next section on the squall line flow suggests that the east–west band is at the southern edge of the squall line rear inflow. Thus, the air entering the east–west band might have some of the thermodynamics properties of the rear inflow.
The alongband flow shows the strong influence of the squall line. To illustrate this, we recast the flow for the first pattern into the squall line reference frame (us, υs) = (13, 1.5 m s−1) in Fig. 11. The faster squall line speed clearly results in a stronger westward wind component along the band (cf. Fig. 11 to Fig. 7a).
If we take a cross section along the squall line motion vector, which is also roughly normal to the squall line and parallel to the east–west band (see line in Fig. 11), we obtain the vertical cross section of Fig. 12. The southern east–west band appears to be supplied at middle levels with low-level moisture from ahead of the squall line by the squall line’s westward-flowing updraft current. In this respect, the southern east–west band is similar to the “transverse” band trailing the 22 February squall line, observed by Jorgensen et al. (1997) and examined in the modeling study of Trier et al. (1997). Such along-line transport of moisture was also observed in the shear-parallel band discussed in Zipser et al. (1981).
There are a few differences worthy of note between the simulated transverse band of 22 February and the east–west band of 20 February. First, the 22 February transverse band was associated with a line-end vortex, which was not observed on 20 February. Second, the simulated 22 February bands were stationary in the storm-relative frame, while the 20 February east–west band moved more slowly eastward and more rapidly northward than the squall line, at least at the earlier times.
2) Squall line flow
Storm-relative zonal and vertical flow in a plane roughly normal to the squall line (see line in Fig. 11) is shown in Fig. 12. The vectors show a westward-tilted updraft feeding an eastward-moving squall line that was oriented north–south, as expected for quasi two-dimensional convection. However, the rear-to-front flow commonly seen in squall lines is less obvious in these plots. Figure 12a shows the winds in comparison to the reflectivity. Figure 12b shows the same winds, but the contours are winds in the plane of the cross section. At 3 km, the wind contours in Fig. 12b suggest a weak rear-to-front flow that is not so clearly observed in the wind-vector representation. This is perhaps not surprising, since this cross section is at the southern edge of the squall line, where the rear-to-front downdraft might be less obvious. Simulations of squall lines without Coriolis forcing (Skamarock et al. 1994) show that the cells at the center of the line are more likely to behave in a two-dimensional manner, with the associated rear inflow. We should expect, therefore, that a two-dimensional model such as Moncrieff (1992) would be more accurate at the center of the line. Note the strong vertical velocities at echo top, illustrating the danger of assuming zero vertical velocities there.
b. Momentum fluxes
In this section, momentum transports for segments of the 20 February system are computed and the results are compared to predictions from Moncrieff’s (1992) archetypal model. The input for the Moncrieff model is based on observed flow structures and the best estimate of the inflow sounding. The procedure is outlined in LeMone and Moncrieff (1994).
Values of observed and predicted momentum flux are compared for two volumes in the southern east–west band and for two domains in the observed (southern) portion of the squall line. The observed fluxes at each level are based on Doppler radar data found by first averaging the fluxes over the number of good points at that level, and then multiplying the average by the number of good points at that level, divided by the maximum number of good points at any level (equivalent to the maximum possible number of good points). This procedure implicitly assumes zero fluxes where there are no data (normally clear air), and significantly reduces artificially large values representing only a small part of the domain (e.g., associated with overshooting tops) to more reasonable values.
Figure 14 indicates the number of good points as a function of height for the domain shown in Fig. 11. Although the maximum number of good points obviously changes with domain size, the shape changed little. That is, the squall line domain drop-off from the figure, at about 9.5 km, defines the storm top equally well for both squall line domains and both east–west line domains.
1) East–west band fluxes
Since the east–west band was so strongly influenced by the north–south squall line the two must be spatially separated in the analysis. Comparison between the Doppler data (Fig. 7a) and the LF data (Fig. 3) shows that the region east of x = 145 km corresponds to the southern part of the squall line. Thus the momentum fluxes of the east–west band are based on data west of x = 145 km. The fluxes are computed only for the first quad-Doppler pattern, when both the minimization technique and the echo-tracking technique indicated an average northward motion for the entire line of about 2.0 m s−1.
The momentum fluxes for the east–west band are calculated in two domains. First the observed and modeled momentum and mass fluxes over the entire east–west band west of x = 145 km are compared with the model (the box in Fig. 7a between y = 64 km and y = 108 km.) Then, since the line has three-dimensional structure, the same comparison is done over a much smaller portion of the east–west band—in particular, the region between x = 110 km and x = 130 km (denoted in Fig. 7a by a single line at x = 120 km).
A cross section through the band (Fig. 10) indicates
Figures 15 and 16 show the momentum and mass fluxes for the large and small domains, respectively. Both momentum-flux profiles are reasonably represented by the Moncrieff model, indicating that we correctly characterized the band as ingesting updraft air from the north side. Such a qualitative match implies that the band acts this way in an integral sense; it is not dependent on careful choice of a north–south cross section. However, the three-dimensionality of the flow is illustrated by the fact that the fluxes from the narrow region (Fig. 16) match those predicted from theory better than those for the larger domain (Fig. 15). Also, the differences between modeled and observed vertical velocity become more pronounced with height, reaching a maximum at the top of the domain. From Fig. 12, vertical velocities at these heights are dominated by the squall line mesoscale updraft.
Taken together, the results support our earlier contention that the lowest-level flow is consistent with a model of a two-dimensional band feeding on the north side, but the squall line influence becomes more dominant with height.
2) Squall line fluxes
The line-normal momentum and mass fluxes were computed for two different domains. The fluxes calculated for the box drawn in Fig. 11 (squall line only) are shown in Fig. 17. A domain bounded by x = 84 to 192 km and y = 45 to 132 km (the entire domain shown in Fig. 11) has fluxes as shown in Fig. 18. For both cases, the inflow winds were computed from Doppler-derived winds east of the “squall line only” box, since there were no clear-air soundings east of the squall line.
Although their profiles have the same general shape, it is not surprising that neither set of fluxes agrees well with the Moncrieff idealization. This is largely because the data are for the southern edge of the squall line, where edge effects and the presence of the east–west band lead to three-dimensional flow. The idealized two-dimensional Moncrieff model would probably best apply to the center of the squall line (Skamarock et al. 1994), which lies to the north of where adequate Doppler data are available. Since both momentum and mass fluxes are significant at heights much higher than those predicted by the Moncrieff model (and indicated by the“good points” in Fig. 14), one suspects that the squall line extends higher at its center. The differences between predicted and observed momentum fluxes are particularly profound for the larger domain. This is because the Moncrieff model assumes that all of the mesoscale flow is related to the squall line itself, with the flow to the rear merely an extension of the squall line flow that contributes little to the flux (Fig. 13). This is hardly the case in reality: this domain contains the southern east–west convective band that is itself transporting momentum and mass.
3) Comparison with earlier work
Both the east–west band and the squall line exhibit momentum-transport characteristics commonly seen in previous work. The vertical divergence of the vertical transport of horizontal momentum is consistent with forward acceleration of air at lower levels, and rearward acceleration aloft. Such behavior has been observed over the eastern tropical Atlantic, the African Continent, and the midlatitudes, as summarized in LeMone and Moncrieff (1994). The fluxes are consistent with the front-to-rear flowing updraft and rear-to-front downdraft observed in linear convective systems since Newton (1950). This is simply seen if we define the normal component of the wind uN as positive in the direction toward which the convective band is moving. For the updraft, w is positive and uN is negative; whereas for the downdraft, w is negative and uN is positive. In both cases, this leads to negative vertical flux of line-normal momentum,
However, synthesizing the fluxes for the entire system is not so simple. As in the case of Hane and Jorgensen (1995), the momentum fluxes take on a “classic” form only when the domains are carefully selected. Even then, as we have seen, the interaction of the squall line with the east–west line precludes a simple flow model that exactly conforms to either the Newton (1950) or Moncrieff (1992) flow model. Extending the domain to include the entire system makes the situation even more complex, since the flow is highly three-dimensional. To idealize the flow using a “cumulus-friction” scheme such as that described by Schneider and Lindzen (1976) would not be correct either. In this treatment it is assumed that momentum is transported as a passive scalar, something that would tend to smooth out the vertical gradient of the horizontal wind. This assumption is violated in the smaller domains. For example, in both squall line domains, the vertical divergence of horizontal momentum accelerates air westward, leading to increased shear above the west wind maximum in Figs. 5 and 6. Thus, we are left with an intermediate situation that is difficult to quantify.
5. Long-lived cell
The second set of quad-Doppler legs began at 2203 UTC, and was oriented north–south. This second set was intended for stratiform and boundary layer studies in the squall line wake region and was flown at heights between 30 and 330 m. Figure 4 shows LF composites from the first two pairs of quad-Doppler legs. While flying this series of legs, the aircraft encountered a fast-moving long-lived cell, which aircraft observers noted had a distinct arcus cloud. The long-lived cell corresponds to the >40 dBZ region in the northern portion of the flight tracks in the figure. Figure 4a shows the long-lived cell as it was encountered by N42 (the western aircraft track) during the 2203 UTC flight leg. Figure 4b corresponds to the time when N43 encountered the cell (eastern aircraft track) during the 2230 UTC flight leg.
The history of the long-lived cell can be determined using the LF radar plots. The cell is discernible in Fig. 3 (the leading edge is marked by an “×”) just before it merged with the northern east–west convective band. The long-lived cell was an unexpected feature and dissipated shortly after the aircraft legs crossed it; thus only two Doppler volume scans are available (at 2203 and 2230) that contain information on the cell.
Figure 19 is a schematic showing the progression of the leading edge of the long-lived cell from 1900 UTC to 2300 UTC. The figure is based on 5-min LF composites between those times. After 2300 UTC it was difficult to separate the cell from reflectivity features associated with the squall line. The positions of the center of the leading edge from Fig. 19 are plotted as a function of time in Fig. 20. The dotted and dot-dashed lines show a change in slope (speed) occurring at about 2113 UTC (8000 s) as the cell merged with the northern east–west band that trailed the squall line (Fig. 3). The zonal speed of this long-lived cell was about 18 m s−1 eastward (dotted line in figure) prior to its interaction with the squall line, and 15.5 m s−1 afterward (dash-dotted line in figure). Both of these speeds were faster than the squall line speed of 12–13 m s−1. This would suggest that the long-lived cell was not a part of the squall line, but rather, that it formed separately and subsequently interacted with the northern east–west band of the squall line system. The meridional speed (dashed line) shows a slight oscillatory motion whose average over the duration of the observations was close to zero. The slope between 2203 UTC (11000 s) and 2230 UTC (12500 s) is consistent with the 2.5 m s−1 northward motion determined by the minimization technique. Since the Doppler analysis is available only over this same short time period (2203–2300) and the minimization technique agrees with the reflectivity tracking for this time period, we will assume the cell was moving with the motion: us = 15.5 m s−1 and υs = 2.5 m s−1 during the Doppler observations.
Figures 21a and 21b are horizontal cross sections of the long-lived cell at z = 1.5 km. The winds are storm relative. The long-lived cell can be distinguished by its intense (>40 dBZ) echo. The cell has several characteristics similar to a supercell. First, the cell was tracked for 4 h, well beyond the lifetime of an ordinary cell (Fig. 19). Second, the cell had a rotating updraft (Fig. 22). The third characteristic is the similarity of the hodograph (Fig. 23) with the supercell hodographs of Chisholm and Renick (1972). Klemp and Wilhelmson (1978) and Rotunno and Klemp (1982, 1985) performed numerical simulations of supercells with no Coriolis effect. They note that the dominance of one updraft rotation direction over the other is related to the turning of the environmental wind with height. In their midlatitude simulations, wind veering with height at lower levels resulted in a counterclockwise rotating updraft in the dominant cell. On 20 February, the hodograph in Fig. 23 shows the wind turning in the opposite direction, suggesting a clockwise rotation, as observed.
Although the long-lived cell resembles a supercell, it is much weaker. The updraft magnitude is far smaller (maximum of 5 m s−1) than that associated with a supercell (25–40 m s−1; Chisholm and Renick 1972), but more in the range of typical convective cells over the tropical oceans (e.g., LeMone and Zipser 1980; Jorgensen et al. 1985; Lucas et al. 1994). Such an observation is not unprecedented. Barnes and LeMone (1986), and Barnes (1995), report on an “ordinary” cumulus congestus with supercell dynamics. McCaul (1987) presents observations of supercell-like convection in a tropical cyclone environment and McCaul and Weisman (1996) successfully simulate small cells that resemble supercells of intermediate strength using hurricane environments. Furthermore, the long-lived cell of 20 February was most likely stronger earlier; the system was in rapid decay by the time of the Doppler observations. Finally, the vertical velocities are likely to be underestimated because of the mesoscale resolution.
Figures 24a and 24b are vertical cross sections through the cell roughly along its motion vector, at the time of Figs. 21a and 21b and along the lines in those figures. The reflectivity pattern is quite different from what would be expected in a supercell, with no evidence of a weak-echo region (e.g., Chisholm and Renick 1972). This is not surprising, since the system is rapidly weakening, and the vertical velocities may be too weak to keep hydrometeors aloft. The collocation of the high reflectivity and the updraft maximum in Fig. 24a may be transient and associated with the rapid weakening of the cell.
6. Concluding remarks
This paper has presented a study of a late-stage, horseshoe-shaped squall line system that occurred on 20 February 1993 during TOGA COARE. The traditional way of looking at squall lines would be to assume a two-dimensional structure moving at a constant velocity. This assumption is not true for 20 February. The squall line was three-dimensional, the various parts of the squall line were moving at different velocities, and those velocities changed with time. This paper has focused on two interesting features that will be discussed further, below; the southern east–west band (southern band in the horseshoe) and a long-lived cell that formed about 150-km west of the squall line and moved into the cold air.
a. An east–west trailing convective band that moved into the squall line cold pool
The band-normal flow and corresponding momentum fluxes compared well with quasi two-dimensional convective line structure. The surprise was that the band was feeding from its north side, which was the stratiform (cold pool) air of the squall line. Doppler radar data suggested that the updraft inflow air was from above 2 km. The radar data shed no light on whether some air may have come from lower levels as well. The western portion of the line weakened rapidly and decreased its northward movement from 5 m s−1 to zero during the first set of quad-Doppler patterns. At higher levels, mass flux within the east–west line domain was strongly affected by the ascending squall line updraft, which was probably a significant source of moisture.
Although the momentum fluxes for the east–west band and the squall line were consistent with those predicted by the two-dimensional idealized momentum flux model of Moncrieff (1992), the system was definitely three-dimensional. This system bears some resemblance to the 22 February case (Jorgensen et al. 1995, 1996b, 1997) in the late stages of its evolution. Both systems formed perpendicular to the low-level shear, and developed several bands oriented parallel to the shear in the cold air. Numerical simulation by Trier et al. (1996, 1997) and Robe (1996) suggest the evolution of these secondary bands is associated with the strength of the shear above the wind maximum and its angle to the low-level shear. The comparison of COARE systems to wind hodographs by LeMone et al. (1997 1998), supports the modeling results.
b. A single, long-lived (≥4 h) cell that penetrated into the cold pool
Although weak by both tropical and midlatitude standards, the cell had many characteristics of a supercell. It had a 4-h lifetime, which is consistent with supercell longevity. The environmental Richardson number of 21.7 was within Weisman and Klemp’s (1982) supercell range. The hodograph had a similar shape to those of supercells (Chisholm and Renick 1972). Finally, the clockwise rotation of the updraft in the presence of a backing wind hodograph was consistent with the theories of Klemp and Wilhelmson (1978) and Rotunno and Klemp (1982, 1985). Small or weak single-celled systems with supercell properties have been documented before by Barnes and LeMone (1986), Barnes (1995), and McCaul (1987) and simulated by McCaul and Weisman (1996). Such cases indicate the Richardson-number regime definition works if applied to cells with similar dynamics but a range of vertical velocity strengths.
We have little direct information about the history of the cell, but we can make some speculative inferences from the data. Figure 3 shows convection well behind the squall line at around 2045 UTC, so forcing might have been present at 1900 UTC when the cell was first detected. The cell’s subsequent history is plausible if one considers its speed relative to the squall line system. Before the cell slowed down as it encountered the northern east–west line at 2100 UTC (8000 s in Fig. 21), it was traveling 18 m s−1, closing the gap with the squall line at a rate of about 5 m s−1. Thus at 2100 UTC the cell was only 40 km closer to the squall line (or still 100 km behind it) than when it formed, conceivably still ingesting some unmodified air. After 2100 UTC, the cell was almost certainly ingesting air modified by the northern east–west line or the squall line. It was a full hour before the cell caught up with the aircraft. How could the cell persist? It would take nearly an hour for an average updraft of 2–3 m s−1 to carry energy-rich air to a storm top of ∼10 km. Thus, the cell could still be processing air ingested at 2100 when it was encountered by the aircraft at 2200. This, combined with some residual mixed-layer air above the cold pool, could have kept the system from disappearing altogether.
c. Future work
Future work will include analysis of the last east–west band that formed on the northwest edge of the squall line stratiform region. A more detailed study of the boundary layer evolution and of the heat and momentum budgets for the entire system will be conducted. This will help frame the system as a whole within the context of the large-scale dynamics. This single case needs to be compared with other case studies from TOGA COARE to derive a more general picture that can ultimately be incorporated into the necessary parameterizations for the larger-scale models.
Acknowledgments
We are very grateful to Tom Matejka for access to and help in running the storm motion software. Carl Hane and Scott Braun were very helpful in their comments on an early version of the manuscript. We would like to thank Brad Smull for many helpful discussions and John Daugherty for his assistance in obtaining the LF composite images. We are grateful to Stan Trier for obtaining the 19 February sounding data from which we were able to construct the upper levels for the 20 February soundings. Dave Johnson was very helpful when editing the Doppler data. We would also like to thank Bob Hueftle for his software and computer help. The background flow fields were from ECMWF data obtained from NCAR.
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ECMWF 850-mb flow field at 0000 UTC on 21 February 1993. The landmasses are outlined. The intensive flux array (IFA) is the odd-shaped quadrangle in the center. The rectangle is the region of the satellite image in Fig. 2.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
GMS infrared satellite image at 2032 UTC on 20 February 1993 surrounding the region of study. The line in the northwest corner is the southeastern edge of the IFA. The islands in the vicinity are outlined. The units are degrees (latitude, longitude) and the system studied was located at about (6°S, 160°E). The shading key is on the right. The box indicates the location of the image produced in Fig. 3. The ×’s correspond to the two sounding locations.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Reflectivity from the lower fuselage (LF) radar on aircraft WP-3D-N42. The plot is centered at (6.1°S, 159.8°E). Reflectivity shading is on the right (dBZ). The lines of arrows designate the aircraft tracks for the time duration of this composite. The composite was produced from data collected between 2042 and 2058 UTC. The × is the leading edge of the long-lived cell discussed in section 5.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
As in Fig. 3 except the composite times are (a) between 2203 and 2220 UTC (the arrow points to the long-lived cell) and (b) between 2230 and 2259 UTC.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Sounding for 20 February 1993 at approximately 2000 UTC, taken to the south of the east–west band (7.4°S, 160°E). (left) Skew T-logp plot. (right) Earth-relative zonal (solid) and meridional (dashed) wind (m s−1).
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
As in Fig. 5 but at approximately 0220 UTC on 21 February 1993 at a location west of the squall line (6°S, 159.3°E).
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Horizontal cross section at z = 1.5 km including reflectivity and storm-relative wind vectors. Contours and vector scaling are indicated on the right of each panel. The storm velocity was us = 10.5 m s−1; υs = 2.0 m s−1. Quad-Doppler leg patterns for flight legs: (a) 2042 and (b) 2134. The flight times for these legs were (a) N42 was between 2042 and 2059 UTC, N43 was between 2047 and 2102 UTC; (b) N42 was between 2134 and 2146 UTC, N43 was between 2132 and 2147 UTC. The boxes and the vertical line in (a) are regions important to momentum-flux calculations. Details are in the text.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
As in the LF composites of Figs. 3 and 4a except that only reflectivities >35 dBZ are shown (black shading). Temperature and dewpoint temperature profiles obtained within the time frame of the quad-Doppler sets are plotted (+ marks their location) relative to the reflectivity features.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Thermodynamic data from N43, from the easternmost flight leg of Fig. 4a. The aircraft was flying at 150 m MSL. The data collected during purls (turns) has been deleted. (a) Solid line is temperature, the dashed line is dewpoint temperature. (b) θe.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Vertical cross section of the southern east–west band at x = 120 indicating vector wind and reflectivity in the cross section plane. Winds are storm relative: us = 10.5 m s−1 and υs = 2.0 m s−1. Scaling is above the figure.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
As in Fig. 7a except for storm velocities us = 13.0 m s−1 and υs = 1.5 m s−1. The box contains the cells from the squall line.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Vertical cross section through the squall line, along the squall line motion vector (line in Fig. 11). Winds are storm relative, us = 13.0 m s−1 and υs = 1.5 m s−1. (a) Contours of reflectivity. (b) Contours of storm-relative wind along the motion vector. The scaling is above each plot.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Schematic showing the main features of the Moncrieff archetypal model [from Fig. 3a of LeMone and Moncrieff (1994)]. The system is moving left to right, in the positive x direction. The nondimensional height p* = (psfc − p)/(psfc − ptop), where p is pressure. Arrows indicate the front-to-rear inflow jump updraft, the front overturning updraft, and the rear overturning current (here a downdraft). The dashed lines separate the flow branches;
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
The number of good data points at each height as a function of height, used to determine storm top. The solid line is the number of points for the u and υ components, the dashed line is the number of good points used for the w winds, and the dot-dashed line at z = 9.5 km represents the storm top used for the Moncrieff model.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Vertical profiles of (a) line-normal momentum flux
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
As in Fig. 15 except the x domain was 110 km ⩽ x ⩽ 130 km; the y domain was unchanged at 64.5 km ⩽ y ⩽ 109.5 km:(a) momentum flux and (b) mass flux.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Fluxes for the limited squall line region 145.5 km ⩽ x ⩽ 187.5 km and 64.5 km ⩽ y ⩽ 109.5 km: (a) line-normal momentum fluxes and (b) mass fluxes.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
As in Fig. 17 except for the whole Doppler field of Fig. 11: (a) momentum fluxes and (b) mass fluxes.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Schematic of the long-lived cell leading-edge positions from 1900 UTC until 2300 UTC in increments of 15 min.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Position (in km) vs time (in ks from 1900 UTC) of the leading edge of the long-lived cell as determined from the LF radar images. The solid line represents the zonal displacement (distance from 158°E), and the dashed line the meridional displacement (distance from 6°S). The slope of the dotted line shows that the speed prior to 8 ks (or 2113 UTC) was 18 m s−1. The dot-dashed line is for after 8 ks and has a slope of 15.5 m s−1.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Horizontal plots showing the vector winds and reflectivity (dBZ) (shaded). Winds are storm relative, us = 15.5 m s−1 and υs = 2.5 m s−1. Quad-Doppler at z = 1.5 km analysis for: (a) 2203 and (b) 2230 UTC. The roughly east–west lines are the locations of the cross sections in Fig. 24. (a) N42 was between 2203 and 2229 UTC, N43 was between 2206 and 2228 UTC; (b) N42 was between 2230 and 2259 UTC, N43 was between 2249 and 2313 UTC.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Vector winds, aircraft tracks, and vertical velocity (shaded) at z = 1.5 km for flight at 2203 UTC, showing the rotation of the updraft. Winds are storm relative, us = 15.5 m s−1 and υs = 2.5 m s−1.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Hodograph from the sounding shown in Fig 6.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
Vertical cross sections through the long-lived cell for (a) 2203 and (b) 2230 UTC showing vector winds and reflectivity (shaded) along the line of motion (see lines in Fig. 21). Winds are storm relative, us = 15.5 m s−1 and υs = 2.5 m s−1.
Citation: Monthly Weather Review 126, 12; 10.1175/1520-0493(1998)126<3189:EADOAL>2.0.CO;2
