Scale Interactions Involved in the Initiation, Structure, and Evolution of the 15 December 1992 MCS Observed during TOGA COARE. Part II: Mesoscale and Convective-Scale Processes

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and Evolution of the 15 December 1992 MCS Observed

during TOGA COARE. Part II: Mesoscale and

Convective-Scale Processes

Alain Protat, Yvon Lemaître

To cite this version:

Alain Protat, Yvon Lemaître. Scale Interactions Involved in the Initiation, Structure, and Evolution of the 15 December 1992 MCS Observed during TOGA COARE. Part II: Mesoscale and Convective-Scale Processes. Monthly Weather Review, American Meteorological Society, 2001, 129 (8), pp.1779 - 1808. �10.1175/1520-0493(2001)1292.0.CO;2�. �hal-01660281�

q 2001 American Meteorological Society

Scale Interactions Involved in the Initiation, Structure, and Evolution of the

15 December 1992 MCS Observed during TOGA COARE.

Part II: Mesoscale and Convective-Scale Processes

A. PROTAT AND Y. LEMAIˆTRE

Centre d’e´tudes des Environnements Terrestre et Plane´taires, Velizy, France

(Manuscript received 20 January 2000, in final form 30 October 2000)

ABSTRACT

This paper, the second of a series, documents the precipitation, and kinematic and thermodynamic structure of a tropical mesoscale convective system observed by instrumented aircraft on 15 December 1992 during TOGA COARE. Radar-derived precipitation fields indicate that the studied system consists of two subsystems, S1 and S2, characterized by distinct internal dynamics and morphological structures. The retrieved kinematic and ther-modynamic structures are compared in detail with the synoptic-scale characteristics described in Part I of this paper, so as to evaluate the scale interactions involved in the internal organization of this convective system. It is shown essentially that the synoptic-scale circulation governs the mesoscale and convective-scale motions and, therefore, determines the internal organization of the selected system. In particular, this study highlights the major role played by the synoptic-scale vertical wind shear in the internal structure of this tropical mesoscale system. Momentum flux calculations show that upward transport of horizontal momentum on the mesoscale is large and mostly carried out at a scale of motion larger than the mesoscale (i.e., by the mean component of the total momentum flux). The westerly rear inflow exhibits characteristics consistent with the density current theory. However, specific mesoscale and convective-scale processes linked to the presence of precipitation modulate this dominant synoptic-scale forcing. A mesoscale interaction between the two distinct subsystems S1 and S2 is identified. The apparition of a shallow density current resulting from the downward spreading of air at the ground within S1 is suspected to be the triggering mechanism for S2.

1. Introduction

One of the main objectives of the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Re-sponse Experiment (TOGA COARE; Webster and Lu-kas 1992) is to understand the processes that control and organize convection in the warm pool region at the different scales of motion (from synoptic to convective scale) and the interaction of deep convection with the larger-scale atmospheric circulation. In order to address these broad TOGA COARE objectives, the scientific motivations of this paper are (i) to document the pre-cipitation, and kinematic and thermodynamic structure of one of the most impressive mesoscale convective systems (MCSs) observed during the TOGA COARE field phase (the 15 Dec 1992 cloud cluster) at both the mesoscale and convective scale, and (ii) to examine the scale interactions involved in the internal organization of this MCS. To study these scale interactions, a detailed comparison of the precipitation, and kinematic and ther-modynamic fields characteristic of the synoptic-scale, mesoscale, and convective-scale circulations is

con-Corresponding author address: Dr. Alain Protat, CETP–UVSQ, 10–12 Avenue de l’Europe, 78140 Ve´lizy, France.

E-mail: protat@cetp.ipsl.fr

ducted. The synoptic-scale mechanisms were examined Protat and Lemaıˆtre (2001, denoted Part I hereafter). This synoptic-scale study was performed using the Eu-ropean Centre for Medium-Range Weather Forecasts (ECMWF) model outputs (from which diagnostic pa-rameters have been derived) and Geosynchronous

Me-teorological Satellite-4 fields of brightness temperature

in the infrared channel (providing a picture of the con-vective activity every 15 min).

Let us first briefly summarize the results of Part I. From the ECMWF analyses at 0600 and 1200 UTC (all times are UTC), a particular region of the synoptic-scale do-main was identified as strongly favorable to the devel-opment of deep convection, with (i) a strong low-level convergence at 850 hPa between a northwesterly flow (corresponding to the beginning of a westerly wind burst period) and a southwesterly flow, (ii) strong convective available potential energy (CAPE) from 1200 to 1800, and (iii) strong production of CAPE at 1200, when the MCS starts intensifying. This favorable region actually corresponds to the area where the studied MCS (hereafter referred to as system S) developed and intensified, which indicates that the synoptic-scale circulation and dynamic features provided the initial conditions for the formation and general evolution of S. The synoptic-scale dynamic

and thermodynamic mechanisms leading to the observed initiation and general evolution of S were therefore ex-amined in detail. It was shown that initially, north of S, an easterly equatorial jet at 500 hPa generated positive

z and potential vorticity (PV) anomalies on its southern

border by 0600 UTC, in response to the important hor-izontal wind shear in this region. Then, thesez and PV anomalies propagated westward with the flow at 500 hPa, leading to the generation of an anticyclonic circulation C, vertically extending from 850 up to 250 hPa and with a peak magnitude at 1200 at 500 hPa and at 1800 at 700 hPa. Vortex stretching and vertical tilting of the hori-zontally oriented vortex tubes along the y axis were ev-idenced as the main processes involved in the intensifi-cation of this circulation C at 700 hPa from 0600 to 1800. This intensification of vertical vorticity at 700 hPa ac-celerated the northwesterly flow at 850 hPa from 0600 to 1800, which promoted in turn a strengthening of the synoptic-scale convergence line responsible for the in-tensification of S. From 1800, the magnitude of vertical vorticity associated with circulation C decreased, which diminished the synoptic-scale low-level convergence, and CAPE was not produced anymore in the S area. These two major changes in the synoptic-scale configuration associated with system S led to its decay. Again, this showed that the synoptic-scale circulation governed both the intensification and decaying periods of this MCS.

In the present paper, the dynamic and thermodynamic characteristics of the mesoscale and convective-scale cir-culations within S are derived from airborne Doppler radar data. These data were collected from 1700 to 2045 UTC by the two radars that operated aboard the National Oceanic and Atmospheric Administration 42 and P3-43 aircraft. The objectives of this study are to (i) come to a better understanding of the morphological structure and internal organization of the studied system at these scales of motion, and (ii) diagnose the downscale inter-action processes (i.e., from synoptic scale to convective scale) involved in the internal organization of the system. In section 2, the Doppler radar installed on the P3 research aircraft is briefly described, as well as the anal-ysis methods used to access the mesoscale and convec-tive-scale dynamic characteristics. In section 3, the me-soscale dynamic and thermodynamic characteristics are interpreted, and comparison is made with the larger-scale atmospheric context. Section 4 presents the re-trieved dynamics and thermodynamics within selected convective-scale domains, along with a detailed com-parison between the convective-scale, mesoscale, and synoptic-scale features. Finally, in section 5, concluding remarks are given.

2. Airborne Doppler radars and description of analysis methods

a. Description of the radars and antenna scanning methodology

The Doppler radar installed on the tails of the P3-42 and P3-43 aircraft is described in detail in Jorgensen et

al. (1983) and Hildebrand and Mueller (1985). The radar is an X-band Doppler radar (3.2-cm wavelength). The scanning methodology is the fore–aft scanning tech-nique, which collects two conical scans of data, one pointing;258 forward from a plane normal to the flight track and one scan pointing aft;258. Using this scan-ning procedure, a three-dimensional region of space sur-rounding the aircraft track is swept out. Along the beams, the range resolution of data is 75 m for ranges less than 19.2 km, 150 m for ranges between 19.2 and 38.4 km, and 300 m for ranges between 38.4 and 76.8 km. As with most TOGA COARE airborne Doppler radar sampling, the flight strategy used on this day was to fly parallel to the leading convective line of the sys-tem, using flight paths long enough that the fore and aft scans fully sampled the storm. The tracks flown on 15 December are described in detail in section 3.

A lower-fuselage non-Doppler C-band radar (5-cm wavelength) was installed as well on both P3 aircraft. This radar collects within a range of about 300-km qua-si-horizontal scans around the altitude of the aircraft. However, it must be noted that the wide beamwidth in the vertical (around 48) corresponds to a 4-km vertical resolution of the measurements at 60-km range. The precipitation field derived from these measurements should therefore be considered as an overview of the precipitating activity.

b. Retrieval of the 3D wind field on the mesoscale and convective scale

In this study, we will analyze the 3D airflow structure on the mesoscale and convective scale. The three-di-mensional wind field is retrieved in the present study using the Multiple Analytical Doppler (MANDOP) analysis [Scialom and Lemaıˆtre (1990, referred to as SL in the following) see also Dou et al. (1996) for the extension of the method to the processing of airborne Doppler radar data]. This analysis, based on a varia-tional concept, lies upon the expression of the three wind components as products of expansions in series of or-thonormal functions along the three axes of the coor-dinate system. The orthonormal functions (Legendre polynomials in the present case) are expanded up to a given order that partly determines the scale of motion resolved by the analysis. Then, the analytical form of the radial wind is variationally adjusted to the radial winds measured by the Doppler radar. The anelastic approximation of the airmass continuity equation is in-troduced in the minimization procedure, as well as the condition w 5 0 at ground level. These physical con-straints are mandatory to access an accurate estimate of the vertical wind component.

As already discussed in SL, Dou et al. (1996), and Protat et al. (1998), the analytical approach used in this analysis benefits from several advantages. In the context of this multiscale approach, the main advantage of the analytical formulation results in the natural filtering and

interpolating properties of such methods. The cutoff wavelength lc2of the analytical formulation in a given direction x is a function of the grid resolutionDx, the domain size Dx, and the order of expansion n of the

analytical functions. As explained in SL, no structure with a wavelength smaller than lc15 2Dx can be re-solved according to Shannon’s theorem. On the other hand, a wave along each axis defined by a Legendre polynomial expanded up to order n reaches zero at most (n2 1) times along the domain size, which implies a minimal wavelengthlc2of 2Dx/(n2 1). Parameters n,

Dx, and Dx must therefore be chosen in the three

di-rections of space such thatlc1, lc2. As shown in SL, the corresponding minimum observable scale is lc 5

0.26lc2. The airborne Doppler radar data have proven to be of a spatial and temporal resolution compatible with convective-scale studies. In order to perform a 3D wind field retrieval on the mesoscale, the MANDOP analysis can be applied with a smaller order of expan-sion than on the convective scale, which will filter out the convective-scale structures resolved in the mea-surements. As an example, for a domain size Dx5 300

km along a direction x and an order of expansion n5 5 for the analytical functions, the minimum observable scale is of about 40 km, which will filter out the con-vective-scale structures.

c. Retrieval of the pressure and temperature perturbations

From the analytical representation of the 3D wind field, the pressure and ‘‘virtual cloud’’ potential tem-perature1_{perturbations are retrieved under an analytical} form by introducing the analytical form of the 3D wind field obtained by the MANDOP analysis in the nondis-sipative and stationary first-order anelastic approxima-tion of the momentum equaapproxima-tion (Protat et al. 1998). This analysis differs from that described in previous studies (e.g., Gal-Chen 1978; Hane and Ray 1985), in that the input is the analytical 3D wind field, not a 3D wind field numerically retrieved at each grid point of a regular grid mesh. In this method, the pressure and temperature perturbations are obtained under an analytical form, and the coefficients of expansion of the wind are those of the pressure and temperature perturbations as well. These perturbations are actually deviations from a ref-erence state that is constant horizontally but varying with height (Protat et al. 1998). In order to access the full 3D pressure and virtual cloud potential temperature fields, a boundary condition provided by an in situ mea-surement (e.g., radiosounding, dropsounding) must be introduced in the method. Such a measurement is

un-1_{The virtual cloud potential temperature perturbation is defined as}

5 2 qcuy0, where is the virtual potential temperature

de-u*c u*y u*y

viation from a reference stateuy0and qcthe cloud water mixing ratio.

Therefore,u*c includes the effects of both temperature deviations, cloud water loading, and water vapor.

fortunately not available around the studied system, which implies that vertical cross sections of dynamic perturbations cannot be interpreted. This also means that a21 K perturbation does not mean that the flow is 1 K colder than the environment, because of the unknown horizontal constant that should be added to the pertur-bation. Then, only the horizontal gradients of dynamic perturbations will be interpreted throughout this paper. The horizontal gradients of pressure and virtual cloud potential temperature analyzed in the present study have been cross-validated (Protat et al. 1998, see their Fig. 11) with those obtained using the single-beam airborne velocity azimuth display (SAVAD) analysis2_{(Protat et} al. 1997) within the S2 system. A very good agreement was obtained between the two independent estimates. This result indicated that the retrieved thermodynamic horizontal gradients could be reasonably trusted.

d. Air and water parcel trajectory analysis

The analytical representation of the 3D wind field can be used to recover three-dimensional trajectories of air and water parcels within a given retrieval domain, pro-vided that the 3D wind field can be assumed as relatively steady state. In fact, from a given initial position of an air parcel in the retrieval domain, each new location of this parcel at a given time T can be calculated from its previous location at time T 2 DT using the analytical 3D wind field and the time intervalDT (which can be chosen as small as needed since the wind field is ana-lytically expressed) so as to determine the displacement vector of the parcel. This procedure allows for obtaining the displacement vector anywhere in the domain, since the analytical form can be calculated at any intermediate location and not only at given grid points.

The water parcel trajectories can be obtained by add-ing an estimate of the terminal fall velocity of the hy-drometeors to the retrieved vertical component of the wind. This terminal fall velocity of the hydrometeors is generally estimated using a empirical relationship as a function of the radar reflectivity. In the present case, vertical profiles of terminal fall velocity have been re-covered within the 15 December 1992 MCS, using the SAVAD analysis (Protat et al. 1997) described just above. This estimate derived from radar measurements is used in the following.

3. Mesoscale analysis of the 15 December 1992 MCS

The mesoscale description of the MCS remains a cru-cial problem despite the significant amount of

instru-2_{The SAVAD analysis provides vertical profiles of mesoscale}

quantities (horizontal wind and its first-order derivatives, terminal fall speed of the hydrometeors, and the horizontal gradients or pres-sure and temperature using the horizontal momentum equations) from the data collected during the circular P3 aircraft tracks (Protat et al. 1997).

FIG. 1. (a) Overall precipitation structure of the 15 Dec 1992 MCS constructed from the P3-42 lower-fuselage non-Doppler C-band radar reflectivities cumulated for the whole aircraft mission (1700–2045 UTC). Subsystems S1 and S2 discussed in the text are roughly indicated in the domain. Shaded areas of reflectivity are every 5 dBZ, from210 (light gray) to 40 dBZ (dark gray). White and black lines represent the trajectories flown by the P3-42 and P3-43 aircraft, respectively. Also given are the P3-42 tail-Doppler reflectivity composites at 2-km altitude for the following time periods: (b) 1715–1730 and (c) 1800–1815 UTC within S1. North is indicated in the upper-right corner of the panels. The X in (a) corresponds to the reference point (0,0) in (b) and (c).

mental means deployed during the TOGA COARE In-tensive Observing Period (IOP). In fact, the radiosound-ing network is too coarse to recover the mesoscale flows, especially on this day of the IOP, characterized by poor radiosounding coverage and frequency. Therefore, in order to access the mesoscale characteristics associated with the selected MCS, it is chosen in the course of this study to process the airborne Doppler radar data in such a way that the largest retrieval zone (typically 250 3 250 km2_{) is covered.}

Figure 1a shows a time-composite reflectivity map of the 15 December 1992 MCS for the whole aircraft mis-sion (1700–2045 UTC), as sampled by the C-band radar mounted on the P3-42 aircraft. For each 5-km grid el-ement of this map, the highest reflectivity value col-lected over the sampling time is retained. Let us recall that such a picture should be considered as an overview of the precipitation structure of the MCS (see section 2a). The trajectories of the P3-42 and P3-43 aircraft are

the white and black lines, respectively. This overview of the precipitation field indicates that the MCS consists of two main areas of strong precipitation (denoted as S1 and S2, respectively, for the northwesternmost and southeasternmost subsystems). Their detailed structure will be discussed later using the high-resolution reflec-tivity data from the tail Doppler radars.

Figure 1a indicates that the P3-42 aircraft, which started collecting data at 1700 UTC, systematically flew at the rear of (i.e., north of ) and along an almost linear convective structure associated with S1 (at a flight al-titude of about 4 km). This sampling strategy enabled collection of data within S1 from 1700 to 1830 UTC. Meanwhile, the P3-43 aircraft systematically flew ahead of (i.e., south of ) and along the linear convective struc-ture associated with S1, at a flight altitude ranging from 200 m to 1 km. This scanning strategy was then repeated from 1915 to 2045 UTC to collect data within the second convective structure S2 (southeast of S1).

FIG. 1. (Continued )

In order to access the mesoscale characteristics as-sociated with this MCS in the largest retrieval domain, Doppler radar data collected during the time interval 1700–2045 UTC must be used. Nevertheless, this

cu-mulation of data during this relatively large interval is possible only if the MCS can be assumed as reasonably steady state. The steady-state assumption is typically evaluated through inspection of the temporal evolution

of the most active part of the convective systems, as revealed by the tail-Doppler radar observations. This evaluation is possible in the present case, since the re-search aircraft flew several straight-flight tracks parallel to each other within both subsystems. Figures 1b and 1c show the reflectivity fields at the 1-km altitude de-rived from observations collected 1 h apart within S1. It is seen that the general organization of precipitation looks reasonably the same in both figures, except in the stratiform region of the system where small differences appear. It also shows that the convective structures re-main fairly fixed in location. These results indicate that a ‘‘quasi-’’ steady-state assumption can be reasonably assumed in the present case, since convection is not found to significantly change within S1. The same con-clusions apply to S2 (not shown). In addition, it will be shown that the structure of the precipitation field on the mesoscale, which is obtained using a long time period of observations, is reasonably similar to that of the pre-cipitation field derived from a much shorter time period of 10–12 min within selected precipitating areas. This validates indirectly the steady-state assumption.

In section 3a, a detailed description of the dynamic characteristics of the mesoscale circulation is presented, and comparison is made with the synoptic-scale circu-lation so as to examine the possible interactions between these scales of motion. The interpretation of the internal organization of the system using air parcel trajectory analysis on mesoscale is presented in section 3b. Mo-mentum fluxes calculations are conducted in section 3c, in order to estimate the respective contribution of the synoptic-scale and mesoscale circulations to the vertical transport of horizontal momentum on mesoscale. Fi-nally, the thermodynamic characteristics of the meso-scale flow are analyzed in section 3d.

a. Mesoscale dynamics

The 3D wind and precipitation fields are given in Fig. 2 at 0.5-, 1.5-, 3-, 5-, 8-, and 10-km altitude. The domain size is 2703 170 km2_{, and the orders of expansion of} the analytical functions in the x and y directions are 6 and 4, respectively. Following the calculations in section 2b, this corresponds to a minimum observable scale of about 30 km. The convective structures are therefore filtered out by the method. The reflectivity fields of Fig. 2 show a more detailed morphological structure than that seen in Fig. 1a. The existence of two subsystems, S1 and S2, within S appears more clearly. These sub-systems are located in the northwestern and southeastern areas of the mesoscale retrieval domain, respectively. Subsystem S1 is broadly characterized by a typical structure of squall line (Fig. 2b), with (i) a very active bow-shaped precipitation area characterized by reflec-tivities stronger than 40 dBZ, denoted LS1in what fol-lows (see dashed line in Fig. 2a), oriented along a south-west–northeast axis, (ii) a region of quite homogeneous precipitation on the northwestern part of S1 (the

strat-iform part), within which exists a more intense precip-itating area (reflectivities stronger than 30 dBZ ) that will be discussed later on, and (iii) a region of weak reflec-tivity echoes, strongly reminiscent of the ‘‘transition zone’’ of weaker precipitation commonly observed within tropical and midlatitude squall lines (e.g., Le-maıˆtre and Testud 1986; Biggerstaff and Houze 1993; Braun and Houze 1994). Note that this transition region in the present case is clearly shifted to the northeast of LS1, instead of lying all along the rear part of the leading edge as is often observed within squall lines. This latter characteristic gives to S1 a three-dimensional structure. Subsystem S2 consists of a strong leading convective line, denoted LS2 in the following (see dashed line in Fig. 2a), and a stratiform region (much less developed than that of S1) at the rear of LS2.

Horizontal flows on the mesoscale have been com-pared with the synoptic-scale ECMWF wind analysis (not shown). It has been clearly found that they were comparing fairly well at every altitude, but that a spatial shift of about 200 km appeared between the mesoscale and synoptic-scale circulations. This shift is particularly obvious for the area of convergence between the west-erly and southwestwest-erly flows at the 1.5-km altitude. In-deed, this convergence area is located within the me-soscale domain (Fig. 2b), according to the radar obser-vations, while inspection of the ECMWF analysis of the horizontal wind at 850 hPa shows that this convergence area is located about 200 km west of the mesoscale domain (see Fig. 9c of Part I and the location of the mesoscale box in the analysis domain). This shift is not really surprising. First, there is a temporal shift between the analysis and the radar observations, and more im-portantly the scale resolved by the ECMWF model (around 200–300 km) and by the mesoscale 3D wind field (30 km; see section 2b) are very different. This spatial shift is therefore of a scale smaller than the scale resolved by the ECMWF model. In addition, it will be shown in section 4 that condensation and evaporation processes play an important role in the dynamic of the MCS on the mesoscale. These local processes (with re-spect to the synoptic scale) are not resolved by the ECMWF model, but are parameterized. An underesti-mation of the effect of these mesoscale processes on the local intensification of the synoptic-scale flows would certainly lead to a spatial shift. In fact, as shown in section 4, evaporation is responsible for a significant cooling of the northwesterly rear inflow. The resulting density current is propagating toward the southeast/east. This displacement, if not well represented by the pa-rameterizations in the model, could explain why the convergence line is shifted in the ECMWF analysis slightly west of where it is observed by the airborne radars.

We now turn to a detailed description of the mesoscale airflow circulation. The retrieved 3D wind field at the 1.5-km altitude (Fig. 2b) is characterized by a relatively homogeneous southwesterly flow, within which two

gions of strong convergence appear, coinciding with the leading convective lines of both subsystems. This me-soscale circulation at 1.5-km altitude is consistent with the synoptic-scale ECMWF analysis of the horizontal wind at the 850-hPa level (see Fig. 9b of Part I). The convergence zone associated with S1 is better defined than that associated with S2, with a convergence be-tween a southwesterly flow ahead of LS1and a relatively homogeneous westerly flow at the rear part of LS1, with-in the stratiform part of S1. This westerly flow extends vertically from the ground up to 3-km altitude (see Figs. 2a–d). Likewise, strong convergence is found within S2 between a southwesterly flow ahead of LS2, and a west-erly flow at the rear (within the stratiform part). This westerly flow is however much more shallow at the rear of LS2than at the rear of LS1, roughly less than 1.5 km deep (see again Figs. 2a–d). This suggests that this west-erly flow at the rear of S2 results from processes (and in particular microphysical processes) within the strat-iform part of S2, while the much deeper westerly flow associated with S1 may be linked to the synoptic-scale circulation. This difference in the low-level rear inflows will be studied in section 4 on the convective scale.

At 3-km altitude (Fig. 2c), the westerly flow still gen-erates convergence within S1, while convergence is clearly less intense within S2, due to a veering of the flow with height from westerly to southwesterly be-tween 1- and 3-km altitude. This relatively homoge-neous southwesterly flow associated with S2 at 3-km altitude appears around the 5-km altitude within S1 (Fig. 2d). In the upper part of the troposphere, strong diver-gence occurs within S1. The horizontal wind is much weaker in magnitude and more perturbed in the 7–10-km layer (Figs. 2e,f). Strongly divergent flows are found, with northwesterlies and south-southeasterlies in the southeastern and northwestern parts of the domain, respectively. This strong divergence signature at higher levels is found as well at the synoptic scale within and in the vicinity of the mesoscale retrieval domain, as shown by the ECMWF analysis at the 250-hPa level (Fig. 3).

Figure 4 shows the hodograph of the horizontal mean wind in the mesoscale domain (profile 1) and individual hodographs of the retrieved 3D wind field within the different precipitating entities of the mesoscale domain. This figure shows that the orientation of the two leading convective lines, LS1 and LS2, is almost perpendicular to the mean vertical shear of horizontal wind between 0- and 3-km altitude (see profile 1). This behavior would put this convective system in the ‘‘shear perpendicular’’ category defined by LeMone et al. (1998) for the TOGA COARE convective systems, and in the ‘‘fast movers’’ category of Barnes and Sieckman (1984), Alexander and Young (1992), and Keenan and Carbone (1992). How-ever, these categories all correspond to a relatively fast propagation speed of the systems (roughly .7 m s21_,

or close to the low-level wind maximum, depending on the classification), which is not the case here since S1

and S2 remain fairly fixed in location during the sam-pling time of these entities by the airborne radars. LeMone et al. (1998) categorized therefore this 15 De-cember system as one of the two ‘‘unclassifiable’’ sys-tems out of the 20 cases examined. This may be due to the presence of a significant midlevel vertical shear as-sociated with the inflow ahead of the leading convective lines, as shown by the local hodograph taken ahead of LS2(profile 2 in Fig. 4). This midlevel shear is 1808 to the low-level shear. With a shear-perpendicular config-uration in the low levels and a reversed shear at mid-levels, the low-level shear should determine the orien-tation of the primary convective lines (which is indeed the case here), and the midlevel shear should lead to the formation of secondary bands extending rearward from the primary lines in the later stages of evolution (LeMone et al. 1998, and earlier investigators). Such secondary bands are not observed at the time the radars sampled the MCS.

The hodographs performed within the stratiform re-gions of S1 and S2 mainly confirm that the westerly flow at the rear of S1 (profile 4) is deeper than at the rear of S2 (profile 3). The hodograph representative of the horizontal wind within the stratiform part of S1 (pro-file 4 of Fig. 4) shows that the orientation of the most active precipitating area within this stratiform part is oriented along the horizontal airflow at 5-km altitude, and parallel to the vertical wind shear between 5- and 7-km altitudes. This latter observation is consistent with the ‘‘quasi-universal’’ conceptual scheme of tropical squall line dynamics, with precipitation in ice phase (which, in this case, would be generated within the southwestern part of LS1) evacuated toward the rear part of the leading convective line by a midtropospheric front-to-rear outflow (e.g., Chong et al. 1987; Fovell and Ogura 1988; Houze 1993). The existence of such a midtropospheric outflow and its potential importance in the mesoscale dynamics of the system is discussed in what follows using vertical cross sections and air parcel trajectory analysis.

Such a vertical cross section of reflectivity and wind along the plane of the cross section is given in Fig. 5a. Contrary to the other TOGA COARE case studies doc-umented by Jorgensen et al. (1997) and Hildebrand (1998), the vertical structure of precipitation does not exhibit the rearward tilting typical of the leading con-vective lines of quasi-2D squall lines. Figure 5a shows that upward vertical motions are initiated in the lowest tropospheric layers within S2, and at about the 2–3-km altitude within S1. This difference is probably due to the different depth of the low-level westerly rear inflow of S1 and S2, respectively. It is indeed clearly seen from Fig. 5b, presenting the isotaches of the u component of the wind in the same vertical cross section as Fig. 5a, that the low-level westerly flow is progressively deep-ening to the northwest (left). The vertical cross section of Fig. 5a shows that the deep westerly rear inflow as-sociated with S1 is capped by the 08C isotherm (around

FIG. 2. Horizontal cross sections of the 3D airflow and reflectivity fields at the mesoscale and at (a) 0.5-, (b) 1.5-, (c) 3-, (d) 5-, (e) 8-, and (f ) 10-km altitude. The mesoscale domain is rotated horizontally 158 clockwise from north. North is indicated. The location (CD) of the vertical cross section presented in Fig. 5 is also given. Areas A and B shown in (a) correspond to the two convective-scale retrieval domains discussed in section 3. These convective-scale retrieval domains are both rotated 308 counterclockwise from north. The latitude and longitude given in the figures correspond to (x, y)5 (0, 0). Thick dashed lines correspond to LS1and LS2.

the 4.5-km altitude in the present case). This capping effect of the 08C stable layer has also been noted in the TOGA COARE systems studied by Jorgensen et al. (1997) and Hildebrand (1998). This westerly rear in-flow, which results from the synoptic-scale circulations, is found to be accelerated within both stratiform parts of S1 and S2 (see Fig. 5b). Previous investigations of tropical squall lines documented the existence of a pres-sure deficit in the low levels, at the rear of the leading convective line. This pressure deficit is induced hydro-statically by the rearward spreading of warm and moist air from the updraft and dynamically by the interaction of the updraft and the ambient wind shear (e.g., Rotunno and Klemp 1982; Weisman 1992; Szeto and Cho 1994).

This local pressure deficit in the stratiform part of the squall line induces a negative horizontal pressure gra-dient from the rear part of the stratiform area toward the rear of the leading convective line. According to the horizontal momentum equations, this negative horizon-tal pressure gradient must induce a local acceleration of the horizontal airflow in the direction of the horizontal pressure gradient force, acceleration well observed in the present case at the rear of LS1and LS2(Fig. 5b).

Maximum upward motions associated with LS1 and LS2 are located in the upper part of the troposphere (above 12 km from S1, and around 12 km for S2; see bold contours in Fig. 5a), with a peak magnitude of about 1.5 m s21_{. This characteristic is also observed at}

FIG. 2. (Continued )

the synoptic scale, with maximum upward motions lo-cated around the 8-km altitude at that scale, as shown by the vertical profile of vertical wind component de-duced from the ECMWF analysis at the location of the mesoscale domain and at 1800 UTC (Fig. 6). This ob-servation of an elevated vertical velocity maximum for tropical convection is in agreement with previous stud-ies (e.g., Jorgensen et al. 1997; Hildebrand 1998; Roux 1998). The mesoscale updrafts associated with LS1and LS2 are both diverging in the upper part of the tropo-sphere (see Figs. 2e,f). This upper-level divergence sig-nature produces a symmetric structure of the upper-level outflow, with a first part of the outflow that is advected rearward of the leading lines, and a second outflow that backs ahead of the leading lines [denoted as the ‘‘over-turning updraft’’ in Lemone and Moncrieff (1994)]. Other vertical cross sections through the mesoscale do-main (not shown) confirm this characteristic of the ver-tical structure of the updrafts, with maximum upward

motions of about 1–2 m s21_{located at about 12–13-km}

altitude for S1, and about 11 km for S2.

It is noted that the frontward upper-level outflow was not observed in the 22 February 1993 fast-moving shear-perpendicular squall line observed during TOGA COARE (documented in Jorgensen et al. 1997), while it is clearly observed in the 18 February 1993 shear-parallel non-propagating rainbands observed during TOGA COARE (documented in Hildebrand 1998). The 15 December 1992 subsystems and the rainbands stud-ied by Hildebrand (1998) seem therefore to share two characteristics: a fixed location and the existence of a frontward upper-level outflow.

b. Interpretation of the obtained mesoscale dynamics

As explained in section 2d, three-dimensional air par-cel trajectories can be retrieved using the 3D wind field under a steady-state assumption. In order to reconstruct

FIG. 2. (Continued )

FIG. 3. The 15 Dec 1992 ECMWF analysis of the horizontal wind at 1800 UTC and at the 250-hPa level. The trapeziod represents the IFA, and the rectangle on its southeastern border corresponds to the mesoscale retrieval domain of Fig. 2.

FIG. 4. Hodograph at the mesoscale of the horizontal wind averaged in the mesoscale domain (profile 1), ahead of LS2(profile 2), and in the stratiform parts of S2 and S1 (profiles

3 and 4).

a general picture of the 3D airflow circulation on me-soscale, we choose initial positions ahead of the leading convective lines of S1 and S2 every 10 km in the hor-izontal and every 500 m in the vertical. The individual 3D air parcel trajectories retrieved are then subjectively grouped into ‘‘most representative’’ flows. The same procedure is applied to the rear part of the leading con-vective lines of S1 and S2. A conceptual scheme of the 3D airflow circulation associated with the studied MCS is then constructed from these individual most repre-sentative flows. This conceptual scheme is given in Fig. 7. Also drawn schematically in this figure are the two low-level flows representative of the larger-scale at-mospheric context (see Part I), that is, a westerly flow linked to the beginning of a westerly wind burst period, overlayed by a southwesterly flow. In the mesoscale area, the synoptic-scale westerly flow is characterized by a southern border that progressively deepens toward the north. This slantwise slope is also found on the mesoscale, as discussed in section 3a (Fig. 5b). Figure 5b also shows that vertical variations are superimposed to this general deepening across the domain. These var-iations likely result from the local intensification of the synoptic-scale westerly flow, in response to the presence of S1 and S2, as discussed previously.

The air trajectory composite associated with S1 (Fig. 7) shows the existence of a mesoscale westerly flow denoted 1 in Fig. 7 (within the synoptic-scale westerly flow), which initially extends vertically from the ground

up to 2-km altitude. This flow is oriented along the precipitation structure located in the southwestern part of LS1, slightly overruns the northernmost part of the westerly flow (denoted 2 in Fig. 7), and ends up in the 2–3.5-km layer in the rear part of the stratiform region. This northernmost part of the westerly rear inflow 2 is deeper than flow 1 (located in the 0–3.5-km layer), re-mains quasi-horizontal, and deflects horizontally to the northeast as it approaches the northeastern part of LS1. Within the synoptic-scale southwesterly flow, two me-soscale ascending flows (denoted 3 and 4 in Fig. 7) having distinct upper-level characteristics are identified. Both flows are located initially in the 1.5–4-km layer. As those flows rise up, they progressively deflect west-ward and eastwest-ward, respectively, and end up in the 6– 14-km layer. Updraft 3 is oriented along the most intense precipitating region within the stratiform part of S1 (see the schematic representation of the precipitation field of Fig. 7 and the reflectivity field of Fig. 2a), while updraft 4 is oriented along the northeastern part of LS1. A part of each flow 3 and 4 backs toward the front side of the leading line LS1. These ‘‘overturning updrafts’’ are de-noted 39 and 49 in Fig. 7 and are discussed in section 3a. Interestingly, the advection of precipitating particles within the overturning updraft 49 may in particular ex-plain the existence of an anvil cloud ahead of the north-eastern part of LS1 [at around (x, y) 5 (60, 0) in Fig. 2a]. Finally, the last flow characteristic of the mesoscale circulation within S1 (denoted 5 in Fig. 7) is the

FIG. 5. Vertical cross section in the cross-line direction (CD) indicated in Fig. 2a of (a) reflectivity (shaded) and wind vectors along the plane of the cross section (arrows) and (b) the u component of the retrieved 3D wind field (shaded). The vertical wind component is also shown as bold contours (a) when greater than 0.5 m s21_{(contours every 0.5 m s}21_).

ernmost part of the synoptic-scale westerly flow, located within the 0–1.5-km layer. This flow (5) slightly ascends along and just ahead of LS1(rising up to the 2–2.5-km altitude in the northeastern part of LS1), indicative of a moderate convective instability.

The air trajectory analysis within S2 indicates that the mesoscale rear inflow 6 (located initially in the 0– 1-km layer) within the synoptic-scale westerly flow and the mesoscale southwesterly flow 7 (whose initial depth is difficult to assess, since there is a lack of radar targets ahead of the leading line LS2) both contribute to the upward motion within S2. Also noteworthy is the ex-istence of an overturning updraft (denoted 79 in Fig. 7) backing ahead of the leading convective line LS2, as discussed previously. It is found that the air parcels within flow 7 systematically reach higher levels than those within flow 6, which reach heights less than 6–7

km (not shown). This stronger convective instability of the flow ahead of LS2may be explained by the presence of a synoptic-scale area of CAPE production ahead of the MCS from 1800 UTC (see Part I). This result high-lights again the major role played by the synoptic-scale context in the mesoscale organization of the subsystems. This significant role is examined quantitatively in what follows in terms of momentum fluxes on mesoscale and their mean and eddy contributions.

c. Momentum fluxes on mesoscale

Momentum fluxes are calculated in this section to examine more quantitatively the respective contribution of the synoptic-scale and mesoscale circulations to the vertical transport of horizontal momentum. Figure 8 shows the vertical profiles of mean wind components

FIG. 6. Vertical profile of the ECMWF analysis of vertical wind component at 1800 UTC. This profile is performed at the location (x, y)5 (0, 0) in the mesoscale domain of Fig. 2.

FIG. 7. Conceptual scheme of the mesoscale circulation within the 15 Dec 1992 MCS. Shaded areas roughly indicate the regions of heavier precipitation. Large arrows W and SW correspond to the synoptic-scale low-level flows present in this area. The mesoscale westerly flow denoted 1 is initially vertically extending from ground to 2-km altitude and ends up in the 2–3.5-km layer. Flow 2 is initially located in the 0–3.5-km layer and remains quasi-horizontal. Both flows 3 and 4 are located initially in the 1.5–4-km layer. As those flows rise up, they progressively deflect westward and eastward, re-spectively, and reach the domain top. A part of updrafts 3 and 4 is backing ahead of LS1(flows 39 and 49). Flow 5 is located initially

within the 0–1.5-km layer and ascends slightly just ahead of LS1up

to 2.5-km altitude. Within S2, the rear inflow 6 is located initially in the 0–1-km layer and rises up to 5–7-km altitude. The initial altitude of flow 7 is difficult to assess (lack of radar targets ahead of LS2).

This flow (7) rises up to the domain top, and a part of this ascending flow (denoted 79) in backs ahead of the leading convective line LS2.

and averaged u- and y-momentum fluxes (terms ^r&

^uw& and ^r& ^yw&) computed over the whole mesoscale

domain. Both momentum flux profiles exhibit positive values from the ground up to 10-km altitude (Figs. 8d,e), with a maximum at 3.5- and 5-km altitude, just above the level of maximum winds (Figs. 8a,b), with peak values of about 1.0 and 1.4 kg m21_s22_{, respectively for}

u and y, which is consistent with the magnitudes

ob-served by Caniaux et al. (1995) at the same scale. Pos-itive fluxes in both directions (Figs. 8d,e), owing to positive wind components (Figs. 8a–c) from the ground up to 10-km altitude are typically encountered in the literature for both tropical and midlatitude squall lines (LeMone 1983; Lafore et al. 1988; Matejka and LeMone 1990; Lin et al. 1990; LeMone and Jorgensen 1991; Caniaux et al. 1995; Hane and Jorgensen 1995, and others), as well as in the recently published TOGA COARE study of the 18 February 1993 tropical rain-bands (Hildebrand 1998). Above 10-km altitude, the y-momentum flux is negative, owing to the contribution of the upshear-tilted updrafts (upshear with respect to low-level shear) above the 10-km altitude in the present case (see Fig. 5a) that change the sign of the y com-ponent (Fig. 8b). This importance of the upshear-tilted updrafts in the vertical transport of momentum was also noted for the TOGA COARE rainbands studied by Hil-debrand (1998), who found negative line-normal mo-mentum fluxes in the upper levels associated with shear-tilted updrafts. The cases with upshear-tilted up-drafts were also noted by LeMone and Moncrieff (1994) as being the largest exception to upper-level positive momentum flux of all the convective systems they con-sidered.

The ‘‘total’’ momentum flux (as defined by Hane and Jorgensen 1995) discussed previously may be decom-posed as the sum of the mean and eddy components [e.g., for the u component ^r& ^uw& 5 ^r& (^u&^w&) 1

^u*w*&) for u, where the star denotes the perturbations

from the average]. For both components of the vertical fluxes of horizontal momentum, the mean fluxes con-tribute most strongly to the total flux (Figs. 8d,e). This indicates that the vertical transport of horizontal mo-mentum is mostly carried out at a scale of motion larger than the mesoscale domain size (roughly 200 km). How-ever, above 7.5-km altitude there is significant input to the total profile by eddy momentum transport for the u-momentum flux. The significant contribution of the eddy momentum transport above 7.5-km altitude is likely due to the strong upshear-tilted updraft eddies in the upper levels (Fig. 5a) in our case. This was noted as well by Hildebrand (1998) who computed such fluxes within the 18 February 1993 rainbands observed during TOGA COARE that were characterized by such updrafts as well.

d. Pressure and temperature perturbations on mesoscale

The analysis method used to recover the pressure and virtual cloud potential temperature perturbations from the analytical 3D wind field is described in section 2c. Figure 9 shows theu*c fields retrieved in the mesoscale domain at the 1-, 4-, and 7-km altitude. At low levels (Fig. 9a), the diabatic warming associated with the pres-ence of the two subsystems S1 and S2 clearly appears,

FIG. 8. Vertical profiles of mean wind components (a)^u&, (b) ^y&, and (c) ^w& over the mesoscale domain and the associated (d) u-momentum flux^r& ^uw& and (e) y-momentum flux ^r& ^yw& (solid lines). Superimposed to these total momentum fluxes are their mean (^r& ^u& ^w& and ^r& ^y& ^w&) and eddy (^r& ^u*w*& and ^r& ^y*w*&) components (dotted and dashed lines, respectively).

characterized by positive virtual cloud potential tem-perature perturbations of about 1 K. This 1-K pertur-bation across the subsystems is of the same magnitude as the temperature contrasts observed within the 22 Feb-ruary 1993 squall line of TOGA COARE documented by Jorgensen et al. (1997). It must be noted that, con-trary to the common picture of a two-dimensional trop-ical squall line, there is no evidence of an inflow sig-nificantly colder than the environment at the rear of the 15 December mesoscale system. This also has been

re-ported in other TOGA COARE studies (Jorgensen et al. 1997; Roux 1998).

Figure 9b shows the existence of positive gradients of virtual cloud potential temperature from south to north, which progressively veer with height to positive gradients from east to west (Fig. 9c). This progressive rotation of the temperature gradients with height is con-sistent with the larger-scale horizontal gradients of po-tential temperature analyzed by the ECMWF model at 1800 UTC (not shown) at 700 and 400 hPa, respectively

FIG. 9. Horizontal temperature perturbation fieldu*retrieved by the MANDOP analysis at the

c

mesoscale and at (a) 1-, (b) 4-, and (c) 7-km altitude. North is given in the upper-right corner of the figure. The latitude and longitude given in the figures correspond to (x, y)5 (0, 0).

(around the 3.1- and 7.5-km altitudes). It must be re-called, however, that the horizontal gradients retrieved on the mesoscale include the effects of both temperature contrasts and cloud water loading, which disables any further quantitative comparison.

In what follows, convective-scale domains are se-lected within the mesoscale domain, and the subsys-tems’ internal dynamics are examined. A more detailed interpretation of the retrieved thermodynamic fields

(in-cluding pressure gradients) and processes involved in the organization of these thermodynamic gradients is carried out.

4. Convective-scale analysis of the 15 December 1992 MCS

In the previous section, it was shown that the me-soscale organization of S1 and S2 was largely

mined by the synoptic-scale kinematic and thermody-namic characteristics. As explained in section 2, since the respective minimum observable scale is getting smaller in the present study from synoptic scale (about 200–300 km) to mesoscale (about 30 km; see calcula-tions in section 2b) and convective scale (about 5 km), it is expected that convective-scale features will appear if convective-scale processes are involved in the internal organization of the studied MCS. For this purpose, the 3D fields of wind, precipitation, pressure, and virtual cloud potential temperature perturbations, and the air and water parcel trajectories are analyzed within se-lected convective-scale domains focusing on subsys-tems S1 and S2. In the present case, the radar data collected during a time period of 10–15 min are used, time during which the 3D wind field can reasonably be assumed as steady state. Indeed, as shown on the me-soscale, the disturbance does not experience a signifi-cant internal evolution during the sampling time of S by the airborne radars.

Figure 2a shows the location of the two selected con-vective-scale domains within S. Domains A and B are chosen in such a way that the leading convective lines of S1 and S2 can be studied individually. The horizontal domain size is 603 60 and 70 3 70 km2_{, respectively,} for A and B. The horizontal grid resolution is 1.5 3 1.5 km2 _{and the order of expansion of the analytical} functions is 7 in both cases, which (using the calcula-tions of section 2b) corresponds to minimum observable scales of 5 and 6 km, respectively, for the retrievals within A and B.

a. Convective-scale study of S1

The first convective-scale study is carried out within S1, in the area A shown in Fig. 2a. Airborne radar data during the time interval 1800–1812 UTC are used to recover the convective-scale kinematic and thermody-namic fields.

1) DYNAMIC CHARACTERISTICS

Figure 10 shows the retrieved 3D wind and precip-itation fields at 1-, 3-, 6-, and 8-km altitudes. The con-vective-scale structure of the precipitation field is fairly comparable to the mesoscale structure within the A do-main (see Fig. 2). The retrieved 3D wind field is do-mainly characterized at low levels by a relatively homogeneous westerly rear inflow that enters in confluence with a southwesterly inflow ahead of LS1(see Figs. 10a,b). This characteristic is in very good agreement with the air-flows at synoptic scale (see Part I, Fig. 9) and mesoscale (see Figs. 2a,b). This suggests that the synoptic scale determines the organization of the convective-scale mo-tions within S1. Moreover, it must be noted that the convergence line associated with LS1, already discussed with regard to the mesoscale and synoptic-scale (see section 3 and Part I, respectively), is also present on the

convective scale, vertically extending from 0.5- to 3-km altitude. A rotation of the wind with height from westerlies at 3 km (Fig. 10b) to southerlies at 6 km (Fig. 10c) is observed. Above the 6-km altitude, a strong divergence of the flows appears (Fig. 10d), with the same characteristics as those discussed on the mesoscale and synoptic scale, despite the very different resolved scales.

The structure of the precipitation field appears to be linked to the structure of the 3D wind field. In particular, the horizontal wind field at 8 km (Fig. 10d) indicates that a parcel located initially at 8-km altitude in the southwesterly part of LS1will be advected northeastward along LS1. Such a parcel will be finally drained off either southeastward or northeastward of the convective line, depending on its initial location within the different air-flow at 8-km altitude. A detailed study of this relation-ship between the 3D wind and reflectivity fields is car-ried out in the next subsection, using air and water parcel trajectory analysis.

A vertical cross-section perpendicular to the orien-tation of LS1 is presented in Fig. 11 to evidence the strong similarities between the vertical kinematic char-acteristics on the mesoscale and convective scale. The westerly rear inflow at low levels discussed in section 3, as well as in Part I, is found at the rear of LS1, with a depth of 3 km in this region (Fig. 11). Another con-vective-scale retrieval performed in the northeastern part of LS1(not shown) indicates that the westerly flow is deeper in this northeastern part (i.e., from 4 to 5.5 km as one moves northeastward along the line). This feature was also found on the mesoscale and at larger scale, which shows that this characteristic is not linked to convective-scale processes. The vertical cross section of Fig. 11 also shows that the maximum upward motions are located in the upper troposphere. This result is com-mon to the three scales of motion (see Figs. 6, 5a, and 11, respectively). The convective-scale updraft associ-ated with the more intense precipitating region is split into a rearward and a frontward upper-level outflow, as was found on the mesoscale.

2) AIR AND WATER PARCEL TRAJECTORY ANALYSIS

The air and water trajectory analysis is performed using the systematic procedure described in section 2d, but with initial positions of the air parcels every 5 km in the horizontal and 500 m in the vertical. Figure 12 gives the air parcel trajectories that are subjectively se-lected as the most characteristic of the retrieved con-vective-scale airflow circulation. Within the mesoscale westerly flow located at the rear of LS1, relatively stable flows are observed. Their stability depends on their lo-cation with respect to LS1. The part of the westerly flow that is closer to LS1(Fig. 12a) slightly overlays the rear-most one (Fig. 12b). This configuration is consistent with the mesoscale observations (see conceptual scheme of Fig. 7, flows 1 and 2. Moreover, the updrafts

ciated with the synoptic-scale southwesterly flow are characterized by the same structure on the mesoscale and convective scale (see Fig. 7 and Figs. 12c,d), with the main updraft that is split into a frontward and a rearward component with respect to LS1.

As explained in section 2d, the water parcel trajec-tories can be simply obtained from the air parcel tra-jectories by subtracting an estimate of the terminal fall velocity of the hydrometeors to the retrieved vertical wind component. In the present case, such an estimate has been obtained using the (SAVAD) analysis (Protat et al. 1997). The reflectivity field at 1-km altitude, dis-played in Fig. 10a, shows the significant variability of the precipitation structure along LS1. In the southwestern part of the line, the structure is almost linear and roughly organized along the main ascending flow (see in par-ticular Figs. 12c,d). In contrast, the northeastern part of LS1exhibits a more complex structure that seems to be related to the diverging flows located in the upper tro-posphere, as discussed previously. The water parcel tra-jectory analysis (example given in Fig. 13a) shows that precipitation at the ground within the southwestern part of the line is generated in liquid phase. Indeed, water parcels advected by the main updraft between the ground and the 08C isotherm altitude (Fig. 13a, for a water parcel located at 3.5-km altitude within the up-draft) are falling to the ground in liquid phase within the southwestern ‘‘linear part’’ of LS1 and are not ad-vected farther northeastward. It is seen from Fig. 13a that this parcel is falling almost vertically, in response to its large terminal fall velocity in liquid phase (around 5–10 m s21_).

In contrast, precipitation at the ground within the northeastern part of the line appears to be generated in ice phase. The water parcels located within the updraft at heights greater than the 08C isotherm altitude do not fall within this linear part of LS1 (see example in Fig. 13b, for a parcel located initially by the 5-km altitude), but keep on slightly ascending, most likely in response to a compensation of their weak terminal fall velocity (typically between 0 and 2 m s21_{) by the ascending air}

motions. These parcels are advected by the flow at 6– 8-km altitude along the leading convective line LS1and fall within the northeastern part of LS1(Fig. 13b). In-terestingly, the strong divergent flows at mid- to upper levels (Figs. 10c,d) act to spread the parcels horizontally at these heights, which likely explains the observed en-largement of the precipitation structure at the ground in the northeastern part of the line. It must be noted how-ever that this simple interpretation does not account for the complex combination of microphysical processes that are known to play a significant role within tropical convective systems.

3) THERMODYNAMIC STUDY OF THE CONVECTIVE LINE OF S1

Figures 14a–d show the virtual cloud potential tem-perature perturbations retrieved within area A of Fig.

2a. The field at 0.5-km altitude (Fig. 14a) exhibits a well-marked negative virtual cloud potential tempera-ture gradient along the leading convective line LS1from the southwestern to the northeastern part of the line. Also interesting is the local line of positive perturbations in the southwestern part of the leading convective line. These positive perturbations are associated with the slight ascent of the southwesterly flow at 0.5-km altitude (not shown). Comparisons (not shown) with the vertical velocity field at 0.5-km altitude indicate that the positive virtual cloud temperature perturbations in the left part of the domain are associated with slightly ascending motions (partly seen in Fig. 12a), while the negative perturbations in the northeastern part of LS1 are asso-ciated with downward motions in the low levels (below 1-km altitude), as shown in Fig. 12b at the end of the trajectory. This westerly rear inflow of Fig. 12b is pro-gressively descending from 0.5- to 0.2-km altitude as it crosses the domain. Along this trajectory, the air parcel experiences a cooling of about 2–3 K. This result sug-gests that significant evaporation occurs during the ad-vection of this flow across the A domain (especially at the end of the trajectory) within the northeastern part of LS1.

This hypothesis can be evaluated using the following procedure: if the only diabatic processes acting on a parcel are condensation of water vapor and evaporation of liquid water, the equivalent potential temperatureue

is a conservative quantity, which may be written as

Lc–edq

du 5 du 1e 5 0, (1)

cp

where Lc–eis the latent heat of condensation–evaporation

and cpis the specific heat at constant pressure. Within

areas of evaporation of precipitation, Lc–edq. 0. Since

ueis conserved, this implies that du , 0 in these areas.

Hence, as the westerly rear inflow of Fig. 12b interacts with the precipitating areas, evaporation within these areas will effectively tend to cool this flow. More quan-titatively, the retrieved cooling can be evaluated using the simplified model proposed by Hardy (1963). This model provides an estimate of the evaporation rate as a function of a given precipitation rate. We estimated the precipitation rate from the reflectivity measure-ments, using the particle measuring systems 2D-P mi-crophysical measurements acquired on board the Na-tional Center for Atmospheric Research’s Electra air-craft on 15 December 1992 MCS between 1945 and 2120 UTC. This 2D-P probe measures 2D images of particles, whose diameter ranges from 0.2 to 6.4 mm. The reflectivity calculation follows the method proposed by Marecal et al. (1996, 1997) and takes into account the P3-42 radar frequency and polarization. The ob-tained relationship is

1.32

Z 5 268.6R , (2) where Z (mm6_m23_{) is the radar reflectivity and R (mm}

FIG. 10. Horizontal cross sections of the 3D wind and reflectivity fields retrieved by the MANDOP analysis in the convective-scale area (A) of Fig. 2a at (a) 1-, (b) 3-, (c) 6-, and (d) 8-km altitude. The location (C9D9) of the cross section of Fig. 11 is indicated in (a). North is given in the upper-right corner of the panels. The latitude and longitude given in the figures correspond to (x, y)5 (0, 0). The northernmost (southernmost) trajectory shown in all panels is the P3-42 (P3-43) aircraft track.

h21_{) is the precipitation rate. If one assumes an average}

value of 30 dBZ for the reflectivity areas crossed by the rear inflow during its advection through A, then the averaged precipitation rate is of about 2.7 mm h21

dur-ing this advection. The saturation deficit is estimated

within the synoptic-scale westerly flow using a local vertical profile of water vapor mixing ratio q and sat-urated mixing ratio qsanalyzed by the ECMWF model

at 1800 UTC (not shown), leading to a qs2 q of about 5 g kg21_{at 0.5-km altitude. Using the model of Hardy}

FIG. 10. (Continued )

(1963), the evaporation rate is of about 1 g kg21 _h21_.

Then, for an average magnitude of 15 m s21 _{for the}

westerly rear inflow, it will take approximately 1 h for this parcel to cross the A domain, leading to a total evaporation of 1 g kg21_{at 0.5-km altitude. Finally, using}

(1), this corresponds to a potential temperature deficit of about 2.5 K across the domain. This qualitative eval-uation of the temperature deficit is consistent with the gradient of virtual cloud potential temperature (Fig. 14a)

retrieved along the rear inflow. Therefore, the cooling of this westerly rear inflow can indeed be accounted for by evaporation of liquid water.

We now turn to a description of the virtual cloud potential temperature perturbation fields at higher levels (Figs. 14b,c). From 3-km altitude, the gradients rotate rapidly with height (see Fig. 14b), and positive tem-perature gradients are roughly oriented along the leading convective line LS1. This configuration of the

FIG. 10. (Continued )

ature gradients is such that the coldest air mass in the lower layers (Fig. 14a) is overlayed by the warmest air in the right part of the domain. The presence of the warm air mass above 3-km altitude is likely resulting from the ascent of the mesoscale southwesterly flow (denoted 3 in Fig. 7) above the low-level westerly rear inflow. Above 6-km altitude, the positive gradients are progressively veering with height (see Figs. 14b,c). These positive gradients are oriented almost perpendic-ular to LS1at the 10-km altitude (not shown). This result indicates the progressive advection of warm air toward the rear part of LS1, which is consistent with the

rear-ward-tilting part of updraft 3 seen in Fig. 7 on the me-soscale within S1.

The pressure perturbation fields obtained in domain A are displayed in Figs. 15a–c at 1-, 4-, and 7-km al-titude, respectively. At the 1-km alal-titude, the field of pressure perturbation is characterized by a negative pressure gradient of about 21.2 hPa, roughly oriented perpendicular to LS1, from the leading part of LS1to its rear part. The presence of a lower pressure at the rear of the leading line is reminiscent of the well-known mesolow usually encountered at the rear of tropical and midlatitude squall lines (e.g., LeMone et al. 1984). This

FIG. 11. Vertical cross section in the cross-line direction (C9D9) indicated in Fig. 10a of re-flectivity (shaded) and wind vectors along the plane of the cross section (arrows). The vertical wind is also shown as bold contours in Fig. 5a when greater than 1.5 m s21_{(every 0.5 m s}21_).

mesolow is due to the presence of warm updraft air above the colder near-surface rear inflow. This 21.2 hPa pressure gradient across the domain (between the westerly rear inflow and the southwesterly inflow ahead of LS1) may be compared with the theoretical pressure change predicted by the Bernoulli theory (e.g., Berry et al. 1945), assuming a density current behavior for the westerly rear inflow. Indeed, the Bernoulli equation re-lates the magnitude of the westerly rear inflow at the rear part of the leading line to the change in pressure experienced by the westerly rear inflow between the rear part of the leading line and the area where this westerly flow enters in confluence with the southwesterly inflow (assumed as a stagnation point). This Bernoulli equation may be written in the present case as

1 ₂

Dp* 5 2 rV ,W (3) 2

where VW is the magnitude of the westerly rear inflow,

r the air density, and Dp* is the change in pressure

experienced by the westerly rear inflow. The surface rear inflow is of about VW ; 15 m s21(Fig. 10a). This

leads to a pressure change of about 21.3 hPa. This theoretical value is consistent with the retrieved21.2 hPa pressure gradient of Fig. 15a. This result reveals that the front part of the westerly rear inflow exhibits characteristics consistent with the density current the-ory.

The well-marked transition in the orientation of the virtual cloud potential temperature gradients at 3-km altitude (Fig. 14b) also clearly appears in the pressure perturbation field (see Fig. 15b). The retrieved pressure gradients progressively veer with height (see Fig. 15b) and are oriented almost parallel to LS1at 7-km altitude (Fig. 15c). The configuration of the horizontal pressure gradients appears therefore strongly favorable for the development of upward motions in the southwestern

part of LS1, with the highest pressure perturbation in the lowest layers overlayed by the lowest pressure pertur-bation at 4 km, contrary to the other parts of the domain where the configuration of pressure perturbation is re-versed. This rotation of the pressure gradients with height seems to be clearly related to the rotation with height of the vertical wind shear, which occurs very rapidly between the tropospheric layers located below and above 4-km altitude, as shown by the hodograph of the mean horizontal wind in the A domain (Fig. 16). This suggests that a dynamic process linked to this ver-tical wind shear likely plays a significant role in the retrieved structure of the pressure gradients. It is well known that the general organization of tropical con-vection within tropical systems is mainly governed by the vertical distribution of buoyancy. However, dynamic forcings can play a significant role as well in the detailed structure of the thermodynamic fields.

The respective importance of these dynamic pro-cesses can be examined using the Poisson equation that relates the Laplacian of pressure and different terms related to kinematic characteristics of the airflow (vor-ticity, Laplacian of kinetic energy) and the vertical gra-dient of buoyancy. This equation is obtained by taking the divergence of the momentum equation. This cal-culation is given in the appendix, as well as in the for-mulation of Rotunno and Klemp (1982):

p* dv 2 ¹D

1 2

1

2

1 2

1 2 1 2 1 2

FIG. 12. Air parcel trajectory analysis at the convective scale within (S1). (a) and (b) Trajectories representative of the W flow at the rear of LS1, (c) and (d) the SW upward flow ahead of LS1. The arrows indicate the direction of the

air parcel motions.

where ¹2D( p*/ro) is the dynamic part of the Laplacian

of pressure, the second term on the right-hand side of (4) is the term related to the vertical wind shear, and

v 5 hi 1 jj 1 zk is the relative vorticity.

The different terms in (4) are estimated using the analytical representation of the 3D wind field retrieved using the MANDOP analysis. This estimate shows that the horizontal distribution of the dynamic part of the Laplacian is generally similar at all heights to the ver-tical wind shear term (Fig. 17). This result confirms that the dynamic process related to the vertical wind shear is the major dynamic contribution to the general struc-ture of the pressure gradients. It may be noted however that in some regions (especially at 1-km altitude, Fig. 17a), the other terms of (4) play a significant role, al-though each term remains individually smaller than the vertical shear term (not shown). In this particular con-figuration, it is shown by Rotunno and Klemp (1982; see also the appendix) that the pressure perturbation can be assumed locally as proportional to the vertical shear term:

dv

p* } 2 ·= w.h (5)

dz

This relationship indicates that in the direction of the wind shear, positive and negative pressure perturbations should be located at the rear and ahead of the updraft (with respect to the direction of the shear), respectively.

Inspection of the hodograph in Fig. 16 reveals that the vertical wind shear vector points to the north in the low levels. Therefore, we expect (using the approach of Ro-tunno and Klemp 1982) to find a negative pressure gra-dient from south to north, since there is a region of upward motions at the location of LS1. This is effectively observed on the pressure perturbation field at 1-km al-titude (Fig. 15a). The retrieved Laplacian of pressure leads however to a 20.3 hPa pressure perturbation, which is much smaller than the perturbation of 21.3 hPa estimated using the Bernoulli theory. This is most likely due to the dominant contribution of the vertical gradient of buoyancy to the total Laplacian of pressure in this area (due to the presence of a density current at low levels). In the same way, above 4-km altitude, the vertical wind shear vector is pointing to the southwest (Fig. 16), which corresponds to the orientation of the negative pressure gradients at 4- and 7-km altitude (see Figs. 15b,c, respectively).

This study indicates that the structure of the pressure perturbation field and the organization of the areas fa-vorable for the development of vertical motions are strongly related to the vertical distribution of vertical wind shear. Comparisons throughout section 4a between the convective-scale and synoptic-scale airflow circu-lations showed that the convective-scale flows were largely determined by the synoptic-scale circulation (al-though these flows are naturally modified locally by

FIG. 13. Water parcel trajectory analysis at the convective scale within (S1). (a) and (b) Tra-jectories of parcels falling in liquid and ice phases, respectively. The arrows indicate the direction of the water parcel motions.

convective-scale processes). As a result, the vertical wind shear is also mostly determined by the synoptic-scale circulation, which clearly shows the major role played by the synoptic-scale characteristics in the in-ternal structure of S1 observed at smaller scales.

b. Convective-scale study of S2

The second convective-scale study is conducted with-in subsystem S2, with-in area B of Fig. 2a. Airborne radar data collected during the time interval 2031–2041 UTC are processed so as to obtain the dynamic and ther-modynamic fields within area B. Figure 18 shows the retrieved 3D wind and reflectivity fields at 0.5-, 1.5-, 5-, and 8-km altitude. The precipitation structure is found to be close to the mesoscale structure seen in Fig.

2, with a very active leading convective line LS2ahead of S2, and a weakly developed stratiform precipitation area in the northwestern part of S2. The retrieved airflow within B is generally similar to the mesoscale retrieval for every altitude (see section 3, Fig. 2), with a well-defined confluence in the lowest levels ahead of LS2(Fig. 18a) between a relatively homogeneous westerly rear inflow and an unstable south-southwesterly inflow ahead of the leading line. This confluence is progressively shifted rearward of LS2in the upper levels (see Fig. 18b). Above 2-km altitude, a rotation of the wind with altitude is found, from westerly to south-southwesterly. This lat-ter feature is again similar to the mesoscale flow.

Vertical cross sections normal to LS2(Fig. 19) indicate first that the westerly rear inflow is very shallow (less than 1 km deep), as was already documented on the