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Wang, Y., and B. Geerts, 2015: Vertical-plane dual-Doppler radar observations of cumulus toroidal circulations. J. Appl. Meteor. Climatol. doi:10.1175/JAMC-D-14- 0252.1, in press.
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Vertical-plane dual-Doppler radar observations of cumulus toroidal circulations
Yonggang Wang1, and Bart Geerts
University of Wyoming
Submitted to J. Appl. Meteor. Climat. October 2014
Revised version submitted in May 2015
1 Corresponding author address: Yonggang Wang, Department of Atmospheric Science, University of Wyoming, Laramie WY 82071, USA; email: [email protected] 1 Profiling dual-Doppler radar observations of cumulus toroidal circulations 2
3 Abstract 4 5
6 High-resolution vertical-plane dual-Doppler velocity data, collected by an airborne profiling
7 cloud radar in transects across non-precipitating orographic cumulus clouds, are used to examine
8 vortical circulations near cloud top. These vortices are part of a toroidal ring centered at an
9 updraft, usually near the cloud top, and they are essential to cumulus entrainment and dynamics.
10 A large number of transects across toroidal circulations is composited, in order to reveal the
11 typical kinematic structure and associated entrainment patterns. The toroidal ring circulation is
12 ~1 km wide and about half as deep in the sampled clouds (Cu mediocris). The composite flow
13 field shows two nearly-symmetric, counter-rotating vortices, with a core updraft of ~3 m s-1,
14 consistent vortex-top divergence, two flanking downdrafts of the about same strength, and
15 horizontal (toroidal) vorticity of ~0.03 s-1. Variations with vortex size, age, and ambient shear are
16 examined, and the relative dilution of air in the vortex core is estimated by comparing the liquid
17 water content, estimated from path-integrated power attenuation, to the adiabatic value. 18 1. Introduction
19 Cumulus clouds (Cu) are important in the climate system because they affect the vertical
20 structure of radiative heat flux divergence and dynamically couple the planetary boundary layer
21 to the free troposphere through vertical transports of mass, heat, moisture, aerosol, and
22 momentum. These clouds exist over a broad range of horizontal and vertical dimensions (e.g.,
23 Lopez 1977; Wielicki and Welch 1986). A significant fraction of the vertical exchanges in Cu
24 circulations occurs at scales smaller than resolvable scales in numerical weather prediction
25 (NWP) and climate models (e.g., Khairoutdinov et al. 2008), therefore Cu parameterizations
26 have been developed to represent the effect of sub-grid-scale convection on precipitation and the
27 vertical profile of resolved variables (e.g., Bretherton et al. 2004). Such parameterizations make
28 assumptions about the turbulent mixing of Cu clouds with the environment (Siebesma and
29 Cuijpers 1995). They are evaluated by means of high-resolution numerical simulations, such as
30 large-eddy simulations (LES, e.g., Zhao and Austin 2005). In turn, these high-resolution
31 convection-allowing simulations need to be validated with detailed Cu observations (e.g.,
32 Grabowski and Clark 1993; Craig and Dörnbrack 2008). This paper is one such observational
33 study.
34 Specifically, this paper examines updraft-driven toroidal (vortex-ring) circulations in Cu.
35 There is much evidence for the existence of such circulations near the top of buoyant clouds,
36 from modeling simulations (Klaassen and Clark 1985; Grabowski and Clark 1993; Zhao and
37 Austin 2005), laboratory experiments (Woodward 1959; Sanchez et al. 1989; Johari 1992), and
38 observational studies. The latter have used in situ aircraft data (MacPherson and Isaac 1977;
39 Blyth et al. 1988; Jonas 1990; Blyth et al. 2005), trace gas data (Stith 1992), and airborne radar
40 data (Damiani et al. 2006; Damiani and Vali 2007; Wang and Geerts 2013).
1 41 This study uses high-resolution (~30 m) vertical plane dual-Doppler radar data collected
42 along flight tracks across or just above isolated orographic Cu clouds. While the 30 m resolution
43 is sufficient to resolve vortex ring circulations, the shortest revisit time an aircraft is capable of,
44 ~2 min, is too long to capture the evolution of these circulations and entrainment events, given
45 the highly transient nature of Cu. Thus it is meaningful to examine vortex ring circulations in a
46 systematic way by compositing numerous circulations, each treated independently. Wang and
47 Geerts (2013) used this approach to examine the characteristic vertical velocity profile in Cu
48 clouds by means of numerous profiling airborne radar transects and corresponding flight-level
49 dynamical information. That study focused on vertical velocity over the depth of the cloud. It did
50 not examine horizontal winds. This paper builds on Wang and Geerts (2013) through the use of
51 two-dimensional (2D) velocity data to identify and characterize circulation features within Cu
52 clouds. These flow-based entities then are spatially normalized and composited. Division of the
53 entire sample into subgroups allows inspection of the effect of ambient wind shear, evolutionary
54 stage, and other parameters on the vortex ring circulation.
55 Data sources and analysis method are introduced in Section 2. Section 3 describes the
56 characteristic composite structure of vortex ring circulations, and stratifies this as a function of
57 size and age of circulations and ambient wind shear. Further implications are discussed in
58 Section 4. Section 5 lists the main conclusions.
59
60 2. Data sources and analysis methods
61 a. Environment of the sampled cumulus clouds
62 A dataset of 91 vortex rings is used in this study, collected from 58 Cu clouds or Cu
63 clusters penetrated or overflown by the University of Wyoming King Air (UWKA) in two
2 64 campaigns: the High-plains Cu (HiCu) campaign sampled Cu clouds mostly over the Laramie
65 Range (mostly near Laramie Peak) in southeastern Wyoming in the summer of 2003 (Damiani et
66 al. 2006). And the Cu Photogrammetric, In-situ and Doppler Observations (CuPIDO) campaign
67 was conducted over the Santa Catalina Mountain range in southern Arizona in July and August
68 2006 (Damiani et al. 2008; Geerts et al. 2008).
69 Both campaigns targeted relatively isolated non-precipitating Cu mediocris in an
70 environment with little shear. The flight track orientation was either terrain-relative (e.g.,
71 following a ridge allowing multiple penetrations in a row) or a “rosette” pattern with 120°
72 separations, to minimize the time between transects across a single Cu (Damiani et al. 2008). The
73 UWKA did not by design fly along the shear vector. Most sampled clouds in this study are
74 orographic Cu clouds whose spatial relation to other clouds is controlled by the details of the
75 terrain (Demko and Geerts 2010; Wang and Geerts 2011), rather than by shear. Most clouds
76 were observed over or near terrain ridges; one case, in HiCu, involves a rather isolated Cu cloud
77 over a broad valley, about 20 km from a terrain ridge, with deeper clouds over the adjacent
78 mountains. None of the targeted clouds were aligned in cloud streets according to GOES visible
79 satellite imagery (e.g., Fig. 2, Wang and Geerts 2011). The 13 HiCu clouds in this study tend to
80 be more ‘continental’ than the 45 more “monsoonal” CuPIDO clouds, since they generally have
81 a higher cloud droplet concentration, a higher cloud base, lower liquid water content (LWC), and
82 a smaller mean drop size compared to CuPIDO clouds (Wang and Geerts 2013). Still, the
83 sampled CuPIDO clouds occurred on days that were relatively dry in the Arizona monsoon
84 period, either without deep convection, or with deep convection erupting only later in the day.
85 Mobile GAUS (GPS Advanced Upper-air Sounding) radiosonde data are used to describe
86 the typical environment of the Cu clouds sampled during CuPIDO (Fig. 1). The cloud base,
3 87 estimated from the lifting condensation level (LCL), averages around 3.0 km MSL (Fig. 1b). By
88 contrast, the average LCL for the 13 HiCu clouds sampled on three flights is ~4.3 km MSL. This
89 is estimated from near-surface conditions upon take-off and landing in Laramie Wyoming,
90 within ~100 km of the clouds, since no proximity radiosonde data were collected in HiCu.
푑휃푒 91 Potential instability ( < 0, with e equivalent potential temperature and z height) is present 푑푧
92 from the surface to ~4.7 km MSL in the CuPIDO clouds (Fig. 1a). An air parcel rising from the
93 convective boundary layer and conserving its e, will become buoyant relative to the ambient air
∗ 94 at ~3.8 km MSL (e,surface = 휃푒 , the saturated e, since the parcel from the surface is saturated at
95 this level). This is slightly above the mean level of free convection (LFC), about 3.5 km MSL
96 (Fig. 1a). The level of neutral buoyancy generally is not very high, and observed convection was
97 often capped at a stable layer between 6-7 km MSL (Damiani et al. 2008; and Fig. 1a). The
98 ambient specific humidity decreases rapidly with height in the lowest 2.5 km (Fig. 1b), starting
99 near 12 g kg-1. Thus the adiabatic LWC at flight level (4.5-6.5 km MSL) is quite high (Wang et
100 al. 2009).
101
102 b. Cloud radar dual-Doppler synthesis
103 The UWKA carried the 94 GHz (W-band), multiple-fixed beam Doppler radar, the
104 Wyoming Cloud Radar (WCR) (Pazmany et al. 1994; Wang et al. 2012). The WCR operated in
105 two modes in CuPIDO: the up/down profiling mode and vertical-plane dual-Doppler (VPDD)
106 mode (Damiani et al. 2008). The latter uses one antenna pointing downward, and one 30° slant
107 forward of nadir (Fig. 2). The radar radial velocities from the pair of beams (antennas) are
108 corrected for aircraft motion and synthesized to provide orthogonal components of the scatterers’
109 mean velocity in a given volume (Damiani and Haimov 2006). The forward and nadir Doppler
4 110 measurements are nearly simultaneous (just 6 sec of time lag per km of range) but aircraft roll or
111 crab result in a small offset in the curtain-like vertical planes transected by the two beams. The
112 synthesis requires a merging of the radial velocities onto a common grid. Since the flight legs are
113 sufficiently straight and level, and the radar range of interest is quite short (<2 km), the dual-
114 Doppler analysis is simplified by projecting the three-dimensional (3D) data from the two beams
115 onto a mean vertical plane. The grid is constructed with grid cell dimensions (x, z) of (30 m,
116 30 m). Data points coming from the two beams are then transformed to a common time (nadir
117 beam time), and assigned to the grid cells based on their spatial position (using a Cressman
118 filter), with further penalties (lower weights) for deviation of the beam direction from the desired
119 scanning plane, and for low power signal-to-noise ratio values (Daimiani and Haimov 2006).
120 Typical grid cells include many radial velocities from two directions since data were sampled at
121 ~4 m along-track and 15 m range intervals in CuPIDO and HiCu. Doppler velocity data are
122 unfolded to resolve frequency aliasing, if any, before proceeding with the dual-Doppler
123 calculations.
124 These calculations are based on a velocity inverse decomposition problem, as detailed in
125 Damiani and Haimov (2006). In order to achieve a good determination of the 2D vector in the
126 along-track vertical plane, an estimate of the ‘cross-plane’ component, the vector normal to the 127 solution plane (labelled Vxp in Fig. 2), is necessary. For instance, when the aircraft rolls 3° under
128 a 10 m s-1 cross-track wind, then this wind causes a 0.5 m s-1 error in the vertical velocity that is
129 obtained by projecting the slant-vertical vector onto the vertical plane. For this purpose a guess
130 of the horizontal wind vector is also employed. In CuPIDO, this wind vector is obtained from a
131 sounding released from Windy Point during each flight. The flight-level wind was used in HiCu.
132 The wind was relatively light in both environments, so wind contamination errors due to beam
5 133 pointing angles off nadir (or off 30° forward of nadir) should be relatively small. A more in-
134 depth VPDD synthesis error analysis can be found in Damiani (2005) and Damiani and Haimov
135 (2006). In general, the uncertainty of the vertical velocity w is smaller than that of the along-
136 track horizontal velocity u as the former is almost entirely determined by a single beam (the
137 nadir beam), while the latter depends on a combination of the nadir and slant forward beams.
138 Most flight legs used in this study were flown in rather smooth conditions above Cu. Aircraft
139 attitude variations were small for these legs compared to those in Cu penetrations. In such
140 conditions, velocity errors may be largely caused by the non-simultaneity of the observations
141 from the two antennas (~6 seconds time lag per km range). Damiani (2005) suggests an
142 uncertainty of about 1.0 m s-1 at a range of 2 km. (This is about the maximum range of WCR
143 data given the rapid attenuation of the mm-wave signal in clouds with high LWC, as discussed
144 below.) Nevertheless, anomalous vectors were often found at large range and in weak echo
145 regions. These were removed based on comparisons with neighboring grid cells before
146 compositing.
147 It should be noted that the WCR vertical velocity includes a downward fallspeed of the
148 cloud particles. In some cases the optical array probes on the UWKA detected some ~mm size
149 drops and/or small graupel particles on flight legs penetrating the Cu during flights used here
150 (Wang and Geerts 2013). The higher reflectivity values encountered below some flight legs
151 included in this study, up to ~-5 dBZ, suggest that in some cases the WCR vertical velocity
152 includes a fallspeed component. Damiani et al. (2006) found that the typical fallspeed is
153 negligibly small compared to the typical convective up- and down-drafts encountered in the Cu
154 clouds sampled in HiCu, and that the basic Cu flow structure was not affected by hydrometeor
155 fallspeed. Given these considerations, and the difficulties of estimating of the fallspeed in
6 156 spatially inhomogeneous clouds, no correction for the hydrometeor terminal velocity was
157 applied.
158
159 c. Cloud radar power attenuation
160 Most clouds examined in this study were liquid only (Wang and Geerts 2013). The
161 absorption of 94 GHz (W-band frequency) radiation by liquid water can be significant
162 (Lhermitte 1990), thereby attenuating the radar (equivalent) reflectivity with range through
163 cloud. The reflectivity cannot be corrected for attenuation because of the unknown variability in
164 LWC in Cu. We will use the lapse rate of reflectivity with range in cloud as a measure of cloud
165 LWC, as in Wang and Geerts (2013). It should be noted that as long as the signal is above the
166 range-dependent threshold reflectivity for both antennas, the quality of the WCR dual-Doppler
167 velocities is not affected by attenuation.
168
169 d. Sample WCR observations of vortex ring circulations
170 One of the 45 Cu clouds in our CuPIDO dataset, observed on 24 July 2006, was captured
171 nicely by three consecutive flight transects (Fig. 3). We show this example because it is a typical
172 case and because the revisit interval was rather short, allowing cloud evolution to be
173 documented. The flight tracks had an identical orientation and were displaced slightly as the Cu
174 moved with the wind. One of the three tracks was flown in opposite direction but the image was
175 flipped in Fig. 3, thus the three cross-sections have a matching orientation. The nearest M-GAUS
176 sounding from Windy Point reveals a wind shear of 7.3 m s-1 km-1 over the depth of the cloud,
177 directed from right to left. This shear is also evident in the dual-Doppler flow field (vectors in
7 178 Fig. 3): it results in leftward (downshear) tilting updrafts and a leftward movement of upper level
179 echoes relative to lower-level echoes over time.
180 The same Windy Point sounding also suggests a cloud base (LCL) of 4.2 km MSL, which
181 was rather high for CuPIDO. The radar signal vanishes well above this cloud base (Fig. 3, lower
182 panels), because the lower cloud radar echo is quite weak and/or because the WCR power is
183 attenuated along the nadir path by liquid water in the upper cloud region (Section 2c). So the
184 transects in Fig. 3 just show the cloud top. This cloud lacks precipitation-size particles, thus
185 reflectivity is rather low, but the peak reflectivity increases with time, from about -15 to -10 dBZ
186 from the first to the third transect (Fig. 3). At the same time, the echo top rises gradually from
187 5.9 to 6.3 km MSL. Thus this is a slowly growing Cu cluster with relatively small hydrometeors.
188 Some cells in the reflectivity field (lower panels in Fig. 3) are tentatively identified in the
189 three consecutive transects. These cells are tracked according to the environmental wind speed,
190 their relative position to the terrain below, and the evolution of their vertical motion and radar
191 echoes. Cell B is towering at 1807 UTC, reaches peak reflectivity values at 1810 UTC with
192 weakening updrafts, and has dissipated by 1813 UTC. It is remarkable how rapidly cells and
193 circulations evolve. Other transects were flown repeatedly across evolving Cu clouds on this and
194 other flights, and there too the revisit time proved to be too long to document cell evolution in
195 detail. Therefore cloud-top vortices are not examined in an evolutionary sense, but rather are
196 included as independent entities in the composite.
197 A strong updraft can be seen near the top of cell B in the earliest transect, centered at [x,
198 z] = [1.4, 5.7] km (Fig. 3c). As this updraft weakens towards cloud top, the horizontal flow
199 becomes divergent, with strong downshear flow on the left and weaker upshear flow on the right.
200 The horizontal flow at the base of this updraft core is convergent. The updraft is flanked by a
8 201 strong downdraft on the downshear side, and a weaker downdraft on the upshear side (Fig. 3c).
202 In short, the 2D wind field reveals a clear counterclockwise-rotating vortex to the left
203 (downshear side) of the updraft, and a less-defined clockwise circulation on the upshear side.
204 This fits the schematic in Fig. 4. This vortex pair is part of a 3D toroidal circulation, as described
205 in Damiani et al. (2006). We call it a ring although in 2D it is just a vorticity dipole. In the
206 absence of shear, the ring (or toroid) is level. The ambient shear leads to a tilting of the updrafts
207 and toroids (Damiani et al. 2006; Wang and Geerts 2013), resulting in an asymmetric vortex pair
208 in a vertical transect.
209 The strength of the updraft in cell C (centered at [x, z] = [1.2, 5.7] km) is weaker in the
210 2nd transect (Fig. 3g) as cell top rises to flight level. Two counter-rotating vortices surround this
211 updraft, although the diameter of the vortex ring is smaller than that shown in Fig. 3c. Ascending
212 motion can be seen in a new cell E, emerging on the upshear side from a lower level, at [x, z] =
213 [1.8, 5.2] km (Fig. 3g). This cell rises and widens, resulting in a strong updraft and broad vortex
214 ring just below flight level (Fig. 3k). New cells tend to form on the upshear side of a Cu cluster,
215 and downdrafts and mixing occur mainly on the downshear side (Warner 1977; Zhao and Austin
216 2005).
217 Flight-level buoyancy is shown in the top panels of Fig. 3. Buoyancy is proportional to
218 the virtual potential temperature perturbation (dry term) and the mixing ratio of liquid water and
219 ice (hydrometeor loading) [e.g., equation 1 in Wang et al. (2009)]. A “perturbation” requires a
220 basic reference state, which we define as the average over a distance of >500 m and <2000 m to
221 the left and to the right of the vortex ring, in clear air along the flight track. In dry air, as in the
222 left and the middle transects in Fig. 3, only the dry term comes into play. The air 0.1-0.2 km
223 above cloud top is negatively buoyant downshear of the cloud in this case, possibly due to a
9 224 tilted gravity wave, as will be discussed later. In cloud, as in the right transect in Fig. 3, the
225 expression for buoyancy includes the hydrometeor loading term, measured at flight level. In this
226 case the cloud is positively buoyant.
227
228 e. Radar data compositing
229 Two compositing approaches are possible to characterize the typical flow field in Cu
230 clouds. One approach, used in Wang and Geerts (2013), is cloud-based: the clouds’ horizontal
231 and vertical dimensions are defined from radar and ancillary data, these dimensions are
232 normalized, and average reflectivity and vertical velocity patterns are examined. This is useful
233 when examining characteristic thermodynamic and cloud microphysical patterns, but the
234 compositing filters out the complex fine-scale flow structure in Cu clouds. Cu clouds usually
235 contain multiple updrafts and associated circulations.
236 A second approach, used in the present study, is flow-based: circulation features are
237 identified, spatially normalized, and composited. This approach requires multiple-Doppler wind
238 fields, and is inherently more subjective than a cloud-based compositing, because the boundary
239 between turbulent circulations is ill-defined.
240 A manual perusal of all VPDD transects of Cu clouds in the two campaigns yield a total
241 of 91 vortex pairs (16 from HiCu and 75 from CuPIDO). This sample is rather small for three
242 reasons. Firstly, minimum vortex ring dimensions (width, depth) of (200, 100) m are imposed.
243 This excludes cell D in Fig. 3g, for instance. These minima are imposed by the WCR resolution,
244 not by a physical argument. Smaller vortex rings may exist, although they should be shorter-
245 lived. Secondly, a sufficiently strong echo from the less sensitive slant forward antenna for good
246 VPDD synthesis is required. No velocity data are included where the reflectivity value is less
10 247 than two standard deviations above the mean noise level. And thirdly, few flight legs are at a
248 suitable level to capture full vortex circulations because the WCR often lacks the sensitivity to
249 detect entire Cu clouds (Wang and Geerts 2013). For instance, cell E in Fig. 3g is excluded
250 because the circulation is not fully captured. One drawback of the WCR antenna configuration is
251 that dual-Doppler (u, w) synthesis is possible only below flight level, and thus, to capture the full
252 vortex ring circulation, flight tracks near or above cloud top must be used, often yielding no
253 cloud in situ information. Only the third of three passes through the Cu cluster in Fig. 3
254 penetrated the (growing) cloud.
255 We define the normalized distance x * 0 at the circulation center and x* 1 at the
256 circulation edge, and normalized height from the vortex base (z*= 0) to the vortex top (z*= 1)
257 (Fig. 4). The WCR reflectivity and velocity fields for each of the 91 vortex rings then are
258 redistributed in a 2D normalized domain -1< x*<1 and 0< z*<1 with a bin size x* = 0.025 and
259 z* = 0.025. The bin size (x*, z*) is selected as a trade-off between limiting the smoothening
260 of the largest vortices and resolution redundancy for the smallest vortices (Wang and Geerts
* 261 2013). The normalized cloud coordinates are also shown in Fig. 4, with xc 0 at the cloud
* * 262 center and xc 1 at the cloud edge, and normalized height from the cloud base ( zc 0 ) to the
* 263 cloud top ( zc 1). Any vortex ring’s maximum dimensions are confined to the cloud
264 dimensions.
265 Only averages of reflectivity, velocity, and derived variables are examined in this study,
266 not any higher moments. In the data redistribution and compositing processes, radar reflectivity
267 is averaged in units of Z (mm6 m-3). The average Z then is reconverted to dBZ.
268
11 269 3. Composite structure of cumulus toroidal circulations
270 a. Composite reflectivity and kinematic structure
271 Fig. 5a shows the fraction of sample size of vortex ring at each cell grid, or the WCR data
272 frequency. This refers to coverage completeness: data may be missing in part of the 2D
273 normalized domain for any of the 91 vortices, therefore the data frequency is often less than
274 100%, especially near the edge. Averages in each bin are computed for 91 values at the most.
275 The most common depth and width of the 91 sampled vortex rings is 550 m and 1000 m
276 respectively. (The width is the diameter of the vortex pair, as shown in Fig. 4.) The depth and
277 width of toroidal rings are positively correlated, with a typical aspect ratio of 1:2 (Fig. 5c). Many
278 of these circulations probably are larger as they may extend into echo-free clear-air regions
279 outside the cloud edge, as suggested by the common occurrence of cloud-edge downdrafts (Heus
280 and Jonker 2008; Wang et al. 2009). Cu clouds (or clusters of connected clouds) in the CuPIDO
281 and HiCu environments typically contain multiple vortex rings, and thus multiple buoyant cores
282 and hydrometeor growth centers, in various stages of evolution, as illustrated in Fig. 3. Some of
283 the sampled vortex rings encompass the entire cloud, some are part of a Cu cluster. In general
284 they span 20-100% of the cloud width; the average ratio of vortex ring width to cloud width is
285 1:2. Neither the width nor the depth of the vortex rings scale with Cu width or depth (not shown).
286 Previous studies have shown that the vortex ring circulation is often confined to the cloud top
287 (e.g., Blyth et al. 2005; Damiani et al. 2006). In fact some 90% of the sampled vortex rings are
* 288 located in the upper half of Cu (zc > 0.5) (Fig. 5b).
289 The composite structure of the 91 vortex rings is shown in Fig. 6. Missing data only tend
290 to occur on the margins, especially in the upper left and right corners (Fig. 6d), because of the
291 typically convex Cu echo top. The composite vertical velocity field (Fig. 6a) reveals an updraft
12 292 over 2/3 of the domain, peaking at ~3 m s-1, and a downdraft along the margins, with a similar
293 peak value at the edge (often the cloud edge). The fact that the peak downdraft value often
294 occurs at the echo edge suggests that the toroidal circulation often extends into the clear-air
295 region just outside the cloud edge. This has been observed using observations (Rodts et al. 2003;
296 Wang et al. 2009) and simulations (Heus and Jonker 2008). These studies suggest a peak
297 downdraft along the cloud edge, at least partly driven by evaporative cooling in the cloud
298 margin. Therefore the dominance of blue over red in (Fig. 6a) does not necessarily imply that the
299 entire circulation tends to ascend.
300 The double dipole evident in the horizontal wind field (Fig. 6b) suggests kinematic
301 consistency with the vertical wind field (Fig. 6a). Note that the mean along-track wind
302 component of the 2D flow field is removed for each circulation prior to compositing, to retain
303 the vortex-relative flow u’. The horizontal divergence is computed over the physical space for
304 each vortex-ring. The vertical profile of mean horizontal 1D divergence is shown in Fig. 6b. In
305 the upper part of the vortex, the along-track wind is to the left (negative) on the left side of the
306 Cu center, and to the right on the right side. This is associated with a divergence field with a
307 mean magnitude of nearly 0.004 s-1 across the circulation diameter. This is consistent with the
308 updraft deceleration in the upper part of two counter-rotating vortices: assuming the
1 휕푟푢 309 incompressible, azimuthally symmetric continuity equation in cylindrical coordinates, + 푟 휕푟
휕푤 310 = 0, continuity is approximately satisfied near the vortex top, with (∆푢, ∆푤) = (4, 2) m s-1 휕푧
311 and (∆푟, ∆푧) = (600, 300) m based on typical physical distances mentioned above. (Here r equals
312 radius.) Convergence in the lower part of the data domain is only ~0.0015 s-1, which is weaker
313 than the divergence aloft, and inadequate for the observed upward acceleration, whose
314 magnitude is about the same as that of the deceleration aloft. This violation of mass continuity in
13 315 part may be due to the azimuthal symmetry assumption (and thus related to the sample size) and
316 to dual-Doppler velocity uncertainty (Section 2b). More likely it is related to incomplete data
317 over the full depth of the toroid, because of attenuation of the radar signal with range (Section
318 2c), resulting in lack of data for the lower part of the vortex ring, as is the case for cell E in Fig.
319 3l. They may be erroneous because the VPDD uncertainty increases with radar range (Section
320 2b), and more for u than for w, since the u field strongly depends on the less sensitive slant
321 forward beam.
322 The divergence (convergence) at the top (base) of the vortex circulation has important
323 implications for Cu detrainment (entrainment). Strong cloud top divergence and shear occur in
324 turbulent mixtures of cloudy and environmental air (Taylor and Baker 1991; Zhao and Austin
325 2005; Wang and Geerts 2011). Significant dry-air entrainment may occur at the base of the
326 toroid (Zhao and Austin 2005). The circulation is important also for precipitation growth.
327 Hydrometeors grow in the updraft and, as long as their fallspeed is less than the updraft speed,
328 are ejected around the vortex top. The smaller hydrometeors may then be drawn towards
329 circulation center and may be recycled in the updraft, a hydrometeor size sorting process (e.g.,
330 Atlas and Plank 1953; Knight et al. 2008).
331 The vertical distribution of the composite radar reflectivity (Fig. 6c) will be explored
332 later. The horizontal variations of reflectivity from vortex center to edge evoke three
333 observations. First, reflectivity decreases 1-2 dBZ from the vortex center to its edge at any
334 height. This reflectivity decrease is consistent with hydrometeor growth in the core, and
335 hydrometeor evaporation by lateral entrainment and subsidence in the margins, although this
336 evaporation hardly impacts the largest drops, which dominate reflectivity. Second, the horizontal
337 reflectivity gradient is largest close to the edge. This suggests that lateral entrainment of more
14 338 diluted air is confined to a small region close to circulation edge. Third, the reflectivity is more
339 uniform in the upper region of the circulation. This is consistent with the divergent flow there:
340 drops grow in the core updraft and then are carried outward by the divergent vortex-top flow.
341 The composite 2D vector flow field is shown in Fig. 7. It shows two closed nearly-
342 symmetric counter-rotating vortex rings with near-stagnation at the cores of circulation. The
343 horizontal vorticity component perpendicular to the x-z plane, derived from the 2D flow field
휕푢 휕푤 344 [휔 = ( − )], is shown as well in Fig. 7. Note that vorticity is computed in physical space 휕푧 휕푥
345 first, and then composited in normalized space. The magnitude of vorticity, nearly 0.04 s-1, is
346 about one order of magnitude larger than the divergence (Fig. 6b). The vorticity is a significant
347 characteristic of these cloud top toroidal circulations, and can be compared against numerical
348 simulations of sufficient resolution. The slight asymmetry in Fig. 7 relates to ambient wind
349 shear, which will be revisited later.
350
351 b. Vortex rings of different sizes
352 To further characterize the primary Cu circulation structure, we stratify our samples by
353 vortex ring depth and width. Given the relative symmetry around the vortex center (Fig. 6), we
354 double the sample size by compositing vortex halves, so Fig. 8 and Fig. 9 are shown from vortex
355 center to edge only ( 0 x* 1). This increases the sample size and suppresses shear-related
356 asymmetry, which will be isolated later. The fields of vertical and horizontal winds are similar
357 for deep and shallow vortex rings, as well as for narrow and wide vortex rings, except that the
358 peak updraft is 8% (10%) stronger for deep (wide) vortex rings (Fig. 8a, e, and Fig. 9a, d). In
359 wider vortices, the upper-level outflow and low-level inflow are slightly stronger as well (Fig.
360 9b, e), consistent with both the stronger updraft and the wider vortex ring width. The mean
15 361 buoyancy of vortex rings penetrated by the UWKA was -0.007 m s-2 for the narrow ones vs.
362 +0.004 m s-2 for wide ones. This suggests that the narrower towers become depleted of buoyancy
363 more rapidly, which likely is due to entrainment.
364 The maximum horizontal vorticity is slightly larger for the smaller circulations, either
365 shallow (Fig. 8c, g) or narrow (Fig. 9c, f). The reason is that vorticity is scaled by W/L or U/H,
366 and since the wind magnitudes (U, W) vary little, vorticity is basically inversely proportional to
367 size (width L or depth H).
368
369 c. Vortex rings of different ages
370 According to the LES study of Zhao and Austin (2005), the core of toroidal circulations
371 rarely becomes diluted by entrainment until the circulation has travelled up approximately two
372 diameters, i.e. rather late in the Cu life cycle. Vortex rings form by solenoidal forcing
373 surrounding buoyant, ascending cores. Eventually, as the updraft reaches the equilibrium level,
374 the vortex core becomes negatively buoyant, which decelerates the overshooting top. The vortex
375 ring then starts to decay. Thus the sign of net vortex ring vertical motion can be used as a proxy
376 for its age. To study the effect of age on the circulation pattern, we stratify all vortices in two
377 subgroups, based on WCR vertical velocity averaged across the 2D vortex (Fig. 10). The
378 threshold value is the one that partitions all samples in two equal parts (the median), in this case
379 +0.61 m s-1. We consider the upward subgroup as the circulations in an earlier stage and the
380 downward subgroup as the more mature ones.
381 The composite results show that updrafts occupy about 70% of the circulation volume in
382 young Cu vortices, with weak descending flow at the edge (Fig. 10a), and a circulation center
383 closer to the cloud edge. As discussed in Section 3a, the updraft region may occupy a
16 384 proportionally smaller volume considering the fact that the cloud-free part of the circulation
385 cannot be detected by the WCR. Presumably most compensating subsidence occurs in the clear-
386 air cloud margin. Downdrafts occupy about 60% of the circulation volume in mature circulations
387 (Fig. 10b), resulting in a circulation center closer vortex ring center. The upper-level diffluent
388 (low-level confluent) flow is more pronounced for the young (mature) circulations (not shown).
389 Yet there is not much difference of the toroidal vorticity strength for the two subgroups (Fig. 10),
390 suggesting that vorticity doesn’t change much as horizontal buoyancy gradients vanish, i.e.
391 vorticity is relatively conserved. This was also noted in Wang and Geerts (2013).
392
393 d. Vortex rings and adiabatic lift aloft
394 The buoyancy distribution for all vortex rings is shown in Fig. 11. In the absence of shear
395 we expect isentropic layers to dome right above a rising Cu, implying negative buoyancy at
396 flight level, which is approximately isobaric. Such negative buoyancy is observed above 20 of
397 the 27 vortex rings cases in weakly-sheared environments (Fig. 11). The bulging isentropes are
398 part of a gravity wave that may propagate away from its source. In a sheared environment, a Cu
399 cloud penetrating a stratified environment may produce a wave ridge displaced relative to the
400 Cu, as the penetrating Cu acts as an obstacle in the flow (e.g., Clark et al. 1986). Recent
401 observations combining WCR with Wyoming Cloud Lidar (WCL) data collected in transects
402 above the tops of Cu mediocris nicely illustrate this isentropic displacement (Leon et al. 2014):
403 the WCL depicts aerosol layers which in some cases reveal vertically-propagating upshear tilting
404 internal gravity waves. Such waves are characterized by a quadrature phase shift between
405 vertical velocity and buoyancy. Such phase shift appears present in Fig. 3a. Fig. 3a also reveals a
406 cold (warm) anomaly on the upshear (downshear) side of the Cu, as expected for an upshear
17 407 tilting wave. The net buoyancy over the width of the vortex ring can be seen to be about zero in
408 this example. The average buoyancy for the 25 vortex rings overflown by the UWKA in a
409 sheared environment also is close to zero (Fig. 11). For the remaining 39 vortex rings, the
410 UWKA intercepted the Cu cloud, usually just below cloud top such that most of the vortex ring
411 circulation was captured below flight level. An example is the third transect in Fig. 3. In that case
412 the cloud was positively buoyant (Fig. 3i), but in other cases it is negatively buoyant (Fig. 11),
413 depending on the flight level relative to the environment’s equilibrium level.
414 The 27 vortex rings in weak shear, with the WKA remaining above Cu top, are stratified
415 into two subgroups according to the mean flight level buoyancy calculated over the full width of
416 each vortex ring (Fig. 12). The less buoyant the air above the Cu top, the larger its adiabatic lift
417 that is related to the buoyant part of the nonhydrostatic pressure filed (Markowski and
418 Richardson 2010, p. 30), and the more vigorous the underlying Cu cloud. Thus negative
419 buoyancy at flight level is expected to correspond with higher in-cloud buoyancy, a stronger
420 updraft, and higher vortex ring vorticity. The composite results show that the core updraft indeed
421 is stronger, and occupies more of the circulation volume in vortex rings with strong negative
422 flight-level buoyancy, compared to vortex rings with weakly negative or positive buoyancy aloft
423 (Fig. 12). The horizontal vorticity in the former group is larger as well, nearly 50% larger than in
424 the latter group (not shown).
425
426 e. Vortex rings in a sheared environment
427 The impact of ambient wind shear (vertical variation of the horizontal wind) on Cu
428 development has been examined in several studies. Both simulations (Zhao and Austin 2005) and
429 radar observations (Damiani and Vali 2007) have shown that ambient shear acts to tilt not just
18 430 the updraft, but also the axis normal to the toroidal ring in a downshear direction. (This axis is
431 pointed upward in the absence of shear.) This leads to thinning of the upshear downdraft, and its
432 total disappearance under strong shear, leaving only an upshear updraft and a downshear
433 downdraft. This explains why downdrafts and detrainment occur preferentially on the downshear
434 side of a cloud, while updrafts tend to persist on a cloud’s upshear side, as shown in modeling
435 studies (e.g., Cotton and Tripoli 1978) and observational ones (e.g., Warner 1977; Wang and
436 Geerts 2011). We now examine the effect of shear on toroidal circulation, using a subset of cloud
437 top vortices that experience significant along-track shear.
438 The sampled clouds generally experienced little ambient shear (<10 m s-1 km-1) according
439 to proximity radiosonde (in CuPIDO) or aircraft soundings (in HiCu). By design the flight tracks
440 were aligned with the wind shear over the depth of the cloud, but a posteriori analysis shows that
441 the shear vector from the proximity sounding was only slightly more likely (68% of the total
442 sample) to be within ±45° of the flight track orientation than outside that range (32%). We also
443 found that the local shear from the WCR-derived horizontal wind over the depth of the toroidal
444 vortex was often much larger than the along-track component of the sounding-derived shear, and
445 sometimes of the opposite sign. The WCR-derived shear (computed from an average profile,
446 over the width of the cloud) combines ambient flow and convectively-induced cloud-scale
447 motions. This shear is more meaningful than just the ambient shear (from soundings), because it
448 controls the tilting of vortex rings within Cu cloud clusters, as became obvious in the few cases
449 where the ambient and the local along-track shear were of the opposite sign. This WCR-derived
450 shear does not include the average toroidal vorticity because that vorticity is of opposite sign on
451 opposite sides of the ring (Fig. 7) and thus is cancelled out in the averaging.
19 452 We thus derive along-track shear magnitude by linearly interpolating the vertical profile
453 of the mean WCR horizontal wind over the depth of each full vortex ring. To ensure
454 unidirectional shear over the depth of the ring, the linear correlation coefficient for this
455 interpolation is required to be at least 0.6. This condition is satisfied for 41 of the 91 vortex rings.
456 Note that this condition does not require the shear to be strong; it just needs to be uniform over
457 the depth of the vortex ring. The along-track shear magnitude is <10 m s-1 km-1 in just one third
458 of these 41 cases (Fig. 13). In two-thirds of the cases it is <20 m s-1 km-1, and in the remaining
459 cases, mostly shallow cases, the shear is even larger.
460 The sheared cases exhibit a distinct asymmetry (Fig. 14). The downshear subsidence is
461 stronger than the upshear one, and we can see that the updraft is slightly tilted downshear by
462 comparing Fig. 14a with Fig. 6a, as expected from a tilted toroidal ring (Damiani and Vali 2007).
463 The downshear horizontal wind dipole (outflow aloft & inflow below) is well established (Fig.
464 14b) and stronger than in the full composite (Fig. 6b). There is no corresponding dipole on the
465 upshear side. As a result, the upshear vortex is not closed, and a strong vortex prevails on the
466 downshear side, with vorticity of the same sign as the ambient shear vorticity (Fig. 14c). The
467 ambient vorticity enhances the downshear side circulation while weakening the upshear side
468 circulation.
469 To study the impact of wind shear strength on the circulation structure, we stratify the 41
470 uniform-shear cases into two subgroups: circulations in strong shear and those in weak shear.
471 The threshold value used is 12.7 m s-1 km-1 (Fig. 13). The positive vorticity on the downshear
472 side is twice as strong under strong shear (Fig. 15c, g). This is associated with the observation
473 that the downshear horizontal wind dipole (outflow aloft & inflow below) is better established
474 under stronger shear (Fig. 15b, f), in other words the circulation obtains vorticity from the
20 475 environment. Still, there is much negative vorticity even under strong shear in the upwind
476 circulation, although that circulation is not closed.
477 The core updraft is weaker and narrower under strong shear (Fig. 15a, e). The downshear
478 transport of the largest particles near cloud top is more pronounced under stronger shear (Fig.
479 15d, h). The vertical gradient of reflectivity is smaller under stronger shear (Fig. 15d, h). This
480 may indicate that ambient shear tends to reduce LWC, which is consistent with flight-level
481 measurements reported in Wang and Geerts (2013), and with the LES simulation by Zhao and
482 Austin (2005). They show that turbulent mixing is enhanced on the downshear side, reducing the
483 cloud LWC.
484
485 4. Discussion: implications for entrainment
486 An essential component of Cu dynamics regards the mechanisms and scales of material
487 exchanges (entrainment and detrainment) between the moist Cu core and its cloud-free
488 environment (e.g., Raga et al. 1990; Blyth 1993; Grabowski 1993; Carpenter et al. 1998; de
489 Rooy et al. 2013). An ongoing debate regards the source regions of entrainment, specifically the
490 relative role of lateral and vertical mixing. The LES study by Heus et al. (2008) gives strong
491 evidence for lateral entrainment as the main source region. This has been supported by several
492 analyses of in situ data collected in a large number of aircraft penetrations through Cu and their
493 immediate environment (Rodts et al. 2003; Wang et al. 2009; Wang and Geerts 2010). These
494 studies show that much entrainment is associated with toroidal circulations contained within the
495 upper portion of the cloud. While this study does not examine individual entrainment events, it
496 documents the typical strength and size of toroidal circulations in relatively isolated, weakly-
21 497 sheared, non-precipitating Cu mediocris clouds. The composite data in normalized space shown
498 herein can be shared for comparison with modelling studies.
499 The WCR reflectivity lapse rate with range gives some insight into entrainment around
500 cloud top vortices. Wang and Geerts (2013) show that the vertical lapse rate of WCR reflectivity
501 expected from attenuation by small droplets in CuPIDO and HiCu clouds is only slightly less
502 than the observed lapse rate, suggesting that the observed increase in reflectivity with height
503 towards flight level is largely due to absorption by liquid water (Section 2.c), and less to particle
504 scattering effects (i.e., an increase of droplet size with height). The vertical distribution of
505 reflectivity of deep vs. shallow vortices (Fig. 8d and h) confirms that attenuation by LWC is the
506 key factor in the vertical reflectivity profiles: a larger vertical reflectivity gradient is observed for
507 deep circulations, simply because of the larger vertical distance and thus a larger path-integrated
508 attenuation. The profile of LWC can be derived from the reflectivity profile, if we assume that
509 the reflectivity lapse with range is entirely due to absorption by liquid water.
510 The two-way path-integrated attenuation is 10 dB km-1 per g m-3 of liquid water (Vali and
511 Haimov 1999; Wang and Geerts 2013). The reflectivity profile first is averaged across the width
512 of the vortex ring. This average is the basis for the estimation of the LWC profile, which is
* 513 normalized by the adiabatic value LWCa (i.e., LWC LWC ). LWCa is computed from a LWCa
514 proximity sounding, using the LCL pressure and temperature, following Albrecht et al. (1990).
515 The closer the adiabatic fraction LWC* is to 1.0, the less diluted the air parcel is. The reflectivity
516 lapse rate is computed over the width of each vortex. Note that the LWC* derived here can only
517 be an overestimate, as power loss due to particle scattering is ignored, although this bias does not
518 affect the analysis. Note also that LWC* applies over the width of the vortex ring.
22 519 Three observations in the composite LWC* profile of 91 vortices stand out (Fig. 16).
520 First, the LWC* in vortices close to the cloud center is no more than 0.65 at any level,
521 suggesting that quasi-undiluted vortex rings are rather rare. If a vortex dipole is found near the
522 cloud edge, its average LWC* tends to be much lower (Fig. 16a), suggesting that the vortex-base
523 coherent entrainment is more significant for vortices near the cloud edge. Flight-level data for a
524 larger sample of CuPIDO and HiCu penetrations (including many smaller Cu) indicate that the
525 LWC*, averaged over the width of the cloud, peaks at just 0.28, at a level about three quarters of
526 the way up in cloud (Wang and Geerts 2013). So near-surface air entering cloud base generally
527 becomes thoroughly modified by entrainment, with the most undiluted air found in vortex rings.
528 Second, the LWC* within vortex rings increases from base to mid-levels and then
529 decreases toward the top. The fact that maximum LWC* values are observed at mid-levels,
530 where the updraft speed tends to peak, indicates that the least diluted parcels are found there,
531 which is consistent with LES-based findings (Zhao and Austin 2005). According to this
532 modelling work, the dilution at circulation top is caused by shear-driven small-scale entrainment,
533 and the dilution at base level is due to convergent flow which encapsulates ambient air.
534 Third, young, rising circulations have a more undiluted core than mature ones (Fig. 16b),
535 consistent with the shedding thermal model of Blyth (1993), and with Zhao and Austin (2005),
536 who find little dilution in thermal cores until they have risen some two vortex diameters.
537
538 5. Conclusions
539 This observational study examines toroidal circulations near the top of non-precipitating
540 Cu mediocris clouds, using vertical-plane dual-Doppler syntheses of airborne cloud radar data.
541 The sampled clouds are rather isolated orographic Cu with transects oriented arbitrarily relative
23 542 to the ambient wind shear. The 2D (along-track and vertical) flow, resolved to at least 30x30 m2,
543 is used to define and then characterize toroidal circulations, which in a vertical transect appear as
544 an updraft flanked on both sides by a downdraft. The feature-based composite consists of 91
545 vortex rings with a minimum (average) width of 200 m (1200 m), from clouds observed either
546 over a mountain top in Arizona, or over the high plains in Wyoming. The main conclusions are
547 as follows:
548 (1) The composite velocity field shows a ~3 m s-1 updraft flanked by nearly-symmetric
549 counter-rotating vortex rings, with horizontal vorticity of ~0.03 s-1 in magnitude, and
550 slightly more for the smaller vortices. The vortex-top divergence is kinematically
551 consistent with this updraft, but the vortex-base convergence is weaker than the vortex-
552 top divergence, and may extend over a greater depth. The peripheral downdrafts are
553 about as strong as the updraft, and may extend outside the cloud edge.
554 (2) Downdrafts are present even in young, rising vortices, although in a narrower region
555 along the margins. Toroidal circulations tend to decay more slowly than buoyancy and
556 rising motion in evolving convective towers.
557 (3) Ambient shear is associated with the tilted toroidal ring. Ambient shear tends to impart
558 vorticity on the downshear component of the vortex ring, weaken the core updraft and
559 toroidal ring, and transport hydrometeors towards the downshear edge.
560 (4) Toroidal circulations are relatively undiluted, especially in their developing stage, and
561 especially in their core.
562
563
24 564 Acknowledgements: This work was supported by National Science Foundation (NSF) grants
565 ATM-0444254 and ATM-0849225, and by the University of Wyoming Office for Water
566 Programs. The authors thank the UWKA crew for collecting the data and for providing high-
567 quality products for the CuPIDO and HiCu campaigns, and WCR scientist Samuel Haimov for
568 his assistance in the processing of the WCR data. This paper was improved much through the
569 comments of three anonymous reviewers.
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30 682 Figure captions 683 684 Fig. 1: (a) Average profiles of potential temperature (), equivalent potential temperature (e),
* 685 and saturated equivalent potential temperature (e ), obtained from 18 M-GAUS sondes
686 released at Windy Point in Arizona during 18 UWKA flights between 18 July and 17
687 August 2006. (b) As (a), but for specific humidity (qv) and saturated qv. The grey shading
688 denotes the mean value ±1 standard deviation. The horizontal solid lines in (a) and (b) are
689 the mean LFC & LCL respectively. They are bracketed by the mean ±1 standard deviation
690 (dashed lines).
691 Fig. 2: Vertical-plane dual-Doppler concept: a given scatterers’ volume is illuminated nearly 692 simultaneously by two beams of different orientation. V1 and V2 are the Doppler mean 693 radial velocities after removal of the aircraft motion; Vxp denotes the unmeasured ‘cross-
694 plane’ component normal to the plane of the beams. Adapted from Damiani and Haimov
695 (2006).
696 Fig. 3: Left panels (a-d): WCR vertical-plane dual-Doppler (VPDD) velocity vectors (u,w) for a
697 cumulus penetrated at 1807 UTC on 24 July 2006 during the CuPIDO campaign, overlaid
698 onto (b) horizontal wind u (m/s), (c) vertical wind w (m/s), and (d) WCR nadir-beam
699 reflectivity (dBZ). The long arrow on top of panel (b) shows the flight direction, as is
700 colored black (red) where the aircraft is in the clear air (in cloud). The direction of the
701 ambient wind shear is shown as a shorter arrow. Panel (a) on top shows gust probe (u, w)
702 (vectors, scaled as shown), vertical velocity w (m/s) (black trace), and buoyancy B (10-2
703 m/s2) (red trace) at flight-level. Middle panels (e -h): same as the left panels, but three
704 minutes later. Right panels (i -l): same as the left panels, but another three minutes later.
31 705 The black boxes in the middle panels indicate the dimensions of the vortex pairs included in
706 the composite. Five cells are tentatively labelled (A through E) in the lower panels.
707 Fig. 4: Schematic plot of a Cu cloud with a toroidal circulation (light blue shaded area). The
708 toroidal circulation is isolated and remapped in a normalized coordinate system with x* 0
709 at the center and x* 1 at the circulation edge, and normalized height z * 0 as base and
710 z * 1 as top of the circulation. The updraft core separates a clockwise vortex (CV) from a
711 counterclockwise vortex (CCV). The cloud dimensions are normalized as well, assuming
∗ ∗ 712 the same symmetry in the horizontal, and with non-dimensional coordinates [푥푐 , 푧푐 ].
713 Fig. 5: (a) Variation of WCR data frequency with distance from the vortex center (x=0) to the
714 vortex edge (x=700 m) and height from the vortex base (z=0) to the vortex top (z=700 m),
715 based on a composite of 91 vortex rings. (b) Variation of WCR data frequency with
* * 716 normalized distance from the cloud edges (xc = ±1) to the cloud center (xc = 0) and
* * 717 normalized height from the cloud base (zc = 0) to the cloud top (zc = 1). (c) Scatter plot of
718 vortex ring width vs. vortex ring depth. The dashed line is the linear regression line and the
719 dotted line is 1:1 line.
720 Fig. 6: Variation of WCR variables with normalized distance from the vortex edge (x*= ±1) to
721 the vortex center (x*= 0) and normalized height from the vortex base (z*= 0) to the vortex
722 top (z*= 1), based on a composite of 91 vortex rings: (a) vertical velocity w, (b) horizontal
723 velocity perturbation u’, (c) radar reflectivity Z, (d) WCR data frequency. The black line in
724 (b) is the vertical distribution of the mean horizontal divergence (labeled on the upper
725 abscissa).
726 Fig. 7: Composite 2D velocity vectors (u’,w) and associated horizontal vorticity, positive into the
727 page. The spatial dimensions are normalized as in Fig. 6.
32 728 Fig. 8: Variation of WCR variables with normalized distance (from vortex center to edge) and
729 height for deep (left panels) and for shallow (right panels) vortex rings: (a, e) vertical
730 velocity w, (b, f) horizontal velocity perturbation u’, (c, g) horizontal vorticity , (d, h)
731 radar reflectivity Z. The vectors in (c) are the 2D velocity vectors (u’,w). The threshold
732 vortex ring depth (mode) is 462 m.
733 Fig. 9: As Fig. 8 (without the bottom panels showing reflectivity), but (a)-(c) applies to wide
734 vortex rings, and (d) - (f) to narrow vortex rings. The threshold vortex ring width (mode) is
735 783 m.
736 Fig. 10: Variation of WCR variables with normalized distance (from vortex center to edge) and
737 height for (a) rising and (b) sinking (or weakly ascending) vortex rings. The vectors are the
738 2D velocity vectors (u’,w). The discriminating variable is the 2D averaged WCR vertical
739 velocity and the threshold value is +0.61 m s-1.
740 Fig. 11: Histogram of the mean flight level buoyancy for the 91 vortex rings.
741 Fig. 12: As Fig. 10, but only for vortex rings with the UWKA flying above the Cu cloud in a
742 weakly-sheared environment. The composite is for vortex rings with (a) positive or weakly
743 negative mean flight level buoyancy and (b) with strongly negative buoyancy. The
744 threshold value is the one that partitions the total samples in two roughly equal parts, in this
745 case –0.001 m s-2.
746 Fig. 13: Histogram of the mean ambient wind shear for the 41 vortex rings composited in Fig.
747 14. The shear calculated from the base to top of vortex ring. The dashed line is the mode
748 value, dividing all cases into subgroups of strong and weak shear (Fig. 15).
33 749 Fig. 14: As the first three panels of Fig. 8, but for vortex rings in environments with uniform
750 wind shear (variation of wind speed with height) along the flight transect. The black line in
751 (b) is the mean horizontal divergence profiles (labeled on the upper abscissa).
752 Fig. 15: The upper three rows are as in Fig. 14, but for vortex rings observed in stronger ambient
753 shear (left panels) and in weaker ambient shear (right panels). The lower panels (d) and (h)
754 show composite reflectivity for the more strongly and more weakly sheared environments
755 respectively.
756 Fig. 16: Vertical profiles of liquid water content derived from reflectivity attenuation,
757 normalized by its adiabatic value (LWC*) averaged for : (a) vortex rings close to cloud
758 center vs. those closer to the cloud edge; (b) rising vs. (mostly) sinking vortex rings. In both
759 cases the total samples of 91 vortices is split in two.
34 Figures
Fig. 1: (a) Average profiles of potential temperature (), equivalent potential temperature (e), and saturated equivalent * potential temperature (e ), obtained from 18 M-GAUS sondes released at Windy Point in Arizona during 18 UWKA flights between 18 July and 17 August 2006. (b) As (a), but for specific humidity (qv) and saturated qv. The grey shading denotes the mean value ±1 standard deviation. The horizontal solid lines in (a) and (b) are the mean LFC & LCL respectively. They are bracketed by the mean ±1 standard deviation (dashed lines).
35
Fig. 2: Vertical-plane dual-Doppler concept: a given scatterers’ volume is illuminated nearly simultaneously by two beams of different orientation. V and V are the Doppler mean radial velocities after removal of the aircraft motion; 1 2 Vxp denotes the unmeasured ‘cross-plane’ component normal to the plane of the beams. Adapted from Damiani and Haimov (2006).
36
Fig. 3: Left panels (a-d): WCR vertical-plane dual-Doppler (VPDD) velocity vectors (u,w) for a cumulus penetrated at 1807 UTC on 24 July 2006 during the CuPIDO campaign, overlaid onto (b) horizontal wind u (m/s), (c) vertical wind w (m/s), and (d) WCR nadir-beam reflectivity (dBZ). The long arrow on top of panel (b) shows the flight direction, as is colored black (red) where the aircraft is in the clear air (in cloud). The direction of the ambient wind shear is shown as a shorter arrow. Panel (a) on top shows gust probe (u, w) (vectors, scaled as shown), vertical velocity w (m/s) (black trace), and buoyancy B (10-2 m/s2) (red trace) at flight-level. Middle panels (e -h): same as the left panels, but three minutes later. Right panels (i -l): same as the left panels, but another three minutes later. The black boxes in the middle panels indicate the dimensions of the vortex pairs included in the composite. Five cells are tentatively labelled (A through E) in the lower panels.
37
Fig. 4: Schematic plot of a Cu cloud with a toroidal circulation (light blue shaded area). The toroidal circulation is isolated and remapped in a normalized coordinate system with x* 0 at the center and x* 1 at the circulation edge, and normalized height z * 0 as base and z * 1 as top of the circulation. The updraft core separates a clockwise vortex (CV) from a counterclockwise vortex (CCV). The cloud dimensions are normalized as well, assuming the same symmetry in the horizontal, and with non- ∗ ∗ dimensional coordinates [푥푐, 푧푐 ].
38
Fig. 5: (a) Variation of WCR data frequency with distance from the vortex center (x=0) to the vortex edge (x=700 m) and height from the vortex base (z=0) to the vortex top (z=700 m), based on a composite of 91 * vortex rings. (b) Variation of WCR data frequency with normalized distance from the cloud edges (xc = * * * ±1) to the cloud center (xc = 0) and normalized height from the cloud base (zc = 0) to the cloud top (zc = 1). (c) Scatter plot of vortex ring width vs. vortex ring depth. The dashed line is the linear regression line and the dotted line is 1:1 line.
39
Fig. 6: Variation of WCR variables with normalized distance from the vortex edge (x*= ±1) to the vortex center (x*= 0) and normalized height from the vortex base (z*= 0) to the vortex top (z*= 1), based on a composite of 91 vortex rings: (a) vertical velocity w, (b) horizontal velocity perturbation u’, (c) radar reflectivity Z, (d) WCR data frequency. The black line in (b) is the vertical distribution of the mean horizontal divergence (labeled on the upper abscissa).
40
Fig. 7: Composite 2D velocity vectors (u’,w) and associated horizontal vorticity, positive into the page. The spatial dimensions are normalized as in Fig. 6.
41
Fig. 8: Variation of WCR variables with normalized distance (from vortex center to edge) and height for deep (left panels) and for shallow (right panels) vortex rings: (a, e) vertical velocity w, (b, f) horizontal velocity perturbation u’, (c, g) horizontal vorticity , (d, h) radar reflectivity Z. The vectors in (c) are the 2D velocity vectors (u’,w). The threshold vortex ring depth (mode) is 462 m.
42
Fig. 9: As Fig. 8 (without the bottom panels showing reflectivity), but (a)-(c) applies to wide vortex rings, and (d) - (f) to narrow vortex rings. The threshold vortex ring width (mode) is 783 m.
43
Fig. 10: Variation of WCR variables with normalized distance (from vortex center to edge) and height for (a) rising and (b) sinking (or weakly ascending) vortex rings. The vectors are the 2D velocity vectors (u’,w). The discriminating variable is the 2D averaged WCR vertical velocity and the threshold value is +0.61 m s-1.
44
Fig. 11: Histogram of the mean flight level buoyancy for the 91 vortex rings.
45
Fig. 12: As Fig. 10, but only for vortex rings with the UWKA flying above the Cu cloud in a weakly- sheared environment. The composite is for vortex rings with (a) positive or weakly negative mean flight level buoyancy and (b) with strongly negative buoyancy. The threshold value is the one that partitions the total samples in two roughly equal parts, in this case –0.001 m s-2.
46
Fig. 13: Histogram of the mean ambient wind shear for the 41 vortex rings composited in Fig. 14. The shear calculated from the base to top of vortex ring. The dashed line is the mode value, dividing all cases into subgroups of strong and weak shear (Fig. 15).
47
Fig. 14: As the first three panels of Fig. 8, but for vortex rings in environments with uniform wind shear (variation of wind speed with height) along the flight transect. The black line in (b) is the mean horizontal divergence profiles (labeled on the upper abscissa).
48
Fig. 15: The upper three rows are as in Fig. 14, but for vortex rings observed in stronger ambient shear (left panels) and in weaker ambient shear (right panels). The lower panels (d) and (h) show composite reflectivity for the more strongly and more weakly sheared environments respectively.
49
Fig. 16: Vertical profiles of liquid water content derived from reflectivity attenuation, normalized by its adiabatic value (LWC*) averaged for: (a) vortex rings close to cloud center vs. those closer to the cloud edge; (b) rising vs. (mostly) sinking vortex rings. In both cases the total samples of 91 vortices is split in two.
50