Vertical-Plane Dual-Doppler Radar Observations of ... - AMS Journals

OCTOBER 2015

WANG AND GEERTS

2009

Vertical-Plane Dual-Doppler Radar Observations of Cumulus Toroidal Circulations YONGGANG WANG AND BART GEERTS University of Wyoming, Laramie, Wyoming (Manuscript received 25 September 2014, in final form 19 May 2015) ABSTRACT High-resolution vertical-plane dual-Doppler velocity data, collected by an airborne profiling cloud radar in transects across nonprecipitating orographic cumulus clouds, are used to examine vortical circulations near cloud top. These vortices are part of a toroidal ring centered at an updraft, usually near the cloud top, and they are essential to cumulus entrainment and dynamics. A large number of transects across toroidal circulations are composited to reveal the typical kinematic structure and associated entrainment patterns. The toroidal ring circulation is ;1 km wide and about half as deep in the sampled clouds (Cu mediocris). The composite flow field shows two nearly symmetric, counterrotating vortices, with a core updraft of ;3 m s21, consistent vortex-top divergence, two flanking downdrafts of the about same strength, and horizontal (toroidal) vorticity of ;0.03 s21. Variations with vortex size, age, and ambient shear are examined, and the relative dilution of air in the vortex core is estimated by comparing the liquid water content, estimated from path-integrated power attenuation, with the adiabatic value.

1. Introduction Cumulus clouds (Cu) are important in the climate system because they affect the vertical structure of radiative heat flux divergence and dynamically couple the planetary boundary layer to the free troposphere through vertical transports of mass, heat, moisture, aerosol, and momentum. These clouds exist over a broad range of horizontal and vertical dimensions (e.g., Lopez 1977; Wielicki and Welch 1986). A significant fraction of the vertical exchanges in Cu circulations occurs at scales smaller than resolvable scales in numerical weather prediction and climate models (e.g., Khairoutdinov et al. 2008), and therefore Cu parameterizations have been developed to represent the effect of subgrid-scale convection on precipitation and the vertical profile of resolved variables (e.g., Bretherton et al. 2004). Such parameterizations make assumptions about the turbulent mixing of Cu clouds with the environment (Siebesma and Cuijpers 1995). They are evaluated by means of high-resolution numerical simulations, such

Corresponding author address: Yonggang Wang, Department of Atmospheric Science, University of Wyoming, 1000 E. University Ave., Laramie, WY 82071. E-mail: [email protected] DOI: 10.1175/JAMC-D-14-0252.1 Ó 2015 American Meteorological Society

as large-eddy simulations (LES; e.g., Zhao and Austin 2005). In turn, these high-resolution convectionallowing simulations need to be validated with detailed Cu observations (e.g., Grabowski and Clark 1993; Craig and Dörnbrack 2008). This paper is one such observational study. Specifically, this paper examines updraft-driven toroidal (vortex ring) circulations in Cu. There is much evidence for the existence of such circulations near the top of buoyant clouds, from modeling simulations (Klaassen and Clark 1985; Grabowski and Clark 1993; Zhao and Austin 2005), laboratory experiments (Woodward 1959; Sanchez et al. 1989; Johari 1992), and observational studies. The latter have used in situ aircraft data (MacPherson and Isaac 1977; Blyth et al. 1988; Jonas 1990; Blyth et al. 2005), trace gas data (Stith 1992), and airborne radar data (Damiani et al. 2006; Damiani and Vali 2007; Wang and Geerts 2013). This study uses high-resolution (;30 m) verticalplane dual-Doppler radar data collected along flight tracks across or just above isolated orographic Cu clouds. While the 30-m resolution is sufficient to resolve vortex ring circulations, the shortest revisit time an aircraft is capable of, ;2 min, is too long to capture the evolution of these circulations and entrainment events, given the highly transient nature of Cu. Thus it is meaningful

2010

JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY

to examine vortex ring circulations in a systematic way by compositing numerous circulations, each treated independently. Wang and Geerts (2013) used this approach to examine the characteristic vertical velocity profile in Cu clouds by means of numerous profiling airborne radar transects and corresponding flight-level dynamical information. That study focused on vertical velocity over the depth of the cloud. It did not examine horizontal winds. This paper builds on Wang and Geerts (2013) through the use of two-dimensional (2D) velocity data to identify and characterize circulation features within Cu clouds. These flow-based entities then are spatially normalized and composited. Division of the entire sample into subgroups allows inspection of the effect of ambient wind shear, evolutionary stage, and other parameters on the vortex ring circulation. Data sources and analysis method are introduced in section 2. Section 3 describes the characteristic composite structure of vortex ring circulations and stratifies this as a function of size and age of circulations and ambient wind shear. Further implications are discussed in section 4. Section 5 lists the main conclusions.

2. Data sources and analysis methods a. Environment of the sampled cumulus clouds A dataset of 91 vortex rings is used in this study, collected from 58 Cu clouds or Cu clusters penetrated or overflown by the University of Wyoming King Air (UWKA) in two campaigns: the High Plains Cu (HiCu) campaign sampled Cu clouds mostly over the Laramie Range (mostly near Laramie Peak) in southeastern Wyoming in the summer of 2003 (Damiani et al. 2006) and the Cu Photogrammetric, In Situ, and Doppler Observations (CuPIDO) campaign was conducted over the Santa Catalina Mountain Range in southern Arizona in July and August 2006 (Damiani et al. 2008; Geerts et al. 2008). Both campaigns targeted relatively isolated nonprecipitating Cu mediocris in an environment with little shear. The flight-track orientation was either terrainrelative (e.g., following a ridge allowing multiple penetrations in a row) or a ‘‘rosette’’ pattern with 1208 separations to minimize the time between transects across a single Cu (Damiani et al. 2008). By design, the UWKA did not fly along the shear vector. Most sampled clouds in this study are orographic Cu clouds whose spatial relation to other clouds is controlled by the details of the terrain (Demko and Geerts 2010; Wang and Geerts 2011), rather than by shear. Most clouds were observed over or near terrain ridges; one case, in HiCu, involves a rather isolated Cu cloud over a broad valley,

VOLUME 54

about 20 km from a terrain ridge, with deeper clouds over the adjacent mountains. None of the targeted clouds were aligned in cloud streets according to GOES visible satellite imagery (e.g., Fig. 2 of Wang and Geerts 2011). The 13 HiCu clouds in this study tend to be more ‘‘continental’’ than the 45 more ‘‘monsoonal’’ CuPIDO clouds, since they generally have a higher cloud droplet concentration, a higher cloud base, lower liquid water content (LWC), and a smaller mean drop size relative to CuPIDO clouds (Wang and Geerts 2013). Still, the sampled CuPIDO clouds occurred on days that were relatively dry in the Arizona monsoon period, either without deep convection or with deep convection erupting only later in the day. Mobile GPS Advanced Upper-Air Sounding (M-GAUS) radiosonde data are used to describe the typical environment of the Cu clouds sampled during CuPIDO (Fig. 1). The cloud base, estimated from the lifting condensation level (LCL), averages around 3.0 km MSL (Fig. 1b). By contrast, the average LCL for the 13 HiCu clouds sampled on three flights is ;4.3 km MSL. This is estimated from near-surface conditions upon take-off and landing in Laramie, Wyoming, within ;100 km of the clouds, since no proximity radiosonde data were collected in HiCu. Potential instability (due /dz , 0, with ue being equivalent potential temperature and z being height) is present from the surface to ;4.7 km MSL in the CuPIDO clouds (Fig. 1a). An air parcel rising from the convective boundary layer and conserving its ue will become buoyant relative to the ambient air at ;3.8 km MSL (ue,surface 5 u*, e the saturated ue , since the parcel from the surface is saturated at this level). This is slightly above the mean level of free convection (LFC), about 3.5 km MSL (Fig. 1a). The level of neutral buoyancy generally is not very high, and observed convection was often capped at a stable layer between 6 and 7 km MSL (Damiani et al. 2008; Fig. 1a). The ambient specific humidity decreases rapidly with height in the lowest 2.5 km (Fig. 1b), starting near 12 g kg21. Thus the adiabatic LWC at flight level (4.5–6.5 km MSL) is quite high (Wang et al. 2009).

b. Cloud radar dual-Doppler synthesis The UWKA carried the 94-GHz (W band), multiplefixed beam Doppler radar, the Wyoming Cloud Radar (WCR) (Pazmany et al. 1994; Wang et al. 2012). The WCR operated in two modes in CuPIDO: the up–down profiling mode and vertical-plane dual-Doppler (VPDD) mode (Damiani et al. 2008). The latter uses one antenna pointing downward and one at a 308 slant forward of nadir (Fig. 2). The radar radial velocities from the pair of beams (antennas) are corrected for aircraft motion and synthesized to provide orthogonal

OCTOBER 2015

WANG AND GEERTS

2011

FIG. 1. (a) Average profiles of potential temperature u, equivalent potential temperature ue, and saturated equivalent potential temperature u*, e obtained from 18 M-GAUS sondes released at Windy Point during 18 UWKA flights between 18 Jul and 17 Aug 2006. (b) As in (a), but for specific humidity qy and saturated qy. The gray shading denotes the mean value 6 1 std dev. The horizontal solid lines in (a) and (b) are the mean LFC and LCL, respectively. They are bracketed by the mean 6 1 std dev (dashed lines).

components of the scatterers’ mean velocity in a given volume (Damiani and Haimov 2006). The forward and nadir Doppler measurements are nearly simultaneous (just 6 s of time lag per kilometer of range) but aircraft roll or crab results in a small offset in the curtain-like vertical planes transected by the two beams. The synthesis requires a merging of the radial velocities onto a common grid. Since the flight legs are sufficiently straight and level, and the radar range of interest is quite short (,2 km), the dual-Doppler analysis is simplified by projecting the three-dimensional (3D) data from the two beams onto a mean vertical plane. The grid is constructed with gridcell dimensions (dx, dz) of (30 m, 30 m). Data points coming from the two beams are then transformed to a common time (nadir beam time) and assigned to the grid cells based on their spatial position (using a Cressman filter), with further penalties (lower weights) for deviation of the beam direction from the desired scanning plane, and for lowpower signal-to-noise ratio values (Damiani and Haimov 2006). Typical grid cells include many radial velocities from two directions since data were sampled at ;4 m along-track and 15-m range intervals in CuPIDO and HiCu. Doppler velocity data are unfolded to resolve frequency aliasing, if any, before proceeding with the dual-Doppler calculations. These calculations are based on a velocity inverse decomposition problem, as detailed in Damiani and Haimov (2006). To achieve a good determination of the 2D vector in the along-track vertical plane, an estimate of the ‘‘cross plane’’ component, the vector normal to ! the solution plane (labeled V xp in Fig. 2), is necessary. For instance, when the aircraft rolls 38 under a 10 m s21

cross-track wind, this wind causes a 0.5 m s21 error in the vertical velocity that is obtained by projecting the slantvertical vector onto the vertical plane. For this purpose a guess of the horizontal wind vector is also employed. In CuPIDO, this wind vector is obtained from a sounding released from Windy Point (Arizona) during each flight. The flight-level wind was used in HiCu. The wind was relatively light in both environments, so wind contamination errors due to beam pointing angles off nadir (or off 308 forward of nadir) should be relatively small. A more

FIG. 2. Vertical-plane dual-Doppler concept: a given scatterer’s volume is illuminated nearly simultaneously by two beams of dif! ! ferent orientation. The symbols V 1 and V 2 are the Doppler mean ! radial velocities after removal of the aircraft motion; V xp denotes the unmeasured cross-plane component normal to the plane of the beams. Adapted from Damiani and Haimov (2006).

2012


in-depth VPDD synthesis error analysis can be found in Damiani (2005) and Damiani and Haimov (2006). In general, the uncertainty of the vertical velocity w is smaller than that of the along-track horizontal velocity u as the former is almost entirely determined by a single beam (the nadir beam), while the latter depends on a combination of the nadir and slant forward beams. Most flight legs used in this study were flown in rather smooth conditions above Cu. Aircraft attitude variations were small for these legs compared to those in Cu penetrations. In such conditions, velocity errors may be largely caused by the non-simultaneity of the observations from the two antennas (;6-s time lag per kilometer range). Damiani (2005) suggests an uncertainty of about 1.0 m s21 at a range of 2 km. (This is about the maximum range of WCR data given the rapid attenuation of the millimeter-wave signal in clouds with high LWC, as discussed below.) Nevertheless, anomalous vectors were often found at large range and in weak echo regions. These were removed based on comparisons with neighboring grid cells before compositing. It should be noted that the WCR vertical velocity includes a downward fall speed of the cloud particles. In some cases the optical array probes on the UWKA detected some ;millimeter-size drops and/or small graupel particles on flight legs penetrating the Cu during flights used here (Wang and Geerts 2013). The higher reflectivity values encountered below some flight legs included in this study, up to ;25 dBZ, suggest that in some cases the WCR vertical velocity includes a fall speed component. Damiani et al. (2006) found that the typical fall speed is negligibly small relative to the typical convective up- and downdrafts encountered in the Cu clouds sampled in HiCu, and that the basic Cu flow structure was not affected by hydrometeor fall speed. Given these considerations, and the difficulties of estimating of the fall speed in spatially inhomogeneous clouds, no correction for the hydrometeor terminal velocity was applied.

c. Cloud radar power attenuation Most clouds examined in this study were liquid only (Wang and Geerts 2013). The absorption of 94 GHz (Wband frequency) radiation by liquid water can be significant (Lhermitte 1990), thereby attenuating the radar (equivalent) reflectivity with range through cloud. The reflectivity cannot be corrected for attenuation because of the unknown variability in LWC in Cu. We will use the lapse rate of reflectivity with range in cloud as a measure of cloud LWC, as in Wang and Geerts (2013). It should be noted that as long as the signal is above the range-dependent threshold reflectivity for both antennas, the quality of the WCR dual-Doppler velocities is not affected by attenuation.

VOLUME 54

d. Sample WCR observations of vortex ring circulations One of the 45 Cu clouds in our CuPIDO dataset, observed on 24 July 2006, was captured nicely by three consecutive flight transects (Fig. 3). We show this example because it is a typical case and because the revisit interval was rather short, allowing cloud evolution to be documented. The flight tracks had an identical orientation and were displaced slightly as the Cu moved with the wind. One of the three tracks was flown in the opposite direction but the image was flipped in Fig. 3, thus the three cross sections have a matching orientation. The nearest M-GAUS sounding from Windy Point reveals a wind shear of 7.3 m s21 km21 over the depth of the cloud, directed from right to left. This shear is also evident in the dual-Doppler flow field (vectors in Fig. 3): it results in leftward (downshear) tilting updrafts and a leftward movement of upper-level echoes relative to lower-level echoes over time. The same Windy Point sounding also suggests a cloud base (LCL) of 4.2 km MSL, which was rather high for CuPIDO. The radar signal vanishes well above this cloud base (Figs. 3d,h,l), because the lower cloud radar echo is quite weak and/or because the WCR power is attenuated along the nadir path by liquid water in the upper cloud region (section 2c). So the transects in Fig. 3 just show the cloud top. This cloud lacks precipitation-size particles, thus reflectivity is rather low, but the peak reflectivity increases with time, from about 215 to 210 dBZ from the first to the third transect (Fig. 3). At the same time, the echo top rises gradually from 5.9 to 6.3 km MSL. Thus this is a slowly growing Cu cluster with relatively small hydrometeors. Some cells in the reflectivity field (Figs. 3d,h,l) are tentatively identified in the three consecutive transects. These cells are tracked according to the environmental wind speed, their relative position to the terrain below, and the evolution of their vertical motion and radar echoes. Cell B is towering at 1807 UTC, reaches peak reflectivity values at 1810 UTC with weakening updrafts, and has dissipated by 1813 UTC. It is remarkable how rapidly cells and circulations evolve. Other transects were flown repeatedly across evolving Cu clouds on this and other flights, and there too the revisit time proved to be too long to document cell evolution in detail. Therefore cloud-top vortices are not examined in an evolutionary sense, but rather are included as independent entities in the composite. A strong updraft can be seen near the top of cell B in the earliest transect, centered at (x, z) 5 (1.4, 5.7) km (Fig. 3c). As this updraft weakens toward cloud top, the

OCTOBER 2015

WANG AND GEERTS

2013

FIG. 3. (a) Gust probe (u, w; black vectors, scaled as shown), vertical velocity w (m s21; black line), and buoyancy B (1022 m s22; red line) at flight level. (b)–(d) WCR VPDD velocity vectors (u, w) for a cumulus penetrated at 1807 UTC 24 Jul 2006 during the CuPIDO campaign, overlaid onto horizontal wind u (m s21), vertical wind w (m s21), and WCR nadir-beam reflectivity (dBZ), respectively. (e)–(h) As in (a)–(d), but 3 min later. (i)–(l) As in (a)–(d), but another 3 min later. The long arrow on top of (b), (f), and (j) shows the flight direction and 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. The black boxes in (c), (g), and (k) indicate the dimensions of the vortex pairs included in the composite. Five cells are tentatively labeled (A–E) in (d), (h), and (l).

horizontal flow becomes divergent, with strong downshear flow on the left and weaker upshear flow on the right. The horizontal flow at the base of this updraft core is convergent. The updraft is flanked by a strong downdraft on the downshear side, and a weaker downdraft on the upshear side (Fig. 3c). In short, the 2D wind field reveals a clear counterclockwise-rotating vortex to the left (downshear side) of the updraft, and a lessdefined clockwise circulation on the upshear side. This fits the schematic in Fig. 4. This vortex pair is part of a 3D toroidal circulation, as described in Damiani et al. (2006). We call it a ring although in 2D it is just a vorticity dipole. In the absence of shear, the ring (or toroid) is level. The ambient shear leads to a tilting of the updrafts and toroids (Damiani et al. 2006; Wang and Geerts 2013), resulting in an asymmetric vortex pair in a vertical transect. The strength of the updraft in cell C [centered at (x, z) 5 (1.2, 5.7) km] is weaker in the second transect (Fig. 3g) as cell top rises to flight level. Two counterrotating vortices surround this updraft, although the diameter of the vortex ring is smaller than that shown in Fig. 3c. Ascending motion can be seen in a new cell E, emerging on the upshear side from a lower level, at

(x, z) 5 (1.8, 5.2) km (Fig. 3g). This cell rises and widens, resulting in a strong updraft and broad vortex ring just below flight level (Fig. 3k). New cells tend to form on the upshear side of a Cu cluster, and downdrafts and mixing

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* [ 61 at the circulation edge, and normalized height z* 5 0 as the base and z* 5 1 as the 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 nondimensional coordinates (x*, c z*). c

2014


occur mainly on the downshear side (Warner 1977; Zhao and Austin 2005). Flight-level buoyancy is shown in Figs. 3a,e,i. Buoyancy is proportional to the virtual potential temperature perturbation (dry term) and the mixing ratio of liquid water and ice (hydrometeor loading) [e.g., Eq. (1) in Wang et al. (2009)]. A ‘‘perturbation’’ requires a basic reference state, which we define as the average over a distance of .500 and ,2000 m to the left and to the right of the vortex ring, in clear air along the flight track. In dry air, as in the left and the middle transects in Fig. 3, only the dry term comes into play. The air 0.1–0.2 km above cloud top is negatively buoyant downshear of the cloud in this case, possibly because of a tilted gravity wave, as will be discussed later. In cloud, as in the right transect in Fig. 3, the expression for buoyancy includes the hydrometeor loading term, measured at flight level. In this case the cloud is positively buoyant.

e. Radar data compositing Two compositing approaches are possible to characterize the typical flow field in Cu clouds. One approach, used in Wang and Geerts (2013), is cloud based: the clouds’ horizontal and vertical dimensions are defined from radar and ancillary data, these dimensions are normalized and average reflectivity and vertical velocity patterns are examined. This is useful when examining characteristic thermodynamic and cloud microphysical patterns, but the compositing filters out the complex finescale flow structure in Cu clouds. Cu clouds usually contain multiple updrafts and associated circulations. A second approach, used in the present study, is flow based: circulation features are identified, spatially normalized, and composited. This approach requires multiple-Doppler wind fields, and is inherently more subjective than a cloud-based compositing, because the boundary between turbulent circulations is ill defined. A manual perusal of all VPDD transects of Cu clouds in the two campaigns yield a total of 91 vortex pairs (16 from HiCu and 75 from CuPIDO). This sample is rather small for three reasons. First, minimum vortex ring dimensions (width, depth) of (200, 100) m are imposed. This excludes cell D in Fig. 3g, for instance. These minima are imposed by the WCR resolution, not by a physical argument. Smaller vortex rings may exist, although they should be shorter-lived. Second, a sufficiently strong echo from the less sensitive slant forward antenna for good VPDD synthesis is required. No velocity data are included where the reflectivity value is less than two standard deviations above the mean noise level. And third, few flight legs are at a suitable level to capture full vortex circulations because the WCR often lacks the sensitivity to detect entire Cu clouds (Wang

VOLUME 54

and Geerts 2013). For instance, cell E in Fig. 3g is excluded because the circulation is not fully captured. One drawback of the WCR antenna configuration is that dual-Doppler (u, w) synthesis is possible only below flight level, and thus, to capture the full vortex ring circulation, flight tracks near or above cloud top must be used, often yielding no cloud in situ information. Only the third of three passes through the Cu cluster in Fig. 3 penetrated the (growing) cloud. We define the normalized distance x* [ 0 at the circulation center and x* [ 61 at the circulation edge, and normalized height from the vortex base (z* 5 0) to the vortex top (z* 5 1) (Fig. 4). The WCR reflectivity and velocity fields for each of the 91 vortex rings then are redistributed in a 2D normalized domain 21 , x* , 1 and 0 , z* , 1 with a bin size Dx* 5 0.025 and Dz* 5 0.025. The bin size (Dx*, Dz*) is selected as a trade-off between limiting the smoothening of the largest vortices and resolution redundancy for the smallest vortices (Wang and Geerts 2013). The normalized cloud coordinates are also shown in Fig. 4, with x*c [ 0 at the cloud center and x*c [ 61 at the cloud edge, and normalized height from the cloud base (z*c 5 0) to the cloud top (z*c 5 1). Any vortex ring’s maximum dimensions are confined to the cloud dimensions. Only averages of reflectivity, velocity, and derived variables are examined in this study, not any higher moments. In the data redistribution and compositing processes, radar reflectivity is averaged in units of Z (mm6 m23). The average Z then is reconverted to dBZ.

3. Composite structure of cumulus toroidal circulations a. Composite reflectivity and kinematic structure Figure 5a shows the fraction of sample size of vortex ring at each cell grid, or the WCR data frequency. This refers to coverage completeness: data may be missing in part of the 2D normalized domain for any of the 91 vortices, therefore the data frequency is often less than 100%, especially near the edge. Averages in each bin are computed for 91 values at the most. The most common depth and width of the 91 sampled vortex rings are 550 and 1000 m, respectively. (The width is the diameter of the vortex pair, as shown in Fig. 4.) The depth and width of toroidal rings are positively correlated, with a typical aspect ratio of 1:2 (Fig. 5c). Many of these circulations probably are larger as they may extend into echo-free clear-air regions outside the cloud edge, as suggested by the common occurrence of cloud-edge downdrafts (Heus and Jonker 2008; Wang et al. 2009). Cu clouds (or clusters of connected clouds) in the CuPIDO and HiCu

OCTOBER 2015

WANG AND GEERTS

FIG. 5. (a) Variation of WCR data frequency with distance from the vortex center (x 5 0) to the vortex edge (x 5 700 m) and height from the vortex base (z 5 0) to the vortex top (z 5 700 m), based on a composite of 91 vortex rings. (b) Variation of WCR data frequency with normalized distance from the cloud edges (x*c 5 61) to the cloud center (x*c 5 0) and normalized height from the cloud base (z*c 5 0) to the cloud top (z*c 5 1). (c) Scatterplot of vortex ring width vs vortex ring depth. The dashed line is the linear regression line, and the dotted line is the 1:1 line.

environments typically contain multiple vortex rings, and thus multiple buoyant cores and hydrometeor growth centers, in various stages of evolution, as illustrated in Fig. 3. Some of the sampled vortex rings encompass the entire cloud, and some are part of a Cu cluster. In general they span 20%–100% of the cloud

2015

width; the average ratio of vortex ring width to cloud width is 1:2. Neither the width nor the depth of the vortex rings scale with Cu width or depth (not shown). Previous studies have shown that the vortex ring circulation is often confined to the cloud top (e.g., Blyth et al. 2005; Damiani et al. 2006). In fact, some 90% of the sampled vortex rings are located in the upper half of Cu (z*c . 0.5) (Fig. 5b). The composite structure of the 91 vortex rings is shown in Fig. 6. Missing data only tend to occur on the margins, especially in the upper-left and upper-right corners (Fig. 6d), because of the typically convex Cu echo top. The composite vertical velocity field (Fig. 6a) reveals an updraft over two-thirds of the domain, peaking at ;3 m s21, and a downdraft along the margins, with a similar peak value at the edge (often the cloud edge). The fact that the peak downdraft value often occurs at the echo edge suggests that the toroidal circulation often extends into the clear-air region just outside the cloud edge. This has been observed using observations (Rodts et al. 2003; Wang et al. 2009) and simulations (Heus and Jonker 2008). These studies suggest a peak downdraft along the cloud edge, at least partly driven by evaporative cooling in the cloud margin. Therefore the dominance of blue over red in Fig. 6a does not necessarily imply that the entire circulation tends to ascend. The double dipole evident in the horizontal wind field (Fig. 6b) suggests kinematic consistency with the vertical wind field (Fig. 6a). Note that the mean along-track wind component of the 2D flow field is removed for each circulation prior to compositing, to retain the vortexrelative flow u0 . The horizontal divergence is computed over the physical space for each vortex ring. The vertical profile of mean horizontal 1D divergence is shown in Fig. 6b. In the upper part of the vortex, the along-track wind is to the left (negative) on the left side of the Cu center, and to the right on the right side. This is associated with a divergence field with a mean magnitude of nearly 0.004 s21 across the circulation diameter. This is consistent with the updraft deceleration in the upper part of two counterrotating vortices: assuming the incompressible, azimuthally symmetric continuity equation in cylindrical coordinates, (1/r)[›(ru)/›r] 1 (›w/›z) 5 0, continuity is approximately satisfied near the vortex top, with (Du, Dw) 5 (4, 2) m s21 and (Dr, Dz) 5 (600, 300) m based on typical physical distances mentioned above. (Here r is radius.) Convergence in the lower part of the data domain is only ;0.0015 s21, which is weaker than the divergence aloft, and inadequate for the observed upward acceleration, whose magnitude is about the same as that of the deceleration aloft. This violation of mass continuity in part may be due to the

2016


VOLUME 54

FIG. 6. Variation of WCR variables with normalized distance from the vortex edge (x* 5 61) to the vortex center (x* 5 0) and normalized height from the vortex base (z* 5 0) to the vortex top (z* 5 1), based on a composite of 91 vortex rings: (a) vertical velocity w, (b) horizontal velocity perturbation u0 , (c) radar reflectivity Z, and (d) WCR data frequency. The black line in (b) is the vertical distribution of the mean horizontal divergence (labeled on the upper abscissa).

azimuthal symmetry assumption (and thus related to the sample size) and to dual-Doppler velocity uncertainty (section 2b). More likely it is related to incomplete data over the full depth of the toroid, because of attenuation of the radar signal with range (section 2c), resulting in lack of data for the lower part of the vortex ring, as is the case for cell E in Fig. 3l. They may be erroneous because the VPDD uncertainty increases with radar range (section 2b), and more for u than for w, since the u field strongly depends on the less sensitive slant forward beam. The divergence (convergence) at the top (base) of the vortex circulation has important implications for Cu detrainment (entrainment). Strong cloud-top divergence and shear occur in turbulent mixtures of cloudy and environmental air (Taylor and Baker 1991; Zhao and Austin 2005; Wang and Geerts 2011). Significant dry-air entrainment may occur at the base of the toroid (Zhao and Austin 2005). The circulation is important also for precipitation growth. Hydrometeors grow in the updraft and, as long as their fall speed is less than the updraft speed, are ejected around the vortex top. The smaller hydrometeors may then be drawn toward

circulation center and may be recycled in the updraft, a hydrometeor size sorting process (e.g., Atlas and Plank 1953; Knight et al. 2008). The vertical distribution of the composite radar reflectivity (Fig. 6c) will be explored later. The horizontal variations of reflectivity from vortex center to edge evoke three observations. First, reflectivity decreases 1– 2 dBZ from the vortex center to its edge at any height. This reflectivity decrease is consistent with hydrometeor growth in the core, and hydrometeor evaporation by lateral entrainment and subsidence in the margins, although this evaporation hardly impacts the largest drops, which dominate reflectivity. Second, the horizontal reflectivity gradient is largest close to the edge. This suggests that lateral entrainment of more diluted air is confined to a small region close to circulation edge. Third, the reflectivity is more uniform in the upper region of the circulation. This is consistent with the divergent flow there: drops grow in the core updraft and then are carried outward by the divergent vortextop flow. The composite 2D vector flow field is shown in Fig. 7. It shows two closed nearly symmetric counterrotating

OCTOBER 2015

WANG AND GEERTS

2017

FIG. 7. Composite 2D velocity vectors (u0 , w) and associated horizontal vorticity, positive into the page. The spatial dimensions are normalized as in Fig. 6.

vortex rings with near stagnation at the cores of circulation. The horizontal vorticity component perpendicular to the x–z plane, derived from the 2D flow field [v 5 (›u/›z) 2 (›w/›x)], is shown as well in Fig. 7. Note that vorticity is computed in physical space first, and then composited in normalized space. The magnitude of vorticity, nearly 0.04 s21, is about one order of magnitude larger than the divergence (Fig. 6b). The vorticity is a significant characteristic of these cloud-top toroidal circulations, and can be compared against numerical simulations of sufficient resolution. The slight asymmetry in Fig. 7 relates to ambient wind shear, which will be revisited later.

b. Vortex rings of different sizes To further characterize the primary Cu circulation structure, we stratify our samples by vortex ring depth and width. Given the relative symmetry around the vortex center (Fig. 6), we double the sample size by compositing vortex halves, so Figs. 8 and 9 are shown from vortex center to edge only (0 , x* , 1). This increases the sample size and suppresses shear-related asymmetry, which will be isolated later. The fields of vertical and horizontal winds are similar for deep and

shallow vortex rings, as well as for narrow and wide vortex rings, except that the peak updraft is 8% (10%) stronger for deep (wide) vortex rings (Figs. 8a,e and 9a,d). In wider vortices, the upper-level outflow and lowlevel inflow are slightly stronger as well (Figs. 9b,e), consistent with both the stronger updraft and the wider vortex ring width. The mean buoyancy of vortex rings penetrated by the UWKA was 20.007 m s22 for the narrow ones versus 10.004 m s22 for wide ones. This suggests that the narrower towers become depleted of buoyancy more rapidly, which likely is due to entrainment. The maximum horizontal vorticity is slightly larger for the smaller circulations, either shallow (Figs. 8c,g) or narrow (Figs. 9c,f). The reason is that vorticity is scaled by W/L or U/H and, since the wind magnitudes (U, W ) vary little, vorticity is basically inversely proportional to size (width L or depth H).

c. Vortex rings of different ages According to the LES study of Zhao and Austin (2005), the core of toroidal circulations rarely becomes diluted by entrainment until the circulation has traveled up approximately two diameters, that is, rather late in

2018


VOLUME 54

FIG. 8. Variation of WCR variables with normalized distance (from vortex center to edge) and height for (left) deep and (right) shallow vortex rings. The threshold vortex ring depth (mode) is 462 m. (a),(e) Vertical velocity w (m s21); (b),(f) horizontal velocity perturbation u0 (m s21); (c),(g) horizontal vorticity v (s21) and 2D velocity vectors (u0 , w); (d),(h) radar reflectivity Z (dBZ).

OCTOBER 2015

WANG AND GEERTS

2019

FIG. 9. As in Fig. 8 (without the bottom panels that show reflectivity), but for (a)–(c) wide and (d)–(f) narrow vortex rings. The threshold vortex ring width (mode) is 783 m.

the Cu life cycle. Vortex rings form by solenoidal forcing surrounding buoyant, ascending cores. Eventually, as the updraft reaches the equilibrium level, the vortex core becomes negatively buoyant, which decelerates the overshooting top. The vortex ring then starts to decay. Thus the sign of net vortex ring vertical motion can be used as a proxy for its age. To study the effect of age on the circulation pattern, we stratify all vortices in two subgroups, based on WCR vertical velocity averaged across the 2D vortex (Fig. 10). The threshold value is the one that partitions all samples in two equal parts (the median), in this case 10.61 m s21. We consider the upward subgroup as the circulations in an earlier stage and the downward subgroup as the more mature ones.

The composite results show that updrafts occupy about 70% of the circulation volume in young Cu vortices, with weak descending flow at the edge (Fig. 10a), and a circulation center closer to the cloud edge. As discussed in section 3a, the updraft region may occupy a proportionally smaller volume considering the fact that the cloud-free part of the circulation cannot be detected by the WCR. Presumably most compensating subsidence occurs in the clear-air cloud margin. Downdrafts occupy about 60% of the circulation volume in mature circulations (Fig. 10b), resulting in a circulation center closer vortex ring center. The upper-level diffluent (lowlevel confluent) flow is more pronounced for the young (mature) circulations (not shown). Yet there is not much

2020


VOLUME 54

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 (u0 , w). The discriminating variable is the 2D-averaged WCR vertical velocity, and the threshold value is 10.61 m s21.

difference of the toroidal vorticity strength for the two subgroups (Fig. 10), suggesting that vorticity does not change much as horizontal buoyancy gradients vanish, that is, vorticity is relatively conserved. This was also noted in Wang and Geerts (2013).

d. Vortex rings and adiabatic lift aloft The buoyancy distribution for all vortex rings is shown in Fig. 11. In the absence of shear we expect isentropic layers to dome right above a rising Cu, implying negative buoyancy at flight level, which is approximately isobaric. Such negative buoyancy is observed above 20 of the 27 vortex rings cases in weakly sheared environments (Fig. 11). The bulging isentropes are part of a gravity wave that may propagate away from its source. In a sheared environment, a Cu cloud penetrating a stratified environment may produce a wave ridge displaced relative to the Cu, as the penetrating Cu acts as an obstacle in the flow (e.g., Clark et al. 1986). Recent observations combining WCR with Wyoming Cloud Lidar (WCL) data collected in transects above the tops of Cu mediocris nicely illustrate this isentropic displacement (Leon et al. 2014): the WCL depicts aerosol layers that in some cases reveal vertically propagating upshear tilting internal gravity waves. Such waves are characterized by a quadrature phase shift between vertical velocity and buoyancy. Such phase shift appears present in Fig. 3a. Figure 3a also reveals a cold (warm) anomaly on the upshear (downshear) side of the Cu, as expected for an upshear tilting wave. The net buoyancy over the width of the vortex ring can be seen to be about zero in this example. The average buoyancy for the 25 vortex rings overflown by the UWKA in a sheared environment also is close to zero (Fig. 11). For the remaining 39 vortex rings the UWKA intercepted the Cu cloud, usually just

below cloud top such that most of the vortex ring circulation was captured below flight level. An example is the third transect in Fig. 3. In that case the cloud was positively buoyant (Fig. 3i), but in other cases it is negatively buoyant (Fig. 11), depending on the flight level relative to the environment’s equilibrium level. The 27 vortex rings in weak shear, with the WKA remaining above Cu top, are stratified into two subgroups according to the mean flight-level buoyancy calculated over the full width of each vortex ring (Fig. 12). The less buoyant the air above the Cu top, the larger its adiabatic lift that is related to the buoyant part of the nonhydrostatic pressure filed (Markowski and Richardson 2010, p. 30), and the more vigorous the underlying Cu cloud. Thus negative buoyancy at flight level is expected to correspond with higher in-cloud

FIG. 11. Histogram of the mean flight-level buoyancy for the 91 vortex rings.

OCTOBER 2015

WANG AND GEERTS

2021

FIG. 12. As in 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 20.001 m s22.

buoyancy, a stronger updraft, and higher vortex ring vorticity. The composite results show that the core updraft indeed is stronger, and occupies more of the circulation volume in vortex rings with strong negative flight-level buoyancy, compared to vortex rings with weakly negative or positive buoyancy aloft (Fig. 12). The horizontal vorticity in the former group is larger as well, nearly 50% larger than in the latter group (not shown).

e. Vortex rings in a sheared environment The impact of ambient wind shear (vertical variation of the horizontal wind) on Cu development has been examined in several studies. Both simulations (Zhao and Austin 2005) and radar observations (Damiani and Vali 2007) have shown that ambient shear acts to tilt not just the updraft but also the axis normal to the toroidal ring in a downshear direction. (This axis is pointed upward in the absence of shear.) This leads to thinning of the upshear downdraft and its total disappearance under strong shear, leaving only an upshear updraft and a downshear downdraft. This explains why downdrafts and detrainment occur preferentially on the downshear side of a cloud, while updrafts tend to persist on a cloud’s upshear side, as shown in modeling studies (e.g., Cotton and Tripoli 1978) and observational ones (e.g., Warner 1977; Wang and Geerts 2011). We now examine the effect of shear on toroidal circulation, using a subset of cloud-top vortices that experience significant alongtrack shear. The sampled clouds generally experienced little ambient shear (,10 m s21 km21) according to proximity radiosonde (in CuPIDO) or aircraft soundings (in HiCu). By design the flight tracks were aligned with the wind shear over the depth of the cloud, but a posteriori

analysis shows that the shear vector from the proximity sounding was only slightly more likely (68% of the total sample) to be within 6458 of the flight-track orientation than outside that range (32%). We also found that the local shear from the WCR-derived horizontal wind over the depth of the toroidal vortex was often much larger than the along-track component of the soundingderived shear and sometimes of the opposite sign. The WCR-derived shear (computed from an average profile, over the width of the cloud) combines ambient flow and convectively induced cloud-scale motions. This shear is more meaningful than just the ambient shear (from soundings), because it controls the tilting of vortex rings within Cu cloud clusters, as became obvious in the few cases where the ambient and the local along-track shear were of the opposite sign. This WCR-derived shear does not include the average toroidal vorticity because that vorticity is of opposite sign on opposite sides of the ring (Fig. 7) and thus is canceled out in the averaging. We thus derive along-track shear magnitude by linearly interpolating the vertical profile of the mean WCR horizontal wind over the depth of each full vortex ring. To ensure unidirectional shear over the depth of the ring, the linear correlation coefficient for this interpolation is required to be at least 0.6. This condition is satisfied for 41 of the 91 vortex rings. Note that this condition does not require the shear to be strong; it just needs to be uniform over the depth of the vortex ring. The along-track shear magnitude is less than 10 m s21 km21 in just onethird of these 41 cases (Fig. 13). In two-thirds of the cases it is less than 20 m s21 km21, and in the remaining, mostly shallow, cases the shear is even larger. The sheared cases exhibit a distinct asymmetry (Fig. 14). The downshear subsidence is stronger than the

2022


VOLUME 54

FIG. 13. Histogram of the mean ambient wind shear for the 41 vortex rings composited in Fig. 14. The shear is calculated from the base to the top of the vortex ring. The dashed line is the mode value, dividing all cases into subgroups of strong and weak shear (Fig. 15).

upshear one, and we can see that the updraft is slightly tilted downshear by comparing Fig. 14a with Fig. 6a, as expected from a tilted toroidal ring (Damiani and Vali 2007). The downshear horizontal wind dipole (outflow aloft and inflow below) is well established (Fig. 14b) and stronger than in the full composite (Fig. 6b). There is no corresponding dipole on the upshear side. As a result, the upshear vortex is not closed, and a strong vortex prevails on the downshear side, with vorticity of the same sign as the ambient shear vorticity (Fig. 14c). The ambient vorticity enhances the downshear side circulation while weakening the upshear side circulation. To study the impact of wind shear strength on the circulation structure, we stratify the 41 uniform-shear cases into two subgroups: circulations in strong shear and those in weak shear. The threshold value used is 12.7 m s21 km21 (Fig. 13). The positive vorticity on the downshear side is twice as strong under strong shear (Figs. 15c,g). This is associated with the observation that the downshear horizontal wind dipole (outflow aloft and inflow below) is better established under stronger shear (Figs. 15b,f); in other words, the circulation obtains vorticity from the environment. Still, there is much negative vorticity even under strong shear in the upwind circulation, although that circulation is not closed. The core updraft is weaker and narrower under strong shear (Figs. 15a,e). The downshear transport of the largest particles near cloud top is more pronounced under stronger shear (Figs. 15d,h). The vertical gradient of reflectivity is smaller under stronger shear (Figs. 15d,h). This may indicate that ambient shear tends to reduce LWC, which is consistent with flight-level measurements reported in Wang

FIG. 14. As in Figs. 8a–c, 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).

and Geerts (2013), and with the LES simulation by Zhao and Austin (2005). They show that turbulent mixing is enhanced on the downshear side, reducing the cloud LWC.

4. Discussion: Implications for entrainment An essential component of Cu dynamics regards the mechanisms and scales of material exchanges (entrainment

OCTOBER 2015

WANG AND GEERTS

FIG. 15. As in Fig. 14, but for vortex rings observed in (a)–(c) stronger and (e)–(g) weaker ambient shear. (d),(h) Composite reflectivity for the more strongly and more weakly sheared environments, respectively.

2023

2024


VOLUME 54

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 and (b) rising vs (mostly) sinking vortex rings. In both cases the total samples of 91 vortices is split in two.

and detrainment) between the moist Cu core and its cloud-free environment (e.g., Raga et al. 1990; Blyth 1993; Grabowski 1993; Carpenter et al. 1998; de Rooy et al. 2013). An ongoing debate regards the source regions of entrainment, specifically the relative role of lateral and vertical mixing. The LES study by Heus et al. (2008) gives strong evidence for lateral entrainment as the main source region. This has been supported by several analyses of in situ data collected in a large number of aircraft penetrations through Cu and their immediate environment (Rodts et al. 2003; Wang et al. 2009; Wang and Geerts 2010). These studies show that much entrainment is associated with toroidal circulations contained within the upper portion of the cloud. While this study does not examine individual entrainment events, it documents the typical strength and size of toroidal circulations in relatively isolated, weakly sheared, nonprecipitating Cu mediocris clouds. The composite data in normalized space shown herein can be shared for comparison with modeling studies. The WCR reflectivity lapse rate with range gives some insight into entrainment around cloud-top vortices. Wang and Geerts (2013) show that the vertical lapse rate of WCR reflectivity expected from attenuation by small droplets in CuPIDO and HiCu clouds is only slightly less than the observed lapse rate, suggesting that the observed increase in reflectivity with height toward flight level is largely due to absorption by liquid water (section 2c), and less to particle scattering effects (i.e., an increase of droplet size with height). The vertical distribution of reflectivity of deep versus shallow vortices (Figs. 8d,h) confirms that attenuation by LWC is the key factor in the vertical reflectivity profiles: a larger vertical reflectivity gradient is observed for deep circulations, simply because of the larger vertical distance and thus a larger path-integrated attenuation. The profile of LWC

can be derived from the reflectivity profile, if we assume that the reflectivity lapse with range is entirely due to absorption by liquid water. The two-way path-integrated attenuation is 10 dB km21 (g m23)21 of liquid water (Vali and Haimov 2001; Wang and Geerts 2013). The reflectivity profile first is averaged across the width of the vortex ring. This average is the basis for the estimation of the LWC profile, which is normalized by the adiabatic value LWCa (i.e., LWC* 5 LWC=LWCa ). LWCa is computed from a proximity sounding, using the LCL pressure and temperature, following Albrecht et al. (1990). The closer the adiabatic fraction LWC* is to 1.0, the less diluted the air parcel is. The reflectivity lapse rate is computed over the width of each vortex. Note that the LWC* derived here can only be an overestimate, as power loss due to particle scattering is ignored, although this bias does not affect the analysis. Note also that LWC* applies over the width of the vortex ring. Three observations in the composite LWC* profile of 91 vortices stand out (Fig. 16). First, the LWC* in vortices close to the cloud center is no more than 0.65 at any level, suggesting that quasi-undiluted vortex rings are rather rare. If a vortex dipole is found near the cloud edge, its average LWC* tends to be much lower (Fig. 16a), suggesting that the vortex-base coherent entrainment is more significant for vortices near the cloud edge. Flight-level data for a larger sample of CuPIDO and HiCu penetrations (including many smaller Cu) indicate that the LWC*, averaged over the width of the cloud, peaks at just 0.28, at a level about three-quarters of the way up in cloud (Wang and Geerts 2013). So nearsurface air entering cloud base generally becomes thoroughly modified by entrainment, with the most undiluted air found in vortex rings. Second, the LWC* within vortex rings increases from base to midlevels and then decreases toward the top.

OCTOBER 2015

2025

WANG AND GEERTS

The fact that maximum LWC* values are observed at midlevels, where the updraft speed tends to peak, indicates that the least diluted parcels are found there, which is consistent with LES-based findings (Zhao and Austin 2005). According to this modeling work, the dilution at circulation top is caused by shear-driven smallscale entrainment, and the dilution at base level is due to convergent flow that encapsulates ambient air. Third, young, rising circulations have a more undiluted core than mature ones (Fig. 16b), consistent with the shedding thermal model of Blyth (1993), and with Zhao and Austin (2005), who find little dilution in thermal cores until they have risen some two vortex diameters.

4) Toroidal circulations are relatively undiluted, especially in their developing stage, and especially in their core. Acknowledgments. This work was supported by National Science Foundation (NSF) Grants ATM-0444254 and ATM-0849225, and by the University of Wyoming Office for Water Programs. The authors thank the UWKA crew for collecting the data and for providing high-quality products for the CuPIDO and HiCu campaigns and WCR scientist Samuel Haimov for his assistance in the processing of the WCR data. This paper was improved much through the comments of three anonymous reviewers. REFERENCES

5. Conclusions This observational study examines toroidal circulations near the top of nonprecipitating Cu mediocris clouds, using vertical-plane dual-Doppler syntheses of airborne cloud radar data. The sampled clouds are rather isolated orographic Cu with transects oriented arbitrarily relative to the ambient wind shear. The 2D (along-track and vertical) flow, resolved to at least 30 3 30 m2, is used to define and then characterize toroidal circulations, which in a vertical transect appear as an updraft flanked on both sides by a downdraft. The feature-based composite consists of 91 vortex rings with a minimum (average) width of 200 (1200) m, from clouds observed either over a mountain top in Arizona or over the high plains in Wyoming. The main conclusions are as follows: 1) The composite velocity field shows an ;3 m s21 updraft flanked by nearly symmetric counterrotating vortex rings, with horizontal vorticity of ;0.03 s21 in magnitude, and slightly more for the smaller vortices. The vortex-top divergence is kinematically consistent with this updraft, but the vortex-base convergence is weaker than the vortex-top divergence, and may extend over a greater depth. The peripheral downdrafts are about as strong as the updraft, and may extend outside the cloud edge. 2) Downdrafts are present even in young, rising vortices, although in a narrower region along the margins. Toroidal circulations tend to decay more slowly than buoyancy and rising motion in evolving convective towers. 3) Ambient shear is associated with the tilted toroidal ring. Ambient shear tends to impart vorticity on the downshear component of the vortex ring, weaken the core updraft and toroidal ring, and transport hydrometeors toward the downshear edge.

Albrecht, B. A., C. W. Fairall, D. W. Thomson, A. B. White, J. B. Snider, and W. H. Schubert, 1990: Surface-based remote sensing of the observed and the adiabatic liquid water content of stratocumulus clouds. Geophys. Res. Lett., 17, 89–92, doi:10.1029/GL017i001p00089. Atlas, D., and V. G. Plank, 1953: Drop-size history during a shower. J. Meteor., 10, 291–295, doi:10.1175/1520-0469(1953)010,0291: DSHDAS.2.0.CO;2. Blyth, A. M., 1993: Entrainment in cumulus clouds. J. Appl. Meteor., 32, 626–641, doi:10.1175/1520-0450(1993)032,0626: EICC.2.0.CO;2. ——, W. A. Cooper, and J. B. Jensen, 1988: A study of the source of entrained air in Montana cumuli. J. Atmos. Sci., 45, 3944–3964, doi:10.1175/1520-0469(1988)045,3944:ASOTSO.2.0.CO;2. ——, S. G. Lasher-Trapp, and W. A. Cooper, 2005: A study of thermals in cumulus clouds. Quart. J. Roy. Meteor. Soc., 131, 1171–1190, doi:10.1256/qj.03.180. Bretherton, C. S., J. R. McCaa, and H. Grenier, 2004: A new parameterization for shallow cumulus convection and its application to marine subtropical cloud-topped boundary layers. Part I: Description and 1D results. Mon. Wea. Rev., 132, 864– 882, doi:10.1175/1520-0493(2004)132,0864:ANPFSC.2.0.CO;2. Carpenter, R. L., K. K. Droegemeier, and A. M. Blyth, 1998: Entrainment and detrainment in numerically simulated cumulus congestus clouds. Part III: Parcel analysis. J. Atmos. Sci., 55, 3440–3455, doi:10.1175/1520-0469(1998)055,3440: EADINS.2.0.CO;2. Clark, T. L., T. Hauf, and J. P. Kuettner, 1986: Convectively forced internal gravity waves: Results from two-dimensional numerical experiments. Quart. J. Roy. Meteor. Soc., 112, 899– 925, doi:10.1002/qj.49711247402. Cotton, W. R., and G. J. Tripoli, 1978: Cumulus convection in shear flow—three-dimensional numerical experiments. J. Atmos. Sci., 35, 1503–1521, doi:10.1175/1520-0469(1978)035,1503: CCISFD.2.0.CO;2. Craig, G. C., and A. Dörnbrack, 2008: Entrainment in cumulus clouds: What resolution is cloud-resolving? J. Atmos. Sci., 65, 3978–3988, doi:10.1175/2008JAS2613.1. Damiani, R., 2005: The structure of thermals in cumulus from airborne dual-Doppler radar observations. Ph.D. thesis, University of Wyoming, 331 pp. ——, and S. Haimov, 2006: A high-resolution dual-Doppler technique for fixed multi-antenna airborne radar. IEEE Trans. Geosci. Remote Sens., 44, 3475–3489, doi:10.1109/TGRS.2006.881745.

2026


——, and G. Vali, 2007: Evidence for tilted toroidal circulations in cumulus. J. Atmos. Sci., 64, 2045–2060, doi:10.1175/JAS3941.1. ——, ——, and S. Haimov, 2006: The structure of thermals in cumulus from airborne dual-Doppler radar observations. J. Atmos. Sci., 63, 1432–1450, doi:10.1175/JAS3701.1. ——, and Coauthors, 2008: Cumulus, Photogrammetric, In Situ, and Doppler Observations experiment of 2006. Bull. Amer. Meteor. Soc., 89, 57–73, doi:10.1175/BAMS-89-1-57. Demko, J. C., and B. Geerts, 2010: A numerical study of the evolving convective boundary layer and orographic circulation around the Santa Catalina Mountains in Arizona. Part I: Circulation without deep convection. Mon. Wea. Rev., 138, 1902–1922, doi:10.1175/2009MWR3098.1. de Rooy, W., and Coauthors, 2013: Entrainment and detrainment in cumulus convection: An overview. Quart. J. Roy. Meteor. Soc., 139, 1–19, doi:10.1002/qj.1959. Geerts, B., Q. Miao, and J. C. Demko, 2008: Pressure perturbations and upslope flow over a heated, isolated mountain. Mon. Wea. Rev., 136, 4272–4288, doi:10.1175/2008MWR2546.1. Grabowski, W. W., 1993: Cumulus entrainment, fine-scale mixing and buoyancy reversal. Quart. J. Roy. Meteor. Soc., 119, 935– 956, doi:10.1002/qj.49711951305. ——, and T. L. Clark, 1993: Cloud-environment interface instability, Part II: Extension to three spatial dimensions. J. Atmos. Sci., 50, 555–573, doi:10.1175/1520-0469(1993)050,0555: CEIIPI.2.0.CO;2. Heus, T., and H. J. J. Jonker, 2008: Subsiding shells around shallow cumulus clouds. J. Atmos. Sci., 65, 1003–1018, doi:10.1175/ 2007JAS2322.1. ——, G. van Dijk, H. J. J. Jonker, and H. E. A. Van den Akker, 2008: Mixing in shallow cumulus clouds studied by Lagrangian particle tracking. J. Atmos. Sci., 65, 2581–2597, doi:10.1175/ 2008JAS2572.1. Johari, H., 1992: Mixing in thermals with and without buoyancy reversal. J. Atmos. Sci., 49, 1412–1426, doi:10.1175/ 1520-0469(1992)049,1412:MITWAW.2.0.CO;2. Jonas, P. R., 1990: Observations of cumulus cloud entrainment. Atmos. Res., 25, 105–127, doi:10.1016/0169-8095(90)90008-Z. Khairoutdinov, M., C. DeMott, and D. Randall, 2008: Evaluation of the simulated interannual and subseasonal variability in an AMIP-style simulation using the CSU Multiscale Modeling Framework. J. Climate, 21, 413–431, doi:10.1175/ 2007JCLI1630.1. Klaassen, G. P., and T. L. Clark, 1985: Dynamics of the cloudenvironment interface and entrainment in small cumuli: Twodimensional simulations in the absence of ambient shear. J. Atmos. Sci., 42, 2621–2642, doi:10.1175/1520-0469(1985)042,2621: DOTCEI.2.0.CO;2. Knight, C. A., L. J. Miller, and R. A. Rilling, 2008: Aspects of precipitation development in trade wind cumulus revealed by differential reflectivity at S band. J. Atmos. Sci., 65, 2563–2580, doi:10.1175/2007JAS2569.1. Leon, D., J. French, S. Lasher-Trapp, and D. Moser, 2014: Visualizing interactions between convective clouds and their environment using airborne lidar and radar observations. 14th Cloud Physics Conf., Boston, MA, Amer. Meteor. Soc., J1.6. [Available online at https://ams.confex.com/ams/14CLOUD14ATRAD/ recordingredirect.cgi/id/27893.] Lhermitte, R., 1990: Attenuation and scattering of millimeter wavelength radiation by clouds and precipitation. J. Atmos. Oceanic Technol., 7, 464–479, doi:10.1175/1520-0426(1990)007,0464: AASOMW.2.0.CO;2.

VOLUME 54

Lopez, R. E., 1977: The lognormal distribution and cumulus cloud populations. Mon. Wea. Rev., 105, 865–872, doi:10.1175/ 1520-0493(1977)105,0865:TLDACC.2.0.CO;2. MacPherson, J. I., and G. A. Isaac, 1977: Turbulent characteristics of some Canadian cumulus clouds. J. Appl. Meteor., 16, 81–90, doi:10.1175/1520-0450(1977)016,0081:TCOSCC.2.0.CO;2. Markowski, P., and Y. Richardson, 2010: Mesoscale Meteorology in Midlatitudes. Wiley-Blackwell, 407 pp. Pazmany, A., R. McIntosh, R. Kelly, and G. Vali, 1994: An airborne 95 GHz dual-polarized radar for cloud studies. IEEE Trans. Geosci. Remote Sens., 32, 731–739, doi:10.1109/36.298002. Raga, G. B., J. B. Jensen, and M. B. Baker, 1990: Characteristics of cumulus band clouds off the coast of Hawaii. J. Atmos. Sci., 47, 338– 356, doi:10.1175/1520-0469(1990)047,0338:COCBCO.2.0.CO;2. Rodts, S. M. A., P. G. Duynkerke, and H. J. J. Jonker, 2003: Size distributions and dynamical properties of shallow cumulus clouds from aircraft observations and satellite data. J. Atmos. Sci., 60, 1895–1912, doi:10.1175/1520-0469(2003)060,1895: SDADPO.2.0.CO;2. Sanchez, O., D. Raymond, L. Libersky, and A. Petschek, 1989: The development of thermals from rest. J. Atmos. Sci., 46, 2280–2292, doi:10.1175/1520-0469(1989)046,2280:TDOTFR.2.0.CO;2. Siebesma, A. P., and J. W. M. Cuijpers, 1995: Evaluation of parametric assumptions for shallow convection. J. Atmos. Sci., 52, 650–656, doi:10.1175/1520-0469(1995)052,0650:EOPAFS.2.0.CO;2. Stith, J. L., 1992: Observations of cloud-top entrainment in cumuli. J. Atmos. Sci., 49, 1334–1347, doi:10.1175/ 1520-0469(1992)049,1334:OOCTEI.2.0.CO;2. Taylor, G. R., and M. B. Baker, 1991: Entrainment and detrainment in cumulus clouds. J. Atmos. Sci., 48, 112–121, doi:10.1175/1520-0469(1991)048,0112:EADICC.2.0.CO;2. Vali, G., and S. Haimov, 2001: Observed extinction by clouds at 95 GHz. IEEE Trans. Geosci. Remote Sens., 39, 190–193, doi:10.1109/36.898682. Wang, Y., and B. Geerts, 2010: Humidity variations across the edge of trade wind cumuli: Observations and dynamical implications. Atmos. Res., 97, 144–156, doi:10.1016/j.atmosres.2010.03.017. ——, and ——, 2011: Observations of detrainment signatures from non-precipitating orographic cumulus clouds. Atmos. Res., 99, 302–324, doi:10.1016/j.atmosres.2010.10.023. ——, and ——, 2013: Composite vertical structure of vertical velocity in nonprecipitating cumulus clouds. Mon. Wea. Rev., 141, 1673–1692, doi:10.1175/MWR-D-12-00047.1. ——, ——, and J. French, 2009: Dynamics of the cumulus cloud margin: An observational study. J. Atmos. Sci., 66, 3660–3677, doi:10.1175/2009JAS3129.1. Wang, Z., and Coauthors, 2012: Single aircraft integration of remote sensing and in situ sampling for the study of cloud microphysics and dynamics. Bull. Amer. Meteor. Soc., 93, 653– 668, doi:10.1175/BAMS-D-11-00044.1. Warner, J., 1977: Time variation of updraft and water content in small cumulus clouds. J. Atmos. Sci., 34, 1306–1312, doi:10.1175/ 1520-0469(1977)034,1306:TVOUAW.2.0.CO;2. Wielicki, B. A., and R. M. Welch, 1986: Cumulus cloud properties derived using Landsat satellite data. J. Climate Appl. Meteor., 25, 261– 276, doi:10.1175/1520-0450(1986)025,0261:CCPDUL.2.0.CO;2. Woodward, B., 1959: The motion in and around isolated thermals. Quart. J. Roy. Meteor. Soc., 85, 144–151, doi:10.1002/ qj.49708536407. Zhao, M., and P. H. Austin, 2005: Life cycle of numerically simulated shallow cumulus clouds. Part II: Mixing dynamics. J. Atmos. Sci., 62, 1291–1310, doi:10.1175/JAS3415.1.