1. Introduction
Radar observations of the comma-head region of wintertime extratropical cyclones over the central and eastern United States present two different perspectives on snowfall organization. The first perspective, provided by airborne and ground-based vertically pointing radars, is that precipitation often originates in cloud-top generating cells with precipitation fall streaks emerging from the cells. Cloud-top generating cells, a type of elevated convection, are small regions of locally high reflectivity at cloud top from which a reflectivity trail characteristic of falling snow particles originates (American Meteorological Society 2023). They are ubiquitous at cloud top, 1–2 km deep, 0.5–2 km wide, and typically with updrafts of 1–2 m s−1 (McFarquhar et al. 2011; Rosenow et al. 2014; Kumjian et al. 2014). The reflectivity fallstreaks appearing on radar are often sheared, and typically descend and merge into a more stratiform radar echo lower in the clouds. Studies describing cloud-top generating cells and precipitation fall streaks have appeared in the literature over seven decades (Marshall 1953; Gunn et al. 1954; Wexler 1955; Douglas et al. 1957; Wexler and Atlas 1959; Carbone and Bohne 1975; Hobbs and Locatelli 1978; Syrett et al. 1995; Stark et al. 2013; McFarquhar et al. 2011; Kumjian et al. 2014; Rosenow et al. 2014; Rauber et al. 2014b, 2017; Plummer et al. 2014, 2015). Idealized modeling studies show that cloud-top generating cells can result from cloud-top radiative cooling, be enhanced or suppressed by the cloud-top stability profile, and organize differently based on the vertical wind shear across the cloud-top region (Keeler et al. 2016a,b, 2017). Many studies (e.g., Houze et al. 1981; Rutledge and Hobbs 1983; Browning 1983; Sienkiewicz et al. 1989; Syrett et al. 1995; Schultz et al. 2004; Stark et al. 2013; Cunningham and Yuter 2014) have described generating cells as one component of a “seeder–feeder” mechanism (Bergeron 1950), the generating cells “seeding” ice particles into the stratiform “feeder” layer below, with large-scale convergence providing the moisture source for growth of particles below the generating cell level (Matejka et al. 1980; Herzegh and Hobbs 1980; Rutledge and Hobbs 1983; Browning 1983).
The second perspective, provided by weather surveillance radars, is that zones of heavier snowfall are often organized in quasi-linear banded structures characterized by enhanced regions of radar reflectivity factor (hereafter, reflectivity) with quasi-linear shapes (i.e., long axis:short axis ratio ≥ 2:1). Bands are normally embedded within broader regions of lower reflectivity associated with lighter snowfall. Numerous studies have shown that near-surface banding typically occurs in the vicinity of midtropospheric frontal boundaries (e.g., Nicosia and Grumm 1999; Novak et al. 2004, 2009, 2010; Stark et al. 2013; Kumjian and Lombardo 2017). The near-surface primary band is frequently coincident with an axis of low and midlevel frontogenesis (Nicosia and Grumm 1999; Novak et al. 2004, 2009, 2010; Stark et al. 2013; Kumjian and Lombardo 2017). Many cyclones exhibit several bands simultaneously. Multibanded precipitation has been hypothesized to be related to phenomena such as gravity waves (Sanders and Bosart 1985; Yang et al. 2001), frontal irregularities (Hobbs and Locatelli 1978), elevated convection (Rauber et al. 2014a; Rosenow et al. 2014), and other sources, but the exact causes of multibanded precipitation remain poorly understood (Schultz and Knox 2007; Ganetis et al. 2018). Snowfall rates within bands can often exceed 2.5 cm h−1 (1 in. h−1). Novak et al. (2004) and Ganetis et al. (2018) document various types of banding structures, with different storms exhibiting a single band, single large bands co-occurring with sets of smaller bands, multibands only, and nonbanded storms. Banded features can exhibit different horizontal lengths and widths.
Explanations for the presence of a single dominant precipitation band center on the role of frontogenesis resulting from horizontal deformation flow acting upon a preexisting temperature gradient (Bergeron 1928; Petterssen 1936; Sanders 1955; Stone 1966). The relationship between precipitation bands, the vertical circulation associated with frontogenetical forcing, and the release of conditional and/or conditional symmetric instability has been explored in numerous studies (e.g., Schultz and Schumacher 1999; Novak et al. 2009; Lackmann and Thompson 2019). Thorpe and Emanuel (1985), Emanuel (1985), Sanders and Bosart (1985), and Sanders (1986) showed that frontogenetic forcing in the presence of weak positive symmetric stability will increase the intensity of precipitation within the primary band while decreasing the width of the associated updraft. Novak et al. (2008) used high-resolution modeling to link mesoscale band formation with changes in forcing, stability, and moisture. They found that band formation occurred as frontogenetic forcing and conditional stability increased. Novak et al. (2010) further examined the roles of frontogenesis, conditional symmetric instability, conditional instability, and inertial instability in the context of band formation through reanalysis and radar data, finding that in the regions of frontogenetic forcing, stability could be either weakly stable or conditionally unstable.
In general, the primary precipitation band appearing on surveillance radars as the result of frontogenesis must result from any or all of three processes: 1) concentration of ice particles into an elongated narrow region as a result of convergent and/or deformation flow, 2) growth of particles within an elongated updraft as a result of the secondary circulation associated with frontogenesis, and 3) growth of particles within convection triggered within the updraft associated with the secondary circulation. This paper focuses exclusively on the first process, with the goal of providing insight on how cloud-top generating cells and near-surface banded features are related. Specifically, we examine the reorganization of ice particles falling beneath cloud-top generating cells subject to two-dimensional convergence and stretching deformation kinematic flow fields in an attempt to bridge the two perspectives.
We conducted two separate experiments to explore how flow kinematics can reorganize snowfall beneath cloud-top generating cells. In the first experiment we explore whether convergence of particles originating near cloud top in uniformly spaced generating cells, falling at Doppler-radar-observed fall velocities within observed 2D wind fields in the stratiform region of winter storms, can be reorganized consistent with the presence of single and multibanded structures observed with surveillance radars. The wind fields are from the initialization of the High-Resolution Rapid Refresh (HRRR) model, and the radar data from three northeast U.S. winter storms. In the second experiment, we examine the potential role of flow deformation in the reorganization of ice particles using an idealized kinematic model with particle fall velocities and stretching deformation flow having values and depths characteristic of winter cyclones.
Section 2 describes generalized profiles of near-vertical radial Doppler velocities in winter storms. Section 3 presents the idealized model framework used to analyze the impact of two-dimensional convergence and the results of that analysis. Section 4 examines the potential reorganization of ice particles falling beneath cloud-top generating cells subject to stretching deformation flow fields. Section 5 provides the conclusions of the study.
2. Characteristics of the stratiform region of winter cyclones observed during IMPACTS and PLOWS
In a stratiform cloud with minimal updraft velocities, the residence time (tr) of a particle falling from cloud top to the ground is controlled by the particle fall depth and the particle fall velocity profile (Vf). Representative values of particle fall depth and terminal velocity were identified using recent field campaign observations of winter snowstorms. One such field campaign is the Investigation of Microphysics and Precipitation in Atlantic Coast Threatening Snowstorms (IMPACTS). IMPACTS consisted of three 6-week field deployments (2020, 2022, 2023) utilizing a complementary suite of remote sensors on the National Aeronautics and Space Administration (NASA) Earth Resources 2 (ER-2) high-altitude aircraft and in situ instruments on the NASA P-3 aircraft (McMurdie et al. 2019, 2022). The Cloud Physics Lidar (CPL) is a multiwavelength (355, 532, 1064 nm) elastic backscatter lidar that flies on the ER-2 as part of the IMPACTS project (McGill et al. 2002). The CPL provides cloud-top heights through measurements of the 532 nm total attenuated backscatter at 30 m vertical resolution (Yorks et al. 2011). Figure 1 shows that cloud-top heights measured during the IMPACTS 2020 and 2022 deployments were primarily between 6 and 12 km. The Cloud Radar System (CRS) is a nadir pointing W-band (94 GHz) radar flown on the ER-2 during IMPACTS that provides reflectivity and vertical radial velocities (Vr; Walker Mclinden et al. 2021). The median Vr below cloud top from CRS during IMPACTS 2020 and 2022 in the snowfall regions of the sampled winter cyclones was approximately −0.8 m s−1, decreasing to near −1.2 m s−1 at the surface, as shown by Varcie et al. (2023, Fig. 2, their Fig. 8c). This range of velocities is representative of terminal velocities of unrimed ice particles in winter storms (Heymsfield 1972; Mitchell 1996). These values are also consistent with similar measurements made in stratiform winter clouds with the University of Wyoming King Air W-band Cloud Radar (EOL/PLOWs 2023; Rosenow et al. 2014, Fig. 3, their Fig. 10). For this study experiments were conducted where the particle release altitude (zi) ranged from 6 to 10 km with several Vf profiles, Vf decreasing from −0.8 to −1.2 m s−1 between the release altitude and 1 km and a constant Vf of −0.8, −1.0, and −1.2 m s−1.
Percentage of CPL-determined cloud tops at a given altitude from all sampled storms during 2020 and 2022 IMPACTS deployments in winter storms.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
Contour frequency by altitude diagram (CFAD) of vertical radial velocities measured by the CRS on the NASA ER-2 aircraft in the stratiform region of the comma head of a winter storm on 7 Feb 2020. The black contour shows the median radial velocity values (from Varcie et al. 2023, their Fig. 8c).
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
CFAD of vertical radial velocities measured by the W-band University of Wyoming Cloud Radar on the National Center for Atmospheric Research C-130 aircraft in the stratiform region of the comma head of a winter storm on 8–9 Dec 2009. The black contours show the percentage of observations with vertical radial velocities greater than the number noted on the contour. The median Vr contour most closely represents Vf of particles (from Rosenow et al. 2014, their Fig. 10).
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
3. Reorganization of particles by two-dimensional convergence
This section explores whether convergence of particles falling beneath cloud top from uniformly spaced generating cells falling at velocities consistent with Doppler radar measurements within observed 2D wind fields can be reorganized consistent with the presence of single and multibanded structures present on WSR-88D radars.
a. Three banded northeast U.S. snowstorms
Three storms exhibiting different banding structures were selected for this analysis. The first storm on 16–17 December 2020 had a single precipitation band anchored over the Binghamton, New York, area that produced heavy snowfall. The second storm on 29–30 January 2022 had three precipitation bands within the comma head of a rapidly deepening northeast U.S. snowstorm. The third storm on 4 February 2022 produced weak linear bands along a frontal boundary. These storms represent a range of scenarios found in northeast U.S. snowstorms.
1) 16–17 December 2020 storm
A significant snowfall event associated with a major northeast U.S. snowstorm impacted the interior of the mid-Atlantic and New England states on 16–17 December 2020. At 0700 UTC 17 December 2020, a low geopotential height center at 900 hPa, based on the initialization of the 0700 UTC 3-km-resolution HRRR model, was located over southern New Jersey (Fig. 4a). WSR-88D reflectivity measurements from Binghamton (KBGM), Montague, New York (KTYX), and Albany, New York (KENX), at 0700 UTC 17 December 2020 show a clear single band feature approximately 110 km wide with enhanced reflectivity of over 27 dBZ centered near Binghamton (Fig. 5a). This band produced upward of 100 cm (40 in.) of snow in the Binghamton area over a 12 h period (NWS Binghamton). Using the initialization of the 0700 UTC 3-km-resolution HRRR model, the along cross-section component of the wind (υ, positive toward the northwest) was calculated along a cross section normal to the long axis of the band between 1 and 10 km altitude (Fig. 5b). The distance D from the northwest corner of the cross section is used to reference the horizontal position of features described below. High values of υ greater than 40 m s−1 from the southeast in the upper-right region of Fig. 5b are the consequence of a south to southeasterly jet flowing with a significant component along the cross section from southeast to northwest (Fig. 4b). At 900 hPa, diffluent flow was present in the vicinity of the cross section with winds having a ∼5 m s−1 υ component toward the northwest on the west side of the cross section and a component increasing from −5 to −20 m s−1 toward the southeast on the east side (Fig. 5b, see arrows). A sharp vertical gradient of υ was present between 1 and 3 km altitude with 15 m s−1 km−1 shear found across much of the right half of the cross section. Two-dimensional convergence is overlaid on the cross-sectional flow in Fig. 5b. A region of stronger convergence extended from an altitude of 10 to 4 km slantwise downward from D = 300 to 500 km. Additionally, there were convergence zones within the region of strong vertical wind shear from D = 250 to 500 km between 1 and 4 km altitude. Below 1 km altitude, the cross-sectional flow encountered hills and mountains which interfere with the flow. This region was omitted from the analyses in section 4.
The 900 hPa winds (m s−1) and geopotential height (m) from the HRRR model initialization at (a) 0700 UTC 17 Dec 2020, (c) 1500 UTC 29 Jan 2022, and (e) 1900 UTC 4 Feb 2022. The 300 hPa winds (m s−1) and geopotential height (m) at (b) 0700 UTC 17 Dec 2020, (d) 1500 UTC 29 Jan 2022, and (f) 1900 UTC 4 Feb 2022.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
WSR-88D radar reflectivity (dBZ) from (a) KBGM, KTYX, and KENX at 0700 UTC 17 Dec 2020, (c) KENX and KBOX at 1500 UTC 29 Jan 2022, and (e) KBGM, KTYX, and KENX at 1900 UTC 4 Feb 2022. Along cross-sectional wind component υ (m s−1; contours every 5 m s−1) and two-dimensional convergence (shading; 10−4 s−1), for (b) 0700 UTC 17 Dec 2020, (d) 1500 UTC 29 Jan 2022, and (f) 1900 UTC 4 Feb 2022. The arrows in (b), (d), and (f) represent wind direction.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
2) 29–30 January 2022 storm
A major northeast U.S. snowstorm impacted southeastern New England and the eastern mid-Atlantic from 29 to 30 January 2022. Blizzard conditions were reported at major East Coast cities such as Boston, Massachusetts. Several snowbands were observed on the WSR-88D surveillance radars along the East Coast. Figure 5c shows reflectivity at 1500 UTC from the KENX and Boston (KBOX) WSR-88D radars on 29 January 2022 showing a wide band with maximum reflectivity of 30 dBZ and two narrower bands flanking the major band. The higher reflectivity region of the primary band ranged between 30 and 60 km wide over SE Massachusetts, Rhode Island, and eastern Connecticut. A strong northwesterly flow of 30–35 m s−1 was present along the coastal region at 900 hPa, with winds decreasing in magnitude to 15–20 m s−1 to the west (Fig. 4c). These strong winds lead to a maximum of υ > −20 m s−1 toward the southeast end of the cross section for D = 330–600 km below 2–2.5 km altitude (Fig. 5d). A southeasterly jet was present aloft (Fig. 4d). The upper-level υ wind component above 4 km was relatively weak (<15 m s−1) except near 10 km altitude where υ > 15 m s−1. Two-dimensional convergence overlaid on υ in Fig. 5d shows a region of convergent flow sloping upward between 1 and 9 km altitude for D > 400 km. Divergent flow occurred across the west half of the cross section, particularly between D = 300 and 400 km below 4 km altitude.
3) 4 February 2022 storm
A frontal system exhibiting multibanded structure with weaker reflectivity impacted the northeast United States on 4 February 2022. Narrow bands occurred along a long frontal boundary that stretched from Texas to Maine with several embedded shortwaves traversing the front. WSR-88D radars KENX, KBGM, and KTYX showed snowfall occurring over much of upstate New York at 1900 UTC with the snowfall arranged in a series of bands that were 10–20 km wide and had maximum reflectivity of 21–24 dBZ (Fig. 5e). A weak flow of ∼5 m s−1 from the northwest was present at 900 hPa across the region (Fig. 4e). These weak winds were near parallel to the cross section, resulting in a ∼−5 m s−1 υ component in the lower levels in Fig. 5f. A strong 300 hPa jet flowed almost normal to the cross section (Fig. 4f) resulting in a 5–10 m s−1 υ component in the upper levels of the cross section (Fig. 5f). Two-dimensional convergence overlaid on υ in Fig. 5f shows numerous convergence/divergence couplets associated with very weak variations in the υcomponent. Overall general weak convergent flow was present between 5 and 6.5 km altitude for D > 100 km and between 7 and 10 km for D = 250–300 km. Weak divergent flow was present for D < 250 km between 3 and 5 km altitude (Fig. 5f).
b. Kinematic framework
The kinematic framework uses the parallel wind component along each cross section calculated from the HRRR model wind field initialization for each event. For all experiments, particles were arranged in a line across the entirety of D, spaced 10 m apart at either one or three initial particle altitudes, zi = 6, 8, and/or 10 km. The initial spacing of particles at 10 m results in an initial distribution of 1000 particles per 10-km-wide bin. In experiments where particles were released from three altitudes simultaneously, a total of 3000 particles were present in each bin, 1000 at each altitude.
The trajectory of a falling particle depends upon the particle’s terminal velocity, any vertical circulations within the storm, and the horizontal wind field. The clouds were assumed to be stratiform so that particles fell at the velocity represented by the median value of the radial velocities from the Doppler measurements. Ice particle terminal velocity in general depends upon the growth mechanisms that the particle undergoes as it falls from its point of formation to the ground, and the change in air density with altitude (Pruppacher and Klett 1997, 438–439). In stratiform regions where supercooled liquid water is less likely to be present (Varcie et al. 2023) ice particles falling from cloud-top generating cells grow first by diffusion, and later by aggregation (Kumjian et al. 2014). The impact of these growth mechanisms on the particle fall velocity is evident in the contoured frequency by altitude diagrams (CFADs) in Figs. 2 and 3 where the median radial velocity (an approximate estimate of particle terminal velocity) decreases from ∼−0.8 m s−1 high in the cloud to ∼−1.2 m s−1 near the surface. These values are consistent with many measurements of terminal velocities of unrimed particles (see summary in Rosenow et al. 2014, their Fig. 2).
In this paper we do not attempt to simulate the full range of possible microphysical processes as particles fall from cloud top to the ground, but rather parameterize their fall velocity based on the range of median radial velocities evident on CFADs collected in the stratiform region of winter storms (e.g., Figs. 2 and 3). Specifically, we allow the particles to fall from altitudes of 6, 8, and 10 km with fall velocities ranging from −0.8 m s−1 at the starting altitude to −1.2 m s−1 at 1 km altitude. In these experiments we assume that no melting occurs in the lower levels so the particles reach the ground as snow. For completeness, we also conduct simulations using constant fall velocities typical of unrimed ice particles in winter storms (Heymsfield 1972; Mitchell 1996). The fall velocities in these experiments were Vf = −0.8, −1.0, or −1.2 m s−1. The zi values and range of Vf provide for a total residence time, tr = (zi − 1)/Vf, of ice particles between 1.2 and 3.1 h (4167 and 11 250 s) during their fall between cloud top and the 1 km level, where they are assumed to be observable on the lowest scan of a WSR-88D radar.
Particle horizontal and vertical motion was calculated using a two-step bilinear interpolation scheme, similar to that of Draxler and Hess (1998). Each second, the scheme calculated, in the first step, an estimated particle final position (xe, ye) using the wind components at the particle initial position (xi, yi). In the next step, the wind components at the midpoint between (xi, yi) and (xe, ye) were determined and used to calculate the actual particle final position (xf, yf). Particles then fell at the assigned Vf and were transported by the horizontal wind for one second. The process was then repeated until the particles reached 1 km altitude.
c. Results
1) 16–17 December 2020 storm
Critical to this research is to determine if the horizontal flow alone can reorganize ice particles beneath cloud top such that increased particle concentrations are found collocated with, or near high reflectivity quasi-linear bands. The experiment with fall velocities becoming more negative with decreasing altitude from zi = 10 km will be used as the control experiment for the case studies. Figure 6 shows the results of the control experiment, a histogram of particle concentration in 10 km wide bins at 1 km altitude overlaid on top of the KBGM WSR-88D reflectivity at 0700 UTC 17 December 2020, when heavy snow was falling over Binghamton. The residence time of the particles was 8219 s or 2.3 h. The maximum reflectivity in the band was located at D = 233 km from the left end of the cross section. In Fig. 6a, local maxima with two distinct peaks in particle concentration is shown with one collocated with the observed reflectivity maximum at D = 230 km and the other, the largest peak, found at D = 320 km. To the northwest of the band, a more uniform region of concentration values, between 500 and 800 particles per bin, were located within a region of lower reflectivity values ranging between 8 and 18 dBZ. Meanwhile to the southeast of the main band, the concentration reduced to zero. The reflectivity in that area was low (∼2–12 dBZ). Figure 6b shows the experiment where particles were released from 6, 8, and 10 km simultaneously. Maxima in particle concentration are still located in the vicinity of the higher reflectivity, with the maximum concentration again at D = 320 km, although the maxima are smaller relative to the rest of the distribution. The distribution extends farther to the southeast consistent with the reflectivity. Figures 7a–c compare particle concentration distributions for experiments with particle release altitudes of 10, 8, and 6 km, respectively, all with decreasing fall velocities with decreasing altitude. The residence times of particles in the flow for these experiments were 8219, 7258, and 5225 s, respectively. With decreased residence time, less particle reorganization occurred such that distinct maxima became less apparent.
(a) Overlay of 1-km-altitude particle concentration on top of radar reflectivity from KBGM, KTYX, and KENX at 0700 UTC 17 Dec 2020 for (a) particles released at 10 km and (b) particles released at 10, 8, and 6 km simultaneously.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
Particle concentration distribution at 1 km altitude in the 16–17 Dec 2020 storm for particles released at (a) 10, (b) 8, and (c) 6 km with increasing fall velocity with decreasing altitude.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
Figures 8a–i show particle concentration distributions from all experiments using a single particle release altitude and constant particle fall velocity. Figures 8a–c show experiments with zi = 10 km, resulting in a 9 km particle fall distance and longer residence times; Vf in these experiments were −1.2 m s−1 in Fig. 8a, −1.0 in Fig. 8b, and −0.8 m s−1 in Fig. 8c. This resulted in residence times of tr = 7500, 9000, and 11 250 s increasing from Fig. 8a to Fig. 8c. Figures 8d–f have the same Vf, but with zi = 8 km, resulting in a 7 km particle fall distance and tr = 5833, 7000, and 8750 s, respectively. Figures 8g–i also have the same Vf sequence but with zi = 6 km, resulting in a 5 km particle fall distance, and tr = 4167, 5000, and 6250 s, respectively. The concentration in Figs. 8a–c show a broad increase in particle concentrations extending from D = 220 to 330 km with two local maxima, one centered between D = 300 and 330 km, and a second of smaller magnitude near D = 250 km. The values of the peak concentration increased as residence time increased. For example, at tr = 7500 s, the maximum concentration was 3228 particles per bin (Fig. 8a), whereas for tr = 11 250 s, the concentration was 4761 particles per bin (Fig. 8c). In Figs. 8g–i, the particle concentration distributions shifted farther southeastward and with smaller residence times, and exhibited either three or four smaller local maxima compared to Figs. 8a–c.
Particle concentration distribution at 1 km altitude for all values of tr, zi, and Vf for 16–17 Dec 2020.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
Overall, these experiments together highlight the importance of both residence time and the along cross-section flow in particle reorganization. For experiments with zi = 10 km, particles were subject to a strong southeasterly flow that decreased in magnitude, for example, 50 to 10 m s−1 at 8 km from southeast to northwest along the cross section (Fig. 5b). This resulted in an accumulation of particles as they fell to 6 km altitude through a region of convergence of 1.5 × 10−4 to 4 × 10−4 s−1 between 6 and 10 km altitude for D = 300–450 km (see Fig. 5b). Next, particles were subject to narrow horizontal regions of convergent flow of 2.5 × 10−4 to 3 × 10−4 s−1 near D = 250 and 300 km, respectively. This occurred in a layer of 10 m s−1 km−1 vertical wind shear between 2 and 5 km altitude for 225 < D < 280 km, and 15 m s−1 km−1 between 1 and 3 km altitude for D > 300 km (see Fig. 5b). Below 2–2.5 km altitude, the flow was northwesterly. Under these conditions, the combination of greater residence time and movement through two convergent flow regions resulted in the particle concentration maximum seen in Figs. 8a–c for D = 300–330 km and D = ∼250 km. In Figs. 8d–f with lower initial zi and smaller residence times, the particle concentration distributions all had smaller concentration maxima, a result of less or no time exposed to the aforementioned convergent flow region at or above 6 km altitude. In Figs. 8g–i, several local maxima were found near D = 250, 300–320, 380, and 410 km directly corresponding to several convergence maxima between either 4–6 or 2–4 km altitude. Furthermore, the distributions extended farther to the southeast with decreased residence times because particles were not transported as far to the northwest after release and were displaced farther southeast beneath 2 km altitude in the northwesterly flow.
2) 29–30 January 2022 storm
Figure 9a, the control experiment at 1500 UTC 29 January 2022, shows the resulting particle concentration distribution at 1 km altitude overlaid on the WSR-88D reflectivity. At the southeastern side of the cross section, a maximum of 2141 particles per bin appears within 50 km of the two most eastern bands. A lesser peak of particle concentration of 1881 particles per bin directly aligns with the westernmost band. The greatest WSR-88D reflectivity values were near, but not exactly, collocated with the highest concentration values. Farther northwest, numerous local particle concentration maxima and minima extended all the way to the northwest terminus of the cross section at D = 0 near Watertown, New York. The reflectivity shows some weak multibanded structure there, but the locations of the weak reflectivity maxima do not correspond directly with local concentration maxima. Figure 9b shows the experiment where particles were released from all three altitudes simultaneously. As with the control experiment, an approximate doubling of the original particle concentrations occurred in the region of the major band. Figures 10a–c compare results for particle releases at zi = 10, 8, and 6 km. In this storm, the reduction in residence time only had a minor effect on particle reorganization with the smallest residence time having a slightly diminished peak concentration.
As in Fig. 6, but for 1500 UTC 29 Jan 2022. (a) Overlay of 1-km-altitude particle concentration on top of radar reflectivity from KBOX and KENX at 1500 UTC 29 Jan 2022 for (a) particles released at 10 km and (b) particles released at 10, 8, and 6 km simultaneously.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
As in Fig. 7, but for 29–30 Jan 2022.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
Figures 11a–i show particle concentration distributions for all experiments with the constant Vf, for the same zi and tr as Figs. 8a–i. The particle concentration distributions were similar for all experiments with a broad region of increased concentrations for D > 450 km. A maximum particle concentration of 3187 particles per bin was found at D = 600 km in Fig. 11i. Again, the experiment with the maximum residence time in Fig. 11c had the largest concentration maximum, aside from a sharp particle maximum in one bin (Fig. 11i). The broad region of increased particle concentration is a consequence of the zones of convergent flow extending upward from 1 to 8 km between D = 600 and 400 km (see Fig. 5d). Values of convergence in these areas were between 1 × 10−4 and 2 × 10−4 s−1. The northwesterly low-level flow below 5 km altitude at D = 300 and 3 km near D = 500 km transported particles toward the southeast end of the cross section and increased the particle concentration in that region (Fig. 5d). For D < 450 km, the particle concentration distribution exhibited numerous local maxima within a broad region of concentration between 500 and 800 particles per bin. These concentrations are less than the initial concentration value of 1000 particles per bin and can be attributed to divergent flow below 4 km altitude at D = 400 km and below 2 km altitude at D = 500 km.
As in Fig. 8, but for 1500 UTC Jan 2022.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
3) 4 February 2022 storm
Figure 12a, the control experiment, shows the resulting particle concentration distribution at 1 km altitude overlaid on the KBGM, KTYX, and KENX WSR-88D reflectivity at 1900 UTC 4 February 2022. Here local maxima of particle concentration are collocated with very weak multibanded reflectivity structure located throughout central New York State. In particular, the radar composite near D = 180 km shows a weak multibanded region of reflectivity with values between 18 and 27 dBZ collocated directly with particle distribution local maxima of 1100–1200 particles per bin. Toward the southeastern end of the cross section, near the Catskill Mountains of New York, several particle maxima are loosely collocated with increased reflectivity values although the reflectivity bands are slightly northeast of the axis of the cross section. Figure 12b, where particles were released from three altitudes, simultaneously shows similar results. Figures 13a–c, comparing particles released from three altitudes, shows only slightly greater reorganization of particles with greater residence time.
As in Fig. 6, but for 1900 UTC 4 Feb 2022. (a) Overlay of 1-km-altitude particle concentration on top of radar reflectivity from KBGM, KTYX, and KENX at 1900 UTC 4 Feb 2022 for (a) particles released at 10 km and (b) particles released at 10, 8, and 6 km simultaneously.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
As in Fig. 7, but for 4 Feb 2022.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
Figures 14a–i, with the same Vf, tr, and zi as Figs. 8a–i, display particle concentrations with many local minima and maxima in every panel. Unlike the other cases, the concentration distributions across all of the cross section deviated little from its original distribution owing to the weak υ wind component and subsequent weak convergence along the cross section (see Fig. 5f). The weak convergent flow resulted in several local concentration maxima and minima that were relatively similar in magnitude, number, and location for all experiments.
As in Fig. 8, but for 1900 UTC 4 Feb 2022.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
4. Reorganization of particles by deformation
Stretching deformation wind field (m s−1) for D = 1 × 10−4 s−1 with the axis of dilatation at y = 0.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
Schematic of fall velocity profile and the jet and deformation layers used in the calculation.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
Figure 17a shows the initial particle arrangement just above the deformation layer. The particles were arranged at randomly placed points on the left side of the domain consistent with the arrangement described in Keeler et al. (2017) under conditions of no vertical wind shear at cloud top (Fig. 17b). The remaining part of the domain allows sufficient space for particles to be transported eastward by the flow. Each red dot in Fig. 17a represents a circular cluster of particles emanating from a cloud-top generating cell with a 1 km radius. For this arrangement, L is the distance between the minimum and maximum location of ice particles along the x axis, while W is the distance between the minimum and the maximum location of ice particles on one side of the axis of dilatation along the y axis (Fig. 17a). The initial length to width ratio (LWRi) at the top of the deformation layer was 0.5. The final length to width ratio at the surface (LWRs) is shown in Fig. 18a. Any values greater than 0.5 represent stretching of the particle field along the axis of dilatation. The ratio R = LWRs/LWRi provides a direct measure of the stretching of the initial ice particle field, and is shown in Fig. 18b.
(a) Initial ice particle field arrangement based upon (b) from Keeler et al. (2017).
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
(a) LWRs and (b) R for all deformation layer depths and magnitudes. The residence time (s) of particles in the deformation layer is also shown.
Citation: Journal of the Atmospheric Sciences 80, 11; 10.1175/JAS-D-23-0024.1
As illustrated in Figs. 18a and 18b, the magnitude of stretching of the ice particle field depends upon the residence time of the particles within the deformation layer. As noted earlier, in the comma head of winter storms, deformation flow typically transitions to a quasi-linear flow in the vicinity of a frontal boundary that is commonly located around 1–4 km MSL (Rosenow et al. 2014; Varcie et al. 2023). The results shown in Figs. 18a and 18b for deformation depths at or below 4 km most likely represent a typical storm environment. In general, the stretching of the ice particle field is minimal when compared to stretching for much deeper (>7 km) deformation layers, especially with deformation greater than 1 × 10−4 s−1. For example, with a deformation layer depth of 4 km, only with the two strongest deformation fields at 2 × 10−4 and 2.5 × 10−4 s−1 was there a doubling of the length of the particle field along the axis of dilatation with LWRs values of 1.04 and 1.24 and R values of 2.08 and 2.48, respectively. For deformation layers shallower than 4 km, the stretching of the surface ice particle field was less than double that of the original field for all deformation magnitudes. These results indicate that in the comma-head region of winter cyclones, layers of deformation flow having a depth of 4 km or less are likely to produce minimal particle reorganization along the axis of dilatation.
5. Conclusions
In this paper we conducted two separate experiments to explore how flow kinematics can reorganize snowfall beneath cloud-top generating cells. The first experiment explored whether particles falling beneath cloud top from uniformly spaced generating cells at terminal velocity within observed 2D convergent wind fields can be reorganized consistent with the presence of single and multibanded structures present on WSR-88D radars. This experiment demonstrated that the greater the residence time in each of the three storms, the greater the particle reorganization by the two-dimensional flow field beneath cloud top, resulting in larger concentrations of particles in the vicinity of observed precipitation bands. The second experiment examined the role of flow deformation in the reorganization of ice particles placed randomly at cloud top using an idealized kinematic model with particle fall velocities and stretching deformation flow having magnitudes and depths characteristic of winter cyclones. This study found the deformation alone is likely insufficient to reorganize falling particles in typical winter storm environments.
As noted in the introduction, banded precipitation observed on surveillance radars within the comma head of winter cyclones can occur as a result of any or all of the following three factors: 1) kinematic flow rearranging snowfall beneath cloud top into linear banded features near the surface, 2) snow growth as a result of large-scale ascent in an elongated updraft in the secondary circulation associated with frontogenesis, or 3) snow growth due to ascent in convection from the release of mesoscale instabilities within the updraft associated with frontogenesis. The first experiment investigated the first factor by elucidating the role of two-dimensional convergence in reorganizing snowfall beneath cloud top. Results from the first experiment show that the two-dimensional convergent flow in each case resulted in an increase of particle concentrations that were in the vicinity of the low-level observed precipitation bands on radar. The experiments with maximum residence time, having both varying and constant particle fall velocities, especially in the first two storms, exhibited the greatest particle concentrations near the bands as particles were subject to convergent flow regions for a longer duration. This suggests that for a large particle fall depth, fall velocities becoming more negative with decreasing altitude and regions of convergent flow, kinematics alone can assist in band formation by locally increasing particle concentrations. While the findings give information on the concentration of particles into band regions within the comma head, they do not definitively determine the cause of precipitation banding, since the latter two factors were not considered. We note that these findings are limited to the comma-head region and may not apply to banded features in other parts of extratropical cyclones.
The second experiment, testing the role of deformation flow on particle reorganization given typical deformation layer depths and magnitudes in midlatitude winter storms showed that deformation provides for little particle reorganization given typical deformation layer depths and magnitudes within the comma head of such storms. This suggests that the primary cause of particle reorganization by kinematics is through convergent flow across frontal zones within winter cyclone flow structure, while deformation flow contributes marginally to particle reorganization in winter storm environments.
Acknowledgments.
This work was funded by the NASA Earth Venture Suborbital-3 (EVS-3) program under Grants 80NSSC19K0355 (UIUC) and 80NSSC19K0399 (OU).
Data availability statement.
Profiling of Winter Storms (PLOWs) W-band Wyoming Cloud Radar data used to construct Fig. 6 are available at https://data.eol.ucar.edu/master_lists/generated/plows/. IMPACTS lidar and W-band CRS data used to construct Figs. 5 and 7 are available from the NASA EOSDIS Global Hydrology Resource Center Distributed Active Archive Center, Huntsville, Alabama, DOI: https://doi.org/10.5067/IMPACTS/DATA101.
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