Shear-Driven Instabilities as the Origin of Multi-Banded Cloud and Precipitation Structures in an Extratropical Cyclone

Generated using the official AMS L A T EX template v6.1 Shear-Driven Instabilities as the Origin of Multi-Banded Cloud and1 Precipitation Structures in an Extratropical Cyclone2 Stephen R. Guimonda 3 aDepartment of Atmospheric and Planetary Sciences and Severe Weather Research Center, Hampton University, Hampton, VA, USA 4 5 Corresponding author: Stephen R. Guimond, [email protected]6 1 ABSTRACT: This paper investigates the dynamics governing multi-banded cloud and precipitation in extratropical cyclones through a case study from the NASA Investigation of Microphysics and Precipitation for Atlantic Coast-Threatening Snowstorms (IMPACTS) field campaign. On 1 February 2020, a low-pressure system emerged off the North Carolina coast at 1200 UTC, deepening by 7 hPa in six hours as it accelerated northeast over the Atlantic. High-resolution GOES visible imagery revealed multiple bands of high-reflectance cloud to the north/northeast of the center, along with clusters of convective cells closer to the core. Wavelet analysis identified a dominant multi-band wavelength of 30 km and a secondary peak at 15-20 km. Airborne radar measurements from IMPACTS flights showed deep convection near the center and narrow, elevated reflectivity bands linked to the multi-band features farther out. Numerical simulations reproduced the multi-bands, enabling exploration of their dynamical origin. Intrinsic phase speed calculations revealed that, contrary to several previous studies, the dominant multi-bands were not gravity waves. Instead, the features were identified as dynamic instabilities (Kelvin–Helmholtz instability) arising from vertical wind shear and low Richardson numbers near the upper-level outflow. Gravity waves were present in the low to mid levels (0–6 km) generated by convection, but they did not account for the strong perturbations in the mid to upper levels (6–10 km). This study presents new scientific insight into the governing dynamics of multi-banded structures in extratropical cyclones that highlights the role of shear-driven instabilities. 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 2 SIGNIFICANCE STATEMENT: Extratropical cyclones along the United States East Coast can25 produce intense bands of snow and other types of precipitation that cause travel chaos and potential26 loss of life. In this work, a storm of this type was studied using NASA aircraft and satellite27 data as well as computer simulations. The results show that the storm bands were not caused by28 atmospheric waves, as scientists often thought, but by sharp changes in the wind speed with height29 called shear. This shear created unstable layers that rolled and mixed the air, forming organized30 cloud and precipitation patterns. Understanding these fundamental physical processes can help31 forecasters better predict when and where heavy snow bands will form, improving warnings and32 public safety.33 1. Introduction34 Banded structures in extreme weather systems are perturbations to a balanced, background35 flow that can organize and concentrate variables such as moisture, momentum, and energy. In36 extratropical cyclones (ETCs), the focus of this paper, the concentration of these variables can37 lead to intense bands of multi-phase precipitation at the surface that are difficult to measure,38 model and predict with significant consequences for society. For example, snowfall associated39 with ETCs in the winter months can often organize into multiple bands that drop large amounts40 of snow in a short time causing vehicle crashes, flight cancellations and shutdowns of schools and41 businesses. The current understanding of the dynamical processes controlling the formation and42 evolution of these precipitation multi-bands (as opposed to a single, large-scale band) and their43 representation/predictability in numerical models is very limited. These limitations were part of the44 motivating factors for the recently completed Investigation of Microphysics and Precipitation for45 Atlantic Coast-Threatening Snowstorms (IMPACTS; ?) field experiment, which sought to improve46 the understanding of precipitation multi-bands in ETCs from various perspectives.47 ?used radar observations, soundings, and reanalysis data to examine the environments containing48 banded structures in a large set of ETC winter storms. They found that multi-bands were not well49 correlated with frontogenetical forcing and associated deformation zones. This result is consistent50 with the notion that deformation alone cannot explain the regular, oscillatory nature of the various51 fields connected to multi-bands. The authors also examined the presence of conditional symmetric52 instability (CSI) in the environment of various types of banded structures. While CSI was present53 3 in the vast majority of banded cases, there was no clear separation between single, large-scale bands54 and the smaller-scale, multi-band structures. This suggests that CSI may not be the fundamental55 property underlying the formation and evolution of multi-bands.56 In their review paper, ?noted that the banding of clouds and precipitation in ETCs appears to57 be weakly related to CSI. ?used a viscous form of the Sawyer-Eliassen equation to understand58 banding mechanisms associated with frontogenetical forcing. For broad forcing and negative moist59 potential vorticity, which is a condition that reflects the presence of CSI, multiple bands develop60 with an intensity that scales with the degree of instability. However, it is not clear from the theory61 of ?exactly how CSI coupled with moisture and lift, associated with frontogenesis, would produce62 the regularly spaced bands of clouds and precipitation observed in the real atmosphere. In an63 unstable environment, parcels are accelerated exponentially in the direction of the displacement64 and do not maintain an oscillatory behavior.65 ?and ?described several conditions that should be met to associate precipitation multi-bands66 with CSI. One of the key requirements is that the bands have no intrinsic propagation as they should67 be moving directly with the environmental flow. However, several studies of multi-bands do show68 intrinsic propagation, which when coupled with the description above, question the role of CSI in69 the band dynamics.70 Another possible culprit for multi-bands is the presence of a wave phenomenon to organize the71 oscillations in the state variables and provide the lift necessary to release any type of instability72 in the environment. Several previous studies have focused on the role of gravity waves as the73 mechanism for organizing the cloud and precipitation fields into multi-band structures in ETCs74 (e.g., ???). These waves can be generated from flow imbalances (e.g., associated with upper-75 level jets), convective perturbations, and/or flow over topography. ?documented large-amplitude76 mesoscale gravity waves (wavelengths of 200 - 260 km) during several winter storms using time77 series of surface pressure and wind measurements. These gravity waves were found to originate at78 upper levels from jet streak imbalances and the associated geostrophic adjustment process (e.g., ?).79 For large-amplitude waves, a surface reflection of the upper-level perturbation energy was detected80 and hypothesized to become trapped at lower-levels due to strong static stability (“wave ducting”;81 ?). This wave ducting allows for a longer residence time of the gravity wave energy in the lower82 4 levels of the atmosphere resulting in the potential for organized clouds and precipitation as shown83 by satellite and radar instruments.84 ?also highlighted the role of mesoscale (∼200 km) gravity waves using numerical simulations of85 an ETC using various resolutions down to 4 km spacing. The authors proposed a conceptual model86 for the generation and evolution of mesoscale gravity waves based on these simulations. First, the87 waves were initiated in the upper levels of the system from the geostrophic adjustment process.88 Then, convection associated with the frontal features and local instability transported some of the89 gravity wave energy towards the surface where it can be ducted within a statically stable layer. This90 ducted wave then interacts with the moisture field to create a convectively-coupled wave that can91 be maintained and possibly amplified over a significant amount of time.92 Several questions and uncertainties come to mind regarding the applicability of these previous93 gravity wave studies to the general problem of ETC multi-bands. How does convective activity94 preferentially transport the wave energy initiated at upper levels (near the tropopause) downward95 to low levels and keep the wave intact? The presence of a strong static stability layer at lower96 levels and reflecting layer above to enable wave ducting appears to be a special set of circumstances97 and it is not clear how this layer can be formed and maintained in regions of the system that are98 convectively active.99 The goals of the present study are: (1) To determine the key structures and spatial/temporal scales100 of multi-banded precipitation features in ETCs and (2) To determine the origin and dynamical101 processes associated with these bands. To address the above goals and develop potentially new102 understanding of ETC multi-bands, a case study from the NASA IMPACTS field campaign is103 analyzed with multi-scale numerical simulations and a variety of remote sensing measurements.104 Case studies are an important first step towards developing a deep, holistic understanding of a105 physical process, which then allows that understanding to be tested more broadly on a larger106 collection of systems. The technical novelties of the present work are in the study of modern107 remote sensing measurements and numerical models along with some new methods of analysis to108 the problem of ETC multi-bands.109 5 Fig. 1. Synoptic maps of mean sea level pressure and frontal analysis on 1 February, 2020 at (a) 1200 UTC and (b) 1800 UTC. 2. Brief overview of extratropical system110 During the winter of 2020, NASA organized the first phase of a multi-year effort called IMPACTS111 to study the microphysics and dynamics of ETCs with a focus on understanding banded regions of112 precipitation. On 1 February 2020, a double surface low-pressure system along a stationary front113 formed off the coast of the Carolinas with the southern low starting off at ∼1006 hPa on 1200114 UTC 1 February (Fig.1a). During the next 6 hours, the southern low intensified to 999 hPa at115 1800 UTC 1 February (Fig.1b) and to 998 hPa at 0000 UTC 2 February (not shown). During this116 period, multiple bands of convective clouds and precipitation formed to the north and northeast117 of the southern low-pressure center, which allowed detailed study of their characteristics. Flights118 from the NASA P-3 and ER-2 aircraft occurred during ∼1200 - 1800 UTC 1 February sampling119 the environment and banded features associated with the southern low.120 6 3. Data and processing121 a. EXRAD122 The ER-2 X-band Doppler Radar (EXRAD) is an X-band, downward-pointing airborne radar123 that measures radar reflectivity and Doppler velocity from hydrometeors with two beams and ∼20124 m gate spacing. The first beam is fixed and points nominally at nadir, while the second beam scans125 conically at 20 revolutions per minute at a nominal incidence angle of 32°. From the altitude of126 the NASA ER-2 aircraft (∼20 km), the swath width at the first level of useful data is ∼23 km.127 The EXRAD scanning beam mainand side-lobes interact strongly with the ocean surface and128 contaminate the precipitation signal below about 1 km height. The sampling of precipitation from129 the scanning beam is ∼500 m along-track and ∼2°in azimuth while the nadir beam along-track130 sampling is ∼50 m.131 Calculations of the three-dimensional (3D) wind field using the EXRAD scanning beam are132 performed using the 3D variational algorithm described in ?. The retrieval grid is set to 500 m in133 the horizontal dimensions and 250 m in the vertical dimension. Finer grid spacing in the vertical134 is possible, but was not deemed necessary. A two to three grid point running mean filter is applied135 to the raw retrievals in post-processing to remove numerical noise. The effective resolution of136 the wind fields produced from the algorithm has been analyzed with large eddy simulations in ?.137 Results show that scales of 5 Δ𝑥and larger are fully resolved, which translates to 2.5 km for the138 present study. Scales below this threshold, down to the grid scale, are subject to increasing kinetic139 energy attenuation.140 Quality control has been performed on the wind fields to remove data with low signal-to-noise141 ratios and high uncertainties. While a combination of parameters have been studied, the best quality142 fields were found by removing data with standard deviations larger than 6 m/s (error statistics are143 computed as part of the wind algorithm, see ?). The data presented in this paper have this threshold144 applied. Validation of the EXRAD 3D winds with flight level in-situ data from the NASA ER-2145 aircraft during IMPACTS 2020 have been performed. This validation showed zonal wind root146 mean square errors (RMSEs) of 3.99 m/s with a correlation coefficient of 0.92. For the meridional147 wind, the RMSEs are 4.53 m/s with a correlation coefficient of 0.89. These statistics are collected148 7 at various locations across the radar swath and for different time offsets. Further information about149 these error statistics and the EXRAD scanning beam wind retrievals can be found in (?).150 For scientific analysis, the EXRAD scanning beam is used to present the horizontal wind field,151 while the nadir beam is used to display the vertical wind field, since it has higher quality. Several152 corrections to the nadir beam Doppler velocities are needed before the vertical velocity can be153 analyzed for science. The expression for the nadir beam Doppler velocity (𝑉𝑑) is given by154 𝑉𝑑=® 𝑉𝑤·ˆ𝑒−® 𝑉𝑔·ˆ𝑒+𝑉𝑛(1) where ˆ𝑒=𝑥ˆ 𝑖+𝑦ˆ 𝑗+𝑧ˆ 𝑘 𝑟and155 ® 𝑉𝑤=𝑢ˆ 𝑖+𝑣ˆ 𝑗+ (𝑤+𝑣𝑡)ˆ 𝑘, (2) ® 𝑉𝑔=(𝐺𝑆ℎ∗𝑠𝑖𝑛𝑇)ˆ 𝑖+ (𝐺𝑆ℎ∗𝑐𝑜𝑠𝑇)ˆ 𝑗+ (𝐺𝑆𝑣)ˆ 𝑘(3) and 𝑉𝑛represents the effects of non-uniform beam filling.156 In these equations x,y,z are the Earth-relative coordinates of the radar pulse volumes (?), ris157 the range, u,v,w are the components of the Earth-relative wind, 𝑣𝑡is the hydrometeor fallspeed,158 𝐺𝑆ℎ,𝐺𝑆𝑣are the horizontal and vertical components of the aircraft ground speed and Tis the159 aircraft track angle.160 Solving for the vertical velocity yields,161 𝑤=(𝑉𝑑−𝑉𝑛+® 𝑉𝑔·ˆ𝑒)𝑟−𝑢𝑥 −𝑣𝑦 𝑧−𝑣𝑡.(4) The calculation of hydrometeor fallspeeds from the reflectivity measurements follows the studies162 of ?and ?. The non-uniform beam filling effects are removed from the Doppler velocities163 following ?. Aircraft motion can result in antenna pointing angles that intercept the horizontal164 wind field, contaminating the vertical winds. The horizontal wind fields computed from the165 EXRAD scanning beam, described above, are used to remove this contamination from the nadir166 beam following equation 4.167 8 b. GOES-16168 High spatial and temporal resolution imagery of clouds from the advanced baseline imager on169 the Geostationary Operational Environmental Satellite (GOES) - 16 satellite at visible and infrared170 wavelengths are used to track banded structures. Specifically, reflectance data from the visible171 (channel 2) band at 500 m pixel spacing and 60 s time updates is utilized. This fine sampling in172 space and time provides the detailed structure of the cloud lifecycle as well as the organization and173 evolution into multi-bands.174 c. Numerical Simulations175 The Weather Research and Forecasting (WRF) model version 4.2 with the advanced research176 dynamic core is utilized to provide context for the observations. Four domains are utilized with177 a large, parent domain at 2 km grid spacing (domain 1) covering the full movement of the low-178 pressure system and banded features on 1 February 2020. Three nested domains at 0.667 km179 (domain 2), 0.222 km (domain 3) and 0.074 km (domain 4) grid spacing were placed to the North180 and Northeast of the low center to try and capture the finer scales of the multi-bands. All domains181 utilize 121 stretched vertical levels with a spacing of ∼75 m at the surface, ∼200 m at 10 km182 height and ∼900 m near the model top at 20 km height.183 Portions of the multi-bands were captured in domains 2 and 3, but not domain 4. The focus of184 the paper is on domain 1 for a few reasons. First, this domain captures the entirety of the system,185 which allows both large-scale and mesoscale features to be analyzed. Second, the wavelengths186 of dominant features found in the observations are 15-20 km and ∼30 km, which should be well187 resolved by the 2 km domain given the ∼7 - 8 Δ𝑥numerical dissipation range of WRF (e.g., ?).188 The higher resolution domains were analyzed as part of this research and will be noted where189 appropriate.190 The setup of the model is as follows. The NCEP Global Data Assimilation System (GDAS)/Final191 (FNL) operational global analyses at 0.25 °spacing and 6 h temporal spacing are used as the initial192 and boundary conditions for the simulation. This widely used system combines the Global Forecast193 System (GFS) model with various synoptic-scale observations to achieve an optimal state of the194 atmosphere. For the 2 km parent domain the following sub-grid physics schemes were chosen:195 Thompson for microphysics, YSU for boundary layer (vertical diffusion), Smagorinsky-2D for196 9 Two hours later at 1600 UTC, the same fields have changed significantly. The low-level reflectivity310 (Fig. 8a) reveals three bands oriented at different angles and denoted with dashed, black circles.311 The mid-level reflectivity (Fig. 8b) shows some signatures of the low-level bands, such as the312 southernmost circled region, but other bands to the north do not have the same orientation. These313 bands are oriented approximately perpendicular to the along-track axis that denotes the axis of314 band propagation. The upper-level reflectivity (Fig. 8c) shows narrow signatures of multi-bands315 that extend from near the system center out to approximately 300 km radius. The wavelengths316 of the reflectivity bands in Fig. 8 are ∼30 km, which is very similar to those documented from317 the GOES data, shown by the wavelet analysis in Fig. 5. The multi-bands present in the model318 reflectivity appear similar to those observed in the GOES data (Fig. 2).319 Figure 9 shows the absolute vertical vorticity field at 1600 UTC. The low-level (Fig. 9a) vorticity328 shows similar structure to the field at 1400 UTC. The mid-level (Fig. 9b) vorticity shows noticeable329 curvature in the bands with positive/negative oscillations more prominent to the east of the along-330 track axis. The upper-level (Fig. 9c) vorticity field shows a vibrant multi-banded structure to the331 northeast of the system center with vorticity oscillations up to ±1×10−3𝑠−1and wavelengths of ∼332 30 km. This structure is consistent with the reflectivity field shown in Fig. 8c.333 To examine the multi-bands more closely, the model data is output at two minute intervals and344 interpolated to a track-relative grid, centered on the black line in the preceding figures, with a grid345 spacing of 2 km in the across-track and along-track dimension while keeping the native model346 vertical spacing. In addition, the along-track (𝑈𝑎) and across-track (𝑈𝑥) velocities were computed347 on this grid,348 𝑈𝑎=𝑢cos(T) + 𝑣sin(T)(5) 𝑈𝑥=𝑢sin(T) − 𝑣cos(T)(6) where 𝑢and 𝑣are the zonal and meridional velocities and 𝑇is the grid track angle of ∼75 °.349 A positive along-track velocity is moving towards increasing along-track values (looking down350 the track), while a positive across-track velocity is moving towards increasing across-track values351 (from left to right looking down the track). One snapshot of the bands at different levels is shown in352 16 Fig. 6. Horizontal cross sections of the simulated reflectivity (dBZ) in domain 1 (2.0 km grid spacing) on 1 February, 2020 at 1400 UTC. Panels (a), (b) and (c) show the 0 - 3 km, 4 - 7 km and 7 - 10 km height averaged fields, respectively. The black line in all panels denotes the along-track axis (normal to the phase lines) of multi-bands observed in subsequent figures. 320 321 322 323 the next two figures. This snapshot is representative of the multi-band structure under investigation353 and thus, multiple snapshots are not shown.354 Figure 10 shows the absolute vorticity and vertical velocity averaged over the 6 - 10 km height355 range on 1 February, 2020 at 1530 UTC. In these figures, the raw model fields are filtered with a ∼356 20 km across-track running mean and a ∼10 km along-track running mean to reduce small-scale357 variability and pull out the larger scale features that were documented in the observations. The358 sensitivity of the multi-bands to model grid spacing was analyzed by comparing the structures359 in domain 1 (2 km) and domain 2 (0.67 km). The raw fields, before filtering, clearly show360 more oscillations and larger magnitudes in several variables on the higher resolution grid, which361 17 Fig. 7. Horizontal cross sections of the simulated absolute vertical vorticity (s−1) in domain 1 (2.0 km grid spacing) on 1 February, 2020 at 1400 UTC. Panels (a), (b) and (c) show the 0 - 3 km, 4 - 7 km and 7 - 10 km height averaged fields, respectively. The black line in all panels denotes the along-track axis (normal to the phase lines) of multi-bands observed in subsequent figures. 324 325 326 327 is expected. However, after filtering the fields to the same scales noted above, the multi-band362 structure looks similar in both domains with dominant horizontal wavelengths of ∼30 km. Since363 the observations also show dominant wavelengths of ∼30 km, the fields simulated in domain 1 are364 deemed sufficient to examine the dynamics.365 The vertical velocity (Fig. 10b) displays a similar multi-banded structure as the vorticity field370 (Fig. 10a), although the vorticity perturbations are more vibrant and continuous when compared371 to the vertical velocity field. The message from Fig. 10 is that the positive phase lines of vorticity372 in the multi-bands are largely uncorrelated with the positive phase lines of vertical velocity. To373 clarify, the dashed, white lines in Fig. 10a are generally out of phase with the peaks in vertical374 18 Fig. 8. Horizontal cross sections of the simulated reflectivity (dBZ) in domain 1 (2.0 km grid spacing) on 1 February, 2020 at 1600 UTC showing the southern low pressure system with embedded multi-bands. Panels (a), (b) and (c) show the 0 - 3 km, 4 - 7 km and 7 - 10 km height averaged fields, respectively. The black, dashed circles highlight the locations of several bands identified in panel (a). These circles are copied onto the panels in (b) and (c). The black line in all panels denotes the along-track axis (normal to the phase lines) of multi-bands observed in panels (b) and (c). 334 335 336 337 338 339 velocity shown in Fig. 10b, which indicates that the stretching of pre-existing vorticity is not the375 primary driver of the vorticity oscillations.376 Figure 11a highlights a series of vorticity oscillations in the mid-levels (3 - 6 km height average)377 at the same time as Fig. 10 that have some similarities to the upper-level features, such as the378 strong anomaly at ∼75 km along-track. However, the vorticity oscillations in the mid-levels379 are substantially weaker in magnitude and not as well-defined as those in the upper levels. The380 corresponding vertical velocity field (Fig. 11b) continues to be out of phase with the vorticity381 19 Fig. 9. Horizontal cross sections of the simulated absolute vertical vorticity (s−1) in domain 1 (2.0 km grid spacing) showing the southern low pressure system with embedded multi-bands. Panels (a), (b) and (c) show the 0 - 3 km, 4 - 7 km and 7 - 10 km height averaged fields, respectively. The black line in all panels denotes the along-track axis (normal to the phase lines) of multi-bands shown in Figure ??. 340 341 342 343 with the exception of the strong anomaly at ∼75 km along-track, which is a band of convection382 closer to the system center. While there are several bands of vertical velocity between 50 - 250383 km along-track, these bands do not seem to be as organized in the across-track direction as those384 shown in the upper-levels (Fig. 10b).385 Figure 12 shows vertical cross sections of the multi-bands averaged between ±50 km across-386 track. Distinct oscillations in vorticity (Fig. 12a) are visible in the 6 - 10 km layer that extend387 from ∼50 - 300 km along track. Below 6 km, the vorticity pattern is not obvious, although some388 oscillations that are tilted down the track with height are visible in the ∼2 - 6 km layer from ∼389 125 - 200 km along-track. The vertical velocity field (Fig. 12b) shows similar oscillations to the390 20 Fig. 10. Horizontal cross sections, averaged over the 6 - 10 km height range, of simulated data on the track-relative grid revealing properties of multi-bands. Panels (a) and (b) show the simulated absolute vorticity (s−1) and vertical velocity (m s−1), respectively. The white, dashed lines highlight the positive perturbations in vorticity, which are copied onto the vertical velocity plot. 366 367 368 369 vorticity in the 6 - 10 km layer, most apparent in the negative perturbations, but the vertical velocity391 and vorticity are mostly out of phase as previously discussed. The main exception is at 75 km392 along-track, where a strong, positive vertical velocity anomaly is collocated with a strong, positive393 vorticity anomaly. This feature is part of the main rotating convective band located just northeast394 of the system center highlighted in Fig. 8 and Fig. 9. Positive correlations in vorticity and vertical395 velocity are also apparent at ∼125 km along-track below 6 km height.396 What are the dynamics governing the oscillations observed in the upper-levels of the system?397 One might suspect the perturbations are gravity waves and we evaluate that potential here. The398 total phase speed of the bands is calculated by using the two-minute model output to track the lines399 of constant phase using the across-track velocity field (shown later in Fig. 14b) averaged over ±400 21 Fig. 11. The same as in Figure 10, only for data averaged over the 3 - 6 km height range. Note the color bar has been expanded on the vertical velocity panel compared to Fig. 10b. 50 km across-track and 6 - 10 km height. Tracking these phase lines resulted in mean total phase401 speeds of 26.67 m s−1. In order to estimate the possibility of intrinsic propagation, the mean flow402 in the direction of wave propagation must be removed from the total phase speed. The vertical403 cross sections of the bands (Fig. 12) clearly show that they are present within the 6 - 10 km layer.404 Sensitivity tests in the across-track averaging interval were performed for 100 km, 200 km and405 300 km track-relative grids. These tests showed that the mean along-track velocity, averaged over406 the appropriate across-track distance and the 6 - 10 km layer were ∼27.0 ±0.5 m s−1. Thus, the407 measured intrinsic phase speed of the multi-bands in this layer is ∼0ms−1.408 For completeness, the theoretical gravity wave speed for this environment is also calculated. The409 dispersion relation for internal gravity waves is410 22 Fig. 12. Vertical cross sections of simulated data on 1 February, 2020 at 1530 UTC, averaged over the ±50 km across-track range showing (a) absolute vorticity and (b) vertical velocity. (𝜔−¯𝑢𝑘)2𝑘2+𝑚2−𝑁2𝑘2=0 (7) where 𝜔is the angular frequency, ¯𝑢is the large-scale, averaged horizontal windspeed in the411 direction of wave propagation, 𝑁is the Brunt–V¨ ais¨ al¨ a frequency, 𝑘is the horizontal wavenumber,412 and 𝑚is the vertical wavenumber.413 Rearranging Eq. (7) for the intrinsic horizontal phase speed on the left-hand-side yields414 𝜔/𝑘−¯𝑢=𝑁/√︁𝑘2+𝑚2.(8) The right-hand-side of Eq. (8) is evaluated using the data from the simulation. Note that the415 buoyancy frequency was estimated to be 50 times larger than the Coriolis frequency and thus, the416 potential gravity waves are not significantly affected by the Earth’s rotation. Taking an average417 of data over the system at two different time periods and in the 6 - 10 km layer produced values418 of 𝑁around 10−2s−1. The dominant horizontal wavelength in the model is ∼30 km and the419 23 Fig. 13. Vertical cross sections of simulated data on 1 February, 2020 at 1530 UTC, averaged over the ±50 km across-track range showing (a) perturbation vertical velocity (m s−1) and (b) perturbation reflectivity (dBZ). The black arrows in panel (a) denote features discussed in the text. 427 428 429 vertical wavelength is taken to be twice the depth of the perturbations, which equates to 8 km.420 Entering these numbers produces a horizontal phase speed of 12.30 m s−1, which is representative421 of the bands propagating down the track-relative grid to the northeast of the system center. It is422 clear from this calculation that the measured intrinsic phase speeds have a large mismatch with423 the theoretical intrinsic phase speeds for internal gravity waves, even with significant uncertainty424 bounds in various parameters. Thus, the observed multi-bands in the upper-levels cannot be gravity425 waves.426 However, there are more subtle oscillations in several variables in the low to middle levels of430 the system that are revealed through examining perturbation fields. In this analysis, perturbations431 are defined as deviations of the total variables from the 50 km along-track filtered variables. The432 perturbation vertical velocity at 1530 UTC (Fig. 13a) shows the prominent multi-bands in the 6433 24 - 10 km layer along with weaker perturbations in the ∼0 - 6 km layer denoted by black arrows.434 The weaker oscillations exhibit amplitudes approximately three to four times lower than those in435 the upper layer, making them clearly distinguishable despite the similar wavelengths of ∼30 km.436 Animations of vertical velocity (not shown) appear to show these waves emanating from the deep437 convection present at ∼75 km along-track. The perturbation reflectivity (Fig. 13b) is largely438 consistent with the vertical velocity except the low to middle level oscillations are about ten times439 lower in amplitude than the upper layer waves. This is why the multi-bands are not as visible in440 the low-level precipitation field as shown by the reflectivity (Fig. 8a).441 The low to middle level waves (0 - 6 km layer) were tracked in the perturbation vertical velocity442 field with the two minute model output and the total phase speeds were measured. This procedure443 produced total wave phase speeds of ∼30 ±3 m/s. The along-track velocity was averaged across-444 track (±50 km), along-track (0 - 342 km) and height (0 - 6 km) to represent the mean flow moving445 the waves, which resulted in values of ∼14 ±0.5 m/s. Thus, the measured intrinsic phase speeds of446 the waves were ∼16 m/s. The theoretical intrinsic phase speeds for gravity waves were computed447 using the same inputs as before with the exception of a 12 km vertical wavelength (two times the448 6 km depth of the vertical velocity perturbations). These inputs produced values of 17.73 m/s,449 which is close to the measured intrinsic phase speed of ∼16 m/s. Thus, these low to middle level450 waves can be identified as internal gravity waves that are being generated by the convective activity451 closer to the system center.452 If the dominant, upper-level multi-bands are not gravity waves, what is driving their dynamics?456 Figure 14 shows vertical cross sections of the along-track velocity and across-track velocity. The457 along-track velocity (Fig. 14a) shows a jet centered at ∼11 km height with large values of vertical458 shear (maximum values of 0.01 s−1) located between 8 - 10 km height and most notably between459 50 - 225 km along-track. The locations of the large vertical wind shear values match well with460 the locations of the wave motions associated with the multi-bands. For example, the across-track461 velocity (Fig. 14b) reveals clear wave motions in the 6 - 10 km layer and between 50 - 250 km462 along-track. There are perhaps extensions of the wave motions down to ∼4 - 5 km in some regions,463 but overall, the oscillations become less detectable below 6 km height.464 The along-track and across-track velocity fields shown in Fig. 14 match well with the EXRAD465 observations shown in Fig. 4, despite the differences in spatial/temporal coverage (also note the466 25 Acknowledgments. The IMPACTS field campaign and the work of author Guimond are supported590 by the NASA Earth Venture Suborbital (EVS) program and NASA grant 80NSSC24K0302. Author591 Guimond thanks the IMPACTS team members for organizing the campaign, providing forecasting592 support, coordinating the flights and collecting the data. Many thanks are given to Dr. Paul Reasor593 for multiple, lengthy discussions on the work that improved this paper considerably. Feedback on594 the gravity wave analysis from Dr. Steven Koch is also greatly appreciated.595 Data availability statement. 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