Gene a ed using he o icial AMS L
A
T
EX empla e 6.1
Shea -D i en Ins abili ies as he O igin o Mul i-Banded Cloud and1
P ecipi a ion S uc u es in an Ex a opical Cyclone2
S ephen R. Guimonda
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aDepa men o A mosphe ic and Plane a y Sciences and Se e e Wea he Resea ch Cen e ,
Hamp on Uni e si y, Hamp on, VA, USA
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Co esponding au ho : S ephen R. Guimond, [email p o ec ed]6
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ABSTRACT: This pape in es iga es he dynamics go e ning mul i-banded cloud and p ecipi a ion
in ex a opical cyclones h ough a case s udy om he NASA In es iga ion o Mic ophysics
and P ecipi a ion o A lan ic Coas -Th ea ening Snows o ms (IMPACTS) ield campaign. On
1 Feb ua y 2020, a low-p essu e sys em eme ged o he No h Ca olina coas a 1200 UTC,
deepening by 7 hPa in six hou s as i accele a ed no heas o e he A lan ic. High- esolu ion
GOES isible image y e ealed mul iple bands o high- e lec ance cloud o he no h/no heas o
he cen e , along wi h clus e s o con ec i e cells close o he co e. Wa ele analysis iden i ied
a dominan mul i-band wa eleng h o 30 km and a seconda y peak a 15-20 km. Ai bo ne ada
measu emen s om IMPACTS ligh s showed deep con ec ion nea he cen e and na ow, ele a ed
e lec i i y bands linked o he mul i-band ea u es a he ou . Nume ical simula ions ep oduced
he mul i-bands, enabling explo a ion o hei dynamical o igin. In insic phase speed calcula ions
e ealed ha , con a y o se e al p e ious s udies, he dominan mul i-bands we e no g a i y
wa es. Ins ead, he ea u es we e iden i ied as dynamic ins abili ies (Kel in–Helmhol z ins abili y)
a ising om e ical wind shea and low Richa dson numbe s nea he uppe -le el ou low. G a i y
wa es we e p esen in he low o mid le els (0–6 km) gene a ed by con ec ion, bu hey did no
accoun o he s ong pe u ba ions in he mid o uppe le els (6–10 km). This s udy p esen s new
scien i ic insigh in o he go e ning dynamics o mul i-banded s uc u es in ex a opical cyclones
ha highligh s he ole o shea -d i en ins abili ies.
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SIGNIFICANCE STATEMENT: Ex a opical cyclones along he Uni ed S a es Eas Coas can25
p oduce in ense bands o snow and o he ypes o p ecipi a ion ha cause a el chaos and po en ial26
loss o li e. In his wo k, a s o m o his ype was s udied using NASA ai c a and sa elli e27
da a as well as compu e simula ions. The esul s show ha he s o m bands we e no caused by28
a mosphe ic wa es, as scien is s o en hough , bu by sha p changes in he wind speed wi h heigh 29
called shea . This shea c ea ed uns able laye s ha olled and mixed he ai , o ming o ganized30
cloud and p ecipi a ion pa e ns. Unde s anding hese undamen al physical p ocesses can help31
o ecas e s be e p edic when and whe e hea y snow bands will o m, imp o ing wa nings and32
public sa e y.33
1. In oduc ion34
Banded s uc u es in ex eme wea he sys ems a e pe u ba ions o a balanced, backg ound35
low ha can o ganize and concen a e a iables such as mois u e, momen um, and ene gy. In36
ex a opical cyclones (ETCs), he ocus o his pape , he concen a ion o hese a iables can37
lead o in ense bands o mul i-phase p ecipi a ion a he su ace ha a e di icul o measu e,38
model and p edic wi h signi ican consequences o socie y. Fo example, snow all associa ed39
wi h ETCs in he win e mon hs can o en o ganize in o mul iple bands ha d op la ge amoun s40
o snow in a sho ime causing ehicle c ashes, ligh cancella ions and shu downs o schools and41
businesses. The cu en unde s anding o he dynamical p ocesses con olling he o ma ion and42
e olu ion o hese p ecipi a ion mul i-bands (as opposed o a single, la ge-scale band) and hei 43
ep esen a ion/p edic abili y in nume ical models is e y limi ed. These limi a ions we e pa o he44
mo i a ing ac o s o he ecen ly comple ed In es iga ion o Mic ophysics and P ecipi a ion o 45
A lan ic Coas -Th ea ening Snows o ms (IMPACTS; ?) ield expe imen , which sough o imp o e46
he unde s anding o p ecipi a ion mul i-bands in ETCs om a ious pe spec i es.47
?used ada obse a ions, soundings, and eanalysis da a o examine he en i onmen s con aining48
banded s uc u es in a la ge se o ETC win e s o ms. They ound ha mul i-bands we e no well49
co ela ed wi h on ogene ical o cing and associa ed de o ma ion zones. This esul is consis en 50
wi h he no ion ha de o ma ion alone canno explain he egula , oscilla o y na u e o he a ious51
ields connec ed o mul i-bands. The au ho s also examined he p esence o condi ional symme ic52
ins abili y (CSI) in he en i onmen o a ious ypes o banded s uc u es. While CSI was p esen 53
3
in he as majo i y o banded cases, he e was no clea sepa a ion be ween single, la ge-scale bands54
and he smalle -scale, mul i-band s uc u es. This sugges s ha CSI may no be he undamen al55
p ope y unde lying he o ma ion and e olu ion o mul i-bands.56
In hei e iew pape , ?no ed ha he banding o clouds and p ecipi a ion in ETCs appea s o57
be weakly ela ed o CSI. ?used a iscous o m o he Sawye -Eliassen equa ion o unde s and58
banding mechanisms associa ed wi h on ogene ical o cing. Fo b oad o cing and nega i e mois 59
po en ial o ici y, which is a condi ion ha e lec s he p esence o CSI, mul iple bands de elop60
wi h an in ensi y ha scales wi h he deg ee o ins abili y. Howe e , i is no clea om he heo y61
o ?exac ly how CSI coupled wi h mois u e and li , associa ed wi h on ogenesis, would p oduce62
he egula ly spaced bands o clouds and p ecipi a ion obse ed in he eal a mosphe e. In an63
uns able en i onmen , pa cels a e accele a ed exponen ially in he di ec ion o he displacemen 64
and do no main ain an oscilla o y beha io .65
?and ?desc ibed se e al condi ions ha should be me o associa e p ecipi a ion mul i-bands66
wi h CSI. One o he key equi emen s is ha he bands ha e no in insic p opaga ion as hey should67
be mo ing di ec ly wi h he en i onmen al low. Howe e , se e al s udies o mul i-bands do show68
in insic p opaga ion, which when coupled wi h he desc ip ion abo e, ques ion he ole o CSI in69
he band dynamics.70
Ano he possible culp i o mul i-bands is he p esence o a wa e phenomenon o o ganize he71
oscilla ions in he s a e a iables and p o ide he li necessa y o elease any ype o ins abili y72
in he en i onmen . Se e al p e ious s udies ha e ocused on he ole o g a i y wa es as he73
mechanism o o ganizing he cloud and p ecipi a ion ields in o mul i-band s uc u es in ETCs74
(e.g., ???). These wa es can be gene a ed om low imbalances (e.g., associa ed wi h uppe -75
le el je s), con ec i e pe u ba ions, and/o low o e opog aphy. ?documen ed la ge-ampli ude76
mesoscale g a i y wa es (wa eleng hs o 200 - 260 km) du ing se e al win e s o ms using ime77
se ies o su ace p essu e and wind measu emen s. These g a i y wa es we e ound o o igina e a 78
uppe le els om je s eak imbalances and he associa ed geos ophic adjus men p ocess (e.g., ?).79
Fo la ge-ampli ude wa es, a su ace e lec ion o he uppe -le el pe u ba ion ene gy was de ec ed80
and hypo hesized o become apped a lowe -le els due o s ong s a ic s abili y (“wa e duc ing”;81
?). This wa e duc ing allows o a longe esidence ime o he g a i y wa e ene gy in he lowe 82
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le els o he a mosphe e esul ing in he po en ial o o ganized clouds and p ecipi a ion as shown83
by sa elli e and ada ins umen s.84
?also highligh ed he ole o mesoscale (∼200 km) g a i y wa es using nume ical simula ions o 85
an ETC using a ious esolu ions down o 4 km spacing. The au ho s p oposed a concep ual model86
o he gene a ion and e olu ion o mesoscale g a i y wa es based on hese simula ions. Fi s , he87
wa es we e ini ia ed in he uppe le els o he sys em om he geos ophic adjus men p ocess.88
Then, con ec ion associa ed wi h he on al ea u es and local ins abili y anspo ed some o he89
g a i y wa e ene gy owa ds he su ace whe e i can be duc ed wi hin a s a ically s able laye . This90
duc ed wa e hen in e ac s wi h he mois u e ield o c ea e a con ec i ely-coupled wa e ha can91
be main ained and possibly ampli ied o e a signi ican amoun o ime.92
Se e al ques ions and unce ain ies come o mind ega ding he applicabili y o hese p e ious93
g a i y wa e s udies o he gene al p oblem o ETC mul i-bands. How does con ec i e ac i i y94
p e e en ially anspo he wa e ene gy ini ia ed a uppe le els (nea he opopause) downwa d95
o low le els and keep he wa e in ac ? The p esence o a s ong s a ic s abili y laye a lowe 96
le els and e lec ing laye abo e o enable wa e duc ing appea s o be a special se o ci cums ances97
and i is no clea how his laye can be o med and main ained in egions o he sys em ha a e98
con ec i ely ac i e.99
The goals o he p esen s udy a e: (1) To de e mine he key s uc u es and spa ial/ empo al scales100
o mul i-banded p ecipi a ion ea u es in ETCs and (2) To de e mine he o igin and dynamical101
p ocesses associa ed wi h hese bands. To add ess he abo e goals and de elop po en ially new102
unde s anding o ETC mul i-bands, a case s udy om he NASA IMPACTS ield campaign is103
analyzed wi h mul i-scale nume ical simula ions and a a ie y o emo e sensing measu emen s.104
Case s udies a e an impo an i s s ep owa ds de eloping a deep, holis ic unde s anding o a105
physical p ocess, which hen allows ha unde s anding o be es ed mo e b oadly on a la ge 106
collec ion o sys ems. The echnical no el ies o he p esen wo k a e in he s udy o mode n107
emo e sensing measu emen s and nume ical models along wi h some new me hods o analysis o108
he p oblem o ETC mul i-bands.109
5

Fig. 1. Synop ic maps o mean sea le el p essu e and on al analysis on 1 Feb ua y, 2020 a (a) 1200 UTC and
(b) 1800 UTC.
2. B ie o e iew o ex a opical sys em110
Du ing he win e o 2020, NASA o ganized he i s phase o a mul i-yea e o called IMPACTS111
o s udy he mic ophysics and dynamics o ETCs wi h a ocus on unde s anding banded egions o 112
p ecipi a ion. On 1 Feb ua y 2020, a double su ace low-p essu e sys em along a s a iona y on 113
o med o he coas o he Ca olinas wi h he sou he n low s a ing o a ∼1006 hPa on 1200114
UTC 1 Feb ua y (Fig.1a). Du ing he nex 6 hou s, he sou he n low in ensi ied o 999 hPa a 115
1800 UTC 1 Feb ua y (Fig.1b) and o 998 hPa a 0000 UTC 2 Feb ua y (no shown). Du ing his116
pe iod, mul iple bands o con ec i e clouds and p ecipi a ion o med o he no h and no heas 117
o he sou he n low-p essu e cen e , which allowed de ailed s udy o hei cha ac e is ics. Fligh s118
om he NASA P-3 and ER-2 ai c a occu ed du ing ∼1200 - 1800 UTC 1 Feb ua y sampling119
he en i onmen and banded ea u es associa ed wi h he sou he n low.120
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3. Da a and p ocessing121
a. EXRAD122
The ER-2 X-band Dopple Rada (EXRAD) is an X-band, downwa d-poin ing ai bo ne ada 123
ha measu es ada e lec i i y and Dopple eloci y om hyd ome eo s wi h wo beams and ∼20124
m ga e spacing. The i s beam is ixed and poin s nominally a nadi , while he second beam scans125
conically a 20 e olu ions pe minu e a a nominal incidence angle o 32°. F om he al i ude o 126
he NASA ER-2 ai c a (∼20 km), he swa h wid h a he i s le el o use ul da a is ∼23 km.127
The EXRAD scanning beam main- and side-lobes in e ac s ongly wi h he ocean su ace and128
con amina e he p ecipi a ion signal below abou 1 km heigh . The sampling o p ecipi a ion om129
he scanning beam is ∼500 m along- ack and ∼2°in azimu h while he nadi beam along- ack130
sampling is ∼50 m.131
Calcula ions o he h ee-dimensional (3D) wind ield using he EXRAD scanning beam a e132
pe o med using he 3D a ia ional algo i hm desc ibed in ?. The e ie al g id is se o 500 m in133
he ho izon al dimensions and 250 m in he e ical dimension. Fine g id spacing in he e ical134
is possible, bu was no deemed necessa y. A wo o h ee g id poin unning mean il e is applied135
o he aw e ie als in pos -p ocessing o emo e nume ical noise. The e ec i e esolu ion o 136
he wind ields p oduced om he algo i hm has been analyzed wi h la ge eddy simula ions in ?.137
Resul s show ha scales o 5 Δ𝑥and la ge a e ully esol ed, which ansla es o 2.5 km o he138
p esen s udy. Scales below his h eshold, down o he g id scale, a e subjec o inc easing kine ic139
ene gy a enua ion.140
Quali y con ol has been pe o med on he wind ields o emo e da a wi h low signal- o-noise141
a ios and high unce ain ies. While a combina ion o pa ame e s ha e been s udied, he bes quali y142
ields we e ound by emo ing da a wi h s anda d de ia ions la ge han 6 m/s (e o s a is ics a e143
compu ed as pa o he wind algo i hm, see ?). The da a p esen ed in his pape ha e his h eshold144
applied. Valida ion o he EXRAD 3D winds wi h ligh le el in-si u da a om he NASA ER-2145
ai c a du ing IMPACTS 2020 ha e been pe o med. This alida ion showed zonal wind oo 146
mean squa e e o s (RMSEs) o 3.99 m/s wi h a co ela ion coe icien o 0.92. Fo he me idional147
wind, he RMSEs a e 4.53 m/s wi h a co ela ion coe icien o 0.89. These s a is ics a e collec ed148
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a a ious loca ions ac oss he ada swa h and o di e en ime o se s. Fu he in o ma ion abou 149
hese e o s a is ics and he EXRAD scanning beam wind e ie als can be ound in (?).150
Fo scien i ic analysis, he EXRAD scanning beam is used o p esen he ho izon al wind ield,151
while he nadi beam is used o display he e ical wind ield, since i has highe quali y. Se e al152
co ec ions o he nadi beam Dopple eloci ies a e needed be o e he e ical eloci y can be153
analyzed o science. The exp ession o he nadi beam Dopple eloci y (𝑉𝑑) is gi en by154
𝑉𝑑=®
𝑉𝑤·ˆ𝑒−®
𝑉𝑔·ˆ𝑒+𝑉𝑛(1)
whe e 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 𝑉𝑛 ep esen s he e ec s o non-uni o m beam illing.156
In hese equa ions x,y,z a e he Ea h- ela i e coo dina es o he ada pulse olumes (?), is157
he ange, u, ,w a e he componen s o he Ea h- ela i e wind, 𝑣𝑡is he hyd ome eo allspeed,158
𝐺𝑆ℎ,𝐺𝑆𝑣a e he ho izon al and e ical componen s o he ai c a g ound speed and Tis he159
ai c a ack angle.160
Sol ing o he e ical eloci y yields,161
𝑤=(𝑉𝑑−𝑉𝑛+®
𝑉𝑔·ˆ𝑒)𝑟−𝑢𝑥 −𝑣𝑦
𝑧−𝑣𝑡.(4)
The calcula ion o hyd ome eo allspeeds om he e lec i i y measu emen s ollows he s udies162
o ?and ?. The non-uni o m beam illing e ec s a e emo ed om he Dopple eloci ies163
ollowing ?. Ai c a mo ion can esul in an enna poin ing angles ha in e cep he ho izon al164
wind ield, con amina ing he e ical winds. The ho izon al wind ields compu ed om he165
EXRAD scanning beam, desc ibed abo e, a e used o emo e his con amina ion om he nadi 166
beam ollowing equa ion 4.167
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b. GOES-16168
High spa ial and empo al esolu ion image y o clouds om he ad anced baseline image on169
he Geos a iona y Ope a ional En i onmen al Sa elli e (GOES) - 16 sa elli e a isible and in a ed170
wa eleng hs a e used o ack banded s uc u es. Speci ically, e lec ance da a om he isible171
(channel 2) band a 500 m pixel spacing and 60 s ime upda es is u ilized. This ine sampling in172
space and ime p o ides he de ailed s uc u e o he cloud li ecycle as well as he o ganiza ion and173
e olu ion in o mul i-bands.174
c. Nume ical Simula ions175
The Wea he Resea ch and Fo ecas ing (WRF) model e sion 4.2 wi h he ad anced esea ch176
dynamic co e is u ilized o p o ide con ex o he obse a ions. Fou domains a e u ilized wi h177
a la ge, pa en domain a 2 km g id spacing (domain 1) co e ing he ull mo emen o he low-178
p essu e sys em and banded ea u es on 1 Feb ua y 2020. Th ee nes ed domains a 0.667 km179
(domain 2), 0.222 km (domain 3) and 0.074 km (domain 4) g id spacing we e placed o he No h180
and No heas o he low cen e o y and cap u e he ine scales o he mul i-bands. All domains181
u ilize 121 s e ched e ical le els wi h a spacing o ∼75 m a he su ace, ∼200 m a 10 km182
heigh and ∼900 m nea he model op a 20 km heigh .183
Po ions o he mul i-bands we e cap u ed in domains 2 and 3, bu no domain 4. The ocus o 184
he pape is on domain 1 o a ew easons. Fi s , his domain cap u es he en i e y o he sys em,185
which allows bo h la ge-scale and mesoscale ea u es o be analyzed. Second, he wa eleng hs186
o dominan ea u es ound in he obse a ions a e 15-20 km and ∼30 km, which should be well187
esol ed by he 2 km domain gi en he ∼7 - 8 Δ𝑥nume ical dissipa ion ange o WRF (e.g., ?).188
The highe esolu ion domains we e analyzed as pa o his esea ch and will be no ed whe e189
app op ia e.190
The se up o he model is as ollows. The NCEP Global Da a Assimila ion Sys em (GDAS)/Final191
(FNL) ope a ional global analyses a 0.25 °spacing and 6 h empo al spacing a e used as he ini ial192
and bounda y condi ions o he simula ion. This widely used sys em combines he Global Fo ecas 193
Sys em (GFS) model wi h a ious synop ic-scale obse a ions o achie e an op imal s a e o he194
a mosphe e. Fo he 2 km pa en domain he ollowing sub-g id physics schemes we e chosen:195
Thompson o mic ophysics, YSU o bounda y laye ( e ical di usion), Smago insky-2D o 196
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Two hou s la e a 1600 UTC, he same ields ha e changed signi ican ly. The low-le el e lec i i y310
(Fig. 8a) e eals h ee bands o ien ed a di e en angles and deno ed wi h dashed, black ci cles.311
The mid-le el e lec i i y (Fig. 8b) shows some signa u es o he low-le el bands, such as he312
sou he nmos ci cled egion, bu o he bands o he no h do no ha e he same o ien a ion. These313
bands a e o ien ed app oxima ely pe pendicula o he along- ack axis ha deno es he axis o 314
band p opaga ion. The uppe -le el e lec i i y (Fig. 8c) shows na ow signa u es o mul i-bands315
ha ex end om nea he sys em cen e ou o app oxima ely 300 km adius. The wa eleng hs316
o he e lec i i y bands in Fig. 8 a e ∼30 km, which is e y simila o hose documen ed om317
he GOES da a, shown by he wa ele analysis in Fig. 5. The mul i-bands p esen in he model318
e lec i i y appea simila o hose obse ed in he GOES da a (Fig. 2).319
Figu e 9 shows he absolu e e ical o ici y ield a 1600 UTC. The low-le el (Fig. 9a) o ici y328
shows simila s uc u e o he ield a 1400 UTC. The mid-le el (Fig. 9b) o ici y shows no iceable329
cu a u e in he bands wi h posi i e/nega i e oscilla ions mo e p ominen o he eas o he along-330
ack axis. The uppe -le el (Fig. 9c) o ici y ield shows a ib an mul i-banded s uc u e o he331
no heas o he sys em cen e wi h o ici y oscilla ions up o ±1×10−3𝑠−1and wa eleng hs o ∼332
30 km. This s uc u e is consis en wi h he e lec i i y ield shown in Fig. 8c.333
To examine he mul i-bands mo e closely, he model da a is ou pu a wo minu e in e als and344
in e pola ed o a ack- ela i e g id, cen e ed on he black line in he p eceding igu es, wi h a g id345
spacing o 2 km in he ac oss- ack and along- ack dimension while keeping he na i e model346
e ical spacing. In addi ion, he along- ack (𝑈𝑎) and ac oss- ack (𝑈𝑥) eloci ies we e compu ed347
on his g id,348
𝑈𝑎=𝑢cos(T) + 𝑣sin(T)(5)
𝑈𝑥=𝑢sin(T) − 𝑣cos(T)(6)
whe e 𝑢and 𝑣a e he zonal and me idional eloci ies and 𝑇is he g id ack angle o ∼75 °.349
A posi i e along- ack eloci y is mo ing owa ds inc easing along- ack alues (looking down350
he ack), while a posi i e ac oss- ack eloci y is mo ing owa ds inc easing ac oss- ack alues351
( om le o igh looking down he ack). One snapsho o he bands a di e en le els is shown in352
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Fig. 6. Ho izon al c oss sec ions o he simula ed e lec i i y (dBZ) in domain 1 (2.0 km g id spacing)
on 1 Feb ua y, 2020 a 1400 UTC. Panels (a), (b) and (c) show he 0 - 3 km, 4 - 7 km and 7 - 10 km heigh
a e aged ields, espec i ely. The black line in all panels deno es he along- ack axis (no mal o he phase lines)
o mul i-bands obse ed in subsequen igu es.
320
321
322
323
he nex wo igu es. This snapsho is ep esen a i e o he mul i-band s uc u e unde in es iga ion353
and hus, mul iple snapsho s a e no shown.354
Figu e 10 shows he absolu e o ici y and e ical eloci y a e aged o e he 6 - 10 km heigh 355
ange on 1 Feb ua y, 2020 a 1530 UTC. In hese igu es, he aw model ields a e il e ed wi h a ∼356
20 km ac oss- ack unning mean and a ∼10 km along- ack unning mean o educe small-scale357
a iabili y and pull ou he la ge scale ea u es ha we e documen ed in he obse a ions. The358
sensi i i y o he mul i-bands o model g id spacing was analyzed by compa ing he s uc u es359
in domain 1 (2 km) and domain 2 (0.67 km). The aw ields, be o e il e ing, clea ly show360
mo e oscilla ions and la ge magni udes in se e al a iables on he highe esolu ion g id, which361
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Fig. 7. Ho izon al c oss sec ions o he simula ed absolu e e ical o ici y (s−1) in domain 1 (2.0 km g id
spacing) on 1 Feb ua y, 2020 a 1400 UTC. Panels (a), (b) and (c) show he 0 - 3 km, 4 - 7 km and 7 - 10 km
heigh a e aged ields, espec i ely. The black line in all panels deno es he along- ack axis (no mal o he phase
lines) o mul i-bands obse ed in subsequen igu es.
324
325
326
327
is expec ed. Howe e , a e il e ing he ields o he same scales no ed abo e, he mul i-band362
s uc u e looks simila in bo h domains wi h dominan ho izon al wa eleng hs o ∼30 km. Since363
he obse a ions also show dominan wa eleng hs o ∼30 km, he ields simula ed in domain 1 a e364
deemed su icien o examine he dynamics.365
The e ical eloci y (Fig. 10b) displays a simila mul i-banded s uc u e as he o ici y ield370
(Fig. 10a), al hough he o ici y pe u ba ions a e mo e ib an and con inuous when compa ed371
o he e ical eloci y ield. The message om Fig. 10 is ha he posi i e phase lines o o ici y372
in he mul i-bands a e la gely unco ela ed wi h he posi i e phase lines o e ical eloci y. To373
cla i y, he dashed, whi e lines in Fig. 10a a e gene ally ou o phase wi h he peaks in e ical374
18
Fig. 8. Ho izon al c oss sec ions o he simula ed e lec i i y (dBZ) in domain 1 (2.0 km g id spacing) on
1 Feb ua y, 2020 a 1600 UTC showing he sou he n low p essu e sys em wi h embedded mul i-bands. Panels
(a), (b) and (c) show he 0 - 3 km, 4 - 7 km and 7 - 10 km heigh a e aged ields, espec i ely. The black, dashed
ci cles highligh he loca ions o se e al bands iden i ied in panel (a). These ci cles a e copied on o he panels in
(b) and (c). The black line in all panels deno es he along- ack axis (no mal o he phase lines) o mul i-bands
obse ed in panels (b) and (c).
334
335
336
337
338
339
eloci y shown in Fig. 10b, which indica es ha he s e ching o p e-exis ing o ici y is no he375
p ima y d i e o he o ici y oscilla ions.376
Figu e 11a highligh s a se ies o o ici y oscilla ions in he mid-le els (3 - 6 km heigh a e age)377
a he same ime as Fig. 10 ha ha e some simila i ies o he uppe -le el ea u es, such as he378
s ong anomaly a ∼75 km along- ack. Howe e , he o ici y oscilla ions in he mid-le els379
a e subs an ially weake in magni ude and no as well-de ined as hose in he uppe le els. The380
co esponding e ical eloci y ield (Fig. 11b) con inues o be ou o phase wi h he o ici y381
19
Fig. 9. Ho izon al c oss sec ions o he simula ed absolu e e ical o ici y (s−1) in domain 1 (2.0 km g id
spacing) showing he sou he n low p essu e sys em wi h embedded mul i-bands. Panels (a), (b) and (c) show he
0 - 3 km, 4 - 7 km and 7 - 10 km heigh a e aged ields, espec i ely. The black line in all panels deno es he
along- ack axis (no mal o he phase lines) o mul i-bands shown in Figu e ??.
340
341
342
343
wi h he excep ion o he s ong anomaly a ∼75 km along- ack, which is a band o con ec ion382
close o he sys em cen e . While he e a e se e al bands o e ical eloci y be ween 50 - 250383
km along- ack, hese bands do no seem o be as o ganized in he ac oss- ack di ec ion as hose384
shown in he uppe -le els (Fig. 10b).385
Figu e 12 shows e ical c oss sec ions o he mul i-bands a e aged be ween ±50 km ac oss-386
ack. Dis inc oscilla ions in o ici y (Fig. 12a) a e isible in he 6 - 10 km laye ha ex end387
om ∼50 - 300 km along ack. Below 6 km, he o ici y pa e n is no ob ious, al hough some388
oscilla ions ha a e il ed down he ack wi h heigh a e isible in he ∼2 - 6 km laye om ∼389
125 - 200 km along- ack. The e ical eloci y ield (Fig. 12b) shows simila oscilla ions o he390
20
Fig. 10. Ho izon al c oss sec ions, a e aged o e he 6 - 10 km heigh ange, o simula ed da a on he
ack- ela i e g id e ealing p ope ies o mul i-bands. Panels (a) and (b) show he simula ed absolu e o ici y
(s−1) and e ical eloci y (m s−1), espec i ely. The whi e, dashed lines highligh he posi i e pe u ba ions in
o ici y, which a e copied on o he e ical eloci y plo .
366
367
368
369
o ici y in he 6 - 10 km laye , mos appa en in he nega i e pe u ba ions, bu he e ical eloci y391
and o ici y a e mos ly ou o phase as p e iously discussed. The main excep ion is a 75 km392
along- ack, whe e a s ong, posi i e e ical eloci y anomaly is colloca ed wi h a s ong, posi i e393
o ici y anomaly. This ea u e is pa o he main o a ing con ec i e band loca ed jus no heas 394
o he sys em cen e highligh ed in Fig. 8 and Fig. 9. Posi i e co ela ions in o ici y and e ical395
eloci y a e also appa en a ∼125 km along- ack below 6 km heigh .396
Wha a e he dynamics go e ning he oscilla ions obse ed in he uppe -le els o he sys em?397
One migh suspec he pe u ba ions a e g a i y wa es and we e alua e ha po en ial he e. The398
o al phase speed o he bands is calcula ed by using he wo-minu e model ou pu o ack he lines399
o cons an phase using he ac oss- ack eloci y ield (shown la e in Fig. 14b) a e aged o e ±400
21

Fig. 11. The same as in Figu e 10, only o da a a e aged o e he 3 - 6 km heigh ange. No e he colo ba has
been expanded on he e ical eloci y panel compa ed o Fig. 10b.
50 km ac oss- ack and 6 - 10 km heigh . T acking hese phase lines esul ed in mean o al phase401
speeds o 26.67 m s−1. In o de o es ima e he possibili y o in insic p opaga ion, he mean low402
in he di ec ion o wa e p opaga ion mus be emo ed om he o al phase speed. The e ical403
c oss sec ions o he bands (Fig. 12) clea ly show ha hey a e p esen wi hin he 6 - 10 km laye .404
Sensi i i y es s in he ac oss- ack a e aging in e al we e pe o med o 100 km, 200 km and405
300 km ack- ela i e g ids. These es s showed ha he mean along- ack eloci y, a e aged o e 406
he app op ia e ac oss- ack dis ance and he 6 - 10 km laye we e ∼27.0 ±0.5 m s−1. Thus, he407
measu ed in insic phase speed o he mul i-bands in his laye is ∼0ms−1.408
Fo comple eness, he heo e ical g a i y wa e speed o his en i onmen is also calcula ed. The409
dispe sion ela ion o in e nal g a i y wa es is410
22
Fig. 12. Ve ical c oss sec ions o simula ed da a on 1 Feb ua y, 2020 a 1530 UTC, a e aged o e he ±50 km
ac oss- ack ange showing (a) absolu e o ici y and (b) e ical eloci y.
(𝜔−¯𝑢𝑘)2𝑘2+𝑚2−𝑁2𝑘2=0 (7)
whe e 𝜔is he angula equency, ¯𝑢is he la ge-scale, a e aged ho izon al windspeed in he411
di ec ion o wa e p opaga ion, 𝑁is he B un –V¨
ais¨
al¨
a equency, 𝑘is he ho izon al wa enumbe ,412
and 𝑚is he e ical wa enumbe .413
Rea anging Eq. (7) o he in insic ho izon al phase speed on he le -hand-side yields414
𝜔/𝑘−¯𝑢=𝑁/√︁𝑘2+𝑚2.(8)
The igh -hand-side o Eq. (8) is e alua ed using he da a om he simula ion. No e ha he415
buoyancy equency was es ima ed o be 50 imes la ge han he Co iolis equency and hus, he416
po en ial g a i y wa es a e no signi ican ly a ec ed by he Ea h’s o a ion. Taking an a e age417
o da a o e he sys em a wo di e en ime pe iods and in he 6 - 10 km laye p oduced alues418
o 𝑁a ound 10−2s−1. The dominan ho izon al wa eleng h in he model is ∼30 km and he419
23
Fig. 13. Ve ical c oss sec ions o simula ed da a on 1 Feb ua y, 2020 a 1530 UTC, a e aged o e he ±50
km ac oss- ack ange showing (a) pe u ba ion e ical eloci y (m s−1) and (b) pe u ba ion e lec i i y (dBZ).
The black a ows in panel (a) deno e ea u es discussed in he ex .
427
428
429
e ical wa eleng h is aken o be wice he dep h o he pe u ba ions, which equa es o 8 km.420
En e ing hese numbe s p oduces a ho izon al phase speed o 12.30 m s−1, which is ep esen a i e421
o he bands p opaga ing down he ack- ela i e g id o he no heas o he sys em cen e . I is422
clea om his calcula ion ha he measu ed in insic phase speeds ha e a la ge misma ch wi h423
he heo e ical in insic phase speeds o in e nal g a i y wa es, e en wi h signi ican unce ain y424
bounds in a ious pa ame e s. Thus, he obse ed mul i-bands in he uppe -le els canno be g a i y425
wa es.426
Howe e , he e a e mo e sub le oscilla ions in se e al a iables in he low o middle le els o 430
he sys em ha a e e ealed h ough examining pe u ba ion ields. In his analysis, pe u ba ions431
a e de ined as de ia ions o he o al a iables om he 50 km along- ack il e ed a iables. The432
pe u ba ion e ical eloci y a 1530 UTC (Fig. 13a) shows he p ominen mul i-bands in he 6433
24
- 10 km laye along wi h weake pe u ba ions in he ∼0 - 6 km laye deno ed by black a ows.434
The weake oscilla ions exhibi ampli udes app oxima ely h ee o ou imes lowe han hose in435
he uppe laye , making hem clea ly dis inguishable despi e he simila wa eleng hs o ∼30 km.436
Anima ions o e ical eloci y (no shown) appea o show hese wa es emana ing om he deep437
con ec ion p esen a ∼75 km along- ack. The pe u ba ion e lec i i y (Fig. 13b) is la gely438
consis en wi h he e ical eloci y excep he low o middle le el oscilla ions a e abou en imes439
lowe in ampli ude han he uppe laye wa es. This is why he mul i-bands a e no as isible in440
he low-le el p ecipi a ion ield as shown by he e lec i i y (Fig. 8a).441
The low o middle le el wa es (0 - 6 km laye ) we e acked in he pe u ba ion e ical eloci y442
ield wi h he wo minu e model ou pu and he o al phase speeds we e measu ed. This p ocedu e443
p oduced o al wa e phase speeds o ∼30 ±3 m/s. The along- ack eloci y was a e aged ac oss-444
ack (±50 km), along- ack (0 - 342 km) and heigh (0 - 6 km) o ep esen he mean low mo ing445
he wa es, which esul ed in alues o ∼14 ±0.5 m/s. Thus, he measu ed in insic phase speeds o 446
he wa es we e ∼16 m/s. The heo e ical in insic phase speeds o g a i y wa es we e compu ed447
using he same inpu s as be o e wi h he excep ion o a 12 km e ical wa eleng h ( wo imes he448
6 km dep h o he e ical eloci y pe u ba ions). These inpu s p oduced alues o 17.73 m/s,449
which is close o he measu ed in insic phase speed o ∼16 m/s. Thus, hese low o middle le el450
wa es can be iden i ied as in e nal g a i y wa es ha a e being gene a ed by he con ec i e ac i i y451
close o he sys em cen e .452
I he dominan , uppe -le el mul i-bands a e no g a i y wa es, wha is d i ing hei dynamics?456
Figu e 14 shows e ical c oss sec ions o he along- ack eloci y and ac oss- ack eloci y. The457
along- ack eloci y (Fig. 14a) shows a je cen e ed a ∼11 km heigh wi h la ge alues o e ical458
shea (maximum alues o 0.01 s−1) loca ed be ween 8 - 10 km heigh and mos no ably be ween459
50 - 225 km along- ack. The loca ions o he la ge e ical wind shea alues ma ch well wi h460
he loca ions o he wa e mo ions associa ed wi h he mul i-bands. Fo example, he ac oss- ack461
eloci y (Fig. 14b) e eals clea wa e mo ions in he 6 - 10 km laye and be ween 50 - 250 km462
along- ack. The e a e pe haps ex ensions o he wa e mo ions down o ∼4 - 5 km in some egions,463
bu o e all, he oscilla ions become less de ec able below 6 km heigh .464
The along- ack and ac oss- ack eloci y ields shown in Fig. 14 ma ch well wi h he EXRAD465
obse a ions shown in Fig. 4, despi e he di e ences in spa ial/ empo al co e age (also no e he466
25
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