UPCommons
Po al del obe de la UPC
h p://upcommons.upc.edu/e-p in [s
An edi ed e sion o his pape was published by AGU. Published 2025 Ame ican
Geophysical Union.
Wang, X. [e al.], (2025), Spa io empo al a iabili y o Sa u n's zonal winds obse ed
by Cassini. "Jou nal o geophysical esea ch. Plane s”, ol. 130, núm. 1, a icle
e2024JE008515. DOI <h ps://doi.o g/10.1029/2024JE008515>
1
Spa io empo al Va iabili y o Zonal Winds Obse ed by Cassini
Abs ac . The s ong zonal winds on gian plane s a e among he mos ema kable phenomena in
ou sola sys em. Obse a ions eco ded by he Composi e In a ed Spec ome e (CIRS), he
Imaging Science Subsys em (ISS), and he Visual and In a ed Mapping Spec ome e (VIMS)
on he Cassini spacec a a e u ilized o in es iga e spa io empo al a ia ions in Sa u n’s zonal
winds, especially in he equa o ial egion. A mo e gene al he mal wind equa ion wo ks o
in es iga ing he e ical s uc u e o zonal winds a all la i udes, bu i has an in eg a ion gap
nea he equa o caused by he cylind ical in eg a ion pa h. He e, we de elop an algo i hm o
add ess his limi a ion, which is alida ed by he obse ed zonal winds. The new algo i hm is
combined wi h he CIRS- e ie ed empe a u e and he ISS-measu ed winds o gene a e he
comple e pic u e o he e ical s uc u e o Sa u n’s zonal winds o he uppe oposphe e om
50 mba o 500 mba . The comple e pic u e e eals ha he equa o ial zonal winds ha e
complica ed e ical s uc u es. The zonal winds om 10°S and 10°N ini ially dec ease wi h
al i ude and hen inc ease. Addi ionally, he in ense na ow equa o ial je be ween 3°S and 3°N
widens wi h al i ude. Fo he empo al a ia ions o zonal winds, he ISS measu emen s sugges
ha hese a ia ions a e mo e p onounced a ound he opopause (~50 mba ) han a he p essu e
le el o he op isible clouds (~500 mba ). The analysis o a mosphe ic s abili y indica es he
s onges ba o opic ins abili y a ~ 4°N a ound he 50-mba le el, which p obably con ibu es o
signi ican empo al a ia ions o he equa o ial zonal winds a ound he opopause. Fu he mo e,
analysis o he VIMS images sugges s ha he ela i ely deep zonal winds a ound 2000 mba do
no exhibi signi ican empo al a ia ions, e en in he equa o ial egion. The di e en empo al
beha io s o zonal winds in he e ical di ec ion sugges ha empo al a ia ions in zonal winds
a e d i en by seasonally a ying sola lux.
1. In oduc ion
The a mosphe es o all gian plane s in ou sola sys em exhibi dominan a mosphe ic
cu en s in he longi udinal di ec ion. These la ge-scale cu en s, known as zonal winds, can be
es ima ed by a e aging he winds longi udinally o e la ge a eas. Sa u n’s zonal winds can each
speeds o app oxima ely 400 m/s a he p essu e le els o isible clouds, signi ican ly s onge
han he s onges la ge-scale winds on Ea h (~100 m/s). Such s ong zonal winds play c i ical
oles in he a mosphe ic dynamics o he inged plane (e.g., Del Genio e al., 2009; Inge soll,
2020).
The Cassini da ase s o Sa u n, collec ed o e app oxima ely 13 yea s om Sa u n’s
no he n win e (2004-2009) o no he n sp ing (2009-2017), p o ide a unique oppo uni y o
explo e he seasonal a iabili y o he plane 's zonal winds. Addi ionally, di e en scien i ic
ins umen s on he Cassini p obe di e en p essu e le els in Sa u n’s a mosphe e, allowing us o
in es iga e he e ical s uc u e o i s zonal winds. In his s udy, we p ima ily use obse a ions
eco ded by he Imaging Science Subsys em (ISS) and he Composi e In a ed Spec ome e
(CIRS) o explo e he spa io empo al a iabili y o Sa u n’s zonal winds in he uppe oposphe e.
He e, Sa u n’s uppe oposphe e is de ined as he uppe po ion o he oposphe e om he
p essu e le el o he op isible clouds a app oxima ely 500 mba o he opopause a ound 50
mba . Addi ionally, obse a ions conduc ed by he Visual and In a ed Mapping Spec ome e
(VIMS) a e used o explo e he zonal winds a ela i ely deep a mosphe ic laye s a ound 2000
mba . Many s udies o Sa u n’s zonal winds based on Cassini obse a ions exis (e.g., see a
e iew by Inge soll, 2020), bu a sys ema ic analysis o he spa io empo al a iabili y o Sa u n’s
2
global zonal winds, by combining da a om he h ee Cassini ins umen s (ISS, CIRS, and
VIMS), is s ill lacking.
The images eco ded by he mul iple il e s (i.e., wa eleng hs) o he ISS can be used o
measu e zonal winds a di e en p essu e le els. In pa icula , images eco ded by he ISS
con inuum il e s can be used o ack ea u es o he op isible clouds (NH3) a ound 500 mba
and he eby measu e he zonal winds a ha le el. Fu he mo e, he ISS-measu ed zonal winds a
500 mba can se e as a lowe bounda y condi ion o he he mal wind equa ion,
complemen ing he CIRS- e ie ed empe a u e, o in es iga e he e ical s uc u e o zonal
winds abo e he bounda y (e.g., Flasa e al., 2005; Li e al., 2008, 2011; Fle che e al., 2016,
2017). Ra he han employing he classic he mal wind equa ion, we u ilize a mo e gene al
he mal wind equa ion. In p inciple, he gene al he mal wind equa ion can be used o all
la i udes because i does no depend on geos ophic balance. In p ac ice, he equa ion s ill has a
gap in he equa o ial egion due o i s cylind ical in eg a ion pa h (see Fig. 1), p e en ing us om
examining he zonal winds wi hin he gap. We de elop an algo i hm o add ess he in eg a ion
gap so ha he comple e pic u e o global zonal winds can be examined (see sec ion
“Me hodology o zonal-wind measu emen s”). In addi ion o he ISS and CIRS obse a ions,
Cassini VIMS obse a ions a e also analyzed. The VIMS 5-μm images sense he a mosphe ic
laye s a ound 2000 mba , which a e below he a mosphe ic laye s p obed by he ISS and CIRS.
The e o e, he VIMS 5-μm images p o ide a unique oppo uni y o examine Sa u n’s zonal
winds in ela i ely deep a mosphe ic laye s. A sys ema ic analysis o Sa u n’s zonal winds based
on Cassini long- e m mul i-ins umen obse a ions makes i possible o explo e o he dynamics
o his inged plane .
Sa u n’s o a ion pe iod, se ing as he e e ence o measu ing zonal winds, has been
in es iga ed o a long ime (e.g., Desh and Kaise 1981; Giampie i e al., 2006; Ande son and
Schube , 2007; Read e al., 2009a; Helled e al., 2009, 2015; Manko ich e al., 2019; Milli ze
and Hubba d, 2023). A ecen e iew (Sanchez-La ega e al., 2023) includes a good summa y o
he discussion o di e en o a ion pe iods sugges ed by p e ious s udies. In his s udy, he
sys em III o Sa u n’s o a ion pe iod (i.e., 10 hou s, 39 minu es, and 22 seconds) (Desh and
Kaise , 1991), sugges ed by he In e na ional As onomical Union (A chinal e al., 2018), is used
o acili a e he compa ison o zonal winds be ween his s udy and p e ious s udies because mos
p e ious s udies used such a sys em. The con e sion o zonal winds om sys em III o o he
sys ems, which is s aigh o wa d, is no included.
2. Cassini da a se s and da a p ocessing
As p e iously discussed, ou wind measu emen s ely on da a eco ded by h ee
ins umen s aboa d Cassini: ISS, VIMS, and CIRS. We will b ie ly in oduce each ins umen
and i s co esponding da ase s and da a p ocessing me hods he e.
The ISS ins umen unc ions as a wo-dimensional imaging de ice on Cassini, wi h i s
undamen al cha ac e is ics ou lined in he in oduc o y pape (Po co e al., 2004). P e ious
s udies (e.g., Li e al., 2004, 2006a, 2011) ha e de ailed he use o ISS images and image
p ocessing echniques o measu ing zonal winds. Basic image p ocessing in ol es na iga ion,
pho ome ic calib a ion, and map p ojec ion based on he came a's geome ic model and he
pho ome ic calib a ion so wa e (CISSCAL) (Po co e al., 2004), in addi ion o da a om he
Na iga ion and Ancilla y In o ma ion Facili y (NAIF) a he Je P opulsion Labo a o y
(Vasa ada e al., 2006).
3
P ocessed ISS mul i- il e maps acili a e he measu emen o zonal winds a ound wo
p essu e le els (e.g., Po co e al., 2005; Del Genio e al., 2009; Ga cia-Melendo e al., 2010,
2011; Li e al., 2011; Sayanagi e al., 2012; Sanchez-La ega e al., 2016). Maps de i ed om
ISS images eco ded wi h middle and s ong me hane-abso p ion il e s (MT2 and MT3) a e
u ilized o measu ing zonal winds a ound he 60-mba p essu e le el (Ga cia-Melendo e al.,
2010), nea Sa u n’s opopause (i.e., 50 mba ). Addi ionally, maps om ISS images eco ded
wi h h ee con inuum il e s (CB1, CB2, and CB3) a e employed o measu e zonal winds a ound
he p essu e le el o he op isible clouds (NH3) a ~ 500 mba .
Zonal winds a ound 500 mba , de i ed om ISS con inuum images, also se e as
bounda y condi ions o s udying e ical s uc u e o zonal winds. The he mal wind
ela ionship calcula es he e ical s uc u e o zonal winds by in eg a ing me idional empe a u e
g adien s om zonal winds a he 500-mba bounda y le el. This in es iga ion equi es Sa u n’s
empe a u e ield, which is ob ained om obse a ions eco ded by CIRS. The CIRS ins umen ,
a Fou ie - ans o m spec ome e (Flasa e al., 2004), plays a c ucial ole in de e mining he
he mal s uc u e and chemical componen s o Sa u n’s a mosphe e. Spec a om CIRS
obse a ions allow o he e ie al o Sa u n’s a mosphe ic empe a u e a di e en p essu e
le els. The e ie al scheme o a mosphe ic empe a u e om in a ed spec a is de ailed by
Con a h and Gau ie (1980) and Con a h e al. (1998). CIRS obse a ions p o ide limi ed
in o ma ion in he p essu e ange o 5-50 mba and a p essu es g ea e han app oxima ely 500
mba (Flasa e al., 2004; Fle che e al., 2007). Zonal-mean a mosphe ic empe a u e be ween 50
mba and 500 mba in Sa u n’s oposphe e was e ie ed om CIRS high-spa ial- esolu ion
nadi adiance in a p e ious s udy (Fle che e al., 2017), which is di ec ly applicable o his
s udy.
The Cassini ISS and CIRS obse a ions enable he examina ion o zonal winds om 50
mba o 500 mba . Addi ionally, he Cassini VIMS obse a ions allow explo a ion o zonal
winds a deepe laye s. The VIMS, a mapping spec ome e , cap u es images in 352 di e en
wa eleng hs be ween 0.35 μm and 5.1 μm (B own e al., 2004). The s anda d VIMS da a
p ocessing pipeline, de eloped by he VIMS eam, includes p ocedu es such as cosmic ay hi
emo al and la ield calib a ion (McCo d e al., 2004; S omo sky and F y, 2010), wi h u he
da a educ ion and p ocessing u ilizing he In eg a ed So wa e o Image s and Spec ome e s
(ISIS) (Gaddis e al., 1997). The VIMS 5-μm images p obe Sa u n’s a mosphe e a p essu e
le els a ound 2000 mba (Baines e al., 2005, 2007, 2009; Choi e al., 2009), deepe han hose
p obed by Cassini ISS and CIRS. While some p e ious s udies ha e examined VIMS 5-μm
obse a ions (Baines e al., 2005, 2009; Choi e al., 2009; S udwell e al., 2018), esea ch on
empo al a ia ions o ela i ely deep zonal winds, pa icula ly in he equa o ial egion, emains
limi ed.
3. Me hodology o zonal-wind measu emen s
We u ilize Cassini ISS, VIMS, and CIRS obse a ions o in es iga e zonal winds a
a ious p essu e le els in Sa u n’s a mosphe e. Clouds cap u ed in he ISS and VIMS images can
se e as acking ea u es o measu ing zonal winds. The e a e wo me hods o cloud acking:
manual acking and au oma ic co ela ing. Manual acking in ol es obse ing cloud
mo emen s in images aken a di e en imes and ansla ing hese mo emen s in o zonal winds.
Al e na i ely, Limaye (1986) de eloped a compu e algo i hm, known as au oma ic co ela ing,
o ack cloud ea u es in images. This me hod en ails ex ac ing eas -wes s ips o pixels om
image pai s, shi ing hem o iden i y he maximal c oss-co ela ion coe icien , and calcula ing
4
zonal winds based on he lags in he longi ude di ec ion wi h he maximal c oss-co ela ion
coe icien . This echnique has been employed in nume ous p e ious s udies using Cassini ISS
and VIMS images (e.g., Baines e al., 2009; Choi e al., 2009; Ga cia-Melendo e al., 2010, 2011;
Li e al., 2004, 2006, 2011; Sayanagi e al., 2012; Sanchez-La ega e al., 2016; S udwell e al.,
2018). I ’s wo h no ing ha hese wo me hods, manual acking and au oma ic co ela ing, a e
no mu ually exclusi e. Ins ead, hey a e commonly used in combina ion o explo e zonal winds
in plane a y a mosphe es.
Ano he me hod o explo ing Sa u n’s zonal winds in ol es u ilizing he CIRS- e ie ed
empe a u e da a in conjunc ion wi h he he mal wind equa ion. The he mal wind equa ion,
es ablished by Ba chelo (1967) and Pedlosky (1987), ela es e ical wind shea o he
ho izon al empe a u e g adien along isoba ic su aces, making i a aluable ool o
in es iga ing he e ical s uc u e o zonal winds in a mosphe ic and plane a y sciences. The
classical he mal wind equa ion, o mula ed in Ca esian coo dina es unde he assump ion o
geos ophic balance, becomes ine ec i e a low la i udes whe e geos ophic balance b eaks
down nea he equa o .
In ecen yea s, a mo e gene al equa ion linking he empe a u e ield o he wind ield
has been de eloped, employing ei he cylind ical o sphe ical coo dina es (e.g., de la To e
Jua ez e al., 2002; Flasa e al., 2005; Fouche e al., 2008; Li e al., 2007, 2008; Galan i e al.,
2016; Fle che e al., 2017; Ma cus e al., 2019). Unlike he classical equa ion, his gene alized
he mal wind equa ion does no ely on geos ophic balance, ende ing i applicable ac oss all
la i udes, including he equa o ial egion. Fo Sa u n, cha ac e ized by a obus equa o ial je
exceeding 400 m/s, he e m associa ed wi h cen i ugal o ce should be conside ed. The e o e,
he g adien -wind balance ins ead o geos ophic balance is employed in he ela ionship be ween
empe a u e and wind ields (e.g., Flasa e al., 2005; Fouche e al., 2008; Li e al., 2007, 2008),
which can be exp essed in cylind ical coo dina es as
𝜕
𝜕𝑧�𝑟𝑐�𝑢2+ 2𝛺𝑢𝑟𝑐
𝑟𝑐�=𝑅
𝑝𝑟𝜕𝑝
𝜕𝑟𝜕𝑇
𝜕𝜙�𝑝
whe e 𝑧 is a uni ec o along he o a ion axis, 𝑟𝑐 is cylind ical adius, 𝑢 is zonal winds, 𝛺 is he
angula speed o o a ion o a plane , 𝑅 is he speci ic gas cons an , 𝑝 is p essu e, 𝑟 is he adius
o he plane , 𝑇 is empe a u e, and 𝜙 is plane ocen ic la i ude.
We in eg a e he e m con aining he empe a u e g adien on he igh -hand side o Eq. (1)
along he cylind ical pa h o de i e he e m in ol ing he zonal winds on he le -hand side and
hen sol e o he zonal winds. In his p ocess, we conduc upwa d in eg a ion along he
cylind ical pa h om a e e ence p essu e le el (500 mba ), whe e zonal winds a e measu ed
using ISS images cap u ed by he con inuum il e s. The empe a u e g adien on he igh -hand
side is compu ed based on he empe a u e e ie ed by CIRS. When applying Eq. (1), i 's
necessa y o con e Sa u n’s empe a u e, ypically e ie ed in sphe ical coo dina es, o
cylind ical coo dina es o he igh -hand side o he equa ion. While con e ing be ween he wo
coo dina e sys ems is ela i ely s aigh o wa d o middle and high la i udes, i equi es mo e
a en ion a low la i udes due o he signi ican inc ease in la i ude excu sion nea he equa o .
Du ing he upwa d in eg a ion o Eq. (1), he cylind ical pa h o igina ing om he
equa o a he e e ence le el (i.e., 500 mba ) goes up o he op o he in es iga ed a mosphe ic
laye s a 50 mba . This in eg a ion p ocess is depic ed by he ed a ows in Fig. 1. Fo he
a mosphe ic egion o he igh o he ed a ows, he e a e no upwa d cylind ical in eg a ion
pa hs o igina ing om he e e ence le el. Hence, ou cylind ical he mal wind equa ion is no
applicable in his egion. To es ima e he ex en o his egion, we de ine he la i ude a he op
5
laye eached by he cylind ical in eg a ion pa h o igina ing om he equa o as 𝜙𝑐 (see Fig. 1).
Fo a sphe ical body, we ha e 𝜙𝑐=𝑎𝑐𝑜𝑠[𝑟(𝑟+∆𝑟)⁄], whe e and ∆ ep esen Sa u n’s adius
a he e e ence le el and he o al hickness o he in es iga ed a mosphe ic laye s, espec i ely.
The a mosphe ic laye s om 500 mba o 50 mba , in es iga ed by ISS/CIRS, ha e a o al
hickness ∆ ~ 140 km. Sa u n’s equa o ial adius a he e e ence le el (500 mba ) is ~ 60,308
km, which is he sum o he hickness om 1000 mba o he e e ence le el (40 km) and he
equa o ial adius a 1000 mba (60268 km) (see NASA websi e
h ps://nssdc.gs c.nasa.go /plane a y/ ac shee /sa u n ac .h ml). The e o e, we ha e 𝜙𝑐 ~ 3.9°.
Now, we add ess how o add ess he gaps in he in eg a ion pa hs o he cylind ical
he mal wind equa ion (i.e., he egion o he igh o he ed a ows in Fig. 1). Al hough he
la i ude excu sion om he equa o a he e e ence le el (500 mba ) o he op o he ele an
a mosphe e (50 mba ) can each 3.9° along he cylind ical pa h, he la i ude excu sions be ween
neighbo ing a mosphe ic laye s a e much smalle han 3.9° (see Fig. 1) because Sa u n’s
empe a u e was e ie ed o 18 laye s o he a mosphe e be ween 500 mba and 50 mba
(Fle che e al., 2017). Fo ins ance, he la i ude excu sion om he equa o a he e e ence le el
(500 mba ) o he nea es le el below (440 mba ) is app oxima ely ~ 0.9°. We designa e he le el
closes o he e e ence le el as he i s le el, wi h subsequen le els ollowing his sequence
(i.e., he second le el, he hi d le el, and so o h). Fo each le el, he empe a u e e ie ed by
CIRS was mapped on o a egula la i ude g id wi h a la i udinal esolu ion o 1° (Fle che e al.,
2017).
The la i ude excu sion om he e e ence le el o he i s le el (~ 0.9°) implies ha he
zonal wind a he equa o (la i ude = 0°) a he e e ence le el gene a es zonal winds a la i udes
0.9° (0.9°N and 0.9°S) a he i s le el h ough cylind ical in eg a ion o he he mal wind
equa ion. Subsequen ly, we linea ly in e pola e he calcula ed i s -le el zonal winds a 0.9°N
and 0.9°S o ob ain zonal winds a he equa o . This me hod enables us o ill he equa o ial gap
o he i s le el. Zonal winds a egula la i ude g ids o he han he equa o (e.g., 1°, 2°, 3°, e c.)
a he e e ence le el a e also in eg a ed e ically o i egula la i udes a he i s le el due o
he la i ude excu sion caused by cylind ical in eg a ion. Simila ly, we can linea ly in e pola e
zonal winds a i egula la i udes o zonal winds a egula la i udes a he i s le el. A e
ob aining zonal winds a all egula la i udes a he i s le el, we designa e he i s le el as a
new e e ence le el and apply he cylind ical he mal wind equa ion om his new e e ence
le el o he nex le el. This i e a i e p ocess con inues o he op le el, allowing us o ob ain
zonal winds a egula la i udes o all le els.
Al hough he abo e me hod e ec i ely ills obse a ional gaps in he equa o ial egion,
compu ing Sa u n’s equa o ial zonal winds poses a challenge. Analyses based on Cassini/ISS
obse a ions (Ga cia-Melendo e al., 2010) e ealed ine s uc u es o zonal winds a la i udinal
scales o less han 1° in Sa u n’s equa o ial egion. The e o e, linea in e pola ion o Sa u n’s
zonal winds om i egula la i udes o egula la i udes in oduces signi ican unce ain y when
he la i ude excu sion is close o 1° (e.g., 0.9° o he la i ude excu sion om he e e ence le el
o he i s le el) because linea in e pola ion canno esol e ine s uc u es. To add ess his issue,
we: (1) linea ly in e pola e ISS zonal winds a he e e ence le el and CIRS empe a u es om
ela i ely coa se la i udinal esolu ions o a ine esolu ion (0.1°) o esol e small-scale
s uc u es in zonal winds; and (2) linea ly in e pola e CIRS empe a u es om he o iginal 18
e ical laye s be ween 500 mba and 50 mba o 90 le els o educe he la i ude excu sion
be ween neighbo ing laye s, he eby making he in e pola ion o zonal winds om i egula
la i udes o egula la i udes mo e accu a e.
6
Unce ain ies in wind measu emen s a e c ucial o unde s anding spa io empo al
a ia ions o Sa u n’s zonal winds. Fo zonal winds measu ed by cloud- acking echniques wi h
ISS and VIMS images, sys ema ic e o s caused by changes in clouds, wa e-like phenomena,
and in e ac ions be ween clouds and hei en i onmen in oduce unce ain ies in zonal wind
measu emen s (Ga cia-Melendo and Sanchez-La ega, 2001; Li e al., 2004). We es ima e
unce ain ies in cloud- acking zonal winds by he s anda d de ia ion o mul iple wind
measu emen s wi hin each la i ude bin. Addi ionally, unce ain y ela ed o ISS/VIMS image
p ocessing na iga ion p ocedu es is conside ed in ou es ima ion o zonal wind measu emen
unce ain ies.
Fo unce ain ies in compu ed zonal winds om he he mal wind equa ion wi h CIRS-
e ie ed empe a u es, wo main sou ces o unce ain y exis : (1) unce ain y in measu emen s o
cloud- acking zonal winds a 500 mba , used as bounda y condi ions o he he mal wind
equa ion; and (2) unce ain y in CIRS- e ie ed empe a u es, which in luences he empe a u e
g adien and consequen ly a ec s in eg a ion o he he mal wind equa ion. In his s udy, zonal
winds a 500 mba a e om a p e ious s udy (Ga cia-Melendo e al., 2011), which used Cassini
images eco ded a con inuum il e s o measu emen s. The unce ain y in measu emen s o
500-mba zonal winds (~ 10 m/s) (see Ga cia-Melendo e al., 2011) a he bounda y is
p opaga ed o each p essu e le el abo e he bounda y and emains cons an du ing upwa d
in eg a ion.
To es ima e he unce ain y o compu ed zonal winds caused by e o s in e ie ed
empe a u es, we mus examine unce ain y o e ie ed empe a u es. The es ima ed unce ain y
o CIRS- e ie ed empe a u es is 2-4 K, depending on p essu e le el (Fle che e al., 2017).
He e, we use 3 K o unce ain y. We gene a e empe a u e unce ain y using andom numbe s
wi h a magni ude o 3 K. Assuming empe a u e unce ain y is independen in la i udinal
di ec ion and applying he ule o e o p opaga ion o addi ion (Be ing on and Robinson, 2003),
we use unce ain ies a wo neighbo ing la i udes o es ima e unce ain y o empe a u e
di e ence (∂T) in Eq. (1). Likewise, assuming empe a u e unce ain y is independen in e ical
di ec ion, we can app oxima e e ical in eg a ion in Eq. (1) using ule o e o p opaga ion o
addi ion. This app oach allows us o compu e he unce ain y o compu ed zonal winds a e e y
p essu e le el, shown in panel C o Fig. 2. I 's wo h no ing ha unce ain y o compu ed zonal
winds om e o s o e ie ed empe a u e accumula es du ing upwa d in eg a ion.
4. Resul s
4. 1 Ve ical s uc u e o zonal winds
Figu e 2 illus a es he CIRS- e ie ed empe a u e and he co esponding compu ed
zonal winds o he a mosphe ic laye s om 500 mba o 50 mba . The cloud- acking zonal
winds a 500 mba , ob ained om a p e ious s udy based on images eco ded by he ISS
con inuum il e s (Ga cia-Melendo e al., 2011), a e used as he bounda y condi ion o he
he mal wind equa ion. The zonal winds om he p e ious s udy ep esen ime-a e aged
measu emen s o e he pe iod o 2004-2009. The e o e, o main ain consis ency, we a e age he
CIRS- e ie ed empe a u e om he same p e ious s udy (Fle che e al., 2017) o e he same
pe iod (2004-2009), as shown in panel A o Fig. 2.
Panel B o Fig. 2 indica es ha zonal winds essen ially emain cons an in he e ical
di ec ion in he middle and high la i udes, consis en wi h p e ious s udies (e.g., Read e al.,
2009b; Fle che e al., 2016). In he equa o ial egion, he zonal winds exhibi signi ican e ical
a ia ions. Ini ially, he equa o ial winds be ween 10°S and 10°N dec ease wi h al i ude and hen
7
begin o inc ease. Fu he mo e, he p essu e le el a which his change om dec ease o inc ease
occu s a ies wi h la i ude (also e e o he e ical shea o zonal winds depic ed in Fig. 4). Fo
he in ense na ow equa o ial je be ween 3°S and 3°N, i ex ends h oughou he en i e p essu e
ange o 50-500 mba and widens wi h al i ude. The he mal-wind equa ions sugges ha he
e ical shea o zonal winds is p opo ional o he me idional g adien o empe a u e, so he
ela i ely la ge me idional g adien s o Sa u n’s empe a u e in he equa o ial egion con ibu e
o he signi ican e ical a ia ions o zonal winds he e. Addi ionally, he he mal-wind
equa ion implies ha he e ical shea o zonal winds is p opo ional o he in e se o he
Co iolis pa ame e . The Co iolis pa ame e s ongly dec eases om he high/middle la i udes o
he equa o , esul ing in a d ama ic inc ease in he e ical shea o zonal winds wi h dec easing
la i ude (also see panel B o Fig.4).
To alida e he e ical s uc u e o zonal winds compu ed by he mo e gene al he mal-
wind equa ion wi h he CIRS empe a u e, we compa e he compu ed zonal winds a he p essu e
le el wi h he cloud- acking measu emen s based on he ISS images. The ISS images eco ded
a he MT2 and MT3 il e s ha e been used o measu e he zonal winds a he p essu e le els
a ound 60 mba (Ga cia-Melendo e al., 2011), which a e compa ed wi h he CIRS-compu ed
zonal winds a he same p essu e le el. The compa ison, as shown in Fig. 3, sugges s basic
consis ency o zonal winds be ween he wo esul s a middle and high la i udes. A disc epancy
in zonal winds be ween he wo esul s p ima ily appea s in he opical egion, e en hough he
compu ed zonal winds om he CIRS- e ie ed empe a u e cap u ed he dominan s uc u es o
Sa u n’s equa o ial je s a ound he opopause (e.g., he na ow and s ong eas wa d je be ween
3°S and 3°N). Howe e , his disc epancy is gene ally smalle han he unce ain y associa ed
wi h zonal wind measu emen s, indica ing ha he wo esul s o de e mining zonal winds a e
s a is ically consis en .
4. 2 A mosphe ic s abili ies based on he spa ial a ia ions o zonal winds
The e ical s uc u e o zonal winds displayed in panel B o Fig. 2 enables u he
explo a ion o Sa u n’s a mosphe ic dynamics. We i s compu e he s a ic s abili y o Sa u n’s
uppe oposphe e based on he CIRS- e ie ed empe a u e (panel A o Fig. 2):
𝑁2=(𝑔 𝜃
⁄)(𝑑𝜃 𝑑𝑧
⁄), whe e 𝑔 is g a i y, 𝜃 is he po en ial empe a u e, and 𝑧 is heigh . Then
he s a ic s abili y is combined wi h he e ical shea o zonal winds (𝑑𝑢 𝑑𝑧
⁄) o examine he
Richa dson numbe ( 𝑅𝑖=𝑁2(𝜕𝑢 𝜕𝑧
⁄)2
⁄), which can be used o examine he u bulence
de elopmen and ba oclinic s abili y o he a mosphe ic sys ems on he gian plane s (e.g.,
Allison e al., 1995). Panel A o Fig. 4 shows ha he s a ic s abili y o Sa u n’s a mosphe e is
consis en ly posi i e in he uppe oposphe e (i.e., 50-500 mba ), which is consis en wi h a
p e ious s udy (Fle che e al., 2016). Posi i e s a ic s abili y in he uppe oposphe e sugges s
he a mosphe e is con ec i ely s able in ha egion. S a ic s abili y gene ally inc eases wi h
heigh ac oss all la i udes, indica ing ha Sa u n’s a mosphe e becomes mo e s able om he
500-mba p essu e le el o he opopause (~50 mba ). Speci ically, he a mosphe ic laye s
a ound 500 mba exhibi a s a ic s abili y app oaching ze o, sugges ing ela i ely uns able in
hese laye s. I s a ic s abili y con inues o dec ease wi h dep h, i is possible ha he a mosphe ic
laye s benea h he 500-mba laye a e con ec i ely uns able. The e ical shea o zonal winds
(Panel B o Fig. 4) has a much la ge magni ude in he equa o ial egion (i.e., ~20°S-20°N) han
in o he la i udes, consis en wi h he e ical s uc u e o zonal winds shown in Panel B o Fig. 2.
The ela i ely la ge me idional g adien s o empe a u e and he small alues o he Co iolis
pa ame e in he opical egion con ibu e o he dominan e ical shea o zonal winds in his
8
a ea. Panel C o Fig. 4 shows ha he Richa dson numbe is la ge han 3 in all la i udes o
Sa u n’s uppe oposphe e om 500 mba o 50 mba , sugges ing ha u bulence is supp essed
in hese egions. Some a eas in he opical egion om 15°S o 15°N ha e ela i ely small
alues o he Richa dson numbe , implying ha he equa o ial egion ela i ely a o s u bulence
de elopmen .
The e ical s uc u e o zonal winds shown in Fig. 2 also makes i possible o examine
he me idional g adien o he zonal-mean quasi-geos ophic po en ial o ici y, de ined as
e ec i e be a (𝛽𝑒). E ec i e be a is a c i ical pa ame e in a mosphe ic dynamics (Pedlosky,
1987; And ews e al., 1987; Salby, 1996; Hol on e al., 2004). While his pa ame e has been
p e iously analyzed in s udies o Sa u n’s a mosphe e (e.g., Read e al., 2009a, 2009b; Sanchez-
La ega e al., 2011; Fle che e al., 2016; Li e al., 2021), a comple e pic u e o Sa u n’ uppe
oposphe e, including he equa o ial egion, is s ill lacking. E ec i e be a can be exp essed as
𝛽𝑒=𝛽+𝛽𝑦+𝛽𝑧), whe e 𝛽 is he me idional g adien o he plane a y o ici y 𝑓 (i.e., Co iolis
pa ame e ), 𝛽𝑦 is he me idional g adien o he zonal-a e age ela i e o ici y, and 𝛽𝑧 is he
me idional g adien o he s e ching o ici y. The second e m, 𝛽𝑦, is u he de ined as he
cu a u e o zonal winds, exp essed as 𝛽𝑦=−𝑢𝑦𝑦 =−𝜕2𝑢 𝜕𝑦2
⁄. Fo he hi d e m, 𝛽𝑧, i is
gene ally exp essed in he log-p essu e coo dina es, in which he e ical coo dina e is de ined as
𝑧∗=−𝐻𝑙𝑛(𝑝 𝑝0
⁄), wi h 𝐻 as he scale heigh and 𝑝0 as a e e ence p essu e (e.g., 1000 mba ).
Then, we ha e 𝛽𝑧=−(1𝜌
⁄)𝜕[𝜌𝑓2𝑁2(𝜕𝑢 𝜕𝑧∗
⁄)⁄]𝜕𝑧∗
⁄, whe e 𝜌 is a mosphe ic densi y.
E ec i e be a can be used o examine he s abili y o zonal je s wi h a s abili y c i e ion: zonal
je s a e s able and uns able when 𝛽𝑒 > 0 and 𝛽𝑒 < 0, espec i ely. The combina ion o he i s
wo e ms in 𝛽𝑒 is gene ally used o de ine he s abili y o a ba o opic a mosphe e: 𝛽𝑏=𝛽+𝛽𝑦,
whe e we de ine 𝛽𝑏 as ba o opic be a. Zonal je s in a ba o opic a mosphe e a e s able and
uns able when 𝛽𝑏 > 0 and 𝛽𝑏 < 0, espec i ely.
Figu e 5 displays he h ee componen s o e ec i e be a (𝛽𝑒). Panel A shows ha he
me idional g adien o he plane a y o ici y (𝑓) is non-nega i e a all la i udes: i eaches a
maximal alue o 5.48×10-12 m-1s-1 a he equa o and a minimal alue o 0 a he wo poles.
Panel B o Fig. 5 shows 𝛽𝑦, which is de e mined by he me idional s uc u e o zonal winds.
Compa ing wi h he e ical s uc u e o zonal winds shown in Fig. 2, we ind ha he e a e
maxima o 𝛽𝑦 o hese eas wa d je s and minima o 𝛽𝑦 o hese wes wa d je s a he middle and
high la i udes. Fo he low la i udes om 20°S o 20°N, he egion be ween he sou he n peak o
he equa o ial je a ~ 7°S and he peak a he equa o and he egion be ween he no he n peak
o he equa o ial je a ~ 7°N and he peak a he equa o (i.e., he wo dip s uc u es o zonal
winds a ound he equa o ) basically ha e nega i e 𝛽𝑦, and all o he egions ha e posi i e 𝛽𝑦.
Panel C o Fig. 5 shows 𝛽𝑧, sugges ing ha he la ge magni udes o 𝛽𝑧 mainly happen in he
a mosphe ic laye s om 500 mba o ~ 300 mba . In hese laye s (~ 300-500 mba ), Fig. 5 also
sugges s ha he magni udes o he 𝛽𝑧 (panel C) a e much la ge han hose o 𝛽 (panel A) and
𝛽𝑦 (panel B), so 𝛽𝑧 is dominan in he e ec i e be a (𝛽𝑒) in such a mosphe ic laye s.
The h ee componen s o he e ec i e be a (𝛽𝑒) make i possible o examine bo h he
ba o opic and ba oclinic s abili y c i e ia, which a e shown in panel B and panel C o Fig. 6
espec i ely. Panel A o Fig. 6 displays he me idional s uc u e o zonal winds a he e e ence,
which can be used o examine he co ela ion be ween zonal winds and ba o opic s abili y (panel
B o Fig. 6). Basically, ba o opic be a (𝛽𝑏) has he same s uc u e as ha in 𝛽𝑦, because 𝛽𝑦 is
much la ge han 𝛽 in mos la i udes especially in hese la i udes a ound he eas wa d and
wes wa d je s (see Fig. 5). In he middle and high la i udes, zonal winds do no signi ican ly a y
15
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19
Figu e 1. Cylind ical in eg a ion pa hs used in ou he mal wind equa ion. The adius om he
cen e o a plane o he e e ence le el is de ined as . The o al hickness o all a mosphe ic
laye s which we a e in e es ed in is de ined as ∆ . Fo he upwa d in eg a ion, he la i ude a he
op laye eached by he cylind ical in eg a ion pa h o igina ing om he equa o a he e e ence
le el is de ined as ϕc.
20
Figu e 2. Sa u n’s CIRS- e ie ed empe a u e and compu ed zonal winds o he uppe
oposphe e (50-500 mba ). (A) A c oss-sec ion o la i ude and p essu e displaying he CIRS-
e ie ed empe a u e a e aged o e he pe iod o 2004-2009. (B) The e ical s uc u e o zonal
winds. The zonal winds in panel B we e compu ed by e ically in eg a ing he he mal wind
equa ion using zonal winds a he bounda y laye a ~500 mba . The zonal winds a he 500-mba
le el a e measu ed by he ISS images eco ded a he con inuum il e s (CB2 and CB3) (Ga cia-
Melendo e al., 2011). (C) Unce ain y o compu ed zonal winds. The es ima e o unce ain y is
p ima ily based on he e ie al e o s o CIRS empe a u e by applying e o p opaga ion
h ough he he mal wind equa ion.
21
Figu e 3. Compa ison o Sa u n’s 50-mba zonal winds be ween he compu ed esul s based on
he CIRS- e ie ed empe a u e ( ed line) and he ISS measu emen s (blue line). The ISS images
eco ded by MT2 and MT3 il e s we e used o measu e he zonal winds a ~ 50 mba (Ga cia-
Melendo e al., 2011), and he CIRS-de i ed winds a 50 mba come om he esul s shown in
Fig. 2 (panel B).
22
Figu e 4. S a ic s abili y, e ical shea o zonal winds, and Richa dson numbe . (A) S a ic
s abili y (N). (B) Ve ical shea o zonal winds (∂u∂z
⁄). (C) Richa dson numbe (Ri).
23
Figu e 5. Componen s o e ec i e be a. (A) The me idional g adien o he plane a y o ici y
(β). (B) The me idional g adien o he zonally-a e aged ela i e o ici y (βy). (C) The
me idional g adien o s e ching o ici y (βz).
24
Figu e 6. Compa ison be ween he zonal winds and ba o opic & ba oclinic s abili ies (βb and
βe). (A) The me idional p o ile o zonal winds a he 500-mba p essu e le el. (B) The
ba o opic be a (βb), which is used o examine he ba o opic s abili y o Sa u n’s a mosphe e. (C)
The e ec i e be a (βe), which can be applied o in es iga e he ba oclinic na u e o Sa u n’s
a mosphe e.
