1. In oduc ion
The isible and nea -in a ed spec a o he Sola Sys em's “Ice Gian s”, U anus and Nep une, ha e ascina ed
plane a y as onome s o many yea s. The a mosphe es o he Ice Gian s a e obse ed o ha e simila a mosphe es
wi h simila oposphe ic empe a u e p o iles and He/H2 a ios, de e mined om Voyage -2 obse a ions and
pos analyses (Lindal,1992; Lindal e al.,1987; S omo sky e al.,2011), and simila , high mole ac ions o me h-
ane o ∼4% (I win, Toledo, B aude, e al.,2019; Ka koschka & Tomasko,2009; Ka koschka & Tomasko,2011;
S omo sky e al.,2014,2019). Bo h plane s appea blue o bluish-g een o he naked eye, in con as o he mo e
yellowish appea ance o Jupi e and Sa u n. We now know his blueness comes om a combina ion o his highe
abundance o gaseous me hane, which has s ong abso p ion bands in he in a ed and ed po ion o he isible
Abs ac We p esen a eanalysis (using he Minnae limb-da kening app oxima ion) o isible/nea -
in a ed (0.3–2.5μm) obse a ions o U anus and Nep une made by se e al ins umen s. We ind a common
model o he e ical ae osol dis ibu ion i.e., consis en wi h he obse ed e lec i i y spec a o bo h plane s,
consis ing o : (a) a deep ae osol laye wi h a base p essu e >5–7ba , assumed o be composed o a mix u e o
H2S ice and pho ochemical haze; (b) a laye o pho ochemical haze/ice, coinciden wi h a laye o high s a ic
s abili y a he me hane condensa ion le el a 1–2ba ; and (c) an ex ended laye o pho ochemical haze, likely
mos ly o he same composi ion as he 1–2-ba laye , ex ending om his le el up h ough o he s a osphe e,
whe e he pho ochemical haze pa icles a e hough o be p oduced. Fo Nep une, we ind ha we also need o
add a hin laye o mic on-sized me hane ice pa icles a ∼0.2ba o explain he enhanced e lec ion a longe
me hane-abso bing wa eleng hs. We sugges ha me hane condensing on o he haze pa icles a he base o he
1–2-ba ae osol laye o ms ice/haze pa icles ha g ow e y quickly o la ge size and immedia ely “snow ou ”
(as p edic ed by Ca lson e al. (1988), h ps://doi.o g/10.1175/1520-0469(1988)045<2066:CMOTGP>2.0.CO;2),
e-e apo a ing a deepe le els o elease hei co e haze pa icles o ac as condensa ion nuclei o H2S ice
o ma ion. In addi ion, we ind ha he spec al cha ac e is ics o “da k spo s”, such as he Voyage -2/ISS G ea
Da k Spo and he HST/WFC3 NDS-2018, a e well modelled by a da kening o possibly clea ing o he deep
ae osol laye only.
Plain Language Summa y P e ious s udies o he e lec ance spec a o U anus and Nep une ha e
concen a ed on indi idual, na ow wa eleng h egions and he conclusions ha e been di icul o compa e
wi h each o he . He e, we analyse a combined se o obse a ions om h ee di e en ins umen s co e ing
he wa eleng h ange 0.3–2.5μm o a i e a a single ae osol model ha ma ches he obse a ions a all
wa eleng hs simul aneously o bo h plane s. We conclude ha pho ochemical haze p oduced in he uppe
a mosphe es o bo h plane s is s eadily mixed down o lowe laye s, whe e i o ms pa o a e ically hin
laye in a s a ically s able egion abo e he me hane condensa ion le el a 1–2ba . We sugges ha me hane
condenses so apidly upon hese haze pa icles ha i e icien ly “snows” ou a he base o his laye , alling
o lowe , wa me le els, whe e he me hane e apo a es, eleasing he co e haze pa icles o “seed” H2S
condensa ion. Fo Nep une we need o add an addi ional laye o mode a ely la ge me hane ice pa icles a
∼0.2ba . In iguingly, we ind ha a da kening (o pe haps clea ing) o he lowes H2S/haze laye ma ches e y
well he obse ed p ope ies o he da k spo s seen occasionally in Nep une's a mosphe e and e y occasionally
in U anus's a mosphe e.
IRWIN ET AL.
© 2022. The Au ho s.
This is an open access a icle unde
he e ms o he C ea i e Commons
A ibu ion License, which pe mi s use,
dis ibu ion and ep oduc ion in any
medium, p o ided he o iginal wo k is
p ope ly ci ed.
Hazy Blue Wo lds: A Holis ic Ae osol Model o U anus and
Nep une, Including Da k Spo s
P.G. J. I win1 , N. A. Teanby2 , L. N. Fle che 3 , D. Toledo4 , G. S. O on5 , M. H. Wong6 ,
M. T. Roman3 , S. Pé ez-Hoyos7 , A. James1 , and J. Dobinson1
1Depa men o Physics, Uni e si y o Ox o d, Ox o d, UK, 2School o Ea h Sciences, Uni e si y o B is ol, B is ol, UK,
3School o Physics & As onomy, Uni e si y o Leices e , Leices e , UK, 4Ins i u o Nacional de Técnica Ae oespacial (INTA),
Mad id, Spain, 5Je P opulsion Labo a o y, Cali o nia Ins i u e o Technology, Pasadena, CA, USA, 6Cen e o In eg a i e
Plane a y Science, Uni e si y o Cali o nia, Be keley, CA, USA, 7Uni e si y o he Basque Coun y UPV/EHU, Bilbao, Spain
Key Poin s:
• Ice Gian e lec i i y spec a om
0.3 o 2.5μm well app oxima ed by
a single ae osol model comp ised o
h ee o ou dis inc laye s
• S a ic s abili y egion a 1–2ba ,
caused by me hane condensa ion,
seems o lead o build-up o haze and
seeds CH4 snow a i s base
• Da kening o deepes H2S/haze laye ,
based a p>5–7ba , ound o accoun
well o spec al p ope ies o da k
spo s
Co espondence o:
P.G. J. I win,
[email p o ec ed]x.ac.uk
Ci a ion:
I win, P.G. J., Teanby, N. A., Fle che ,
L. N., Toledo, D., O on, G. S., Wong,
M. H., e al. (2022). Hazy blue wo lds:
A holis ic ae osol model o U anus and
Nep une, including da k spo s. Jou nal
o Geophysical Resea ch: Plane s,
127, e2022JE007189. h ps://doi.
o g/10.1029/2022JE007189
Recei ed 12 JAN 2022
Accep ed 16 MAY 2022
Au ho Con ibu ions:
Concep ualiza ion: P.G. J. I win, N.
A. Teanby, L. N. Fle che , D. Toledo, G.
S. O on, M. H. Wong, M. T. Roman, S.
Pé ez-Hoyos, A. James, J. Dobinson
Da a cu a ion: P.G. J. I win
Fo mal analysis: P.G. J. I win
Funding acquisi ion: P.G. J. I win
In es iga ion: P.G. J. I win
Me hodology: P.G. J. I win, N. A.
Teanby, L. N. Fle che , D. Toledo, M. H.
Wong, S. Pé ez-Hoyos
P ojec Adminis a ion: P.G. J. I win
Resou ces: P.G. J. I win
So wa e: P.G. J. I win, N. A. Teanby, L.
N. Fle che , D. Toledo
Valida ion: P.G. J. I win
Visualiza ion: P.G. J. I win
W i ing – o iginal d a : P.G. J. I win
10.1029/2022JE007189
RESEARCH ARTICLE
1 o 44
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
2 o 44
spec um, and enhanced Rayleigh-sca e ing om a mosphe es ha ha e low abundances o ae osols. In addi ion
o CH4, I win e al.(2018) de ec ed he p esence o gaseous H2S in U anus's a mosphe e, which is also p obably
p esen in Nep une's a mosphe e (I win, Toledo, Ga land, e al.,2019). Hence, i would seem ha H2S and NH3
eac oge he o o m a deep cloud o NH4SH(s) (a p essu es o ∼40ba ), which lea es H2S alone o condense
a a lowe p essu e, bu g ea e han ∼3ba (I win e al.,2018; I win, Toledo, B aude, e al.,2019). Gi en he
known empe a u e p o ile and me hane abundance, me hane should condense a ∼1.5ba in bo h plane s, and
hence i migh be expec ed ha a hick cloud o me hane should simila ly sh oud bo h wo lds. Howe e , his
does no seem o be he case, al hough uppe oposphe ic (200–600 mb) b igh clouds a e commonly seen in
Nep une's a mosphe e, and occasionally in U anus's a mosphe e. In addi ion, se e al da k spo s ha e been seen in
Nep une's a mosphe e, mos amously he G ea Da k Spo obse ed by Voyage -2 in 1989 (Smi h e al.,1989),
bu also in mo e ecen Hubble Space Telescope obse a ions (Hammel e al.,1995; Hsu e al.,2019; S omo sky
e al.,2011; Wong e al.,2018). These spo s a e o unknown o igin, bu seem only o be isible a wa eleng hs
<700nm. One da k spo has been epo ed in U anus's a mosphe e (Hammel e al.,2009), which was less da k,
bu appea s o ha e been obse able o wa eleng hs as long as 1.5μm.
A i s glance, he isible/nea -in a ed spec a o hese plane s a e e y simila , as can be seen in Figu e1.
Howe e , i appea s ha a he peaks, Nep une is gene ally sligh ly less b igh , while a longe me hane-ab-
so bing wa eleng hs, and in he UV, Nep une is mo e e lec i e. To simula e hese spec a, a numbe o models
o he e ical dis ibu ion o clouds and hazes ha e been p oposed o U anus (e.g., I win e al.,2015,2018;
Ka koschka & Tomasko,2009; Roman e al.,2018; S omo sky e al.,2019; Tice e al.,2013) and o Nep une
(e.g., I win e al.,2011a; I win, Toledo, B aude, e al.,2019; I win, Toledo, Ga land, e al.,2019; Ka koschka
& Tomasko,2011; Luszcz-Cook e al.,2016). All hese models mos ly ha e a hick ae osol laye a 2–4ba s
(assumed o be pho ochemical haze and pe haps mixed wi h H2S ice) and some so o o e lying haze. This ae o-
sol laye has been modelled as a uni o mly mixed (wi h heigh ) haze (e.g., I win e al.,2015; Tice e al.,2013),
o as a disc e e de ached haze (e.g., I win, Toledo, B aude, e al.,2019), o has been modelled ab ini io om
mic ophysical models (e.g., Toledo e al.,2019; Toledo e al.,2020). The eason ha all hese cons i uen s a e
hough o be pho ochemically p oduced hazes, a he han clouds, is ha away om he disc e e, b igh uppe
oposphe ic me hane ice clouds, hey a e op ically hin, appea o be spa ially homogeneous and also need
a some wa eleng hs o ha e single-sca e ing albedos conside ably less han uni y (e.g., I win e al.,2011a;
I win e al.,2015) in o de o be consis en wi h he obse ed limb-da kening/limb-b igh ening. The pa icles in
he uppe - oposphe ic/lowe -s a osphe ic haze, in pa icula , a e seen o be a he da k in he 1–2μm egion
(e.g., I win e al.,2011a), and he pa icles in he “main” 2–4-ba laye also seem o ha e signi ican abso p ion
ea u es. By con as , eshly condensed me hane (and p esumably also H2S ice) is expec ed o be nea ly conse -
a i ely sca e ing.
His o ically, cloud/haze e ie al s udies ha e aken a se o obse ed spec a, co e ing a pa icula ange o
wa eleng hs, and ound a cloud/haze model consis en wi h hese obse a ions using simple cloud/haze pa ame-
e isa ions and ad hoc adjus men s o single-sca e ing albedo and sca e ing phase unc ion asymme y. Di e en
s udies ha e used di e en wa eleng h anges and di e en ad hoc cloud/haze models, which has made i di icul
o in e p e hese s udies simul aneously o gain a deepe , simple ep esen a ion o he ae osol s uc u es o hese
wo lds. Wha makes such a holis ic app oach e en mo e di icul is ha we ha e no “g ound u h” in o ma ion
on wha he ice gian ae osols a e made o and wha hei spec al p ope ies a e. Hence, he p oblem is ex emely
degene a e and mul iple solu ions exis . Recen ly, a emp s ha e been made o i a wide ange o wa eleng hs
simul aneously using mode a ely sel -consis en models. I win e al.(2015) modelled IRTF/SpeX obse a ions
(0.8–1.8μm) o U anus, eco ded nea he disc cen e, using a simple wo-componen model comp ising a e i-
cally hin ae osol laye based a ∼2ba , wi h a iable opaci y, base p essu e and ac ional scale heigh , combined
wi h an ex ended haze o a iable opaci y, bu ixed base p essu e o 1.0ba and ixed ac ional scale heigh
o 1.0 (i.e., uni o mly mixed). This cloud/haze scheme was linked wi h a sel -consis en cloud-sca e ing model
ha i ed o he imagina y e ac i e index spec a o he wo cons i uen s, econs uc ing he eal pa using a
K ame s-K onig analysis and hen calcula ed he ex inc ion c oss-sec ions, single-sca e ing albedos and phase
unc ions using Mie heo y. I was ound ha he pa icles in he “main” ∼2-ba ae osol laye mus be signi i-
can ly mo e abso bing a wa eleng hs longe han 1μm. Ano he s udy o ind a model able o accoun o he
obse ed e lec i i y spec um o e a wide wa eleng h ange is ha o S omo sky e al.(2019), who eanaly-
sed HST/STIS obse a ions (0.3–1.0μm) o U anus (Ka koschka & Tomasko,2009). Like I win e al.(2015),
S omo sky e al.(2019) a ou ed a simple wo-componen cloud/haze s uc u e o he mo e complex i e-laye
W i ing – e iew & edi ing: P.G. J.
I win, N. A. Teanby, L. N. Fle che , D.
Toledo, G. S. O on, M. H. Wong, M.
T. Roman, S. Pé ez-Hoyos, A. James, J.
Dobinson
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
3 o 44
s uc u e used in hei p e ious analysis (S omo sky e al.,2014), and like I win e al.(2015) we e able o make
hei cloud/haze model consis en ou o 1.6μm wi h IRTF/SpeX and Keck/NIRC2 obse a ions by inc easing he
pa icles' imagina y e ac i e index a longe wa eleng hs. This inc ease o in e ed nimag wi h wa eleng h has
also been epo ed by de Klee e al.(2015). S omo sky e al.(2019) no ed ha a plausible condensable species
in he 1–3ba egion is H2S, bu since he spec al cha ac e is ics o his condensa e a e no cu en ly known,
he de e mined wa eleng h dependence o nimag could no be used o cons ain i s iden i y. Finally, S omo sky
e al.(2019) epo ed he possible de ec ion o a second, deepe ae osol laye nea ∼10ba , which hey en a i ely
sugges ed o be composed o NH4SH.
While a emp s ha e been made o model U anus spec a o e a wide wa eleng h ange, he same canno be said
o Nep une. Nep une is a signi ican ly smalle a ge han U anus and hence mo e di icul o spa ially esol e,
especially a longe wa eleng hs. I is also signi ican ly mo e cloudy (i.e., uppe oposphe ic me hane ice clouds
a e widesp ead, e.g., I win e al.,2016), which a lowe spa ial esolu ion makes i di icul o disen angle sunligh
e lec ed om he backg ound ae osol s uc u e om ha e lec ed om he disc e e b igh clouds. Howe e ,
gi en hese obse a ional di icul ies i is su p ising ha o ou knowledge no a emp has p e iously been made o
i he spec a o bo h hese plane s wi h a single model, e en hough he obse able a mosphe es o hese plane s
ha e simila oposphe ic empe a u e and composi ion and ha e simila obse able spec a, al hough we do no e
ha he U anus and Nep une models o Ka koschka and Tomasko(2009) and Ka koschka and Tomasko(2011)
a e e y simila . In his pape we p esen a holis ic ae osol model o bo h U anus and Nep une and also p opose
a simple way o explaining he phenomenon o “da k spo s”, which a e occasionally seen in hese a mosphe es,
bu whose na u e has un il now been a mys e y.
2. Obse a ions
The obse a ions analysed in his s udy come om a a ie y o sou ces. The imaging obse a ions om HST/
WFC3 and Voyage -2/ISS ( o Nep une) a e desc ibed la e , bu he e we gi e an o e iew o he spec al obse -
a ions conside ed.
Figu e 1. Composi e HST/STIS and IRTF/SpeX cen al-me idian-a e aged I/F spec a o U anus and Nep une compa ed
wi h each o he o e he HST/STIS (0.3–1.0μm) and IRTF/SpeX (0.8–2.5μm) spec al anges. No e ha he HST/STIS da a
ha e been smoo hed o he IRTF/SpeX esolu ion o 0.002μm. Also o e plo ed, o e e ence, in he op panel a e he ed,
g een, blue sensi i i ies o he human eye (S ockman,2019; S ockman & Sha pe,2000).
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
4 o 44
2.1. U anus Spec al Obse a ions
We analysed HST/STIS obse a ions o U anus om 2002 (Ka koschka & Tomasko,2009), 2012 (S omo sky
e al.,2014) and 2015 (S omo sky e al.,2019). Since ou p ima y in en ion in his pape was no o e isi
he ques ion o la i udinal a iabili y o me hane abundance o pola b igh ening, we concen a ed on he 2002
da a (Ka koschka & Tomasko,2009), when he disc o U anus appea ed pa icula ly ea u eless, allowing us o
combine he da a om all la i udes oge he . This obse a ion was made on 19 Augus 2002, be ween 01:43 and
10:57 UT. HST/STIS is ac ually a long sli spec ome e , bu he sli was aligned pa allel o he cen al me idian
and hen s epped om he cen al me idian o he edge o he plane o o m a “cube” o hal he plane , whe e a
each loca ion on he disc a comple e spec um co e ing 300.4–1,020.0nm was eco ded a a esolu ion o 1nm,
sampled e e y 0.4nm.
We also analysed an obse a ion o U anus made using IRTF/SpeX, ano he long-sli spec ome e . In his case,
he sli was aligned on he disc cen e and he luxes in eg a ed along he cen al me idian. This s anda d e e ence
spec um is a ailable on he IRTF Spec al Lib a y websi e (h p://i web.i a.hawaii.edu/∼spex/IRTF_Spec al_
Lib a y), epo ed by Rayne e al.(2009), and was made in SXD mode (0.8–2.5μm) on 18 May 2000. These da a
ha e a spec al esolu ion o 0.002μm.
Finally, we analysed obse a ions o U anus made wi h Gemini/NIFS in H-band (i.e., 1.47–1.8μm) in 2009 and
2010 (I win e al.,2011b; I win, Teanby, e al.,2012). Gemini/NIFS is an in eg al ield-uni (IFU) spec ome e
ha simul aneously eco ds spa ial and spec al in o ma ion, and whe e each pixel o “spaxel” is composed o a
comple e spec um co e ing he a ge ed spec al ange wi h a spec al esol ing powe o R∼5,200. The ac ual
cube used o ou e ie al s udy was eco ded on 2 Sep embe 2009, which had good spa ial esolu ion and was
easonably clea o disc e e ea u es.
To enable easy in e compa ison and simula ion speed he HST/STIS and Gemini/NIFS da a we e smoo hed o he
spec al esolu ion o IRTF/SpeX o 0.002μm (i.e., 2nm), and sampled wi h a s ep o 0.001μm.
Du ing he ime pe iod spanned by hese obse a ions, U anus mo ed h ough i s o bi abou he Sun and Table1
lis s he da e, sub-Ea h la i ude (plane ocen ic) ϕE, and also he appa en a ge -cen e ed longi ude o he Sun Ls
(which gi es a con enien measu e o season, wi h 0° being no he n sp ing equinox, 90° being no he n summe
sols ice, e c.) o he obse a ions. In addi ion, we lis he disc-in eg a ed pho ome ic magni udes o U anus as
obse ed and epo ed by Lockwood(2019) in he y (551nm) and b (472nm) il e s o he S ömg en pho o-
me ic sys em, which gi es a measu e o he o e all disc b igh ness and blueness. I can be seen ha he IRTF/
SpeX and HST/STIS obse a ions we e bo h made wi h Ls∼335° and ϕE∼−25°. Howe e , he Gemini/NIFS
obse a ion comes om jus a e he no he n sp ing equinox in 2007 wi h ϕE=7.9°. Hence, while he IRTF/
SpeX and HST/STIS obse a ions will be sligh ly mo e weigh ed o condi ions in he sou he n hemisphe e, he
Gemini/NIFS obse a ions will be mo e weigh ed o equa o ial egions and in a sligh ly la e season. Howe e ,
nei he se o obse a ions will sample well he hazes in he pola egions. F om 2000 o 2009 he disc-a e aged
magni ude o U anus dec eased by ∼0.03 and became sligh ly mo e blue as he sou he n pola “hood” o “cap”
U anus obse a ions
Da e Ins umen Wa eleng h ange LsSub-ea h la i ude ϕEb-mag 471nm y-mag 511nm b-y
18 May 2000 IRTF/SpeX 0.8–2.5μm 330.4° −27.6° 5.769 5.560 0.209
19 Augus 2002 HST/STIS 300–1,020nm 339.3° −21.4° 5.779 5.577 0.202
2 Sep embe 2009 Gemini/NIFS 1.47–1.8μm 6.8° +7.9° 5.785 5.592 0.193
Nep une obse a ions
Da e Ins umen Wa eleng h ange LsSub-ea h la i ude ϕEb-mag 471nm y-mag 511nm b-y
30 June 2000 IRTF/SpeX 0.8–2.5μm 259.5° −28.7° 7.830 7.704 0.126
3 Augus 2003 HST/STIS 300–1,020nm 266.2° −29.1° 7.809 7.689 0.120
7 Sep embe 2009 Gemini/NIFS 1.47–1.8μm 279.5° −28.8° 7.819 7.694 0.125
Table 1
Summa y o Spec al Obse a ions o U anus and Nep une
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
5 o 44
(e.g., S omo sky & F y,2008) became less isible. Howe e , hese changes a e ela i ely small, enabling us o
assume ha all h ee se s o obse a ions we e obse ing app oxima ely he same disc o U anus. Howe e , ca e
should be aken when compa ing his wo k wi h Voyage -2 s udies o U anus's ae osol s uc u e, since U anus
was hen nea sou he n summe sols ice and had a well de eloped “hood” and ma kedly highe albedo and hus
b igh ness (Lockwood,2019).
2.2. Nep une Spec al Obse a ions
We analysed HST/STIS obse a ions o Nep une (Ka koschka & Tomasko,2011) made on 3 Augus 2003,
be ween 4:38 and 14:15 UT. As o he U anus HST/STIS da a hese o m a “cube” o hal o Nep une's disc,
co e ing 300.4–1,020.0nm.
We also analysed a e e ence obse a ion o Nep une made using IRTF/SpeX and in eg a ed along he cen al
me idian, a ailable on he IRTF Spec al Lib a y (Rayne e al.,2009). The SXD componen o his e e ence
spec um analysed he e (0.8–2.5μm), was obse ed on 30 June 2000.
Finally, we analysed obse a ions o Nep une made wi h Gemini/NIFS in 2009 (H-band) and 2011 (I, J, and
H-band, i.e., 0.94–1.16μm, 1.14–1.36μm, and 1.47–1.8μm, espec i ely) (I win e al.,2011a,2016). The ac ual
cube used o ou e ie al s udy was eco ded in he H-band on 7 Sep embe 2009 and was chosen o i s good
spa ial esolu ion and easonably limi ed dis ibu ion o disc e e cloud ea u es.
Du ing he ime pe iod spanned by hese obse a ions, Nep une also mo ed h ough i s o bi abou he Sun
and Table1 again lis s he da e, sub-Ea h la i ude ϕE, appa en a ge -cen e ed longi ude o he Sun Ls, and
he disc-in eg a ed pho ome ic magni udes (Lockwood,2019) o he obse a ions. Nep une's sou he n summe
sols ice occu ed in 2005, bu Nep une's slowe o bi abou he Sun means ha Ls and ϕE di e ed li le du ing he
o al elapsed pe iod, and can be assumed o be ∼270° and ∼−29°, espec i ely. Howe e , i can be seen ha all
h ee da a se s will be weigh ed owa ds condi ions in he sou he n hemisphe e, wi h he sou h pola egion clea ly
isible. F om 2000 o 2009 he disc-a e aged magni udes and colou o Nep une we e ound no o a y signi i-
can ly (Lockwood,2019), again enabling us o assume ha all h ee se s o obse a ions we e obse ing app oxi-
ma ely he same disc o Nep une. Howe e , ca e should again be aken when compa ing his wo k wi h Voyage -2
s udies o Nep une's ae osol s uc u e, and indeed he Voyage -2/ISS obse a ions desc ibed la e in his pape ,
since Nep une was hen s ill app oaching sou he n summe sols ice and was no iceably da ke (Lockwood,2019).
Once again, o enable easy in e compa ison he HST/STIS and Gemini/NIFS da a we e smoo hed o IRTF/SpeX
spec al esolu ion.
3. Analysis
3.1. A mosphe ic and Radia i e T ans e Modelling
We modelled hese obse a ions using he adia i e ans e and e ie al ool, NEMESIS (I win e al.,2008;
I win e al.,2022a,2022b). To accoun o mul iple sca e ing, NEMESIS employs a plane-pa allel ma ix ope a-
o model (Plass e al.,1973), whe e in eg a ion o e zeni h angle is pe o med wi h a Gauss-Loba o quad a u e
scheme, while he azimu h in eg a ion is done wi h Fou ie decomposi ion. We ha e ound ha i e zeni h angles
a e usually su icien o model he gian plane I/F spec a and he numbe o azimu h Fou ie componen s is se
om he iewing and sola zeni h angles as
𝐴𝐴𝐴𝐴
𝐹𝐹
=⌊Θ∕3⌋
, whe e Θ=max[θ,θ0] and whe e θ is he obse a ion
zeni h angle (in deg ees) and θ0 is he sola zeni h angle (in deg ees). This scaling o NF wi h Θ is necessa y o
econs uc eliably he sca e ing unc ions a highe zeni h angles, bu comes a a conside able compu a ional
cos . Calcula ions a in e media e zeni h angles a e in e pola ed be ween he ma ix ope a o calcula ions a he
nea es abula ed iewing and sola zeni h angles. The i e-angle zeni h angle quad a u e scheme used he e is
lis ed in Table 1 o I win e al.(2021).
NEMESIS was un in co ela ed-k mode, wi h he me hane k- ables gene a ed om a numbe o di e en sou ces
as desc ibed in Sec ion3.3. Fo H2–H2 and H2–He collision-induced abso p ion we used he coe icien s o
Bo ysow e al.(1989); Bo ysow and F ommhold(1989); Bo ysow e al.(2000), assuming a he mally equilib-
ia ed o ho:pa a hyd ogen a io o bo h U anus and Nep une. Rayleigh sca e ing was included as desc ibed
in I win, Toledo, B aude, e al.(2019), and he e ec s o pola iza ion and Raman sca e ing we e included as
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
6 o 44
desc ibed in Sec ion3.3. We used he sola spec um o Chance and Ku ucz(2010), ex apola ed o longe /
sho e wa eleng hs wi h he sola spec um o Ku ucz(1993). This combined sola spec um was smoo hed wi h
a iangula line shape o FWHM=0.002μm o consis ency wi h he U anus and Nep une esampled spec a.
3.2. A mosphe ic Models
The e e ence empe a u e and mole ac ion p o ile o U anus is he same as ha used by I win e al.(2018) and
is based on he “F1” empe a u e p o ile de e mined om Voyage 2 and HST/STIS obse a ions (S omo sky
e al.,2011), wi h He:H2=0.131 and including 0.04% mole ac ion o neon. We adop ed a simple “s ep”
model o he me hane p o ile wi h a iable deep mole ac ion (a p io i 4%), a iable ela i e humidi y abo e
he condensa ion le el and a limi ing s a osphe ic mole ac ion o 1×10
−4 (Enc enaz e al.,1998; O on
e al.,2014). Fo he a mosphe ic s a ic s abili y s udy discussed la e , we also added sa u a ion-limi ed p o iles
o H2S and NH3. When dealing wi h condensing gases such as CH4, once he p o ile o ha gas was de e mined,
he abundance o H2 and He was scaled a each le el, keeping He:H2=0.131, o ensu e ha he mole ac ions
added up o 1.0.
The e e ence empe a u e and mole ac ion p o ile o Nep une is he same as ha used by I win, Toledo,
B aude, e al.(2019) and I win e al.(2021) and is based on he “N” p o ile de e mined by Voyage -2 adio-oc-
cul a ion measu emen s (Lindal,1992), wi h He:H2=0.177 (15:85) and including 0.3% mole ac ion o N2.
We again adop ed a simple “s ep” me hane model wi h a a iable deep mole ac ion, a iable ela i e humidi y
abo e he condensa ion le el and limi ing he s a osphe ic mole ac ion o 1.5×10
−3 (Lellouch e al.,2010).
Again, he abundances o H2 and He we e adjus ed a each le el o ensu e he mole ac ions added up o 1.0,
keeping He:H2=0.177.
3.3. Spec al Modelling
The HST/STIS and IRTF/SpeX obse a ions o bo h U anus and Nep une we e i s combined o gi e composi e
cen al-me idian-a e aged spec a o bo h plane s, which a e shown in Figu e1. To c ea e hese combined spec-
a, we ook he HST/STIS obse a ions o U anus and Nep une om 2002 o 2003, espec i ely, a e aged hem
along he cen al me idian (masking disc e e cloud ea u es in he Nep une STIS da a) and hen scaled he IRTF/
SpeX U anus and Nep une spec a o ma ch a o e lapping wa eleng hs om 0.85 o 1.0μm. This scaling was
necessa y as he IRTF/SpeX da a a e in uni s o line-in eg a ed o al lux and needed o be con e ed o I/F. Gi en
unce ain y in he sli size and posi ion i was no possible o do his ab ini io wi h su icien accu acy and hence
e-scaling was necessa y o ensu e consis ency wi h HST/STIS da a. The Gemini/NIFS da a, al hough no used
in his ini ial analysis, we e also a e aged along he cen al me idian and hei e lec i i ies adjus ed o ma ch he
scaled IRTF/SpeX spec um a o e lapping wa eleng hs o la e use.
Un il now, ou adia i e ans e model NEMESIS has no inco po a ed Raman sca e ing, bu since he HST/
STIS obse a ions ex end o 0.3μm, whe e S omo sky(2005a) shows ha Raman sca e ing is signi ican , i
was necessa y he e o inco po a e his e ec . To do his, we ollowed he app oach o S omo sky(2005a) and
conside ed only he S(0), S(1) and combined “Q” ansi ions, using he c oss-sec ion abso p ion coe icien s o
Fo d and B owne(1973). Radia ion sca e ed om sho o longe wa eleng hs was in oduced a he longe
wa eleng hs as an addi ional pseudo- he mal-emission e m, using he assump ion o S omo sky(2005a) ha
his Raman e-emi ed adia ion is e ec i ely iso opic, wi h wa enumbe shi s o 354.69cm
−1, 587.07cm
−1
and 4,160.00cm
−1, espec i ely o he S(0), S(1) and combined “Q” ansi ions. In addi ion o including Raman
sca e ing, we also u he e ised NEMESIS o inco po a e a co ec ion o pola isa ion e ec s as desc ibed by
S omo sky(2005b).
Using ou upg aded NEMESIS model we show in Figu e2 syn he ic spec a calcula ed om ou assumed U anus
and Nep une a mosphe es o ae osol- ee condi ions, including Rayleigh sca e ing, Raman sca e ing, H2-H2
and H2-He collision-induced abso p ion (CIA), and abso p ion by gaseous me hane. As can be seen, he measu ed
e lec i i y (I/F) o bo h U anus and Nep une dec eases apidly wi h wa eleng h and is well ma ched o e all by
a 1/λ
4 cu e, sugges ing ha any ae osols which a e p esen a e small and o low in eg a ed opaci y. In Figu e2
we compa e calcula ions made using h ee di e en a ailable sou ces o me hane abso p ion da a. The band
da a o Ka koschka and Tomasko(2010), con e ed o k- ables by I win e al.(2011a), co e s he en i e wa e-
leng h ange and ep oduces mos o he obse ed ea u es well. Howe e , a longe wa eleng hs we can also use
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
7 o 44
k- ables gene a ed om HITRAN2016 me hane line da a (Go don e al.,2017), and a mo e ecen compila ion
o me hane line da a om he TheoRETS p ojec (Rey e al.,2018). The HITRAN2016 da a can be seen o be
in good ag eemen wi h he band/k-da a a wa eleng hs longe han 1.0μm, while he TheoRETS da a ex ends
easonably well o e en sho e wa eleng hs o 0.75μm. Howe e , nei he se ex ends o isible wa eleng hs and
since ou aim in his s udy is o ind a holis ic ae osol model o U anus and Nep une ha ma ches all wa eleng hs
co e ed by HST/STIS, IRTF/SpeX and Gemini/NIFS simul aneously we used he band/k-da a o Ka koschka
and Tomasko(2010)/I win e al.(2011a) in his s udy. I is also appa en om Figu es1 and2 ha Nep une is
mo e e lec i e han U anus a me hane-abso bing wa eleng hs longe han ∼1μm, indica ing ha Nep une has a
highe opaci y o uppe -a mosphe e ae osols, which mus be o a size g ea e han ∼1μm in o de o be isible a
hese longe wa eleng hs. Fu he mo e, i would appea ha any ae osols in U anus's uppe a mosphe e mus be
o e y low opaci y, since a pu e Rayleigh/Raman sca e ing calcula ion al eady ma ches he obse ed e lec i i y
a me hane-abso bing wa eleng hs easonably well.
In o de o analyse he obse a ions, we needed o de e mine he dep hs o which sunligh can pene a e a di e -
en wa eleng hs. In Figu e3 we show con ou plo s o he wo-way ansmission om space, o a e ical pa h,
o di e en le els in he a mosphe es o U anus and Nep une o ae osol- ee condi ions, including Rayleigh sca -
e ing, Raman sca e ing, me hane abso p ion and hyd ogen-helium collision-induced abso p ion. He e i can be
seen ha he pene a ion dep h is e y simila o U anus and Nep une, bu ha a adia i e ans e model wishing
o simula e he obse a ions needs po en ially o co e a e y wide ange o p essu e le els. Hence, he p essu e
ange o bo h U anus and Nep une models was se o co e 40–0.001ba and he a mosphe e spli in o 39 laye s
(equally spaced in log p essu e) o ou adia i e ans e calcula ions.
To bes analyse he combined HST/STIS, IRTF/SpeX and Gemini/NIFS obse a ions, and place s ong cons ain
on he e ical s uc u e and spec al dependence o pa icle sca e ing p ope ies, we needed o de elop an
e icien way o modelling he obse ed cen e- o-limb a ia ions o he HST/STIS and Gemini/NIFS da a and
combine hese wi h he wide wa eleng h- ange cen al-me idian-a e aged IRTF/SpeX obse a ions, which
p o ide impo an cons ain s on pa icle size and be e p obe lowe p essu e le els a he longe wa eleng hs. To
Figu e 2. Combined HST/STIS and IRTF/SpeX cen al-me idian-a e aged I/F spec a o U anus and Nep une compa ed
wi h calcula ions om an ae osol- ee a mosphe e including only Rayleigh/Raman sca e ing and gaseous abso p ion om
me hane and hyd ogen-helium collision-induced abso p ion. The obse a ions a e plo ed in black, while calcula ions using
di e en sou ces o me hane abso p ion om band da a (Ka koschka & Tomasko,2010) and line da a se s HITRAN2016
(Go don e al.,2017) and TheoRETS (Rey e al.,2018) a e o e -plo ed in ed, pu ple and cyan, espec i ely. Also plo ed in
g een in bo h panels a e simple 1/λ
4 cu es, showing he gene al end o he combined spec a. N.B., he HITRAN2016 and
TheoRETS do no co e he en i e ange and so a sho e wa eleng hs he calcula ions e e o Rayleigh/Raman sca e ing
only.
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
8 o 44
do his we employed he Minnae limb-da kening app oxima ion (Minnae ,1941), whe e o an obse a ion a
a pa icula wa eleng h, he e lec i i y R is app oxima ed as:
𝑅𝑅
=𝑅𝑅0𝜇𝜇
𝑘𝑘
0
𝜇𝜇
𝑘𝑘−1.
(1)
He e, μ and μ0 a e he cosines o he iewing and sola zeni h angles, espec i ely, R0 is he i ed nadi e lec-
ance, and k is he i ed limb-da kening pa ame e . I win e al.(2021) applied his model o VLT/MUSE obse -
a ions o Nep une made in 2018 and ound i o gi e a e y good app oxima ion o he obse a ions and was
also well ep oduced by he NEMESIS adia i e ans e model. Hence, in his s udy we used he Minnae
app oxima ion o simpli y ou calcula ion o he disc-a e aged limb-da kening and cen al-me idian a e aged
spec a ollowing he scheme:
1. As p e iously desc ibed, he HST/STIS and Gemini/NIFS obse a ions we e i s a e aged o he IRTF/SpeX
esolu ion o 0.002μm and sampled on a egula g id o spacing 0.001μm. The masked HST/STIS da a
we e hen a e aged along he cen al me idian and used o scale he IRTF/SpeX obse a ions o make he
combined HST/IRTF p ocessed obse a ions sel -consis en . The Gemini/NIFS da a we e also a e aged along
he cen al me idian (masking ou disc e e cloud ea u es) and hemsel es scaled o be consis en wi h he
combined HST/STIS and IRTF/SpeX obse a ions.
2. The a e aged HST/STIS and Gemini/NIFS “cubes” we e hen masked o exclude disc e e cloud ea u es and
he emaining obse a ions a all la i udes Minnae -analysed o de i e spec a o he disc-a e aged R0(λ) and
k(λ). This was simpli ied in his case since U anus and Nep une a e so dis an ha he sola zeni h angle and
iewing zeni h angle can be app oxima ed o be he same (i.e., μ=μ0) and hence R=R0μ
2k−1.
3. The i ed Minnae pa ame e s R0(λ) and k(λ) we e used o gene a e econs uc ed spec a o HST/STIS
and Gemini/NIFS a wo zeni h angles (0°, 61.45°), co esponding o wo o he i e zeni h angles o he
Gauss-Loba o mul iple-sca e ing adia i e ans e model used in NEMESIS. The highe angle is la ge
enough o ensu e we ully cap u e he obse ed limb-da kening/limb-b igh ening, and is coinciden wi h one
o he Gauss-Loba o quad a u e angles, hus ob ia ing he need o any in e pola ion (I win e al.,2021).
Howe e , i is no so la ge ha he compu a ional cos becomes excessi e.
The wo esul ing econs uc ed HST/STIS spec a, wo econs uc ed Gemini/NIFS spec a and he measu ed
IRTF/SpeX cen al-me idian line-a e aged spec um we e hen used as a se o “measu ed” obse a ions o
NEMESIS. By i ing an ae osol model o he HST/STIS and Gemini/NIFS p ocessed spec a a 0° and 61.45°
zeni h angles, and ex ac ing ou bes i s o he Minnae pa ame e s R0(λ) and k(λ), we could hen simply ep o-
duce he obse a ions a any o he angle om Equa ion1, assuming ha he Minnae app oxima ion holds a
all he o he zeni h angles o ou zeni h-angle quad a u e scheme, which I win e al.(2021) ound o be a good
Figu e 3. Two-way ansmission om space, o a e ical pa h, o di e en le els in ou s anda d U anus and Nep une
a mosphe es o ae osol- ee condi ions. These calcula ions include Rayleigh sca e ing, Raman sca e ing and abso p ion
om gaseous me hane and hyd ogen-helium collision-induced abso p ion.
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
9 o 44
app oxima ion o hei analysis o VLT/MUSE Nep une obse a ions. Howe e , we s ill needed an e icien way
o simula ing he cen al-me idian-a e aged IRTF/SpeX spec a. We could ha e compu ed spec a a mul iple
loca ions along he cen al me idian and a e aged hese, bu his would ha e been slow, especially nea he disc
edges. Ins ead, o each i e a ion we calcula ed spec a a wo zeni h angles (0° and 42.47°), ex ac ed Minnae
pa ame e s R0 and k a each wa eleng h (using k=(1+log(Rμ/R0)/ log(μ))/2, whe e R0 is he nadi -calcula ed
adiance and Rμ is he adiance calcula ed a μ=cos(42.47°)) and used hese o compu e he cen al-me idian
line-a e age as ollows. The eason we chose he middle zeni h angle o ou quad a u e scheme (42.47°) he e,
ins ead o he second la ges (61.45°) as we did o he HST/STIS obse a ions, is ha calcula ions a lowe zeni h
angles equi e ewe Fou ie azimu h componen s and a e mo e apid; since we only needed o app oxima e he
line-a e age in his case, a he han limb-da kening, he lowe angle was ound o be su icien ly accu a e.
In AppendixB we show ha he mean adiance in eg a ed along he cen al me idian o a plane whose limb-da k-
ening is well ep esen ed by he Minnae app oxima ion can be w i en (assuming μ=μ0) as:
𝑅𝑅
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 =𝑅𝑅0
∫𝜋𝜋∕2
0
(cos 𝜃𝜃)2𝑘𝑘d
𝜃𝜃𝜃
(2)
Hence, i we ha e an es ima e o he Minnae limb-da kening coe icien , k, and nadi adiance, R0, we can
easily compu e he co esponding cen al me idian line-a e aged adiance. This unc ion canno be in eg a ed
analy ically and so we p e-compu ed a able o
𝐴𝐴 𝑅𝑅
𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙
∕
𝑅𝑅
0
e sus k and hen in e pola ed his o he alue o k
de i ed a each wa eleng h. Hence, using calcula ions a jus wo angles o de e mine k we we e able o accu-
a ely simula e he cen al-me idian line-a e aged IRTF/SpeX obse a ions using Equa ion2. Fo he HST/STIS
and Gemini/NIFS da a, we u he e i ied ha he cen al-me idian-line-a e age calcula ed om Equa ion2
using he disc-a e aged Minnae pa ame e s was consis en wi h he measu ed IRTF/SpeX obse a ions. Fo he
Nep une Gemini/NIFS obse a ions, his es necessi a ed some i e a ion on he deg ee o which disc e e clouds
we e masked in o de o gene a e he bes o e all se o sel -consis en Minnae coe icien s. All i e spec a
could hen be i ed simul aneously, o indi idual spec a i ed sepa a ely as necessa y.
Ou s a ing assump ion in his analysis is ha he cloud/haze s uc u es o U anus and Nep une a e subs an ially
he same, bu ha Nep une has hicke uppe - oposphe ic/lowe -s a osphe ic haze. Hence, o begin wi h we
analysed he simple case o he U anus obse a ions and ex ended o Nep une obse a ions la e .
3.4. Analysis o HST/STIS U anus Obse a ions
We i s analysed he HST/STIS econs uc ed obse a ions o U anus a zeni h angles o 0° and 61.45° om 0.5
o 1.0μm. We conduc ed a i s -pass e ie al using a con inuous dis ibu ion o haze pa icles, in o de o le he
da a ( a he han a p io i assump ions) de e mine he loca ion o ae osol laye s. In his i s pass, he pa icle sizes
we e assumed o ollow a Gamma dis ibu ion wi h mean adius 0.1μm and a iance σ=0.3. We also i ed o
he imagina y e ac i e index spec um (a p io i alue se o 0.001) o hese pa icles a six wa eleng hs om
0.5 o 1.0μm, s ep 0.1μm, and hen econs uc ed he eal e ac i e index spec um using he K ame s-K onig
ela ion, assuming he eal e ac i e index a 0.8μm was ixed o a alue o 1.4. The esul ing complex e ac-
i e index spec um was hen used o calcula e, using Mie heo y, he ex inc ion c oss-sec ion, single-sca e ing
albedo, and phase unc ion spec a. Howe e , since we expec he pa icles (ice and haze) o be non-sphe ical,
he phase unc ion spec a we e app oxima ed wi h combined Henyey-G eens ein phase unc ion pa ame e s o
a e age o e ea u es peculia o sphe ical pa icles such as he “ ainbow” and “glo y.” Fo he me hane p o ile
we assumed a “s ep” unc ion wi h e ie able deep abundance up o he condensa ion le el, bu wi h he ela-
i e humidi y abo e he condensa ion le el ixed o 100% and he s a osphe ic abundance limi ed o no exceed
1×10
−4. The e ie al was a emp ed wi h wo widely spaced a p io i ae osol abundance p o iles (assumed o
ha e cons an opaci y/ba a all p essu e le els) o achie e a “b acke ed” e ie al, whe e he e ie ed p o iles
will o e lap whe e hey a e well cons ained by he measu emen s and end back o hei espec i e a p io i alues
a p essu es whe e he e is li le sensi i i y. Figu e4 shows he i s o he econs uc ed spec a oge he wi h he
i ed ae osol abundance p o iles. As can be seen, he i s uggles sligh ly a sho wa eleng hs, bu o he wise
we ind ha he HST/STIS obse a ions a e well i ed by an ae osol s uc u e wi h a hin, well de ined peak a
∼1.5ba and a second laye a p essu es g ea e han ∼4ba . Al hough we can clea ly de ec he op o his deepe
laye , we canno cons ain i s base p essu e as he b acke ed e ie als end back o hei espec i e a p io i alues
a p essu es exceeding app oxima ely 5–7ba ; his makes sense gi en ha he wo-way ansmission o space o a
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
16 o 44
3.7. Analysis o IRTF/SpeX Nep une H+K Band Obse a ions
Ha ing ound a good i o ou U anus obse a ions, we hen u ned ou a en-
ion o he Nep une obse a ions. Be o e analysing he combined HST/STIS,
IRTF/SpeX and Gemini/NIFS da a se s we i s o all sough o unde s and
he g oss di e ences be ween he U anus and Nep une IRTF/SpeX obse a-
ions, in pa icula he high e lec i i ies seen a me hane abso p ion wa e-
leng hs longe han 1μm o Nep une, bu no seen o U anus.
The 1.65–2.4μm egion is pa icula ly good o de e mining uppe a mos-
phe ic ae osol densi y since he s ong me hane abso p ion band a 1.7μm
lies nex o s ong H2-H2/H2-He collision-induced abso p ion bands cen ed
a 2.1μm. The weigh ing unc ions o he me hane-abso bing and hyd ogen/
helium-CIA-abso bing egions co e a simila ange o p essu e le els in he
uppe oposphe e (0.6–0.1ba ) and hus his spec al egion can be used o
esol e he degene acy be ween ae osol opaci y and uppe oposphe ic me h-
ane abundance and e ie e eliable es ima es o bo h (Roman e al.,2018).
Figu e10 shows a “b acke ed” e ie al o he IRTF/SpeX spec um in he
wa eleng h ange 1.65–2.4μm, assuming wo widely sepa a ed con inuous
dis ibu ions o small ae osols o mean adius 0.1μm, a iance σ=0.3, and
ixed nimag=0.1. As can be seen, a sha ply peaked ae osol p o ile is a ou ed,
peaking a ∼0.2ba , wi h he local me hane ela i e humidi y e ie ed o be
∼32%. A i s glance his i ed ae osol s uc u e seems con a y he esul s
o mic ophysical modelling (Toledo e al.,2019,2020) whe e, since pho o-
chemically p oduced haze pa icles a e p oduced in he s a osphe e and hen
p og essi ely mixed o deepe and deepe p essu es, we expec a dis ibu ion
wi h dec easing opaci y/ba wi h inc easing p essu e. To unde s and wha
was going on he e, we needed o examine he e lec i i ies o e a wide
wa eleng h ange, which, as we did o U anus, we achie ed wi h a Nep une
“snippe ” analysis, which we ou line in he nex sec ion.
3.8. Analysis o Combined HST/STIS and IRTF/SpeX Nep une Obse a ions - Snippe Analysis
As o ou U anus analysis, we spli he HST/STIS and IRTF/SpeX obse a ions in o small, manageable “snip-
pe s” o wa eleng h wid h 0.1μm, spaced e e y 0.05μm and e ie ed he e ical ae osol p o ile o a Gamma
dis ibu ion o pa icles wi h mean adius 0.1μm and a iance σ=0.05, a ying also he imagina y e ac i e
index nimag and keeping n eal=1.4. The esul ing e ie ed ae osol e ical/wa eleng h s uc u e is shown in
Figu e11. As can be seen, he ae osol s uc u e sha es many simila i ies wi h he equi alen U anus esul s
(Figu e5), wi h a deep Ae osol-1 laye seen a p>∼4ba and a middle Ae osol-2 laye a ∼2ba (sligh ly deepe
han o U anus). A sho wa eleng hs i can also be seen ha he opaci y/ba inc eases wi h heigh in he uppe
oposphe e/lowe s a osphe e, and decays apidly wi h wa eleng h, consis en wi h ou expec a ions wi h small,
pho ochemically p oduced haze pa icles. Howe e , o Nep une he e is clea ly also a componen o e ically
con ined pa icles cen ed a ∼0.2ba , which mus ha e a la ge mean size in o de ha hei opaci y does no
d op no iceably wi h wa eleng h. We belie e he e ha we a e de ec ing in he IRTF/SpeX da a he signa u e o an
addi ional componen o la ge -sized pa icles a ∼0.2ba , which we su mise o be condensed me hane ice. Such
uppe oposphe ic me hane condensa ion clouds a e o en seen in Nep une obse a ions, especially in he egions
a 20–40°N and 20–40°S and a e seen o be highly empo ally and spa ially a iable. We ha e ied o mask
ou such egions in he HST/STIS and Gemini/NIFS da a. Howe e , since we do no ha e an image o Nep une
obse ed simul aneously wi h he IRTF/SpeX cen al-me idian line a e age, we do no know how signi ican his
componen o uppe oposphe ic me hane clouds is in he eco ded IRTF/SpeX spec um. Hence, we need o be
ca e ul when in e p e ing he IRTF/SpeX Nep une da a, especially when used in combina ion wi h he o he da a
se s. Howe e , he good co espondence be ween he scaled IRTF/SpeX and Gemini/NIFS da a se s, achie ed,
as desc ibed ea lie , by op imising he cu -o le el o b igh clouds in he Gemini/NIFS da a, eassu es us ha
hese da a a e easonably sel -consis en .
Pa ame e U anus Nep une
Opaci y τ1 (a 0.8μm) 0.8–1.1 0.5–0.8
F ac. Sc. H . sh10.08–0.12 0.14–0.18
Radius 10.05μm ( ixed) 0.05μm ( ixed)
P essu e p21.4–1.5ba 2.0–2.1ba
Opaci y τ2 (a 0.8μm) 2.0–3.5 1–2
Radius 20.3–0.8μm 0.3–0.8μm
P essu e p31.6ba ( ixed) 1.6ba ( ixed)
Opaci y τ3 (a 0.8μm) 0.03±0.01 0.04±0.01
Radius 30.05μm ( ixed) 0.05μm ( ixed)
P essu e p4n/a 0.2ba ( ixed)
Opaci y τ4 (a 0.8μm) n/a 0.030±0.005
Radius 4n/a 2.5±0.5μm
Deep CH4 mole ac ion 3±1% 7±1%
T opopause CH4 RH 100% ( ixed) 35±5%
No e. Tha he ac ional scale heigh o he Gaussian-shaped Ae osol-2 laye
(and Ae osol-4 laye o Nep une) was ixed a 0.1 and he ac ional scale
heigh o he Ae osol-3 laye was ixed a 2.0. Also ha he quo ed opaci ies
o he Ae osol-1 laye , τ1 a e in eg a ed om space down o a p essu e le el
o 5ba .
Table 2
Fi ed Model Pa ame e s o Combined HST/STIS, IRTF/SpeX and Gemini/
NIFS Da a
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
17 o 44
3.9. Simul aneous Re ie al o Combined HST/STIS, IRTF/SpeX, and Gemini/NIFS Nep une
Obse a ions
Ha ing ound om he “snippe ” analysis ha ou expec ed ae osol solu ion o Nep une was e y simila o ha
o U anus, we a emp ed o i he combined STIS/SpeX/NIFS Nep une da a se in he same way, excep ha
we also added a hin laye o me hane ice cen ed a 0.2ba and wi h a iable mean adius and ixed a iance
σ=0.3 (N.B. al hough we ha e modelled his laye as being homogeneous, i is also possible ha his componen
is composed o sub-pixel-scale clouds). We i s i ed he 0.8–0.9μm egion sepa a ely wi h a ange o andomly
a ied a p io i Ae osol-1 ac ional scale heigh s and Ae osol-2 base p essu es and adii and used hose achie ing
χ
2/n<1 as he a p io i o he ull e ie als, ixing he Ae osol-2 adii. Figu e12 shows one o ou bes i s o
Figu e 9. Fi ed nimag spec a o U anus ( op ow) and Nep une (bo om ow) o he lowe cloud/haze a 10ba (Ae osol-1), he middle cloud/haze a 1–2ba
(Ae osol-2) and he e ically ex ended uppe oposphe ic/lowe s a osphe ic haze (Ae osol-3). The illed con ou plo s show he linea addi ion o he bes - i ing
imagina y index dis ibu ions. O e -plo ed on hese dis ibu ions a e he ex ac ed mean nimag spec a, whe e ed a e he weigh ed a e ages o all bes - i ing e ie ed
spec a, g een a e he con ou -map-weigh ed a e ages, and cyan a e he e ie ed spec a om he ep esen a i e e ie al case shown o each plane . These spec a a e
lis ed in Tables3 and4. N.B., he a p io i alue o nimag was se o 0.001 and his is he alue he e ie als end back o when he da a a e no longe cons aining. The
IRTF/SpeX da a o U anus we e unca ed a 1.9μm as i can be seen om Figu e1 ha he obse a ions a e oo noisy o use a longe wa eleng hs.
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
18 o 44
λ(μm)
Ae osol-1
Mean 1
(>5–7ba )
Mean 2 Sample
Ae osol-2
Mean 1
(1–2ba ) Mean
2 Sample
Ae osol-3
Mean 1
(ex ended)
Mean 2 Sample
0.3 1.95×10
−3 5.62×10
−4 3.88×10
−4 1.10×10
−2 9.90×10
−3 8.59×10
−3 3.07×10
−3 2.98×10
−3 3.31×10
−3
0.4 6.73×10
−5 6.17×10
−5 2.19×10
−5 1.61×10
−3 1.64×10
−3 1.44×10
−3 1.50×10
−3 1.48×10
−3 1.51×10
−3
0.5 1.10×10
−6 1.66×10
−5 1.00×10
−6 1.35×10
−3 1.03×10
−3 1.07×10
−3 1.91×10
−4 1.90×10
−4 2.54×10
−4
0.6 2.96×10
−4 2.36×10
−4 2.30×10
−4 9.65×10
−4 1.10×10
−4 1.86×10
−5 1.70×10
−4 9.34×10
−5 2.99×10
−4
0.7 1.39×10
−3 7.88×10
−4 9.66×10
−4 1.37×10
−3 3.78×10
−4 8.37×10
−4 1.38×10
−3 2.59×10
−4 4.79×10
−4
0.8 2.12×10
−4 1.99×10
−4 6.88×10
−5 4.89×10
−3 1.69×10
−3 5.03×10
−3 7.74×10
−3 8.92×10
−4 7.96×10
−4
0.9 7.21×10
−4 2.51×10
−4 3.04×10
−4 4.24×10
−3 8.63×10
−4 3.84×10
−3 7.87×10
−3 3.21×10
−3 2.60×10
−3
1.0 2.46×10
−3 1.52×10
−3 6.26×10
−4 1.13×10
−2 7.70×10
−3 1.29×10
−2 1.52×10
−3 1.60×10
−3 1.14×10
−3
1.1 5.18×10
−2 1.16×10
−2 5.08×10
−3 6.91×10
−3 2.29×10
−3 3.92×10
−4 8.38×10
−2 1.97×10
−3 6.73×10
−2
1.2 3.23×10
−3 9.75×10
−3 2.37×10
−3 5.25×10
−2 3.55×10
−3 9.09×10
−3 7.20×10
−2 1.79×10
−3 1.20×10
−1
1.3 7.82×10
−3 5.05×10
−3 3.72×10
−3 1.72×10
−2 4.62×10
−3 1.12×10
−2 1.16×10
−2 2.37×10
−3 7.53×10
−2
1.4 4.46×10
−3 3.78×10
−3 1.18×10
−3 5.20×10
−1 3.46×10
−1 2.52×10
−1 2.16×10
−1 9.62×10
−3 2.46×10
−1
1.5 3.20×10
−4 3.52×10
−4 1.45×10
−4 1.06×10
−1 9.83×10
−2 6.72×10
−2 2.19×10
−2 6.77×10
−3 2.31×10
−2
1.6 4.19×10
−4 4.89×10
−4 2.01×10
−4 6.21×10
−2 5.65×10
−2 5.87×10
−2 3.53×10
−2 3.34×10
−2 3.62×10
−2
1.7 2.64×10
−3 2.49×10
−3 1.49×10
−3 1.23×10
−1 7.95×10
−2 4.01×10
−2 1.19×10
−3 2.28×10
−3 1.85×10
−3
1.8 6.98×10
−4 1.70×10
−3 6.35×10
−4 2.75×10
−3 4.89×10
−3 3.07×10
−3 7.35×10
−4 8.57×10
−4 9.75×10
−4
1.9 1.02×10
−3 1.00×10
−3 5.47×10
−4 1.47×10
−3 1.12×10
−3 1.67×10
−3 8.44×10
−4 9.53×10
−4 9.42×10
−4
No e. He e, o each ae osol ype, “Mean 1” is he weigh ed a e age o all bes - i ing e ie ed spec a, while “Mean 2” a e he a e ages o he con ou maps shown in
Figu e9. “Sample” is he e ie ed spec a om he ep esen a i e bes - i ing sample case shown o each plane .
Table 3
Es ima ed nimag Spec a o U anus Ae osols
Figu e 10. Example “b acke ed” i s o he longwa e pa o he IRTF/SpeX spec um o Nep une using wo di e en
con inuous a p io i dis ibu ions o ae osol pa icles o adius 0.1μm and and ixed nimag=0.1. The le panel compa es
he modelled spec a ( ed and cyan-dashed o wo di e en p io s) o ha obse ed (g ey), while he igh panel shows he
e ie ed ae osol p o iles o he wo di e en a p io i, indica ed in ed and cyan espec i ely, showing ha he spec um is
bes i in bo h cases wi h a laye ha has peak opaci y jus below he opopause nea 0.2ba . No e ha in he igh -hand
panel he a p io i and e ie ed e o anges a e shaded in g ey and edged by dashed colou ed lines.
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
19 o 44
he combined Nep une da a se , whe e we can see ha we again ma ch he obse ed e lec i i ies and limb-da k-
ening e y well. The e ical ae osol s uc u e e ie ed o his case is shown in Figu e13, which is comp ised
o a deep Ae osol-1 laye a ixed base p essu e 10ba wi h ac ional scale heigh 0.18 and in eg a ed opaci y
o 5ba (a 0.8μm) 0.81 (coinciden ally he same alue as o ou sampled U anus e ie al shown ea lie ), a
compac Ae osol-2 laye a 2.08ba and opaci y 1.8 composed o pa icles o mean adius 0.68μm, an ex ended
haze (Ae osol-3), based a 1.6ba wi h ixed ac ional scale heigh 2.0 and opaci y 0.05, and a de ached me hane
ice ae osol laye nea he opopause (0.2ba ), o opaci y 0.03 comp ised o pa icles o mean adius 2.8μm.
The me hane deep mole ac ion is 7.7% and ela i e humidi y a he opopause is 34% in his case. I should be
s essed he e ha once again he e is no single solu ion ha i s be e han all o he s; as we ha e pe o med mul i-
ple sligh ly pe u bed e ie als he e is a gene al class o solu ions ha i bes , o which his is one ep esen a i e
example. The comple e se o e ie ed pa ame e s is shown in Figu e14 and he ange and e o s on ou bes i
solu ions a e lis ed in Table2. I is wo h no ing, howe e , ha he e ie ed imagina y e ac i e index spec a o
he main ae osol componen s, shown in Figu e9, and lis ed in Table4 a e simila o hose e ie ed o U anus,
sugges ing a simila composi ion. I is also wo h no ing ha he opaci y o he middle Ae osol-2 laye a ∼2ba
is app oxima ely hal ha de e mined o U anus's a mosphe e, while he opaci y o he deepe Ae osol-1 laye
is also g ea ly educed. The lowe Ae osol-2 opaci y means ha he Ae osol-1 laye has a g ea e con ibu ion o
he modelled spec a and so we ha e g ea e cons ain on he Ae osol-1 imagina y e ac i e index spec um as
can be seen. Fo he me hane ice laye a 0.2ba , his is e ie ed o be composed o mode a ely la ge pa icles
( =2–3μm), which means hey a e mos e lec i e a he longe wa eleng hs whe e he inc eased sca e ing a
me hane-abso bing wa eleng hs is seen. I also means ha hey a e e ec i ely conse a i ely o wa d-sca e ing
a isible wa eleng hs, and hus hey ha e e y li le e ec he e (as can be seen la e in Figu e18). Finally, since
we disc imina ed agains cloudy egions when we compiled ou mean da a se s, he opaci y we e ie e o he
Ae osol-4 laye will o cou se be signi ican ly less han a ue disc-a e age ha includes such clouds.
One cu ious ea u e o hese e ie als is he signi ican ly la ge deep me hane abundance we e ie e o Nep une
o 7±1%, e sus 3±1% o U anus. An analysis o ecen Nep une/MUSE obse a ions (I win e al.,2021)
ound alues a ying om 5±1% a he equa o o 3±1% a he sou h pole, which compa ed easonably well
wi h p e ious analyses o hese HST/STIS obse a ions and o he s (e.g., Ka koschka & Tomasko,2009; Ka ko-
schka & Tomasko,2011; S omo sky e al.,2011,2014) who ound alues o ∼4% a equa o ial la i udes and
∼2% a pola la i udes o bo h plane s. In his s udy, we ha e analysed disc-a e aged spec a so we migh ha e
expec ed o e ie e a me hane abundance o ∼3%–4% o bo h U anus and Nep une, and gi en ha we would
see mo e o he pola egions in he Nep une disc-a e ages han in he U anus obse a ions we migh expec o
Figu e 11. As Figu e5, bu o Nep une, showing a con ou plo o e ical ae osol s uc u e (opaci y/ba ) in e ed om ou
“snippe ” Nep une e ie als, whe e o each wa eleng h he ae osol s uc u e is e ie ed om he wa eleng hs in a bin o
wid h 0.1μm cen ed on ha wa eleng h. The ed line in he opaci y/ba key is again he assumed a p io i alue.
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
20 o 44
e ie e lowe me hane abundances o Nep une han we do o U anus. In p ac ice he de e mina ion o “deep”
me hane abundance (i.e., immedia ely below he me hane condensa ion le el) is almos inex icably ied up wi h
he assumed cloud/haze pa ame e isa ion scheme, and also he assumed e ical dis ibu ion o me hane. Ou
simple haze model, which is designed o ma ch he obse a ions a all wa eleng hs simul aneously, leads o i s
ha do no ma ch he 800–860nm ange as well as o he models ha a e able concen a e on his egion alone
(e.g., I win e al.,2021) and achie e close i s, lowe me hane abundances, and sligh ly di e en ae osol p o iles.
Also, in his wo k we ha e assumed he same simple “s ep” model o he me hane p o ile (cons an mole ac ion
up o some ac ion o he sa u a ed apou p essu e cu e se by he ela i e humidi y) as I win e al.(2021),
while o he au ho s used a “descended” me hane p o ile (e.g., S omo sky e al.,2019). Finally, al hough he e
is li le c oss-co ela ion seen in ou “co ne -plo s” (Figu es8 and14) i is possible ha he me hane abundance
is co ela ed wi h some o he cloud pa ame e s, pe haps Ae osol-1, and hence o Nep une he me hane abun-
dance is being sligh ly o e es ima ed and he Ae osol-1 pa ame e s unde - o o e -es ima ed. Hence, in p ac ice
he me hane e ie al p oblem is ex emely degene a e and while he e we ind a di e ence in he e ie ed deep
me hane abundances o U anus and Nep une, he e is no su icien e idence o claim ha his is a obus esul .
Pe haps wi h a e ised haze pa ame e isa ion scheme, o di e en Ae osol-1 pa icle assump ions, we may de e -
mine alues ha a e close o each o he . We hope o e u n o his ques ion in u u e wo k.
Figu e 12. Example o one o he bes i ed spec a o Nep une, wi h χ
2/n=2.79 o ou assumed e o s. He e, he
measu ed spec a and assumed e o ange a e shown in g ey and he i s a 0° and 61.45° a e shown in ed and blue,
espec i ely, o bo h he HST/STIS and Gemini/NIFS obse a ions. Fo he IRTF/SpeX obse a ion, he simula ed cen al-
me idian line a e age is shown in ed. I can be seen ha we achie e a e y good i o he da a o all h ee da a se s.
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
21 o 44
3.10. HST/WFC3 Obse a ions o Da k Spo s in he A mosphe es o U anus and Nep une and Thei
Spec al Cha ac e is ics
The analysis o a ailable e lec ance spec a o U anus and Nep une e eals e y simila ae osol s uc u es o
bo h plane s, wi h a deep Ae osol-1 laye based a p>5–7ba de ec able a isible wa eleng hs, a middle Ae o-
sol-2 laye a 1–2ba seen a o he wa eleng hs, a e ically ex ended s a osphe ic haze (Ae osol-3), de ec able
mos ly a isible wa eleng hs, and inally, o Nep une, he p esence o condensa ion laye o mode a ely la ge
me hane ice pa icles nea he opopause. Such a model can hen be used simula e he gene al appea ance a all
wa eleng hs o ei he plane wi h good accu acy. Howe e , he e is one aspec in which U anus and Nep une seem
o di e subs an ially and ha is he p esence o “da k spo s.”
The i s da k spo s obse ed in an Ice Gian a mosphe e we e he G ea Da k Spo (GDS) and Da k Spo 2 (DS2),
seen by Voyage 2 in Nep une's a mosphe e in 1989 (Smi h e al.,1989; S omo sky e al.,1993). The GDS was
mos isible a a wa eleng h o 0.48μm, bu was unde ec able longwa d o 0.7μm. Since he Voyage lyby
se e al new da k spo s ha e been seen in Nep une's a mosphe e om Hubble Space Telescope obse a ions in
1994, 1996, 2015 and 2018 (Hammel e al.,1995; Hsu e al.,2019; S omo sky e al.,2001; Wong e al.,2018).
These ha e all had simila spec al cha ac e is ics o hose no ed o he GDS, namely ha hey a e isible nea
0.5μm, bu no isible longwa d o 0.7μm. Fo U anus, he e has o da e only been one da k spo de ec ed, which
was obse ed in 2006 (Hammel e al.,2009). Unlike he Nep une da k spo s he U anus da k spo seems o ha e
been de ec able o longe wa eleng hs.
The da k spo s seem o be some so o o ex s uc u e and he colou a ion mus be due o ei he a da kening o
he ae osol pa icles, o a change in opaci y o he ae osol laye , o pe haps a combina ion o bo h e ec s. Pu ing
aside he U anus da k spo obse a ion o one momen , he da kening e ec needs o be con ined o a a he
small and pa icula ange o wa eleng hs. I could e y well be caused by a spec ally limi ed da kening o he
ae osol pa icles, bu we would hen need o ha e qui e a pa icula pe u ba ion o he cloud/haze sca e ing
p ope ies and simul aneously con ine ha change somehow o be wi hin a o ex. On he o he hand, i da k
spo s a e caused by cloud/haze opaci y changes, we need o explain how i s signa u e is so spec ally con ined.
We belie e ha he e ie als desc ibed in p e ious sec ions p o ide he answe . The deep Ae osol-1 laye based
a p>5–7ba is only isible a wa eleng hs less han ∼0.7μm and i ha we e o ha e lowe opaci y, o educed
e lec i i y, hen we migh expec o see a da k spo a jus hose wa eleng hs.
Figu e 13. Fi ed e ical ae osol s uc u e o Nep une's a mosphe e om ou example bes - i e ie al, p esen ed in e ms
o opaci y/ba (le ) and opaci y/km ( igh ) a 0.8μm. The deep Ae osol-1 laye is shown as a solid line, he middle Ae osol-2
laye as a do ed line, he oposphe ic/s a osphe ic ex ended haze (Ae osol-3) as a dashed line, and he de ached me hane ice
haze nea he opopause as he dashed-do ed line. The ed line ma ks he 5-ba le el, which is oughly he le el whe e ou
sensi i i y uns ou .
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
22 o 44
To see i his phenomenon was appa en in ou modelled U anus obse a ions we gene a ed syn he ic images o
U anus om ou bes - i ing cloud/haze model in he se en wa eleng h channels obse ed by HST/WFC3 wi h
he OPAL p og am in 2014 (Simon e al.,2015). The loca ion o he il e s used (F467M, F547M, FQ619N,
F658N, FQ727N, F845M, and FQ924N) a e compa ed wi h he cen al-me idian line-a e aged HST/STIS
U anus spec um in Figu e15 and in Figu e16 we compa e he obse a ions wi h syn he ic images. The middle
and bo om ows o Figu e16 show syn he ic images a each il e wa eleng h, which we e cons uc ed using he
ollowing p ocedu e:
Figu e 14. “Co ne ” plo o 30 e ie als o he combined HST/STIS, IRTF/SpeX and Gemini/NIFS Nep une da a se wi h χ
2/n<10. The da a poin s a e colou -
coded by he χ
2/n o he i . Along he leading diagonal, ins ead o plo ing he ma ginalised e o s as would be usual o such plo s, we plo χ
2/n as a unc ion o i ed
pa ame e . Al hough some pa ame e s a e be e cons ained han o he s, i can be seen ha he e is li le c oss-co ela ion be ween any o he i ed pa ame e s.
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
23 o 44
1. In ou baseline simula ions we used ou op imal i o he econs uc ed spec a a 0° and 61.45° o ex ac
Minnae pa ame e s I0(λ) and k(λ) and, using
𝐴𝐴𝐴𝐴
=𝐴𝐴0𝜇𝜇
𝑘𝑘
0
𝜇𝜇
𝑘𝑘−1
, cons uc ed syn he ic disc images o U anus a
each modelled HST/STIS wa eleng h, I e e ence(λ) o he HST/WFC3 obse a ion zeni h angles μ and μ0.
2. Then, om ou i ed cloud/haze model, we calcula ed modelled spec a (a 0° and 61.45°) wi h ei he : A) he
opaci y o he Ae osol-1 laye based a p>5–7ba se o ze o; o B) he imagina y e ac i e indices o he
pa icles in his laye se o 0.001 a all wa eleng hs (which da kens he pa icles a sho wa eleng hs). We
hen ex ac ed modi ied R0(λ) and k(λ) Minnae pa ame e s o bo h cases, which we used o gene a e wo
addi ional se s o syn he ic U anus images, Imodi ied(λ).
3. We hen cons uc ed a weigh ing ac o , w, o simula e a cloud/haze da kening/clea ing nea
he disc cen e, wi h la i ude Φ0 = 20°N and cen al me idian longi ude Λ0 = 0°, se ing
𝐴𝐴𝐴𝐴
𝑤𝑤= exp
(
((Φ−Φ
0)∕ΔΦ)
2
+((Λ−Λ
0)∕ΔΛ)
2)
, whe e Φ is he la i ude on he disc, Λ is he longi ude ela-
i e o he cen al me idian, and whe e ΔΦ=5° and ΔΛ=10°.
4. We hen made weigh ed a e ages o ou wo se s o images a each HST/STIS wa eleng h: Imean(λ)=(1− w)
I e e ence(λ)+ wImodi ied(λ).
5. Finally, he combined images we e con ol ed wi h he HST/WFC3 il e unc ions o c ea e he syn he ic
images.
F om Figu e16 i can be seen ha aside om he la i udinal cloud/haze and me hane abundance a ia ions isi-
ble in he obse ed images (which we did no a emp o simula e he e) we cap u e easonably well he obse ed
limb-da kening/limb-b igh ening a all wa eleng hs. Al hough he HST/WFC3 OPAL 2014 obse a ions did no
λ(μm)
Ae osol-1
Mean 1
(>5–7ba )
Mean 2 Sample
Ae osol-2
Mean 1
(1–2ba ) Mean
2 Sample
Ae osol-3
Mean 1
(ex ended)
Mean 2 Sample
0.3 2.89×10
−4 1.87×10
−4 1.52×10
−4 3.13×10
−3 3.46×10
−3 3.40×10
−3 6.39×10
−3 4.78×10
−3 4.46×10
−3
0.4 1.00×10
−5 1.57×10
−5 5.27×10
−6 1.13×10
−3 1.26×10
−3 1.27×10
−3 1.01×10
−2 8.23×10
−3 7.62×10
−3
0.5 1.19×10
−5 6.76×10
−6 2.16×10
−6 1.61×10
−3 1.49×10
−3 1.79×10
−3 5.47×10
−3 4.66×10
−3 3.14×10
−3
0.6 4.54×10
−4 1.91×10
−4 2.02×10
−4 1.76×10
−4 1.71×10
−4 9.71×10
−5 3.56×10
−3 2.19×10
−3 1.31×10
−3
0.7 1.13×10
−3 9.28×10
−4 1.14×10
−3 2.22×10
−3 3.03×10
−4 2.24×10
−4 1.71×10
−2 1.46×10
−2 1.77×10
−2
0.8 1.13×10
−3 1.51×10
−3 1.79×10
−3 1.48×10
−3 2.83×10
−4 2.19×10
−4 3.61×10
−2 3.53×10
−2 3.48×10
−2
0.9 4.00×10
−4 3.62×10
−4 3.83×10
−4 3.52×10
−4 2.97×10
−4 3.09×10
−4 4.13×10
−2 3.21×10
−2 4.06×10
−2
1.0 1.64×10
−3 1.46×10
−3 1.75×10
−3 6.36×10
−3 2.16×10
−3 6.65×10
−3 4.66×10
−3 4.80×10
−3 2.39×10
−3
1.1 2.28×10
−3 2.43×10
−3 2.43×10
−3 8.36×10
−3 7.09×10
−3 1.07×10
−2 5.29×10
−3 1.62×10
−3 1.82×10
−3
1.2 3.35×10
−3 2.57×10
−3 3.11×10
−3 3.73×10
−2 1.97×10
−2 2.68×10
−2 4.05×10
−2 1.44×10
−3 1.75×10
−3
1.3 1.45×10
−2 4.40×10
−3 5.66×10
−3 3.28×10
−2 2.21×10
−2 3.55×10
−2 2.49×10
−2 2.34×10
−3 2.50×10
−3
1.4 6.87×10
−3 2.69×10
−3 3.71×10
−3 5.31×10
−1 6.08×10
−2 3.50×10
−1 3.73×10
−1 2.45×10
−2 1.26×10
−2
1.5 6.23×10
−4 4.53×10
−4 4.43×10
−4 5.33×10
−2 1.03×10
−2 3.79×10
−2 3.10×10
−1 3.16×10
−1 2.77×10
−1
1.6 4.76×10
−4 3.41×10
−4 3.41×10
−4 3.85×10
−2 3.66×10
−2 4.54×10
−2 3.46×10
−1 4.04×10
−1 3.26×10
−1
1.7 1.46×10
−2 1.34×10
−3 1.09×10
−3 9.55×10
−2 9.45×10
−3 5.42×10
−2 2.89×10
−1 9.08×10
−2 3.57×10
−1
1.8 2.53×10
−3 1.05×10
−3 9.41×10
−4 2.69×10
−3 2.10×10
−3 2.70×10
−3 2.27×10
−1 6.91×10
−3 3.76×10
−2
1.9 3.84×10
−3 9.95×10
−4 1.08×10
−3 1.61×10
−3 1.13×10
−3 1.32×10
−3 2.88×10
−1 2.07×10
−3 6.00×10
−2
2.0 1.28×10
−3 9.79×10
−4 1.19×10
−3 1.16×10
−3 1.01×10
−3 9.86×10
−4 8.22×10
−1 1.57×10
−3 9.92×10
−1
2.1 1.08×10
−3 9.89×10
−4 1.06×10
−3 1.07×10
−3 1.00×10
−3 8.06×10
−4 1.59×10
−2 1.69×10
−3 1.38×10
−2
2.2 1.12×10
−3 9.82×10
−4 9.00×10
−4 1.03×10
−3 1.00×10
−3 8.60×10
−4 2.68×10
−3 1.18×10
−3 2.59×10
−3
2.3 9.54×10
−4 9.76×10
−4 1.03×10
−3 9.92×10
−4 1.00×10
−3 7.84×10
−4 1.42×10
−3 1.02×10
−3 1.41×10
−3
2.4 9.04×10
−4 1.02×10
−3 1.04×10
−3 1.01×10
−3 1.00×10
−3 7.71×10
−4 1.10×10
−3 1.00×10
−3 1.12×10
−3
No e. Again, o each ae osol ype, “Mean 1” is he weigh ed a e age o all bes - i ing e ie ed spec a, while “Mean 2” a e he a e ages o he con ou maps shown
in Figu e9. “Sample” is he e ie ed spec a om he ep esen a i e bes - i ing sample case shown o each plane .
Table 4
Es ima ed nimag Spec a o Nep une Ae osols
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
24 o 44
con ain any da k spo s, i he e we e a hole in he deep Ae osol-1 laye in U anus's a mosphe e, o a da kening,
i can be seen in he middle and bo om ows o Figu e16 ha i would p oduce a da k spo a p ecisely he same
wa eleng hs as seen by HST/WFC3, ha is, a 467 and 547nm. Howe e , while o he Ae osol-1-da kening case
he spo is in isible a longe wa eleng hs, o he clea ing case i is s ill jus isible a 658, 845 and 924nm. In
Figu e 15. HST/STIS cen al-me idian-a e aged I/F spec a o U anus ( op panel) and Nep une (bo om panel).
O e plo ed in he op panel o U anus a e he ed, g een, blue sensi i i ies o he human eye (S ockman,2019; S ockman
& Sha pe,2000), oge he wi h he HST/WFC3 il e s: F467M, F547M, FQ619N, F658N, FQ727N, F845M, and FQ924N
(D essel,2021). O e plo ed in he bo om panel o Nep une a e he HST/WFC3 il e s: F467M, F547M, FQ619N, F657N,
FQ727N, F763N and F845M, oge he wi h he “clea ”, “UV”, “ iole ”, “blue”, “g een” and “o ange” Voyage -2/ISS NAC
sensi i i ies (Smi h e al.,1977), and he “CH4-U” (i.e., 547nm), “CH4-JS” (i.e., 619nm) and “o ange” Voyage -2/ISS WAC
sensi i i ies (dashed lines).
Figu e 16. Obse ed and econs uc ed HST/WFC3 images o U anus. Top ow shows HST/WFC3 obse a ions made in
2014 du ing he OPAL p og am, cen ed a he wa eleng hs: 467, 547, 619, 658, 727, 845, and 924nm. Middle ow shows
images econs uc ed om ou i s o he HST/STIS da a, which also includes a hole in he deep Ae osol-1 laye (p>5–7ba )
nea he disc cen e. Bo om ow shows images econs uc ed om ou i s o he HST/STIS da a, whe e he deep Ae osol-1
laye is da kened nea he disc cen e by se ing nimag=0.001 a all wa eleng hs. I can be seen ha o he da kening case
he modelled da k spo is isible a 467 and 547nm, bu no a longe wa eleng hs, whe eas o he clea ing simula ion he
modelled spo is isible a 467 and 547nm, bu also ain ly a 658, 845 and 924nm. In addi ion, he modelled spo is da ke
a 467nm when he Ae osol-1 laye is da kened a he han emo ed.
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
25 o 44
addi ion, he da kening simula ion esul s in a spo ha is da ke a 467nm han in he clea ing simula ion, which
is again mo e consis en wi h he obse a ions.
Tu ning o Nep une, we gene a ed syn he ic images om ou bes - i ing model in he se en wa eleng h channels
obse ed by HST/WFC3 wi h he OPAL p og am in 2018 (Simon e al.,2019), which epo ed he de ec ion o
a new da k spo , NDS-2018. The channel il e unc ions used (F467M, F547M, FQ619N, F657M, FQ727N,
F763M and F845M) a e shown in Figu e15 and he obse ed images can be seen in he op ow o Figu e17.
In he middle and bo om ows, we p esen ou simula ions wi h a da k spo cen ed a Φ0=15°N, Λ0=0°, and
also wi h a clea ing/da kening a la i ude Φ0=60°S. He e, we can again see ha we p edic he appea ance o he
clea ing o he deep Ae osol-1 laye o be mos clea ly de ec able a he wo sho es wa eleng hs, e y simila
o he obse ed spo . Howe e , o he clea ing simula ion, he modelled spo is s ill jus isible a 657, 763 and
845nm, which is con a y o he obse a ions and also con a y o he da kening simula ion, whe e he modelled
spo is comple ely in isible a he longe wa eleng hs. In addi ion, he spo modelled wi h he da kening hypo he-
sis is da ke a 467nm han he clea ing case, which is again mo e consis en wi h he obse ed p ope ies.
Conside ing U anus and Nep une oge he i can be seen ha al hough a clea ing o he Ae osol-1 laye based a
p>5–7ba p oduces almos he igh esponse, i does no p edic he spo o be da ke a 467nm han 547nm,
and he simula ed spo can s ill jus be seen a longe con inuum wa eleng hs, con a y o he obse a ions. In
con as , ou simula ed images whe e we da ken he Ae osol-1 laye p oduces a ea u e ha much mo e closely
esembles he eal NDS-2018 on Nep une. We ind ha emo ing he Ae osol-1 laye does no da ken he spo
su icien ly a sho wa eleng hs since he e is s ill signi ican Rayleigh sca e ing om he ai i sel a hese
dep hs. Howe e , by da kening his ae osol laye , he con as o he da k spo a sho wa eleng hs is g ea ly
inc eased. Add o ha he disappea ance o he ea u e a longe wa eleng hs by da kening he Ae osol-1 pa i-
cles, a he han emo ing hem al oge he , and on balance we conclude ha da kening he pa icles p o ides a
be e ma ch o he obse a ions. Fu he e idence in suppo o his hypo hesis comes om an analysis o ea lie
HST/WFC3 Nep une images (Ka koschka,2011), whe e he au ho sugges ed ha he da k bel a 30–60°S was
bes explained by a da kening o he haze a p essu es >3ba . Ka koschka(2011) wen on o specula e ha since
da k spo s ha e e y simila spec al cha ac e is ics o he 30–60°S bel , hey migh be explained by e ical
mo ions b inging da k ma e ial om dep h up o al i udes whe e i can be obse ed. Finally, we also see ha
ou p edic ed Nep une da k spo is sligh ly da ke han he equi alen spo modelled o U anus, which can be
explained by he ac ha he opaci y o he o e lying ∼2-ba Ae osol-2 laye on Nep une is lowe han i is on
Figu e 17. Obse ed and econs uc ed HST/WFC3 images o Nep une. Top ow shows HST/WFC3 obse a ions made in
2018 du ing he OPAL p og am, cen ed a he wa eleng hs: 467, 547, 619, 657, 727, 763, and 845nm. Middle ow shows
images econs uc ed om ou i s o he HST/STIS da a, which also includes a hole in he deep Ae osol-1 laye (p>5–7ba )
nea he cen al me idian a 15°N, and a clea ing a 60°S. Bo om ow shows images econs uc ed om ou i s o he HST/
STIS da a, whe e he Ae osol-1 laye is da kened nea he cen al me idian a 15°N and a all longi udes a 60°S by se ing
nimag=0.001 a all wa eleng hs. As o he U anus case shown in Figu e16, we can see ha a da k spo is isible a 467 and
547nm and ha again, while o he Ae osol-1-da kening case he spo is in isible a longe wa eleng hs, o he clea ing
case i is s ill jus isible a 657, 763 and 845nm. Also, as o U anus, he da kening simula ion esul s in a spo ha is da ke
a 467nm han in he clea ing simula ion, which is mo e consis en wi h obse a ions.
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
32 o 44
Re u ning o he Ae osol-2 laye , me hane condensa ion ac s o c ea e a clea ing benea h i in wo ways. Conden-
sa ion on o haze pa icles a he base o he laye causes hem o snow ou di ec ly, and he s able laye p oduced
by la en hea ing and educed molecula weigh educes Kzz and slows he a e a which haze pa icles in he Ae o-
sol-2 laye mix in o he deepe le els. Wi hin he laye , he mechanism o he local enhancemen o haze opaci y
is cu en ly unknown and unde s anding o his newly disco e ed ea u e will equi e a u u e mic ophysical
modelling s udy. Towa d he op o he compac Ae osol-2 laye , he dec ease in haze densi y wi h al i ude (in he
p esence o eddy mixing) implies some so o pa icle densi y sou ce a he base o he laye , a he han abo e
i , because eddy mixing alone can only modi y he slope o a g adien om he sou ce egion o he sink egion,
no e e se i . The ac ion o me hane, nea sa u a ion, could be signi ican . Conside ing he likely hyd oca bon
composi ion o haze pa icles, i is possible ha me hane condensa ion, e en a subsa u a ed apou p essu es,
could in luence he su ace chemis y o haze pa icles (in analogy o hyd ophilic ae osols signi ican in e es-
ial hazes). I is also possible ha while me hane condensa ion a he base is apid, leading o he o ma ion o
la ge pa icles, he e will also be some componen o smalle pa icles in he size dis ibu ion. The ac ional
abundance o hese smalle haze/ice pa icles is likely o ge la ge as we mo e up o lowe p essu es and lowe
empe a u es in he Ae osol-2 laye , whe e he sa u a ed apou p essu e o me hane will be much lowe . Hence,
wha we may be seeing in he Ae osol-2 laye is a mix u e o pho ochemical haze and me hane ice. Mic ophys-
ics in he unique en i onmen o he Ae osol-2 laye may hus be complex, and i is clea ha he haze pa icles
canno be conside ed s a ic ace s o mixing.
While his scena io p o ides an a ac i e model o he backg ound ae osol s uc u e o bo h plane s, he a mos-
phe e o Nep une is mo e ene ge ic and con ains equen cloud ea u es ha appea o be me hane condensa ion.
Fo he mos pa hese appea o o m in he upwelling egions a 20–40°N and 20–40°S and a p essu es o 0.6 o
0.1ba (e.g., I win e al.,2016; Mol e e al.,2019). Howe e , I win e al.(2011a) epo he appea ance o se e al
clouds a 60–70°S in 2009 ha a e deep in he a mosphe e a 1–2ba and may be a e examples o me hane clouds
o ming nea he me hane condensa ion le el i sel .
As o he na u e o he pho ochemical haze, he e a e se e al candida es. Kha e e al.(1993) epo he spec a o
“ holins” gene a ed by i adia ing H2O/C2H6 mix u es, which ha e minimal abso p ion a 0.8μm and inc easing
abso p ion as we mo e o UV, o longe wa eleng hs. While he spec um o hese “ holins” is no iden ical o
hose de i ed he e i is quali a i ely simila . Ano he candida e is ace ylene soo (Dalzell & Sa o im,1969),
which also has inc easing abso p ion a long wa eleng hs. Indeed, such hazes sha e some cha ac e is ics wi h
he phenomenon o “blue hazes” commonly obse ed in he Smoky Moun ains o eas e n Tennessee and he
Blue Ridge Moun ains o Vi ginia (Fe man e al.,1981). Examining he sca e ing c oss-sec ions o he e ie ed
ae osol pa icles, we ind ha he small pa icles assumed o be p esen in he deep Ae osol-1 componen , and
ound o be necessa y in he ex ended Ae osol-3 componen abo e ∼1.5ba , would appea o be blue a isible
wa eleng hs. Howe e , he la ge pa icles in he 1–2ba Ae osol-2 laye would appea whi e in he isible.
The s abili y o he 1–2-ba egion in he Ice Gian a mosphe es has also been concluded by Guillo (1995)
and Lecon e e al.(2017). In iguingly, Teanby e al.(2020) no ed ha a s able laye a his p essu e le el has
impo an implica ions o he in e nal oxygen en ichmen o Nep une (Ca alié e al.,2017; Teanby e al.,2020).
Limi ed mixing a 1–2ba could pe mi ex e nally sou ced CO en e ing Nep une's a mosphe e om come s o
be apped in he uppe oposphe e, which emo es he need o ha e ex eme in e nal oxygen en ichmen in
o de o explain he wide wings in Nep une's sub-mm CO lines. P e ious wo k had sugges ed CO o be p esen
h oughou he oposphe e, which equi es an ex emely high in e nal oxygen en ichmen compa ed wi h he
sola composi ion by a ac o o a leas a ew hund ed (Ca alié e al.,2017; Lellouch e al.,2005; Luszcz-Cook &
de Pa e ,2013; Moses e al.,2020) in o de o ac as a deep sou ce o oposphe ic CO. I ex e nally sou ced CO
can be kep in he uppe oposphe e by limi ed mixing his opens up he possibili y o a mo e ock- ich U anus
and Nep une (Teanby e al.,2020), in keeping wi h mo e modes oxygen en ichmen s o ∼50 in e ed om he
obse ed D/H a io (Feuch g ube e al.,1997).
Finally, in AppendixD we ou line a e iew o me hods o calcula ing he eddy di usion coe icien , Kzz, in
plane a y a mosphe es. Wi h some modi ica ion o model pa ame e s sugges ed by Acke man and Ma ley(2001)
we ound we could de i e a Kzz p o ile ha was consis en wi h uppe s a osphe ic de e mina ions o Kzz by
Fouche e al.(2003), as can be seen in Figu e21. Wi h hese pa ame e s we ind a local minimum o Kzz a he
me hane condensa ion le el, bu also a smalle minimum nea he opopause; his second Kzz minimum may help
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
33 o 44
o explain he de ached me hane ice laye (Ae osol-4) seen nea he opopause o Nep une, whe e he a mosphe e
may be dynamically igo ous enough o mix me hane up o such le els.
4.2. Na u e o Da k Regions in he A mosphe es o he Ice Gian s
In his pape we ha e shown ha da k egions seen occasionally in Nep une's a mosphe e, and a ely in U anus's
a mosphe e, can be explained by a da kening, o opaci y change o he deep Ae osol-1 laye , which we ha e
sugges ed may be composed o a mix u e o H2S ice and pho ochemically p oduced haze. Such a condensa-
ion le el is consis en wi h he es ima e om g ound-based mic owa e s udies ha he deep abundance o H2S
in U anus's and Nep une's a mosphe es a e
𝐴𝐴53
.8
+18.9
−13.4×
sola (Tolle son e al.,2021) and
𝐴𝐴37+13
−6 ×
sola (Mol e
e al.,2021), espec i ely. We belie e he eason ha such egions a e mo e commonly epo ed on Nep une han
U anus is ha he o e lying 1–2–ba Ae osol-2 laye on Nep une has lowe opaci y, making he deep Ae osol-1
laye mo e isible.
In e p e ing he esul s o ou adia i e ans e analysis wi h espec o he s uc u e o da k o ices is compli-
ca ed, especially i he da k spo s a e o be explained by a da kening o pa icles in he deep haze laye . Pa icle
colou ( esul ing om changes o nimag) canno be unambiguously a ibu ed o composi ion and/o he e ogeneous
mic ophysical s uc u e, and hus linking hese quan i ies o o ex dynamics and s uc u e would be specula i e
gi en he limi ed in o ma ion cu en ly a ailable. E en o Jupi e , whe e mo e de ailed in o ma ion is a ailable,
links be ween o ex s uc u e and ae osol p ope ies emain en a i e (e.g., Wong e al.,2011). I is possible ha
da k spo s a e gene a ed by seconda y-ci cula ion upli wi hin o ices d edging up and concen a ing a “ch omo-
pho e” ma e ial om wa me dep hs below, which is da k a isible wa eleng hs. Howe e , i is no clea wha
his ma e ial migh be, and pho olysis, which migh be hough necessa y o gene a e da k pa icles, is unlikely o
be signi ican a p essu es o ∼5–7ba since he UV lux will be e y low. Ra he han in e p e ing such ea u es
as being caused by he addi ion o a new “ch omopho e”, an al e na i e explana ion migh be ha such egions
a e anomalously wa m a he H2S condensa ion le el and so H2S ice sublima es in o he apou s a e, e ealing he
da ke CCN pho ochemical haze co e, simila o he man ling p ocess p oposed in (Wes e al.,1986) o explain
bel -zone colo di e ences in Jupi e 's a mosphe e. Such a scena io may be consis en wi h cooling abo e he
an icyclone mid-plane and wa ming below, as seen in nume ical simula ions (Hadland e al.,2020; Lemasque ie
e al.,2020; S a man e al.,2001) and heo e ical models (Ma cus e al.,2013). Howe e , mo e obse a ions a e
needed o ully cons ain why he pa icles in he Ae osol-1 laye appea o be da ke in he cen e o da k spo s
and a da k la i udes.
Ou esul s place in e es ing cons ain s on he e ical s uc u e o da k spo s. Geos ophic an icyclones in s a i-
ied luids—whe he sal lenses in he Ea h's oceans o he G ea Red Spo in Jupi e 's a mosphe e—a e cha ac-
e ized by high densi y anomalies in hei uppe egions, and low densi y anomalies in hei lowe egions (e.g.,
da k con ou s in Figu e 2 o Ba celó-Llull e al.(2017), Figu e 3 o Ma cus e al.(2013), Figu e S8 o Lemasque -
ie e al.(2020)). Thus, how gian plane a mosphe ic o ices a ec he obse able ae osol s uc u e depends on
he loca ion o ae osol laye s wi h espec o he o ex mid-plane. An icyclones a e also mo e e icien ly mixed,
compa ed o he s a i ied backg ound a mosphe e (e.g., Hassanzadeh e al.,2012).
Figu e22 compa es di e ences in model Jupi e and Nep une o ex s uc u es ha migh be consis en wi h ou
deep ae osol esul s. In Jupi e 's case, obse able ae osol laye s ( he NH3 ice cloud laye plus he oposphe ic
haze abo e i ) in e sec he uppe pa o he o ex, whe e he high densi y anomaly is associa ed wi h coole
empe a u es (e.g., Cheng e al.,2008). The coole empe a u es enhance haze (e.g., N2H4) condensa ion (Wes
e al.,1986), and e icien mixing deli e s cloud and haze p ecu so s o high al i udes, p oducing he inc eased
ae osols ha a e seen wi hin he uppe po ion o Jo ian an icyclones (Ban ield e al.,1998).
Deple ed, o da kened, ae osols in Nep une's da k spo s, as possibly sugges ed by ou analysis, may indica e
ha he o ex midplane is loca ed a highe al i udes han he deep Ae osol-1 laye . Highe empe a u es in he
low-densi y anomaly would inhibi H2S condensa ion. Depending on he e ical dis ibu ion o he da k haze
CCNs popula ing he deep laye , mixing wi hin he an icyclone may also play a ole by al e ing he concen a ion
o CCNs a he H2S condensa ion laye . This scena io may also cons ain he op o he o ex in his model. E i-
cien mixing wi hin he an icyclone would dis up he middle Ae osol-2 laye nea 1–2ba , which is no obse ed.
We ha e demons a ed ha we can model he da k spo appea ance a all HST/WFC3 wa eleng hs (Figu e10)
wi hou any changes o he middle Ae osol-2 laye , which would mean ha he high-densi y anomaly o he da k
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
34 o 44
o ex may eside en i ely below his le el. Models whe e bo h he Ae osol-1 and Ae osol-2 laye s we e deple ed
ende ed o ices isible a longe HST/WFC3 wa eleng hs, in con adic ion wi h he obse a ions. I o ices a e
indeed bounded by app oxima ely he 2-ba and 10-ba su aces, hei hickness is less han wo a mosphe ic p es-
su e scale heigh s. This hickness is much smalle han ha o Jupi e , whe e emo e sensing o he isible clouds
cons ains o ex ops o abou he 0.5-ba le el (e.g., Ban ield e al.,1998; Cheng e al.,2008; Wes e al.,2004)
and o ex bases o le els nea he 10-ba le el, o pe haps as deep as 800ba in he special case o he G ea Red
Spo (Bol on e al.,2021; Pa isi e al.,2021). The mal in a ed obse a ions, howe e , (e.g., Fle che e al.,2010)
ind ha he he mal e ec s o o ices each e en highe o he opopause. Jo ian o ices hus span anges o
3–7 scale heigh s. The po en ial di e ence in o ex hicknesses be ween Jupi e and Nep une may pe haps be
ela ed o he deep s a i ica ion o hese ou e plane a mosphe es, which is s ill no known o high p ecision.
Di ec measu emen s a ele an p essu e le els a e only a ailable o a single ime and place: he Galileo P obe
en y si e a Jupi e (Magalhães e al.,2002; Sei e al.,1998). Gi en he dependence o o ex e ical/ho izon-
al aspec a io on he di e ence be ween in e nal and en i onmen al s a i ica ion (Hassanzadeh e al.,2012),
and he oughly compa able ho izon al dimensions o o ices on Jupi e and Nep une (Li e al.,2004; Wong
e al.,2018), he hicke e ical dimensions o Jupi e 's o ices may indica e ha he en i onmen al s a i ica ion
is weake on Jupi e compa ed o Nep une. Howe e , his igh ly cons ained hickness scena io uns coun e o
he obse a ion ha such da k spo dis u bances a e o en accompanied by wha appea o be o og aphic clouds
nea he opopause, o example, he “scoo e ” cloud ha accompanied Voyage -2's GDS. Hence, i would seem
ha he e ec o he o ices mus ac ually ex end much highe . A possible scena io ha migh be consis en wi h
all he e idence may be ha he mid-plane o he o ex coincides wi h he s a ically s able 1–2-ba Ae osol-2
laye , ha is, he me hane condensa ion le el, which could lea e his laye una ec ed, bu would a ec bo h uppe
and lowe clouds.
4.3. Dependence o Solu ions on Me hane Abso p ion Spec a
The main e ie als p esen ed he e ha e been conduc ed using k- ables gene a ed om he me hane band model
coe icien s o Ka koschka and Tomasko(2010). We used hese coe icien s as hey co e he en i e spec al
ange o ou obse a ions leading, we hope, o sel -consis en esul s. The line da a se s ha a e a ailable, o
example, WKLMC@80K (Campa gue e al.,2013) ha e been shown o p o ide be e i s o he H-band obse -
a ions (e.g., I win, de Be gh e al.,2012), bu a e limi ed in hei wa eleng h co e age and so canno co e
he en i e 0.3–2.5μm egion. La e da abases, such as HITRAN16 (Go don e al.,2017), and TheoRETS (Rey
e al.,2018) ex end he lowe wa eleng h limi o 1.0 and 0.75μm, espec i ely, bu hese s ill ail o co e he
spec al egion whe e da k spo s a e mos isible. We epea ed some o ou e ie als o 0.76–2.5μm egion
Figu e 22. Possible explana ions o e ical s uc u e o da k spo s in U anus and Nep une's a mosphe es, compa ed wi h
o ex model o Jupi e 's a mosphe e. Cloud s uc u e may be a ec ed di e en ly, depending on whe he cloud laye s
in e sec wi h he high-densi y (cool) o low-densi y (wa m) anomalies associa ed wi h an icyclonic o ices. Le hand
panel shows a model o o ices in Jupi e 's a mosphe e, whe e he uppe coole pa o he o ex in e sec s wi h he NH3
condensa ion laye , leading o enhanced ice o ma ion he e, and enhanced haze o ma ion abo e i (ex ending close o he
opopause). In con as , he igh hand panel shows a simila model o Nep une's a mosphe e, whe e he lowe wa m egion
o e laps wi h he H2S condensa ion le el, causing a da kening, o clea ing, o he Ae osol-1 laye . To explain he lack o any
changes in he Ae osol-2 laye a he loca ion o da k spo s, he high-densi y (cool) anomaly may need o eside deepe han
he Ae osol-2 laye . Howe e , a deep o ex op is challenging o econcile wi h obse a ions o o og aphic companion clouds
nea da k spo s. Al e na i ely, he mid-plane may need o coincide wi h he Ae osol-2 laye .
Jupi e an icyclone Nep une an icyclone
NH
3
ice
cloud laye (~0.7 ba )
High-densi y
(cool)
Low-densi y
(wa m) Ae osol-1
laye (~7 ba )
Ae osol-2
laye (~2 ba )
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
35 o 44
alone, using k- ables gene a ed om he me hane band pa ame e s (Ka koschka & Tomasko,2010) and also om
he TheoRETS da abase and ound be e i s o he obse a ions wi h TheoRETS, and b oadly simila e ie ed
ae osol s uc u es and sca e ing pa ame e s o he wo di e en sou ces o me hane abso p ion da a. Howe e ,
signi ican di e ences we e ound be ween he ae osol s uc u es e ie ed om he 0.76–2.5μm using using he
me hane band/k-da a and hose e ie ed om he ull 0.3–2.5μm ange, wi h signi ican ly mo e opaci y o he
deep Ae osol-1 laye es ima ed when using he es ic ed wa eleng h ange. This may go some way o explaining
he di e ence be ween he e ical p o iles o ae osol e ie ed he e and hose om p e ious s udies, concen a -
ing on he 820nm o H-band egions alone, ha did no include a sepa a e deep Ae osol-1 laye and gene ally pu
he main Ae osol-2 laye deepe a 2–3ba , and o he 820nm e ie als deduced a lowe me hane abundance
o Nep une (I win e al.,2021). I is only he me hane band da a o Ka koschka and Tomasko(2010) ha allows
us o analyse he whole ange simul aneously and deduce he p esence o he deepe laye Ae osol-1 laye , whose
spa ial a ia ions a e, we sugges , esponsible o da k spo ea u es.
We did a emp ying o combine he band and line da a oge he , bu he e a e signi ican di e ences in he wa e-
leng h egions o o e lap and we ound, gene ally, ha he i s we e wo se when using a combina ion o me hane
da a om di e en sou ces. In o de o ex end his analysis we eally need o he line da a sou ces o ex end o
0.3μm so ha we a e able o analyse he whole spec al ange wi h a sel -consis en se o abso p ion da a. We
look o wa d o he ime when his migh be possible.
4.4. Spa ial Decon olu ion
While he HST/STIS obse a ions p esen ed he e ha e been spa ially decon ol ed wi h a Lucy-Richa dson decon-
olu ion scheme, his has no ye been possible wi h he Gemini/NIFS da a we ha e analysed. Fo U anus we do
no conside his o be oo signi ican a p oblem since he disc o U anus seen in 2009 was mode a ely ea u eless.
Howe e , o he Nep une obse a ions, he e we e signi ican le els o high me hane ice clouds. Al hough we
masked hese egions when ex ac ing he Minnae coe icien s o he backg ound egions, gi en he likely shape
o he Poin -Sp ead-Func ion (PSF) i is possible ha he unmasked egions we e s ill con amina ed by ligh om
he b igh , cloudy egions, which may help o explain why he NIFS Nep une da a show e y li le limb-b igh -
ening a me hane-abso bing wa eleng hs, in con as o he expec a ions om he i s o he combined da a and
also o he beha iou seen in he U anus NIFS obse a ions. We hope, when possible, in u u e wo k o a emp
o spa ially decon ol e hese Gemini/NIFS obse a ions o explo e his.
5. Conclusions
Modelling he isible/nea -in a ed e lec i i y spec a o U anus and Nep une o e a wide wa eleng h ange o
0.3–2.5μm ep esen s a conside able challenge. In e ec we a e ying o ind a cloud/haze s uc u e o unknown
cons i uen s, o unknown size and unknown complex e ac i e index spec a, using as ou main p obe o e ical
le el he abso p ion spec um o gaseous me hane, which also has unknown sys ema ic e o s. Add o ha he
unce ain measu emen e o o he obse ed da a hemsel es and i can be seen ha his is a conside ably degen-
e a e p oblem! Hence, he e a e mul iple solu ions ha i equally well and all may need o be e ised once he
a ailable line da a o me hane ha e been ex ended o he isible. Howe e , by pe o ming ou “snippe analyses”,
we ha e shown how we can di e en ia e be ween spec al and e ical a ia ions o he Ice Gian ae osols. Using
he snippe analyses o cons ain ou adi ional e ie al app oach (modi ied o use mul iple s a ing poin s o
a oid he solu ions becoming apped in local χ
2/n minima) we ha e de e mined an ae osol model o U anus and
Nep une ha ma ches he obse a ions well and is simple, elegan , has some basis in e ms o haze p oduc ion
and likely p essu e le els o s a ic s abili y, and se endipi ously can also explain he obse ed cha ac e is ics o
Nep une's (and U anus's) da k spo s.
In summa y, in his wo k we ha e ound ha we can model he obse ed e lec i i y spec a o bo h U anus and
Nep une om 0.3 o 2.5μm wi h a single, simple ae osol model, summa ised in Figu e23, comp ised o :
1. A deep laye based a p>5–7ba (Ae osol-1) o wha we assume o be sub-mic on-sized pa icles, which
we sugges o be coinciden wi h he main H2S cloud/haze condensa ion laye and composed o a mix u e o
pho ochemically p oduced haze pa icles and H2S ice. These pa icles a e highly sca e ing a 500nm, bu
become mo e abso bing a bo h sho e and longe wa eleng hs;
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
36 o 44
2. A e ically hin ae osol laye o mic on-sized pa icles jus abo e he me hane condensa ion le el a 1–2ba
(Ae osol-2), possibly composed o a mix u e o pho ochemically p oduced haze and me hane ice, ha a e less
e lec i e han he deepe Ae osol-1 haze pa icles a isible wa eleng hs and a e also mo e abso bing a bo h
sho e and longe wa eleng hs;
3. A e ically ex ended haze o small pa icles based a 1–2ba (Ae osol-3) wi h a ac ional scale heigh o ∼2
and simila e ac i e index spec um o he main 1–2-ba Ae osol-2 laye ;
4. Fo Nep une, an addi ional e ically hin componen o mode a e-sized me hane ice pa icles (∼2μm),
loca ed a ∼0.2ba jus below he opopause.
We ind his model o be consis en wi h HST/STIS, HST/WFC3, IRTF/SpeX, Gemini/NIFS and Voyage -2/ISS
obse a ions. Ou main conclusions a e:
1. The UV- and long-wa eleng h-abso bing na u e o he e ie ed imagina y e ac i e index spec um o he
1–2-ba Ae osol-2 laye is no consis en wi h ou expec a ion o CH4 o H2S ice. The spec al dependence is
mo e consis en wi h he imagina y e ac i e index spec um de i ed o he oposphe ic/s a osphe ic haze.
Hence, we sugges ha he 1–2-ba Ae osol-2 laye con ains a conside able ac ion o pho ochemical haze,
p oduced a highe al i udes, which has somehow become concen a ed and modi ied a his le el in a egion
o s a ic s abili y c ea ed by e ical g adien in molecula weigh and also la en hea elease om me hane
condensa ion.
2. The haze pa icles in he 1–2-ba Ae osol-2 laye ac as cloud-condensa ion nuclei (CCN) o me hane
condensa ion a he lowe bounda y, which condenses so quickly ha me hane ice immedia ely “snows ou ”
o e-e apo a e a deepe le els, edeposi ing he haze pa icles he e. The la ge e ie ed size o he pa icles
in he Ae osol-2 laye compa ed wi h he highe , e ically ex ended Ae osol-3 laye may in pa e lec his
cloud-seeding p ocess and may also jus a ise due o coagula ion and coalescence in his e ically s able laye .
Figu e 23. Summa y o e ie ed ae osol dis ibu ions o U anus (le ) and Nep une ( igh ), compa ed wi h he assumed
empe a u e/p essu e p o iles. On each plo is also shown he condensa ion lines o CH4 (g een) and H2S (pink), assuming
mole ac ions a 10ba o 4% o CH4 and 1×10
−3 o H2S, o mo e he condensa ion le els o he app oxima e le els o he
Ae osol-1 and Ae osol-2 laye s. The de aul solu ion is composed o : (a) an ex ended laye o haze, pho ochemically p oduced
in he s a osphe e and mixed by eddy di usion o lowe le els (Ae osol-3); (b) a hicke haze laye o la ge pa icles
( ∼1μm) nea he CH4 condensa ion le el (Ae osol-2); (c) apid o ma ion o la ge me hane ice/snow pa icles a he base o
his laye , which apidly all and edeposi he haze co es a lowe al i udes; and (d) an H2S cloud based a p>5–7ba , which
o ms on he haze pa icles (Ae osol-1). Fo Nep une, we ind we also need a componen o mode a e-sized (∼2μm) me hane
ice pa icles nea he opopause. No e ha he Ae osol-2 laye on Nep une has no iceably less opaci y han ha on U anus, by
a ac o o ∼2.
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
37 o 44
3. The haze pa icles a deepe le els ac as CCNs o H2S condensa ion a ∼4–10ba (Ae osol-1). A he low
pa ial p essu es o H2S seen a hese le els and he highe p essu e, his condensa ion is slowe , o ming a
cloud o wha we ha e assumed o be sub-mic on-sized pa icles, which ha e spec al p ope ies consis en
wi h a mix o da k haze and ice.
4. In Nep une's a mosphe e, inc eased e lec ance in me hane abso p ion bands a wa eleng hs longe han
∼1μm can be accoun ed o by he addi ion o an op ically and e ically hin componen o mic on-sized
me hane ice pa icles, based nea 0.2ba , jus below he opopause.
5. Da kening o he pa icles in he deep haze/H2S-ice Ae osol-1 laye (o o a lesse ex en a clea ing o his laye )
leads o spec al pe u ba ions ha ma ch well he obse ed cha ac e is ics o da k spo s and he da k la i ude
bands seen in Voyage -2/ISS and HST/WFC3 obse a ions o Nep une (i.e., isibili y only a λ<∼700nm).
Such pe u ba ions also p o ide a good i o obse ed limb-da kening p ope ies o hese ea u es. A he
same ime, he Ae osol-2 laye (1–2ba ) appea s o be unpe u bed by da k egions. This po en ially limi s
he e ical hickness o da k spo s (and da k la i udes) o dis u bances a p essu es g ea e han ∼3-ba , and
pe haps spanning less han 2 scale heigh s, a signi ican di e ence om hicke an icyclones seen in Jupi e 's
a mosphe e. Howe e , such an in e p e a ion does no es easily wi h he obse a ion ha such ea u es a e
equen ly accompanied by o og aphic clouds, based nea he opopause. Hence, i may be ha he o ex
mid-plane coincides wi h he 1–2-ba Ae osol-2 laye .
6. The opaci y o he 1–2-ba Ae osol-2 laye in U anus's a mosphe e is ound o be signi ican ly hicke han
ha o Nep une by a ac o o ∼2; since hese pa icles a e ound o be UV-abso bing, his explains U anus's
lowe obse ed UV e lec i i y and also explains why U anus appea s o ha e a pale blue colou o he human
eye han Nep une since hese pa icles a e ound o ha e a oughly whi e isible e lec i i y spec um. The
lowe opaci y o Nep une's Ae osol-2 laye also explains why da k spo s, caused, we sugges , by pe u ba ions
o he deep Ae osol-1 H2S/haze laye a e easie o obse e in Nep une's a mosphe e han in U anus's. We
sugges ha he Ae osol-2 laye on Nep une may be hinne han ha o U anus due o Nep une's dynamically
o e u ning a mosphe e being mo e e icien a clea ing his haze laye h ough me hane condensa ion.
7. Fu u e obse a ions o U anus and Nep une wi h ins umen s such as HST/STIS o VLT/MUSE, able o
e u n high spec al esolu ion hype spec al cubes a isible wa eleng hs, may help o esol e he ques ion o
whe he da k spo s and da k egions a e caused by a da kening o a clea ing o he Ae osol-1 laye . This will,
we hope, be he ocus o u u e wo k.
Appendix A: Bouyancy Fo ces
Conside he o ce ac ing in he e ical di ec ion z on a pa cel o ai a al i ude z0 o c oss-sec ional a ea A, heigh
ⅆz, and densi y ρ:
𝜌𝜌𝜌𝜌
d𝑧𝑧d
2
𝑧𝑧
d𝑡𝑡
2=−𝜌𝜌𝜌𝜌𝜌𝜌d𝑧𝑧+𝜌𝜌0𝜌𝜌𝜌𝜌d
𝑧𝑧
(A1)
whe e ρ0 is he densi y o he su ounding ai and g is he g a i a ional accele a ion. Di iding by Aρdz we ha e:
d2
𝑧𝑧
d𝑡𝑡
2=−𝑔𝑔(𝜌𝜌−𝜌𝜌0)
𝜌𝜌.
(A2)
The densi y can be w i en as
𝐴𝐴𝐴𝐴
=
𝑀𝑀𝑀𝑀
𝑅𝑅𝑅𝑅
, whe e M is he molecula weigh o he ai , p is he p essu e, T is he
empe a u e and R is he gas cons an . Hence, we can ew i e his equa ion as:
d
2𝑧𝑧
d
𝑡𝑡2=−𝑔𝑔
(
𝑀𝑀𝑀𝑀
𝑅𝑅𝑅𝑅 −𝑀𝑀0𝑀𝑀
𝑅𝑅𝑅𝑅0
)
𝑀𝑀𝑀𝑀
𝑅𝑅𝑅𝑅
(A3)
whe e we ha e assumed he pa cel and he su oundings ha e he same p essu e. Rea anging his equa ion we
ind:
d
2𝑧𝑧
d𝑡𝑡2=−𝑔𝑔
(
1−𝑀𝑀0
𝑀𝑀
𝑇𝑇
𝑇𝑇0
)
=−𝑔𝑔
(
1−𝑀𝑀0
𝑀𝑀
𝜃𝜃
𝜃𝜃0
)
(A4)
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
38 o 44
whe e θ is he po en ial empe a u e o he pa cel (i.e., he empe a u e i would ha e i comp essed o expanded
adiaba ically o a e e ence p essu e p0), de ined o he pa cel o be
𝐴𝐴𝐴𝐴
=𝑇𝑇
(
𝑝𝑝0
𝑝𝑝)𝛾𝛾
, whe e γ=R/Cp and Cp is
he mola hea capaci y a cons an p essu e. The po en ial empe a u e o he su ounding ai is simila ly
𝐴𝐴𝐴𝐴
0=𝑇𝑇0
(
𝑝𝑝0
𝑝𝑝
)𝛾𝛾
and hence
𝐴𝐴𝑇𝑇
𝑇𝑇0
=
𝜃𝜃
𝜃𝜃
0
.
I he pa cel mo es adiaba ically hen i s po en ial empe a u e and molecula weigh emain cons an (i no
condensa ion) so any buoyancy mus be due o changes in M0 and T0. We know ha he accele a ion
𝐴𝐴𝐴𝐴
=d
2
𝑧𝑧
d𝑡𝑡
2
=0
a z=z0 by de ini ion and so
d2
𝑧𝑧
d
𝑡𝑡2∼(d𝑎𝑎
d
𝑧𝑧)𝑧𝑧
0
(𝑧𝑧−𝑧𝑧0
)
(A5)
whe e
(
d𝑎𝑎
d𝑧𝑧
)
𝑧𝑧0
=𝑔𝑔𝜃𝜃
𝑀𝑀
d
d𝑧𝑧(𝑀𝑀0
𝜃𝜃0)=𝑔𝑔𝜃𝜃
𝑀𝑀
𝜃𝜃0
d𝑀𝑀
0
d𝑧𝑧−𝑀𝑀0
d𝜃𝜃
0
d𝑧𝑧
𝜃𝜃2
0
.
(A6)
A z=z0, θ=θ0 and M=M0, and hence:
(
d𝑎𝑎
d𝑧𝑧
)
𝑧𝑧0
=𝑔𝑔
(
−1
𝜃𝜃0
d𝜃𝜃0
d𝑧𝑧+1
𝑀𝑀0
d𝑀𝑀0
d𝑧𝑧
)
(A7)
o
(
d𝑎𝑎
d𝑧𝑧
)
𝑧𝑧
0
=𝑔𝑔d
d𝑧𝑧
(
ln
(
𝑀𝑀0
𝜃𝜃0
)).
(A8)
Hence
d
2𝑧𝑧
d𝑡𝑡2=−𝑔𝑔d
d𝑧𝑧
(
ln
(
𝜃𝜃0
𝑀𝑀0
))
(𝑧𝑧−𝑧𝑧0)
.
(A9)
This is simple ha monic mo ion, wi h an angula equency, N, known as he B ün -Väisälä equency, gi en by
𝑁𝑁
2=𝑔𝑔d
d𝑧𝑧
(
ln
(
𝜃𝜃0
𝑀𝑀0
)).
(A10)
This is di e en om he mo e amilia de ini ion o he B ün -Väisälä equency ha igno es molecula weigh
changes:
𝑁𝑁
2=𝑔𝑔
d
d𝑧𝑧
(ln 𝜃𝜃0)
.
(A11)
Appendix B: Disc-A e aging
The disc-a e aged adiance
𝐴𝐴 𝐼𝐼
o a plane o appa en adius R is de ined as:
𝐼𝐼
=1
𝜋𝜋𝜋𝜋2∫
𝑟𝑟=𝜋𝜋
𝑟𝑟
=0 ∫
𝜙𝜙=2𝜋𝜋
𝜙𝜙
=0
𝐼𝐼𝑟𝑟d𝑟𝑟d
𝜙𝜙
(B1)
whe e is he adial posi ion on he disc and ϕ is he azimu h angle. Subs i u ing =R sin θ, whe e θ is he local
zeni h angle, his becomes
𝐼𝐼
=1
𝜋𝜋∫
𝜃𝜃=𝜋𝜋∕2
𝜃𝜃=0
∫
𝜙𝜙=2𝜋𝜋
𝜙𝜙=0
𝐼𝐼sin 𝜃𝜃cos 𝜃𝜃d𝜃𝜃d
𝜙𝜙𝜙
(B2)
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
39 o 44
Assuming he adiance I is azimu hally symme ic, ha is, does no depend on ϕ, his simpli ies o
𝐼𝐼
=2
∫𝜋𝜋∕2
0
𝐼𝐼(𝜃𝜃)sin 𝜃𝜃cos 𝜃𝜃d𝜃𝜃=
∫𝜋𝜋∕2
0
𝐼𝐼(𝜃𝜃)sin 2𝜃𝜃d
𝜃𝜃
(B3)
o
𝐼𝐼
=2
∫1
0
𝐼𝐼(𝜇𝜇)𝜇𝜇d
𝜇𝜇
(B4)
whe e μ=cos θ. I we assume ha I(μ) is well app oxima ed by Minnae limb da kening and ha μ=μ0, hen
I(μ)=I0μ
2k−1. Hence, he disc-a e aged adiance
𝐴𝐴 𝐼𝐼
will be
𝐼𝐼
=2𝐼𝐼0
∫1
0
𝜇𝜇2𝑘𝑘d𝜇𝜇=2𝐼𝐼0
2
𝑘𝑘
+1
.
(B5)
The “disc-a e aged” IRTF/SpeX spec a a e ac ually line-in eg als along he cen al me idian, o which:
𝐼𝐼
=
∫
𝐼𝐼d𝑦𝑦d𝑥𝑥
∫
d𝑦𝑦d𝑥𝑥∼Δ𝑥𝑥
∫
𝐼𝐼d𝑦𝑦
2𝑅𝑅Δ𝑥𝑥=
∫
𝐼𝐼d
𝑦𝑦
2𝑅𝑅
(B6)
whe e y is he dis ance along he sli , x is he posi ion ac oss i , and Δx is he sli wid h (assumed o be small).
Subs i u ing y=R sin θ his becomes
𝐼𝐼
=1
2∫
𝜋𝜋∕2
−
𝜋𝜋
∕2
𝐼𝐼(𝜃𝜃)cos 𝜃𝜃d𝜃𝜃=∫
𝜋𝜋∕2
0
𝐼𝐼(𝜃𝜃)cos 𝜃𝜃d
𝜃𝜃𝜃
(B7)
Assuming I(θ) is Minnae -dependen (i.e., I(θ)=I0( cos θ)
2k−1) his becomes
𝐼𝐼
=𝐼𝐼0∫
𝜋𝜋∕2
0
(cos 𝜃𝜃)2𝑘𝑘d
𝜃𝜃𝜃
(B8)
Sadly, his is no simply in eg able o a gene al, non-in ege k, bu i may be e alua ed nume ically. This can be
done ei he by p e- abula ing
𝐴𝐴 𝐼𝐼∕
𝐼𝐼
0
as a unc ion o k, o al e na i ely calcula ing I(θ) a all he quad a u e zeni h
angles o he adia i e ans e model and in eg a ing I(θ) cos(θ) using he quad a u e scheme weigh s. Bo h
app oaches we e es ed and ound o gi e simila esul s. Howe e , wi h he 5-poin Gaussian-Loba o scheme we
gene ally use, he la e app oach was ound o be much slowe since calcula ions a he highe zeni h angles need
many mo e Fou ie componen s o ully esol e he azimu hal pa o he adiance calcula ion. Ins ead, calcula -
ing a jus wo zeni h angles (0, 42.47°), ex ac ing he minnae -k coe icien s I0 and k, and using he p e- abu-
la ed dependence o
𝐴𝐴 𝐼𝐼∕
𝐼𝐼
0
on k o calcula e
𝐴𝐴 𝐼𝐼
was ound o be mo e han wice as as and o equi alen accu acy.
Appendix C: Cloud Opaci y Uni s
The de aul uni s o pa icle c oss-sec ions, χ(λ), in NEMESIS a e cm
2/pa icle, while he de aul uni s o ae osol
densi y, D(p), a e pa icles/g am. Hence, χ(λ)D(p) gi es ae osol c oss-sec ion in uni s o cm 2/g (i.e., cm 2 pe g am
o a mosphe e).
To ge opaci y we need o mul iply his c oss-sec ion by he pa h amoun , u, which has uni s o g am/cm
2, and can
be calcula ed as u=ρz, whe e z is he pa h leng h in cm and ρ is he a mosphe ic densi y in uni s o g am/cm
3.
Hence, he opaci y o a pa h a wa eleng h, λ, is τ(λ)=χ(λ)D(p)u=χ(λ)D(p)ρz, which is uni -less. The opaci y
pe km in a e ical pa h o a mosphe e is hen simply
𝐴𝐴d𝜏𝜏
d𝑧𝑧
= 105𝜒𝜒(𝜆𝜆)𝐷𝐷(𝑝𝑝)
𝜌𝜌
.
O he au ho s commonly exp ess cloud p o iles in uni s o opaci y/ba ,
𝐴𝐴d𝜏𝜏(𝜆𝜆)
d𝑝𝑝
, which by he chain ule can be calcu-
la ed as
𝐴𝐴d𝜏𝜏(𝜆𝜆)
d𝑧𝑧
.
d𝑧𝑧
d𝑝𝑝
. Assuming hyd os a ic equilib ium, p=p0e
z/H, whe e H is he Scale Heigh and z is measu ed
downwa ds, and hus
𝐴𝐴d𝑝𝑝
d𝑧𝑧
=
𝑝𝑝
𝐻𝐻
and
𝐴𝐴d𝜏𝜏(𝜆𝜆)
d𝑝𝑝
= 105𝜒𝜒(𝜆𝜆)𝐷𝐷(𝑝𝑝)𝜌𝜌
𝐻𝐻
𝑝𝑝
. Subs i u ing o he Scale Heigh , H=RT/Mg and o
a mosphe ic densi y, ρ=pM/RT, we conclude ha he cloud opaci y pe ba is
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
40 o 44
d𝜏𝜏(𝜆𝜆)
d𝑝𝑝
= 105
𝜒𝜒(𝜆𝜆)𝐷𝐷(𝑝𝑝)
𝑔𝑔(𝑝𝑝)
(C1)
whe e g(p) is he g a i a ional accele a ion a p essu e le el, p.
In NEMESIS we usually no malise he ae osol densi y p o ile, D(p) and c oss-sec ion spec a, χ(λ), such ha he
c oss sec ion is 1.0 a a e e ence wa eleng h, λ0, and he no malised dus opaci y p o ile D′(p)=D(p)χ(λ0). In
his case, he opaci y/ba a λ0 is ela ed o he scaled ae osol densi y, D′(p), as
d𝜏𝜏(𝜆𝜆
0
)
d𝑝𝑝
= 105
𝐷𝐷′(𝑝𝑝)
𝑔𝑔(𝑝𝑝).
(C2)
Appendix D: Eddy Di usion Coe icien s
Following he me hod o Acke man and Ma ley(2001) we assume he eddy di usion coe icien Kzz is he same
as ha o ee con ec ion, which Gie asch and Con a h(1985) de i e o be:
𝐾𝐾
𝑧𝑧𝑧𝑧 =𝐻𝐻
3(
𝐿𝐿
𝐻𝐻)
4∕3
(
𝑅𝑅𝑅𝑅
𝜇𝜇𝜇𝜇𝑎𝑎𝑐𝑐𝑝𝑝)1∕3
(D1)
whe e H is he a mosphe ic scale heigh , μ is he a mosphe ic molecula weigh , cp is he speci ic hea capaci y
a cons an p essu e (i.e., J K
−1kg
−1), R is he gas cons an (8.31J K
−1mol
−1), ρa is he a mosphe ic densi y (kg
m
−3), and F is he con ec i e hea lux (W m
−2). This equa ion can also be sligh ly mo e simply e-exp essed as:
𝐾𝐾
𝑧𝑧𝑧𝑧 =𝐻𝐻
3
(
𝐿𝐿
𝐻𝐻
)
4∕3
(
𝑅𝑅𝑅𝑅
𝜌𝜌𝑎𝑎𝐶𝐶𝑝𝑝
)1∕3
(D2)
whe e Cp is he mola hea capaci y a cons an p essu e (i.e., J K
−1mol
−1).
In his equa ion, L is he u bulen mixing leng h. Fo a eely con ec ing a mosphe e, his is ypically assumed
o be he a mosphe ic scale heigh , bu in egions o a mosphe ic s abili y, Acke man and Ma ley(2001) apply a
scaling ac o :
𝐿𝐿=𝐻𝐻max (Λ,Γ∕Γ𝑑𝑑)
(D3)
whe e Γ is he local lapse a e (i.e.,
−d𝑇
d𝑧
) and Γd is he d y adiaba ic lapse a e. The pa ame e Λ is p esen o
p e en L becoming nega i e and was assumed by Acke man and Ma ley(2001) o ha e a alue o 0.1. In his
s udy, whe e a la ge pa o he a mosphe ic s abili y is assumed o come om he e ical a ia ion o molecula
weigh , we modi ied his scaling o:
𝐿𝐿
=𝐻𝐻max
(
Λ,Γ
Γ𝑑𝑑
(
1−𝛼𝛼d𝜇𝜇
d𝑧𝑧
))
(D4)
whe e he ac o α was se o be:
𝛼𝛼
=
1−0
.
0001
max
(|||
d𝜇𝜇
d𝑧𝑧
|||).
(D5)
Also, o o ce he p o ile o Kzz o be consis en wi h s a osphe ic de e mina ions o Fouche e al.(2003), we
educed he ac o Λ om 0.1 o 0.0001.
Da a A ailabili y S a emen
The U anus HST/STIS da a se s used in his s udy a e a ailable om F y and Ka koschka(2018), while he
Nep une/STIS da a se is a ailable om I win(2022). HST obse a ions we e ob ained om he Da a A chi e a
STScI (h ps://a chi e.s sci.edu), which is ope a ed by AURA unde NASA con ac NAS5-26555. Obse a ions
wi h STIS a e associa ed wi h p og ams 9035, 9330, 12894, and 14113. Obse a ions wi h WFC3 a e associ-
a ed wi h p og ams 13937 and 15262. The IRTF/SpeX obse a ions a e a ailable om h p://i web.i a.hawaii.
Jou nal o Geophysical Resea ch: Plane s
IRWIN ET AL.
10.1029/2022JE007189
41 o 44
edu/~spex/IRTF_Spec al_Lib a y/Re e ences_ iles/Plane s.h ml. The U anus Gemini/NIFS da a a e a ailable
a h ps://a chi e.gemini.edu/sea ch o m/GN-2009B-Q-52/, while he Nep une Gemini/NIFS da a a e a ailable
a h ps://a chi e.gemini.edu/sea ch o m/GN-2009B-Q-85/. The Voyage ISS images we e downloaded om
h ps://bi .ly/3qjuqk6. The spec al i ing and e ie als we e pe o med using he NEMESIS adia i e ans e
and e ie al algo i hm I win e al.(2008) and can be downloaded om I win e al.(2022a), wi h suppo ing
websi e in o ma ion a I win e al.(2022b). The da a p oduc s gene a ed in his s udy (p ocessed spec a and
e ie ed a mosphe ic pa ame e s) a e a ailable om I win e al.(2022).
Re e ences
Acke man, A. S., & Ma ley, M. S. (2001). P ecipi a ing condensa ion clouds in subs ella a mosphe es. Ac a Pa hologica Japonica, 556(2),
872–884. h ps://doi.o g/10.1086/321540
Asplund, M., G e esse, N., Sau al, A. J., & Sco , P. (2009). The chemical composi ion o he Sun. Annual e iew o as onomy and as ophysics,
47(1), 481–522. h ps://doi.o g/10.1146/annu e .as o.46.060407.145222
Ban ield, D., Gie asch, P.J., Bell, M., Us ino , E., Inge soll, A. P., Vasa ada, A. R., e al. (1998). Jupi e ’s cloud s uc u e om Galileo imaging
da a. Ica us, 135(1), 230–250. h ps://doi.o g/10.1006/ica .1998.5985
Ba celó-Llull, B., Sang à, P., Pallàs-Sanz, E., Ba on, E. D., Es ada-Allis, S. N., Ma ínez-Ma e o, A., e al. (2017). Ana omy o a sub opical
in a he mocline eddy. Deep-Sea Resea ch Pa I: Oceanog aphic Resea ch, 124, 126–139. h ps://doi.o g/10.1016/j.ds .2017.03.012
Bol on, S., Le in, S., Guillo , T., Li, C., Kaspi, Y., O on, G., e al. (2021). Mic owa e obse a ions e eal he deep ex en and s uc u e o Jupi e ’s
a mosphe ic o ices. Science, 374(6570), 968–972. h ps://doi.o g/10.1126/science.ab 1015
Bo ysow, A., Bo ysow, J., & Fu, Y. (2000). Semi-empi ical model o collision-induced abso p ion spec a o H2-H2 complexes in he second
o e one band o hyd ogen a empe a u es om 50 o 500 K. Ica us, 145(2), 601–608. h ps://doi.o g/10.1006/ica .2000.6384
Bo ysow, A., & F ommhold, L. (1989). Collision-induced in a ed spec a o H 2-He pai s a empe a u es om 18 o 7000 K. II. O e one and
ho bands. Ac a Pa hologica Japonica, 341, 549. h ps://doi.o g/10.1086/167515
Bo ysow, A., F ommhold, L., & Mo aldi, M. (1989). Collision-induced in a ed spec a o H 2-He pai s in ol ing 0 1 ib a ional ansi ions and
empe a u es om 18 o 7000 K. Ac a Pa hologica Japonica, 336, 495. h ps://doi.o g/10.1086/167027
Campa gue, A., Leshchishina, O., Wang, L., Mondelain, D., & Kassi, S. (2013). The WKLMC empi ical line lis s (5852-7919 cm
−1) o me hane
be ween 80 K and 296 K: “Final” lis s o a mosphe ic and plane a y applica ions. Jou nal o Molecula Spec oscopy, 291, 16–22. h ps://
doi.o g/10.1016/j.jms.2013.03.001
Ca lson, B. E., Rossow, W. B., & O on, G. S. (1988). Cloud mic ophysics o he gian plane s. Jou nal o he A mosphe ic Sciences, 45(14),
2066–2081. h ps://doi.o g/10.1175/1520-0469(1988)045<2066:CMOTGP>2.0.CO;2
Ca alié, T., Veno , O., Selsis, F., He san , F., Ha ogh, P., & Lecon e, J. (2017). The mochemis y and e ical mixing in he oposphe es
o U anus and Nep une: How con ec ion inhibi ion can a ec he de i a ion o deep oxygen abundances. Ica us, 291, 1–16. h ps://doi.
o g/10.1016/j.ica us.2017.03.015
Chance, K., & Ku ucz, R. L. (2010). An imp o ed high- esolu ion sola e e ence spec um o ea h’s a mosphe e measu emen s in he ul a-
iole , isible, and nea in a ed. Jou nal o Quan i a i e Spec oscopy & Radia i e T ans e , 111(9), 1289–1295. h ps://doi.o g/10.1016/j.
jqs .2010.01.036
Cheng, A. F., Simon-Mille , A. A., Wea e , H. A., Baines, K. H., O on, G. S., Yanamand a-Fishe , P.A., e al. (2008). Changing cha ac e is ics
o Jupi e ’s li le ed SPOT. The As onomical Jou nal, 135(6), 2446–2452. h ps://doi.o g/10.1088/0004-6256/135/6/2446
Dalzell, W. H., & Sa o im, A. S. (1969). Op ical cons an s o soo and hei applica ion o hea - lux calcula ions. Jou nal o Hea T ans e , 91(1),
100–104. h ps://doi.o g/10.1115/1.3580063
de Klee , K., Luszcz-Cook, S., de Pa e , I., Ádámko ics, M., & Hammel, H. B. (2015). Clouds and ae osols on U anus: Radia i e ans e mode-
ling o spa ially- esol ed nea -in a ed Keck spec a. Ica us, 256, 120–137. h ps://doi.o g/10.1016/j.ica us.2015.04.021
D essel, L. (2021). WFC3 ins umen handbook o cycle 29, (Vol. 13,p.13).
Enc enaz, T., Feuch g ube , H., A eya, S. K., Beza d, B., Lellouch, E., Bishop, J., e al. (1998). ISO obse a ions o U anus: The s a osphe ic
dis ibu ion o C2H2 and he eddy di usion coe icien . As onomy and As ophysics, 333, L43–L46.
Fe man, M. A., Wol , G. T., & Kelly, N. A. (1981). The na u e and sou ces o haze in he shenandoah alley/Blue Ridge Moun ains a ea. Jou nal
o he Ai Pollu ion Con ol Associa ion, 31(10), 1074–1082. h ps://doi.o g/10.1080/00022470.1981.10465329
Feuch g ube , H., Lellouch, E., de G aauw, T., Béza d, B., Enc enaz, T., & G i in, M. (1997). Ex e nal supply o oxygen o he a mosphe es o
he gian plane s. Na u e, 389(6647), 159–162. h ps://doi.o g/10.1038/38236
Fle che , L. N., O on, G. S., Mousis, O., Yanamand a-Fishe , P., Pa ish, P.D., I win, P.G. J., e al. (2010). The mal s uc u e and composi ion o
Jupi e ’s G ea Red Spo om high- esolu ion he mal imaging. Ica us, 208(1), 306–328. h ps://doi.o g/10.1016/j.ica us.2010.01.005
Fo d, A. L., & B owne, J. C. (1973). Rayleigh and Raman c oss sec ions o he hyd ogen molecule. A omic Da a, 5(3), 305–313. h ps://doi.
o g/10.1016/S0092-640X(73)80011-7
Fouche , T., Lellouch, E., & Feuch g ube , H. (2003). The hyd ogen o ho- o-pa a a io in he s a osphe es o he gian plane s. Ica us, 161(1),
127–143. h ps://doi.o g/10.1016/S0019-1035(02)00014-3
F y, P., & Ka koschka, E. (2018). Hype spec al cubes om mosaicked STIS obse a ions o U anus (“URANUS-STIS”) [da ase ]. Mikulski
A chi e o Space Telescopes. h ps://doi.o g/10.17909/ 9kq4n. Re ie ed om h ps://a chi e.s sci.edu/p epds/u anus-s is/
Gie asch, P.J., & Con a h, B. J. (1985). Ene gy con e sion p ocesses in he ou e plane s. In G. E. Hun (Ed.), Recen ad ances in plane a y
me eo ology (pp.121–146).
Go don, I. E., Ro hman, L. S., Hill, C., Kochano , R. V., Tan, Y., Be na h, P.F., e al. (2017). The HITRAN2016 molecula spec oscopic da a-
base. Jou nal o Quan i a i e Spec oscopy & Radia i e T ans e , 203, 3–69. h ps://doi.o g/10.1016/j.jqs .2017.06.038
Guillo , T. (1995). Condensa ion o me hane, ammonia, and wa e and he inhibi ion o con ec ion in gian plane s. Science, 269(5231), 1697–
1699. h ps://doi.o g/10.1126/science.7569896
Hadland, N., Sanka , R., LeBeau, J., Paul, R., & Palo ai, C. (2020). EPIC simula ions o Nep une’s da k spo s using an ac i e cloud mic ophysical
model. Mon hly No ices o he Royal As onomical Socie y, 496(4), 4760–4768. h ps://doi.o g/10.1093/mn as/s aa1799
Hammel, H. B., Lockwood, G. W., Mills, J. R., & Ba ne , C. D. (1995). Hubble space elescope imaging o Nep une’s cloud s uc u e in 1994.
Science, 268(5218), 1740–1742. h ps://doi.o g/10.1126/science.268.5218.1740
Acknowledgmen s
We a e g a e ul o he Uni ed Kingdom
Science and Technology Facili ies
Council o unding his esea ch (I win:
ST/S000461/1, Teanby: ST/R000980/1).
Glenn O on was suppo ed by unding o
he Je P opulsion Labo a o y, Cali o nia
Ins i u e o Technology, unde con ac
80NM0018D0004 wi h he Na ional
Ae onau ics and Space Adminis a ion
(NASA). Michael H. Wong and Glenn
O on ecei ed suppo o p og am
GO/DD-13937 and ela ed p og ams om
NASA h ough a g an om he Space
Telescope Science Ins i u e (STScI),
which is ope a ed by he Associa ion o
Uni e si ies o Resea ch in As oniomy,
Inc. (AURA) unde NASA con ac
NAS5-26555.Leigh Fle che and Mike
Roman we e suppo ed by a Eu opean
Resea ch Council Consolida o G an
(unde he Eu opean Union's Ho izon
2020 esea ch and inno a ion p og amme,
g an ag eemen No 723890) a he
Uni e si y o Leices e . San iago Pé ez-
Hoyos is suppo ed by g an PID2019-
109467GB-I00Z, unded by MCIN/
AEI/10.13039/501100011033. We a e
also g a e ul o he assis ance o La y
S omo sky and Pa F y in loca ing and
eading he HST/STIS da a. We a e also
g a e ul o he PDS Ring-Moon Sys ems
Node's OPUS sea ch se ice o p o iding
access o he Voyage -2 ISS images.
Finally, he Gemini/NIFS obse a ions
used we e ob ained a he in e na ional
Gemini Obse a o y, a p og am o NSF's
NOIRLab, which is managed by AURA
unde a coope a i e ag eemen wi h he
Na ional Science Founda ion on behal
o he Gemini Obse a o y pa ne ship:
he Na ional Science Founda ion (Uni ed
S a es), Na ional Resea ch Council
(Canada), Agencia Nacional de In es i-
gación y Desa ollo (Chile), Minis e io
de Ciencia, Tecnología e Inno ación
(A gen ina), Minis é io da Ciência,
Tecnologia, Ino ações e Comunicações
(B azil), and Ko ea As onomy and Space
Science Ins i u e (Republic o Ko ea).
This wo k was enabled by he loca ion o
he Gemini and NASA IRTF elescopes
wi hin he Maunakea Science Rese e,
adjacen o he summi o Maunakea. We
a e g a e ul o he p i ilege o obse ing
U anus and Nep une om a place ha is
unique in bo h i s as onomical qual iy
and i s cul u al signi icance.
