A pe ec -model pe spec i e on he signal- o-noise pa adox in
ini ialized decadal p edic ions
Rashed Mahmood,a,b Ma kus G. Dona ,a,c F ancisco J. Doblas-Reyes,a,c E ienne Tou igny,a
a Ba celona Supe compu ing Cen e , Ba celona, Spain
b Na ional Cen e o Clima e Resea ch (NCKF), Danish Me eo ological Ins i u e,
Copenhagen, Denma k
c Ca alan Ins i u ion o Resea ch and Ad anced S udies (ICREA), Ba celona, Spain
Co esponding au ho : Rashed Mahmood, [email p o ec ed]
ABSTRACT
Ini ialized clima e p edic ions ha e shown success in p edic ing in e annual o decadal
clima e a ia ions in some egions. Howe e , he ini ialized p edic ions also su e om
di e en issues a ising om impe ec ini ializa ions and inconsis encies be ween he model
and he eal wo ld clima e and p ocesses. In pa icula , a so-called signal- o-noise pa adox
has been iden i ied in ecen yea s. The pa adox implies ha models can p edic obse a ions
be e han hey p edic hemsel es despi e some physical inconsis encies be ween modeled
and eal wo ld clima e. This is o en in e p e ed as an indica o o model de iciencies.
He e we p esen esul s o a pe ec -model decadal p edic ion expe imen , whe e he
p edic ions ha e been ini ialized using clima e s a es om he model's own ansien
simula ion. This expe imen a oids issues ela ed o model inconsis encies, ini ializa ion
shock and he clima e d i ha a ec eal-wo ld ini ialized clima e p edic ions. We ind ha
he pe ec -model decadal p edic ions a e highly skill ul in p edic ing he nea -su ace ai
empe a u e and sea le el p essu e o he e e ence un on decadal imescales. In e es ingly,
we also ind signal- o-noise issues– meaning ha he pe ec -model e e ence un is
p edic ed wi h highe skill han any o he ini ialized p edic ion membe s. This
coun e in ui i e esul sugges s ha he signal- o-noise pa adox may no be due jus o model
de iciencies in ep esen ing he obse ed clima e in ini ialized p edic ions. We illus a e ha
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his signal- o-noise p oblem , on mul i-annual o decadal imescales, is ela ed o analysis
p ac ices ha conca ena e ime se ies om di e en discon inuous ini ialized simula ions,
which in oduces inconsis encies compa ed o he con inuous ansien clima e ealiza ions
and he obse a ions. In pa icula , he conca ena ion o p edic ions ini ialized independen ly
in o a single ime se ies b eaks i s au o-co ela ion.
1. In oduc ion
Decadal clima e p edic ions aim o p edic he clima e up o en yea s in o he u u e.
These p edic ions conside he a ying adia i e o cing om changing g eenhouse gases and
ae osols, and a e ini ialized owa ds an obse a ional clima e s a e wi h he aim o align he
phasing o clima e a iabili y be ween he model and he eal-wo ld and also imp o ing he
o ced esponse (e.g. Dobal-Reyes e al. 2013; Meehl e al. 2021). Fo his, he ini ialized
clima e p edic ions a e pe o med by s a ing he models om econs uc ed o assimila ed
obse a ional da a (Smi h e al. 2007; Keenlyside e al. 2008; Boe e al. 2016). The
indi idual model in eg a ions end o show small signal- o-noise a ios and he e o e
ensembles o simula ions a e pe o med by adding small pe u ba ions o he ini ial
condi ions (Sienz e al. 2016).
The ini ialized p edic ion sys ems ha e shown success in p edic ing in e annual o
decadal clima e a ia ions, wi h added alue om ini ializa ion o e he o ced his o ical o
p ojec ion simula ions in some egions (e.g. Smi h e al. 2007; Keenlyside e al. 2008;
Doblas-Reyes e al. 2013; Kushni e al. 2019; A hanasiadis e al. 2020; Smi h e al. 2020;
Delgado-To es e al. 2022). Ini ialized p edic ions, howe e , also su e om some issues
ha po en ially educe hei skill such as model e o s, impe ec ini ial condi ions,
ini ializa ion shock and he subsequen clima e d i (e.g. Kha in e al. 2012; Sanchez-Gomez
e al. 2016; K öge e al. 2018; Bilbao e al. 2021). The ini ial shocks in he decadal
p edic ions de elop as a consequence o inconsis encies be ween he model a ac o and he
obse a ional clima e s a es. Thus s a ing he model simula ions away om he model’s
a ac o causes as and slow adjus men s ha do no ep esen meaning ul clima e
ajec o ies due o he ini ializa ion shocks and d i . The so-called pe ec -model p edic ion
expe imen s, ha ini ialize decadal p edic ions om clima e s a es o a ansien his o ical
un, ha e been used o in es iga e model-speci ic p edic abili y in he absence o such issues
ela ed o ini ializa ion shock and model d i (e.g. Liu e al. 2019, 2023).
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A p ominen issue in decadal p edic ion esea ch in ecen yea s has been he indica ion
ha he ini ialized clima e p edic ions appea o be a ec ed by he p esence o a so-called
‘signal- o-noise pa adox (he ea e e e ed o as SNP)’ a a ious p edic ion imescales
(Eade e al. 2014; Duns one e al. 2016; Scai e and Smi h 2018; Smi h e al. 2019). The
pa adox sugges s ha he model can p edic obse a ions wi h highe skill han i sel , despi e
some physical inconsis encies be ween modeled and eal wo ld clima e. The exac sou ces o
he exis ence o he SNP in clima e simula ions a e s ill being deba ed (Weisheime e al.
2024) wi h some s udies poin ing owa ds he esponsibili y o undamen al model
de iciencies (e.g. O’Reilly e al. 2018; Smi h e al. 2019, 2020; Zhang and Ki man 2019) and
o he s o he unce ain ies in he s a is ical p ope ies o he quan i ies used o analysis
(Weisheime e al. 2019; B öcke e al. 2023). Cu en ly he e is no gene al consensus on he
o igin o he SNP in he clima e model simula ions.
This s udy aims o explo e p edic abili y and possible signal- o-noise issues in an
idealized amewo k, a so-called pe ec -model p edic ion expe imen , whe e he model
p edic ions a e ini ialized om a his o ical clima e simula ion o he same model. This
implies ha , by de ini ion, he p edic ions a e ini ialized om clima e s a es ha a e
compa ible wi h he model-speci ic clima e a ac o and he e o e he p edic ions a e no
a ec ed by shock o d i . The p edic ions a e hen e alua ed agains he e e ence un om
which hey we e ini ialized (i.e. eplacing he obse a ions used in eal-wo ld p edic ions o
ini ializa ion and e alua ion by a ansien simula ion wi h he same clima e model used o
he p edic ions). This implies ha he clima e model used o he p edic ions is physically
ully consis en wi h he clima e ealiza ion i aims o p edic . A simila app oach was used by
Liu e al. (2019) o unde s and limi s o achie able skill in p edic ing clima e on annual o
decadal imescales albei using a di e en clima e model.
Besides in es iga ing he model-speci ic p edic abili y, we explo e possible indica ions o
he SNP in he ini ialized p edic ions in he pe ec -model expe imen . As explained abo e,
hese p edic ions a e (by de ini ion) no a ec ed by physical inconsis encies be ween he
p edic ions and he e e ence, as bo h a e om he same model and no a ec ed by
ini ializa ion shocks o clima e d i s which a ec he eal-wo ld clima e p edic ions. In
pa icula , possible signal- o-noise issues, should hey exis in he pe ec -model p edic ions,
could no be explained by po en ial model sho comings, as he p edic ions a e pe o med
wi h he same model agains which he p edic ions a e e alua ed and ini ialized wi h pe ec
“obse a ions”. The pe ec -model p edic ion expe imen s p o ide he e o e an idealized
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en i onmen o exclude o isola e speci ic ac o s, which has he po en ial o shed new ligh
on model p edic abili y and issues no o iously a ec ing decadal clima e p edic ions.
2. Da a and Me hods
The model simula ions used in his s udy a e ca ied ou using he Eu opean Conso ium’s
coupled a mosphe e-ocean gene al ci cula ion model e sion 3 (EC-Ea h3) wi h he same
con igu a ions as used o he Decadal Clima e P edic ion P ojec (DCPP) expe imen
(Bilbao e al. 2021) as pa o he Coupled Model In e compa ison P ojec phase 6 (CMIP6)
simula ions. The EC-Ea h3 model comes wi h di e en con igu a ions including op ions o
high, low and s anda d esolu ions (Dösche e al. 2022). Fo his expe imen we use he e he
s anda d esolu ion e sion o he EC-Ea h3. The a mosphe ic componen o he model is
based on he Eu opean Cen e o Medium-Range Wea he Fo ecas s (ECMWF) In eg a ed
Fo ecas Sys em (IFS) wi h ~80 km ho izon al esolu ion and 91 e ical le els. The ocean
componen o he model is based on Nucleus o Eu opean Modelling o he Ocean (NEMO)
e sion 3.6 wi h 1° ho izon al esolu ion and 75 e ical le els. Mo e de ails abou he EC-
Ea h3 model ha e been documen ed by e.g. Dösche e al. (2022) and Bilbao e al. (2021).
Fi s we conduc ed a e e ence his o ical simula ion in o de o gene a e and sa e he
model s a e a he beginning o No embe e e y yea , using CMIP6 his o ical o cings.
Running a new e e ence his o ical simula ion was necessa y o p o ide ini ial condi ions
based on exac ly he same e sion o he model ha we used o he pe ec model
p edic ions. Simila o he DCPP expe imen s o CMIP6, also o he idealized p edic ion
expe imen he model was ini ialized e e y yea om 1960 o 2014. Di e en o he DCPP
hindcas s, we used as ini ial condi ions he model s a es om he e e ence his o ical
simula ion ins ead o model econs uc ions based on obse a ions. A o al o 10 ensemble
membe s we e pe o med by sligh ly (a an o de o 10-5 K) pe u bing he a mosphe ic ini ial
condi ions. The p edic ions we e hen un o up o 11 yea s a e ini ialisa ion. An ensemble
mean was compu ed by a e aging all 10 membe s o he pe ec model ini ialisa ion
expe imen (he ea e e e ed o as ”Pe ec _Ini ”). Fo compa ison we also use a en
membe ensemble o DCPP ini ialized wi h obse a ional da a (he ea e e e ed o as
“ClimP ed_Ini ”).
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While much o his s udy ocuses on he di e en expe imen s (i.e. bo h Pe ec _Ini and
ClimP ed_Ini hindcas s) wi h he EC-Ea h3 model, we also analyzed a mul i-model
ensemble o decadal hindcas s p o ided wi hin he DCPP-A componen o CMIP6. We use
da a om a o al o 8 o he CMIP6 models apa om EC-Ea h3 (Table S1, in supplemen a y
ma e ial). All da a se s we e emapped o a uni o m 5°✕5° g id be o e pe o ming any
analysis, ollowing ecommenda ions by Godda d e al. (2012). We con e ed all da a se s o
mon hly anomalies using he e e ence clima ology pe iod o 1981 o 2010. Fo he ini ialized
p edic ions, anomalies we e compu ed using a lead- ime dependen clima ology (Ga cía-
Se ano and Doblas-Reyes 2012), o accoun o he d i in he hindcas s ini ialized wi h
ac ual obse a ions. We ocus ou analysis on o ecas s yea s 2-9, which is simila o o he
s udies ocusing on decadal imescales (e.g. Smi h e al. 2019; Scai e and Smi h 2018). A
o al o 45 s a -da es om 1960 o 2004 we e used o analysis in o de o use model
simula ions du ing he CMIP6 his o ical pe iod. In his s udy, we use nea -su ace ai
empe a u e ( as) and mean sea le el p essu e (psl).
The skill assessmen o he Pe ec _Ini is ca ied ou using he same his o ical simula ion
om which he p edic ions we e ini ialized as e alua ion e e ence, while o ClimP ed_Ini
we use obse a ions as e alua ion e e ence. The obse ed nea -su ace empe a u e da a was
ob ained om HadCRUT4 (Mo ice e al. 2012), which combines nea -su ace ai empe a u e
o e land and sea su ace empe a u e o e ocean. Fo sea le el p essu e we used eanalysis
da a om ERA5 (He sbach e al. 2020) as obse a ional e e ence.
Fo skill assessmen s we conside he anomaly co ela ion coe icien (ACC), which
measu es he ag eemen be ween wo ime se ies (i.e. he p edic ion ensemble mean and a
e e ence) wi h ocus on common a ia ions a he han hei magni udes. Since he ACC can
be s ongly a ec ed by he wa ming end, he added alue om ini ialisa ion o he clima e
p edic ions is also assessed by calcula ing he esidual co ela ions. These co ela e he
p edic ed and obse ed esiduals a e emo ing an es ima e o he o cing esponse ollowing
Smi h e al. (2019). He e we es ima e he o cing esponse om he ensemble mean o en
his o ical simula ions o he EC-Ea h3 model. We also analyze he a io o p edic able
componen s (RPC) ollowing (Scai e and Smi h 2018) o explo e he SNP in di e en
ensembles. Speci ically we compu ed he RPC by aking he squa e oo o he a io o
squa ed co ela ions be ween he ensemble mean and he e alua ion e e ence and he
ensemble mean wi h indi idual membe s. Acco ding o Scai e and Smi h (2018), he RPC
can be w i en as:
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RPC = √𝑟(𝑒𝑚,𝑜)
2
𝑟(𝑒𝑚,𝑚𝑒𝑚𝑏)
2 (1)
Whe e 2(em,o) is he co ela ion be ween he model ensemble mean wi h he obse a ion
(o he e e ence un in he pe ec -model case), and 2(em,memb) is he co ela ion be ween he
model ensemble mean wi h a membe (no included in he ensemble mean). Fo 2(em,memb) we
use he median o he co ela ions be ween he model ensemble mean and he indi idual
membe s.
The ini ialized hindcas s udies ypically cons uc ime se ies by conca ena ing he
ele an o ecas ime a e ages om he di e en (annual) ini ializa ions. These a e ypically
conca ena ed o he ensemble membe s wi h he same iden i ie (e.g. 1i1p1 1 om di e en
ini ializa ion imes); howe e he di e en ini ializa ions wi h he same iden i ie a e in ac
independen o each o he . The esul ing hindcas ime se ies o a membe iden i ie is
he e o e based on se e al discon inuous simula ion chunks, and his discon inui y could
po en ially a ec he co ela ion be ween he ensemble mean and he indi idual ensemble
membe s. We will e isi his issue in sec ion 3.2.
3. Resul s
3.1 Skill o he ini ialized p edic ions
We i s e alua e he (po en ial) skill o he di e en ensembles in simula ing nea -su ace
ai empe a u e (Figu e 1) and sea le el p essu e (Figu e 2). We ind high ACC alues o
he Pe ec _Ini o e mos o he globe, sugges ing ha he pe ec ly ini ialized ensemble is
highly skill ul in p edic ing i s e e ence un (Figu e 1a). The skill in Pe ec _Ini ex ends o
mos egions o he globe including some egions whe e he hindcas s ini ialized wi h
obse a ions wi h he same EC-Ea h3 model do no show much skill, such as he no heas
and sou heas Paci ic and se e al land egions (c Figu e 1a and 1d).
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Fig. 1. Skill assessmen o di e en ensembles in simula ing nea -su ace ai empe a u e o he a e age
o o ecas yea s 2-9 based on ACC (le column), esidual co ela ion (middle column), and he a io o
p edic able componen s ( igh column). The op ow shows esul s o Pe ec _Ini and he bo om ow o
ClimP ed_Ini . The s ippling ep esen s egions whe e ACC (a and d) and esidual co ela ions (b and e)
a e no s a is ically signi ican a he 95% con idence le el. Fo RPC (c and ) he egions whe e ACC is
nega i e a e s ippled. The black ma ke s indica e he g id poin used o plo ing nea -su ace ai
empe a u e and SLP ime se ies in Fig 3.
Simila ly o SLP we ind ha he Pe ec _Ini expe imen shows highe and widesp ead
skill (in p edic ing i s e e ence un) o e many egions o he globe compa ed o he skill o
he eal wo ld p edic ions (c Figu e 2a and 2d). No skill is ound in he eal wo ld
p edic ions o SLP o e he opical and sub opical Indian and A lan ic oceans and he
bo de ing con inen al egions. Pe ec _Ini , on he o he hand, shows posi i e ACC alues
o e mos o hese egions al hough a some loca ions ACC is no s a is ically signi ican a
he 95% con idence le el. These esul s indica e ha he e may be some decadal-scale
p edic abili y in he clima e sys em o he EC-Ea h3 model which is cu en ly no being
cap u ed by he eal-wo ld (i.e. ClimP ed_Ini ) p edic ions.
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Fig. 2. Same as Fig. 1 bu o mean sea le el p essu e (SLP).
The skill measu e based on ACC can be s ongly a ec ed by he esponse o ex e nal
o cings in bo h he Pe ec _Ini and he ClimP ed_Ini p edic ions. To e alua e he added
alue om ini ializing he clima e p edic ions, Figu e 1b and 1e show esidual co ela ions
ob ained a e emo ing an es ima e o he o cing esponse ollowing Smi h e al. (2019). We
ind mo e widesp ead added alue om ini ializa ion in he Pe ec _Ini compa ed o he
ClimP ed_Ini p edic ions. Fo example, o e he A lan ic, Indian, pa s o he Paci ic oceans
and some neighbo ing con inen al a eas signi ican added skill in Pe ec _Ini is ound, while
he ClimP ed_Ini only shows added skill o e he no h A lan ic subpola gy e and cen al
no h Paci ic. Simila ly o sea le el p essu e he Pe ec _Ini p edic ions show highe and
mo e widesp ead posi i e esidual co ela ion alues compa ed o ClimP ed_Ini (Figu e 2b
and 2e). The eal-wo ld p edic ions su e s ongly om he deg ada ion o he skill
especially in he A lan ic and he Indian oceans hence no added alue (and e en nega i e
esidual co ela ions) is ound in hese egions in ClimP ed_Ini . We no e ha he skill (and
added skill) in he pe ec -model p edic ions does no necessa ily imply p edic abili y o he
eal wo ld. While he pe ec -model ce ainly a oids some issues ha pe sis in a ec ing he
eal-wo ld p edic ions, he de e io a ion o skill in he eal-wo ld p edic ions can also be due
o inconsis encies be ween he model and he eal-wo ld clima e, o example ela ed o
mis ep esen ing some key p ocesses. S ill, hese esul s indica e he p edic abili y ha can be
achie ed wi h he EC-Ea h3 model in he case ha pe ec ini ial condi ions we e a ailable
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(i.e. pe ec knowledge o he ini ial s a e in each clima e sys em a iable) and he model
being physically consis en wi h he e e ence o be p edic ed.
3.2 Diagnosing he signal- o-noise pa adox
The a io o p edic able componen s has been used in he pas o diagnose he pa adoxical
beha io ha clima e p edic ions end o p edic he obse a ions wi h highe skill han hey
p edic an indi idual ealiza ion o he p edic ion model (e.g. Scai e and Smi h 2018, Smi h e
al. 2019). This issue is indica ed by RPC alues la ge han 1, and has o en been in e p e ed
as indica ion o some model sho comings. I is he e o e in e es ing o analyze he RPC in
he pe ec -model p edic ions, as hese, by de ini ion, a e ee o he model sho comings in
compa ison o he pe ec -model e e ence (because hey a e all pa o he same model
wo ld).
Bo h he ClimP ed_Ini and Pe ec _Ini show a eas wi h RPC alues la ge han 1 o
nea -su ace ai empe a u e (Figu e 1c and 1 ) and sea le el p essu e (Figu e 2c and 2 ),
implying a coun e in ui i e sugges ion ha he model can p edic he obse a ions and e en
he pe ec -model e e ence be e han ano he model membe used o make he p edic ions
(no e ha RPC is only meaning ul in a eas whe e he ACC is no nega i e). While we ind RPC
alues g ea e han one in case o nea -su ace ai empe a u e also, howe e , he pa adox is
ela i ely mo e p ominen when p edic ing sea le el p essu e, whe e RPC alues can each 2
o e en highe . Such la ge RPC is o en discussed as an indica ion o model de iciencies (e.g.
Scai e and Smi h 2018; Smi h e al. 2019), howe e in he case o pe ec -model p edic ions
he model used o make he p edic ions is physically consis en wi h he e e ence and
he e o e he e canno be a de iciency ega ding he physical ep esen a ion o clima e.
To de elop an unde s anding o he beha io o he di e en p edic ions we i s inspec
he ime se ies a one a bi a y g id poin in he Paci ic egion as shown in Figu e 3. I is
immedia ely appa en how he indi idual ensemble membe s show e y di e en
cha ac e is ics compa ed o bo h he ensemble mean and he e alua ion e e ences - o bo h
he Pe ec _Ini and he ClimP ed_Ini . The ini ialized ensemble membe s appea much
noisie compa ed o bo h he ansien e e ence simula ion and also he obse a ional
e e ence ime se ies. This is in ag eemen wi h A hanasiadis e al. (2020) who also no ed ha
he ime se ies gene a ed om discon inuous ini ialized hindcas s a e gene ally noisie han
he obse a ional e e ence. As also men ioned by A hanasiadis e al. (2020), he 8 yea
a e ages used o he e alua ing e e ences (i.e. obse a ion and he ansien clima e
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indica e ha he la ge RPC alues, which a e o en used o diagnose he SNP in he ini ialized
clima e p edic ions, could be a esul o conca ena ing indi idual membe ime se ies om
independen ini ializa ions wi h he same ensemble membe iden i ie (such as ensemble
membe #1 om he independen simula ions wi h ini ializa ion in 1960, 1961, 1962, e c).
4 Discussion and Conclusions
We ind ha he pe ec -model p edic ions show mo e widesp ead (po en ial) skill in
p edic ing model-speci ic nea -su ace ai empe a u e and sea le el p essu e o e mos
egions o he globe compa ed o he eal-wo ld p edic ions in p edic ing hei co esponding
e e ences. Al hough i is well unde s ood ha he highe skill o a pe ec model p edic ion
canno be di ec ly ansla ed o he skill o eal-wo ld p edic ions, he esul s om hese
expe imen s sugges ha he p edic ion can po en ially be imp o ed by p o iding model
consis en and accu a e ini ial-condi ions (Liu e al. 2019) and imp o ing he model quali y.
We also ind ha he added alue om ini ializa ion in he pe ec -model simula ions ex ends
o la ge egions globally while i emains e y limi ed in he eal wo ld p edic ions. These
esul s indica e ha he e may be p edic abili y in he clima e sys em on decadal imescales
ha is cu en ly no being cap u ed by he eal- wo ld p edic ion sys em, bu could also poin
o undamen al di e ences be ween he model-speci ic and he eal-wo ld clima e sys ems.
New and imp o ed ini ializa ion me hods may p o ide mo e skill ul global clima e
p edic ions on decadal imescales i he model and eal-wo ld clima e a e close in e ms o
ele an p ocesses.
Simila o p e ious s udies (e.g. Scai e and Smi h 2018), we also ind ha he SNP
pe sis s in he la es e sions o he ini ialized clima e p edic ions especially on mul i-annual
o decadal (and longe ) imescales, diagnosed by RPC alues la ge han 1, and sugges ing
ha he models can p edic he eal wo ld clima e wi h highe skill han hey can p edic
ano he model ealiza ion. Su p isingly, he pe ec model p edic ions also show la ge a eas
wi h RPC>1, implying ha he model is be e in p edic ing i s e e ence un han he
indi idual membe s. These esul s sugges ha he SNP is no likely domina ed by he issues
a ising om impe ec ini ializa ion o he eal-wo ld p edic ions, bu also ha he SNP is no
necessa ily an indica o o model de iciencies i i also occu s in a pe ec -model expe imen .
Indeed, we show he e ha he conca ena ion o p edic ions co esponding o ini ializa ions in
consecu i e and somehow independen yea s in o a single ime se ies b eaks he au o-
co ela ion o he esul ing ime se ies. The measu es ha conside such indi idual membe
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ajec o ies, such as he RPC, can he e o e be misleading – and should no be in e p e ed as
an indica o o po en ial model de iciencies. In he RPC case, he changes in au o-co ela ion
esul in lowe alues o he ensemble mean co ela ion wi h an indi idual membe (which is
a ec ed by he b oken au o-co ela ion a e conca ena ing p edic ions ini ialized a di e en
poin in ime and assigned o he same ensemble membe iden i ie ), compa ed o i s
co ela ion wi h he e e ence (which is no a ec ed by he discon inui y in oduced by he
conca ena ion).
We also ind ha he un ealis ic changes in he au o-co ela ion o indi idual membe s o
an ini ialized p edic ion sys em is no limi ed o he EC-Ea h3 model. We ind simila ly
lowe au o-co ela ions in o he decadal clima e p edic ions o he CMIP6 decadal p edic ion
ensembles, con i ming ha he p ac ice o conca ena ing simula ions wi h di e en ini ial
s a da es in o a ime se ies assigned o an ensemble membe leads o lowe co ela ion o he
ensemble mean wi h indi idual membe s. The e o e, ou esul s p o ide an al e na i e
explana ion o he SNP in ini ialized clima e p edic ions compa ed o p e ious s udies ha
sugges ed di e ences in ini ial ensemble and obse a ion sp eads (Maye e al. 2021), o e all
model de iciencies (e.g. Smi h e al. 2019; Scai e and Smi h 2018; S ommen and Palme
2018), di e ences in s a is ical p ope ies o he quan i ies used o analysis (e.g. Weisheime
e al. 2019; B öcke e al. 2023), and limi ed sample size (Weisheime e al. 2019). I is likely
ha a combina ion o ac o s play a ole in causing he SNP. Ou s udy highligh s he
impo ance o a i icially educing he au o-co ela ion o indi idual ensemble membe s when
combining da a om di e en discon inuous ini ializa ions (e.g. wi h he same ensemble
membe iden i ie ) in o a single ime se ies.
While his issue o cons uc ing ime se ies om discon inuous simula ions also a ec s
seasonal hindcas s (which a e ini ialized a speci ic da es e e y yea ), he desc ibed e ec s on
he au o-co ela ion o he ime se ies a e la ge o mul i-annual o decadal (o longe )
p edic ions han o e.g. seasonal p edic ions (Figu e S5 and S6). Howe e , hese e ec s
become ele an as soon as we a e age o e mul iple yea s (as shown o wo-yea
p edic ions in Figu es S7, S8). Tha is because when calcula ing mul i-annual a e ages in
con inuous ime se ies (e.g. obse a ions o ou ansien e e ence simula ion), hese mo ing
windows ha e se e al da a poin s in common, which leads o high au o-co ela ions. Bu
when calcula ing mul i-yea a e ages om discon inuous ini ialised simula ions, e en
empo ally o e lapping a e ages may no ha e da a poin s in common as hey come om
di e en independen simula ions. In he speci ic example o he 8-yea a e ages p esen ed in
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his s udy, he e e ence ime se ies include se en annual da a poin s which a e common
among wo consecu i e 8-yea a e ages. This is no he case when calcula ing hese mul i-
annual a e ages om he discon inuous simula ions ini ialized independen ly in each yea ,
o example. Ou inding ha hese au o-co ela ion issues a ec p edic ions a e aging o e
se e al o ecas yea s may explain ha he signal- o-noise issues (as quan i ied e.g. by
RPC>1) a e ypically la ge in decadal han in seasonal p edic ions (Eade e al. 2014; Smi h
e al. 2019). A hanasiadis e al. (2020) poin ed ou a simila issue o ime se ies om
ini ialized hindcas s being noisie han hei obse a ional e e ences and hey applied an
addi ional empo al smoo hing using se en-poin unning a e ages ac oss he s a da es (i.e.
in addi ion o he smoo hing in oduced by he 8-yea a e age p edic ions) o add ess his
symp om. This app oach has no been used he e because a e aging p edic ions ac oss he
s a da es makes he na u e o he p edic ion and he obse a ional e e ence e y di e en .
This addi ional a e aging leads o a o ecas p oduc ha , al hough smoo he , migh no ha e
mo e skill because olde p edic ions a e included in i . Smi h e al. (2020) cons uc ed e y
la ge ensembles by combining he ini ialized simula ions om se e al (lagged) s a da es.
While he p ima y a ionale o his app oach was o subs an ially inc ease he ensemble size,
a colla e al e ec o his app oach could be o inc ease he empo al smoo hness o he ime
se ies ( o he ensemble mean a leas ), due o using he in o ma ion om se e al
consecu i e ini ializa ions.
The ime se ies cons uc ed om conca ena ing simula ions wi h di e en s a da es in o
a speci ic ensemble membe does no ep esen physically meaning ul con inuous clima e
ajec o ies, con a y o he e e ence ime se ies used in he alida ion. This implies ha
diagnos ic me ics ha conside e.g. he co ela ion o an ensemble mean wi h he indi idual
ensemble membe ime se ies, such as he RPC, will be a ec ed by his a i ac om he
conca ena ion o di e en (discon inuous) ini ialized simula ions. As a consequence, la ge
RPC alues (o low co ela ions o a p edic ion ensemble a e age wi h indi idual ini ialized
ensemble membe ime se ies) should no necessa ily be in e p e ed as an indica o o
po en ial model de iciencies.
While he e is la ge e idence ha he ini ialized clima e p edic ions unde es ima e he
magni ude o he p edic ion signal, in pa icula o a mosphe ic ci cula ion (e.g. Scai e and
Smi h 2018; Smi h e al. 2020), ou esul s sugges ha he so-called pa adox ( ha he eal-
wo ld clima e is p edic ed wi h highe skill han an indi idual ensemble membe ) may be an
analysis- ela ed a i ac . Ou s udy shows ha his pa adoxical e ec is la gely a consequence
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o a i icially changing he s a is ical cha ac e is ics o he indi idual ini ialized ensemble
membe s by combining he in o ma ion om di e en independen ini ializa ions. While he
so-called pa adox may be a consequence o how we p ocess and analyze he da a, he
p oblem o he small p edic able signals ela i e o noise emains (Siege e al. 2016; Smi h
e al. 2020). This signal- o-noise issue may be oo ed in models no cap u ing ele an
p ocesses, and he unde es ima ion o he signal magni ude is no pa adoxical as such. Fu u e
clima e model de elopmen s and imp o emen s a e hoped o esol e his issue o small
signal- o-noise a ios.
Acknowledgmen s.
This esea ch con ibu ed o he Spanish Minis y o Science and Inno a ion p ojec s
PRECEDE (g an no. EUR2022-134059) and PATHFINDER (g an no. PID2021-
127943NB-I00). We a e also g a e ul o pa ial suppo by he Ho izon Eu ope p ojec s
ASPECT (g an numbe 101081460) and Impe us4Change (g an numbe 101081555) and
suppo by he Depa amen de Rece ca i Uni e si a s de la Gene ali a de Ca alunya o he
Clima e Va iabili y and Change (CVC) Resea ch G oup (Re e ence: 2021 SGR 00786).
High-pe o mance compu ing esou ces used o pe o m some o he expe imen s we e
ob ained om he ECMWF special p ojec spesicc -2024 “Unde s anding in e -annual o
decadal p edic abili y in he EC-Ea h3 model and he po en ial bene i s om pe ec
ini ialisa ion” as well as PRACE (HiRes-NTCP, p ojec 3: g an no. 2017174177) and he
Red Española de Supe compu ación (AECT-2019-2-0003 and AECT-2019-3-0006 p ojec s).
Da a A ailabili y S a emen .
All model simula ion da a (excep Pe ec model simula ions) used in his s udy a e eely
a ailable om ESGF nodes (e.g. h ps://esg -node.ipsl.upmc. /) and obse a ional and
eanalysis da a a e a ailable om hei espec i e sou ces. The pe ec model simula ion and
he co esponding e e ence un da a can be made a ailable upon eques .
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