Sensi i i y o bias co ec ion s ep on gene a ing hyd ological scena ios
É ienne Guilpa a,*, Vahid Espanmanesha, Amau y Tilman aand Ma c-And é Bou gaul b
a
Depa men o Ci il and Wa e Enginee ing, La al Uni e si y, Pa illon Ad ien-Poulio , 1065, a . de la Médecine, Québec (Qc) G1V 0A6, Canada
b
Depa men o Geog aphy, La al Uni e si y, Pa illon Abi ibi-P ice 2405 ue de la Te asse, Québec (Qc) G1V 0A6, Canada
*Co esponding au ho . E-mail: [email p o ec ed]; e gu[email p o ec ed]
ÉG, 0000-0001-9762-4159
ABSTRACT
Significan shi s in hyd o-clima ic egimes a e expec ed in many pa s o he wo ld du ing he 21s cen u y, a ec ing he wa e cycle.
Vulne abili y, impac , and adap a ion s udies o en use ailo ed modeling chains o assess he expec ed e ec s o clima e change, bu he
obus ness o hese chains is a ely in es iga ed. This highligh s he need o mo e igo ous e alua ion o modeling chains o ensu e ha
hey a e eliable o in o med decision-making p ocesses. To add ess his gap, we p opose a amewo k o e alua ing he sensi i i y o
hyd ological scena io p oduc ion o he bias co ec ion s ep. We apply he amewo k o he Senegal Ri e Basin, using h ee bias co ec ion
me hods (linea scale, empi ical quan ile mapping, and nes ed bias co ec ion) and h ee p ocedu es (clima e-co ec ion, hyd ological-co ec-
ion, and clima e-hyd ological-co ec ion). Ou esul s show ha he choice o modeling chain has a significan impac on u u e hyd o-
clima ic ajec o ies. In pa icula , he combina ion o clima e-and-hyd ological-co ec ion p ocedu es may be op imal when bo h clima e
biases and hyd ological model e o s a e significan . Mo eo e , using mul iple bias co ec ion me hods can s eng hen he ensemble o
u u e hyd o-clima ic condi ions. These findings ha e implica ions o ulne abili y–impac –adap a ion s udies and unde sco e he impo -
ance o igo ous modeling chain design and sensi i i y analysis.
Key wo ds: bias co ec ion, clima e change, hyd ological scena io p oduc ion, Senegal Ri e Basin
HIGHLIGHTS
•The choice o bias co ec ion me hod can significan ly impac he esul ing hyd ological scena ios.
•Remo ing he biases wi h a clima e-co ec ion p ocedu e, hyd ological-co ec ion p ocedu e, o a combina ion o bo h also no ably
influences he hyd ological-scena io ou comes.
•Reso ing o se e al bias co ec ion me hods can be seen as a ac o o s eng hen he ensemble o u u e hyd o-clima ic condi ions.
1. INTRODUCTION
Fo o e a cen u y (IPCC 2021), an h opogenic ac o s such as global wa ming and land con e sion ha e al e ed he Ea h’s
clima e o he poin whe e he s a iona y hypo hesis is no longe ealis ic (Milly e al. 2008). Significan shi s in p ecipi a ion
and e apo a ion egimes a e expec ed in many pa s o he wo ld (Nikulin e al. 2012;Knu i & Sedlácek 2013), which in u n
a ec he wa e cycle and wa e managemen (Olms ead 2014).
Wa e esou ces sys em pe o mances a e highly dependen on wa e a ailabili y. To add ess he non-s a iona y issues
imposed by clima e changes, many modeling amewo ks ha e been p oposed since he 2000s. Those amewo ks can be
b oadly classified in o wo ca ego ies (Füssel 2007): (i) de e minis ic amewo ks ( he so-called ‘ op-down’app oach) and
(ii) s ess- es s ( he ‘bo om-up’app oach).
In op-down app oaches, a modeling chain is de eloped o de i e u u e hyd o-clima ic condi ions and o assess hei
impac s on wa e esou ces sys ems. In gene al, he fi s link o he modeling chain is he clima e simula ion. Fo ca chmen
scale s udies, he use o a se o downscaled simula ions p o ided by egional ci cula ion models (RCMs) is encou aged as
hei efined esolu ion allows o he eflec ion o hyd o-clima ic ea u es and basin he e ogenei y, which global ci cula ion
models (GCMs) canno p o ide (Ma aun 2016;Gio gi 2019;Lee e al. 2019). As highligh ed by Be gs öm e al. (2001) and
men ioned in Teu schbein & Seibe (2012), he hyd ological a iables om RCMs (such as uno ) migh no be di ec ly used
This is an Open Access a icle dis ibu ed unde he e ms o he C ea i e Commons A ibu ion Licence (CC BY 4.0), which pe mi s copying, adap a ion and
edis ibu ion, p o ided he o iginal wo k is p ope ly ci ed (h p://c ea i ecommons.o g/licenses/by/4.0/).
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due o hei inabili y o cap u e ce ain physical eedbacks (such as infil a ion and e-e apo a ion) a he local scale in RCMs.
Ins ead, i is ecommended o eed an independen land su ace model (LSM) wi h RCM clima e in o ma ion. The modeling
chain ypically includes a clima e model, an LSM (such as a hyd ological model), and a wa e managemen model (WMM).
On he o he hand, bo om-up app oaches aim a imp o ing ou unde s anding o egional and sec o al clima e- ela ed ul-
ne abili ies by conduc ing s ess- es s. In his case, u u e hyd o-clima ic condi ions may be used as s esso s o iden i y he
hyd o-clima ic condi ions ha lead o sys em ailu e. GCM/RCM p ojec ions a e hen used o assess he possibili y o
sys em ailu e due o clima e change (B own & Wilby 2012;Culley e al. 2016). Gene ally speaking, he use o GCM and
RCM simula ions has become a common p ac ice in mos ulne abili y, impac , and adap a ion (VIA) s udies (B own
e al. 2015;Gio gi & Gu owski 2015;Enaya i e al. 2021).
Howe e , bo h GCM and RCM ou pu s display sys ema ic e o s, ailing o ep oduce he obse ed clima e’s s a is ics accu-
a ely (Boé e al. 2007;Gio gi e al. 2009;Teu schbein & Seibe 2012) due o di e ences in hei concep ualiza ion,
disc e iza ion, and assump ions (Knu i & Sedlácek 2013). These biases exis in bo h he his o ical and p ojec ion pa s o
he simula ions, and can p opaga e ac oss he modeling chain. To add ess his issue, se e al me hods ha e been de eloped
since he 2000s (Ma aun e al. 2010;Johnson & Sha ma 2012;Chen e al. 2021). Uni a ia e bias co ec ion me hods such as
linea scaling (Boé e al. 2007) adjus a single s a is ical pa ame e , such as he mean, while mul i a ia e me hods co ec s a -
is ical pa ame e s while add essing spa ial and/o empo al co ela ions be ween a iables (V ac & F iede ichs 2015;
Cannon 2018). Rega dless o he me hod, biases a e iden ified in a e e ence pe iod and hen emo ed om he his o ical
and p ojec ed pa s o he simula ion, assuming ha biases emain cons an o e ime.
P ope ly emo ing he bias ac oss a modeling chain is a challenging opic, which can be summa ized in wo ques ions.
Fi s , how does using di e en ypes o bias co ec ion me hods a ec u u e ajec o ies? Second, should we co ec he cli-
ma e simula ions be o e d i ing a LSM (also known as he ‘clima e-co ec ion p ocedu e’), o should we eed an LSM wi h
aw clima e simula ions and hen co ec he hyd ological ou pu s (also known as he ‘hyd ological-co ec ion p ocedu e’)?
Ghimi e e al. (2019) del ed in o he consequences o employing mul iple bias co ec ion me hods on hyd ological ou pu s
(wi h a clima e-co ec ion p ocedu e). Howe e , his in es iga ion was es ic ed o he his o ical pa o he simula ions and
did no encompass any equency-based bias co ec ion me hods (which could subs an ially al e yea - o-yea a iabili y:
Nguyen e al. 2016). Chen e al. 2021 s udied he impac s o adop ing ei he a clima e-co ec ion p ocedu e o a hyd ologi-
cal-co ec ion p ocedu e ac oss 12 small o medium wa e sheds (wi h he empi ical quan ile mapping me hod). Ne e heless,
hei ocus was solely on he his o ical pa o he simula ions. The e o e, he exis ing li e a u e lacks a comp ehensi e
explo a ion o he sensi i i y associa ed wi h he bias co ec ion s ep in gene a ing hyd ological scena ios. This gap includes
he in eg a ion o (i) di e se bias co ec ion me hods and (ii) dis inc bias co ec ion p ocedu es such as clima e and hyd o-
logical adjus men s, all wi h a specific ocus on he p ojec ion pa o he simula ions.
In his s udy, we p opose o in es iga e his gap. We designed a amewo k o e alua e he sensi i i y o hyd ological scen-
a io p oduc ion o he bias co ec ion s ep o a u u e ho izon. In addi ion o he clima e-co ec ion p ocedu e and
hyd ological-co ec ion p ocedu e, he amewo k inco po a es he clima e-and-hyd ology co ec ion p ocedu e, which
embeds bo h p ocedu es.
The amewo k is illus a ed using he Senegal Ri e Basin (SRB) as a case s udy. This basin has expe ienced significan
shi in i s p ecipi a ion egime since 1940s, and unde goes ac ually flou ishing de elopmen . Applying ou amewo k o
such a basin will help basin au ho i ies in documen ing plausible u u e hyd o-clima ic ajec o ies, an a ea whe e he
u u e hyd o-clima ic ajec o ies display no clea end (IPCC 2022). I will also p o ide o he scien ific communi y a con-
c e e example o how sensi i e a modeling chain can be o he bias co ec ion s ep.
2. FRAMEWORK PRESENTATION
The p oposed amewo k aims a showing how sensi i e is he p oduc ion o hyd ological scena ios o he bias co ec ion s ep
using ei he a clima e-co ec ion o a hyd ological-co ec ion p ocedu e, o a combina ion o bo h.
Figu e 1(a) p o ides an o e iew o he gene ic amewo k. Each panel in he Figu e 1(a) ep esen s a specific bias co ec-
ion me hod (deno ed as X). Wi hin each panel, h ee cases a e defined as ollows.
Afi s case ha co esponds o he clima e-co ec ion p ocedu e (deno ed X
C
, and depic ed by he g een boxes in
Figu e 1(a)). The bias co ec ion me hod is applied o clima e simula ions o p o ide clima e scena ios. The LSM is hen
ed wi h hese clima e scena ios o p oduce hyd ological scena ios.
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A second case ha e e s o he hyd ological-co ec ion p ocedu e (deno ed X
H
, and depic ed by he blue boxes in
Figu e 1(a)). The LSM is ed wi h aw (unco ec ed) clima e simula ions o p oduce hyd ological simula ions. The co ec ion
me hod is hen applied o hese hyd ological simula ions.
A hi d case ha e e s o he clima e-and-hyd ological-co ec ion p ocedu e (deno ed X
CH
, and depic ed by he o ange
boxes in Figu e 1(a)). Fi s , we co ec he clima e simula ions and hen eed he LSM wi h hese clima e scena ios. Finally,
we apply he co ec ion me hod o he LSM ou pu s.
The p ocedu es desc ibed abo e a e based on ce ain expec a ions and assump ions. The clima e-co ec ion p ocedu e (X
C
)
aims o elimina e clima e biases, bu he e o s o he LSM may s ill pe sis . The hyd ological-co ec ion p ocedu e (X
H
)
Figu e 1 |(a) F amewo k p oposed o e alua e he sensi i i y o he hyd ological scena io p oduc ion o he bias co ec ion s ep. The
amewo k consis s o es ablishing npanels, each e e ing o a specific bias co ec ion me hod X. Inside each panel, h ee cases a e defined.
G een, blue, and o ange boxes e e o he clima e-co ec ion p ocedu e, hyd ological-co ec ion p ocedu e and he clima e-and-hyd olo-
gical-co ec ion p ocedu e, espec i ely. (b) Applica ion o he gene ic amewo k o he Senegal Ri e Basin.
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add esses bo h clima e biases and LSM e o s simul aneously, bu using unco ec ed clima e da a in he LSM can po en ially
impac he model’s ope a ion (see Sec ion 5.3 o u he de ails). By combining bo h he clima e-co ec ion and hyd ological-
co ec ion p ocedu es (X
CH
), we can ensu e he emo al o clima e biases and LSM e o s wi hou any po en ial dis o ion o
he LSM. Finally, he e alua ion phase assesses he sensi i i y o hyd ological scena io gene a ion o he bias co ec ion s ep.
3. STUDY CASE: THE SRB
3.1. Backg ound
The Senegal Ri e d ains a basin sha ed by ou coun ies: Guinea, Mali, Mau i ania and Senegal (Figu e 2(a)). The head-
wa e s a e loca ed in he Fou a Jalon (Guinea), whe e he Bafing Ri e uns no hwa d un il me ging wi h he Bakoye in
Mali, o ming he Senegal Ri e . Running no h-wes , i collec s wa e om he Faleme i e be o e eaching Bakel, a key-
poin o he wa e alloca ion decision in he basin. Downs eam o Bakel, inc emen al inflows a e insignifican (Bade
e al. 2015). So, only he ac i e pa o he basin has been modeled, whose co esponding ou le is Bakel (d aining an a ea
o 393,754 km
2
).
The obse ed annual flow a Bakel is 21.5 +8.7 km
3
pe yea (calcula ed on 1904–2011 using mon hly inflow ime-se ies
(Bade e al. 2015)). The monsoon onse b ings he we season ( ypically om July o Oc obe ), which ep esen s 88% o he
annual discha ge (Figu e 2(b)). The d y season ollows ( om No embe o June) du ing which ∼12% o he annual flow is
discha ged. Du ing he 21s cen u y, he SRB expe ienced shi s be ween well-dis inc d y, we , and neu al pe iods
(Figu e 2(c))(Bodian 2014;Bade e al. 2015;Faye e al. 2015;Guilpa e al. 2021).
In he 1970s, l’O ganisa ion pou la mise en aleu du fleu e Sénégal (OMSV, he basin au ho i ies) ini ia ed he cons uc-
ion o wo majo hyd aulic in as uc u es: he Manan ali dam on he Bafing and he Diama dam close o he i e mou h.
Today, wa e - ela ed ac i i ies in he basin a e flou ishing. New majo in as uc u es will suppo he de elopmen o i iga-
ion, na iga ion and hyd opowe gene a ion (CSE e al. 2011). Also, he s o age capaci y will inc ease om 6.5 km
3
( oday) o
Figu e 2 |(a) The Senegal Ri e Basin, bounda ies, in as uc u es and i e ne wo k. The basin has been delimi ed wi h he help o he
A cGis model ( e sion 10.4), and he digi al ele a ion model o he SRTM ( esolu ion: 1 a c-second) We ne (2001). (b) Boxplo o mon hly
inflows a Bakel ( he blue line ep esen s he annual cycle). (c) Annual olume o flow a Bakel ( he ed line ep esen s he en yea mo ing
a e age). Da a come om he ac ualiza ion o he SRB monog aph (Bade e al. 2015).
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13 and o 27 km
3
wi h he cons uc ion o he so-called second gene a ion o dams by 2050 ( o each a o al o six dams) and
he cons uc ion o he hi d-gene a ion dams by he end o he cen u y ( o each a o al o 12 dams).
Due o no able changes in p ecipi a ion pa e ns, ongoing basin de elopmen , and he subs an ial disc epancies in clima e
models p ojec ing he u u e hyd o-clima ic condi ions (IPCC 2022), he SRB s ands as an ideal case s udy o implemen ing
he p oposed amewo k.
3.2. Implemen a ion o he amewo k in he SRB
This s udy aims o e alua e he sensi i i y o hyd ological scena io p oduc ion o he bias co ec ion s ep. The fi s s ep owa d
achie ing his goal is o ca e ully selec he bias co ec ion me hods o es ing.
The choice o a bias co ec ion me hod is dependen on he objec i es o he s udy. In ea lie s udies ocused on ulne -
abili y–impac –adap a ion, mean-based adjus men s and dis ibu ion-based adjus men s we e he mos commonly used
me hods. Howe e , in ecen yea s, equency-based co ec ion me hods ha e eme ged as a iable al e na i e (Nguyen
e al. 2016). Fo he pu poses o wa e managemen , he long- e m pe sis ence o hyd ological a iables is o pa icula impo -
ance in high s o age-capaci y sys ems, which is he case o he SRB.
Also, we p opose an applica ion o he gene al me hod by in ol ing he h ee ollowing bias co ec ion me hods
(Figu e 1(b)). Consequen ly, his p o ides us wi h nine dis inc cases, comp ising he ollowing me hods:
1. The Linea Scaling me hod (LS) (Boé e al. 2007): This me hod ocuses on co ec ing he mean o he simula ion. Fu he
de ails on he algo i hm can be ound in he Supplemen a y Ma e ial (Sec ion C.1.).
2. Empi ical Quan ile Mapping me hod wi h a scale ans o ma ion (EQM-ST) (Piani e al. 2010): EQM-ST seeks o adjus he
mean and dis ibu ion o he simula ion a he mon hly ime-s ep by defining a sequence o quan iles. Re e o he Sup-
plemen a y Ma e ial (Sec ion C.2.) o mo e in o ma ion on he algo i hm.
3. Nes ed Bias Co ec ion me hod (NBC) (Johnson & Sha ma 2012): NBC adjus s he mean, s anda d de ia ion, and Lag-1
au oco ela ion a bo h mon hly and yea ly ime s eps. Fu he de ails on he me hod and i s applica ion can be ound in he
Supplemen a y Ma e ial (Sec ion C.3.).
Be o e applying bias co ec ion me hods, i is impo an o discuss how he end in hyd o-clima ic a iables is handled. In his
s udy, we ollow he guidelines p o ided by Ma aun (2016). P ecipi a ion is a majo d i e o he inflows in he basin, meaning i
plays a c i ical ole in de e mining he amoun o wa e ha flows in o he i e sys em. The physical p ocesses inhe en o Wes
A ican monsoon a e poo ly ep esen ed by he GCMs (Philippon e al. 2010) and by he RCMs (Sylla e al. 2016). Indeed, p o-
cesses in ol ed in p ecipi a ion dynamics ange om global scale (as sea su ace empe a u e pa e ns) o cumulus-scale, and
significan biases a e epo ed in RCM ou pu s o e he pas pe iods (Akinsanola e al. 2015). Because he p ecipi a ion p o-
cesses a e s ill poo ly ep esen ed, so p ecipi a ion ends in simula ions migh be implausible, and he associa ed biases a e
ime-dependen . As a esul , he e a e significan biases in he ou pu s o hese models. In pa icula , he biases in he simula ion
o p ecipi a ion a e ime-dependen , which means ha hey change wi h ime. Gi en he limi a ions in simula ing p ecipi a ion,
we do no conside he ends in p ecipi a ion o be eliable enough o use in bias co ec ion me hods. As p ecipi a ion is he
main d i e o he inflows in he basin, we do so when we apply a bias co ec ion me hod o inflows. Howe e , as he end
in po en ial e apo anspi a ion (PET) is mainly d i en by he inc ease o he empe a u e due o global wa ming
(Ndiaye e al. 2021), we conside ha ends in PET simula ions a e mo e eliable. The e o e, in his s udywe explici ly conse e
he end in PET by emo ing i p io o applying a bias co ec ion me hod, and hen adding i back a e wa d. This helps
o ensu e ha any e o s in he simula ed PET da a a e co ec ed while s ill p ese ing he unde lying end in he da a.
Please no e ha he selec ed Land Su ace Model (LSM) equi es spa ially a e aged ime-se ies o un, as explained in Sec-
ion 3.2.1. When applying a clima e-co ec ion p ocedu e, each g id cell o clima e simula ions is independen ly co ec ed,
ollowed by spa ial a e aging o e he basin. On he o he hand, when applying a hyd ological-co ec ion p ocedu e, he cli-
ma e simula ions a e fi s spa ially a e aged o eed he LSM. Finally, bias co ec ion me hods a e applied o LSM ou pu s.
Figu e 1(b) illus a es he necessa y elemen s o de i ing u u e hyd ological condi ions in he SRB, which include a se o
clima e simula ions, selec ing an app op ia e LSM, and clima e and hyd ological obse a ions o co ec and calib a e he
LSM. I is also impo an o define a e e ence pe iod and a ho izon o he e alua ion.
As depic ed in Figu e 1(b), he ollowing elemen s a e equi ed o de i e he u u e hyd ological condi ions in he SRB:
1. A se o clima e simula ions.
2. Selec ing an LSM.
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3. A se o clima e and hyd ological obse a ions in o de o co ec he clima e simula ions as well as calib a e and ali-
da ion he LSM.
4. Defining a e e ence pe iod and a ho izon on which he e alua ion will be ca ied ou .
3.2.1. The GR2M as he LSM
Since he da a a e oo spa se and incomple e in he SRB o use a dis ibu ed hyd ological model based on physics, ou choice
inclines owa d a concep ual LSM. Ope a ing a a mon hly ime-s ep and al eady ha ing p o en good pe o mances in he
SRB (A doin-Ba din 2004;Bodian e al. 2012;Guilpa e al. 2021), we adop ed he concep ual hyd ological model
GR2M (Figu e 3)(Mouelhi 2003). Due o i s concep ualiza ion, he GR2M is no able o accoun o dam ope a ions.
Thus, he GR2M equi es a na u alized ime-se ies o inflows o he calib a ion/ alida ion s ep, whe ein he e ec s o
dam ope a ions ha e been emo ed. The model calib a ion and alida ion p ocess a e ca ied ou using he di e en ial
spli -sample es desc ibed by Klemeš(1986), along wi h he h ee-s a es Hidden Ma ko Model classifica ion me hod de el-
oped by Guilpa e al. (2021). The Kling–Gup a e ficiency (KGE) is used as he objec i e unc ion o he model. We se he
wa ming-up pe iod o he GR2M model o wo yea s. Mo e in o ma ion on he calib a ion and alida ion p ocedu es can be
ound in he Supplemen a y Ma e ial (Sec ion A).
3.2.2. Obse a ion da a se s
The GR2M equi es PET and p ecipi a ion (P) da a o unning. Obse ed inflows (Q) a e also needed o he calib a ion/ ali-
da ion s ep. Thus, we cons i u ed ou hyd o-clima ic da abase wi h obse a ions (PET, P, and Q) and wi h clima e simula ions
(PET and P).
We selec ed (i) he p ecipi a ion dis ibu ed da ase om he HSM-SIREM da abase (Boye e al. 2006;Dieulin e al. 2019)
(co e ing he 1940–1998 pe iod); and (ii) he PET om he Clima e Resea ch Uni da abase (Ha is e al. 2020) (co e ing he
pe iod om 1901 o 2018). Na u alized inflows a e e ie ed om Bade e al. (2015) (1903–2012).
3.2.3. The clima e simula ion da ase
GCMs used o simula e he SRB’s clima e ha e a coa se spa ial esolu ion o app oxima ely 200 km, insu ficien o cap u ing
he egion’s s ong clima ic a iabili y (Faye e al. 2015). To ob ain a mo e de ailed ep esen a ion, we used high- esolu ion
RCMs om he CORDEX-A ica p ojec (Gio gi & Gu owski 2015). F om he ensemble o CORDEX-A ica clima e
Figu e 3 |The GR2M hyd ological model.
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simula ions, we ex ac ed 55 p ecipi a ion simula ions and 22 e apo anspi a ion simula ions (lis ed in Table 1). These simu-
la ions co e he pe iod om 1951 o 2099 and p o ide a mo e accu a e ep esen a ion o he p opaga ion o he monsoon
on owa d he no h in he SRB.
As he GR2M equi es wo spa ially a e aged ime-se ies o un, clima e simula ions and clima e scena ios we e a e aged
o e he basin. Ha ing a ou disposal 55 simula ions o Pand 22 simula ions o PET, we combined hem o ge 1,210 hyd o-
logical scena ios o each case (LS
C
,LS
H
,LS
CH
, EQM
C
, EQM
H
, EQM
CH
, NBC
C
, NBC
H
, and NBC
CH
).
3.2.4. Iden ifica ion o he e e ence pe iod and he ho izon
In he SRB, he clima e has exhibi ed d y, no mal, and we pe iods in he pas , which a e no ully cap u ed in he his o ical
pa o he GCM and RCM simula ions (Figu e C in he Supplemen a y Ma e ial). Also, pa icula a en ion mus be paid o
a oid any non-s a iona y issues when defining he ans e unc ions. To a oid ha kind o ins abili y du ing he co ec ion
ac o compu a ion, we se he e e ence pe iod o be as long as possible. Thus, he e e ence pe iod s e ches om 1951 o
1998 when co ec ing clima e a iables, and om 1953 o 1998 when co ec ing hyd ological a iables ( he 1951 and 1952
yea s a e conside ed as a wa ming pe iod by he GR2M, as men ioned be o e).
To a oid compu a ion and ans e issues o he yea ly Lag-1 au oco ela ion when using he NBC me hod, he leng h o he
u u e ho izon is se equal o ha o he e e ence pe iod. Thus, he u u e ho izon o his s udy s e ches om 2050 o 2095.
This allows us o gene a e eliable hyd ological scena ios o he u u e pe iod while a oiding any ins abili y du ing he com-
pu a ion o co ec ion ac o s.
4. RESULTS
The esul s o he s udy a e s uc u ed as ollows. Fi s , we p esen he hyd o-clima ic ajec o ies in he SRB o p ecipi a ion
(P), PET, and s eamflow (Q) based on di e en bias co ec ion me hods (Sec ion 4.1). Nex , we assess he pe o mance o
bias co ec ion p ocedu es in ep oducing he hyd ological condi ions o he e e ence pe iod (Sec ion 4.2) and he u u e
ho izon (Sec ion 4.3).
As he h ee bias co ec ions aim o co ec he mean, dis ibu ion, and/o long- e m pe sis ence o ime-se ies, he pe o m-
ance o he co ec ions is he e o e e alua ed using he mean, he s anda d de ia ion and he Ac -Lag1 alue a he yea ly
Table 1 |Simula ions ex ac ed om CORDEX-A ica; GCMs–RCMs coupling and RCP used in his s udy
RCMs
CCLM4-8-17 CSC HIRHAM5 RACMO22T RCA4 REMO2009 CRCM5
GCMs CCCma-CAn ESM2 þþ /þþþ
**/***
þþ
CNRM-CERFACS-CM5 þþ/þþþ þþ/þþþ
**/***
CSIRO-Mk3-6-0 þþ/þþþ
**/***
NOAA-GFDL-GFDL-ESM2G þþ/þþþ
**/***
MOHC-HadGEM2-ES þþ/þþþ þ/þþ/þþþ þ/þþ/þþþ
*/**/***
ICHEC-EC-EARTH þþ/þþþ þþ/þþþ þþ/þþþ þ/þþ/þþþ þ/þþ/þþþ
*/**/***
IPSL-CMSA-LR þþ/þþþ
**/***
MPI-M-MPI-ESM-LR þþ/þþþ þ/þþ/þþþ þ/þþ/þþþ
*/**/***
þþ
MIROC-MIROC5 þ/þþ/þþþ
*/**/***
NCC-No ESM1-M þ/þþ/þþþ
*/**/***
Symbols þ,þþ, and þþþ e e o RCP2.6, RCP4.5, and RCP8.5 p ecipi a ion simula ions, espec i ely. Simila ly, symbols *, **, and *** e e o RCP2.6, RCP4.5, and RCP8.5 PET
simula ions.
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ime-s ep (please e e o Sec ion D (Supplemen a y Ma e ial) o de ails abou i s compu a ion). These me ics a e also el-
e an o an ad ised wa e alloca ion policy in he SRB (Espanmanesh & Tilman 2022).
4.1. P, PET, and Q ajec o ies in he SRB
Figu e 4 p esen s he hyd o-clima ic ajec o ies in he SRB depending on he bias co ec ion me hod.
The end o he p ecipi a ion simula ions ensemble (i.e. he mean o all he simula ions) exhibi s low alues o he whole
pe iod (0.13 mm/y, 1951–2095), leading o a d op o 2.0% o he p ecipi a ion a es be ween he e e ence pe iod
(652 mm/y, 1951–1998) and he u u e ho izon (639 mm/y, 2050–2095). Simila esul s wi h LS, EQM-ST and NBC clima e
scena ios a e ound wi h low modifica ion a es (1.3%, þ1.0%, and 2.2%, espec i ely). This illus a es ha clima e models
display no consensus in he end o p ecipi a ion in he SRB.
Figu e 4 |P ecipi a ion, PET, and inflow ajec o ies in he SRB. The dashed black line e e s o he mean o he simula ions (55 o P, 22 o
PET, and 1,210 o Q), he con inuous black line o he mean o he LS-scena ios, he blue line o he mean o he EQM-ST scena ios, and he
ed line o he mean o he NBC scena ios. G een lines e e o he obse a ions. The his o ical pa , he p ojec ion pa and he s udied
ho izon a e displayed.
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The PET simula ion ensemble end displays highe alues o he whole pe iod (þ1.8 mm/y), leading o a significan
inc ease (þ175 mm/y, o þ7.3%) o he PET be ween he e e ence pe iod (2,223 mm/y) and he u u e (2,399 mm/y).
This inc ease is mainly a ibu ed o he inc ease o empe a u e, as highligh ed by Ndiaye e al. (2021). Al hough he PET
is supposed o be explici ly conse ed du ing he bias co ec ion s ep (see Sec ion 3.2), we no e ha LS, EQM-ST and
NBC clima e scena ios display di e en end alues (þ7.6%, þ4.9%, and þ8.3%, espec i ely), and he sp ead is significan
wi h he EQM-ST me hod. Du ing he co ec ion, we assume a linea end. This is gene ally ue o simula ions o ced by he
RCP 8.5 scena io, bu no o simula ions o ced by RCP 2.6 and RCP 4.5. Indeed, as s a ed in hese wo RCP scena ios, a
dec ease o he g eenhouse gas emissions is assumed du ing he 21s cen u y, leading o a comp ession o he empe a u e
inc ease ha impac s he PET end. Also, in mos simula ions o RCP 2.6 and RCP 4.5, when he end is emo ed in he
p ojec ion pa o he simula ions, he esidual PET alues a e igge ed, and he associa ion wi h quan ile is disc up ed
wi h he EQM-ST me hod. Consequen ly, he co ec ion applied o he u u e ho izon becomes excessi e, leading o
alues lowe han expec ed, which impac he end a he final s age. He e, we highligh he limi s o he willingness o expli-
ci ly conse e a end in a bias co ec ion p ocedu e.
Table 2 gi es end alues and mean annual olumes o inflow depending on he p ocedu e and he bias co ec ion me hod.
Fi s , we no e ha he u u e ho izon emains gene ally d ye han he e e ence pe iod. The educ ion in he i e ’s annual
olume is a ibu ed no solely o he sligh decline in p ecipi a ion a es, bu also o he PET inc ease. He e, we obse e ha
he e ec s o clima e change become e iden fi s in he ise o PET a he han in an al e a ion o he ain all pa e n.
Second, we no e ha he mean annual olumes o he e e ence pe iod a e aligned wi h he obse a ions (19.3 km
3
/y) wi h
a hyd ological-co ec ion p ocedu e, while an unde es ima ion wi h he clima e-co ec ion p ocedu e (a ound 16.4 km
3
/y)
can be no iced. The unde es ima ion emains on he u u e ho izon, and he clima e-co ec ion p ocedu e leads o minimizing
he annual olume by 15.4% o 9.8% compa ed wi h he hyd ological-co ec ion p ocedu e and clima e-and-hyd ological-co -
ec ion p ocedu e. This can be a ibu ed he GR2M e o s (which a e no emo ed in he clima e-co ec ion p ocedu e).
A ho ough examina ion o his issue is unde aken in he ollowing sec ions.
4.2. S a is ical e alua ion o bias co ec ion p ocedu es o he e e ence pe iod
In his sec ion, we fi s ocus on he bias in clima e simula ions and he e ec i eness o bias co ec ion me hods in elimina ing
bias o e he e e ence pe iod. Then, we ocus on he hyd ological scena ios p oduced h ough h ee co ec ion p ocedu es:
he clima e-, hyd ological-, and clima e-and-hyd ological-co ec ion p ocedu es. This app oach allows us o elucida e he
po en ial p opaga ion o bias h oughou he modeling chain.
The le panel o Figu e 5 illus a es he s a is ical pa ame e s ( he annual mean, s anda d de ia ion, and Ac -Lag1) o bo h
he clima e simula ions and scena ios o he e e ence pe iod.
The p ecipi a ion simula ions exhibi a pseudo-Gaussian dis ibu ion cen e ed a ound he mean annual p ecipi a ion a e
obse ed. Ne e heless, he s anda d de ia ion and Ac -Lag1 o p ecipi a ion simula ions a e unde es ima ed. All PET simu-
la ions display a d y bias (i.e. an o e es ima ion o he PET), high s anda d de ia ion, and a weak long- e m pe sis ence. These
cha ac e is ics illus a e ha clima e models gene a e simula ions wi h a oo-s ong yea - o-yea a iabili y compa ed wi h he
obse a ions.
Gene ally speaking, he h ee bias co ec ion me hods success ully adjus he s a is ic o clima e simula ions hey aim a
co ec ing. Howe e , NBC seems o well adjus he s anda d de ia ion and he Ac -lag1 o he p ecipi a ion simula ions.
Table 2 |T end alues o e 1951–2095 (fi s ow), mean annual olumes o inflow depending on he p ocedu e, and he bias co ec ion
me hods o he his o ical ho izon (second ow) and he u u e ho izon ( hi d ow)
Clima e-co ec ion Hyd ological-co ec ion
Clima e-and-hyd ological-
co ec ion
Simula ion LS EQM-ST NBC LS EQM-ST NBC LS EQM-ST NBC
T end [km
3
/y] 0.016 0.009 0.01 0.016 0.024 0.53 0.014 0.011 0.008 0.015
His o ical An. Vol. [km
3
/y] 19.5 16.4 16.3 16.3 19.3 19.3 19.3 19.3 19.3 19.3
Fu u e An. Vol. [km
3
/y] 17.8 15.4 17.2 14.4 17.0 17.6 17.7 18.2 20.2 17.4
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