Long-Te m We ing and D ying T ends in Land Wa e
S o age De i ed F om GRACE and CMIP5 Models
L. Jensen1, A. Eicke 1, H. Dobslaw2, T. S acke3, and V. Humph ey4
1Geodesy and Geoin o ma ics, Ha enCi y Uni e si y Hambu g, Hambu g, Ge many, 2Helmhol z Cen e Po sdam,
Ge man Resea ch Cen e o Geosciences (GFZ), Po sdam, Ge many, 3Max Planck Ins i u e o Me eo ology, Hambu g,
Ge many, 4Ins i u e o A mosphe ic and Clima e Science, ETH Zü ich, Zü ich, Swi ze land
Abs ac Coupled clima e models pa icipa ing in he CMIP5 (Coupled Model In e compa ison
P ojec Phase 5) exhibi a la ge in e model sp ead in he ep esen a ion o long- e m ends in soil mois u e
and snow in esponse o an h opogenic clima e change. We e alua e long- e m (Janua y 1861 o Decembe
2099) wa e s o age ends om 21 CMIP5 models agains obse ed ends in e es ial wa e s o age
(TWS) ob ained om 14 yea s (Ap il 2002 o Augus 2016) o he GRACE (G a i y Reco e y And Clima e
Expe imen ) sa elli e mission. This is complica ed due o he incomple e ep esen a ion o TWS in CMIP5
models and in e annual clima e a iabili y masking long- e m ends in obse a ions. We hus e alua e
i s he sp ead in p ojec ed ends among CMIP5 models and iden i y egions o b oad model consensus.
Second, we assess he ex en o which hese p ojec ed ends a e al eady p esen du ing he his o ical
pe iod (Janua y 1861 o Augus 2016) and hus po en ially de ec able in obse a ional eco ds a ailable
oday. Thi d, we quan i y he deg ee o which 14-yea endencies can be expec ed o ep esen long- e m
ends, inding ha egional long- e m ends s a o eme ge om in e annual a ia ions a e jus 14
yea s while s able global end pa e ns a e de ec able a e 30 yea s. We classi y egions o s ong model
consensus in o a eas whe e (1) clima e- ela ed TWS changes a e suppo ed by he di ec ion o GRACE
ends, (2) misma ch o ends hin s a possible model de ici s, (3) he sho obse a ion ime span and/o
an h opogenic in luences p e en eliable conclusions abou long- e m we ing o d ying. We he eby
demons a e he alue o sa elli e obse a ions o wa e s o age o u he cons ain he esponse o he
e es ial wa e cycle o clima e change.
1. In oduc ion
The e es ial b anch o he global wa e cycle is an impo an componen o he Ea h's coupled clima e
sys em: Wa e a ailable in he soil c i ically de e mines biomass p oduc ion ha e ec i ely akes up ca bon
dioxide om he a mosphe e and hus cons i u es he land co e and consequen ly also he albedo o he
Ea h's su ace. The a ailabili y o wa e a he su ace in luences he a e o e apo anspi a ion and he eby
he amoun o la en hea abso bed by he a mosphe e locally and ad ec ed o dis an egions along wi h he
oposphe ic winds; and wa e in he o m o snow co e he mally isola es he soil om he ai abo e i .
The accu a e ep esen a ion o he e es ial wa e dynamics and i s a ious eedbacks o he a mosphe ic
wa e , ene gy and ca bon cycles is hus c i ically impo an o in e ac i ely coupled global nume ical cli-
ma e models ha a e used o in e in o ma ion abou he cu en s a e and he u u e e olu ion o he Ea h's
clima e condi ions (T enbe h, 2010).
Due o hei di ec e ec on he a ailabili y o eshwa e esou ces, in es iga ing clima e change impac s
on he global wa e cycle is o g ea socie al ele ance. Changes in e es ial wa e s o age (TWS) migh
e lec long- e m we ing o d ying in a ious egions o he wo ld, and he iden i ica ion o such egions is o
subs an ial impo ance o wa e esou ces managemen . Howe e , coupled clima e models used o p edic
u u e clima ic condi ions s ill exhibi a sp ead in he ep esen a ion o long- e m ends in soil mois u e and
o he land wa e ela ed a iables (Guo & Di meye , 2006; Figu e 12.23 in Be g e al., 2017; Collins e al.,
2013; Yuan & Qui ing, 2017).
Compa ing he ou pu o nume ical models wi h obse a ions is c ucial o demons a e hei eliabili y and
o es p edic i e capaci ies, bu measu emen s o wa e s o age changes a e di icul o ob ain. A classical
RESEARCH ARTICLE
10.1029/2018JD029989
Key Poin s:
• By compa ing e es ial wa e
s o age ends om CMIP5 models
and GRACE sa elli e da a, we
iden i y ho spo egions o we ing
and d ying
• Model analysis e eals ha egional
long- e m ends s a o eme ge om
in e annual a ia ions a e 14 yea s
• La ge model sp ead in wa e s o age
ends demons a es impo ance o
GRACE o cons ain esponse o he
wa e cycle o clima e change
Co espondence o:
L. Jensen,
lau a.jensen@hcu-hambu g.de
Recei ed 14 NOV 2018
Accep ed 17 AUG 2019
Accep ed a icle online 29 AUG 2019
©2019. 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.
JENSEN ET AL. 9808
Published online 3 SEP 2019
Ci a ion:
Jensen, L., Eicke , A., Dobslaw, H.,
S acke, T., & Humph ey, V. (2019).
Long‐ e m we ing and d ying ends in
land wa e s o age de i ed om
GRACE and CMIP5 models. Jou nal o
Geophysical Resea ch: A mosphe es,
124, 9808–9823. h ps://doi.o g/
10.1029/2018JD029989
Jou nal o Geophysical Resea ch: A mosphe es 10.1029/2018JD029989
app oach o he de e mina ion o TWS a basin scale is he in eg a ion o he wa e balance equa ion (p e-
cipi a ion minus e apo anspi a ion minus uno ), see Rodell e al. (2004). Howe e , his is challenging
on a global scale, since s eam low measu emen s a e spa se and e apo anspi a ion is gene ally di icul
o measu e (Wa enbu ge e al., 2018). Especially, ends in wa e s o age canno be eco e ed well by his
me hod due o biases in he wa e lux obse a ions (Hi schi & Sene i a ne, 2017).
Complemen a y o con en ional me eo ologic obse a ions o a mosphe ic wa e luxes, he sa elli e mis-
sion G a i y Reco e y And Clima e Expe imen (GRACE; Tapley e al., 2004) in ope a ion om 2002 o 2017
allowed o he i s ime he obse a ion o wa e s o age changes wi h global co e age om space. By e al-
ua ing ela i e dis ance changes be ween wo spacec a a e y low al i udes o 400–500 km, ime a ia ions
in he Ea h's g a i y ield a e mapped ha can be unambiguously ela ed o changes in TWS. Due o he
indi ec obse a ion concep , GRACE essen ially senses wa e mass anomalies independen ly o hei su -
ace exposu e and hus in eg a es all mass changes e ically om he su ace down o he deepes aqui e s.
This unique capabili y o he g a ime ic me hod makes GRACE highly complemen a y o al e na i e adio-
me ic sa elli e echniques o soil mois u e emo e sensing ha a e only sensi i e o changes in he op ew
cen ime e s o soil (Do igo e al., 2015). GRACE mission da a ha e been used in a ious hyd ome eo olog-
ical applica ions, o example, Famiglie i and Rodell (2013), and i is a ed among he op i e p io i ies o
he u u e Ea h obse a ion capaci y by he mos ecen Na ional Ae onau ics and Space Adminis a ion
decadal su ey (Commi ee on he Decadal Su ey o Ea h Science and Applica ions om Space e al.,
2018). The successo mission GRACE-FO (Follow On), launched in May 2018, is expec ed o con inue his
impo an obse a ional eco d o e he nex decades (Flech ne e al., 2016), which will acili a e he sep-
a a ion be ween in e annual a iabili y and long- e m clima ological ends in TWS. Because he limi ed
ime span o GRACE da a makes he iden i ica ion o clima e- ela ed signals s ill challenging, his s udy
aims o in es iga e how GRACE TWS ends could (and should) be compa ed o model-de i ed ends.
TWS as obse ed wi h GRACE has al eady been used o alida e bo h global hyd ological models (Döll e al.,
2014; Eicke e al., 2014; Gün ne , 2008; Syed e al., 2008) and land su ace models (Scanlon e al., 2018;
Zhang e al., 2017) which a e d i en by a p esc ibed me eo ological o cing. In his s udy, we ocus on in e -
ac i ely coupled Ea h Sys em Models (ESMs) pa icipa ing in CMIP5 (Coupled Model In e compa ison
P ojec Phase 5, Taylo e al., 2011). Compa ing GRACE ends wi h long- e m coupled clima e model p o-
jec ions is challenging in mainly wo aspec s: (i) In con as o GRACE TWS (i.e., he ull in eg a ed wa e
column, including all wa e ese oi s), TWS in he models is e lec ed ypically only by means o snow s o -
age and soil mois u e. The ep esen a ion o he la e c i ically depends on he dep h o he soil column and
he numbe o e ical laye s conside ed. In pa icula , cu en ESMs do no explici ly simula e g oundwa-
e s o age changes. As g oundwa e -su ace in e ac ions play an impo an ole in he global hyd ological
cycle, his poses an addi ional sou ce o unce ain y in long- e m model p ojec ions o we ing and d ying.
(ii) Coupled uns in CMIP5 s a ing om p eindus ial condi ions and ex ending o e he whole his o ical
pe iod un il he p esen day a e o ced wi h empo ally a iable sola adia ion, ae osols, CO2concen a-
ions, and land use. Those expe imen s a e hus expec ed o ep oduce he clima e a iabili y in a s a is ical
sense only. As a esul , di e en ealiza ions o he in e annual and decadal clima e a iabili y a e supe im-
posed o e he clima ological ends so ha a di ec compa ison wi h he 14-yea GRACE TWS ime se ies
only has limi ed explana o y powe . While a egional s udy o he Mississippi Basin (F eedman e al., 2014)
showed easonably good ag eemen o he annual ampli ude o GRACE da a and a subse o CMIP5 models,
Fasullo e al. (2016) ound he ends om his o ical CESM1-CAM5 uns compa ed o GRACE o be domi-
na ed by in e nal a iabili y a he han by he o ced esponse. Di e en d i e s o TWS ends obse ed by
GRACE we e in es iga ed by Rodell e al. (2018), who also made use o CMIP5 model p ecipi a ion p ojec-
ions o a ibu e we ing and d ying endencies in some egions o clima e-d i en p ecipi a ion changes. To
ou knowledge, an ex ensi e global compa ison o soil mois u e and snow ends modeled o e mo e han
wo cen u ies (in he ollowing e e ed o as bicen ennial) agains GRACE obse a ions has ne e been
conduc ed wi h an ensemble o models such as CMIP5.
In esponse o hese challenges, we ocus in his s udy in pa icula on he co espondence o bicen ennial
ends in TWS as simula ed by he majo i y o CMIP5 models and TWS endencies as obse ed by GRACE
and in es iga e egions o ag eemen and disag eemen on we ing o d ying ends in models and sa elli e
obse a ions.
JENSEN ET AL. 9809
Jou nal o Geophysical Resea ch: A mosphe es 10.1029/2018JD029989
Figu e 1. TWS ends om ITSG-G ace2018s (p elimina y) o he ime span Ap il 2002 o Augus 2016 (wi hou
G eenland, S alba d, Gul Coas o Alaska, and An a c ica). S ippling indica es egions wi h nonsigni ican ends
(𝛼=0.05).
This pape is s uc u ed as ollows: Fi s , we compu e global maps o TWS ends om GRACE da a (sec ion
2) and CMIP5 models (sec ion 3) oge he wi h an e alua ion o he a iabili y among di e en models and
wi hin his o ical and u u e ime spans. We es ima e he in luence o he di e en ime se ies leng hs o
GRACE and models by means o wo model s udies using model TWS endencies om ime pe iods anging
om 14 o mo e han 200 yea s (sec ion 4). The TWS end maps om GRACE and CMIP5 models a e
subsequen ly compa ed (sec ion 5). Nex , we in es iga e ho spo and noncompliance egions o we ing and
d ying ends ega ding hei unce ain y (sec ion 6), which migh be caused by model de ici s o na u al
in e annual a iabili y and human impac s a ec ing he GRACE-de i ed ends. Sec ion 7 summa izes he
esul s and add esses u u e wo k.
2. TWS T ends F om GRACE Da a
To ob ain a global g id o obse ed TWS ends we use he ITSG-G ace2018s end Le el 2 da a (Maye -Gü
e al., 2018), which was ob ained om es ima ing a long- e m mean g a i y ield model oge he wi h linea
end and annual cycle om all a ailable GRACE Le el 1B RL03 da a. The ITSG-G ace2018s end used he e
is a p elimina y e sion con aining Le el 1B da a o he ime span Ap il 2002 o Augus 2016 (∼14 yea s). I
will be upda ed once he comple e ime se ies o Le el 1B RL03 da a (Ap il 2002 o June 2017) is a ailable.
Howe e , o he end only mino changes a e expec ed by ex ending he ime se ies by less han 1 yea .
The sphe ical ha monic coe icien s (Le el 2) o he end in g a i a ional po en ial a e gi en up o deg ee
nmax =120 and a e pos p ocessed as ollows: The e ec o geocen e mo ion is aken in o accoun by aug-
men ing he GRACE da a wi h he linea ends o deg ee 1 ha monic coe icien s p o ided by Swenson e al.
(2008). The zonal Δc20 end coe icien is eplaced using a esul om Sa elli e Lase Ranging (Cheng e al.,
2013). To educe mass ends o igina ing om glacial isos a ic adjus men (GIA), we sub ac a model om
A e al. (2013) and o mi iga e he e ec o co ela ed noise a DDK4 il e (Kusche, 2007) is applied. We
calcula e he TWS end on a 2◦×2◦geog aphical g id (Figu e 1) acco ding o
ws(𝜆, 𝜃)= M
4𝜋R2𝜌w
nmax
∑
n=1
n
∑
m=−n
(2n+1)
(1+k′
n)ΔcnmYnm(𝜆, 𝜃)(1)
whe e 𝜆and 𝜃deno e he sphe ical coo dina es, Mand Ra e he mass and he adius o he Ea h,
𝜌w=1,000 kg/m3is he densi y o wa e , k′
ndeno e he Load Lo e Numbe s (Lambeck, 1988), Δcnm
a e he il e ed sphe ical ha monic coe icien s o he g a i a ional po en ial, and Ynm(𝜆, 𝜃)a e he su ace
JENSEN ET AL. 9810
Jou nal o Geophysical Resea ch: A mosphe es 10.1029/2018JD029989
sphe ical ha monic unc ions. Co esponding s anda d de ia ions o he TWS ends a e ob ained
by a iance p opaga ion om ealis ic e o assump ions p o ided wi h he Δcnm coe icien s o he
ITSG-G ace2018s end.
The signi icance o he end can be es ed wi h a pa ame e es . The es ima ed end di ided by i s es ima ed
s anda d de ia ion is compa ed o he c i ical alue o he no mal dis ibu ion o a ce ain signi icance le el
1−𝛼which we se o 95% in his s udy. Gene ally, he eliabili y o ends om GRACE is high. Among
he solu ions o di e en GRACE p ocessing cen e s ends o e he same ime pe iod a e e y simila
(Scanlon e al., 2018), e en i a di e en ep esen a ion (mascons ins ead o sphe ical ha monics) is chosen.
Thus, selec ing ano he GRACE solu ion (e.g., om JPL o CSR) does no al e he indings o ou s udy
(no shown).
GRACE-de i ed ends migh no o igina e pu ely om TWS changes e e ywhe e, as esidual ec onic
e ec s om GIA (Ca on e al., 2018), pos seismic de o ma ion a e la ge ea hquakes (Han e al., 2008,
2010), o esidual a mosphe ic mass a iabili y (Fagiolini e al., 2015) can o e lay TWS ends. Fu he mo e,
leakage o signal in o neighbo ing g id cells due o il e ing and esidual noise ha could no be emo ed
du ing il e ing migh also dis o TWS ends.
As he GRACE TWS ends a e only calcula ed om 14 yea s o da a, he esul s can be domina ed by
low- equency clima e a iabili y ela ed o El Niño–Sou he n Oscilla ion (Ni e al., 2018; Phillips e al.,
2012), he sola cycle (Bha acha yya & Na asimha, 2005), he quasi-biennial oscilla ion and o he cou-
pled clima e modes (G ay e al., 2018), and episodic e en s as olcanic e up ions (Iles e al., 2013), which
may ei he conceal he long- e m end o p oduce a spu ious ansien end. App oaches o educe hese
in e annual a iabili ies in he GRACE eco d a e cu en ly being discussed (e.g., Eicke e al., 2016).
3. TWS T ends F om CMIP5 Model Da a
As CMIP5 models do no p o ide a s anda d ou pu a iable o o al wa e s o age, we use he sum o o al
soil mois u e con en (m so) and su ace snow amoun (snw) as an app oxima ion o i . In he emaining
pa o he pape we e e o his TWS app oxima ion as model TWS (mTWS). The mTWS di e s in se e al
aspec s om GRACE-de i ed TWS: Soil mois u e laye s in ESMs ha e a dep h ha can a y widely be ween
jus a ew and up o ens o me e s depending on he model and hus does no necessa ily cap u e he ull soil
mois u e con en a e e y loca ion. Fu he mo e, g oundwa e and su ace wa e a e no explici ly included
in mTWS as hese s a es a e gene ally no ep esen ed in CMIP5 models. Howe e , a ce ain ac ion o
hese quan i ies migh be implici ly included in o al soil mois u e as he anspo o ocean and a mosphe e
is limi ed and he wa e balance is la gely closed by mos o he models (Liepe & Lo, 2013). Mo eo e ,
his o ical CMIP5 uns do no con ain egional an h opogenic in e en ion o he han land use changes in
hei se up (e.g., g oundwa e deple ion o dam building is no ep esen ed), whe eas GRACE obse a ions
include hei consequences. The ep esen a ion o mTWS di e s om model o model due o di e en oo
dep hs, numbe o soil laye s, and model physics (Huang e al., 2016). Snw also exhibi s la ge in e model
di e ences in ep esen a ion (B u el-Vuilme e al., 2013). We he e o e no e ha mTWS o di e en models
migh no be ully compa ible.
A e adding mon hly m so and snw o each model, we conca ena e he co esponding mTWS simula-
ions o he his o ical uns (1850–2005) and he RCP8.5 scena ios (2006–2100) o calcula e ends o ime
spans ha go beyond he yea 2006. Fo hose models, whe e mo e han one un is a ailable, we calcula e
he ensemble mean which we ega d as he mos obus ealiza ion o long- e m mTWS end es ima es.
A e wa d, he mTWS alues a e emapped o a common 2◦×2◦geog aphical g id.
A bicen ennial mTWS end map ( ime span Janua y 1861 o Decembe 2099, i.e., ea lies /la es common
da e o all models o his o ical/RCP8.5 expe imen s) is calcula ed om he ime se ies o mTWS g ids o
each model. Fo each g id cell he linea end is calcula ed by i ing a unc ion
𝑓( )=a+b· +c·cos(𝜔 )+d·sin(𝜔 )+e·cos(2𝜔 )+𝑓·sin(2𝜔 )(2)
wi h pa ame e s o bias (a), linea end (b), annual and semiannual cycle (c,d,e, ) o he ime se ies by
means o leas squa es adjus men . The s anda d de ia ion o he end is es ima ed om he pos i esidu-
als. No e ha we exclude he glacia ed egions o G eenland, S alba d, Gul Coas o Alaska, and An a c ica,
since no all models p ope ly ep esen glacie mass balance dynamics domina ing TWS in hose egions.
JENSEN ET AL. 9811
Jou nal o Geophysical Resea ch: A mosphe es 10.1029/2018JD029989
Figu e 2. Co ela ions o he bicen ennial mTWS end maps o 34 CMIP5 models.
In o al 34 CMIP5 models p o ide a leas one un o m so and snw. Howe e , as some o hese 34 models a e
ei he di e en e sions o he same model o a e uns wi h pa ly iden ical componen s (land su ace and/o
a mosphe e model), i canno be assumed ha each model p oduces a comple ely independen es ima e o
he m so and snw ields (Knu i e al., 2013). In o de o ob ain an unbiased mul imodel a e age mTWS end
map and a eliable conclusion abou model consensus, we iden i y he independen models by compa ing
he simila i y o mTWS end maps o all models. As a measu e o he simila i y o wo maps we use he
Pea son p oduc -momen co ela ion coe icien 2calcula ed om he ec o ized maps, gi ing e e y land
pixel o he 2◦×2◦g id equal weigh . As end ou lie s in single pixels can dis o he co ela ion coe icien
we apply a simple h eshold o he mTWS end maps, excluding absolu e end alues abo e 23 mm/yea .
This is he 2𝜎bounda y o he 14-yea GRACE TWS end (Figu e 1), hus i is e y unlikely ha bicen ennial
ends abo e hese h eshold a e ealis ic.
The co ela ions o he bicen ennial mTWS end maps (a e applying he 23 mm/yea h eshold) a e cal-
cula ed o all 34 models and a anged in a ma ix (Figu e 2). De ailed in o ma ion and e e ences o he
models lis ed in Figu e 2 a e gi en, o example, in Fla o e al. (2013) and a e no ei e a ed he e. As expec ed,
models ha use common a mosphe e o land su ace componen s exhibi a e y high co ela ion. In o de
o only conside models ha a e independen and o jus i y he applica ion o equal weigh o each model
esul , in he emaining pa o he s udy we use only one ins ance om each g oup o models ha a e highly
co ela ed ( 2>75%). In Figu e 2 he models ha a e excluded due o his h eshold a e deno ed in g ay
on and he emaining 21 models a e highligh ed in bold on . The c i e ia o choosing a speci ic model
among highly co ela ed models was based on i s es ima ed age (mos ecen publica ion), deg ee o special-
iza ion (mos gene al), o spa ial esolu ion (closes o 2◦×2◦). Gene ally, a e excluding all bu one om
he highly co ela ed models, he co ela ion among end maps om di e en models is e y low (mean
2=10%, maximum 2=67%) and o some pai s o models i is e en nega i e (minimum 2=−55%). This
analysis demons a es he la ge inhomogenei y among CMIP5 models ega ding ends in mTWS.
In o de o u he in es iga e model sp ead we de ine di e en ime spans (Table 1) o which we cal-
cula e and discuss mTWS end maps in he ollowing. Fi s , he 21 models ha emain a e excluding
highly co ela ed models, a e used o calcula e a median end map o he bicen ennial ime span Janua y
JENSEN ET AL. 9812

Jou nal o Geophysical Resea ch: A mosphe es 10.1029/2018JD029989
Table 1
No a ion o Di e en Time Spans Tha A e In es iga ed o mTWS
T ends
Time span No a ion
Jan 1861 o Dec 2099 bicen ennial end
Jan 1861 o Aug 2016 his o ical end
Sep 2016 o Dec 2099 RCP8.5 end
Jan 1986 o Dec 2035 50a endency
Jan 1996 o Dec 2025 30a endency
Ap 2002 o Aug 2016 14a endency
1861 o Decembe 2099 (Figu e 3a), ha is, o each geog aphical g id cell he
median o he ends o all models is de e mined. We use he median ins ead
o he a i hme ic unweigh ed mean because i is much less a ec ed by ou lie s
and hus can be assumed o be a mo e obus es ima e o he end. How-
e e , o iden i y nonsigni ican ends in he median map (s ippled egions in
Figu e 3a) we ca y ou e o p opaga ion o he a i hme ic mean, because
his is no s aigh o wa d o he median. Figu e 3a is no a ec ed by a model
d i in mTWS, as ends om p eindus ial con ol simula ions (i.e., model
uns only o ced wi h na u al, none ol ing a mosphe ic concen a ions) o
he same CMIP5 models we e ound o be an o de o magni ude smalle and
hus a e negligible (no shown). Acco ding o he 21 models, he la ges ends
occu mainly in sou he n Eu ope and Tu key, in Cen al Ame ica and in he
wes o No h Ame ica, in he no h o Sou h Ame ica and in he Himalaya
egion. The clima ological ends de i ed he e a e in ag eemen wi h he esul s o a p e ious s udy (Be g e
al., 2017) ha ocused on o al soil mois u e, e en hough signi ican di e ences a e p esen in high la i udes
since mTWS also includes snowpack.
To assess he eliabili y o he median mTWS ends, we compu e he le el o consensus o he 21 models,
ha is, he numbe o models wi h he same bicen ennial end di ec ion o a gi en g id cell (Figu e 3b).
The highe he consensus, he highe he ce ain y ha he ag eemen is no by chance, o example, i 15 o
mo e o 21 models ag ee on he sign, he p obabili y ha his is jus chance is only 4% o less (Di meye e
al., 2013). Hence, he highe he consensus in a g id cell, he mo e we can us he di ec ion o he end in
his g id cell acco ding o he models. In many egions high consensus co esponds o la ge ends and ice
e sa. Howe e , his is no alid e e ywhe e, meaning ha also he sign o small ends can be ep esen ed
by a majo i y o models (e.g., India) and in e sely, he e migh be model disag eemen abou he di ec ion
o la ge ends (e.g., No he n Russia). Fo he bicen ennial mTWS end, we ind 39% o he global land
a ea o exhibi a d ying (30%) o we ing end (9%) ha is suppo ed by a leas 71% (15 o 21) o he models.
These indings a e no ee o unce ain ies as he consensus map (Figu e 3b) migh be a ec ed by sys ema ic
de ici s in CMIP5 models, such as in pa icula he lack o g oundwa e s o age in aqui e s a di e en dep h
and hus e y di e en esidence imes (Pokh el e al., 2014).
To in es iga e i mTWS ends as calcula ed o he bicen ennial ime span a e in p inciple al eady de ec able
in obse a ional eco ds a ailable oday, we compu e (in addi ion o he bicen ennial ime span) mTWS
ends o a his o ical ime span Janua y 1861 o Augus 2016 (un il he end o he GRACE ime span;
Figu e 4a). Fo compa ison, also he mTWS ends o he RCP8.5 ime span Sep embe 2016 o Decembe
2099 a e displayed (Figu e 4b). O e all, we ind a simila pa e n o he his o ical and he RCP8.5 end
(pa e n co ela ion o 55%), hough he his o ical end has a much smalle magni ude (only abou 20% o
RCP8.5). Fu he mo e, he po ion o land a ea whe e he median ends a e no signi ican (s ippled a eas,
95% con idence le el) is la ge o he his o ical ime span han o he RCP8.5 ime span. Howe e , in 73%
o he land a ea he his o ical end is al eady signi ican and in 68% i is in ag eemen wi h he RCP8.5 end
map. In high-consensus egions (ag eemen o bicen ennial end sign in ≥71% o he models, Figu e 3b) o
which we es ic he analysis in sec ion 5 and 6, he a ea o ag eemen be ween signi ican his o ical and
RCP8.5 ends is 92%. This indica es ha in mos egions he cu en ends a e se o con inue in he same
di ec ion and e en inc ease in he u u e, he eby sugges ing ha he p ocesses shaping he clima e change
oo p in on TWS a e al eady ac ing oday. The consensus among he CMIP5 models is gene ally lowe o
he his o ical ime span (Figu e 4c) han o he RCP8.5 ime span (Figu e 4d), which is ela ed o he ac
ha s onge ends gene ally imply highe consensus and RCP8.5 is he scena io wi h he s onges clima e
change signal. The pa e ns o he consensus maps a e simila o all h ee ime spans (bicen ennial, his-
o ical, and RCP8.5), hus we in e ha egions o la ge model ag eemen a e la gely independen om he
selec ed ime span ( o cen ennial ends).
4. In luence o Obse a ion Time Span
F om Figu es 3 and 4 i can be concluded ha o cen ennial ime spans a empo ally s able pa e n o d ying
and we ing ends exis s in he models. Howe e , we canno expec o eadily ind hese end pa e ns in
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Figu e 3. (a) Median o bicen ennial mTWS end maps om 21 CMIP5 models (wi hou G eenland, S alba d, Gul
Coas o Alaska, and An a c ica). S ippling indica es egions whe e he mean end is no signi ican ly di e en om
ze o (𝛼=0.05). (b) Consensus map o bicen ennial mTWS ends om 21 CMIP5 models. Red colo s indica e ha
≥#models ag ee on a nega i e (i.e., d ying) end, blue colo s indica e ha ≥#models ag ee on a posi i e
(i.e., we ing) end.
a sho ime pe iod o only 14 yea s o which GRACE obse a ions a e a ailable. Fo sho ime pe iods,
in e annual a ia ions may be domina ing he end es ima ion in many egions o he wo ld.
To es ima e he in luence o he obse a ion ime span on he expec ed ag eemen wi h he bicen ennial
end, we pe o m wo model s udies using endency maps o di e en ime spans calcula ed om he
CMIP5 models. In he i s model s udy we in es iga e a e which ime span long- e m clima ic ends in
mTWS migh be clea ly dis inguished om in e annual a ia ions. In he second model s udy we es ima e
he deg ee o which e en a e long ime spans he obse ed ends migh s ill be in disag eemen wi h he
long- e m clima ic end. In con as o he o he sec ions o he pape , whe e we ely on he ensemble means,
o hese model s udies we only use one indi idual un ( 1i1p1) pe model in o de o p ese e in e annual
a iabili y. This is impo an as na u al a ia ions would la gely a e age ou by calcula ing ensemble means.
By using CMIP5 model ou pu o simula ing di e en ly long obse a ion ime spans, we p esume ha
indi idual model uns ep esen na u al a iabili y ealis ically in e ms o ela i e magni ude, equency,
and du a ion.
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Figu e 4. ( op) Median o mTWS end maps om 21 CMIP5 models o (a) his o ical (Janua y 1861 o Augus 2016) and (b) RCP8.5 (Sep embe 2016 o
Decembe 2099) ime span. S ippling indica es egions whe e he mean end is no signi ican ly di e en om ze o (𝛼=0.05). Please no e he di e en colo
scales in (a) and (b). (bo om) Consensus maps o bicen ennial mTWS ends om 21 CMIP5 models o (c) his o ical and (d) RCP8.5 ime span.
Fo he i s s udy we i ends in a leas squa es sense o ime spans o di e en leng hs anging om
14 o 100 yea s in s eps o 5 yea s wi h he cen e yea 2010. Examples o endency maps ob ained o
he 50a, 30a, and 14a ime pe iods a e gi en in Figu e 5. The median endency maps o all 18 ime spans
a e each co ela ed o he bicen ennial median end map (Figu e 5a). Fo he 14a obse a ion pe iod he
global co ela ion is only 23%, bu wi h inc easing ime span i asymp o ically app oaches 100% (blue cu e
in Figu e 5a). A e he 30a ime span he global co ela ion is 57% which is he same o de o simila i y
ha we ind o he his o ical and RCP8.5 ime spans (55%). Thus we conclude ha a ound 30 yea s o
TWS obse a ions would be he minimum ime o globally ob ain a TWS end compa able o long- e m
model esul s. Howe e , e en hough he ag eemen be ween end pa e ns migh be low a 14a globally,
his migh no be he case locally, o ins ance, when only conside ing egions ha exhibi s ong model
ag eemen . When calcula ing he co ela ion o he 14a endency and he bicen ennial end only o g id
cells wi h a model consensus o ≥71%, he co ela ion coe icien inc eases o 39% ( ed cu e in Figu e 5a),
when addi ionally excluding nonsigni ican g id cells, i inc eases o 52% (yellow cu e in Figu e 5a).
In his model s udy we e alua e he (global) spa ial pa e n co ela ion which only con ains limi ed in o -
ma ion abou he ag eemen o ends o indi idual g id cells. This means ha hough his expe imen
b ings ou wha o expec om he simila i y o he spa ial pa e ns, i does no p o ide he likelihood o a
local mTWS endency compu ed om a ce ain ime span o ac ually ma ch he bicen ennial end in ha
g id cell. As we a e in e es ed in egions whe e 14a GRACE TWS endencies ag ee wi h bicen ennial mTWS
model ends and wan o a e he esul s wi h espec o wha o expec om his sho ime span, we pe -
o m a second model s udy: Fo each o he 21 CMIP5 models we cu 22 slices o 14a mTWS da a wi h a
dis ance o 5 yea s (cen e ed a ound he yea 1970) and es ima e 22 14a endencies. Fo each g id cell he
ac ion o endencies ha ag ee o disag ee (in e ms o sign) wi h he bicen ennial mTWS end om ha
pa icula model is calcula ed. Subsequen ly, he global mean o all ac ions and all models is compu ed.
This p ocedu e is epea ed o di e en ime spans om 1 o 100 yea s in s eps o 5 yea s (Figu e 6). Acco d-
ing o he models he p obabili y ha a 14a endency is in ag eemen wi h he long- e m end is on a e age
53%, which is sligh ly be e han andom chance. E en a e a cen u y he e is s ill a chance o 27% ha
an indi idual endency does no ma ch he bicen ennial end e en hough he global pa e n co ela ion is
al eady high wi h 87%. This indica es ha he e is na u al a iabili y in he models e en o e long ime pe i-
ods o 100 yea s and mo e, which Laepple and Huybe s (2014) ound o be caused by sea su ace empe a u e
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Figu e 5. (a) Co ela ion o he mTWS endency maps o di e en ime spans (cen e yea 2010) wi h he bicen ennial mTWS end map. (b–d) Median o
mTWS endency maps om 21 CMIP5 models o (b) 50a ime span, (c) 30a ime span, and (d) 14a ime span. Each ime span is cen e ed a ound he yea 2010.
No e he di e en colo scales due o la ge a iabili y o sho e ime spans. S ippling indica es egions wi h nonsigni ican ends (𝛼=0.05).
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