Tracking the Dynamics and Uncertainties of Soil Organic Carbon in Agricultural Soils Based on a Novel Robust Meta-Model Framework Using Multisource Data

Ci a ion: E molie a, T.; Ha lik, P.;
Lessa-De ci-Augus ynczik, A.; F ank,
S.; Balko ic, J.; Skalsky, R.;
Deppe mann, A.; Nakha ali, M.;
Komendan o a, N.; Kahil, T.; e al.
T acking he Dynamics and
Unce ain ies o Soil O ganic Ca bon
in Ag icul u al Soils Based on a No el
Robus Me a-Model F amewo k
Using Mul isou ce Da a. Sus ainabili y
2024,16, 6849. h ps://doi.o g/
10.3390/su16166849
Academic Edi o : Xiaodong Nie
Recei ed: 9 July 2024
Re ised: 1 Augus 2024
Accep ed: 6 Augus 2024
Published: 9 Augus 2024
Copy igh : © 2024 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
sus ainabili y
A icle
T acking he Dynamics and Unce ain ies o Soil O ganic Ca bon
in Ag icul u al Soils Based on a No el Robus Me a-Model
F amewo k Using Mul isou ce Da a
Ta iana E molie a 1,*, Pe Ha lik 1, And ey Lessa-De ci-Augus ynczik 1, S e an F ank 1, Ju aj Balko ic 1,
Ras isla Skalsky 1, And e Deppe mann 1, Mahdi (And è) Nakha ali 1, Nadejda Komendan o a 1,
Tahe Kahil 1, Gang Wang 2, Ch is ian Folbe h 1and Pa el S. Knopo 3
1In e na ional Ins i u e o Applied Sys ems Analysis (IIASA), 2361 Laxenbu g, Aus ia;
[email p o ec ed] (P.H.); [email p o ec ed] (A.L.-D.-A.); [email p o ec ed] (S.F.);
[email p o ec ed] (J.B.); [email p o ec ed] (R.S.); [email p o ec ed] (A.D.);
[email p o ec ed] (M.N.); [email p o ec ed] (N.K.); [email p o ec ed] (T.K.); [email p o ec ed] (C.F.)
2Depa men o Soil and Wa e Sciences, China Ag icul u al Uni e si y, Beijing 100193, China;
[email p o ec ed]
3
Ins i u e o Cybe ne ics, Na ional Academy o Sciences o Uk aine, 03187 Kyi , Uk aine; [email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac : Moni o ing and es ima ing spa ially esol ed changes in soil o ganic ca bon (SOC) s ocks
a e necessa y o suppo ing na ional and in e na ional policies aimed a assis ing land deg ada ion
neu ali y and clima e change mi iga ion, imp o ing soil e ili y and ood p oduc ion, main aining
wa e quali y, and enhancing enewable ene gy and ecosys em se ices. In his wo k, we epo
on he de elopmen and applica ion o a da a-d i en, quan ile eg ession machine lea ning model
o es ima e and p edic annual SOC s ocks a plow dep h unde he a iabili y o clima e. The
model enables he analysis o SOC con en le els and espec i e p obabili ies o hei occu ence as a
unc ion o exogenous pa ame e s such as mon hly empe a u e and p ecipi a ion and endogenous,
decision-dependen pa ame e s, which can be al e ed by land use p ac ices. The es ima ed quan iles
and hei ends indica e he unce ain y anges and he espec i e likelihoods o plausible SOC
con en . The model can be used as a educed- o m scena io gene a o o s ochas ic SOC scena ios. I
can be in eg a ed as a submodel in In eg a ed Assessmen models wi h de ailed land use sec o s such
as GLOBIOM o analyze cos s and ind op imal land managemen p ac ices o seques e SOC and
ul ill ood–wa e –ene gy—en i onmen al NEXUS secu i y goals.
Keywo ds: ood–wa e –ene gy–en i onmen al NEXUS; soil heal h; clima e a iabili y; SOC dynam-
ics; unce ain y anges; obus es ima ion; machine lea ning; quan ile eg ession
1. In oduc ion
The moni o ing, modeling, and mapping o soil o ganic ca bon (SOC) is impo an
o many easons. SOC is an indica o o soil o ganic ma e (SOM) con en , which is a
majo de e minan o soil quali y and e ili y o ood p oduc ion. Soils wi h highe SOC
can be e il e , deg ade o ganic molecules, and pu i y wa e . SOC accumula ion can
subs an ially con ibu e o clima e change mi iga ion [
1
–
3
]. Soils ha e ecen ly become pa
o he global ca bon agenda o clima e change mi iga ion and adap a ion. The “4p1000
ini ia i e” was launched a COP21 by UNFCC unde he amewo k o he Lima–Pa is
Ac ion Plan (LPAP) in Pa is on 1 Decembe 2015. The name o he ini ia i e e lec s ha
a compa a i ely small p opo ional inc ease (4%) o he global SOC s ocks in he opsoil
o all non-pe ma os soils would be simila in magni ude o he annual global ne ca bon
dioxide (CO
2
) g ow h [
4
]. SOC s ock is a land deg ada ion neu ali y indica o used by he
Uni ed Na ions Con en ion o Comba Dese i ica ion (UNCCD) [
5
]. The EU Soil S a egy
Sus ainabili y 2024,16, 6849. h ps://doi.o g/10.3390/su16166849 h ps://www.mdpi.com/jou nal/sus ainabili y
Sus ainabili y 2024,16, 6849 2 o 23
o 2030 con ibu es o he objec i es o he EU G een Deal and is a pa o he Biodi e si y
S a egy. The new s a egy upda es he 2006 EU Soil Thema ic S a egy [
6
,
7
] and in ends o
add ess land deg ada ion ends. The EU Mission Boa d o Soil Heal h and Food p oposed
a se ies o quan i a i e a ge s o make he soils o Eu ope heal hie . Among hem, he aim
is o e e se he cu en SOC concen a ion losses in c oplands (0.5%/y on a e age a a
20 cm dep h) o an inc ease o 0.1–0.4%/y by 2030.
The e is subs an ial complexi y and spa ial a iabili y in po en ial SOC changes espe-
cially due o he e ec s o land use changes, managemen p ac ices, and in he p esence
o clima e changes [
8
], which exhibi highly a iable and unce ain pa e ns o mon hly
and seasonal empe a u e and p ecipi a ion (i.e., he wo impo an clima e- ela ed SOC
modi ie s). Some s udies show ha an inc ease o 1
◦
C in he ai empe a u e could cause
a 10–28% g ea e C elease (11–34 Pg C/y ) [
9
]. The unc ion and s uc u e o e es ial
ecosys ems can be a ec ed by he p ecipi a ion pa e ns. Inc eased p ecipi a ion can aise
soil espi a ion on a e age by 30%, whe eas dec eased p ecipi a ion educes soil espi a ion
by 12% [
10
], hus a ec ing soil ca bon s ock and he o e all global ca bon cycle. Hence,
soil’s ole as a sou ce o sink depends on he empe a u e and p ecipi a ion [11].
The e is a s ong ela ionship be ween SOC and N con en , i.e., he highe SOC con en
indica es a highe N con en . In many case s udies, he a io o ca bon o ni ogen in SOM
(abou 58% o SOM is made up o SOC) is abou 10:1 [
12
,
13
], which can a y. In gene al,
mic obes can equi e mo e ni ogen han is ound in o ganic ma e , namely a abou an 8:1
a io. Fo e ec i e mic obial li e and he inc ease in ca bon s o age in soils, he addi ion o
syn he ic e ilize s plays a majo ole. Ni ogen e ilize s inc ease he mic obial biomass,
inc ease bo h he eadily decomposable and less eadily decomposable pools o soil ca bon
( he la e o which o m om he dead mic obes), and inc ease he “new” ca bon inpu s
( om esidues) while also slowing he loss o “old” soil ca bon [
14
,
15
]. The highe sha e o
ca bon in soil is mo e bene icial o soil mic obes o make a ailable essen ial nu ien s like
N, phospho us, and zinc o c ops, hus enhancing soil heal h and p oduc i i y. The op imal
a io is es ima ed o be abou 24:1 [12,13].
SOC ep esen s he dynamic balance o ca bon in lows and ou lows in ime. The
p ima y sou ce o SOC is SOM, de i ed om a ious plan ma e ials including lea es,
s ems, and oo s. These ma e ials a e decomposed by mic obial p ocesses, leading o
espi a ion back in o he a mosphe e and ecycling by mic obes (measu ed as Ca bon
Use E iciency), mine aliza ion, o leaching om he soil [
16
,
17
]. In ag icul u e, ypical
con ibu o s o SOM a e manu e, c op esidues, and compos . These ma e ials, i no
p ope ly humi ied, a e mo e eadily p ocessed by mic obes, leading o as e u no e a es.
Mic obial ac i i y can be u he enhanced by adequa e p ecipi a ion and empe a u e.
Land use p ac ices can al e SOC con en . Such ag icul u al ac i i ies as op imized
ecycling o esidues, balanced nu ien inpu s, and educed illage can slow down SOC
losses [
18
,
19
]. Al hough c op esidues a e a eeds ock o enewable bioene gy p oduc ion,
i is equen ly ad ised o ha es only a po ion o he esidues o ensu e he p ese a ion
o SOC s ocks. Also, c op esidues ha emain in he ield a e c ops a e ha es ed a e
bene icial o soil heal h as hey dec ease he isk o soil e osion by wind and wa e .
Amelung e al. [
4
] a gue o he apid and sus ainable scaling up o soil ca bon
seques a ion p ac ices in o de o con ibu e o clima e change mi iga ion. C opland
soils o e he majo po en ial o ca bon seques a ion [
4
]. The implemen a ion o soil
ca bon seques a ion measu es equi es a di e se se o op ions i ed o soil condi ions
and managemen oppo uni ies and accoun ing o si e-speci ic ade-o s. The cos s and
bene i s o hese op ions a e ye o be es ima ed wi h comp ehensi e land use planning
models such as he Global Biosphe e Managemen Model, GLOBIOM [20].
Models a e c ucial o unde s and pas and u u e SOC dynamics in he p esence o
na u al and an h opogenic d i e s and unce ain y. The wo main app oaches widely used
o assess he impac s o clima e change, soil pa ame e s, and land managemen p ac ices
on soil nu ien con en and p oduc i i y a e he ollowing:
Sus ainabili y 2024,16, 6849 3 o 23
a.
P ocess-based simula ion models, e.g., such as MIc obial-MIne al Ca bon S abiliza-
ion model (MIMICS, [
21
]), DeNi i ica ion-DeComposi ion model (DNDC, [
22
]), and
En i onmen al Policy In eg a ed Clima e model (EPIC [
23
–
29
]), which ep esen key
dynamic p ocesses a ec ing soil nu ien s, land emissions, and p oduc i i y (yields);
b.
S a is ical and machine lea ning models, which es ima e unc ional ela ionships
be ween his o ical obse a ions o clima e, soil cha ac e is ics, nu ien composi ion,
and land p oduc i i y [30–34].
The Ag icul u al Model In e compa ison and Imp o emen P ojec (AgMIP) and he
In e -Sec o al Impac Model In e compa ison P ojec (ISIMIP) p o ide impo an conclu-
sions ega ding he wo app oaches [
35
]. P ocess-based models’ compu a ion can be an
ex emely ime-consuming p ocedu e. These models include soil C and N pools and luxes,
which equi e long spin-up o each equilib ium s a es. Because o simpli ica ions and
no maliza ions, he p ocess-based models can ail o cap u e he impac s o ex eme cli-
ma e e en s. Repa ame e iza ion and ecalib a ion can be demanded o each new se o
da a, e.g., clima e p ojec ions, and his edious ask calls o p ope pa ame iza ion and
calib a ion op imiza ion p ocedu es.
The s a is ical and machine lea ning models a e gaining popula i y o hei analysis
o ege a ion esponses, c op yields, and soil nu ien con en o clima ic condi ions, land
managemen p ac ices, and soil p ope ies [
32
,
36
]. Howe e , he s a is ical models can
lack he necessa y da a o es ima ing SOC con en in esponse o new land, soil, and
wa e managemen p ac ices, which a e op imal o easible in di e en adminis a i e and
clima ic egions. In his si ua ion, he a ailable his o ical da a can be en iched by he esul s
de i ed using biophysical models.
Thus, he wo app oaches ha e di e en s eng hs and weaknesses. Ou goal is o
combine he wo app oaches by using mul isou ce da a, which a e la ge han he his o ical
da a, i.e., by inco po a ing bo h his o ical and model-simula ed da a and esul s. The e o e,
in his pape , we de elop a hyb id me a-model o gene a ing s ochas ic and dynamic SOC
scena ios based on his o ical da a and on he inpu s–ou pu s o a dynamic p ocess-based
simula ion model En i onmen Policy In eg a ed Clima e (EPIC) [23,24,37,38].
We ain he me a-model using EPIC esul s on SOC con en o easible scena io com-
bina ions o esidue e en ion and e iliza ion a es. Al hough he me a-model eplica es
EPIC esul s ( he e o e, i is called a me a-model, i.e., a model o a model), i can also be
used elying pu ely on he a ailable his o ical da a and obse a ions. The combina ions o
scena ios o m he so-called EPIC hype cube, which has been designed based on s udies by
Balko ic e al. [23].
The me a-model is ep esen ed by a quan ile eg ession machine lea ning model o
p edic ing SOC con en quan iles (pe cen iles) [
39
,
40
]. The es ima ed quan iles and hei
ends iden i y he anges and he espec i e p obabili ies o plausible SOC con en le els
e lec ing he a iabili y and he unce ain y o he explana o y a iables (also e e ed o as
independen a iables o co a ia es) [
41
]. Pa ame e s such as empe a u e and p ecipi a ion
can be ega ded as exogenous, whe eas soil p ope ies depend on land use, wa e , and soil
managemen p ac ices and, he e o e, hese can be conside ed as “endogenous” decision-
d i en pa ame e s. By including esidue e en ion as an explana o y a iable, i is possible
o es ima e he p os and cons o policies on using c op esidues as eeds ocks o bio uel
p oduc ion. Op imizing he ecycling and emo al a es o c op esidues is essen ial o soil
heal h p ese a ion and o sus ainable bio uel p oduc ion.
The de eloped me a-model can be used as a educed- o m scena io gene a o o
s ochas ic SOC con en scena ios, i.e., alue and espec i e p obabili y. I can also be
inco po a ed as a submodel in mo e complex In eg a ed Assessmen (IAM) land use models,
e.g., he Global Biosphe e Managemen model, GLOBIOM [
20
,
42
,
43
]. The me a-model
ope a es a di e en spa ial scales and p o ides an e ec i e means o scaling biophysical
and land use model esul s o he equi ed esolu ions. By in oducing SOC cons ain s (e.g.,
equal o he 50 h o 75 h quan ile as es ima ed om he me a-model), he GLOBIOM model
can de i e an op imal combina ion o land use p ac ices inc easing SOC o he desi ed le el.
Sus ainabili y 2024,16, 6849 4 o 23
SOC and o he ood–ene gy–wa e –en i onmen al secu i y cons ain s iden i y he o e all
cos s o achie ing he ood–wa e –ene gy–en i onmen al NEXUS secu i y.
The pape is o ganized as ollows. Sec ion 2discusses SOC as an impo an soil
heal h indica o . Imp o ing SOC con en is an essen ial mo i a ion o de eloping a obus
quan ile-based me a-model and linking i wi h he land use model GLOBIOM. Sec ion 2.2
p esen s a sho o e iew o he wo main app oaches, p ocess-based simula ion models
and s a is ical models, o analyze he impac s o wea he a iabili y, clima e change, land
p ac ices on SOC con en , possible anges, and espec i e p obabili ies in he p esence
o inhe en unce ain ies. Sec ion 2.2.3 explains he choice o co a ia es included in he
me a-model. The p ope choice o he explana o y a iables gua an ees he i ness o
he s a is ical model. Sec ion 3ou lines s a is ical and machine lea ning app oaches o
es ima e and p edic SOC con en le els and hei p obabili y dis ibu ions. The da a
and selec ed esul s o he s udies a e p esen ed in Sec ion 4. Quan ile-based SOC me a-
models ha e been de eloped o all NUTS2 egions o he EU. The p obabili y dis ibu ion
unc ions o SOC con en in di e en yea s a e analyzed acco ding o c i ical quan iles
(25 h, 50 h, and 75 h) as well as mean alues. The esul s iden i y he in e annual a iabili y
and non-no mali y o SOC con en changes, which can be explained by he p ecipi a ion
and empe a u e a iabili y a ec ing componen s o SOC di e en ly o di e en soil
cha ac e is ics unde al e na i e land use p ac ices as discussed in his sec ion. The c i ical
quan iles o le els can be iden i ied by expe s, e.g., by he EU Mission Boa d o Soil Heal h
and Food. Sec ion 5summa izes he main conclusions and di ec ions o u he s udies.
2. Modeling SOC Dynamics: P ocess-Based s. S a is ical Models
2.1. SOC Analysis and Modeling
The In e go e nmen al Technical Panel on Soils (ITPS) de ines soil heal h as “ he
abili y o he soil o sus ain he p oduc i i y, di e si y, and en i onmen al se ices o
e es ial ecosys ems”. SOC is an essen ial ing edien allowing soils o p o ide hese
se ices, making i a key indica o o soil heal h. SOC imp o es he biological, chemical,
and physical p ope ies o soil, which in u n, inc ease soil p oduc i i y, wa e -holding
capaci y, and s uc u al s abili y [44].
The measu emen s o soil heal h a e usually pe o med a he le el o abou 30 cm
soil dep h [
45
]. FAO [
44
] es ima es ha he op 30 cm o soil con ains mo e ca bon han
he a mosphe e and ege a ion combined. This is ele an o add essing he land deg ada-
ion neu ali y (LDN) a ge o he Uni ed Na ions Con en ion o Comba Dese i ica ion
(UNCCD) (UN) and he ecen ly adop ed he Eu opean G een New Deal, which aims o
b ing he EU coun ies o clima e neu ali y by 2050 [46].
I is epo ed [
47
–
50
] ha in many Eu opean coun ies, he opsoil o ganic ca bon (OC)
s ocks a e dec easing. As SOC cons i u es he la ges e es ial ca bon pool, any changes in
his pool may ha e p o ound implica ions o bo h land p oduc i i y and ca bon emissions.
Co e c opping, dec eased illage, imp o ed c op po olios and c op o a ions,
con e ing c opland o g assland, and op imized e iliza ion applica ion and o ganic
amendmen s o he soil a e men ioned as essen ial p ac ices ha po en ially inc ease SOC
s ocks [
47
]. Adding Ex e nal O ganic Ma e (EOM) can imp o e soil quali y h ough im-
p o ed soil e ili y, inc eased wa e e en ion capaci y, educed soil e osion, and inc eased
c op p oduc i i y. By inc easing c op p oduc i i y, e.g., h ough balanced e iliza ion,
plan s’ CO
2
ixa ion is imp o ed, and highe amoun s o c op esidue migh be le on he
soil, inc easing he C inpu and, hence, he SOC s ocks.
The p ocess o SOC accumula ion is la gely unce ain and is subjec o a iable ac o s
such as clima e change, al e ing pa e ns o empe a u e and p ecipi a ion, and esponses
o mic obial communi ies o clima e changes. T acking SOC dynamics in an inhe en ly
unce ain en i onmen calls o s ochas ic SOC models.
Sus ainabili y 2024,16, 6849 5 o 23
2.2. Modeling SOC Dynamics: P ocessed-Based s. S a is ical Models
2.2.1. P ocess-Based EPIC Model
The e a e a a ie y o p ocess-based models inco po a ing SOC quan i ica ion me hod-
ologies. Among o he s, he g idded ag icul u al models (GAMs) CENTURY (JRC.D.3
model amewo k, h p://www.n el.colos a e.edu/p ojec s/cen u y/, accessed on 6 Ap il
2024), Ro hams ed ca bon model (Ro hC, [
51
,
52
]), DeNi i ica ion-DeComposi ion (DNDC)
model [
53
–
55
], and EPIC-IIASA model [
23
,
24
] ha e been e alua ed as ools o ag icul u al
sec o analysis a a ious scales. These models a e inc easingly used in EU-scale assess-
men s o suppo land use policies, such as ca bon emissions and emo als om land use
and land use change [
35
]. In his wo k, we make use o EPIC model inpu s and esul s.
EPIC is equipped wi h mechanisms o model he dynamics and he u no e o SOC, in
pa icula , on ag icul u al lands.
En i onmen Policy In eg a ed Clima e (EPIC, [
23
,
24
]) is a widely used and es ed
model o simula ing many ag oecosys em p ocesses including plan g ow h, c op yield,
illage, wind and wa e e osion, uno , soil densi y, and leaching. C and N modules
inco po a ed in EPIC buil on concep s om he Cen u y model [
56
–
58
] o connec he
simula ion o soil C dynamics o c op managemen , illage me hods, and e osion p ocesses.
The added C and N ou ines in e ac di ec ly wi h soil mois u e, empe a u e, e osion,
illage, soil densi y, leaching, and ansloca ion unc ions in EPIC. Equa ions we e also
added o desc ibe he e ec s o soil ex u e on soil C s abiliza ion.
A majo bene i o using GAMs like EPIC-IIASA o he es ima ion o SOC changes is
he abili y o EPIC o simula e and de i e esul s o bo h exis ing and po en ial ag icul u al
p ac ices ac oss la ge a eas. These p ac ices can change as long as he e ec s o clima e
change con inue o a ec a me s and new policies ega ding clima e mi iga ion and ca bon
emissions a e implemen ed o ul ill en i onmen al goals [23,24].
2.2.2. S a is ical and Machine Lea ning Models
We expand he exis ing SOC modeling app oaches by de eloping a da a-d i en
quan ile eg ession obus me a-model based on s a is ical and machine lea ning ap-
p oaches [
39
,
40
]. The me a-model simula es he dependencies o he esponse a iable SOC
om such co a ia es as soil p ope ies, (daily o mon hly) empe a u e and p ecipi a ion
pa e ns, and land managemen p ac ices. The quan ile eg ession app oach allows o he
de i a ion o spa io- empo al plausible SOC con en anges and espec i e p obabili ies in
he p esence o unce ain co a ia es.
SOC models a e es ima ed o all NUTS2 egions o he EU. The models a e ained
om mul isou ce da a including his o ical obse a ions and EPIC esul s. They ep esen a
simpli ied amewo k ha cap u es complex in e ac ions among he dependen a iable
and he co a ia es. Seasonal changes in empe a u e, p ecipi a ion, plan phenology, illage,
e iliza ion, c op esidue ecycling, clima e change, and he in e ac ions among hese and
mul iple o he ac o s all ha e he po en ial o change he SOC con en . I is impo an
o unde s and he in e plays be ween all he SOC d i e s, SOC s ocks, and changes. The
models can be used o iden i y ela ionships o in e es and he cha ac e is ics ha d i e
hese ela ionships. Reduced o ms o me a-models demand less compu ing esou ces and
sa e compu a ional ime. Fo his, he me a-models can be used as educed- o m scena io
gene a o s and as submodels o mo e complex IAM models.
2.2.3. S a is ical and Machine Lea ning Models
The da a used in his wo k co e he pe iod om 1980 o 2020. The selec ed co a ia es
a e he ollowing: mon hly empe a u e and p ecipi a ion, ni ogen e iliza ion a es,
ha es ed esidues and esidue ecycling le els, he ca bon con en in c op esidues, and
ele an soil cha ac e is ics such as a ailable wa e -holding capaci y, he concen a ion
o SOC in he opsoil laye , clay con en , bulk densi y, e ec i e soil p o ile dep h, and
ele a ion. The p ope choice o co a ia es gua an ees he i ness o models. Va ying he
alues o co a ia es enables an unde s anding o how a single independen a iable can

Sus ainabili y 2024,16, 6849 6 o 23
in luence he ou come. Some o he a gumen s o choosing he co a ia es as SOC d i e s
a e p esen ed below.
Tempe a u e and p ecipi a ion a e men ioned among he main SOC de e minan s [
9
–
11
,
59
].
The inc ease in ai empe a u e and, as a consequence, he inc ease in soil empe a u e and
mic obial ac i i y, speeds up SOC decomposi ion a es by inc easing soil C mine aliza ion
and espi a ion. Wa me empe a u es expec ed wi h clima e change and he po en ial o
mo e ex eme empe a u e e en s will impac plan p oduc i i y, i s nu i ional con en ,
and soil quali y.
Tempe a u e e ec s a e u he s ipula ed by de ici s and excesses in soil wa e [
60
,
61
]. Soil
wa e con en has been shown o be posi i ely co ela ed wi h mic obial C use e iciency
(CUE) [
62
,
63
]. High soil wa e con en s can, howe e , lead o educ ions in mic obial ac i i-
ies due o oxygen limi a ion, and d ough has been shown o se e ely educe mic obial
espi a ion, g ow h, and CUE [
64
]. The esea ch in [
65
,
66
] emphasizes ha ain all and i s
in ensi y ha e a s ong co ela ion wi h he a e o ca bon s ock accumula ion. The e o e, a
be e unde s anding o he in e ac ions among a iable empe a u e and soil mois u e and
SOC can help de elop mo e e ec i e adap a ion s a egies o o se he impac s o clima e
ex emes on soil heal h.
SOC in ag oecosys ems is in luenced by physical and chemical soil p ope ies. Soil
ex u e (p opo ions o clay, sand, sil ) ep esen s one o he key soil pa ame e s a ec ing
oo g ow h and soil he mal and hyd aulic conduc i i y [
67
], which in u n a ec SOC
le els. Soil clay con en can se e as a p oxy o soil pH le el as clay soils a e usually mo e
alkaline wi h pH alues anging om 7.5 o 10. The pH in luences SOC by egula ing
such soil ac i i ies as, e.g., he soil–plan sys em’s capaci y o supply and abso b nu ien s
( e med as soil nu ien bioa ailabili y) and SOM u no e [
68
]. The le el o ini ial SOC
can also ha e an e ec on SOC.
The addi ion o N o e ime p esen s an essen ial ade-o and unce ain y o SOC
accumula ion. On he one hand, su icien N emo es limi a ions o plan p oduc i i y
and mic obial ac i i y and s imula es SOC inc ease. On he o he hand, he o e supply
o N can aise he mic obe’s demand o ca bon. The demand o ca bon may exceed he
a ailable labile ca bon, which may cause mic obes o each o mo e s able ca bon [
69
,
70
].
Soil N loss due o p ecipi a ion inc ease can al e he C:N a io and, he e o e, a ec SOC
accumula ion p ocesses. The inc eased p ecipi a ion, howe e , does no di ec ly lead o
highe N losses as he N dynamics a e also in luenced by soil ex u e and managemen .
The ege a ion pa ame e s and he mic obial ac i i y can show s ong spa io- empo al
seasonal a iabili y and unce ain y because o unce ain y in d i e s, i.e., empe a u e,
mois u e, C and N a ailabili y and inpu s, and soil p ope ies. The e o e, SOM decay
and SOC con en le els depend on he unce ain and andom explana o y d i e s. Thus,
he abili y o soil o s o e OC depends on clima e–soil–land use/managemen s ochas ic
in e ac ions [
45
]. This calls o using a quan ile-based app oach o iden i y plausible anges
in SOC con en and espec i e p obabili ies in he p esence o unce ain d i e s.
3. Es ima ing SOC Le el Dependencies on Land P ac ices and Clima e Changes
The quan ile-based SOC me a-models ha e been de eloped o all NUTS2 egions
in he EU. The choice o spa ial esolu ion is due o he policy- ele an he e ogenei y o
NUTS2. Each NUTS2 can be cha ac e ized by i s indi idual se o p e ailing land use
p ac ices, ag onomic and non-ag onomic d i e s a ec ing land managemen and soil
p ope ies, and he e o e, he le el o SOC. These d i e s a e sec o al policies, ma ke
p ices, clima e change, and na u al esou ces. The Common Ag icul u al Policy (CAP) is
one o he main EU policies in luencing ag icul u al managemen p ac ices. Regionally
o na ionally, ene gy and clima e policies can ha e e en mo e in luence on c opping
pa e ns han he CAP. CAP consis s o di e en policy ins umen s wi h di e en impac s
on he c opping pa e ns, g een a ming, c op di e si ica ion ins ead o mono-c opping,
en i onmen - iendly a ming, main enance o pe manen g assland, and p ese a ion o
“ecological ocus a eas”. Ru al de elopmen p og ams, in pa icula , u al de elopmen
Sus ainabili y 2024,16, 6849 7 o 23
unding, subs an ially de e mine ag icul u al p ac ices a he le el o NUTS2 [
71
]. To
in es iga e SOC dependencies pu ely on land o m, soil, and clima ic cha ac e is ics, he
analysis can be pe o med a he le el o ag oecological zones (AEZs), i.e., geog aphical
a eas exhibi ing simila clima e, land o m, soils, and/o land co e , and ha ing a speci ic
ange o po en ials and cons ain s o land use.
3.1. Expe imen al Design
The me a-models we e es ima ed based on mul isou ce da a combining his o ical
obse a ions and EPIC model inpu s and esul s (simila o [
39
,
40
]). The ime span co e s
yea s om 1980 o 2020. The EPIC esul s we e de i ed o a ious combina ions o
c ops, esidue e en ions, and chemical nu ien e iliza ion in ensi ies [
23
,
24
]. Ni ogen
e iliza ion in ensi ies dis inguish ou al e na i e le els (scena ios): BAU (scena io wi h
NUTS2- and c op-speci ic N applica ions), 50 kg N/ha, 100 kg N/ha, and 250 kg N/ha. The
ni ogen e iliza ion scena ios a e combined wi h ou c op esidue e en ion al e na i es:
0% e en ion (100% esidues ha es ed), 30% e en ion (70% esidues ha es ed), 60%
e en ion (40% esidues ha es ed), and 90% e en ion (10% esidues ha es ed).
3.2. Da a
We use he inpu s and he esul s o he Pan-Eu opean e sion o he EPIC-IIASA model
calib a ed and alida ed o EU coun ies [
23
,
24
], [
72
]. The daily me eo ological da a we e
ob ained om he Join Resea ch Cen e’s (JRC) C op G ow h Moni o ing Sys em (CGMS)
me eo ological da abase [
34
] a a 50 km g id esolu ion. Wea he a iables include daily and
mon hly a e ages o p ecipi a ion (P cp, mm) and empe a u e (T ), maximum empe a u e
(Tmax, C), minimum empe a u e (Tmin, C), and sola adia ion (S ad, MJ m−2).
Land co e in o ma ion was aken om a combined CORINE 2000 and PELCOM map
a a 1 km esolu ion p o ided by JRC. Digi al e ain in o ma ion was de i ed om SRTM
(Shu le Rada Topog aphic Mission; [
73
]) and GTOPO sou ces (Global 30 A c Second
Ele a ion Da a; h p://e os.usgs.go , accessed on 5 May 2019).
Soil da a we e acqui ed om he Eu opean Soil Bu eau Da abase (ESBD . 2.0),
including he Soil Geog aphic Da abase o Eu ope, he Soil P o ile Analy ical Da abase
o Eu ope, he Pedo-T ans e Rules Da abase, he Da abase o Hyd aulic P ope ies o
Eu opean Soils [
74
], and he Map o O ganic Ca bon Con en in opsoils in Eu ope [
75
]. Soil
a iables include d y bulk densi y (BDd y, g/cm
3
), clay pe cen age (clay, %), soil pH (pH),
d ained uppe limi (dul, mm/mm), soil sa u a ed hyd aulic conduc i i y (ksa , mm/day),
wil ing poin (ll, mm/mm), soil o ganic ma e (om, %), sand pe cen age (sand, %), and
sa u a ed olume ic wa e con en (sa , mm/mm) a nine di e en dep hs o soil: 0–5, 5–10,
10–15, 15–30, 30–45, 45–60, 60–80, 80–100, and 100–120 cm. Soil da a can be conside ed
ime-in a ian ac o s; howe e , hey a e a ec ed by a ious land use and soil p ac ices.
Fo hese, he SOC con en and changes in esponse o wea he pa ame e s unde ce ain
p ac ices (and, hus, soil p ope ies) a e de i ed om EPIC simula ions. In he same way,
he e ec s o o he loca ion-speci ic p ac ices can be included.
Adminis a i e egions we e ob ained om he Geog aphic In o ma ion Sys em o
he Eu opean Commission (GISCO) and wa e sheds om he Eu opean Ri e Ca chmen
Da abase, e sion 2 (ERC; p o ided by Eu opean En i onmen Agency, h p://www.eea.
eu opa.eu, accessed on 5 May 2019). Ag icul u al s a is ics on c op yields and e ilize
consump ion we e e ie ed om he S a is ical O ice o he Eu opean Communi ies
(EUROSTAT) and IFA/FAO da ase s [
76
]. In o ma ion on ain ed and i iga ed c op a eas
was aken om he Eu opean I iga ion Map (EIM) p esen ed in [77].
The da a we e ha monized a a esolu ion o abou 120,000 EPIC simula ion uni s
(SimUs). The SimUs a e ep esen ed, as a ule, by one a ea wi h “ ep esen a i e” cha ac e -
is ics o soil, opog aphy, and p esen wea he . I su icien ime se ies da a a e a ailable,
he me a-model can be es ima ed a he le el o SimUs.
Sus ainabili y 2024,16, 6849 8 o 23
3.3. Machine Lea ning Quan ile Reg ession Me a-Model
S a is ical and machine lea ning models p o ide quan i a i e ways o deal wi h such
ques ions as es ima ing he con ibu ion o each independen a iable (also called p edic o
o co a ia e) and hei combina ions o he a ge a iable (dependen o esponse a iable).
S a is ical app oaches used o spa ially p edic SOC di e subs an ially, wi h mul iple
linea eg ession, o dina y k iging, co-k iging, eg ession-k iging, and geog aphically
weigh ed eg ession being he mos commonly used echniques [
74
]. Models o en used
o soil nu ien con en and c op yield p edic ion include andom o es , neu al ne wo ks,
con olu ional neu al ne wo ks, ecu en neu al ne wo ks, e c. Howe e , due o he o en
“black-box” na u e o hese models, he ac abili y o he esul s is no s aigh o wa d. The
p edic ion accu acy is sensi i e o model s uc u e and pa ame e calib a ion, and i can
be di icul o explain he accu acy o inaccu acy o he de i ed esul s. The complex and
non-linea “black-box” s uc u e hinde s he explici in eg a ion o hese models wi h IAMs.
3.3.1. Linea Reg ession Model
A linea eg ession (LR) can be conside ed one o he machine lea ning algo i hms,
which is one o he mos popula models in machine lea ning. I is widely used because i
is simple and ac able. The simplici y means i is easy o unde s and he esponses o he
dependen a iables o each explana o y, i.e., he eg ession coe icien o an independen
a iable e lec s he change in he dependen a iable as a esul o a uni change in
he espec i e independen a iables. The LR assumes ha he esiduals a e no mally
dis ibu ed, which means ha LR ails o cap u e ex eme alues o he independen
a iables. I uses he me hod o leas squa es o calcula e he condi ional mean o he
dependen a iable ac oss di e en alues o he explana o y a iables. The LR model o
calcula ing he mean akes he o m
yi=β0+β1xi1+β2xi2+β3xi3+· · · +βmxim +ϵi, (1)
whe e
i=
1,
. . . n
is he numbe o obse a ions and
m
is he numbe o independen
a iables. The andom a iables
ϵi
a e ypically assumed o be mu ually independen and
o ollow a no mal dis ibu ion wi h ze o mean and a iance σ2
i>0.
Coe icien s o he LR a e ound by minimizing he Mean Squa e E o “goodness-o -
i ” unc ion (O dina y Leas Squa es (OLS))
MSE =(yi−(β0+β1xi1+β2xi2+β3xi3+· · · +βmxim))2,
which gi es he “bes eg ession line”. Thus, he bes es ima es o
βi
p o ide he es ima e
o he condi ional mean o he a iables
yi
in (1). The p edic ions ocus on a single ea u e,
i.e., he mean o he dis ibu ion o he esponse a iables yi.
The le el o SOC can a y depending on seasonal pa e ns o empe a u e and p e-
cipi a ion, in di e en soils, and o a ious combina ions o c op esidue ecycling and
nu ien e iliza ion a es. The quan iles o SOC con en and SOC con en changes p o ide
anges o possible SOC le els in di e en condi ions. The SOC dynamics can show he
non-no mally dis ibu ed pa e ns, e.g., i he SOC 50 h pe cen ile is di e en om he
SOC mean alue. Fo s a is ical es ima ion and machine lea ning p oblems in he p esence
o non-no mal p obabili y dis ibu ions, i is mo e na u al o use he median o o he
quan ile-based c i e ia ins ead o he ma hema ical expec a ion. I is also impo an ha
he quan ile-based eg ession allows o he es ima ion o he likelihood o possible SOC
le els o occu in di e en en i onmen al condi ions, which is use ul o wo king ou SOC
no ms, e.g., by “The EU Mission Boa d o Soil Heal h and Food” [46].
3.3.2. Quan ile Reg ession (QR) Model
Unlike egula LR, which uses he me hod o leas squa es o es ima e he condi ional
mean o he dependen a iables, quan ile eg ession es ima es he quan iles o he esponse
a iable condi ional on obse a ions o independen a iables. The quan ile eg ession es i-
Sus ainabili y 2024,16, 6849 9 o 23
ma es a e mo e obus agains ou lie s. Fo hese s udies, he condi ional quan ile unc ions
a e o majo in e es also o in es iga ing and p edic ing he anges and he p obabili y
dis ibu ion o he SOC con en based on key ac o s such as highly a iable empe a u e
and p ecipi a ion, unce ain soil cha ac e is ics, and land managemen p ac ices.
In he p esen wo k, SOC le els a e analyzed and dis inguished acco ding o hei
alues, i.e., mean and c i ical quan iles. SOC quan iles a e app oxima ed by i ing sepa a e
quan ile-based eg ession models. In classical LR app oaches, he eg ession coe icien s
(
β
-coe icien s) ep esen he mean inc ease in he esponse a iable p oduced by one uni
inc ease in he associa ed explana o y a iables. Con e sely, he
β
-coe icien s ob ained
om QR ep esen he change in a speci ic quan ile o he esponse a iable p oduced
by a one-uni inc ease in he associa ed d i e . In his way, QR allows one o s udy how
ce ain d i e s a ec median (quan ile
τ=
0.5), ex emely low (e.g.,
τ=
0.05), o high (e.g.,
τ=
0.95) SOC s ock alues. The e o e, i gi es a mo e comp ehensi e desc ip ion o he
e ec o p edic o s on he whole SOC s ock p obabili y dis ibu ion (i.e., no jus he mean)
and may be used o analyze di e en ial SOC s ock esponses o en i onmen al ac o s.
Le us i s in oduce he no ion o a quan ile (pe cen ile) unc ion o a andom a iable.
Quan iles a e alues ha di ide he p obabili y dis ibu ion o a andom a iable in o a
speci ic numbe o in e als (con inuous) wi h equal p obabili ies. I is assumed ha
a andom a iable
X
has a con inuous and s ic ly mono onic cumula i e dis ibu ion
unc ion
FX:R→[0,1]
,
FX(x)=P(X≤x)
. The
p
-quan ile unc ion o
X
,
QX(p)
, e u ns
he alue
x
such ha
FX(x)=P (X≤x)=p
, which can be ew i en as he in e se o he
cumula i e dis ibu ion unc ion Q(p)=F−1
X(x)=in {x:FX(x)≥p}.
Fo a andom sample
X1
,
X2
,
. . .
,
Xn
,
. . .
wi h empi ical dis ibu ion unc ion
ˆ
FX(x)
,
he
p
h empi ical quan ile unc ion can be de ined as
ˆ
Q(p)=ˆ
F−1
X(x)=in x:ˆ
FX(x)≥p
.
The p h empi ical quan ile can be de e mined by sol ing he minimiza ion p oblem
ˆ
Q(p)=a gminx


∑
i|Xi≥x
p|Xi−x|+(1−p)∑
i|Xi<x
|Xi−x|


Quan ile eg ession is an ex ension o linea eg ession ha is used when he con-
di ions o linea eg ession a e no me (i.e., linea i y, homoscedas ici y, independence,
o no mali y).
Fo he quan ile eg ession, we make an assump ion ha he
p
h quan ile is gi en
as a linea unc ion o he explana o y a iables. In he case o he empi ical eg es-
sion and andom obse a ions o dependen and independen a iables
Y1
,
Y2
,
. . .
,
Yn
and
X1
,
X2
,
. . .
,
Xn
,
. . .
, he coe icien s
β(τ)
o he
τ
h empi ical quan ile eg ession can be
de e mined by sol ing he minimiza ion p oblem
∑
i
τmax0,Yi−β′(τ)Xi+(1−τ)max0, β′(τ)Xi−Yi(2)
o p oblem
∑
i
maxτYi−β′(τ)Xi,(1−τ)(β′(τ)Xi−Yi), (3)
which is simila o he p oblem in [
39
,
40
]. The minimiza ion p oblem can be educed o a
linea p og amming p oblem [39].
Fo quan ile eg ession, i is possible o calcula e any quan ile (pe cen age) o pa icu-
la alues o he dependen a iables. Sol ing he p oblem o all
τ∈[0,1]
, i is possible o
eco e he en i e condi ional quan ile unc ion, i.e., he condi ional dis ibu ion unc ion,
o
Y
. I
τ=
0.5, he minimiza ion p oblem de i es he median. Taking a simila s uc u e
o he linea eg ession model, he “bes ” quan ile eg ession model equa ion o he
τ
h
quan ile is
Qτ(yi)=β0(τ)+β1(τ)xi1+β2(τ)xi2+β3(τ)xi3+· · · +βm(τ)xim,
Sus ainabili y 2024,16, 6849 16 o 23
Sus ainabili y2024,16,xFORPEERREVIEW15o 22

Sweden,Finland,F ance,Ge many,Spain,andI aly,which ep esen  heNo h,Middle,
andSou ho Eu ope.Visualizedquan ilesa e25 h(g een),50 h(blue),and75 h(yellow).
Inaddi ion, he igu esdisplay hemean alueo  heSOCcon en change(in ed) o  he
yea s om1980 o2020.Thees ima eso  heSOCquan ilele el𝑄󰇛𝑦󰇜ineachSimUs
wi hinallNUTS2 egionsandEUcoun iesha eap obabili yo 
𝑃𝑟𝑜𝑏󰇝𝑄󰇛𝑦󰇜𝛽󰇛𝜏󰇜𝛽󰇛𝜏󰇜𝑥𝛽󰇛𝜏󰇜𝑥𝛽󰇛𝜏󰇜𝑥⋯𝛽󰇛𝜏󰇜𝑥󰇞 𝜏. (5)
Theya ecalcula edwi hcoefficien s𝛽󰇛𝜏󰇜(5) o eachquan ile𝜏(pe cen ile100𝜏),
whe e𝑖1,…𝑛is henumbe o obse a ionsand𝑚is henumbe o co a ia es(inde-
penden  a iables).Coefficien s𝛽󰇛𝜏󰇜 a e unc ionso quan ile𝜏.Equa ion(5)means
ha 100𝜏pe cen o  heda aa eless han he alueo  he𝜏—quan ile.Equa ion(5)p o-
ides hebasis o  he alida iono  hequan ile eg essionmodel.

Figu e7.TheSOCchangedynamics,in /ha,Finland,byNUTS2 egion,be weenconsequen yea s
om1980 o2000.

Figu e8.TheSOCchangedynamics,in /ha,Sweden,byNUTS2 egion,be weenconsequen yea s
om1980 o2020.
Figu e 8. The SOC change dynamics, in /ha, Sweden, by NUTS2 egion, be ween consequen yea s
om 1980 o 2020.
Sus ainabili y2024,16,xFORPEERREVIEW16o 22


Figu e9.TheSOCchangedynamics,in /ha,F ance,byNUTS2 egion,be weenconsequen yea s
om1980 o2020.

Figu e10.TheSOCchangedynamics,in /ha,Ge many,byNUTS2 egion,be weenconsequen 
yea s om1980 o2020.
Figu e 9. The SOC change dynamics, in /ha, F ance, by NUTS2 egion, be ween consequen yea s
om 1980 o 2020.

Sus ainabili y 2024,16, 6849 17 o 23
Sus ainabili y2024,16,xFORPEERREVIEW16o 22


Figu e9.TheSOCchangedynamics,in /ha,F ance,byNUTS2 egion,be weenconsequen yea s
om1980 o2020.

Figu e10.TheSOCchangedynamics,in /ha,Ge many,byNUTS2 egion,be weenconsequen 
yea s om1980 o2020.
Figu e 10. The SOC change dynamics, in /ha, Ge many, by NUTS2 egion, be ween consequen
yea s om 1980 o 2020.
Sus ainabili y2024,16,xFORPEERREVIEW17o 22


Figu e11.TheSOCchangedynamics,in /ha,I aly,byNUTS2 egion,be weenconsequen yea s
om1980 o2020.

Figu e12.TheSOCchangedynamics,in /ha,Spain,byNUTS2 egion,be weenconsequen yea s
om1980 o2020.
5.Conclusions
Thispape de elopsquan ile eg essionme a-models o  heanalysisandp edic ion
o soilo ganicca bon(SOC)con en andSOCchanges o allNUTS2 egionso  heEU.
Figu e 11. The SOC change dynamics, in /ha, I aly, by NUTS2 egion, be ween consequen yea s
om 1980 o 2020.
Sus ainabili y 2024,16, 6849 18 o 23
Sus ainabili y2024,16,xFORPEERREVIEW17o 22


Figu e11.TheSOCchangedynamics,in /ha,I aly,byNUTS2 egion,be weenconsequen yea s
om1980 o2020.

Figu e12.TheSOCchangedynamics,in /ha,Spain,byNUTS2 egion,be weenconsequen yea s
om1980 o2020.
5.Conclusions
Thispape de elopsquan ile eg essionme a-models o  heanalysisandp edic ion
o soilo ganicca bon(SOC)con en andSOCchanges o allNUTS2 egionso  heEU.
Figu e 12. The SOC change dynamics, in /ha, Spain, by NUTS2 egion, be ween consequen yea s
om 1980 o 2020.
They a e calcula ed wi h coe icien s
βm(τ)
(5) o each quan ile
τ
(pe cen ile 100
τ
),
whe e
i=
1,
. . . n
is he numbe o obse a ions and
m
is he numbe o co a ia es (inde-
penden a iables). Coe icien s
βm(τ)
a e unc ions o quan ile
τ
. Equa ion (5) means ha
100
τ
pe cen o he da a a e less han he alue o he
τ
—quan ile. Equa ion (5) p o ides
he basis o he alida ion o he quan ile eg ession model.
5. Conclusions
This pape de elops quan ile eg ession me a-models o he analysis and p edic ion
o soil o ganic ca bon (SOC) con en and SOC changes o all NUTS2 egions o he EU.
The e exis mul iple s a is ical and machine lea ning app oaches o es ima e and p edic
soil nu ien s, in pa icula , SOC con en . Howe e , he complex and non-linea “black-box”
s uc u e o hese models hinde s he in e p e a ion and he explici in eg a ion o hese
models wi h IAMs.
LR models a e he simples and mos popula among o he app oaches because o hei
simplici y and ac abili y. Howe e , LR can ail o cap u e ex eme alues as hey assume
no mally dis ibu ed esiduals. They calcula e a single pa ame e — he condi ional mean
o he dependen ( esponse) a iable ac oss di e en alues o he explana o y a iables.
The QR models a e nonpa ame ic as hey assume no dis ibu ion o esiduals. They gi e
much deepe insigh s in o he comple e condi ional dis ibu ion o SOC s ock alues as
a unc ion o spa ial and empo al p edic o s. SOC con en in di e en yea s is analyzed
acco ding o c i ical quan iles (25 h, 50 h, and 75 h) as well as mean alues. Fo example,
he dynamics o he 25 h and 75 h quan iles show how unce ain y anges can change in
ime, i.e., i low/high quan ile inc eases o dec eases. The NUTS2-le el QR models allow
Sus ainabili y 2024,16, 6849 19 o 23
o he in es iga ion o he dynamics o speci ic SOC con en le els ha a e o in e es o
expe s, e.g., by he EU Mission Boa d o Soil Heal h and Food.
By ocusing on low (o high) quan iles, eg ession coe icien s
β
in o m us abou
p edic o s ha mainly in luence he absence (o p esence) o high/low SOC s ock alues
in space and ime. Conside ing independen QR models o di e en alues o quan ile
τ
allows o he possibili y ha he impo ance o ce ain p edic o s may change acco ding o
SOC le el.
The models a e ained using mul isou ce da a, i.e., he a ailable his o ical measu e-
men s and he esul s o he EPIC model. The esul s o he EPIC model a e de i ed o
easible scena io combina ions o di e en esidue e en ion and chemical e iliza ion a es.
The combina ions o scena ios o m he so-called EPIC hype cube, which has been designed
based on s udies by Balko ic e al. [23].
We ound disc epancies be ween he 50 h pe cen ile and he mean alue o he SOC
con en changes, which indica es ha he in e annual changes in he SOC con en a e
non-no mally dis ibu ed. The non-no mali y can be explained by he a iabili y o he
mon hly p ecipi a ion and empe a u e pa e ns a ec ing componen s o SOC di e en ly
o di e en soil cha ac e is ics and managemen p ac ices. By de eloping me a-models o
a b oade ange o quan iles, e.g.,
τ∈[0,1]
, i is possible o eco e he whole dis ibu ion
o SOC con en esponses o al e ing wea he , soil, and managemen condi ions in SimUs
wi hin espec i e NUTS2.
The NUTS2-le el me a-models can be used o ind ou an op imal combina ion o
esidue e en ion and e iliza ion a es o imp o ing soil heal h, c op p oduc i i y, and
sus ainable bio uel p oduc ion. Compa ed o a biophysical model (e.g., EPIC), he compu-
a ions wi h he me a-models a e less memo y-, ime-, and da a-demanding. The models
can be easily explici ly in eg a ed in o a la ge IAM such as GLOBIOM. In his way, he wo
models ( he biophysical and he economic land use planning models) a e linked o de i e
he cos s o op imal and obus land use decisions and ood–wa e –ene gy–en i onmen
NEXUS secu i y managemen op ions unde cons ain s on SOC as discussed in Sec ion 2.
Au ho Con ibu ions: Me hodology concep ualiza ion, T.E., P.H., A.L.-D.-A., J.B., R.S., A.D., T.K.,
N.K. and G.W.; me hodology, T.E., P.H., J.B., R.S., T.K., N.K. and P.S.K.; so wa e, T.E., A.L.-D.-A. and
M.N.; alida ion, T.E., P.H., A.L.-D.-A., M.N., J.B., R.S. and C.F.; o mal analysis, T.E., A.L.-D.-A., M.N.,
J.B., R.S. and C.F.; in es iga ion, T.E., A.L.-D.-A., J.B., R.S., M.N. and C.F.; esou ces, T.E., A.L.-D.-A.,
J.B., R.S. and C.F.; da a T.E., A.L.-D.-A., M.N., J.B., R.S. and C.F.; w i ing—o iginal d a p epa a ion,
T.E., A.L.-D.-A., S.F., J.B. and R.S. w i ing— e iew and edi ing, T.E., A.L.-D.-A., S.F., J.B., R.S., A.D.,
M.N., N.K. and G.W.; isualiza ion, T.E., A.L.-D.-A., J.B., R.S. and M.N.; supe ision, T.E., P.H. and
S.F.; p ojec adminis a ion, T.E., P.H., S.F., A.D. and N.K. All au ho s ha e ead and ag eed o he
published e sion o he manusc ip .
Funding: This esea ch has been unded by he Eu opean Union’s H2020 P ojec s ENGAGE (G an
Ag eemen No. 821471) and COACCH (P oposal ID 776479), Eu opean Union’s Ho izon Eu ope
esea ch and inno a ion ac ion unde g an ag eemen No. 101086179 (AI4SoilHeal h), and he
EU PARATUS p ojec (CL3-2021-DRS-01-03, SEP-210784020). This wo k ecei ed suppo om
and con ibu es o a join p ojec be ween he In e na ional Ins i u e o Applied Sys ems Analysis
(IIASA) and he Na ional Academy o Sciences o Uk aine (NASU) on “In eg a ed obus modeling
and managemen o ood-ene gy-wa e -land use nexus o sus ainable de elopmen ” ( he Na ional
Resea ch Founda ion o Uk aine, g an No. 2020.02/0121).
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : The o iginal con ibu ions p esen ed in he s udy a e included in he
a icle, u he inqui ies can be di ec ed o he co esponding au ho . The da a and ma e ial can be
a ailable upon eques o in e es ed esea che s.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Sus ainabili y 2024,16, 6849 20 o 23
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