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Test of validity of a dynamic soil carbon model using data from leaf litter decomposition in a West African tropical forest

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Test of validity of a dynamic soil carbon model using data from leaf litter decomposition in a West African tropical forest

Author: Guendehou, G.H.S.,Liski, J.,Tuomi, M.,Moudachirou, M.,Sinsin, B.,Mäkipää, R.
Year: 2013
Source: https://jukuri.luke.fi/bitstream/10024/517496/1/test.pdf
GMDD
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Soil ca bon
modeling in opical
o es s
G. H. S. Guendehou e al.
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Geosci. Model De . Discuss., 6, 3003–3032, 2013
www.geosci-model-de -discuss.ne /6/3003/2013/
doi:10.5194/gmdd-6-3003-2013
© Au ho (s) 2013. CC A ibu ion 3.0 License.
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This discussion pape is/has been unde e iew o he jou nal Geoscien i ic Model
De elopmen (GMD). Please e e o he co esponding inal pape in GMD i a ailable.
Tes o alidi y o a dynamic soil ca bon
model using da a om lea li e
decomposi ion in a Wes A ican opical
o es
G. H. S. Guendehou1,2, J. Liski3, M. Tuomi3, M. Moudachi ou4, B. Sinsin5, and
R. Mäkipää2
1Cen e Béninois de la Reche che Scien i ique e Technique, 03 BP 1665 Co onou, Bénin
2Finnish Fo es Resea ch Ins i u e, P.O. Box 18, 01301 Van aa, Finland
3Finnish En i onmen Ins i u e, P.O. Box 140, 00251 Helsinki, Finland
4Labo a oi e de Pha macognosie, Facul é des Sciences e Techniques,
Uni e si é d’Abomey-Cala i, 01 BP 918 Co onou, Bénin
5Labo a oi e d’Ecologie Appliquée, Facul é des Sciences Ag onomiques,
Uni e si é d’Abomey-Cala i, 01 BP 526 Co onou, Bénin
Recei ed: 8 Ap il 2013 – Accep ed: 6 May 2013 – Published: 28 May 2013
Co espondence o: G. H. S. Guendehou ([email p o ec ed],
[email protected])
Published by Cope nicus Publica ions on behal o he Eu opean Geosciences Union.
3003
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G. H. S. Guendehou e al.
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Abs ac
We e alua ed he applicabili y o he dynamic soil ca bon model Yasso07 in opical
condi ions in Wes A ica by simula ing he li e decomposi ion p ocess using as e-
qui ed inpu in o he model li e mass, li e quali y, empe a u e and p ecipi a ion col-
lec ed du ing a li e bag expe imen . The expe imen was conduc ed o e a six-mon h5
pe iod on lea li e o i e dominan ee species, namely A zelia a icana, Anogeissus
leioca pa, Ceiba pen and a, Dialium guineense and Diospy os mespili o mis in a semi-
deciduous e isol o es in Sou he n Benin. Since he p edic ions o Yasso07 we e
no consis en wi h he obse a ions on mass loss and chemical composi ion o li e ,
Yasso07 was i ed o he da ase composed o global da a and he new expe imen-10
al da a om Benin. The e-pa ame e ized e sions o Yasso07 had a good p edic i e
abili y and e ined he applicabili y o he model in Benin o es ima e soil ca bon s ocks,
i s changes and CO2emissions om he e o ophic espi a ion as main ou pu s o he
model. The indings o his esea ch suppo he hypo hesis ha he high a ia ion o
li e quali y obse ed in he opics is a majo d i e o he decomposi ion and needs15
o be accoun ed in he model pa ame e iza ion.
1 In oduc ion
In opical condi ions in A ica, li le a en ion has been paid o li e decomposi ion and
quan i ica ion o changes in he soil o ganic ca bon (SOC), hough o es soil in his
egion accoun s o 11 % o he wo ld’s soil ca bon pool (FAO, 2010). Quan i ica ion o 20
SOC dynamics in opical A ica is equi ed o imp o e he es ima ion o he global ca -
bon balance. The SOC changes a e epo ed unde he Clima e Change Con en ion
as a pa o he na ional g eenhouse gas in en o ies o he o es y sec o (UNFCCC,
2008, 2010), bu majo i y o he coun ies in opical A ica ei he epo no changes
in SOC s ocks o apply de aul s ock change ac o s o he In e go e nmen al Panel25
on Clima e Change me hodologies (pa ex. IPCC, 2003, 2006) oge he wi h ough
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es ima ion o he land use and land use change. Unde he Uni ed Na ions F amewo k
Con en ion on Clima e Change (UNFCCC) mechanism o he Reducing Emissions
om De o es a ion and Fo es Deg ada ion in De eloping Coun ies (REDD), he coun-
ies ha e economic incen i es o he conse a ion, he sus ainable managemen and
he enhancemen o hei o es ca bon s ocks and obus me hods leading o con iden 5
and e i ied ca bon s ock es ima es a e inc easingly equi ed. A numbe o s udies ha e
epo ed SOC s ocks es ima ed om only spo adic soil sampling and digi al maps ( o
example Manu e al., 1991; P udencio, 1993; Volko e al., 1999; Hen y e al., 2009)
and he epo ed alues in he exis ing da abases in A ica (Ba jes, 1996, 2002, 2005,
2006; FAO, 2008) consis o global es ima es wi h limi ed indica ions on changes and10
dis ibu ion acco ding o ecosys ems.
The dynamics o SOC is in luenced by li e quan i y and quali y, clima e and
me abolism o decomposing o ganisms and go e ned by o he physical, chemical and
biological ac o s, such as soil p ope ies, which all may be di icul o quan i y (Swi
and Ande son, 1989; Ae s, 1997; Coû eaux e al., 1998; La elle e al., 1993). O e all15
changes in he SOC s ock may be quan i ied wi h measu emen s, bu epea ed mea-
su emen s o soil ca bon s ocks a e labo ious, ime and esou ces consuming e o s
wi h he added d awback o he di icul y o p edic ing u u e le els. Also, ex apola -
ing only a ew SOC measu emen s o a la ge scale may lead o high unce ain y due
o he spa ial a ia ion o SOC. Thus, p ocesses aking place in soil and SOC s ock20
changes a e s udied mos ly h ough he use o decomposi ion models (Coleman and
Jenkinson, 1996; Cu ie and Abe , 1997; Ku z and Apps, 1999; Che o e al., 2001;
Liski e al., 2005; Sie a e al., 2012). The applica ion o he model-based app oach
could also help coun ies o mee SOC epo ing equi emen s in opical A ica, whe e
esou ces a e limi ed. Howe e , model esul s and hei applicabili y depend on model25
s uc u e and pa ame e s, as well as on a ailable inpu in o ma ion and assump ions
used (Pel oniemi e al., 2007; Palosuo e al., 2012).
To ou knowledge, no SOC model calib a ed using li e decomposi ion da a om
o es s in A ica is a ailable. The li e quali y is known o be he mos impo an
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de e minan o he decomposi ion a e a egional scale (e.g. Tian e al., 1992; Be g
e al., 1993; La elle e al., 1993; Ae s, 1997; Lo ange e al., 2002; Guendehou e al.,
2014) and he plan species ichness o opical o es s yields high a ia ion in he li -
e quali y (Goma-Tchimbakala and Be nha d-Re e sa , 2006; Ba bhuiya e al., 2008;
Cusack e al., 2009). Howe e , only a ew li e ypes om opical ee species we e5
included in he da ase ha was used o he pa ame e iza ion o he widely applied soil
ca bon model (Coleman and Jenkinson, 1996; Che o e al. 2001; Tuomi e al., 2009)
and many soil models a e pa ame e ized only o empe a e and bo eal condi ions.
In his pape , we assessed he applicabili y o he dynamic soil ca bon model
Yasso07 in opical condi ions in Wes A ica, by simula ing he li e decomposi ion10
p ocess using da a on li e mass, li e quali y, empe a u e and p ecipi a ion. The da a
was collec ed om a li e bag expe imen conduc ed on lea li e om i e dominan
ee species, namely A zelia a icana,Anogeissus leioca pa,Ceiba pen and a,Dialium
guineense, and Diospy os mespili o mis, in he na u al semi-deciduous o es Lama in
Sou he n Benin. We es ed he hypo heses ha he decomposi ion p ocess in opics15
is a ec ed by he high a ia ion o li e quali y and e-pa ame e iza ion o he Yasso07
model wi h he di e se li e da a om opics imp o es he p ecision o he mass loss
p edic ions.
2 Ma e ial and me hods
2.1 Expe imen al si e20
The expe imen al si e is he Lama o es , a na u al semi-deciduous o es loca ed in
a humid opical clima e in Sou he n Benin (Nagel e al., 2004) a 6◦550–7◦000N, 2◦040–
2◦120E (Fig. 1). The si e alls wi hin he opical mois zone acco ding o he classi i-
ca ion scheme o clima e egions o he IPCC (IPCC, 2006). The highes (38 ◦C) and
he lowes (15 ◦C) empe a u es we e usually eco ded in Feb ua y–Ma ch and in De-25
cembe , espec i ely. The mean annual empe a u e is 27 ◦C. The p ecipi a ion shows
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a bimodal dis ibu ion pa e n. The mean annual p ecipi a ion in he expe imen al si e
is 1100 mm; ain all is, in gene al, mo e han 100 mmmon h−1 h oughou he yea ,
excep in Janua y, Feb ua y and Decembe . Yea s a e di ided in o ou seasons: wo
ainy and wo d y seasons. The p incipal ainy season occu s be ween mid-Ma ch and
mid-July and he sho e ainy season be ween mid-Sep embe and mid-No embe .5
The mon hly a e age o ela i e humidi y is always mo e han 51 %. Table 1 shows he
mon hly clima ic da a eco ded by he na ional me eo ological se ice a he ime o he
decomposi ion expe imen .
The soil o he Lama o es is epo ed as a a e hyd omo phic clayey e isol (40 o
60 % o clay) in Wes A ica, wi h a poo d ainage and a pH ange o 5–5.5 in he 0–10
30 cm ho izon (Küppe s e al., 1998). The pH inc eases up o 6.5–7 in deepe ho izons
due o he appea ance o limes one a a dep h o 150 cm. This soil has been desc ibed
as ich in calcium (Ca) and magnesium (Mg) due o a “g ani o-gneissic” pa en ma e ial
om he seconda y and e ia y ages. The mean al i ude in he o es is 60 m ( on
Bo hme e al., 1986).15
The ee species ichness o he Lama o es was desc ibed by Akoègninou (1984),
Mondjannagni (1969), Pa adis and Houngnon (1977). Küppe s e al. (1998) epo ed 67
amilies based on an in en o y ca ied ou in 1998. The a e age densi y in he na u al
dense pa o he o es whe e he expe imen ook place is 12 species/400 m2, and
he ela i e abundance o dominan ee species is abou 40 ees/400 m2(Küppe s20
e al., 1998). The cu en esea ch ocused on i e dominan ee species including A.
a icana,A. leioca pa,C. pen and a,D. guineense and D. mespili o mis ( on Bo hme
e al., 1986; Küppe s e al., 1998; Nagel e al., 2004). No human ac i i ies such as
ha es ing o e iliza ion a e implemen ed in he expe imen al si e. In Lama o es , he
amoun o lea li e all anges om 26 o 42 d y ma e y −1; he li e all ollows25
a unimodal dis ibu ion pa e n, wi h he maximum li e p oduc ion obse ed du ing he
d y season, o en in Janua y (Djego, 2006).
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2.2 Li e bag expe imen , mass loss measu emen , and chemical analyses
The ma e ial used consis ed o lea li e o A. a icana, A. leioca pa, C. pen and a, D.
guineense, and D. mespili o mis. Only senescen lea es eady o all om he ees
we e collec ed. Lea es we e d ied in open-ai and hen o en-d ied a 75 ◦C o cons an
weigh . In o de o use all he amoun o li e collec ed, an ini ial mass o d ied lea es5
o A. a icana (20 g), A. leioca pa (30 g), C. pen and a (20 g), D. guineense (30 g), and
D. mespili o mis (30 g) was placed in he li e bags in polyes e (20 cm ×20 cm, mesh
size 0.33 mm) on he o es loo . Li e bags we e di ided be ween ou plo s es ab-
lished in a nea ly ec angula con igu a ion; he dis ance be ween he plo s (be ween
25 and 30 m) was assumed la ge enough o minimize he spa ial au oco ela ion be-10
ween plo s. In each plo , li e bags we e placed in ows and columns on he o es loo :
he e we e i e columns each con aining he i e li e species and six ows each con-
aining he six collec ions. In o al, 30 li e bags we e placed in a plo . In each ow, he
i e bags we e placed. Bags we e no mo ed un il collec ion da e and no dis u bances
occu ed du ing he expe imen . Bags we e collec ed e e y ou weeks om he ou 15
plo s (be ween Feb ua y and July 2010), he emaining li e was d ied in open ai and
in he o en a 75 ◦C o cons an weigh . The emaining mass was measu ed and he
mass loss es ima ed. The emaining d ied li e was kep in a eeze in a plas ic bag
be o e he chemical analyses.
The chemical analyses on li e p io o decomposi ion and on decomposed li e 20
we e ca ied ou in he labo a o y o he Finnish Fo es Resea ch Ins i u e. Based on
he solubili y di e ence o he essen ial cons i uen s o lea li e in di e en sol en s,
he analyses enabled o de e mine he concen a ion o compounds soluble in e hanol,
compounds soluble in wa e , compounds hyd olysable in acid, and compounds nei-
he soluble no hyd olysable (he eina e e e ed o as Klason lignin). Ex ac ion was25
conduc ed in a sonica ing wa e ba h, i s o 90 min wi h e hanol, hen o 90 min wi h
wa e (Ka hu e al., 2010). The e hanol- and wa e ex ac ed esidue was di ided in o
acid-hyd olysable (72 % H2SO4) and non-hyd olysable ac ions using he Klason lignin
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me hod (E land, 1977). Samples we e il e ed, o en-d ied a 75 ◦C o cons an weigh
and weighed be ween he ex ac ions, and he amoun s o di e en ac ions we e de-
e mined as p opo ions o he mass o o ganic ma e . The ash con en o he samples
was de e mined a e keeping he d ied samples in a mu le u nace a 550 ◦C o e nigh .
Due o he high numbe o chemical pa ame e s o de e mine on each collec ed sam-5
ples (160 pa ame e s), samples o he same li e species and same collec ion we e
pooled o chemical analyses in o de o educe he amoun o wo k, and assuming his
yields he a e age chemical composi ion o he ou plo s.
2.3 Model desc ip ion, simula ions o li e decomposi ion p ocess and da a
analysis10
In he model Yasso07, esh o ganic ma e in lea , ine oo , and woody li e is di ided
in o ou chemically dis inguishable compound g oups: acid-hyd olysable compounds
(A), wa e -soluble compounds (W), e hanol-soluble compounds (E), nei he soluble,
no hyd olysable compounds (N) ha decompose a hei unique a es (Tuomi e al.,
2009). In addi ion, he e is a humus (H) ac ion, assumed o consis o mo e ecalci an 15
compounds, ha ecei es a pa o p oduc s esul ing om he decomposi ion o A, W,
E, N (Fig. 2). The decay a es (as measu e o mic obial ac i i y) o he compound
g oups depend on he clima ic condi ions desc ibed by empe a u e and p ecipi a ion
(Meen emeye , 1978; Be g e al., 1993; Ae s, 1997; Liski e al., 2003; Pa on e al.,
2007). The decomposi ion o compound g oups esul s in mass loss om he sys em20
and in mass lows be ween he compound g oups. The mass loss consis s o emo al
om he soil as he e o ophic espi a ion (CO2) and leaching while he emaining mass
o ms mo e ecalci an compounds, o example humus.
Ma hema ically, Yasso07 is a linea compa men al sys em, a se o i s o de di e -
en ial equa ions (Tuomi e al., 2011b):25
˙
x( )=A(C)x( )+b( )−ωiIPa,x(0) =x0(1)
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whe e x=(xA,xW,xE,xN,xH)Tis a ec o desc ibing he masses o he i e compa -
men s as a unc ion o ime ( ); A(C) is a ma ix desc ibing he decomposi ion a es and
he mass lows be ween he compa men s as a unc ion o clima ic condi ions (C); ec-
o b( ) is he li e inpu o he soil; ωia e ee pa ame e s desc ibing he p ecipi a ion
induced leaching a es; I=(1,1,1,1,1)Tis a cons an column ec o ; Pais he annual5
p ecipi a ion. Vec o x0=(xA,0,xW,0,xE,0,xN,0,xH,0) desc ibes he ini ial chemical com-
posi ion s a e o he sys em. Ma ix Ais de ined as a p oduc o he mass low ma ix
Apand he diagonal decomposi ion coe icien ma ix k(C)=diag(kA,kW,kE,kN,kH)(C),
whe e kia e he decomposi ion a e coe icien s o he compa men s (Tuomi e al.,
2009).10
Ap=






−1p1p2p30
p4−1p5p60
p7p8−1p90
p10 p11 p12 −1 0
pHpHpHpH−1






whe e pi∈[0,1] a e ela i e mass low pa ame e s be ween he compa men s.
p1:. ela i e mass low magni ude, W →A; p2: ela i e mass low magni ude, E →A;
p3:. ela i e mass low magni ude, N →A; p4: ela i e mass low magni ude, A →W;
p5:. ela i e mass low magni ude, E →W; p6: ela i e mass low magni ude, N →W;15
p7:. ela i e mass low magni ude, A →E; p8: ela i e mass low magni ude, W →E;
p9:. ela i e mass low magni ude, N →E; p10: ela i e mass low magni ude, A →N;
p11:. ela i e mass low magni ude, W →N; p12: ela i e mass low magni ude, E →N;
pH:. mass low o humus.
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The clima e dependence o he decomposi ion a e ac o s ki o mula ed in Eq. (2)
was jus i ied ea lie by Tuomi e al. (2009):
ki(C)=αiexpβ1T+β2T2(1 −expγPa) (2)
whe e Tis empe a u e (Celsius scale), Pa: annual p ecipi a ion, αi: decomposi ion
a e pa ame e , β1and β2: empe a u e dependence pa ame e s, γ: p ecipi a ion de-5
pendence pa ame e . αi,β1,β2, and γa e ee pa ame e s.
The s uc u e and ma hema ical o mulas o Yasso07 a e desc ibed in mo e de ail in
p e ious publica ions (Tuomi e al., 2009, 2011a).
The da a needed o un he model Yasso07 include: li e amoun , li e quali y (dis-
ibu ion o li e be ween A, W, E, N) oge he wi h unce ain y da a (exp essed as10
s anda d de ia ions) and clima ic da a ( empe a u e and p ecipi a ion).
The simula ion was conduc ed on each indi idual s udied li e species. An ini ial
mass o li e wi h i s chemical composi ion (Figs. 3–7) and clima ic da a (Table 1) we e
used as inpu s in o he dynamic soil ca bon model Yasso07. The p edic ions o Yasso07
we e compa ed wi h he obse a ions on change in mass, and change in chemical15
composi ion. Then, Yasso07 was i ed o a da ase whe e new da a om Benin we e
me ged wi h a global da a ( om Eu ope; Be g e al., 1991a,b, 1993, No he n and
Cen al Ame ica, Gholz e al., 2000; T o ymow e al., 1998). Also, Yasso07 was i ed
only o he new expe imen al da a om Benin. This esul ed in wo new e sions o
he Yasso07: Y07A o e e o Yasso07 i ed o he da ase including global and Benin20
da a, and Y07B o e e o Yasso07 i ed only o new da a om Benin. The p edic ions
o hese wo e sions we e compa ed wi h he obse a ions using mean esiduals and
s anda d de ia ions he eo .
When analysing he da a, he Bayesian in e ence o in o ma ion om he measu e-
men s o he pa ame e alues (see o example, Ellison, 2004) was used. Following he25
me hod o Tuomi e al. (2009, 2011a), he Ma ko chain Mon e Ca lo (MCMC) pos e io
sampling echnique was used in da a analyses. The eason o selec ing his me hod
was i s abili y o p oduce a sample om he pos e io p obabili y densi y o he model
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Table 1. Mon hly clima ic da a eco ded du ing he li e bag expe imen in 2010 by he me e-
o ological s a ions Bohicon ( o empe a u e) and To o ( o p ecipi a ion) closes o he Lama
o es .
Mon h Tempe a u e P ecipi a ion
(◦C) (mm)
Feb 31.4 80.1
Ma 30.6 192.4
Ap 30.2 100.3
May 29.0 157.1
Jun 28.1 90.1
Jul 26.6 149.0
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Table 2. Pa ame e alues o he o iginal calib a ion o Yasso07 and o he pa ame e iza ion o
Yasso07 using only da a om Benin and he ea e all da a (global da a and da a om Benin
oge he ).
Pa ame e Uni Benin da a All da a O iginal calib a ion∗
In e p e a ion
MAP 95 % CI MAP 95 % CI MAP 95 % CI
αAy −13.97 ±0.74 0.39 ±0.03 0.72 ±0.09 d a e o A
αWy −120.55 ±3.10 4.54 ±0.30 5.9 ±0.8 d a e o W
αEy −117.00 ±3.50 0.34 ±0.04 0.28 +0.07, −0.04 d a e o E
αNy −13.57 ±0.50 0.13 ±0.02 0.031 +0.011, −0.004 d a e o N
p1– 0.02 ±0.02 0.00 +0.01, −0.00 0.48 ±0.06 m low, W →A
p2– 0.01 +0.04, −0.01 0.01 ±0.01 0.01 +0.15, −0.01 m low, E →A
p3– 0.79 ±0.33 0.87 ±0.03 0.83 +0.16, −0.23 m low, N →A
p4– 0.71 ±0.15 0.99 ±0.01 0.99 +0.01, −0.05 m low, A →W
p5– 0.05 ±0.05 0.05 +0.01, −0.00 0.00 +0.08, −0.00 m low, E →W
p6– 0.04 +0.16, −0.04 0.00 +0.01, −0.00 0.01 +0.20, −0.01 m low, N →W
p7– 0.05 ±0.05 0.00 +0.01, −0.00 0.00 +0.01, −0.00 m low, A →E
p8– 0.06 +0.07, −0.06 0.00 +0.01, −0.00 0.00 +0.01, −0.00 m low, W →E
p9– 0.13 ±0.08 0.133 ±0.03 0.02 +0.23, −0.02 m low, N →E
p10 – 0.01 +0.04, −0.01 0.01 ±0.01 0.00 +0.01, −0.00 m low, A →N
p11 – 0.02 +0.05, −0.02 0.19 ±0.01 0.02 ±0.02 m low, W →N
p12 – 0.88 ±0.11 0.44 ±0.01 0.95 +0.05, −0.16 m low, E →N
β110−2◦C−10.087 +0.01, −0.00 0.069 ±0.01 0.095 ±0.02 Tdependence
β210−3◦C−2−0.0029 +0.01, −0.00 −0.00050 0.001 −0.0014 +0.0006, −0.0009 Tdependence
γm−1−2.500 ±0.05 −0.939 ±0.09 −1.21 ±0.14 Pdependence
ωEy −1m−1– 0.005 −0.2008 ±0.01 −0.151 ±0.008 Pleaching Eu ope
ωAy −1m−1–+0.01, −0.00 −0.0006 ±0.01 0.000 +0.0, −0.002 Pleaching Ame ica
ωBy −1m−1−0.061 ±0.19 −0.943 ±0.04 – – Pleaching Benin
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Figu e 1: Loca ion o he s udy a ea in Benin
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Fig. 1. Loca ion o he s udy a ea in Benin.
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Soil ca bon
modeling in opical
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G. H. S. Guendehou e al.
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Figu e 2: Flow diag am o he model Yasso07 and he ela i e magni udes o each mass low be ween 615
labile compound g oups o o ganic ca bon and mo e ecalci an humus; acid-hyd olysable (A), wa e -616
soluble (W), e hanol-soluble (E), and compounds nei he soluble no hyd olysable (N). The ca bon lows 617
whose magni udes di e s a is ically (95% con idence) om ze o (solid a ows) be ween and ou o he 618
A, W, E, and N ac ions (squa e boxes); he small lows (do ed a ows) in o humus (bo om box), each 619
app oxima ely 0.5%; and he mass lows (dashed a ows) whose maximum a pos e io i (MAP) es ima es 620
we e indis inguishable om ze o bu whose 95% Bayesian con idence in e al was b oade han 0.05 621
(Tuomi e al. 2011b). 622
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Fig. 2. Flow diag am o he model Yasso07 and he ela i e magni udes o each mass
low be ween labile compound g oups o o ganic ca bon and mo e ecalci an humus; acid-
hyd olysable (A), wa e -soluble (W), e hanol-soluble (E), and compounds nei he soluble no
hyd olysable (N). The ca bon lows whose magni udes di e s a is ically (95 % con idence) om
ze o (solid a ows) be ween and ou o he A, W, E, and N ac ions (squa e boxes); he small
lows (do ed a ows) in o humus (bo om box), each app oxima ely 0.5 %; and he mass lows
(dashed a ows) whose maximum a pos e io i (MAP) es ima es we e indis inguishable om
ze o bu whose 95 % Bayesian con idence in e al was b oade han 0.05 (Tuomi e al., 2011b).
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