modelling the genesis of equatorial podzols: age and implications … · 2020. 1. 22. · 2012;...

Biogeosciences 14 2429ndash2440 2017wwwbiogeosciencesnet1424292017doi105194bg-14-2429-2017copy Author(s) 2017 CC Attribution 30 License

Modelling the genesis of equatorial podzols age andimplications for carbon fluxesCeacutedric Doupoux1 Patricia Merdy1 Ceacutelia Reacutegina Montes2 Naoise Nunan3 Adolpho Joseacute Melfi4Osvaldo Joseacute Ribeiro Pereira2 and Yves Lucas1

1Universiteacute de Toulon PROTEE Laboratory EA 3819 CS 60584 83041 Toulon Cedex 9 France2University of Satildeo Paulo NUPEGEL CENA Av Centenaacuterio 303 CEP 13416-903 Piracicaba SP Brazil3CNRS iEES Paris 78850 Thiverval-Grignon France4University of Satildeo Paulo IEE ESALQ Satildeo Paulo SP Brazil

Correspondence to Ceacutedric Doupoux (cedricdoupouxgmailcom)

Received 14 December 2016 ndash Discussion started 18 January 2017Revised 5 April 2017 ndash Accepted 11 April 2017 ndash Published 12 May 2017

Abstract Amazonian podzols store huge amounts of carbonand play a key role in transferring organic matter to the Ama-zon River In order to better understand their C dynamics wemodelled the formation of representative Amazonian pod-zol profiles by constraining both total carbon and radiocar-bon We determined the relationships between total carbonand radiocarbon in organic C pools numerically by settingconstant C and 14C inputs over time The model was an ef-fective tool for determining the order of magnitude of thecarbon fluxes and the time of genesis of the main carbon-containing horizons ie the topsoil and deep Bh We per-formed retrocalculations to take into account the bomb car-bon in the young topsoil horizons (calculated apparent 14Cage from 62 to 109 years) We modelled four profiles repre-sentative of Amazonian podzols two profiles with an old Bh(calculated apparent 14C age 68times 103 and 84times 103 years)and two profiles with a very old Bh (calculated apparent 14Cage 232times 103 and 251times 103 years) The calculated fluxesfrom the topsoil to the perched water table indicate that themost waterlogged zones of the podzolized areas are the mainsource of dissolved organic matter found in the river net-work It was necessary to consider two Bh carbon pools toaccurately represent the carbon fluxes leaving the Bh as ob-served in previous studies We found that the genesis timeof the studied soils was necessarily longer than 15times 103 and130times 103 years for the two younger and two older Bhs re-spectively and that the genesis time calculated consideringthe more likely settings runs to around 15times 103ndash25times 103

and 150times 103ndash250times 103 years respectively

1 Introduction

Podzols are soils characterized by the formation of a sandybleached horizon (E horizon) overlying a dark horizon withilluviated organic matter as well as Fe and Al compounds(spodic or Bh horizon) In wet tropical areas podzols can bevery deep with E horizons thicker than 10 m and Bh hori-zons thicker than 4 m (Chauvel et al 1987 Dubroeucq andVolkoff 1998 Montes et al 2011) This means that they canstore huge quantities of organic matter Montes et al (2011)estimated the C stocks in Amazonian podzols to be around136 Pg C

This C constitutes a non-negligible portion of the C storedin the Amazonian basin Indeed the carbon stored in theaboveground live biomass of intact Amazonian rainforestsis estimated to be 93plusmn 23 Pg C (Malhi et al 2006) Suchlarge amounts of carbon may play a central role in the globalcarbon balance (Raymond 2005) which raises the questionof the magnitude of the carbon fluxes during podzol genesisand in response to drier periods that might occur in the fu-ture due to climate change A schematic of the main carbonfluxes in Amazonian podzols (Leenheer 1980 Lucas et al2012 Montes et al 2011) is presented in Fig 1 It shouldbe noted that the organic matter (OM) released by the topsoilhorizons can be transferred downwards to the Bh horizonsbut may also be rapidly transferred laterally to the river net-work via a perched water table on top of the Bh that circulatesin the E horizon The OM stored in the upper part of the Bhcan also be remobilized and be transferred to the river net-work by the perched water table Some of these fluxes have

Published by Copernicus Publications on behalf of the European Geosciences Union

2430 C Doupoux et al Modelling the genesis of equatorial podzols

Figure 1 Schematic of the main C fluxes in a podzol

been estimated in a small number of case studies or extrap-olated from studies of the chemistry of large rivers (Tardyet al 2009) but most of them remain unknown Studiesmeasuring carbon budgets at the profile scale or during soilprofile genesis in temperate boreal or tropical podzols arerare (Schaetzl and Rothstein 2016 Van Hees et al 2008)Schwartz (1988) studied giant podzol profiles in the Congothat began to form 40times 103 years ago but where carbon accu-mulation in Bh was discontinuous because of a drier climatebetween 30 and 12 kyr BP The 14C age of organic C fromthe Bh horizon of podzol profiles situated in the Manaus re-gion (Brazil) was found to range from 1960 to 2810 yearsand it was concluded that the podzols developed in less than3times 103 years (Horbe et al 2004) As pointed out by Sierraet al (2013) in order to corroborate this conclusion it is nec-essary to produce a model that accounts for C additions andlosses over time Montes et al (2011) roughly estimated theC flux to the Bh horizon to be 168 gC mminus2 yearminus1 Sierra etal (2013) used a compartment model that was constrained by14C dating to estimate the carbon fluxes in a Colombian shal-low podzol (Bh upper limit at 09 m) They showed that the Cfluxes from topsoil horizons to the Bh horizon were smaller(21 gC mminus2 yearminus1) than the fluxes estimated in Montes etal (2011) However they did not account for the age andgenesis time of the Bh horizon

In order to better understand the fluxes of C in Amazonianpodzols and in particular to determine the rate of carbon ac-cumulation in Bh horizons during podzol genesis the size ofthe C fluxes to rivers via both the perched and deep water ta-bles and the vulnerability of the podzol C stocks to potentialchanges in the moisture regime due to global climate changefour representative podzol profiles from the high Rio Negrobasin were used to constrain a model of C fluxes The highRio Negro basin was chosen because it is a region that hasthe highest occurrence of podzol in the Amazon (Montes et

al 2011) (Fig 2) The four representative profiles were se-lected from a database of 80 podzol profiles issued from 11test areas which have been studied in detail and of which 11have been dated this database will be the subject of a furtherpublication The four profiles were used to constrain the sim-ulations of C fluxes We used a system dynamics modellingsoftware package (Vensim) to simulate the formation of rep-resentative Amazonian podzol profiles by constraining bothtotal carbon and radiocarbon with the data collected

2 Methods

21 Podzol profiles and carbon analysis

Four podzol profiles were selected from our database as rep-resentative both from the point of view of the profile charac-teristics and the 14C age of the Bh organic matter (Table 1and Fig 3) The MAR9 profile was developed on the Icaacutesedimentary formation and has a waterlogged A horizon athin eluvial (E) horizon a sandy-clay loam Bh with youngorganic matter (OM) and a low C content the DPQT pro-file was developed on a late Quaternary continental sedimentyounger than the Iccedilaacute formation and has an E horizon of in-termediate thickness a sandy Bh with young OM and a lowC content the UAU4 profile was developed on the Icaacute sed-imentary formation has a thick E horizon and a sandy Bhwith old OM and the C content is high the P7C profile wasdeveloped on crystalline basement rock and has a thick wa-terlogged O horizon an E horizon of intermediate thicknessa silt-loam Bh with old OM and a high C content It shouldbe noted that in the cases of the DPQT and UAU4 profilesthe lower limit of the Bh was not reached because the augerhole collapsed meaning that for these profiles the Bh C stockis an underestimate

Soil samples were analysed for C content with a TOC-LCPN SSM-5000A Total Organic Carbon Analyzer (Shi-madzu) Radiocarbon measurements were carried out at thePoznan Radiocarbon Laboratory Poland We assumed thatthe proportion of bomb carbon in the Bh organic matter wasnegligible and calculated a conventional uncalibrated agefrom the radiocarbon pMC (percent modern carbon) valueAs the Bh organic matter is an open system mixing organiccarbon of different ages this age is an apparent age Sam-ples from the topsoil had a pMC higher than 100 whichindicates that a significant part of the carbon in the topsoil ispost-bomb and therefore should not be neglected Assumingthat the topsoil horizons reached a steady state before 1950we retrocalculated the pre-1950 pMC value of these samplesusing a dedicated model described in Sect 22

The data given in Table 1 were calculated by linear ex-trapolation of values measured on samples taken at differentdepths between 11 and 28 samples per profile were used forthe C stocksrsquo calculation and between 6 and 8 samples perprofile were used for radiocarbon measurements

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C Doupoux et al Modelling the genesis of equatorial podzols 2431

Table 1 The main characteristics of the podzol profiles used in the study C stock and ages are given plusmn error Fat and FaBh measuredmodern fraction of topsoil and Bh organic matter respectively Apparent 14C ages of OM were calculated assuming Libbyrsquos half-life (aftercorrection for bomb carbon for the topsoil horizons as explained hereafter)

Profile identification MAR9 DPQT UAU4 P7C

GPS coordinates 0049prime486primeprime S 0015prime240primeprime N 0010prime112primeprime N 0036prime426primeprime S6724prime251primeprimeW 6246prime254primeprimeW 6748prime563primeprimeW 6654prime006primeprimeW

Depth of the EndashBh transition (m) 075 16 66 15

Topsoil horizons

C stock (gC mminus2) 17 722plusmn 886 8056plusmn 403 7519plusmn 376 74 129plusmn 3706Fat 11124plusmn 00036 10797plusmn 00034 11094plusmn 00036 10921plusmn 00035Apparent 14C age of OM (year) 62plusmn 25 108plusmn 27 65plusmn 25 109plusmn 29

Bh horizons

Texture Sandy-clay loam Sandy Sandy Silt loamC stock (gC mminus2) 55 644plusmn 2782 53 180plusmn 2659 107 813plusmn 5391 158 465plusmn 7923FaBh 04315plusmn 00021 03496plusmn 00016 00557plusmn 00013 00440plusmn 00007Apparent 14C age of OM (year) 6751plusmn 42 8442plusmn 37 23 193plusmn 207 25 096plusmn 134

Figure 2 Location of the studied profiles Grey areas in the detailed map indicate hydromorphic podzol areas Orange spots identify testareas

22 Model design

We used an approach comparable to previous studies whichdealt with carbon budgets and radiocarbon data (eg Bais-den et al 2002 Menichetti et al 2016 Sierra et al 20132014 Tipping et al 2012) The model structure based onthe schematic shown in Fig 1 and the names of compart-ments and rate constants are given in Fig 4 As the turnovertime of the OM in the topsoil horizons is short relative to theaverage OM turnover time in the Bh only one topsoil carbonpool was used whereas two pools (fast and slow) were usedto describe organic carbon dynamics in the Bh horizon TheC can leave the topsoil pool by mineralization transfer to theBh pools or via the river by the perched water table it canleave the Bh pools by mineralization transfer to the river bythe perched water table or via the deep water table We choseto neglect the flux of C from the fast Bh pool to the slow

Bh pool in order to facilitate the numerical resolution of thesystem comprising equations describing both the carbon andradiocarbon contents

The equations describing changes in the carbon content ofthe different pools are presented below (see Fig 4 to see thefluxes with which each rate constant is associated)

dCt

dt= CIminus (kt+αt-fBh+αt-sBh+αt-r)Ct (1)

dCfBh

dt= αt-fBhCtminus (kfBh+αfBh-r+αfBh-d)CfBh (2)

dCsBh

dt= αt-sBhCtminus (ksBh+αsBh-r+αsBh-d)CsBh (3)

where CI is the C input from litter and roots into the topsoilC pool Ct the amount of C stored in the topsoil C pool CfBhand CsBh the amount of C stored in the fast and slow BhC pools respectively kt kfBh and ksBh the C mineralization

wwwbiogeosciencesnet1424292017 Biogeosciences 14 2429ndash2440 2017


Figure 3 Sketch of the studied profiles

rate constants in the topsoil and the fast Bh and slow BhC pools respectively αt-fBh and αt-sBh the transfer rates fromthe topsoil pool to the fast and slow Bh C pools respectivelyαt-r αfBh-r and αsBh-r the transfer rates from respectively thetopsoil and the fast Bh and slow Bh pools to the river by theperched water table and αfBh-d and αsBh-d the transfer ratesfrom the fast Bh and slow Bh pools to the deep water tablerespectively

The equations describing changes in the radiocarbon con-tent of the different pools are the following

dFatCt

dt= CIFav minus (kt+αt-fBh+αt-sBh+αt-r)FatCt (4)

minus λFatCt

dFafBhCfBh

dt= αt-fBhFatCtminus (kfBh+αfBh-r (5)

+αfBh-d)FafBhCfBhminus λFafBhCfBh

dFasBhCsBh

dt= αt-sBhFatCtminus (ksBh+αsBh-r (6)

+αsBh-d)FasBhCsBhminus λFasBhCsBh

where λ is the 14C radioactive decay constant Fav the radio-carbon fraction in the organic matter entering the topsoil Cpool and Fai the radiocarbon fraction in each pool i the ra-diocarbon fractions being expressed as absolute modern frac-tion ie the 14C 12C ratio of the sample normalized for 13Cfractionation to the oxalic acid standard 14C 12C normal-ized for 13C fractionation and for radio decay at the year ofmeasurement (Stuiver and Polach 1977)

Figure 4 Model design

With regard to the apparent age of the topsoil organic mat-ter enriched in post-bomb carbon we considered a singlepool that reached a steady state before 1955 (Fig 5) whichallowed the retrocalculation of the radiocarbon fraction Fatin 1955 based on the following equation

CtFati+1 = CtFati minus λCtFati +(Favi minusFati

)CIhArr Fati (7)

=CtFati+1 minusCIFavi

Ctminus λCt+CI

where Fati and Fati+1 are the radiocarbon fractions of the top-soil C pool in years i and i+1 respectively and Favi the ra-diocarbon fraction in the organic matter entering the topsoilC pool in year i Starting from the Fat2015 value (value at theyear of measurement) the Fat1955 value (pre-bomb value) iscalculated by successive iterations giving an expression as afunction of CI which is then computed by approximation tosatisfy the steady-state condition We used the troposphericD14CO2 record from 1955 to 2011 at Wellington (NIWA2016) to estimate the annual value of Favi

An underlying assumption of this work is that soil forma-tion processes remained constant over time An alternativeassumption might be for example that all the Bh organicmatter had accumulated in a very short time after whichthe Bh was no longer subjected to external exchanges Thisscenario could also produce profile ages close to the ob-served 14C profile ages Such a case however is unlikelyThe climate of the high Rio Negro region is likely to haveremained humid and forested since the Pliocene althoughless humid episodes may have occurred during the Holoceneglacial episodes (Colinvaux and De Oliveira 2001 Van derHammen and Hooghiemstra 2000) It is also possible thatthe rate at which soil formation proceeded decelerated overtime This will be commented on below



Figure 5 Evolution of the 14C pool in a topsoil that reached a steady state before 1955

23 Model running and tuning

We used the Vensimreg Pro (Ventana Systems inc) dynamicmodelling software to simulate the C dynamics After settingthe initial values for C pools the model was run in the op-timize mode leaving the model to adjust the rate constantsin order to minimize the difference between simulated andmeasured C pool values and ages However frequently themodel did not converge when run in this way We found thatit was because of the great difference between the conver-gence times between the topsoil C pool and the slow Bh Cpool The long times required to model the genesis of theBh horizons resulted in numerical errors when modelling thetopsoil behaviour because the values of exponential expo-nents exceeded the maximum values that the computer couldhandle (see for example Eq 12 below) To circumvent thistechnical problem we optimized the model separately for thetopsoils and for the Bh horizons and we found that at thetimescale of the formation of Bh the topsoil C pool and thetopsoil C fluxes to river and Bh horizons could be consideredconstant

Although the model structure in Fig 4 contains two Cpools in the Bh horizon we calculated the numerical solu-tions of equations considering both carbon budget and radio-carbon age for a single-pool Bh in order to determine whetherthe model could be simplified Furthermore this approachallowed us to better assess the weight of the different rateconstants in the long-term behaviour of a given pool Thecalculation in the simplified configuration is shown in Fig 6

In this configuration the carbon content of the pool isgiven by

dCBh

dt= αt-BhCtminusβBhCBh (8)

where Ct is the amount of C stored in the topsoil pool αt-sBhthe transfer rates from the topsoil pool to the Bh pool CBhthe amount of C stored in the Bh pool and βBh the transferrate of C leaving the Bh pool The solution of this equation

Figure 6 Simplified design for one pool

with the initial condition CBh = C0Bh when t = 0 is

CBh =αtminusBhCt

βBh+

(C0Bhminus

αt-BhCt

βBh

)eminusβBht (9)

The equation related to radiocarbon content is the following

dFaBhCBh

dt= αt-BhCtFatminus (βBh+ λ)FaBhCBh (10)

where FaBh is the radiocarbon fraction in the BhConsidering that the C input from the topsoil to the Bh and

its radiocarbon fraction are constant with time it comes fromthe two previous equations

dFaBhdt= (11)

βBhαt-BhCtFa t minusFa Bh(βBhαt-BhCt + λ

(αtminusBhCt minus (αt-BhCt minusβBhC0Bh)e

minusβBh t))

αt-BhCt minus (αt-BhCt minusβBhC0Bh)eminusβBh t

The analytical solution of this equation with the initial con-dition FaBh = Fat when t = 0 is

FaBh = (12)

βBhFateminusλt

(βBhC0 Bh+αt-BhCt

(e(βBh+λ)t minus 1

)+ λC0Bh

)(βBh+ λ)

(βBhC0 Bh+αt-BhCt

(eβBht minus 1

))



Figure 7 Single-pool modelling of CBh of the P7C profile C0Bhset to 0

3 Results and discussion

31 Modelling the formation of a single-pool Bh

This section presents conceptual results on the basis of thesimplified diagram given in Fig 6 and in which the flux leav-ing the Bh is described by a single rate βBh This single raterepresents loss from the pool through the mineralization oforganic carbon through lateral flow in the perched water ta-ble to the river and through percolation of dissolved organiccarbon (DOC) to the deep water table

311 Obtaining the carbon stock

Unsurprisingly the greater the difference between input andoutput C fluxes the faster a given CBh stock is reached Witha constant input flux and a constant output rate the outputflux progressively increases with time becauseCBh increasesuntil the input and output fluxes become equal after whichthe CBh reaches a steady state

When the model is constrained only by the measuredvalues of C stocks a number of solutions are possible(Fig 7) The example given in Fig 7 is based on datafrom the P7C profile (Table 1) Curves 1 and 2 describethe evolution of CBh with time when the βBh rate is con-strained to reach a steady state for the currently observed Cstock (158 465 gC mminus2) The input flux was set at 21 and168 g mminus2 yearminus1 for curves 1 and 2 respectively valuesproposed by Montes et al (2011) and Sierra et al (2013) re-spectively The resulting constrained values of αt - Bh and βBhrates are given in the figure The times required to reach 99 of the steady-state values are 43times 103 and 345times 103 yearsfor curves 1 and 2 respectively We used here and thereafteran arbitrary 99 threshold because as shown in Fig 8 thisvalue gives a result sufficiently close to the horizontal asymp-tote to give a reasonable evaluation of the time necessary toreach a steady state

The currently observed C stock can be reached in a shortertime however if for a given input flux the value of βBhis reduced below the value needed to obtain the currently

Figure 8 Single-pool modelling of both CBh and Bh 14C age of theP7C profile Corresponding values of C input fluxes and βBh ratesare given in Table 2

observed C stock at a steady state An example is givenby curve 3 the input flux is set at 21 g mminus2 yearminus1 as forcurve 1 but the βBh rate is reduced by 1 order of magni-tude In such a case it would require 78times 103 years to ob-tain the currently observed C stock A value of βBh set to 0gives the minimum time required to obtain the carbon stock(50times 103 years if the input flux is set to 21 g mminus2 yearminus1)

312 Obtaining both carbon stock and 14C age

When the model was constrained by both carbon stock and14C age then a unique solution for reaching the steady statewas obtained This is shown for the P7C profile in Fig 8(solid lines) where 99 of the measured values of CBh andapparent 14C age (158 465 gC mminus2 and 25 096 years respec-tively) were obtained in approximately 590times 103 years car-bon input fluxes to the Bh and βBh rate were constrained tovery low values 095 g m2 year1 and 59times 10minus6 yearminus1 re-spectively Note that for higher values of the βBh rate therewas no solution because the 14C age could never be reached

The simulation of the minimum time required for the ob-served carbon stock and 14C age to be reached is also shownin Fig 8 (dashed lines) This simulation was obtained by ad-justing the input rate with an output flux close to 0 but differ-ent from zero for numerical reasons We used βBh = 10minus10

after checking that the difference between the minimum timeobtained using βBh = 10minus10 and βBh = 10minus20 was negligible(lower than 00005 )

The minimum time required for the C stock and 14C ageto be reached and the time required to reach 99 of the Cstock and 14C age at a steady state are given along with theassociated C input fluxes and βBh rates in Table 2 for eachof the studied profiles Under each of the conditions the timerequired is an exponential function of the apparent 14C ageof the Bh (Fig 9)



Table 2 Results of simulation for a single-pool Bh minimum genesis time and time to steady state

MAR9 DPQT UAU4 P7C

Bh apparent 14C age (year) 6751 8442 23 193 25 096Corresponding FaBh value 04315 03496 00557 00440Ct (gC mminus2) 17 722 8056 7519 74 129Fat value of the C input 09923 09866 09919 09865

Minimum time required for obtaining C stock and 14C age (βBh = 10minus10)

Time (year) 15 929 21 011 143 000 180 100αt-Bh rate (yearminus1) 197times 10minus4 314times 10minus4 100times 10minus4 119times 10minus5

Input C flux (gC mminus2 yearminus1) 349 253 075 088

Time required to reach 99 of the steady-state value


Input C flux (gC mminus2 yearminus1) 536 363 080 092βBh rate (yearminus1) 956times 10minus5 683times 10minus5 741times 10minus6 581times 10minus6

Mean residence time at steady state (year) 10 381 14 451 128 349 166 805

Figure 9 Relationship between the 14C age of the Bh and the timeneeded to form the Bh (single-pool modelling)

Taking into account the maximum absolute error does notsignificantly change the simulation results the maximum ab-solute error in the genesis times is lower than 10 09 35 and29 for MAR9 DPQT UAU4 and P7C respectively Sincesuch percentages do not alter the orders of magnitude andtrends discussed below the error will not be considered inthe following

The time taken for the Bh horizon of a given profile toform is likely between the two values shown in Table 2 andFig 9 The minimum time required for obtaining C stockand 14C age is an absolute minimum which assumes that theC output from the Bh was zero which is not likely On theother hand there is no evidence that a steady state has beenreached especially in the case of the two youngest profiles(MAR9 and DPQT) Consequently the time taken for theformation of the Bh horizons is very likely comprised be-tween 15times103 and 65times103 years for the two youngest pro-

files and between 140times 103 and 600times 103 years for the twooldest durations compatible with rough estimates given inDu Gardin (2015) These results also show that the input Cfluxes to the Bh and correspondingly the output C fluxes are3 to 5 times higher for younger than for older profiles andthat the older profiles would have an output rate of 1 order ofmagnitude lower than the younger profiles It is not immedi-ately clear why such large differences would exist Previousstudies have shown (1) that a part of the accumulated Bh OMis remobilized and exported towards the river network (Bardyet al 2011) and (2) that the water percolating from the Bhto deeper horizon OM contains significant amounts of DOCeven in older profiles (around 2 mg Lminus1 Lucas et al 2012)These observations are not consistent with the obtained verylow βBh rates which give input and output C fluxes lowerthan 1 gC m2 yearminus1 for profiles UAU4 and P7C This sug-gests that a single Bh C pool is incorrect and that two poolsof Bh C are required to adequately represent Bh C dynamics

32 Modelling the formation of the whole profile with atwo-pool Bh

321 Topsoil horizons

As explained in Sect 23 the topsoil horizons were mod-elled separately because the time needed to reach a steadystate is very much shorter for the topsoil horizons than forthe Bh horizons The steady-state condition was given byβt = CIC

minus1t Observations data were Ct Fa v Fa t and kt

The kt mineralization rate was set to 257times10minus3 yearminus1 fol-lowing preliminary mineralization experiments (unpublisheddata) The optimizing parameter was βt and a multiple costfunction minimized the differences between modelled and



Table 3 Modelling the topsoil horizons Ct topsoil C stock CI C input flux from roots and litter time to steady state time required to reach99 of the steady-state values for Ct and 14C age βt sum of the output rates (βt = kt+αt-r+αtminus fBh+αt)

MAR 9 DPQT UAU4 P7C

Ct (g mminus2) 17 722 8056 7519 74 129Apparent14C age (year) 62 108 65 109Fat value 09923 09866 09919 09865CI (g mminus2 yearminus2) 286 74 116 676Time to steady state (year) 399 696 420 705βt (yearminus1) 161times 10minus2 923times 10minus3 154times 10minus2 912times 10minus3

Figure 10 Effect of the fast Bh pool size on the whole Bh genesis time and the 14C age of the fast Bh (a) Absolute values (b) valuesexpressed in

observed values for Ct and Fat The model outputs for thetopsoil horizons of the studied profiles are given in Table 3

The results suggest that the topsoil OM in the four profilesneeded only between 400 and 700 years to reach a steadystate if the present-day topsoils are indeed in a steady stateThe total C flux through the topsoil (CI) is high for theMAR9 profile (286 g mminus2 yearminus1) and very high for the P7Cprofile (676 g mminus2 yearminus1) in accordance with their hightopsoil C stock (17 722 and 74 129 g mminus2 respectively) andthe very young age of their organic matter Note that thetopsoil OM ages are younger than ages reported by Trum-bore (2000) for boreal temperate or tropical forests Differ-ences between modelled fluxes through the topsoil are con-sistent with the field observations the lowest fluxes (UAU4and DPQT) correspond to well-drained topsoil horizonswith a relatively thin type Mor A horizon when the highestfluxes (P7C) correspond to a podzol having a thick O horizonin a very hydromorphic area The MAR9 profile is interme-diate It should be noted that the flux through the P7C topsoilwould be more than 15 times higher than the commonly ac-

cepted value for the C annually recycled by the abovegroundlitter in equatorial forests (around 425 gC mminus2 yearminus1 ndash Wan-ner 1970 Cornu et al 1997 Proctor 2013) indicating astrong contribution of the belowground litter (root litter)

322 Bh horizons

The partitioning of the C flux leaving the topsoil between theriver (rate αt-r) the fast pool of the Bh (rate αt-fBh) and theslow pool of the Bh (rate αt-sBh) is unknown This is alsothe case for the partitioning of the C flux from the Bh poolsbetween the river (rates αfBh-r and αsBh-r) and the deep hori-zons (rates αfBh-d and αsBh-d) Consequently the system isnot sufficiently constrained with the 14C age of the bulk Bhand there is an infinity of solutions for modelling the Bh for-mation

We therefore carried out a sensitivity analysis to determinehow the main parameters (size of the fast pool of the BhC flux input and output C rates for the Bh pools) affectedthe profile genesis time and to understand the relationshipsbetween these parameters



Figure 11 Effect of constraining the output C fluxes from the Bh on the genesis time UAU4 effect of the fast Bh output flux MAR9 andP7C effect of the slow Bh output flux

Sensitivity to the size of the fast Bh pool Fig 10 showssimulation results with an output C flux from Bh set to be2 g mminus2 yearminus1 at the end of the genesis time and with valuesfor CfBh ranging from 25times 103 to 40times 103 g mminus2 through5times 103 10times 103 and 20times 103 In most configurations thepresence of a fast pool in the Bh extends the time takenfor the whole Bh genesis relative to a single-pool Bh Thislengthening of the genesis time increases as a function of the14C age of the whole Bh and as a function of the size of thefast Bh pool (CfBh) A size of the fast Bh pool set to 5 of the whole Bh stock would give a low estimate of the Bhgenesis time

Sensitivity to the C fluxes leaving the Bh pools the genesistime of the profile lengthens with increasing C flux from thebulk Bh The lengthening of the genesis depends howeveron how the C fluxes leaving the Bh C pools vary and on thesource of the variation (Fig 11) In the situation where thereis a progressive increase in the Bh output beginning from 0and this increase is due to the fast Bh pool the lengthening ofthe genesis time is fast at first and then slows An example isgiven in Fig 11 for the UAU4 profile for two values of CfBhWhen the increase is due to the slow Bh pool the lengtheningof the genesis time is slow at first and then becomes veryhigh An example is given in Fig 11 for the MAR9 and P7Cprofiles respectively

The conclusion of this sensitivity study is that when thesize of the fast Bh pool or the C output fluxes from the Bhpools begins to grow from zero the genesis time of the pro-files increases rapidly by a factor of 5 to 20 for the twoyoungest profiles and 15 to more than 60 for the two old-est profiles

Modelling the formation of the whole profiles observationdata were CBh (sum of CfBh and CsBh) Fa t Fa Bh (Fa valueof the bulk Bh) αt-fBh kfBh ksBh αfBh-d and αsBh-d The fastBh pool was constrained to a steady-state condition The Fa tvalue was given by the topsoil horizon modelling The C fluxfrom topsoil to the fast Bh pool was set at 1 g mminus2 yearminus1 to

get a total C flux from the topsoil to Bh horizons close tothe value obtained by Sierra et al (2013) (21 g mminus2 yearminus1)The size of the present-day observed fast Bh (CfBh) was ar-bitrarily set at 5 of the total Bh (see above) The present-day output flux from Bh to deep horizons was constrainedto 058 and 005 gC mminus2 yearminus1 for the fast and slow Bhpools respectively in order to have a sufficient flux to deephorizon without zeroing the flux from the slow Bh to theriver to account for the export to the river of very humi-fied OM as observed by Bardy et al (2011) As the kfBhand the ksBh mineralization rate had to be set below 1times10minus4

and 1times 10minus6 yearminus1 respectively for solutions to be pos-sible values of 5times 10minus5 and 5times 10minus7 yearminus1 respectivelywere chosen Optimizing parameters were αt-sBh βfBh andβsBh and a multiple cost function minimized the differencesbetween modelled and observed values for CBh and Fa BhResults are shown in Fig 12 and corresponding parametersin Table 4 The resulting present-day instantaneous turnovertimes of C in the whole Bh are 12 940 16 115 67 383 and98 215 gC for profiles MAR9 DPQT UAU4 and P7C re-spectively

33 Age carbon fluxes and carbon turnover

Considering that the forest aboveground litter production isaround 425 gC mminus2 yearminus1 the proportion of the litter above-ground OM produced by the forest transferred to the rivernetwork is 56 12 22 and 114 for profiles MAR9 DPQTUAU4 and P7C respectively The high values for the MAR9and P7C profiles indicate a significant contribution of below-ground litter and indicate how waterlogging of the podzolsurface horizons affects the transfer of carbon from the at-mosphere to dissolved organic carbon

With regard to the Bh horizons it should be noted thatthe total C flux leaving these horizons can be distributed inany manner between mineralization transfer to depth andtransfer to the river However at least two pools are required



Figure 12 Modelled C fluxes 14C ages and C stock in the four studied profiles

for the total C flux leaving the Bh to be sufficiently largeto match the measured values Obtaining the measured oldages requires a long genesis time (around 195times103 years forUAU4 and 274times 103 years for P7C) and very small inputand output carbon fluxes Because younger profiles such asMAR9 and DPQT can form with higher fluxes it is likelythat the flux rates changed during the development of theprofile reducing progressively with time Higher flux ratesduring the earlier periods of profile development howeverwould lengthen the profile genesis time (Fig 11) so thatthe genesis time estimated here for the slow Bh (around17times103 22times103 195times103 and 274times103 for MAR9 DPQTUAU4 and P7C respectively) can be considered a good es-timate of the minimum time required to form the presentlyobserved soils This is especially true for the DPQT andUAU4 profiles as their Bh C stock value is a low estimate(cf Sect 21) Another source of overestimation of the gen-esis time is that to simplify the calculations we have notconsidered changes in atmospheric 14C content over the past50 000 years when it was shown that for most of this pe-

riod conventional ages have to be corrected by more than10 (Reimer et al 2009) The estimated ages are very oldwhen compared to temperate mature podzol that developedin 1times 103ndash6times 103 years (Sauer et al 2007 Scharpenseel1993)

4 Conclusion

Modelling the carbon fluxes by constraining both total car-bon and radiocarbon was an effective tool for determiningthe order of magnitude of the carbon fluxes and the timeof genesis of the different carbon-containing horizons Heremodelling the upper horizons separately was necessary be-cause of numerical constraints due to the great differencesin carbon turnover time between topsoil horizons and BhSteady-state values obtained for the topsoil horizon couldsubsequently be introduced in Bh modelling The approachwe used can be applied to a wide range of situations if neces-sary with simplifying assumptions to sufficiently reduce thedegree of freedom of the system



Table 4 Parameters used for the modelling shown in Fig 12

Rates (yearminus1) MAR9 DPQT UAU4 P7C

βt 161times 10minus2 919times 10minus3 154times 10minus2 912times 10minus3

kt 257times 10minus3 257times 10minus3 257times 10minus3 257times 10minus3

αt-fBh 564times 10minus5 124times 10minus4 133times 10minus4 135times 10minus5

αt-sBh 185times 10minus4 290times 10minus4 861times 10minus5 101times 10minus5

αt-r 133times 10minus2 620times 10minus3 126times 10minus2 653times 10minus3

βfBh 359times 10minus4 376times 10minus4 186times 10minus4 126times 10minus4

kfBh 500times 10minus5 500times 10minus5 500times 10minus5 500times 10minus5

αfBh-r 101times 10minus4 108times 10minus4 279times 10minus5 301times 10minus6

αfBh-d 209times 10minus4 218times 10minus4 108times 10minus4 732times 10minus5

βsBh 200times 10minus6 200times 10minus6 120times 10minus6 157times 10minus6

ksBh 500times 10minus7 500times 10minus7 500times 10minus7 500times 10minus7

αsBh-r 635times 10minus7 886times 10minus7 183times 10minus7 762times 10minus7

αsBh-d 946times 10minus7 990times 10minus7 488times 10minus7 332times 10minus7

The results obtained showed that the organic matter of thepodzol topsoil is very young (14C age from 62 to 109 years)with an annual C turnover ie the carbon flux passing annu-ally through the horizon that increases if the topsoil is hydro-morphic This indicates that the most waterlogged zones ofthe podzolized areas are the main source of dissolved organicmatter to the Amazonian hydrographic network

The model suggests that the Amazonian podzols are ac-cumulating organic C in the Bh horizons at rates rangingfrom 054 to 317 gC mminus2 yearminus1 equivalent to 0005 to0032 tC haminus1 yearminus1 of very stable C Climate models pre-dict changes in precipitation patterns with greater frequencyof dry periods in the Amazon basin (Meehl and Solomon2007) possibly resulting in less frequent waterlogging Thechange in precipitation patterns could have a dramatic effecton the C dynamics of these systems with an increase in themineralization of topsoil OM and an associated reduction inDOC transfer to both the deep Bh and the river network Itmay be noted that a 14C dating of the river DOC would helpto determine the proportion of DOC topsoil origin and of Bhhorizon origin The topsoil horizons reached a steady statein less than 750 years The organic matter in the Bh hori-zons was older (14C age around 7 kyr for the younger profileand 24times 103 years for the older) The study showed that itwas necessary to represent the Bh C with two C pools in or-der to replicate a number of carbon fluxes leaving the Bhhorizons that have been observed in previous studies Thissuggests that the response of the Bh organic C to changesin water regime may be quite complex The formation ofthe slow Bh pool required small input and output C fluxes(lower than 35 and 08 g cmminus2 yearminus1 for the two youngerand two older Bhs respectively) Their genesis time was nec-essarily longer than 15times103 and 130times103 years for the twoyounger and two older Bhs respectively The time neededto reach a steady state is very long (more than 48times 103 and450times103 years respectively) so that a steady state was prob-

ably not reached The genesis time calculated by consideringthe more likely settings runs around 15times 103ndash25times 103 and180times103ndash290times103 years respectively the determination ofthese ages which can be considered as low estimates canhelp to constrain the dating of the sedimentary formations onwhich podzols have developed Finally a greater frequencyof dry periods during the year might also possibly result inan increase in Bh mineralization rates and therefore of CO2degassing from the Bh this question will be the object of afurther publication

Sample availability

IGSN registration numbers of the profiles used in this paperIEYLU0001 IEYLU0002 IEYLU0003 and IEYLU0004

Competing interests The authors declare that they have no conflictof interest

Acknowledgements This work was funded by grants from(1) Brazilian FAPESP (Satildeo Paulo Research Foundation Processnumbers 201103250-2 201251469-6) and CNPq (3034782011-0 3066742014-9) (2) French ARCUS (joint programme ofReacutegion PACA and French Ministry of Foreign Affairs) and(3) French ANR (Agence Nationale de la Recherche processnumber ANR-12-IS06-0002 ldquoC-PROFORrdquo)

Edited by V BrovkinReviewed by two anonymous referees

References

Baisden W T Amundson R Brenner D L Cook A CKendall C and Harden J W A multiisotope C and N mod-eling analysis of soil organic matter turnover and transport



as a function of soil depth in a California annual grasslandsoil chronosequence Global Biogeochem Cy 16 82-1ndash82ndash26doi1010292001GB001823 2002

Bardy M Derenne S Allard T Benedetti M F and Fritsch EPodzolisation and exportation of organic matter in black watersof the Rio Negro (upper Amazon basin Brazil) Biogeochem-istry 106 71ndash88 doi101007s10533-010-9564-9 2011

Chauvel A Lucas Y and Boulet R On the genesis of the soilmantle of the region of Manaus Central Amazonia Brazil Ex-perientia 43 234ndash241 doi101007BF01945546 1987

Colinvaux P A and De Oliveira P E Amazon plant diversity andclimate through the Cenozoic Palaeogeogr Palaeocl 166 51ndash63 doi101016S0031-0182(00)00201-7 2001

Cornu C Luizatildeo F J Rouiller J and Lucas Y Comparativestudy of litter decomposition and mineral element release in twoAmazonian forest ecosystems litter bag experiments Pedobi-ologia 41 456ndash471 1997

Dubroeucq D and Volkoff B From oxisols to spodosols andhistosols Evolution of the soil mantles in the Rio Negrobasin (Amazonia) Catena 32 245ndash280 doi101016S0341-8162(98)00045-9 1998

Du Gardin B Dynamique hydrique et biogeacuteochimique drsquounsol agrave porositeacute bimodale Cas des systegravemes ferralsols-podzolsdrsquoAmazonie Presses Acadeacutemiques Francophones 2015

Horbe A M C Horbe M A and Suguio K Tropical Spodosolsin northeastern Amazonas State Brazil Geoderma 119 55ndash68doi101016S0016-7061(03)00233-7 2004

Leenheer J A Origin and nature of humic substances in the watersin the Amazon river basin Acta Amaz 10 513ndash526 1980

Lucas Y Montes C R Mounier S Loustau Cazalet M IshidaD Achard R Garnier C Coulomb B and Melfi A J Bio-geochemistry of an Amazonian podzol-ferralsol soil system withwhite kaolin Biogeosciences 9 3705ndash3720 doi105194bg-9-3705-2012 2012

Malhi Y Wood D Baker T R Wright J Phillips O LCochrane T Meir P Chave J Almeida S Arroyo LHiguchi N Killeen T J Laurance S G Laurance W FLewis S L Monteagudo A Neill D A Vargas P N PitmanN C A Quesada C A Salomatildeo R Silva J N M LezamaA T Terborgh J Martiacutenez R V and Vinceti B The regionalvariation of aboveground live biomass in old-growth Amazonianforests Glob Change Biol 12 1107ndash1138 doi101111j1365-2486200601120x 2006

Meehl G and Solomon S Climate Change 2007 The PhysicalScience Basis Cambridge University Press 2007

Menichetti L Kaumltterer T and Leifeld J Parametrization conse-quences of constraining soil organic matter models by total car-bon and radiocarbon using long-term field data Biogeosciences13 3003ndash3019 doi105194bg-13-3003-2016 2016

Montes C R Lucas Y Pereira O J R Achard R GrimaldiM and Melfi A J Deep plant-derived carbon storage in Ama-zonian podzols Biogeosciences 8 113ndash120 doi105194bg-8-113-2011 2011

NIWA Data set Natl Inst Water Atmos Res New Zeal availableat httpdsdatajmagojpgmdwdcggpubdatacurrent14co2eventbhd541s00niwaasot14co2nlevdat (last access 5 De-cember 2016) 2016

Proctor J NPP Tropical Forest Gunung Mulu Malaysia 1977ndash1978 R1 Data set Oak Ridge Natl Lab Distrib Act Arch Cen-

ter Oak Ridge Tennessee USA doi103334ORNLDAAC4742013

Raymond P A Carbon cycle the age of the Amazonrsquos breathNature 436 469ndash470 doi101038436469a 2005

Reimer P J Baillie M G L Bard E Bayliss A Beck J WBlackwell P G Bronk Ramsey C Buck C E Burr G SEdwards R L Friedrich M Grootes P M Guilderson T PHajdas I Heaton T J Hogg A G Hughen K A Kaiser KF Kromer B McCormac F G Manning S W Reimer R WRichards D A Southon J R Talamo S Turney C S M vander Plicht J and Weyhenmeyer C E IntCal09 and Marine09radiocarbon age calibration curves 0ndash50000 years cal BP Ra-diocarbon 51 1111ndash1150 doi101017S00338222000342022009

Sauer D Sponagel H Sommer M Giani L Jahn R and StahrK Podzol Soil of the year 2007 A review on its genesis oc-currence and functions J Plant Nutr Soil Sci 170 581ndash597doi101002jpln200700135 2007

Schaetzl R J and Rothstein D E Temporal variation in thestrength of podzolization as indicated by lysimeter data Geo-derma 282 26ndash36 doi101016jgeoderma201607005 2016

Scharpenseel H W Major carbon reservoirs of the pedospheresource ndash sink relations potential of D14C and δ13C as sup-porting methodologies Water Air Soil Poll 70 431ndash442doi101007BF01105014 1993

Schwartz D Some podzols on Bateke sands and their ori-gins Peoplersquos Republic of Congo Geoderma 43 229ndash247doi1010160016-7061(88)90045-6 1988

Sierra C A Jimeacutenez E M Reu B Pentildeuela M C ThuilleA and Quesada C A Low vertical transfer rates of carbon in-ferred from radiocarbon analysis in an Amazon Podzol Biogeo-sciences 10 3455ndash3464 doi105194bg-10-3455-2013 2013

Sierra C A Muumlller M and Trumbore S E Modeling radiocar-bon dynamics in soils SoilR version 11 Geosci Model Dev 71919ndash1931 doi105194gmd-7-1919-2014 2014

Stuiver M and Polach H A Radiocarbon discussion reporting of14C data Forensic Sci Int 19 355ndash363 1977

Tardy Y Roquin C Bustillo V Moreira M Martinelli L Aand Victoria R Carbon and Water Cycles Amazon River BasinApplied Biogeochemistry Atlantica Biarritz France 2009

Tipping E Chamberlain P M Froumlberg M Hanson P J andJardine P M Simulation of carbon cycling including dissolvedorganic carbon transport in forest soil locally enriched with 14CBiogeochemistry 108 91ndash107 doi101007s10533-011-9575-1 2012

Trumbore S Age of Soil Organic Matter and Soil Res-piration Radiocarbon Constraints on Belowground CDynamics Ecol Appl 10 399ndash411 doi1018901051-0761(2000)010[0399AOSOMA]20CO2 2000

Van der Hammen T and Hooghiemstra H Neogene and Quater-nary History of Vegetation Climate and Plant Diversity in Ama-zonia Quaternary Sci Rev 19 725ndash742 doi101016S0277-3791(99)00024-4 2000

Van Hees P A W Johansson E and Jones D L Dynamics ofsimple carbon compounds in two forest soils as revealed by soilsolution concentrations and biodegradation kinetics Plant Soil310 11ndash23 doi101007s11104-008-9623-3 2008

Wanner H Soil Respiration Litter Fall and Productivity of Tropi-cal Rain Forest J Ecol 58 543 doi1023072258289 1970


Abstract

Introduction

Methods

Podzol profiles and carbon analysis

Model design

Model running and tuning

Results and discussion

Modelling the formation of a single-pool Bh

Obtaining the carbon stock

Obtaining both carbon stock and 14C age

Modelling the formation of the whole profile with a two-pool Bh

Topsoil horizons

Bh horizons

Age carbon fluxes and carbon turnover

Conclusion

Competing interests

Acknowledgements

References


Figure 1 Schematic of the main C fluxes in a podzol

been estimated in a small number of case studies or extrap-olated from studies of the chemistry of large rivers (Tardyet al 2009) but most of them remain unknown Studiesmeasuring carbon budgets at the profile scale or during soilprofile genesis in temperate boreal or tropical podzols arerare (Schaetzl and Rothstein 2016 Van Hees et al 2008)Schwartz (1988) studied giant podzol profiles in the Congothat began to form 40times 103 years ago but where carbon accu-mulation in Bh was discontinuous because of a drier climatebetween 30 and 12 kyr BP The 14C age of organic C fromthe Bh horizon of podzol profiles situated in the Manaus re-gion (Brazil) was found to range from 1960 to 2810 yearsand it was concluded that the podzols developed in less than3times 103 years (Horbe et al 2004) As pointed out by Sierraet al (2013) in order to corroborate this conclusion it is nec-essary to produce a model that accounts for C additions andlosses over time Montes et al (2011) roughly estimated theC flux to the Bh horizon to be 168 gC mminus2 yearminus1 Sierra etal (2013) used a compartment model that was constrained by14C dating to estimate the carbon fluxes in a Colombian shal-low podzol (Bh upper limit at 09 m) They showed that the Cfluxes from topsoil horizons to the Bh horizon were smaller(21 gC mminus2 yearminus1) than the fluxes estimated in Montes etal (2011) However they did not account for the age andgenesis time of the Bh horizon

In order to better understand the fluxes of C in Amazonianpodzols and in particular to determine the rate of carbon ac-cumulation in Bh horizons during podzol genesis the size ofthe C fluxes to rivers via both the perched and deep water ta-bles and the vulnerability of the podzol C stocks to potentialchanges in the moisture regime due to global climate changefour representative podzol profiles from the high Rio Negrobasin were used to constrain a model of C fluxes The highRio Negro basin was chosen because it is a region that hasthe highest occurrence of podzol in the Amazon (Montes et

al 2011) (Fig 2) The four representative profiles were se-lected from a database of 80 podzol profiles issued from 11test areas which have been studied in detail and of which 11have been dated this database will be the subject of a furtherpublication The four profiles were used to constrain the sim-ulations of C fluxes We used a system dynamics modellingsoftware package (Vensim) to simulate the formation of rep-resentative Amazonian podzol profiles by constraining bothtotal carbon and radiocarbon with the data collected

2 Methods

21 Podzol profiles and carbon analysis

Four podzol profiles were selected from our database as rep-resentative both from the point of view of the profile charac-teristics and the 14C age of the Bh organic matter (Table 1and Fig 3) The MAR9 profile was developed on the Icaacutesedimentary formation and has a waterlogged A horizon athin eluvial (E) horizon a sandy-clay loam Bh with youngorganic matter (OM) and a low C content the DPQT pro-file was developed on a late Quaternary continental sedimentyounger than the Iccedilaacute formation and has an E horizon of in-termediate thickness a sandy Bh with young OM and a lowC content the UAU4 profile was developed on the Icaacute sed-imentary formation has a thick E horizon and a sandy Bhwith old OM and the C content is high the P7C profile wasdeveloped on crystalline basement rock and has a thick wa-terlogged O horizon an E horizon of intermediate thicknessa silt-loam Bh with old OM and a high C content It shouldbe noted that in the cases of the DPQT and UAU4 profilesthe lower limit of the Bh was not reached because the augerhole collapsed meaning that for these profiles the Bh C stockis an underestimate

Soil samples were analysed for C content with a TOC-LCPN SSM-5000A Total Organic Carbon Analyzer (Shi-madzu) Radiocarbon measurements were carried out at thePoznan Radiocarbon Laboratory Poland We assumed thatthe proportion of bomb carbon in the Bh organic matter wasnegligible and calculated a conventional uncalibrated agefrom the radiocarbon pMC (percent modern carbon) valueAs the Bh organic matter is an open system mixing organiccarbon of different ages this age is an apparent age Sam-ples from the topsoil had a pMC higher than 100 whichindicates that a significant part of the carbon in the topsoil ispost-bomb and therefore should not be neglected Assumingthat the topsoil horizons reached a steady state before 1950we retrocalculated the pre-1950 pMC value of these samplesusing a dedicated model described in Sect 22

The data given in Table 1 were calculated by linear ex-trapolation of values measured on samples taken at differentdepths between 11 and 28 samples per profile were used forthe C stocksrsquo calculation and between 6 and 8 samples perprofile were used for radiocarbon measurements







Topsoil horizons


Bh horizons



22 Model design




dCt


dCfBh


dCsBh








dFatCt


minus λFatCt

dFafBhCfBh



dFasBhCsBh







)CIhArr Fati (7)


Ctminus λCt+CI










dCBh





CBh =αtminusBhCt

βBh+

(C0Bhminus

αt-BhCt

βBh

)eminusβBht (9)


dFaBhCBh




dFaBhdt= (11)



minusβBh t))



FaBh = (12)

βBhFateminusλt

(βBhC0 Bh+αt-BhCt


)+ λC0Bh

)(βBh+ λ)

(βBhC0 Bh+αt-BhCt

(eβBht minus 1

))





















MAR9 DPQT UAU4 P7C





















MAR 9 DPQT UAU4 P7C






322 Bh horizons




















4 Conclusion






















Sample availability





References





































Abstract

Introduction

Methods


Model design







Topsoil horizons

Bh horizons


Conclusion

Competing interests

Acknowledgements

References






Topsoil horizons


Bh horizons



22 Model design




dCt


dCfBh


dCsBh








dFatCt


minus λFatCt

dFafBhCfBh



dFasBhCsBh







)CIhArr Fati (7)


Ctminus λCt+CI










dCBh





CBh =αtminusBhCt

βBh+

(C0Bhminus

αt-BhCt

βBh

)eminusβBht (9)


dFaBhCBh




dFaBhdt= (11)



minusβBh t))



FaBh = (12)

βBhFateminusλt

(βBhC0 Bh+αt-BhCt


)+ λC0Bh

)(βBh+ λ)

(βBhC0 Bh+αt-BhCt

(eβBht minus 1

))





















MAR9 DPQT UAU4 P7C





















MAR 9 DPQT UAU4 P7C






322 Bh horizons




















4 Conclusion






















Sample availability





References





































Abstract

Introduction

Methods


Model design







Topsoil horizons

Bh horizons


Conclusion

Competing interests

Acknowledgements

References





dFatCt


minus λFatCt

dFafBhCfBh



dFasBhCsBh







)CIhArr Fati (7)


Ctminus λCt+CI










dCBh





CBh =αtminusBhCt

βBh+

(C0Bhminus

αt-BhCt

βBh

)eminusβBht (9)


dFaBhCBh




dFaBhdt= (11)



minusβBh t))



FaBh = (12)

βBhFateminusλt

(βBhC0 Bh+αt-BhCt


)+ λC0Bh

)(βBh+ λ)

(βBhC0 Bh+αt-BhCt

(eβBht minus 1

))





















MAR9 DPQT UAU4 P7C





















MAR 9 DPQT UAU4 P7C






322 Bh horizons




















4 Conclusion






















Sample availability





References





































Abstract

Introduction

Methods


Model design







Topsoil horizons

Bh horizons


Conclusion

Competing interests

Acknowledgements

References







dCBh





CBh =αtminusBhCt

βBh+

(C0Bhminus

αt-BhCt

βBh

)eminusβBht (9)


dFaBhCBh




dFaBhdt= (11)



minusβBh t))



FaBh = (12)

βBhFateminusλt

(βBhC0 Bh+αt-BhCt


)+ λC0Bh

)(βBh+ λ)

(βBhC0 Bh+αt-BhCt

(eβBht minus 1

))





















MAR9 DPQT UAU4 P7C





















MAR 9 DPQT UAU4 P7C






322 Bh horizons




















4 Conclusion






















Sample availability





References





































Abstract

Introduction

Methods


Model design







Topsoil horizons

Bh horizons


Conclusion

Competing interests

Acknowledgements

References




















MAR9 DPQT UAU4 P7C





















MAR 9 DPQT UAU4 P7C






322 Bh horizons




















4 Conclusion






















Sample availability





References





































Abstract

Introduction

Methods


Model design







Topsoil horizons

Bh horizons


Conclusion

Competing interests

Acknowledgements

References



MAR 9 DPQT UAU4 P7C






322 Bh horizons




















4 Conclusion






















Sample availability





References





































Abstract

Introduction

Methods


Model design







Topsoil horizons

Bh horizons


Conclusion

Competing interests

Acknowledgements

References

















4 Conclusion






















Sample availability





References





































Abstract

Introduction

Methods


Model design







Topsoil horizons

Bh horizons


Conclusion

Competing interests

Acknowledgements

References




















Sample availability





References





































Abstract

Introduction

Methods


Model design







Topsoil horizons

Bh horizons


Conclusion

Competing interests

Acknowledgements

References



































Abstract

Introduction

Methods


Model design







Topsoil horizons

Bh horizons


Conclusion

Competing interests

Acknowledgements

References

modelling the genesis of equatorial podzols: age and implications … · 2020. 1. 22. · 2012;...

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