ORIGINAL PAPER

A benchmark for soil organic matter degradation under variablysaturated flow conditions

M. Jia1 & D. Jacques2 & F. Gérard3& D. Su1

& K. U. Mayer1 & J. Šimůnek4

Received: 12 January 2019 /Accepted: 18 July 2019# Springer Nature Switzerland AG 2019

AbstractSoil contains the largest terrestrial pool of organic matter, and the cycling of organic carbon in soils plays a crucial role incontrolling atmospheric carbon dioxide (CO2) and global climate change. Although considerable progress has been made inprevious modeling studies on the fate of soil organic matter (SOM), only a few models used a process-based approach forinvestigating these strongly coupled and complex soil systems, which involve SOM oxidation, transient water flow, and masstransport processes in aqueous and gaseous phases. Typically, physically based models for water flow, as well as solute and gastransport, are not coupled with state-of-the-art SOM degradation models. Reactive transport models (RTMs) provide a flexibleframework for implementing different SOM degradation concepts and integrating biogeochemical processes with water flow andmass transport. Given the complex nature of carbon cycling in soils coupled with flow and mass transport, code intercomparisonusing well-defined benchmarks is inmany cases the only practical method ofmodel verification. The benchmark presented in thismanuscript focuses on SOM oxidation under variably saturated flow conditions. The benchmark consists of three problemscharacterized by increasing complexity. The problems were solved using two different reactive transport codes, namely HP1 andMIN3P-THCm. The first supporting problem introduces a batch-type simulation to assess kinetic networks of SOM degradation.In the second supporting problem, transient water flow, solute transport, gas generation, and diffusive gas transport are consid-ered. The principal problem combines the kinetic networks of SOM degradation with reactive transport under variably saturatedflow conditions, including CO2 transport from soils to the atmosphere. Simulation results for the benchmark problems demon-strate an overall excellent agreement between the two codes, building confidence in the ability of RTMs to simulate complex C-cycling in dynamic environments.

Keywords Reactive transport modeling .Model intercomparison . Soil organic matter . Benchmarking . HP1 .MIN3P-THCm

1 Introduction

At the global scale, soil organic matter (SOM) contains threeor four times more carbon than is found either in the atmo-sphere or terrestrial vegetation [1]. SOM turnover is an essen-tial process regulating atmospheric gases, particularly the pro-duction of CO2, and it thus has a significant influence onglobal climate change [2]. SOM is a highly complex materialwith extreme variations in physical and chemical properties,spatial distribution, and temporal evolution at different scales[3]. Understanding the role of SOM dynamics using directmeasurements alone is challenging, largely due to the com-plexity of biotic and abiotic interactions, and the heteroge-neous and evolving nature of SOM. However, models canbe useful tools for integrating complex data sets and providingtheir quantitative interpretations. They have thus becomepromising tools for the assessment of complex carbon

Electronic supplementary material The online version of this article(https://doi.org/10.1007/s10596-019-09862-3) contains supplementarymaterial, which is available to authorized users.

* M. Jiamjia@eoas.ubc.ca

* D. Jacquesdjacques@sckcen.be

1 Department of Earth, Ocean and Atmospheric Sciences, TheUniversity of British Columbia, Vancouver, BC, Canada

2 Belgian Nuclear Research Centre SCK.CEN, B-2400 Mol, Belgium3 Supagro, Univ. Montpellier, CIRAD, INRA, IRD, Eco&Sols,

Montpellier, France4 Department of Environmental Sciences, University of California

Riverside, Riverside, CA 92521, USA

Computational Geoscienceshttps://doi.org/10.1007/s10596-019-09862-3

turnover processes in soil [4]. Models simulating flow andtransport processes in soils are essential for assessing ecosys-tem services provided by the soil at different scales [5].Accurate representation of SOM dynamics is thus an impor-tant component of such models. Abiotic factors such as watercontent and temperature can strongly affect SOM degradationrates, whereas mass transport processes govern both the mi-gration of dissolved organic matter (DOM) in the aqueousphase and the CO2 transport in the gaseous phase [6]. As aresult, the SOM turnover models allow us to improve ourassessment of soil ecosystem services and to develop a betterunderstanding of intricate biogeochemical interactions in soilsand their effect on climate change.

During the last 80 years, different approaches have beenused to describe SOM dynamics across a broad range of tem-poral and spatial scales [7]. At present, an increasinglyexpanding range of SOMmodels is being used in sustainabil-ity research and decision-making [4]. A generally acceptedconcept for modeling of SOM degradation is to define a num-ber of compartments or SOM pools, where each pool is com-posed of SOM with varying chemical composition and deg-radation characteristics [8–10]. These SOM models differ inthe number of compartments and their connectivity by havingparallel compartments, compartments in series, and feedbackbetween compartments. Most of the existing SOM compart-ment degradation models can be represented by a generalizedsystem of linear equations, as discussed by Sierra [11] andexamples therein. Besides connectivity, degradation formula-tions representing the effect of substrate concentration (i.e.,SOM pools) and decomposers (biota) vary between models,ranging from simple first-order kinetics without representationof decomposers to nonlinear representations including dy-namic interactions with decomposers [12].

Many SOM degradation models have a fixed mathematicalstructure with a rigid, static, and problem-specific character thatlacks the flexibility and extensibility to evaluate different SOMdynamics within the same numerical framework. However, theanalysis of different SOM dynamics (e.g., for the definition of ahierarchy of models, for model abstraction, for multi-model en-semble predictions, or for scenario and sensitivity analyses)would benefit from a flexible modeling framework that allowsimplementations of different model structures within the samemathematical framework. Only a few models combine SOMdegradation with transient water flow and relevant solute andgas transport processes, while at the same time accounting forthe influence of dynamic soil water contents and temperatures onSOM degradation processes [13, 14]. On the other hand, typicalwater and mass transport models for soils commonly lack thestate-of-the-art formalisms to cope with SOM degradation. Forexample, while the DAYCENT model focuses on assessingmulti-pool SOM degradation, it has no explicit description ofgas transport and gas exchange, which limits its ability to simu-late the temporal evolution of SOM turnover processes [15, 16].

Braakhekke et al. [17] included in their model the transport ofdissolved SOM using a constant rate of advection for all solutes.However, this model cannot be applied under all soil conditions(e.g., to grassland soils). Models developed by Fang andMoncrieff [18] described in detail the gas transport and ex-change, while greatly simplifying SOM degradation. Jassalet al. [19] developed a complex model for simulating CO2 trans-port in the forest floor that considered diffusion in the gaseousphase as well as diffusion and dispersion in the aqueous phase.However, this model only considered two SOM pools with sim-plified first-order degradation rates for biological CO2 produc-tion. Šimůnek and Suarez [20] also developed a CO2 productionand transport model that accounted for transient variably

Fig. 1 Schematics for organic matter degradation models: a modelwithout leachable soil organic matter (SOM-L) and b model withleachable soil organic matter (SOM-L). Orange lines indicate FOMdegradation to easily decomposable soil organic matter (SOM-P1),brown lines indicate degradation to slowly decomposable soil organicmatter (SOM-P2), green lines indicate assimilation into microbialbiomass (Biomass), blue lines indicate respiration and production ofinorganic carbon species (CO2), and red lines indicate degradation toSOM-L. The dashed black line represents kinetic exchange betweenSOM-L and dissolved organic matter (DOM)

Comput Geosci

saturated water flow, advective-dispersive solute transport, andCO2 production in soil, but the model structure was fixed (hard-coded).Moreover, environmental parameters (such as water con-tent or temperature) that affect degradation rates are often calcu-lated separately from the SOM degradation model using a flowand transport model (e.g., Pansu et al., 2010 [21]; Batlle-Aguilaret al., 2011 [22]) or are directly derived from observations [23].However, this approach is not suitable for simulating the diffu-sion of gaseous CO2 originating from respiration of SOM orleaching and sorption of DOM because of the close couplingbetween flow, transport, and SOM degradation.

In our study, we illustrate that existing generic reactivetransport models (RTMs) represent a flexible and extensibleframework for implementing different SOM degradationmodel structures while providing tight integration of SOMdegradation with flow and mass transport processes. Several

RTMs can integrate transient variably saturated flow and masstransport equations with a biogeochemical reaction networkinvolving equilibrium and kinetic processes. Some recentstudies have included SOM degradation dynamics intoRTMs. For example, Thayssen et al. [24] implemented themodel of Šimůnek and Suarez [20] into the RTM HP1 [25].Within the same RTM, the SOM degradation network directlyaccounted for the effect of environmental variables such as thespatiotemporal evolution of moisture and temperature and theeffect of bio-diffusion of SOM pools [26]. However, the moresophisticated nature of RTMs leads to challenges during theirimplementation and code development [27]. Additional com-plexities arise when model structures of SOM degradation aredefined by users via input files. To improve the reliability ofsimulation tools, model verification is essential [28]. As aresult, benchmarking of different RTMs by implementing

Table 1 Stoichiometry of SOM degradation reactions for networks 1 and 2

R Reaction FOM SOM-P1

SOM-P2

CO32

−H+ Biomass SOM-

LDOM

General reactions

1 FOM ➔ SOM-P1 − 1 1 0 0 0 0 0 0

2 Biomass➔ SOM-P1 0 1 0 0 0 − 1 0 0

3ǂ SOM-L ➔ DOM 0 0 0 0 0 0 − 1 1

Non-explicit biomass/linear interaction/exponential interaction

4 SOM-P1➔ SOM-P2 + CO32− + H+ + biomass 0 − 1 0.1 0.6 1.2 0.3 0 0

5 SOM-P2➔ CO32− + H+ + biomass 0 0 − 1 0.6 1.2 0.4 0 0

6ǂ SOM-P1➔ SOM-P2 + CO32− + SOM-L + H+ + biomass 0 − 1 0.1 0.55 1.1 0.3 0.05 0

7ǂ SOM-P2➔ CO32− + H+ + SOM-L + biomass 0 0 − 1 0.5 1.0 0.4 0.1 0

8ǂ SOM-L ➔ CO32− + H+ + biomass 0 0 0 0.9 1.8 0.1 − 1 0

Stoichiometric coefficients for products > 0 and for reactants < 0ǂOnly for network 2

Table 2 Overview of benchmark cases

Benchmark Type Description

Supporting problem 1

C1a1 B Degradation network 1 with non-explicit biomass

C1a2 B Degradation network 2 with non-explicit biomass

C1b1 B Degradation network 1 with a linear substrate-biomass term

C1b2 B Degradation network 2 with a linear substrate-biomass term

C1c1 B Degradation network 1 with an exponential substrate-biomass term

C1c2 B Degradation network 2 with an exponential substrate-biomass term

Supporting problem 2

C2a T Transient water flow and conservative solute transport

C2b T Transient water flow, solute transport, and diffusion in the gas phase with a kinetic production term

Principal problems

P1 B-T Transient variably saturated flow, solute transport, and organic matter degradation

P2 B-T Transient variably saturated flow, solute transport, and organic matter degradation with a kinetic adsorption-desorption term

Comput Geosci

the same formulation for SOM degradation is an importantprerequisite to increasing confidence in using such modelsfor simulating SOM degradation processes in soil systems.

This study is aimed at presenting a benchmark problemon C-cycling in soils that includes SOM degradation, tran-sient water flow, and mass transport processes. We illustratesome of the issues mentioned above by accounting for (i)two different SOM degradation models, (ii) different equa-tions describing the role of decomposers, and (iii) waterflow and mass transport processes including the transportof DOM and total inorganic carbon (TIC) and diffusive CO2

transport in soil air under variably saturated flow condi-tions. The benchmark provides a relatively high degree of

complexity involving nonlinear coupling and facilitates adirect intercomparison of different implementations of thegoverning equations in the two participating codes (i.e.,HP1 [25] andMIN3P-THCm [29]). Three individual bench-mark problems of varying complexity were solved in orderto evaluate formulations and implementations of soil carbonturnover, and flow and transport processes. Results obtainedwith both reactive transport codes are presented and com-pared. Within the scope of the current benchmark, the effectof selected environmental factors (e.g., oxygen availabilityand temperature dependency) on SOM degradation was notconsidered. However, RTMs allow the inclusion of suchprocesses with relative ease [26, 30].

Table 3 Parameters of SOM degradation reactions for networks 1 and 2

Symbol Parameter description Values Unit

General parameters

ρb Soil bulk density 1.43 kg dm−3 bulk

iF Addition rate of FOM 1.40 × 10−8 g dm−3 bulk s−1

rB Decay rate of biomass pool 9.80 × 10−8 s−1

Non-explicit dependency

kα,SOM-P1 Rate constant for SOM-P1 degradation 3.50 × 10−7 s−1

kα,SOM-P2 Rate constant for SOM-P2 degradation 5.80 × 10−8 s−1

kα,SOM-L* Rate constant for SOM-L degradation 3.50 × 10−8 s−1

Linear dependency

kβ,SOM-P1 Rate constant for SOM-P1 degradation 3.50 × 10−6 L H2O mol−1 s−1

kβ,SOM-P2 Rate constant for SOM-P2 degradation 5.60 × 10−7 L H2O mol−1 s−1

kβ,SOM-L* Rate constant for SOM-L degradation 4.20 × 10−7 L H2O mol−1 s−1

Exponential dependency

kγ,SOM-P1 Rate constant for SOM-P1 degradation 3.50 × 10−7 s−1

kγ,SOM-P2 Rate constant for SOM-P2 degradation 5.80 × 10−8 s−1

kγ,SOM-L* Rate constant for SOM-L degradation 3.50 × 10−8 s−1

c Exponential coefficient 12.01 L H2O mol−1

*Only for network 2

Table 4 Parameters for kinetic adsorption-desorption of SOM-L and DOM

Symbol Parameter description Value Unit

MIN3P-THCm formalism (Eq. 15)

k1 Rate coefficient for fractional term 5.80 × 10−7 s−1

k2 Rate coefficient for the Michaelis-Menten term 1.93 × 10−7 mol C dm−3 bulk s−1

K Half saturation constant for the Michaelis-Menten term 1.67 × 10−1 mol L−1 H2O

5.35 × 10−2* mol L−1 H2O

HP1 formalism (Eqs. 13 and 14)

ksor First-order kinetic sorption term 5.8 × 10−7 s−1

Smax Binding capacity of DOM 0.40 g C dm−3 bulk

KL Binding affinity of DOM 6.01 L H2O mol−1

18.68* L H2O mol−1

*Only for the principal problem (P2)

Comput Geosci

2 Mathematical formulation of SOMdegradation and model formulations

The mathematical framework for multicomponent reactivetransport models including transient variably saturated waterflow, advective-dispersive solute and gas transport, equilibri-um chemistry, and kinetic reaction networks is provided in[31] and is therefore not repeated here. The model descriptiongiven here focuses on specific equations of the benchmark.

2.1 Organic matter degradation schemes

In the benchmark, the SOM degradation model structure fol-lows the classical compartment-type models with a number offunctionally different SOM pools. The first degradationscheme includes four carbon pools with fresh organic matter(FOM), soil organic residues (SOM-P), microbial biomass,and inorganic carbon (Fig. 1a). The soil organic residues aredivided between a fast-decomposing pool (SOM-P1) and aslow-decomposing pool (SOM-P2). Both aboveground plantlitter and the decay of fine roots provide a source for FOM,which can act as a source for energy-rich substrates, increasingthe rate of SOM mineralization [17]. For the sake of modelsimplicity, we make the following assumptions: (i) no distinc-tion in degradation rates is made between aboveground litterand root litter; (ii) the input of FOM to the soil is continuousand unlimited; and (iii) the FOM degradation rate (iF) can bedescribed by a zero-order kinetics rate equation and FOMinputs contribute only to SOM-P1. The slowly decomposingSOM pool (i.e., SOM-P2) is derived from rapidlydecomposing SOM (SOM-P1) via humification, which is inagreement with the findings of Jenkinson [8]. Although dif-ferent functional groups ofmicrobial populations coexist, onlya single pool is considered to account for microbial biomass.In many cases, quantitative information on microbial commu-nities is limited [9], justifying this approach. SOM decompo-sition involved enzymatic oxidation which produces carbondioxide (CO2), which is, via transport through the soil gasphase, partly returned to the atmosphere (soil respiration).The partitioning of CO2 between the aqueous phase and soilgas is also included via Henry’s law. The four carbon poolsprovide a simplified, yet general model structure, accountingfor organic carbon fluxes between the main components of thesystem. A set of four mass balance equations defines the deg-radation scheme:

RSOM−P1 ¼ iF þ rB−rSOM−P1 ð1ÞRSOM−P2 ¼ vSOM−P1→P2rSOM−P1−rSOM−P2 ð2Þ

RB ¼ vSOM−P1→BrSOM−P1 þ vSOM−P2→BrSOM−P2−rB ð3Þ

RTIC ¼ vSOM−P1→TICrSOM−P1 þ vSOM−P2→TICrSOM−P2 ð4Þ

where Rx [mol L−1 H2O s−1] defines the degradation reac-tion rates, subscript x denotes different SOM pools (B = bio-mass, TIC = inorganic carbon), and rx denotes the degradationrates described in the next section. Parameter va→b representsa fraction of degradation products of pool a going to pool b.Fractions va→b for a given pool a sum up to one, ensuring thatmass balance is closed. Table 1 provides the stoichiometry ofthe reactions used in network 1.

The second degradation scheme (Fig. 1b), named network2, is a variant of network 1. In addition to network 1, network2 includes a leachable SOM pool (SOM-L), representingSOM that is reversibly adsorbed onto soil constituents and isthus the most important source of SOM deeper in a soil profile[17]. SOM-L partitions between the solid and aqueous phasesaccording to a kinetic adsorption/desorption isotherm. Thedesorbed fraction corresponds to DOM that is transported byadvection and dispersion throughout the soil profile.Compared to SOM and biomass concentrations, DOM con-centrations are relatively small, althoughDOM transport plays

Table 5 Boundary and initial conditions—supporting problemC1, totalcomponent concentrations

Components Initial Unit

H+a 5.00 mol L−1 H2O

Ca2+ 1.00 × 10−10 mol L−1 H2O

CO32− 1.00 × 10−10 mol L−1 H2O

FOM 1.40 × 10−3 kg C kg−1 bulk

SOM-P1 1.75 × 10−4 kg C kg−1 bulk

SOM-P2 7.00 × 10−5 kg C kg−1 bulk

Biomass 7.00 × 10−5 kg C kg−1 bulk

SOM-Lb 1.33 × 10−5 kg C kg−1 bulk

DOMb 8.33 × 10−3 mol L−1 H2O

aAs pHbOnly for network 2

Table 6 Boundary and initial conditions—supporting problemC2, totalcomponent concentrations in units of [mol L−1 H2O]

Components Recharge Initial

Supporting problem C2a

H+ 2.00 × 10−3 2.00 × 10−10

CO32− (as a conservative tracer) 1.00 × 10−3 1.00 × 10−10

Supporting problem C2b

H+a 3.70 × 10−3 3.70 × 10−3

CO32−a 1.90 × 10−3 1.90 × 10−3

H+b – 3.70 × 10−3

CO32−b – 1.90 × 10−3

a For shallow soilb For deep soil

Comput Geosci

an important role regarding the fate of SOM [17]. This ex-panded degradation scheme requires modification of the massbalance equations for Network 1 and the definition of an ad-ditional mass balance equation for SOM-L, resulting in:

RSOM−P1 ¼ iF þ rB−rSOM−P1 ð5Þ

RSOM−P2 ¼ vSOM−P1→P2rSOM−P1−rSOM−P2 ð6ÞRB ¼ vSOM−P1→BrSOM−P1 þ vSOM−P2→BrSOM−P2

þ vSOM−L→BrSOM−L−rB ð7Þ

RSOM−L ¼ vSOM−P1→SOM−LrSOM−P1

þ vSOM−P2→SOM−LrSOM−P2−rSOM−L−rS ð8Þ

RTIC ¼ vSOM−P1→TICrSOM−P1 þ vSOM−P2→TICrSOM−P2

þ vSOM−L→TICrSOM−L ð9Þ

where rS (=−RaDOM ) is the rate describing desorption kinet-

ics (see Section 2.3). The stoichiometry of the degradationreactions for network 2 is given in Table 1.

2.2 Organic matter degradation rates

Three different equations describing SOM decomposi-tion are implemented to account for the influence ofbiomass: (i) linear dependence only on substrate (non-explicit biomass), (ii) linear dependence on substrateand biomass (linear interaction), and (iii) linear depen-dence on substrate and exponential dependence on bio-mass (exponential interaction). In the first case, the bio-mass is a non-limiting factor and, thus, the rate of SOMdegradation is not dependent on the simulated biomassconcentration [9]:

rX ¼ kαCX ð10Þ

where kα is the first-order degradation rate [s−1] and Cx isthe concentration of the substrate [mol L−1 H2O]. However,this simple approximation is often unrealistic, because thedegradation of recalcitrant SOM is more strongly affected bythe quantity of enzymes associated with biomass than by theconcentration of the substrate [23]. Thus, a linear dependenceon both quantities of microbial biomass and substrate, describ-ing a co-limitation by decomposers and substrate, provides analternative formulation [32]:

Table 7 Physical properties forthe flow and transport model Symbol Parameter description Value Unit

θr* Residual water content 0.08 m3 m−3

θs* Saturated water content 0.45 m3 m−3

Sw* Residual saturation 0.178 –

α* Shape parameter 1.0 m−1

n* Shape parameter 1.4 –

Ks Saturated hydraulic conductivity 2.894 × 10−6 m s−1

l* Pore connectivity parameter 0.5 –

DL Longitudinal dispersivity 0.1 m

Dw Free phase diffusion coefficient in the aqueous phase 2.315 × 10−9 m2 s−1

Da Free phase diffusion coefficient in the gas phase 2.315 × 10−5 m2 s−1

*Soil hydraulic properties are described using the van Genuchten-Mualem model [35]

Table 8 Boundary and initial conditions—principal problem, totalcomponent concentrations

Components Recharge Initial Unit

Shallow soil

H+ 3.70 × 10−3 3.70 × 10−3 mol L−1 H2O

Ca2+ 1.00 × 10−10 1.00 × 10−10 mol L−1 H2O

CO32− 1.90 × 10−3 1.90 × 10−3 mol L−1 H2O

FOM 3.50 × 10−4 3.50 × 10−4 kg C kg−1 bulk

SOM-P1 1.75 × 10−4 1.75 × 10−4 kg C kg−1 bulk

SOM-P2 7.00 × 10−5 7.00 × 10−5 kg C kg−1 bulk

Biomass 7.00 × 10−5 7.00 × 10−5 kg C kg−1 bulk

SOM-La 1.33 × 10−5 1.33 × 10−5 kg C kg−1 bulk

DOMa 2.33 × 10−3 2.33 × 10−3 mol L−1 H2O

Deep soil

H+ – 3.70 × 10−3 mol L−1 H2O

Ca2+ – 1.00 × 10−10 mol L−1 H2O

CO32− – 1.90 × 10−3 mol L−1 H2O

FOM – 4.30 × 10−10 kg C kg−1 bulk

SOM-P1 – 4.30 × 10−10 kg C kg−1 bulk

SOM-P2 – 4.30 × 10−10 kg C kg−1 bulk

Biomass – 4.30 × 10−10 kg C kg−1 bulk

SOM-La – 4.30 × 10−10 kg C kg−1 bulk

DOMa – 1.00 × 10−10 mol L−1 H2O

aOnly for network 2

Comput Geosci

rX ¼ kβCXCB ð11Þ

where kβ is the second-order degradation rate [L H2Omol−1 s−1] and CB is the concentration of the microbialbiomass [mol L−1 H2O]. Although this formulation con-siders the quantity of microbial biomass, this linear depen-dence does not adequately describe the non-linear effects ofbiomass concentrations on SOM degradation. Alternatively,we can consider an exponential formulation that follows theformulation of Wutzler and Reichstein [12]:

rX ¼ kγ 1−e−cCB� �

CX

ð12Þ

where kγ is the first-order degradation term [s−1] and c [LH2O mol−1] is a shape parameter. The decay of microbialbiomass (rB) is always modeled as first-order kinetics.

2.3 Sorption of dissolved organic matter

Kinetic adsorption-desorption reactions involving SOM-Land DOM are described using a first-order kinetic rate equa-tion:

rS ¼ −kS CSOM−L−CeqSOM−L

� � ð13Þ

where kS is the first-order rate constant [s−1] and Ceq

SOM−L isthe equilibrium concentration [mol L−1 H2O]. The equilibrium

DOM

[mol

L-1water]

Time [day]

SOM

/Biomas

s[g

dm-3bu

lk]

0 500 1000 15000

0.05

0.1

0.15

0.2

0.25

0.3(c) Exponential interaction

Time[day]

SOM

/Biomas

s[g

dm-3bu

lk]

0 500 1000 15000 0

0.1 0.1

0.2 0.2

0.3 0.3

Time [day]

SOM

/Biomas

s[g

dm-3bu

lk]

0 500 1000 15000 0

0.1 0.1

0.2 0.2

0.3 0.3DOM

[mol

L-1water]

(f) Exponential interaction

Time [days]

SOM

/Biomas

s[g

dm-3bu

lk]

0 500 1000 15000

0.05

0.1

0.15

0.2

0.25

0.3(b) Linear interaction

DOM

[mol

L-1water]

(e) Linear interaction

Time[day]

SOM

/Biomas

s[g

dm-3bu

lk]

0 500 1000 15000

0.05

0.1

0.15

0.2

0.25

0.3

SOM-P1SOM-P2Biomass

(a) Non-explicit Network 1

Time[day]

SOM

/Biomas

s[g

dm-3bu

lk]

0 500 1000 150000

50.050.0

1.01.0

51.051.0

2.02.0

52.052.0

3.03.0

DOMSOM-P1SOM-P2BiomassSOM-L

(d) Non-explicit Network 2

Fig. 2 Results for supporting problem C1 based on SOM degradation fornetworks 1 (a–c) and 2 (d–f) for linear substrate dependence only, linearbiomass-substrate interaction, and exponential biomass-substrate

interaction. Note that symbols represent HP1 results, while solid linesrepresent MIN3P-THCm results

Comput Geosci

concentration is calculated based on the Langmuir isotherm[33]:

CeqSOM−L ¼ KLSmaxCDOM

1þ KLCDOMð14Þ

where KL is the coefficient of binding affinity [L H2O mol−1]and Smax is the maximum adsorption capacity [mol L−1 H2O].The formulation of sorption of DOM was modified for theMIN3P-THCm simulations to allow its inclusion based on theexisting geochemical reaction network available in the code [29].To this end, Eqs. 13 and 14 were combined and written in themathematically equivalent form of a Michaelis-Menten rate ex-pression:

rS ¼ −k1CSOM−L þ k2CDOM

K þ CDOM

� � ð15Þ

where k1 = kS and k2 = kS × Smax. K is the half saturationconstant in the Michaelis-Menten term and equals 1/KL.

2.4 Mass conservation, solute, and gas transport

In addition to degradation processes, transport of geochemicalspecies is considered in the benchmark. The mass conserva-tion equation for component j present in the aqueous andgaseous phases and described in terms of total componentconcentrations takes the form:

∂∂t

SaφTaj

h iþ ∂

∂tSgφT

gj

h i

þ ∇⋅ qaTaj

h i−∇⋅ SaφDa∇Ta

j

h i−∇⋅ SgφDg∇Tg

j

h i−Qj

¼ 0 ð16Þ

whereT aj [mol L

−1 H2O] defines the total aqueous component

concentrations; Tgj [mol L

−1 gas] defines the total component

concentrations in the gas phase; φ [m3 void m−3 bulk] is theporosity; Sa [m

3 H2O m−3 void] and Sg [m3 gas m−3 void] are

saturations of the aqueous and gas phases, respectively; qa [m

Time [days]

Water

conten

t[-]

0 100 200 3000.15

0.2

0.25

0.3

0.35

0.4

0.45

d = 10 cm

Time [days]

Water

conten

t[-]

0 100 200 3000.15

0.2

0.25

0.3

0.35

0.4

0.45

d = 50 cm

Time [days]

Water

conten

t[-]

0 100 200 3000.15

0.2

0.25

0.3

0.35

0.4

0.45

d = 100 cm

Time [days]

Water

conten

t[-]

0 100 200 3000.15

0.2

0.25

0.3

0.35

0.4

0.45

d = 6 cm

Time [days]

Water

conten

t[-]

0 100 200 3000.15

0.2

0.25

0.3

0.35

0.4

0.45

d = 25 cm

Time[days]

Water

conten

t[-]

0 100 200 3000.15

0.2

0.25

0.3

0.35

0.4

0.45MIN3P-THCmHP1

d = 3 cm

Fig. 3 Results for supporting problem C2a showing transient evolution of water contents at selected depths (3, 6, 10, 25, 50, and 100 cm from top tobottom)

Comput Geosci

s−1] is the Darcy flux vector; andDa [m2 s−1] is the hydrodynam-

ic dispersion tensor applicable to all dissolved species in thesystem. The tortuosity implicitly contained in the pore gas diffu-sion coefficientDg is calculated based on the classical Millingtonand Quirk [34] model. Finally, Qj are source-sink terms [moldm−3 bulk s−1] due to kinetically controlled reactions and fluxesacross the boundaries.

2.5 Reactive transport codes

The benchmark problems were simulated using two reactivetransport codes: HP1 [25, 26] andMIN3P-THCm [29]. Themostimportant difference between HP1 and MIN3P-THCm is thesolution technique of the coupled reactive-transport equations.While HP1 solves the coupled reactive-transport equations usingsequential non-iterative approach (SNIA),MIN3P-THCm solvesthem simultaneously using the global implicit method (GIM).Details about the governing equations for variably saturated wa-ter flow, advective-dispersive solute transport, gas diffusion, and

geochemical equilibrium and kinetic reactions, as well as aboutnumerical methods used, are given in [31]. Input and databasefiles, as well as selected output files for the two codes HP1 andMIN3P-THCm, are provided as text files as part of the SI.

3 Benchmark definitionsand parameterization

The benchmark consists of a principal problem and twosupporting problems (Table 2). The first supporting problem(C1) (Section 3.1) focuses on the simulation of kinetic reactionnetworks for SOM degradation. The second supporting problem(C2) (Section 3.2) considers transient water flow and solute trans-port, as well as gas generation and gas transport. Finally, theprincipal problem (P) (Section 3.3) combines the processes ofthe supporting problemsC1 andC2 in a reactive transportmodel-ing framework, explicitly describing SOM degradation undervariably saturated flow conditions.

Time [days]

Con

servativeso

lute

[mol

L-1H

2O]

0 100 200 300

0.000

0.002

0.004

0.006

0.008

MIN3P-THCmHP1

d = 3 cm

Time [days]

Con

servativeso

lute

[mol

L-1H

2O]

0 100 200 300

0.000

0.002

0.004

0.006

0.008

d = 6 cm

Time [days]

Con

servativeso

lute

[mol

L-1H

2O]

0 100 200 300

0.000

0.001

0.002

0.003

0.004

0.005

0.006

d = 10 cm

Time [days]

Con

servativeso

lute

[mol

L-1H

2O]

0 100 200 300

0.000

0.001

0.002

0.003

0.004

0.005

0.006

d = 25 cm

Time [days]

Con

servativeso

lute

[mol

L-1H

2O]

0 100 200 300

0.000

0.001

0.002

0.003

0.004

d = 50 cm

Time [days]

Con

servativeso

lute

[mol

L-1H

2O]

0 100 200 300

0.000

0.001

0.002

0.003

0.004

d = 100 cm

Fig. 4 Results for supporting problem C2a showing transient evolution of conservative solute concentrations at selected depths (3, 6, 10, 25, 50, and100 cm from top to bottom)

Comput Geosci

3.1 Kinetic networks for SOM degradation(supporting problem C1)

The first supporting problem (C1) verifies the implementationof two different SOM degradation networks, each evaluated forthe three decomposer equations defined above (Eqs. 10–12) ina batch simulation, i.e., without transport. The parameters forthe two degradation networks are loosely based on literaturedata [9, 17, 22] and are provided in Tables 3 and 4. Initialconditions for the supporting problem C1 are provided inTable 5. The equilibrium reaction network for inorganic C spe-ciation is provided in the SI (Section S.1). All geochemicalreactions and associated thermodynamic data for aqueous com-

ponents (i.e., H+, Ca2+, CO2−3 , and DOM), secondary aqueous

species (i.e., OH−, HCO−3 , H2CO3, and CaHCOþ

3 ), and equi-librium gas partitioning (i.e., CO2) with water are provided inthe SI (Tables S.1–S.3). The simulations were run for 1825 days(i.e., 5 years) with a maximum time step of 0.1 days.

3.2 Transient water flow, solute transport, and gasgeneration (supporting problem C2)

While transient variably saturated water flow is a highly non-linear problem and thus difficult to solve numerically, thenumerical solution of the advection-dispersion equation foradvection-dominated transport is subject to numerical disper-sion. To ensure that flow and transport processes are solvedaccurately under dynamic flow conditions, model verificationis conducted first without the added complexity of SOM turn-over models. The second supporting problem (C2) was de-signed to focus on the simulation of transient water flow, con-servative solute transport, gas generation, and diffusive gastransport. The supporting problem C2 is subdivided into twoparts: (i) transient water flow and conservative solute transport(C2a) and (ii) transient water flow, solute transport, gas gen-eration, and gas diffusion (C2b). A summary of the initial andboundary conditions for the supporting problems C2a and

Time [days]

Actual

solute

outflux

[mol

m-2da

y-1 ]

0 100 200 300

0

0.002

0.004

0.006

0.008 (d)

Time [days]

Actual

water

outflux

[mda

y-1 ]

0 100 200 300

0

0.01

0.02

0.03

0.04 (b)

Time [days]

Actual

water

influ

x[m

day-

1 ]

0 100 200 300

0

0.01

0.02

0.03

0.04 MIN3P-THCmHP1

(a)

Time [days]

Actual

solute

influ

x[m

olm

-2da

y-1 ]

0 100 200 3000

0.01

0.02

0.03

0.04

0.05 (c)

Time [days]

Cum

.soluteinflu

x[m

olm

-2]

0 100 200 3000

0.2

0.4

0.6

0.8

1 (e)

Time [days]

Cum

.soluteou

tflux

[mol

m-2]

0 100 200 300

0

0.1

0.2

0.3 (f)

Fig. 5 Results for supporting problem C2a showing transient evolutionof a actual influx of water across the surface and b actual outflux of wateracross both the surface and boundary, c actual influx of a conservativesolute across the surface and d actual outflux of a conservative solute

across the bottom of the domain, and e cumulative influx of aconservative solute across the surface and f cumulative outflux of aconservative solute across the bottom of the domain

Comput Geosci

C2b is provided in Table 6. All geochemical parameters andassociated thermodynamic data for the supporting problemsC2a and C2b are provided in the SI (Tables S.1–S.3). Gasgeneration due to soil respiration for the supporting problemC2b is included via a zero-order source term.

3.2.1 Transient water flow and conservative solute transport(supporting problem C2a)

The supporting problem C2a focuses on the verificationof transient water flow and conservative solute transportin a partially saturated, one-dimensional soil profile with adepth of 100 cm. Table 7 summarizes all parameters forthe flow and transport simulations. The top boundary forflow is defined as a prescribed flux based on daily poten-tial water fluxes (calculated as the difference betweenrainfall and potential evaporation). A free drainage bound-ary condition is applied at the bottom. The initial condi-tion is set to a pressure head of − 150 cm. For solutetransport, a third-type (Cauchy) boundary condition is

applied at the top boundary for recharge conditions(Table 6). During rainfall events, the top boundary is de-fined as a prescribed flux for solute transport, while underevaporative conditions, the top boundary changes and isclosed for solute transport, leading to solute beingretained and causing concentration build-up. At the bot-tom, a free exit boundary condition is set. Initially, soluteconcentrations are negligible throughout the profile. Thesimulation was run for 365 days with a maximum timestep of 0.025 days.

3.2.2 Transient water flow, solute transport, gas generation,and gas diffusion (supporting problem C2b)

The supporting problem C2b builds on C2a and adds gasdiffusion and the generation of CO2 resulting from soilrespiration. The flow and transport models are similar toC2a with some modifications to the boundary conditionsand initial solute concentrations. A mixed-type boundarycondition is similar to the third-type boundary condition

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.0015

0.002

0.0025MIN3P-THCmHP1

d = 3 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.0015

0.002

0.0025

d = 6 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.0015

0.002

0.0025

0.003

d = 10 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.0015

0.002

0.0025

0.003

d = 25 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.0015

0.002

0.0025

0.003

d = 50 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.0015

0.002

0.0025

0.003

d = 100 cm

Fig. 6 Results for supporting problem C2b showing transient evolution of aqueous CO2 concentrations at selected depths (3, 6, 10, 25, 50, and 100 cmfrom top to bottom)

Comput Geosci

in C2a for solute transport. However, influx and outfluxof CO2 are also permitted through the gas phase (Table 6).The initial conditions throughout the domain are identicalto the boundary condition (Table 6). In addition, soil res-piration is considered in the upper 30 cm of the soil pro-file. The CO2 generation term is described by a zero-orderreaction with a rate constant of 5.79 × 10−10 mol dm−3

bulk s−1. The simulation was run for 365 days with amaximum time step of 0.0005 day. Note that C2b pro-vides the foundation for the principal problem, since boththe decomposition of substrates and microbial biomassproduce CO2, resulting in the release of CO2 to the atmo-sphere, depending on soil physical properties and mois-ture dynamics.

3.3 Principal problems

The objective of the principal problem is to verify the integra-tion of biogeochemistry, flow, and transport for the case of a

non-explicit biomass rate equation only (Eq. 10), because thisform is the most common way of implementing SOM degra-dation models [12]. The first principal problem (P1) includesthe processes of the supporting problems C1a (non-explicitcase) and C2b, using the same parameters, except that thefirst-order kinetic gas production term of C2b is replaced bythe SOM degradation network. The second principal problem(P2) is similar to P1, but also includes kinetic adsorption ofDOM, following reaction network 2. The relevant adsorptionparameters (i.e., the rate constant and the half-saturation con-stant for theMichaelis-Menten term) were slightly modified toincrease the sensitivity of the results to changes in water con-tents. The principal problems include advective-dispersivesolute transport, diffusive gas transport, kinetic reaction net-works for SOM degradation, kinetic sorption/desorption ofDOM (in the case of P2), aqueous complexation, and gasexchange reactions. The principal problems provide an oppor-tunity to evaluate the ability of generic reactive transportcodes to simulate SOM degradation under transient variably

Time [days]

Actual

solute

influ

x[m

olm

-2da

y-1 ]

0 100 200 300

0

0.02

0.04

0.06

0.08(c)

Time [days]

Actual

solute

outflux

[mol

m-2da

y-1 ]

0 100 200 300

0

0.02

0.04

0.06

0.08(d)

Time [days]

Actual

gasinflu

x[m

olm

-2da

y-1 ]

0 100 200 300

0

0.02

0.04

0.06

0.08 (e)

Time [days]

Actual

gasou

tflux

[mol

m-2da

y-1 ]

0 100 200 300

0

0.02

0.04

0.06

0.08 (f)

Time [days]

Actual

water

influ

x[m

day-

1 ]

0 100 200 300

0

0.01

0.02

0.03

0.04 MIN3P-THCmHP1

(a)

Time [days]

Actual

water

outflux

[mda

y-1 ]

0 100 200 300

0

0.01

0.02

0.03

0.04 (b)

Fig. 7 Results for supporting problem C2b showing transient evolutionof a actual influx of water across the surface and b actual outflux of wateracross both the surface and bottom of the domain, c actual influx of a

solute across the surface and d actual outflux of a solute across the bottomof the domain, and e actual influx of gas across the bottom and f actualoutflux of gas across the surface of the domain

Comput Geosci

saturated flow conditions. The associated kinetic degradationand adsorption parameters are provided in Tables 3 and 4.Initial conditions and thermodynamic parameters for the

principal problems are provided in Table 8 and SITables S.1–S.3, respectively. The simulation time and timestepping are the same as in the supporting problems C2.

Time [days]

Cum

.soluteinflu

x[m

olm

-2]

0 100 200 300

0.0

1.0

2.0

3.0 MIN3P-THCmHP1

(a)

Time [days]

Cum

.soluteou

tflux

[mol

m-2]

0 100 200 300

0.0

1.0

2.0

3.0(b)

Time [days]

Cum

.gas

influ

x[m

olm

-2]

0 100 200 3000.0

2.0

4.0

6.0 (c)

Time [days]Cum

.gas

outflux

[mol

m-2]

0 100 200 3000.0

2.0

4.0

6.0 (d)

Fig. 8 Results for supporting problemC2b showing transient evolution of a cumulative influx of a solute across the surface and b cumulative outflux of asolute across the bottom of the domain and c cumulative influx of gas across the bottom and d cumulative outflux of gas across the surface of the domain

Time[day]

SOM

/Biomas

s[g

dm-3bu

lk]

0 100 200 3000

0.1

0.2

0.3

0.4

SOM-P1BiomassSOM-P2

d = 3 cm

Time[day]

SOM

/Biomas

s[g

dm-3bu

lk]

0 100 200 3000

0.1

0.2

0.3

0.4

d = 10 cm

Time [days]

SOM

/Biomas

s[g

dm-3bu

lk]

0 100 200 3000

0.1

0.2

0.3

0.4

d = 6 cm

Time [days]

SOM

/Biomas

s[g

dm-3bu

lk]

0 100 200 3000

0.1

0.2

0.3

0.4

d = 25 cm

Fig. 9 Results for principal problem P1 for SOM degradation network 1(no biomass dependence) showing transient evolution of SOM andbiomass concentrations at selected depths (3, 6, 10, and 25 cm from top

to bottom). Note that symbols represent HP1 results, while solid linesrepresent MIN3P-THCm results

Comput Geosci

Time[day]

SOM

/Biomas

s[g

dm-3bu

lk]

0 100 200 3000 0

0.1 0.1

0.2 0.2

0.3 0.3DOMSOM-P1SOM-P2BiomassSOM-L

Time[day]

SOM

/Biomas

s[g

dm-3bu

lk]

0 100 200 3000 0

0.1 0.1

0.2 0.2

0.3 0.3

DOM

[mol

L-1water]

d =6 cm

Time[days]

SOM

/Biomas

s[g

dm-3bu

lk]

0 100 200 3000 0

0.1 0.1

0.2 0.2

0.3 0.3

DOM

[mol

L-1water]

d= 10 cm

Time [day]

SOM

/Biomas

s[g

dm-3bu

lk]

0 100 200 3000 0

0.1 0.1

0.2 0.2

0.3 0.3

DOM

[mol

L-1water]

d = 25 cm

DOM

[mol

L-1water]

0

0.1

0.2

0.3d = 3 cm

Fig. 10 Results for principal problem P2 based on SOM degradationnetwork 2 (no biomass dependence) showing transient evolution ofDOM, SOM, biomass, and SOM-L concentrations at selected depths (3,

6, 10, and 25 cm from top to bottom). Note that symbols represent HP1results, while solid lines represent MIN3P-THCm results

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005

d = 6 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005

d = 25 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005

d = 50 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005

d = 100 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005

d = 10 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005 MIN3P-THCmHP1

d = 3 cm

Fig. 11 Results for principal problem P1 showing transient evolution of aqueous CO2 concentrations at selected depths (3, 6, 10, 25, 50, and 100 cmfrom top to bottom)

Comput Geosci

4 Results and discussion

4.1 Kinetic networks for SOM degradation(supporting problem C1)

The evolution of SOM-P1, SOM-P2, and microbial biomassin network 1 is similar for various formulations of degradationas a function of its dependency on biomass (Fig. 2a–c). Twodistinct periods can be observed during the evolution of mi-crobial biomass. The concentration of microbial biomass in-creases rapidly during the first 100 days, followed by a grad-ual decline and an approach towards quasi-steady-state condi-tions after 500 days. The rapid accumulation of biomass oc-curs because a fraction of the decomposed substrates (i.e.,SOM-P1 and SOM-P2) is rapidly assimilated by the microbialbiomass at high substrate concentrations, although the decayof microbial biomass concurrently leads to the production ofSOM-P1. After 500 days, the rate of substrate assimilationgradually decreases due to a decline of substrate concentra-tions. Also, SOM-P1 and SOM-P2 reach constant concentra-tions after 500 days, when quasi-steady-state conditions are

reached. Wutzler and Reichstein [12] also found that SOMpools eventually reach steady-state levels for the degradationrate formulations (Eqs.10–12) used in this study. Similar re-sults are obtained for network 2 (Fig. 2d–f). As a result of thefirst-order implementation of the sorption process (Eqs.13–15), the concentrations of SOM-L and DOM slowly approachequilibrium conditions as shown in Fig. 2d–f. In addition, Fig.2 illustrates the effect of different degradation rate formula-tions as a function of the dependency on biomass on ap-proaching the quasi-steady-state conditions. For example,the concentrations of SOM-P1 are slightly higher for thenon-explicit formulation in comparison to the linear and ex-ponential equations. These differences are related to the de-pendency of the FOM assimilation rate on SOM degradationrates. More detailed analysis of this topic is beyond the scopeof the current contribution, and the reader is referred to [12].

Figure 2 shows a near perfect agreement between the re-sults obtained by HP1 and MIN3P-THCm, with almost iden-tical transient evolution of all organic pools for networks 1 and2. The results for the inorganic pool also showed excellentagreement (results not shown).

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005 MIN3P-THCmHP1

d = 3 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005

d = 6 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005

d = 25 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005

d = 10 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005

d = 50 cm

Time [days]

CO

2(aq)

[mol

L-1H

2O]

0 100 200 300

0.001

0.002

0.003

0.004

0.005

d = 100 cm

Fig. 12 Results for principal problem P2 showing transient evolution of aqueous CO2 concentrations at selected depths (3, 6, 10, 25, 50, and 100 cmfrom top to bottom)

Comput Geosci

4.2 Transient water flow, solute transport, and gasgeneration (supporting problem C2)

Simulation results for supporting problem C2a show that tran-sient evolution of water contents (Fig. 3) and conservativesolute concentrations (Fig. 4) are affected by rainfall and evap-oration (Fig. 5a, b). Significantly different temporal responsesin water contents and solute concentrations can be observed inthe shallow (0–30 cm) and deep (30–100 cm) soil. Whilehigh-frequency temporal variability can be observed in shal-low depths, low-frequency variability can be observed indeeper horizons. This behavior is the result of high-frequency temporal variability of rainfall and evaporation thatdirectly propagates to water content, leading to substantialfluctuations of solute concentrations in the shallow soil, buta more muted response at greater depths. Both models agreewell in describing both pronounced fluctuations in water con-tents and conservative solute concentrations near the surfaceas well as in more dampened responses deeper in the soilprofile (Figs. 3 and 4). Moreover, there is a near perfect

agreement between the two codes in simulated actual conser-vative solute influxes and outfluxes (Fig. 5c, d), and cumula-tive conservative solute influxes and outfluxes (Fig. 5e, f)across the surface and bottom of the soil profile.

The supporting problem C2b considers soil respiration, ex-solution of CO2, diffusive gas transport of CO2, and CO2

emissions to the atmosphere. In the simulations, diffusion isconsidered to be the dominant transport process in the gasphase, and respiration is restricted to the shallow soil (0–30cm). The simulation results for water contents are identical tothe results for supporting problem C2a (results not shown).The concentrations of aqueous CO2 slightly increase withdepth (Fig. 6), which can be attributed to the aqueous CO2

transported downwards with infiltrating water and longer dif-fusion paths towards the ground surface. The largest massfluxes for CO2 occur in the gas phase and lead to emissionsto the atmosphere (Figs. 7f and 8d). An overall excellentagreement is reached between the results of HP1 andMIN3P-THCm for aqueous CO2 concentrations in the soilprofile (Fig. 6), actual water fluxes (Fig. 7a–b), and actual/

Time [days]

Actual

water

outflux

[mda

y-1]

0 100 200 300

0

0.01

0.02

0.03

0.04 (b)

Time [days]

Actual

water

influ

x[m

day-1

]

0 100 200 300

0

0.01

0.02

0.03

0.04 MIN3P-THCmHP1

(a)

Time [days]

Actual

solute

influ

x[m

olm

-2da

y-1]

0 100 200 300

0

0.02

0.04

0.06

0.08 (c)

Time [days]

Actual

solute

outflux

[mol

m-2da

y-1 ]

0 100 200 300

0

0.02

0.04

0.06

0.08 (d)

Time [days]

Actual

gasinflu

x[m

olm

-2da

y-1 ]

0 100 200 300

0.00

0.10

0.20

0.30(e)

Time [days]

Actual

gasou

tflux

[mol

m-2da

y-1 ]

0 100 200 300

0.00

0.10

0.20

0.30(f)

Fig. 13 Results for principal problem P1 showing transient evolution of aactual influx of water across the surface and b actual outflux of wateracross both the surface and bottom of the domain, c actual influx of a

solute across the surface and d actual outflux of a solute across the bottomof the domain, and e actual influx of gas across the bottom and f actualoutflux of gas across the surface of the domain

Comput Geosci

cumulative CO2 fluxes in the aqueous and gaseous phasesacross the surface and bottom of the soil profile (Figs. 7c–fand 8, respectively). Slight discrepancies exist in actual gas-eous CO2 outfluxes and cumulative aqueous CO2 influxes(Figs. 7f and 8a, respectively) across the soil-atmosphereboundary. However, the effect on the mass balance is negligi-ble, since differences in solute influxes are cancelled out bythe differences in gas effluxes. To assess these differences inmore detail, a sensitivity analysis on the effect of timestepping was conducted with the HP1 and MIN3P-THCmcodes (see SI, Fig. S.1). The maximum time step was variedby one order of magnitude. The sensitivity analysis shows thatthe results for MIN3P-THCm do not change significantly as afunction of time stepping, while the HP1 simulations showmore pronounced differences as a function of time stepping.In addition, the sensitivity analysis shows that the results ofHP1 approach those of MIN3P-THCm for smaller time steps.Therefore, the main reason for the small observed differencescan be attributed to the different coupling techniques (GIM inMIN3P-THCm and SNIA in HP1), which introduces smallyet acceptable operator splitting errors in the HP1 solutionfor larger time steps. The impact of these differences on theinterpretation of results is negligible. In addition, the currentbenchmark study does not account for the ingress of atmo-spheric O2. However, this is not a limitation of RTMs. BothHP1 and MIN3P-THCm are able to simulate atmospheric O2

ingress and soil CO2 egress, as was demonstrated in a previousbenchmarking study on the generation and attenuation of acidrock drainage [36].

4.3 Principal problems

The evolution of different SOM pools shows similartrends as was seen in the supporting problems C1.However, the evolution of DOM is smoothened due towater content fluctuations. As depicted in Figs. 9 and10 for networks 1 and 2, respectively, both models arecapable of describing SOM degradation during variablysaturated flow conditions and results agree well. CO2

produced by SOM degradation is partially released tothe atmosphere via diffusion in the gas phase (Figs.13f and S.4f), while CO2 is also transported to the bot-tom of the soil profile by infiltrating water (Figs. 11and 12). Note that CO2 concentrations close to the soilsurface are relatively low due to the surface boundarycondition, which mimics rapid CO2 release to the atmo-sphere. Agreement between the results of HP1 andMIN3P-THCm is excellent for water content (Figs. S.2and S.3) in the soil profile, actual water fluxes (Figs.13a, b and S.4a, b), actual aqueous/gaseous CO2 fluxes(Figs. 13c–f and S.3c–f), and cumulative aqueous/gaseous CO2 fluxes (Figs. 14a–d and S.5a–d) acrossthe surface and bottom of the soil profile. However,slight differences are observed for actual gaseous CO2

outfluxes (Figs. 13f and S.4f). Analogous to thesupporting problem C2b, the reason for these differ-ences can be attributed to small operator splitting errorsin HP1. However, differences are again small and donot affect the interpretation of modeling results.

Time [days]

Cum

.soluteinflu

x[m

olm

-2]

0 100 200 3000.0

1.0

2.0

3.0MIN3P-THCmHP1

(a)

Time [days]

Cum

.soluteou

tflux

[mol

m-2]

0 100 200 3000.0

1.0

2.0

3.0 (b)

Time [days]

Cum

.gas

influ

x[m

olm

-2]

0 100 200 300

0

20

40

60(c)

Time [days]

Cum

.gas

outflux

[mol

m-2]

0 100 200 300

0

20

40

60(d)

Fig. 14 Results for principal problem P1 showing transient evolution of a cumulative influx of a solute across the surface and b cumulative outflux of asolute across the bottom of the domain and c cumulative influx of gas across the bottom and d cumulative outflux of gas across the surface of the domain

Comput Geosci

5 Conclusions

A benchmark problem was established to evaluate the imple-mentation of SOM degradation models under variably saturat-ed flow conditions in generic reactive transport models. Tworeactive transport codes were involved in the benchmark study(namely HP1 and MIN3P-THCm). Both codes were capableof capturing the degradation of SOM and associated masstransport processes. Overall, excellent agreement was obtain-ed between the two codes. Small differences in simulatedresults can be attributed to different solution methods (i.e.,SNIA and GIM). However, differences between the simula-tion results are practically negligible and do not affect theinterpretation of modeling results. Consequently, good agree-ment between the results provides confidence in the use ofmulticomponent reactive transport codes for implementingC-cycling models in dynamic environments. In comparisonto classical SOM degradation models, multicomponent reac-tive transport codes have several distinct advantages such asthe providing of a flexible framework for implementing dif-ferent SOM degradation model structures and the tight-coupling with flow and mass transport processes. In addition,reactive transport codes also allow accounting for (i) soil statevariables in degradation models (e.g., Jacques et al., 2018[26]), (ii) geochemical reactions for pH and redox buffering,(iii) soil interactions with a single root and root architecture(e.g., Gérard et al., 2017 [37], Nowak et al., 2006 [38]), (iv)the effect of SOM on contaminant mobility (e.g., Letermeet al., 2014 [39]), (v) bioturbation (e.g., Jacques et al., 2018[26]), and (vi) soil structure and its effects on SOM degrada-tion and the transport of O2 (e.g., Kuka et al., 2007, [40];Keiluweit et al., 2016 [41]). The results presented here indi-cate that computer codes capable of solving this benchmarkprovide a promising platform for addressing similar problemsinvolving a range of climate conditions, soil types, soil mois-ture dynamics, and biogeochemical reactions.

Funding information Funding for this research was provided byAgriculture and Agri-Food Canada through the project Valuing diversityin agro-ecosystems: The interplay of natural habitat, integrated BMPs,and field cropping systems on GHG emissions and carbon stocks,supporting M. Jia with a Research Assistantship and through anNSERC (Natural Sciences and Engineering Research Council ofCanada) discovery grant held by K. Ulrich Mayer.

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