quantifying wetland methane emissions with process-based ...j. tang et al.: methane emission...

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Biogeosciences

Quantifying wetland methane emissions with process-based modelsof different complexities

J. Tang1,2, Q. Zhuang1,2,3, R. D. Shannon4, and J. R. White5

1Dept. of Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana, USA2Purdue Climate Change Research Center, West Lafayette, Indiana, USA3Department of Agronomy, Purdue University, West Lafayette, Indiana, USA4Department of Agricultural & Biological Engineering, Pennsylvania State University, University Park, Pennsylvania, USA5Biogeochemical Laboratories & Center for Research in Environmental Sciences, Indiana Univ., Bloomington, Indiana, USA

Received: 2 July 2010 – Published in Biogeosciences Discuss.: 16 August 2010Revised: 10 November 2010 – Accepted: 13 November 2010 – Published: 25 November 2010

Abstract. Bubbling is an important pathway of methaneemissions from wetland ecosystems. However theconcentration-based threshold function approach in currentbiogeochemistry models of methane is not sufficient to rep-resent the complex ebullition process. Here we revise anextant process-based biogeochemistry model, the TerrestrialEcosystem Model into a multi-substance model (CH4, O2,CO2 and N2) to simulate methane production, oxidation, andtransport (particularly ebullition) with different model com-plexities. When ebullition is modeled with a concentration-based threshold function and if the inhibition effect of oxy-gen on methane production and the competition for oxygenbetween methanotrophy and heterotrophic respiration are re-tained, the model becomes a two-substance system. Ignor-ing the role of oxygen, while still modeling ebullition with aconcentration-based threshold function, reduces the model toa one-substance system. These models were tested througha group of sensitivity analyses using data from two temper-ate peatland sites in Michigan. We demonstrate that onlythe four-substance model with a pressure-based ebullition al-gorithm is able to capture the episodic emissions inducedby a sudden decrease in atmospheric pressure or by a sud-den drop in water table. All models captured the retardationeffect on methane efflux from an increase in surface stand-ing water which results from the inhibition of diffusion andthe increase in rhizospheric oxidation. We conclude that to

Correspondence to:J. Tang([email protected])

more accurately account for the effects of atmospheric pres-sure dynamics and standing water on methane effluxes, themulti-substance model with a pressure-based ebullition algo-rithm should be used in the future to quantify global wetlandCH4 emissions. Further, to more accurately simulate the porewater gas concentrations and different pathways of methanetransport, an exponential root distribution function should beused and the phase-related parameters should be treated astemperature dependent.

1 Introduction

Methane (CH4) emitted from natural wetlandsis a signifi-cant component of its atmospheric budget. Biogeochemistryand atmospheric inversion models estimate the total wet-land emissions to be 100–230 Tg CH4 y−1, around 25% ofthe global emissions into the atmosphere under the currentclimate condition (Denman et al., 2007). Inverse modelingestimates the strengths of various CH4 sources and sinksby comparing the model simulated CH4 concentrations tospatially discrete and temporally continuous observations ofthe atmospheric CH4 concentrations (e.g.Houweling et al.,1999). Since all sources/sinks are treated simultaneously inthe inversion, the total CH4 emissions into the atmospherecan be well constrained. However, there are various limi-tations including the sparse in-situ observation networks ofatmospheric CH4 and unclear sources and sinks due to insuf-ficient understanding of the biogeochemical processes. Asa result, the estimates for different sources/sinks from inverse

Published by Copernicus Publications on behalf of the European Geosciences Union.

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3818 J. Tang et al.: Methane emission modeling

modeling are usually subject to great uncertainties. Process-based models integrate and extrapolate the knowledge fromfield studies at limited sites to regional and global scales. Be-cause of sparse site-level information and inadequate repre-sentation of CH4 processes in these models, the uncertain-ties in the quantification from biogeochemical modeling arealso substantial (e.g.,Walter et al., 2001; Zhuang et al., 2004,2009; Denman et al., 2007).

To date, a group of process-based models with differentcomplexities have been developed to quantify the spatial andtemporal patterns of wetland CH4 emissions. Among them,the one-substance models are widely used (e.g.,Walter andHeimann, 2000; Zhuang et al., 2004; van Huissteden et al.,2006). These models focus on CH4 only, and assume thatmethanogenesis and methanotrophy occur in anoxic and oxiczones, respectively, which are spatially separated by the po-sition of water table. In contrast, the two-substance modelconsiders CH4 and O2 simultaneously, and the methanogen-esis and methanotrophy occur according to the status of bothgases in soils (e.g.,Arah and Kirk, 2000). This is accom-plished by introducing the inhibition effect of O2 on CH4production and the competition for O2 between heterotrophicrespiration and methanotrophy. As such, CH4 oxidation andheterotrophic respiration dominate in the oxic zone whileCH4 production dominates in the anoxic zone. The two-substance models have been used in modeling CH4 emis-sions from rice paddies (Matthews et al., 2000), and showedreasonable results compared with field measurements. Otherexisting models are conceptually of either one-substance ortwo-substance model structure (e.g.,Potter, 1997; Zhanget al., 2002).

In biogeochemistry models, three pathways for gas trans-port are considered: (1) molecular diffusion, (2) plant-aidedtransport and (3) ebullition, though some models lump thethree pathways together (e.g.,Cao et al., 1995; Sass et al.,2000; Zhang et al., 2002). Ebullition, if considered explic-itly, is often modeled as a threshold phenomenon using theHeaviside function with some universally prescribed thresh-old concentration of the dissolved gases (e.g.,Walter andHeimann, 2000; Matthews et al., 2000). Field and analyticalstudies suggest such a simple algorithm does not fully repre-sent the physical processes of ebullition (Bazhin, 2001, 2004;Baird et al., 2004; Tokida et al., 2005, 2007). Specifically,several factors have not been considered in the concentration-based threshold function algorithms: (1) the composition ofthe bubbles affected by multiple substances such as CO2 andN2; (2) the effects of the hydrostacy affected by water tabledynamics and atmospheric pressure variation (Bazhin, 2001;Tokida et al., 2005, 2007) and (3) the ebullition threshold de-fined in terms of gas volumes is fuzzy rather than determin-istically predictable because of possible re-dissolution andgas entrapping, during the course of ebullition (Martens andKlump, 1980; Kellner et al., 2006; Coulthard et al., 2009).

In this study, we revise the CH4 module in a biogeo-chemistry model, the Terrestrial Ecosystem Model (TEM)

(Zhuang et al., 2004) by incorporating the effects of multi-ple substances in a soil profile and a probabilistic pressure-based algorithm for ebullition. We apply the revised modelto two temperate peatland ecosystems to demonstrate the im-portance of considering the effects of multiple substancesin soils on episodic emissions during atmospheric pressurechanges (Mattson and Likens, 1990). We also demonstratethe retardation effects of increases in standing water depthon CH4 effluxes when different model complexities are as-sumed (Jauhiainen et al., 2005; Zona et al., 2009).

2 Methods

2.1 Overview

We developed a four-substance CH4 module within a biogeo-chemistry model, the Terrestrial Ecosystem Model (Zhuanget al., 2004). The model was calibrated and applied to datafrom two temperate peatland sites in Michigan to demon-strate the capabilities of models with different complexitiesin simulating CH4 effluxes. A group of sensitivity analyseswere conducted to assess the need for a four-substance modelwith an improved ebullition algorithm.

2.2 The revised CH4 module

The governing equation for a non-adsorbed substrate in a soilcolumn (Fig.1) is:

∂y

∂t=

∂

∂z

(D

∂y

∂z

)+ P − Q − E − R

min(0,zwt) ≤ z ≤ Zsoil (1)

where

∂∂z

(D

∂y∂z

): Diffusion

P : ProductionQ : ConsumptionE : EbullitionR : Plant transport

(2)

and zwt (unit: m) is the water table depth, being negativewhen it is above the soil surface. For substancei, the bulkconcentrationyi (unit: mol m−3) is related to its aqueousconcentrationyi,w (unit: mol m−3 water) and gaseous con-centrationyi,a (unit: mol m−3 air) through

yi = εyi,a + θyi,w = (ε + θαi)yi,a (3)

whereε(z,t) (unit: m3 air m−3 soil) is air-filled porosity,αi

is the Bunsen coefficient for gasi (see Appendix A for itscalculation) andθ(z,t) (unit: m3 water m−3 soil) is the vol-umetric soil moisture.

The boundary conditions for Eq. (1) are

y0(t) = y(0,t) for volatiles (4)

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J. Tang et al.: Methane emission modeling 3819

Bubbles

N2

O2CO

2CH4

Lower boundary

Soil profile(T(z), θ(z))

Atmosphere

Standing water

Diffusion

Ps>=head

Planttransport

Fig. 1. Diagram showing the three major gas-transport pathwaysinvolved in the multi-substance CH4 model. See text for detailsabout the calculations.

∂y

∂z= 0 for nonvolatiles (5)

at the upper boundary (z = min(0,zwt)) and

∂y

∂z= 0 (6)

at the lower boundary (z = Zsoil) for all substrates.

2.2.1 Chemistry involved in methane production andconsumption

In wetland ecosystems, CH4 is produced primarily throughmethanogenesis

CH2O + CH2O → CO2 + CH4 (7)

and consumed through methanotrophy

CH4 + 2O2 → CO2 + 2H2O (8)

Methanogenesis can proceed in either of the two path-ways (Conrad, 1989), i.e. CO2+4H2→CH4+2H2O, orCH3COO−

+H+→CO2+CH4, both of which can equiva-

lently be reduced to Eq. (7). Though there are other path-ways, e.g. HCOO−+

12H2O+

14CO2→

14CH4+HCO−

3 , andCH3OH→

34CH4+

12H2O+

14CO2, leading to CH4 produc-

tion, we assumed they are minor as indicated in previousstudies (Conrad, 1989). If one makes the assumption that

dissolved oxygen is negligible in the aqueous phase, thenthe water table serves as a boundary in the soil between theoxic zone above the water table and the anoxic zone belowthe water table. Consequently, the equation to solve for thewetland CH4 profile in a soil column is reduced to a sys-tem of a single substance, i.e. CH4, only. Such was adoptedin Walter et al.(2001) andZhuang et al.(2004), where thebubbling was modeled as a switch-on and -off process witha prescribed threshold CH4 concentration, CH4,max (unit:mol m−3 water).

If one considers the competition for O2 in CH4 oxidationand respiration processes, a third stoichiometry is involved:

CH2O + O2 → CO2 + H2O (9)

With such, we obtained a two-substance model consideringboth CH4 and O2 in a soil profile. Characterization of the aer-obic and anaerobic zone in a soil column by the water tablein the one-substance system is now revised by introducingthe inhibition of O2 on CH4 production

PCH4 = P ∗

CH4/(1 + ηyO2,w) (10)

where P ∗

CH4(unit: mol m−3 s−1) is the maximum CH4

production potential when the environment is completelyanoxic, andη (unit: m3 water mol−1) is a parameter repre-senting the sensitivity of methanogenesis to the concentra-tion of dissolved oxygenyO2,w in pore water. A value of400 m3 water mol−1 from Arah and Kirk (2000) was usedfor η. P ∗

CH4is defined in Appendix B.

Accordingly, the methanotrophy is restricted by the avail-ability of O2 as

QCH4 = Q∗

CH4

yCH4,w

kCH4 + yCH4,w

yO2,w

kO2 + yO2,w(11)

whereQ∗

CH4(unit: mol m−3 s−1) is the oxidation potential

when aqueous O2 and CH4 are not limited, andkCH4 andkO2 are Michaelis-Menten constants (unit: mol m−3 water)for CH4 and O2. We use values of 0.44 mol m−3 water and0.33 mol m−3 water, respectively, forkCH4 andkO2 (Arah andKirk , 2000). Q∗

CH4is defined in Appendix B.

The consumption of O2 due to heterotrophic respirationand CH4 oxidation is modeled as

QO2 = 2QCH4 + V ∗

RyO2,w

kR + yO2,w(12)

whereV ∗

R is the maximum rate of respiration when O2 isnot the limiting factor,kR is the Michaelis-Menten constant,using a value of 0.22 mol m−3 water (Arah and Kirk, 2000).As in Matthews et al.(2000), we assumed only the pro-cess of heterotrophic respiration competes with the processof methanotrophy for O2, thusV ∗

R is twice that ofP ∗

CH4. We

also neglected the O2 consumption by electron acceptor re-oxidation (Segers and Leffelaar, 2001; van Bodegom et al.,2001) for the moment. Since no O2 is produced in the soil,PO2 is set to zero.

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(1) Initialize the total bubble flux E to zero(2) DO I = N, N0, −1(3) Compute potential bubble flux Eb at layer l IF Eb <= 0 .AND. E = 0 THEN GOTO step(2) ELSE IF Eb >= 0 THEN(4) Combine the bubbles, E=E+Eb ELSE(5) Draw a random number u from uniform distribution U[0,1] IF u <= abs(Eb)/(abs(Eb)+E) THEN IF abs(Eb) <= E THEN(6) Dissolve bubbles to make equality in Eq.(14) hold at layer l, and update, E=E−abs(Eb) ELSE(7) Dissolve bubbles with the amount E, thus E=0 ENDIF ENDIF ENDIF ENDIF ENDDO(8) Release E to the atmosphere or add directly to the soil layer that is right above the water table.Here, N is node ID of the bottom layer of the computation grids, and N0 is node IDof the water table.

Fig. 2. The probabilistic algorithm used in the S4 model to computeebullition.

Carbon dioxide is produced in methanogenesis, methan-otrophy and aerobic respiration:

PCO2 = PCH4 + QO2 − QCH4 (13)

Just as for O2 consumption, CO2 production from electronacceptor reduction (Conrad, 1989) was also neglected here.In the soil, consumption of CO2 is zero, therefore,QCO2 = 0.

For N2, we assumed no production and consumption in thesoil profile, therefore,PN2 = QN2 = 0.

2.2.2 The pressure-based ebullition algorithm

We revised TEM to consider effects of hydrostacy on ebulli-tion. Tokida et al.(2007) observed an abrupt change in theCH4 emission rates associated with a decreasing atmosphericpressure, and the mixing ratio of CH4 in the gas bubbles wasno more than 50% (see their Fig. 2).Zona et al.(2009) foundthat, when the surface standing water increased, the CH4 ef-flux was effectively retarded. Such behavior has not beenexplicitly considered and modeled in the process-based CH4models with the conventional algorithms of ebullition usinga prescribed threshold of water dissolved CH4 (e.g., Wal-ter and Heimann, 2000; Arah and Kirk, 2000; Zhuang et al.,2004). Tokida et al.(2007) suggested a three-substance sys-tem, including CH4, CO2 and N2, should be used to modelthe ebullition. Indeed,Bazhin(2001, 2004) suggested thatebullition is triggered at a certain depth when the total pres-sure of the water-dissolved gases exceeds the hydrostaticpressure imposed at that depth by the water table and at-mospheric pressure. Therefore, the simple concentration-based threshold approach was replaced by an equation ofhydrostatic equilibrium. In this study, we considered a four-substance system, i.e. CH4, O2, CO2 and N2, and ignored

other possible trace gases (e.g. argon and hydrogen). We for-mulated the bubbling criterion (Fig.1) as

Ps =

∑i

Psi =

∑i

yi,w(z)

Hi(z)≥ P0

(p+

b

z0+

zd

z0

)= head (14)

wherePsi is the partial pressure andHi (see Appendix A forthe formula) is the Henry’s law constant for gasi, p (= p/P0)is the scaled atmospheric pressure,P0 = 105 Pa,z0 = 10 m,andzd = min(z−zs,z−zwt), and

b =

{zs − zwt, if zwt < 0∫ zwtzs

θ(z)θs(z)

dz, if zwt ≥ 0(15)

wherezs is the depth of soil surface, set to 0.0; and head(unit: Pa) is the total hydrostatic pressure head imposed byatmosphere and water above depthz. The second equation inEq. (15) accounts for the capillary force by considering therate of saturation of the soil. Further we assumed bubblingonly occurs below the water table, thuszd is always non-negative. Note, in Eq. (14), we did not consider the effects ofbubble shapes and number of bubbles, which would impactthe surface tension between the bubble and water interfaceand consequently the bubbling criterion (Peck, 1960). Wealso neglected the change of water distribution caused by theebullition (Rosenberry et al., 2003), which would cause somebubbles to be trapped and released later.

With Eq. (14), the potential ebullition for gasi at a certaindepthz is computed as

Ebi =

∫ Zsoil

zwt

(yi(s) − yi(s))δ(s − z)ds (16)

where the equilibrium bulk concentration is

yi = (ε/αi + θ)yi,w (17)

and the equilibrium aqueous concentration is

yi,w = headPsi

PsHi(z) (18)

andδ(s) is the Dirac delta function. The potential ebullitioncomputed from Eq. (16) can either be positive or negative,with positive implying bubble formation, and negative im-plying potential bubble re-dissolution.

To partly account for the fact that a fraction of the bub-bles could be re-dissolved during their travel to the at-mosphere (e.g.,Martens and Klump, 1980), we used thealgorithm in Fig. 2 to compute the ebullition. In thisprobabilistic algorithm, the possibility (pr) of re-dissolutionis proportional to the potential fraction of re-dissolutionabs(Eb(z))/[abs(Eb(z)) + E(z)] (if Eb(z) is negative cal-culated from Eq.16). We modeled the re-dissolution asa yes/no process, if the random numberu drawn from a uni-form distributionU [0,1] is less thanpr, dissolve the bubbleswith an amount of abs(Eb(z)) (or E(z) if E(z)≤abs(Eb(z))),



otherwise, bubbles continue moving upward without re-dissolution, and combine with possible bubbles generated atupper layers.

The algorithm was applied starting from the bottom of soilcolumn to the level of water table. The total ebullitionE iseither released directly to the atmosphere or added to the soilcolumn, depending on the location of water table. When thewater table is at or above the soil surface, the gases carried inthe bubbles are directly emitted to the atmosphere; otherwise,they are added to the soil layer right above the water table.

There is an alternative way to implement the above ebul-lition algorithm, i.e. using the volumetric criteria, such as inKellner et al.(2006); Granberg et al.(2001), and most re-cently in Wania et al.(2010). Using the ideal gas law, thevolume of substances in gaseous phase in equilibrium withthe aqueous phase can be computed at all depths. The gasvolumes are then compared with some predefined thresholdto trigger the bubbles. However, such a threshold is fuzzyand varies temporally and spatially due to a group of dif-ferent factors (Baird et al., 2004; Kellner et al., 2006). Ourimplementation relates the ebullition directly to the pressure.As such, the ebullition criteria can be determined physicallyusing the available information on gas content and soil waterelevations. Also, our algorithm does not need to make anyassumption of the relative fractions of different gases in thebubbles (Kellner et al., 2006). Arguably, ebullition can evenoccur without the existence of CH4, as long as the buoyancyis greater than the weight of the bubble. There are processesthat have not been accounted for in the algorithm, e.g. en-trapped gas due to a wetting process from the soil surfacedown into the column, which could cause bubble formation(Kellner et al., 2006). Solutions should be found in futurestudies to address such events. It is likely that our algorithmwill not always give superior results to that obtained using thevolume-threshold-based method in other studies (e.g.,Waniaet al., 2010, and comparison is needed). However, ease of im-plementation will favor inclusion of this approach for othergases in future modeling.

2.2.3 Other transport routes and modelimplementations

We revised the pathways of diffusion and plant-aided trans-port in Zhuang et al.(2004) (see Appendix C for details).These and other processes described in previous sectionsgave the governing equations for CH4, CO2, O2 and N2 in-volved in the four-substance model in Appendix C.

As a result, the net CH4 efflux was computed

FCH4 = −

(DCH4

∂yCH4

∂z

)z=0

+(1−POX)

∫ zs

Zsoil

RCH4dz

+ Heaviside(zs−zwt)ECH4(zwt) (19)

wherePOX is set to 0.5 for the one-substance model (Walterand Heimann, 2000) and 0.0, otherwise.

We used the mass balance approach to calculate the dif-fusive flux to avoid the ambiguity in choosing the depthfor computation (Rothfuss and Conrad, 1998). The gov-erning equation Eq. (1) was solved using the method oflines (Schiesser, 1991) with a first order implicit projector-corrector method for the reaction terms. The integration wasdone with a time step of 2400 s. The soil column was ap-proximated to a depth of 4 m with an exponentially stretchinggrid (a total of 40 nodes) that has finer grid resolution at thetop and coarser grid resolution at the bottom (Oleson et al.,2004).

The revised TEM CH4 module has three different levels ofcomplexity: the one-substance model (S1 model hereafter)was obtained by (1) retaining the processes of methanogen-esis and methanotrophy, (2) excluding processes involvingother traces gases and (3) modeling ebullition with the con-ventional algorithm using a prescribed threshold CH4,maxequal to 1.31 mol m−3 water (at 25◦C); similarly, the two-substance model (S2 model hence after) was obtained byconsidering CH4 and O2 simultaneously and modeling theebullition with the concentration-based threshold approach,where O2,max equal to 1.23 mol m−3 water (at 25◦C) andCH4,max equal to 1.31 mol m−3 water (at 25◦C); when fourgases were considered and ebullition was modeled with thenew probabilistic pressure-based algorithm, a four-substancemodel (S4 model hereafter) was obtained.

2.3 Study sites

Two temperate peatlands located in southern Michigan on theEdwin S. George Reserve, a University of Michigan field sta-tion were used to test our revised CH4 module. Three yearsof measurements from 1991 to 1993 were taken at BuckHollow Bog and Big Cassandra Bog (42◦27′ N, 84◦1′ W).Buck Hollow Bog is an open peatland covered by a wet lawnof Sphagnumspecies, with a dense cover ofScheuchzeriapalustris, an arrow-grass. Three flux chambers were groupedin a triangular pattern approximately 10 m apart to measurethe net CH4 flux in the Buck Hollow Bog. Measurementswere taken at four sites at the Big Cassandra Bog. Sites 2and 3 were used in this study, because these two sites aresimilar in terms of ecosystem conditions. The sites at the BigCassandra Bog are dominated bySphagnumandPolytrichummosses and are covered by a dense stand ofChamaedaphnecalyculata. Measurements of net CH4 fluxes were made us-ing static chambers, and gas samples were collected and an-alyzed within 3–4 days of collection on a Shimadzu GC-14Agas chromatograph with a flame ionization detector. Envi-ronmental variables including water table depth and soil tem-perature from 5 cm above the peat surface to 100 cm withinthe peat column were monitored and used as driving data forthe model in this study. Available pore water concentrationprofiles (with a detection limit 0.1 µM) were also used in ourassessment of the model. For a detailed description of thestudy sites and assessment of measurements, readers can re-fer toShannon and White(1994).



−200 0 200 400 600 800 1000 1200 1400−0.5

0

0.5

1

1.5

2

Ordinal day

Fig. 3. The time series of scaled NPP (scaled with the median peakNPP at the site from a 100-year simulations) used as driving data inthis study. Same data were used at both sites, with truncation intoproper time periods.

2.4 Standard simulations

Standard simulations were conducted to evaluate the per-formances of the different models at both sites. The dif-ferent model formulations were considered to include indi-vidual parameters whose values were calibrated in a model-specific way by trial and error. Specifically, we modifiedthe parameter values to match the simulated fluxes and porewater concentrations as closely as possible to the measure-ments (Table1), so that the differences between differentmodel simulations were mainly due to different model for-mulations. We used the measured water table depth and soiltemperature as environmental forcing. Since no site-specificmeasurements of atmospheric pressure were available, wesimply set total pressure to 1 atm, a standard value that hasbeen used in other model studies (Walter and Heimann, 2000;Zhuang et al., 2004). For soil porosity, we assumed a valueof 0.83 v v−1 for depths shallower than 0.5 m, linearly de-creasing to 0.53 v v−1 at 0.9 m, and constant at 0.53 v v−1 tothe lower boundary of 4 m. The scaled NPP data (Fig.3) re-quired to model CH4 production were derived from simula-tions using TEM driven with monthly climate data (Mitchellet al., 2004). For the atmospheric mixing ratio of the gasesinvolved, we assume 0.209 v v−1 for O2, 0.781 v v−1 for N2,385 ppmv for CO2 and 1740 ppbv for CH4 (Forster et al.,2007).

2.5 Model sensitivity studies

To test the responses of the different models to water tabledynamics, we ran our models with the time series of watertable depth artificially increased or decreased over a specifictime period during the emission season. As shown in Fig.4,for the Buck Hollow site, we increased the water table by10 cm between ordinal day 150 and 160 (1 January 1991 wasset to ordinal day 1), and decreased by 10 cm between ordi-nal day 590 and 600; for the Big Cassandra site, we increasedthe water table depth by 10 cm between ordinal day 135 and145, and decreased by 10 cm between ordinal day 689 and

−200 0 200 400 600 800 1000 1200 1400−20

−10

0

10

20

wat

er ta

ble

(cm

)

(a)

0 200 400 600 800 1000 1200−50

−25

0

25

50

Ordinal day

wat

er ta

ble

(cm

) (b)

SyntheticMesurement

Fig. 4. The time series of water table depth used as driving data inthis study at:(a) Buck Hollow site;(b) Big Cassandra site.

699. These days were chosen such that the differences of theCH4 effluxes between the standard simulations and sensitiv-ity simulations were significant enough to be identified. Theresults were analyzed by comparing simulations with thosefrom standard simulations.

Two sets of experiments were used to test the model re-sponse to atmospheric pressure change. First, we conductedsensitivity simulations using a time series of artificially per-turbed low pressure or high pressure events (specifically930 hPa low and 1045 hPa high) on two arbitrarily chosendays during the high-emission season in summer (Fig.5).These two days were chosen based on the same criteria asthat used in the water table sensitivity study. The effectof changing atmospheric pressure was analyzed by com-paring the change in pathways of CH4 transport with thatfrom the standard simulation. This was used to analyzewhether the response is physically consistent or not. A sec-ond test was carried out to evaluate the overall effect of at-mospheric pressure variability using a time series of atmo-spheric pressure (Fig.6) extracted from the European Centrefor Medium-Range Weather Forecasts (ECMWF) Interim re-analysis dataset at the grid that encompassed the site for thesame time period of measurement. The response was againanalyzed by comparing the results to the standard simula-tions.

3 Results and discussion

3.1 Comparisons between standard model simulationsand site-level observations

All models resulted in similar CH4 fluxes (Table2). Specif-ically, for the Buck Hollow site, the S1, S2 and S4 mod-els all captured the temporal variability of the CH4 fluxes(Fig. 7a). Because of the probabilistic feature of the S4model, mulitple runs were conducted. The differences fromthese multiple runs were indistinguishable because the emis-sion routes at these two sites were dominated by plant-aided transport, and bubble redissolution rarely occured. The



Table 1. Parameters calibrated for standard model simulations.

PCH4 PQ10 OCH4 Rveg(mol m−3 s−1) (None) (mol m−3 s−1) (None)

Buck Hollow site

S1-model 3.5×10−7 12.7 1.10×10−7 1.2×10−3

S2-model 2.5×10−6 12.7 1.10×10−8 1.2×10−3

S4-model 1.25×10−6 12.7 1.10×10−8 1.2×10−3

Big Cassandra site

S1-model 7.5×10−8 6 1×10−7 1×10−3

S2-model 2.75×10−6 6 5×10−8 1×10−3

S4-model 1.375×10−6 6 1×10−7 1×10−3

−200 0 200 400 600 800 1000 1200 1400

0.9

1

1.1

Ordinal day

p(A

tm)

(a)

0 200 400 600 800 1000 1200

0.9

1

1.1

Ordinal day

p(A

tm)

(b)

Fig. 5. Synthetic atmospheric pressure used in simulations for sen-sitivity analysis at:(a) Buck Hollow site;(b) Big Cassandra site.

mean from an ensemble simulation of size four was shownfor comparison. The S4 model performed best in termsof linear fitting and the root mean square error (RMSE)against the measurements (Table2). The S1 model presentedthe second best results, with the simplest model structure.Over the three-year period, the simulated mean daily fluxeswere 107.00 mg CH4 m−2 d−1, 168.82 mg CH4 m−2 d−1 and114.43 mg CH4 m−2 d−1, respectively by the S1, S2 and S4model. The S2 model gave almost 50% higher emission thandid the S1 and S4 model. In the S1 simulation, the max-imum production rate was at least an order of magnitudesmaller than those of S2 and S4 models because it includedno inhibition effect of O2 on methanogenesis (Table1). Themaximum oxidation rates (OCH4) were similar in magnitude.Note that the simulations (except S4) were not very sensitiveto OCH4.

The importance of different CH4 transport pathways var-ied in different models (Fig.7a). Diffusion played a signif-icant role in the release of CH4 into the atmosphere, eventhough plant transport remained the dominant pathway in S4simulations. In S2 simulations, plant transport accountedfor more than 90% of the efflux into the atmosphere. The

−200 0 200 400 600 800 1000 1200 1400960

970

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1020

Atm

osph

eric

pre

ssur

e (h

Pa)

Ordinal day

Fig. 6. Transient atmospheric pressure used in simulations for sen-sitivity analysis. The same time series was applied at both sites,with truncation into proper time periods.

modeled diffusion contribution to efflux reached a short-termmaximum between day 170 and 180 in the S1 simulations.This was due to a sudden and substantial decrease in wa-ter table from above the peat surface to below the peat sur-face (Fig.4). This increased the concentration gradient ofthe CH4 near the peat surface and thus increased diffusion.Such short-term changes were also found in the S2 and S4simulations, but with smaller magnitudes. All the modelssuggested that the efflux through ebullition was small, whichagrees with measurements (Shannon and White, 1994). Inthe S4 simulation, the ebullition played a larger role than itdid in S1 and S2 simulations.

S1 performed the best in simulating pore water concen-trations; followed by the S2 model and then the S4 model(Fig. 7a). For 12 June 1993, none of the models presenteda satisfying result. The discrepancy might be due to the non-linearities of the transient simulations. For example, the porewater concentrations at a certain day were impacted by re-sults in previous days. Uncertainty in the driving data (e.g.soil temperature) is another source of such discrepancy.

At the Big Cassandra site, the simulated effluxes were lesssatisfying than the Buck Hollow Bog site, though S4 modelperformed the best, followed by the S2 model and then S1



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SimulationObservation

TotalPlt+DiffDiff


TotalPlt+DiffDiff

Fig. 7a. Methane effluxes, component-wise emissions and pore water concentration profiles from one-substance model (S1 model) in thestandard simulations.(a) Panels for the Buck Hollow site.(b) Panels for the Big Cassandra site. Dashed lines indicate the level of watertables.

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TotalPlt+DiffDiff

Fig. 7b. Methane effluxes, component-wise emissions and pore water concentration profiles from two-substance model (S2 model) in thestandard simulations.(c) Panels for the Buck Hollow site.(d) Panels for the Big Cassandra site. Dashed lines indicate the level of watertables.



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TotalPlt+DiffDiff


TotalPlt+DiffDiff

Fig. 7c. Methane effluxes, component-wise emissions and pore water concentration profiles from four-substance model (S4 model) in thestandard simulations.(e) Panels for the Buck Hollow site.(f) Panels for the Big Cassandra site. Dashed lines indicate the level of watertables.

Table 2. Comparison of CH4 efflux from the standard simulations to the measurements at the two Michigan peatlands. All statistics weretested for significance and were found significant withp < 0.001.

Slope Intercept RMSE R2

(None) (mg CH4 m−2 d−1) (mg CH4 m−2 d−1) (None)

Buck Hollow site

S1-model 0.79 83.5 165.1 0.51S2-model 0.65 50.1 168.6 0.60S4-model 0.84 68.0 154.5 0.55

Big Cassandra site

S1-model 0.31 15.9 86.6 0.13S2-model 0.52 −1.0 74.5 0.27S4-model 0.78 −10.8 61.2 0.31

model. Particularly for the second half year of 1991 and theyear 1992, the results compared poorly with measurements.This underperformance may be due to an inadequate repre-sentation of the methanogenesis substrate, which was simu-lated in TEM but has not been specifically calibrated for wet-land ecosystems. For the three-year period, the mean dailyfluxes were 42.51 mg CH4 m−2 d−1, 50.83 mg CH4 m−2 d−1

and 45.51 mg CH4 m−2 d−1, respectively, by the S1, S2 and

S4 models. Still, S2 simulated the highest CH4 emissionamong the three models. At this site, plant transport was themost important pathway, and ebullition was relatively unim-portant. All three models presented similar results for porewater concentrations (Fig.7a).



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Ordinal day

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100(f) S4

Ordinal day

+ −

Fig. 8. Water table sensitivities with models of different complexities. Left-hand panels are for Buck Hollow site; right-hand panels are forBig Cassandra site. The red symbol “+” indicates the period of artificially increased water table depth, and the green symbol “−” indicatesthe period of artificially decreased water table depth.

3.2 Model sensitivity analyses

3.2.1 Sensitivity to water table change

We found that the response to a 10 cm change in surfacestanding water caused a change in the CH4 efflux by as muchas−50∼ 300 mg CH4 m−2 d−1 (Fig. 8). Such responses de-pend on site characteristics and model complexity. At theBig Cassandra site, models S1 and S2 yielded a stronger re-sponse in effluxes to the water table increase than did theS4 model, while the opposite occurred for the water tabledecrease. At the Buck Hollow site, the responses of differ-ent models to the water table change were similar, but S1gave a much stronger response to the water table decreasethan did models S2 and S4. Nevertheless, all the modelssuccessfully predicted the retardation effect of an increasein surface standing water on CH4 efflux (Fig. 9). This canbe explained by the low diffusivity of gases in water relativeto air. A higher column of surface standing water representsa longer distance of diffusion before gas can escape into theatmosphere. This phenomenon may account for CH4 accu-mulation in the peat column, which in turn enhances plantmediated transport and the oxidation of CH4 in the rhizo-sphere, which decreases the efflux. When water table depthdecreases, the diffusion distance is reduced, and efflux to theatmosphere increases (Fig.9). In places where emergent vas-cular plants are sparse, a decrease in water table depth couldenhance CH4 efflux through ebullition. This was tested by re-

moving the plants and using the remaining parameters fromTable2 in the simulations. The results are shown in Fig.10.We found that the S1 and S2 models had negligible ebulli-tion compared to that from model S4 in response to changesin water table. The burst of ebullition predicted by model S4was more significant at the onset of a drop in standing wa-ter level. Then it decreased as the water table continuouslydropped and finally reached zero ebullition when the CH4accumulation was too low to support ebullition. In contrast,the S1 and S2 models predicted that diffusion was the majorpathway of CH4 efflux and greatly underestimated the CH4emissions through ebullition. Field data from Buck Hollowsite also supported ebullition as important when the vegeta-tion is sparser (Shannon et al., 1996). These findings sug-gest that while models S1 and S2 performed relatively wellwith careful calibrations, the positive results were fortuitous.They represent an inadequate formulation but an artful pa-rameterization of the problem.

3.2.2 Sensitivity to atmospheric pressure change

For the first sensitivity test of the models to atmosphericpressure change, S1 and S2 models showed much weaker(101

∼ 102 weaker) responses than that of the S4 model(Fig.11). In both S1 and S2 models, a change in atmosphericpressure can only affect the atmospheric concentration of thegases. Given the small feasible range of atmospheric temper-ature change and atmospheric pressure change, the change in



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Fig. 9. Zoom-in plots for the water table sensitivity with models of different complexities at the Buck Hollow site. Left-hand panels werefor the period where the water table depth is increased by 10 cm compared to the measured data, right-hand panels are for the period wherethe water table depth is decreased by 10 cm. The arrows indicate when the specified water table change starts and ends.

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S1 modelS2 modelS4 model

Fig. 10. Methane effluxes through ebullition at the Buck Hollowsite when no vegetation is present to support plant aided transport.See text for details.

atmospheric CH4 concentration is small, implying a smallchange of the diffusion rate and thus the methane efflux inthese two models. However, in the S4 model, the atmo-spheric pressure was further related to the ebullition fluxes.When a low atmospheric pressure occurred, the ebullitioncriterion became less restrictive, and bubbles were more eas-ily formed, enhancing the ebullition. In this simulation, a de-crease in atmospheric pressure could trigger an episodic in-crease in CH4 efflux by as much as 120 mg CH4 m−2 d−1 at

the Buck Hollow site and as much as 80 mg CH4 m−2 d−1 atthe Big Cassandra site, comparable to the enhancement dueto a decrease in surface standing water table depth.

Results from the sensitivity tests of transient atmosphericpressure were analyzed, which we found were very differ-ent with the different models (see Fig.12). For instance, incases of low atmospheric pressure events at the Buck Hollowsite, the S4 model usually predicted higher fluxes through en-hancement of ebullition. For the S1 model, response to atmo-spheric pressure change was negligible. The S2 model alsoresponded significantly to the change of atmospheric pres-sure, but showed lower fluxes in accordance with a lowerconcentration of atmospheric CH4 at the upper boundary. Incases of high pressure events, S4 yielded reduced the fluxesby suppressing ebullition, S2 yielded enhanced fluxes dueto a higher atmospheric concentration of CH4 at the upperboundary, and S1 showed little response. Similar resultswere found at the Big Cassandra site. The change of atmo-spheric pressure also changed the rate of plant aided transportand diffusion. However, in our formulation of the algorithm,ebullition is the preferred route if it is triggered (which wealso believe is true in the field, e.g.Tokida et al., 2005). Byanalyzing the cumulative differences, we found for the three-year period at the Buck Hollow site that the S4 model pre-dicted around 5% more emitted CH4 using the transient at-mospheric pressure data than it did using the standard 1 atmpressure. The S2 model, in contrast, predicted around 3%



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Ordinal day

− +

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(f) S4

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− +

Fig. 11. Atmospheric pressure sensitivities with models of different complexities.(a), (c) and(e) panels are for Buck Hollow site;(b), (d)and(f) panels are for Big Cassandra site. The red symbol “+” indicates the day of artificially perturbed high pressure event, and the greensymbol “−” indicates the day of artificially perturbed low pressure event. Note the scale of results from S4 model is 102 of that from S2model, and 103 of that from S1 model.

less emission when the transient atmospheric pressure wasused. Similar results were found for the Big Cassandra site,with smaller differences, in accordance with the lower emis-sion rates.

3.3 The importance of using temperature dependentparameters

In our standard and sensitivity simulations with the revisedCH4 module, we treated the phase-related parameters, suchas diffusivities, Henry’s law constants and Bunsen coef-ficients as temperature dependent. Analysis showed that,within the typical temperature range (e.g.,−5 to 30◦C), thediffusivity of CO2 in water changed± 5%, the Henry’s lawconstant and Bunsen coefficient changed± 50% (results notshown). For CH4, its diffusivity in air changed± 10% andin water changed± 5%, but the Henry’s law constant andBunsen coefficient changed± 40%. To test if fixing theseparameters at a specific reference temperature could signif-icantly affect the results, we conducted a set of simulationswith the phase-related parameter values corresponding to areference temperature of 12.5◦C.

We found, for the S1 model, that the temperature depen-dence of these parameters did not change the efflux signif-icantly (Fig. 13). However, compared to the standard sim-ulation, both the S2 and S4 models predicted a higher CH4

efflux during high emission periods. Given that soil tempera-tures at the two sites were often above the reference tempera-ture during the high-emission summer season, the lower sol-ubility computed with the reference temperature allowed lessO2 and CH4 to be stored in the soil, given almost the samerate of CH4 production. Further, considering the inhibitioneffect of O2 on methanogenesis and the stimulus effect of O2on methanotrophy, the higher emissions associated with theS2 and S4 models using coefficient values at the referencetemperature is then explained as a stimulus of gas transportto the atmosphere. We conclude that fixing phase-related pa-rameters at their reference temperature values is safe for theS1 model, but that temperature-dependent parameters shouldbe used in the S2 and S4 models.

3.4 The role of root density distribution

Previous CH4 modeling has used a linear function for the ver-tical distribution of root density (e.g.,Walter and Heimann,2000; Zhuang et al., 2004; also see Eq. (D2) in Appendix D).However, root biomass is often found to be exponentiallydistributed (Jackson et al., 1996), and an exponential rootdistribution could also be used (e.g.,van Huissteden et al.,2006). Here we implemented both linear and exponentialroot distribution functions in our revised CH4 module to testif they make a difference in CH4 effluxes (Tables1–4) and



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Fig. 12. Differences in the response to transient atmospheric pressure and that to constant atmospheric pressure with models of differentcomplexities.(a) Time series of the absolute difference at the Buck Hollow site.(b) Time series of cumulative difference at the Buck Hollowsite. (c) Time series of the absolute difference at the Big Cassandra site.(d) Time series of cumulative difference at the Big Cassandrasite. The difference is defined by subtracting the fluxes simulated with the standard 1 atm pressure from that using the transient atmosphericpressure data.

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Fig. 13. Impact of temperature dependence of phase-related parameters on the CH4 efflux simulations with models of different complexitiesat: (a) Buck Hollow site;(b) Big Cassandra site. The black line denotes wherey = x. The results from standard simulations were plotted asabscissa.



Table 3. Parameters calibrated for model simulations using a linear root distribution function.

PCH4 PQ10 OCH4 Rveg(mol m−3 s−1) (None) (mol m−3 s−1) (None)

Buck Hollow site

S1-model 3.0×10−8 12.7 1.10×10−7 4.0×10−2

S2-model 2.0×10−6 12.7 1.10×10−8 4.0×10−2

S4-model 7.5×10−7 12.7 1.10×10−8 4.0×10−2

Big Cassandra site

S1-model 5.0×10−8 6 1×10−7 1.5×10−3

S2-model 1.5×10−6 6 5×10−8 1.5×10−3

S4-model 5.0×10−7 6 1×10−7 1.5×10−3

Table 4. Comparison of CH4 efflux from the simulations using a linear root distribution function to the measurements at the two Michiganpeatlands. All statistics were tested for significance and were found significant withp<0.001, except those denoted in the parentheses.

Slope Intercept RMSE R2

(None) (mg CH4 m−2 d−1) (mg CH4 m−2 d−1) (None)

Buck Hollow site

S1-model 1.21 54.9 154.1 0.66S2-model 0.78 47.9 139.8 0.64S4-model 0.68 127.6 216.6 0.22

Big Cassandra site

S1-model 0.10 32.1 103.7 0.19 (p=0.2)S2-model 0.10 26.5 183.6 0.07 (p<0.01)S4-model 0.27 13.2 104.6 0.14

pore water concentrations. In both configurations, the pa-rameter values were obtained from calibration based on mea-surement data. The differences between the simulations werethus mainly due to the different model configurations.

We found the contributions from different pathways weredifferent when two different root density distribution func-tions were used (Figs.7a and14a). In the standard simula-tion using an exponential root density distribution function,ebullition played a minor role, whereas in the simulation em-ploying a linear root density distribution, the ebullition wasmore significant, particularly in the S2 and S4 models. Theebullition was enhanced more at the Big Cassandra site thanat the Buck Hollow site, suggesting that the responses of themodels to two different root distribution functions are sitedependent and related to the net CH4 production character-istics of the site. In the simulation employing the linear rootdistribution function, model-derived pore water CH4 concen-tration profiles underestimated field observations in the upperlevel of the peat column (Fig.14a). The lower CH4 concen-trations ware due to a poor representation of transport in the

upper portion of the soil column when a linear root densityfunction was used. Conversely, the exponential root distribu-tion extends smoothly down into depth of the peat column,producing more realistic pore water CH4 concentration pro-files. Therefore, though rigorous parameterization can leadto a good fit of the modeled CH4 fluxes with respect to themeasurements, the model fails to capture other aspects of themeasurements when an improper formulation of the problemis used. Also, in our case, the exponential distribution is a su-perior representation of root density as a function of depth.

3.5 Issues for regional application of the differentCH4 models

The CH4 models of different complexities developed in thisstudy can be used for regional hindcast and projection of wet-land CH4 emissions provided that necessary climate forc-ing data are available. This is not a problem when theseCH4 models are used inside a biogeochemistry model, suchas TEM, where the necessary climate forcing data to the



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Fig. 14a. Methane effluxes, component-wise emissions and pore water concentration profiles from one-substance model (S1 model) in testsimulations using a linear root distribution function.(a) Panels for the Buck Hollow site.(b) Panels for the Big Cassandra site. Dashed linesindicate the level of water tables.

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Fig. 14b. Methane effluxes, component-wise emissions and pore water concentration profiles from two-substance model (S2 model) in testsimulations using a linear root distribution function.(c) Panels for the Buck Hollow site.(d) Panels for the Big Cassandra site. Dashed linesindicate the level of water tables.



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TotalPlt+DiffDiff

Fig. 14c.Methane effluxes, component-wise emissions and pore water concentration profiles from four-substance model (S4 model) in testsimulations using a linear root distribution function.(e) Panels for the Buck Hollow site.(f) Panels for the Big Cassandra site. Dashed linesindicate the level of water tables.

CH4 models can be computed explicitly when the biogeo-chemistry model is driven by a climate dataset including airtemperature, cloud fraction, precipitation and vapor pressure(Zhuang et al., 2004). The three CH4 models have almostthe same requirement for climate forcing, except that theS4 model requires surface pressure data for a better perfor-mance. For historical simulations, the surface pressure datacan easily be obtained from various climate data sources,e.g. datasets from NCEP Reanalysis and ECMWF InterimReanalysis. For projections, GCM model outputs wouldbe a source for the necessary climate data. In some cases,when sea level pressure data rather than surface pressuredata are output from GCMs (e.g. models involved in IPCCAR4,http://www.ipcc-data.org/ar4/gcmdata.html). The sur-face pressure data can then be derived from a combination ofsea level pressure data, information of air temperature, el-evation and vapor pressure (Wallace, 2006). Although theCH4 models developed here have different complexities, theyhave almost the same number of parameters that require cal-ibration. The more complicated S2 and S4 models have evenfewer parameters to calibrate. For instance, the S2 and S4models compute the fraction of CH4 oxidation in the rhizo-sphere explicitly – no parameterization is needed as in the S1model.

The parameters of the CH4 models should be handledcarefully in regional applications. For instance, upscalingmaximum CH4 production potential (PCH4) and maximumCH4 oxidation potential (QCH4) from the calibrated sites toa region is critical. Currently, we use the maximum monthlyNPP derived from a 50-year historical TEM simulation toscale the parameterPCH4 and the maximum monthly soil res-piration to scale the parameterQCH4. Both NPP and soil res-piration are simulated with TEM. The extrapolation is basedon the fact that CH4 productivity is usually positively relatedwith NPP (e.g.Chanton et al., 1995), and CH4 oxidation ispositively related with respiration (e.g.Nakano et al., 2004).The scaling is based upon the vegetation cover data. The re-maining model parameters derived from the calibrated siteare used for our regional extrapolations. Thus, as a nextstep, we will test how different ways in extrapolating the site-specific parameters to a region affect the uncertainties in thewetland CH4 emissions quantified with the CH4 models ofdifferent complexities. Also, an analysis of uncertainty dueto equifinality will be attempted to investigate robustness ofthe parameterization from calibration at the limited numberof sites (Tang and Zhuang, 2008).

The regional water table dynamics are another majorsource of uncertainty in quantifying regional wetland CH4emissions. Standing water depth on top of soils is also es-sential to a proper quantification of regional CH4 effluxes.


http://www.ipcc-data.org/ar4/gcm_data.html


In particular, when the S4 model is used in regional simula-tions, there are grid cells, where vegetation is sparse, emittingCH4 mainly via ebullition. In contrast, the S1 and S2 mod-els greatly underestimate the CH4 emissions in such cases(e.g. Fig.10). In these simulations, water table depths playa significant role in affecting CH4 production, oxidation, soilpressure profile, and diffusion process. To more accuratelysimulate water table dynamics, we are currently testing sev-eral different algorithms (e.g.Granberg et al., 1999; Weisset al., 2006). The methane models with different complexi-ties will be further coupled with existing soil physics models(e.g.Zhuang et al., 2001, 2003; Tang and Zhuang, 2010) andwith the tested water table depth model to conduct regionaland global analyses of wetland CH4 emissions.

4 Conclusions

We revised an extant process-based biogeochemistry model,the Terrestrial Ecosystem Model to account for the effects ofmultiple substances in a soil profile on CH4 production, oxi-dation, and transport. The new development allows CH4 ef-fluxes to be modeled with different levels of model complex-ity. When four-substances (O2, N2, CO2 and CH4) are con-sidered, the inhibitory effect of O2 on CH4 production andthe stimulatory effect of O2 on CH4 oxidation are well ac-counted for, and ebullition is modeled in a physically logicalmanner. When ebullition is modeled with a concentration-based threshold approach and the inhibition effect of O2on CH4 production, and the competition for O2 betweenmethanotrophy and heterotrophic respiration are considered,the model becomes essentially a two-substance system. Ifwe ignore the role of O2, while modeling bubble ebullitionwith the concentration-based threshold function, the modelis reduced to a one-substance system. These models weretested through a group of sensitivity analyses at two temper-ate peatland sites in Michigan. We showed that only the four-substance model with the new ebullition algorithm is able toaccount for the effects of a sudden drop in atmospheric pres-sure or in water table on episodic emissions. All models sim-ulated the retardation of CH4 efflux after an increase in sur-face standing water due to inhibited diffusion and enhancedrhizospheric oxidation. We conclud that, to more accuratelyaccount for the effects of atmospheric pressure dynamics andwater table dynamics on methane effluxes, the four-substancemodel with the probabilistic but physics-based ebullition al-gorithm should be used in the future to quantify global wet-land CH4 emissions. Further, to more accurately simulate thepore water gas concentrations and different pathways of CH4transport, an exponential root distribution function should beused and the phase-related parameters should be treated astemperature dependent.

Appendix A

The Henry’s law constants (unit: M atm−1) (Sander, 1999)are computed as

H = 6.1×10−4exp

[−1300

(1

T−

1

298.0

)]for N2 (A1)

H = 1.3×10−3exp

[−1500

(1

T−

1

298.0

)]for O2 (A2)

H = 3.4×10−2exp

[−2400

(1

T−

1

298.0

)]for CO2 (A3)

H = 1.3×10−3exp

[−1700

(1

T−

1

298.0

)]for CH4 (A4)

whereT is temperature (unit: K).The Bunsen coefficient or solubility for gasi is related to

Henry’s law constant as

αi = Hi ×T

12.2(A5)

The diffusivities (unit: m2 s−1) (Frank et al., 1996; Arahand Stephen, 1998; Winkelmann, 2008) in air are computedas

Da= 1.93×10−5×

(T

273.0

)1.82

for N2 (A6)

Da= 1.8×10−5×

(T

273.0

)1.82

for O2 (A7)

Da= 1.47×10−5×

(T

273.15

)1.792

for CO2 (A8)

Da= 1.9×10−5×

(T

298.0

)1.82

for CH4 (A9)

The diffusivities (unit: m2 s−1) in water are computed as

Dw = 2.57×10−9×

(T

273.0

)for N2 (A10)

Dw = 2.4×10−9(

T

298.0

)for O2 (A11)

Dw = 1.81×10−6exp

(−2032.6

T

)for CO2 (A12)

Dw = 1.5×10−9×

(T

298.0

)for CH4 (A13)



Appendix B

The maximum CH4 production potential is defined as

P ∗

CH4= PCH4f (SOM(z,t))f (T (z,t))f (pH(z,t))f (Eh(z,t)) (B1)

wheref (SOM(z,t)), f (T (z,t)), f (pH(z,t)), f (Eh(z,t)) aremultiplier functions of methanogenesis substrate availability(modeled as a function of scaled NPP), soil temperature, pHvalue and redox potential, as defined inZhuang et al.(2004).PCH4 (unit: mol m−3 s−1) is a scaling parameter for modelcalibration. Another site specific parameter that needs cali-bration is theQ10 coefficient (PQ10) of f (T (z,t)).

The maximum CH4 oxidation potential is defined as

O∗

CH4= OCH4f (T (z,t))f (θ(z,t))f (Eh(z,t)) (B2)

wheref (T (z,t)), f (θ(z,t)), f (Eh(z,t)) are functions ofsoil temperature, soil moisture and redox potential (seeZhuang et al., 2004 for detailed descriptions). ParameterOCH4 (unit: mol m−3 s−1) is calibrated for every represen-tative site. TheQ10 coefficient for temperature effect is setto 2 throughout this study.

Appendix C

For the diffusive flux, the diffusion constant in Eq. (1) is de-fined for the bulk medium, which is conventionally computed(Stephen et al., 1998) as

Di =1

τ

εDi,a + αiθDi,w

ε + αiθ(C1)

where subscripts a and w denote the diffusivity in air and inwater (see Appendix A for ways of computation).τ is thetortuosity factor in the soil, taken as 1.5 throughout the study(Arah and Stephen, 1998).

For gas transport through the aerenchyma of wetlandplants, we, following the argument in other studies (Teal andKanwisher, 1966; Matthews et al., 2000; Segers and Leffe-laar, 2001), assumed the N2, CO2 and CH4 are transportedin a similar way, such that

Ri = R∗

i (yi,a−yi,atm) = λrLvDi,af (t)(yi,a−yi,atm) (C2)

whereλr (unit: m air (m root)−1) is the specific conduc-tivity of the root system andLv (unit: m root m−3 soil) isthe root length density. A value of 3.0×10−4 was used forλr. The vertical distribution ofLv in soil is assumed fol-lowing the Gale-Grigal model (Jackson et al., 1996) (see theexponential model in Appendix D). The temporal variationf (t) of the root is modeled similarly toZhuang et al.(2004)andWalter and Heimann(2000). Also, we assumed the fourgases can either be transported from the atmosphere to theroots or from the roots to the atmosphere. When the one-substance model is switched on, the oxidation of CH4 in therhizosphere (Beckett et al., 2001) is not considered explicitly,

rather, as inWalter and Heimann(2000), we assume 50% ofCH4 is oxidized.

In the S4 model, the governing equation for CH4 is

∂yCH4

∂t=

∂

∂z

(DCH4

∂yCH4

∂z

)+

P ∗

CH4

1+ηyO2,w

−Q∗

CH4

yCH4,w

kCH4 +yCH4,w

yO2,w

kO2 +yO2,w

−ECH4 +R∗

CH4

(yCH4,atm−yCH4,a

)(C3)

for CO2 is

∂yCO2

∂t=

∂

∂z

(DCO2

∂yCO2

∂z

)+

P ∗

CH4

1+ηyO2,w

+Q∗

CH4

yCH4,w

kCH4 +yCH4,w

yO2,w

kO2 +yO2,w

+V ∗

RyO2,w

kR+yO2,w−ECO2 +R∗

CO2

(yCO2,atm−yCO2,a

)(C4)

for O2 is

∂yO2

∂t=

∂

∂z

(DO2

∂yO2

∂z

)−2Q∗

CH4

yCH4,w

kCH4 +yCH4,w

yO2,w

kO2 +yO2,w

−V ∗

RyO2,w

kR+yO2,w−EO2 +R∗

O2

(yO2,atm−yO2,a

)(C5)

and for N2 is

∂yN2

∂t=

∂

∂z

(DN2

∂yN2

∂z

)−EN2 +R∗

N2

(yN2,atm−yN2,a

)(C6)

Appendix D

The root length density in Eq. (C2) is defined as

Lv = Rvegf (z) = −Rveg×100log(β)β100z (D1)

whereβ is 0.943 for Buck Hollow Bog, and 0.910 for BigCassandra Bog.Rveg is a scaling parameter needed in cali-bration to account for differences in conducting capabilitiesfor different plants. Note, the integrated root distributionfunction f (z) from lower boundary to soil surface equalsone. The alternative root distribution used in Sect.3.4, isdefined as

f (z) =

2Rd

(1−

zRd

)for 0≤ z ≤ Rd

0 otherwise(D2)

where Rd is root depth, computed using the Gale-Grigalmodel. This is different from the formula adopted inWal-ter and Heimann(2000) andZhuang et al.(2004) in that wehere imposed the constraint such that the vertical integrationof f (z) equals one.



Symbol Definition Unit

αi Bunsen coefficient for substancei unitlessβ coefficient for root distribution unitlessδ(s) Dirac delta function unitlessε(z,t) air-filled porosity m3 air m−3 soilη inhibition coefficient of O2 on methanogenesis m3 water mol−1

θ(z,t) soil moisutre m3 water m−3 soilλr specific conductivity of the root system m air m−1 rootτ tortuosity factor in the soil unitlessb pressure imposed by water column above water table (zwt < 0)

or soil surface (zwt≥0) mCH4,max threshold concentration for CH4 ebullition mol m−3 waterDi bulk diffusivity of substancei in soil m2 s−1

Di,a diffusivity of substancei in air m2 s−1

Di,w diffusivity of substancei in water m2 s−1

E(z) total ebullition of the gases at depthz mol m−2

Ebi(z) potential ebullition of gasi at depthz mol m−2

Hi Henry’s law constant for substancei M atm−1

kCH4 Michaelis-Menten coefficient for CH4 mol m−3 waterkO2 Michaelis-Menten coefficient for O2 mol m−3 waterkR Michaelis-Menten coefficient for respiration mol m−3 waterLv root length density m root m−3 soilO2,max threshold concentration for O2 ebullition mol m−3 waterp atmospheric pressure PaP ∗

CH4maximum CH4 production potential mol m−3 s−1

PCH4 scaling parameter forP ∗CH4

mol m−3 s−1

POX fraction of CH4 oxidized in rhizosphere unitlessPQ10 Q10 coefficient for methanogenesis unitlesspr probability of bubble redissolution unitlessPs(z,t) total gas pressure at depthz, time t PaPs,i(z,t) partial gas pressure at depthz, time t by substancei PaP0 pressure scaling factor Pap scaled atmospheric pressure unitlessQ∗

CH4maximum CH4 oxidation potential mol m−3 s−1

QCH4 scaling parameter forQ∗CH4

mol m−3 s−1

R∗i

scaled rate of plant aided transport s−1

Rd root depth mRveg vegetation type dependent scaling parameter of gas conducting

capability unitlessV ∗

R maximum rate of respiration mol m−3 s−1

yi bulk concentration of substancei mol m−3

yi,a gaseous concentration of substancei mol m−3 airyi,w aqueous concentration of substancei mol m−3 wateryi,atm concentration of substancei in the atmosphere mol m−3 airyi equilibrium bulk concentration of substancei mol m−3

yi,w equilibrium aqueous concentration of substancei mol m−3 waterzwt depth of water table mzs depth of soil surface mz0 water depth scaling factor mZsoil depth of lower boundary m



Acknowledgements.J. Tang is supported with graduate fellowshipsfrom the Purdue Climate Change Research Center and the NASAEarth System Science program. The study is in part supportedby the Department of Energy (Abrupt Climate Change program)and the National Science Foundation (projects ARC-0554811 andEAR-0630319). The study is also a contribution of the MethaneWorking Group of the National Center for Ecological Analysis andSynthesis (NCEAS). Comments from two anonymous reviewersand the editor greatly helped to improve the early version of thismanuscript.

Edited by: A. Arneth

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