from soil covering landfill, and DunfieM et al. [1993, Figure 4] ...... Sciences, Oxford. Brookes University, Gipsy Lane Campus, Headington, Oxford, OX3 0BP.
GLOBAL BIOGEOCHEMICAL
CYCLES, VOL. 15, NO. 3, PAGES 709-720, SEPTEMBER 2001
Methane oxidation in a peatland core D. M. E. Pearce • andR. S. Clymo Schoolof BiologicalSciences,QueenMary, Universityof London,London,United Kingdom
Abstract. We made an experimenton a 30 cm diametercore of Sphagnum-dominated vegetationandpeatto estimatethe parameterscontrollingmethaneoxidationduringmovementto
theambient air:13CH4 wasadded atthewatertable,andexcess 13CO2 appeared in thegasspace abovethe core.At 20øC in otherwiseundisturbedconditions,•22% of CH4 was oxidizedto CO2 duringpassageup throughthe overlying 10-cm thick unsaturatedpeat and plants.We simulated the experiment,with sevenparameters:transfercoefficientsin water, in the gasphase,and throughthe containerwall; the rate of CH4 and of CO2 generation;and the two parametersof a hyperbolicrelationbetweenCH4 concentration andthe rate of CH4 oxidation.We optimizedthese parametersto fit the experimentalresults,and then were able to generalizeto any temperature
(0ø-25øC)andany depth(0-55 cm) of watertable.Changingtemperature hasimportanteffects on the proportionof CH4 oxidized.
1.
Introduction
The net upwardflux canbe inferredfrom the curveand is •2% of
Peatlandscover •3% of the Earth'sland surface[Clymo, 1984].
the net efflux from the surface of hollows. Detailed measurements
[Daulat and Clymo, 1998] showhigh peaksin CH4 concentration
About3.5million km2,enough toformasquare ofside1800km,are profiles10-15 cm belowthe watertable.Thesepeaksarebarelya in the Borealzone [Gorham,1991], especiallyin the formerUSSR, Fennoscandinavia, Canada,and the northernparts of the United States.The vegetationof muchof thisBorealpeatlandis dominated by Sphagnumthat, becauseit decaysunusuallyslowly, comesto form a disproportionately largepart of the peat [Clymo,1984]. The surfacelayers of a peatlandincludingthe live plants and downto the depthto which the watertabledropsin a dry summer are collectivelycalledthe acrotelm[Ingram, 1978]. Below this is the peat proper: the permanentlywaterloggedand permanently anoxic catotelm,throughoutwhich the hydraulicconductivityis relativelylower, by severalordersof magnitude,than it is in the acrotelm.In the acrotelmthewatertablemovesup anddownasthe balanceamongprecipitation,evaporation,runoff, and downward percolationdictate,andthe attendanttransitionfrom predominantly oxic conditions
above the water table to anoxic ones below also
movesup and down [Clymoand Pearce, 1995]. In this articlethe unsaturatedzone is consideredto be the acrotelm,and the saturated zone is considered to be the catotelm.
few centimeters thick and move up and downwith the water table with a lag of only a few hours.The speedandsizeof thesechanges indicatethatthisis the main zoneof CH4 production.Diffusionand perhapssomemassflow carriesthe CH4 upwardto the atmosphere throughpeat,plant litter, and intercellulargas spacesin plants. Overall, peatlandsremove CO2 from the atmosphere,sequester someof it asplantmatterin peat [Clymo,1984; Clymoet al., 1998], and returnmostof it to the atmosphereas a resultof decay.They alsogenerateand emit CH4, eachmoleculeof which has (totalled over 100 years)•20 timesgreaterpotentialfor climatechangethan the incomingCO2 moleculefrom which it originated[Houghtonet al., 1996]. The net effect on climateof carbonsequestration and CH4 emissionvaries with conditionsand with the age of the peatland [Alm, 1997; Clymo, 1998; Rivers et al., 1998]. It is not yet clearwhetherthe effect is generallypositiveor negative,but there is no doubt that the net effiux of CH4 must have a substantial influence,so any processthat affectsthis efflux is important.
There have been numerousreportsthat the efflux of CH4 from hollowsis greaterthanit is fromhummocks, beginningwith Clymo 1- 10 m. Hummocks, from 10 to 60 cm tall, alternatewith hollows, and Reddaway [1971] and summarizedby Bartlett and Harriss whose water table is above the surface in winter and below it in [1993] and Crill et al. [1993]. Almost as numeroushave been the summer,and pools,whosewater tableis at the surfaceat all times. suggestions that this differencemay resultfrom CH4 oxidationin Each of these microformshas its own characteristicvegetation the acrotelmof hummocks,thoughmostof thesereportscouldnot whosepropertiescontributeto the maintenanceof the microform excludethe possibilitythat the differencesare a resultof different [Malmer et al., 1994]. Feedbackmechanismsensurethe continued ratesof production.However,Daulat and Clymo[ 1998] foundthat coexistenceof hummocksand hollows [Belyeaand Clymo, 1998]. in experimentsin which the water tablewas moved,the profile of At Ellergower Moss in southwestScotland, a typical small effiux in relation to water table was almost the same for hummocks rainwater-dependent raisedbog, the concentrationof CH4 in the as it was for hollows. This is better support for the oxidation permanentlywaterloggedand anoxic catotelmincreasesapproxhypothesis,thoughit is indirect. imatelyhyperbolicallywith depth[Clymoand Pearce, 1995]. This Severalauthorshave made experimentsin which slurdes,small is consistentwith continuedslow productionof CH4 at all depths. piecesor coresof peat, soil, or sediment,were put in a closed container(in somecaseswith inhibitorsof CH4 oxidationsuchas CH3F) and the disappearance of CH4 from the gas phaseor the 14 13 3 •NowatSchool ofBiological andMolecular Sciences, OxfordBrookes appearance thereof C or C or H tracerin CO2 was recorded The surfaceof mostBorealpeatlandsis patternedon a scaleof
University,Headington,Oxford, United Kingdom.
liversen et al., 1987; Yavitt et al., 1988, 1990; Whalen et al., 1990; Whalen and Reeburgh, 1990; Reeburgh et al., 1991; Whalen et al., 1991; Crill, 1991; Whalen et al., 1992; Sundh et al., 1992, 1993; Crill et al., 1994; Sundh et al., 1994; Nedwell and Watson, 1995; Andersen et al., 1998; Saarnio et al., 1998;
Copyright2001 by the AmericanGeophysicalUnion. Papernumber2000GB001323. 0886-6236/01/2000GB001323
$12.00 709
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Gulledgeand Schimel, 1998; Brummeand Borken, 1999]. Other workershave observedprofiles of phospholipidfatty acids that are specificto methane-consuming bacteria[Sundhet al., 1995], while Fechner and Hemond [1992] and Reeburghet al. [1997] have inferred rates of oxidation from concentrationprofiles. Reeburghet al. [1993] suggested that 30% of the CH4 produced in high-latitude wetlands was oxidized before it reached the atmosphere. It is clear from theseworks that the potentialfor CH4 oxidation is widespread,but most of the observations have attendantdifficultiestoo:theymeasureonly potentialor net potential,or theyuse inhibitors whose specificity may be uncertain [Ormeland and Capone,1988], or the experimentswere madein highly disturbed or far from naturalconditions.One cannotextrapolatethe resultsto different depthsof acrotelmbecausethey reveal little about the ratesof thoseprocesses that contributeto the overallresult:the rate of CH4 production,the rate of transport,and the rate of oxidation. As far as we know nobodyhas yet tried to make directmeasurementsof the rate of CH4 oxidationin minimally disturbedpeatland conditionsand to establishthe valuesof parameterswith which to assessthe importanceof CH4 oxidationin peatlandsin the wide range of conditionsfound in nature: a crucial element in the potentialfor climatechange.
OF METHANE
IN PEATLAND
2.2. Experiments
Three preliminaryexperimentswere made to establishsuitable quantitiesand conditions.Here we describetheir outcomein the designof the main experiment. We neededa temperaturethat would encouragemicrobiological activityandthatwould not be far outsidethe normalrange[Daulat and Clymo, 1998] for a peatland hummock, but we were not concerned about close control. The bucket and core were therefore
taken to the mass spectrometer(MS) room, whose temperature
varied in the range 18ø-22øC: the mean summertemperature measuredat 5, 10, and 20 cm deep in a hummockat Ellergower
Mossin southwest Scotlandwas 12ø- 13øC[Daulatand Clymo, 1998]. The corewas allowedto equilibratefor 24 hoursbeforethe experimentbegan.The bucket remainedunmovedthroughoutthe experiment.
About500cm3 of equalpartsof thegases •3CH4andKr was shakenover 10% KOH to remove tracesof CO2. The Kr was to act
as an unmetabolizedmarker of physicalprocesses.The gas phase
wastransferred to another container holding 1050cm3 of distilled
waterthathadbeendeoxygenated by boilingandhadbeenallowed to coolto roomtemperaturein a glassvesselwith a water seal.The water and gaseswere shakenfor 30 min to producea saturated solution.This volumeof solutionwas sufficientto occupya layer In this article we first describemeasurementsof the rate of CH4 1.5 cm deepin the bucket.The samevolume of waterwas removed oxidation in a peatland mesocosm, using13CH4 as tracer.The from the core by siphoning,and the gas-saturatedsolutionwas experimentis expensive,so we then simulateit in a computer injectedlaterally along a radial line in equal aliquotsthroughsix model and estimatethe controllingparametervalues so that the "Subaseal"bungsequally spacedaroundthe height of the final experimentalresultsmay be applied to other temperaturesand water table. The water-saturated peat was then 20 cm thick; the otherdepthsof acrotelm. unsaturatedlayer of peat, plant litter, and living plants through which CH4 and Kr would have to move upwardwas 10 cm thick, and the headspacein which the gaseswould mix was also 10 cm 2. Materials and Methods thick. The bucket lid, which containeda vertical samplingport with lateralholesin the head spaceand a fan attachedto the lower The principleof the experimentwas simple.A 30 cm diameter (intemal)face,was then sealedon. The lid alsocontaineda tubeto core from the living surfaceof a peat bog, encompassing the a water-sealedU tube that allowedpressureinsideand outsidethe acrotelmand the top of the catotelm,was put in a bucketon which bucket to remain the same +0.3 cm head of water. a lid was sealed,enclosingsomeair abovethe surfaceof the core
each headspace gas sampling• thefanwas turned on,and (theheadspace). Watersaturated with13CH4 andwithunmetabo-theBefore U tube outletwas blocked.A 5 cm syringewas usedto take a lizable Kr as a physicaltracer was injectedat the water table. sample of theheadspace gas.These5 cm3 samples weretaken Samplesof gas were then taken at intervalsfrom the headspace, every 30 min for 8 hourson the first two days,every hour on the
andtheconcentration of •3CH4andof •3CO2 (andothergases) was third day,onceon the fourthday,and thenat eightlongerintervals
measuredwith a massspectrometer.
2.1. Experimental Cores The peat core was taken from a hummock dominated by Sphagnumcapillifoliumwith 5-10% cover of Calluna vulgaris shootsall lessthan 10 cm tall. It was one of a largeseriescollected in northem Scotland[Daulat and Clymo, 1998]. An open-ended cylindrical stainlesssteel cutter, of 30 cm diameterand with sharpenedsinuousteethat the lower end, was pusheddown with
up to the 52nd day giving, coincidentally,52 samples.The lid remainedsealedall this time. In the figureswe describethe results to day 3 as "shortterm" and thoseto day 52 as "long term." 2.3.
Subsidiary Experiments Two subsidiary(control)experiments were made.In the first the main experimentwas repeatedwith a sister core collectedand storedin the sameway as the oneusedin the main experimentbut
theaddition ofKr or13CH4. Thisexperiment wasa control alternating rotationby •30 ø to a depthof 50 cm.A wedgeof peat without
was cut and removedfrom besidethe cylinderto form a sloping ramp.A spadewas forcedthroughthepeatbelowthe bottomof the cutterand the cutterwith core of vegetationand peat draggedout up the rampandbriefly laid horizontalwhile the corewascutat the bottomto 30 cm long. A bucket,30 cm diameter,40 cm tall, and made of 3 mm thick polyethylene,was laid horizontallyso the cutterteeth fitted just inside its top. The cutter,core, and bucket were then stoodupright,and the coreslid slowly of its own accord into the bucket. The core in its bucket was taken to London and
intendedto reveal any unanticipatedisotopicfractionationof CH4 and CO2 duringthe long incubation. In the second control experiment the bucket contained no
vegetation or peatbut washalf filledwith 14 dm3 of freshly distilledwater and (in the gas phase)nitrogenand tracesof CH4,
excess •3CH4, andCO2.Thisexperiment wastotestthepossibility thattheremightbeexchange of 13Cbetween CH4andCO2orthat CH4 might oxidize in the absenceof vegetationand peat. The surfaceof the water was at the samepositionin the bucketas the water table in the first two experiments.
kept outsidefor about a year before the experimentwas made. During thistime the watertablewasmaintainedat a depthof 10 + 1 cm below the top of the Sphagnumby automaticallyadding 2.4. Measurements on Gas Samples The5 cm3 gassample wasallowed to expand intoa partially distilled water or allowing outflow from the core. For reasons explainedin Daulat and Clymo[1998] we use "height" relativeto evacuatedglassbulb, and 10 subsamples were admitted,one after the water table and "depth" relativeto someotherdatum,usually the other,to a KratosMS50 RF magneticsectormassspectrometer. The machine was set to allow automatic discrimination of mass/ the vegetationsurface.
PEARCE
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OXIDATION
charge(m/e) differencesof 0.005 units, i.e., the ability to distin-
OF METHANE
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711
deviationwould have been stronglybiased by these values, so
guish, forexample, m/e16.032(12CH4 +)from15.995(160160++).we usedthe median and, as a measureof variability,the spanof Each scantook •2 min. In two cases,therewere only nine scans, values containing 0.19 of the total observations below the and in one case, there were only eight scans.The experiments median and the same value above the median. (This is like an reportedhere generated1017 such scanswith 14 clear peaks in interquartilerange but with the boundsat 19% on either side of most of them. the median rather than at 25%.) If a sample distributionwere Gaussian,then this span would be numericallythe same as the 2.5. Numerical Treatments standarddeviation. We call this measurethe G span and have The massspectrometerscanswere first calibratedfor m/e on the plotted it on the figures. The calculation of proportionilesin two most widely spacedunambiguouslyidentifiablem/e peaks. general is describedin appendix A. Usuallythesewere 68.995(internal12C19F3 +) and 14.003 In Figures 1-4, curveshave been fitted using a self-adjusting (14N14N-•-). Special carewastakentoseparate thefollowing peaks simplex [Nelder and Mead, 1965]. In Figure lb we use the
exponential y = Yme(-at),consistent witha decay process with m/e closeto oneanother: 12CH4 + and160160++' 13CH4 + negative 1601H +, and 160180 ++' 1H2•80 + and 4øAr ++. In somecases, from initial maximum "Ym" at constantproportionalrate "a," and witha similar process butfallingto a however,a singlereal peakhad beenpartially splitby the machine Y = Yme(-at)+ c consistent "c." In all the otherswe usey = ym(1-- exp(-at)) into two or more, and thesewere recombined.Eachpeak was then baseline with constantrate of addition"b" (wherethe asymptote expressedas a proportionof the total intensitiesin the scan.This consistent allowed for small differencesin subsamplesize. Finally, these Ym= b/a) as well as constantproportionalrate of decay "a." We proportionswere convertedusing a separatestandardto partial refer to these as "first-order flux equations,"but the curves in pressures.In the figuresthesepartial pressuresare given as ppm. Figures1-4 are simplyto aid the eyeto judgewhethersuchsimple may be consistentwith the observedkinetics. We abstractedfrom the recordsthe following speciesat the m/e processes
iven:12CH4 + at 16.032,13CH4 + at 17.035,4øAr ++ at 19.981, N•SN+ at29.003,1602+ at32.000,12C1602 + at43.990,13CO2 + at 44.993,and84Kr + at 83.912.NaturalCH4andCO2bothcontain a 3. Results proportion 0.0111of •3C.Wewereinterested mainlyin thefateof the extra•3Cwe hadadded.In the figureswe havetherefore G-spanrangebarsare shownin Figures1-4. In many casesthey subtracted frommeasured 13CH4 and13CO2 theamount calculatedare smallerthan the size of the symbolmarking the median.It is ascoming fromthesimultaneously measured 12CH4 and12CO2. clear that "measurementerror" is small and mostly smallerthan We call the remainder
"excess." "samplingerror" (judged from deviationsfrom trends),which is A measureof centrality and variation was then calculatedfor itself much smaller than the effects in which we are primarily each m/e of interest for the (usually) 10 scans. The results interested. We therefore make no further comment on measurement contained•10% of wildly erraticvalues, most of them only 1/ or samplingerror. 10 or less of the mean of the other nine in the samplewhich 3.1. First Control Experiment had a coefficient of variation of •0.05. We do not know the reason for these aberrantvalues, the mass spectrometerwas 17 The experiment withoutthe addition of Kr or 13CH4gave years old, but they are clearly distinct. Mean and standard results verysimilarto the mainexperiment for 12CH4,12CO2,
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Figure1. Timecourse ofpartial pressure of 84Krintheheadspace overa hummock core.Values aremedians; bars are+1 G span(seeappendix A). (a) Short-term (3 day)course. Thecurve(seetext)is fittedtoy = ym(1-- e--at).(b) Long-term (52 day)course. Thedashed curve(seetext)is fittedtoy - Yme-at;thecontinuous curveis fittedtoy = Ym e-at + c.
712
PEARCE AND CLYMO: OXIDATION OF METHANE IN PEATLAND
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Figure2. Timecourse of partial pressure of 12CH4 andof "labelled" excess 13CH4 in theheadspace overa
hummock core."Excess" isthetotalminus thatnaturally present inthemeasured 12CH4. Values aremedians; barsare ñ1G span (seeappendix A). (a)Short-term course. Thecurves (seetext)arefittedtoy = ym(1- e-at).(b)Long-term course. Thecurve (seetext)through the12CH4 points isfittedtoy --ym(1- e-at).Forexcess 13CH4 thepoints are simplylinkedby straightlines.
lSN14N, and4ømr. Thequotient 13C/12C forbothCH4andCO2 3.3.1. Physicalbehaviorof Kr. Figure1 showsresultsfor was unchanged throughoutthe experiment,and that of CO2 the addedKr, whichwe hopedwouldbehavephysically in a was close to naturalabundance, indicatinglittle changein similar wayto theadded 13CH4 butwithout thecomplications microbialsubstrates or activities.The partialpressure of Kr, introducedby biologicalinteractions. The short-termbehaviorof excess 13CH4, andexcess 13CO2 wereindistinguishable from Kr is shownin Figurel a. (NaturalKr hasseveralmoderately zero (as expected). abundant isotopes. Theyall behaved in thesameway sowe show
84mr only.) It took•7 hours before extra Krfirstappeared inthe
3.2. SecondControl Experiment In the experiment (resultsnot shown),in whichthe bucketwas
headspace. Thepartialpressure thenjumpedbeforesettling to a steady,but slowly decreasing,rate of increase.The peak
12CH4 fellmuchlessto 96%of itsstarting value. At 20øCthe
decayto a raisedbaseline.
was reachedafter •7 daysand thendecreased for halffilledbywaterandhalfbya mixtureof nitrogen, traces of CH4, concentration curveis fittedto a simple excess 13CH4, andCO2, thepartial pressures fellforthefirst7days thenext40 days(Figure1b). Thedashed decay,butthecontinuous oneis fittedto exponential toward asteady value: 12CO2 fellto50%ofitsstarting value, while exponential
solubility of CO2is 0.880cm3 cm-3, whileforCH4thevalueis
Thereare severalphysicalprocesses at work here.(1) In the
0.033cm3 cm-3, •1/25 aslarge. (Gassolubility coefficients are shortterm,Kr diffusesupwardfromthewatertablethroughthe
zone.Mostof themovement mustbein thegasphase, similarto partitioncoefficients not upperlimitsas theyare for unsaturated solids.)Thesecoefficients appliedto the gasandwatervolumes wherethe diffusioncoefficientis muchlargerthan it is in the water.Theprocess will, however, be modified by usedwouldleadto partialpressures of 12CO2 and12CH4 of 53% interdigitating exchange between thegasandliquidphases. (2) Depletion in the and 97% of the initial values,consistent with thoseobserved. therateatwhichgas The mostimportant conclusion fromthisexperiment is thatin waterat thewatertablewill slowlydiminish theabsence of vegetation andpeat,therateof transfer of •3Cfrom enters the unsaturated zone because it has first to diffuse from downthrough waterto thewatertable.(3) Theheadspace CH4 to CO2 is very small:autooxidation or exchange can be deeper ignoredin the main experiment.
gas movesout slowly throughthe polyethylenecontainerand
fallento 18%, andby day 52 it had fallento 15%.
originallyadded,thusdecreasing therateat whichit movesto the
possiblythroughsmallleaksaroundthe edgeof the lid. (4) Substantial amounts of CO2areproduced in decomposition and 3.3. Main Experiment raisethe pressurein the headspace sufficientlyto bubbleout Whenthelid wasremovedtheCallunaplants,whichhadbeenin throughthewaterseal,takingothergaseswith them.Thiswould the darkfor 52 days,were(not surprisingly) distinctlyyellow. leadto an approximately negativeexponential declinein concenThey andthe Sphagnum did resumegrowthwhenreturnedout- tration,as we observed. The kineticsof process 3 and4 arenot doors.Duringtheexperiment theplantsmusthavebeenrespiring separable in themainexperiment, butwenotethatin thesubsidiary andthushavebeena source of CO2.Theaboveground partshada experiment therewas no significantdropin gas concentrations dry massonly•1% of thatof theunsaturated layerof peat,the afterthe initial solutionchanges. (5) Kr diffusesslowlydown mainsourceof CO2,sowe ignorethiscomplication. The concen- through thewaterin thepeatbelowthelayertowhichit wasadded, trationof 02 fell steadilyfromthe initial20%:by day22 it had andthisdecreases the concentration in thelayerto whichKr was
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Figure3. Timecourse of partialpressure of 4øAr,•sN•qN(m/e= 29), andof 12CO2 in theheadspace overa hummockcore.Valuesaremedians;barsare+1 G span(seeappendixA). (a) Short-termcourse.The firstday'sresults
for•sN•qN andthesecond day'sresults for4øArareomitted toavoidconfusion withthe12CO2 results. Thecurve(see text)is fittedtoy = ym(1- e-"t) forall the results, notjusttheshort-term ones. (b) Long-term course. Thecurve(see at 40 15 14
text)for12002isfittedtoy = ym(1- e- ) foralltheresults. Totheresults for Ar and N N, whichwereexpected to be constant,straightlines were fitted. The slopesdo not differ significantlyfrom zero (P < 0.01). headspace.Gas originally in a 1.5 cm thick layer becomesspread downthrougha 20 cm thick layer.However,becausethe solubility 3 3 o coefficientis only 0.067 cm cm- , only •5 ¬ of the remainingKr is in the saturatedzone, and the rest is in the unsaturatedzone and headspace. It is possiblethatthe initialjump followsthe establishment of the gas:liquidpartition,asin process1. The slowlydiminishingrateof appearancein the first 7 days is consistentwith a diminishing concentrationat the water table (process2) or the onset of loss throughthe headspace walls (process3) andwater seal(process4), or a combinationof these.The long-termexponentialdeclineseen in Figure3 may be dominatedby lossesthroughthe walls (process 3) or (more plausibly)the water seal (process4) and by diffusion downwardinto the saturatedzone (process5). However,the main conclusionmust be that there are severalprocessesat work here with consequences that can only be postulated.Later we simulate
followed with the sameparametervaluesthroughoutthe experiment. Figure 3 also showsthat as one would expect,the partial
pressure of •SN14N (m/e= 29)andof 4øArchanges little. 3.3.3.
Oxidation
of CHq.
The relation between all 52
measurements of thepartialpressure of 12CO2 (m/e= 44) and 13CO2 (m/e= 45)isshown inFigure 4 forcomparison withtheline tobeexpected fromthenatural abundances of •2Cand•3C.There is littledoubtthatthereis an excess of 13CO2. Theexcess •3Cis barely 10% of the total, but becausethe measurementerror and samplingerror(judgedfrom the scatteraboutthe trends)were both
small, themainresult shown inFigure 4bisclear: theexcess 13CO2 is •90 ppmata time,7 days,whenexcess 13CH4 is at a peakof 120 ppm. In terms of carbon,theseconcentrationsare 22 and 78
ppm,so•22% of the13CH4 hasbeenoxidized to 13CO2 during passageup throughthe unsaturatedlayer. We have assumedthat thereis no microbiologicaldiscrimination
between •2Cand•3Cintheproduction andoxidation of CHq.This them. Forthe time beingl thekinetics ofKrprovide adescriptive background forthose of 3CH4. is untruein detail, but the effect is relatively small. 3.3.2. Effiux of CH4 and CO2.
Figure 2 shows the short-
termandlong-term results forexcess 13CH4. Itsbehavior is very similar to thatof 84Kr:aninitialjumpat 7 hours, a periodto 7 4.
Simulating the Experiment
days when the first-orderflux equationis followed (Figure 1), and a much longerperiodduringwhich thereis a decline,in this 4.1. Main Simulation and Parameter Optimization case to •1/5 of the peak value. The decline is proportionally The purposeof the simulationwas to get best fit values of greaterthan was that of Kr, and the differencemay be a resultof parameters, whichcouldthenbe usedto extendthe applicabilityof removalby oxidationto CO2, thoughthis evidencealone would the experiment.Details of the simulationare given in appendixB. be weak. It consistsof a seriesof layers,0.5 cm thick in the peat,differentin Thebehavior of 12CH4 (alsoFigure2) seems straightforward: it the headspaceand containerwalls. The initial concentrationof the substances (Kr,12CH4, 12CO2, "excess" 13CH4, and follows the first-orderflux equationin both the short and long fivemeasured 13CO2) is setin eachlayer,as areinitialratesof the term, thoughthe fitted efflux in the long term is only half that in "excess" the shortterm. We supposethe CH4 is beingproducedby micro- processes in eachlayer assumedto be governingtransferbetween biologicalprocesses within the peat,andthe efflux is the net effiux adjacent layers.Theseassumptions requiredsevenparameters: Dg, after any internal oxidation. D•,, andDo, the transfercoefficientsof gasesin the gasphase,in Figure3 shows theshort-term andlong-term results for 12CO 2. water, and in the walls of the containeror throughthe water seal rateofproduction ona dry The behavior is even simpler: the first-order flux equation is (cm2s-I); PMandPc,theproportional
714
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•
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OF METHANE
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12002 partial pressure (ppm)
Figure4. (a)Relation ofpartial pressure of 13CO 2 tothatof 12CO2 forthe52samples oftheheadspace overa hummock core.Valuesaremedians; barsare+1 G span(seeappendix A). Thestraight lineis notfittedbutis that expected forthenaturalabundance of 13CO2 in themeasured•2CO2.At the h•ghest ß ß pressures, ß pamal eqmvalent to
longest times, theexcess of •3CO2 isonly• 10%ofthenatural abundance. (b)Timecourse ofpartial pressure of excess •3CO 2.Theerror bars include contributions fromboth•3CO2 and12CO 2asbothareinvolved inthecalculation ofexcess •3CO2. Thecurve (seetext)isfittedtoy = ym(1- e-at).
massbasisof methane andcarbon dioxide (yr-1);andHv (nmol value. ThusDc with a large sensitivityis ratherexactlydeters-1) andHx (nmoldm-3),the maximum rateandthe half- mined, while P3• is inexact. maximumconcentration of a hyperbolarelatingCH4 oxidation Concentration profilesin themodelareshownin Figure6. These rate to CH4 concentration in water.The last two are formally aremuchasexpected,with largepeaksin CH4 concentration below equivalentto Vmax andKmof Michaelis-Menten enzymekinetics, the watertable,similarto thoseobserved by Daulat and Clymo butwe donotimplythatwe arestudying a simpleenzymereaction [1998]. in a well-stirred
All
solution.
the amounts to be transferred are calculated from the
presentconcentrations and rates.Only after all the amountshave
4.2.
Extension
of the Simulation
been calculatedare the transferseffectedgiving new concentrationsin each layer. New rates (which dependon the new concentrations) are now calculated.This completesone iteration. Typically,themodeltime increment was• 10-15 s. The process was theniteratedsome100,000timesto coverthe first 13 days of the experimentaldata (it was infeasibleto run the model regularlyto the full 52 day data set). This gave a seriesof concentrations of the five variablesin the headspace that were compared with thosemeasured, to give a criterionmeasuring the badnessof fit. Such a "run" produceda singlevalue of the criterion.An optimization technique usedmultiplerunsto get a set of parametervaluesthat minimizedthe criterion.By that
Finally,we modifiedthe modelto simulatedifferenttemperaturesandthicknesses of the unsaturated layerbut keptthe best fit parameter values.The relationbetweendiffusionrateof gases in waterand temperature in the range0ø-25øC is exponential
[Briggs etal., 1961]withanincrease of 0.02øC -• equivalent to a Q•o of 1.2.
The relationbetweenrate of CH4 and CO2 productionand temperature is alsoexponential[e.g.,Dunfieldet al., 1993;Daulat and Clymo,1998;Nedwelland Watson,1995] with Q•o values from 4 to 6 with isolatedvaluesas high as 16. For the simulation
we usedQ1oof 5.0,equivalent to anexponent of 0.16øC -•
TherelationbetweenCH4 oxidationrateandtemperature is less clear.King and Adamsen[1992] workingon 6 cm diametercores times. of soilfroma mixeddeciduous andconiferforestfound[Kingand After the difficultiesdescribedin appendixB had been over- Adamsen,1992,Figure2] no consistent effectof temperature in come,the simulationprovedwell behaved.The best fit of the five therange0ø-30øC(butsummarize theseresults by rateconstant = gasesin the headspace is shownin Figure 5. The concentration aTTM, which seems implausible). Crill[1991 ], working onsimilar (y axis)scaleis logarithmic to coverthe rangeof concentrations,samples with similartechniques, alsofoundlittleeffectof temperand this misleadinglyemphasizes poomessof fit at low con- aturein therange5ø-27øC.However,otherauthors reportlarger centrations.The parametervalues for the best fit are shown in effects.Whalenet al. [1990, Figure5b] used7 cm diametercores time the model had been evaluated several tens of millions of
Table 1. It was not feasible to estimate the variance of these values, but some indication can be had from the relative
from soil coveringlandfill,andDunfieMet al. [1993,Figure4] usedpeatslurdes.Both showedratesof CH4 oxidationnearzeroat
sensitivities, which are the proportionalrate of changeof the temperatures below5øCand•1-5 txmol cm-3 d-1 (converted toa criterionfor a commonproportionalchangein the parameter volumebasis)at 25øC. Both reporta Q•o: 1.9 and 1.4-2.1,
PEARCE AND CLYMO' OXIDATION
106 105
*:
OF METHANE
IN PEATLAND
105
108
104
107
103
106
715
!
104
12CH 4 103 0.01
Kr
12C02
o
lO
0.01
lO5 0.1
1
10
105
104
104
øø• Excess •3CH o 4
0.1
O.Ol
105
103
o o o
102 1
0.1
'
103
1
10
Excess 13C02
o o o
102
102 0.01
0.1
1
10
o
0.01 0.1
1
10
Time (d) [log scale]
Figure5. Timecourse of measured (filledsymbols with+1 G spanbars)andmodeled (opensymbols) concentrations of fivegases in theheadspace, usingthebestfit of seven parameters (seetextandappendix B). Both axesarescaled logarithmically spanning 3 orders ofmagnitude, toaccommodate thelongtimesandbigdifferences in concentration.This causesdeviationsat low concentrations to be unduly prominent.
respectively. Finally,Nedwelland Watson[1995], usingpeat betweenoxidationrate and Celsiustemperature,with zero interslurdes,reporta goodfit to an Arrheniusplot anda Q•o of 2.2 ceptat 0øC. Figure 7 showsthe resultsof 66 suchsimulations. For a but showno data.We note that this rangeof absolutetemperature of height30 cm andtemperature 10øC,the simulation (273ø-298øK)is so smallthat many functionalrelationshipshummock that•40% of theCH4wouldbeoxidized beforereaching would appearto be a goodfit on an Arrheniusplot. One may suggests A 50% errorin the temperature exponentfor doubtthe validityand use of "activationenergy"derivedfrom the atmosphere. produces a slightly greater proportion oxidized at5øCbut suchplotsof complexsystems, but eventhe conceptof a Q•o diffusion proportionat 25øC.The proportion impliesan exponential relationship, with a nonzerointerceptat a very slightlydecreased 0øC. Whalenet al. [1990, Figure5b] and Dunfieldet al. [1993,
oxidizedis in directproportionto an errorin the oxidationrate,
Figure4] arebetterfittedby a linearrelationwith verysmallor and(notshown)errorsin therateof CH4 andCO2(decay)have zerointercept at 0øCthantheyareby an exponential one.Forthe almostno effecton the proportionoxidized,thoughthey do of simulation therefore we have assumed a linear relationship
courseaffect the effiux of thesegases.
Table 1. ParameterValuesandRelativeSensitivities for the "Best Fit" (Minimum)ChterionValue Units
Name
Parameter
Value
Transfercoefficientof gasin the gasphase Transfercoefficientof gas in water Transfercoefficientof gas in the container
Dc
Relative
Sensitivity c
Symbol cm2 s- • cm2 s-• cm2 s-•
2.0 6.5e-6b 0.032
2.0 1.3 3.0
yr-• yr- •
0.50 0.25
-0.7 4.0
nmol s-• nmol dm-3
0.01 2.1
0.5 - 1.8
wall a
Pc Hr Hx
Proportional rateof CH4 generation Proportional rateof CO2 generation Maximum rate of oxidation of CH4 to CO2 Concentration
for half-maximum
rate of
oxidation
aIncludes transfer through thepolyethylene andthemoresignificant escape through thewatertrap. bread 6.5e-6 as 6.5 x 10-6.
cProportional change intheoptimization criterion whentheparameter valueischanged by5%,expressed aslog•0.Larger is more sensitive.
716
PEARCE
AND
CLYMO:
OXIDATION
OF METHANE
IN PEATLAND
Conc.(nmol1-1) [logscale] 10-2 10o 102 104 106 108
10-2 100 102 104 106 108
0
o
.....
10'2 10o 102 104 106 108 .........
' ' '
o
o,
Headspace
Wat• 10
10
10
2O
2O
2O
o
Unsaturated ß ß....-'o
Saturated
3O
120H4
4O
3O
3O
4O
4O
1200 2
10-2 10o 102 104 106 108
lO-2 lO0 lO2 lO4 lO6 lO8 o
o
lO
2o
__ •.---e
•ee
/o •.,..-.o 3o
Excess 130H4
30 1 Excess 13C02
4O
4O
Figure 6. Concentration profilesof five gasesin water (filled symbols)and in the gasphase(opensymbols)in the modelafter 13 days,usingthe bestfit of sevenparameters(seeappendixA). Thereis no waterphasein the headspace and no gasphasein the saturatedlayer.The concentration axis is scaledlogarithmically.
After7 days,whenthe concentration of 13CH4in the head- layers, and 64.8% was still in the saturatedlayers where it had space wasatitsmaximum (Figure 2), 2.0%of theadded 13Cwas beenadded.Already oxidizedto CO2 was 0.9% in the headspace in CH4 in the headspace,23.6% was in CH4 in the water in the and 2.0% in the unsaturatedlayers. About 5.3% had escaped unsaturatedlayers, 1.2% was in the gas phaseof the unsaturated from the system.
1.0
A
O
Oxid 25 øC Diff 20 o•15•o
0.9
*
0.8
o
,'•
/
O.7
0.6
.o/,
0.5
0.4.
'ø
/ o/,
0.3 0.2 0.1
i
0 0
10
i
20
i
30
i
40
i
50
Thickness of unsaturated layer (cm)
Figure7. Calculated proportion that13CO2 formsof total•3Cin theheadspace (=proportion of CH4 oxidized) in relation to thicknessof the unsaturatedlayer and of temperature(see text). The points connectedby lines use
temperature exponent of diffusion = 0.02øC -• (Qlo= 1.2),of gasproduction = 0.16øC -1 (Qlo= 5), andoxidation versus temperature slopemultiplier = 1.0.Sensitivity fordiffusion isshown byupward pointing triangles forexponent = 0.03øC-' (Qlo = 1.4) at 5ø and25øC;sensitivityfor oxidationby downwardpointingtriangleswith factor= 1.5 at the sametwo temperatures. "M" indicatesthepointestablished fromthe experiments. All the otherpointsareinferred from the model.At 0øC, all valuesare zero;theseandunphysicalvalues>1.0 are omitted.
PEARCE
5.
AND
CLYMO:
OXIDATION
Discussion
5.1. Main Experiment
The mainresultof thisexperiment is thatat •20øC, 22% of the
added 13CH4 wasoxidized to 13CO2 onitswayupthrough the10
OF METHANE
IN PEATLAND
717
atmospheric trace gases but did not consider the role of diffusion.Yet this is not a new idea: much of the early work on uptake of solutesby plantswas shown [Olsen, 1953a, 1953b; Bircumshawand Riddiford, 1952; Briggs et al., 1961] to be studying diffusion rather than the biochemical processesthe authors intended.
cm of unsaturatedSphagnumto the headspace.The experiment was made with an intact systemthat was actively growing for a year before the experiment and resumed growth after it. The systempreservedthe microbial and fungal communitiesand the naturalphysicaljuxtapositionsof organismsand materials.However,it is widely believedthat part at leastof the CH4 in peatlands is producedfrom simplecarbohydrates secretedfrom activeroots [e.g., Chantonet al., 1995] and the plantswere in the dark during the experiment.It is also true that the temperatureof the experi-
factor of 10. The resultswere little affected. This is not a good representationof turbulent flow, but we recall that the spaces betweenstructuralelementsin the unsaturatedzone are no bigger than a few millimeters, and turbulentmixing is probably small
mentwas • 10øChigherthanwouldbe commonin the field and
anyway.
The experimentwas made in a closedcontainerwith minimal mass flow of air. In the field, one would expectwind-induced mixing in theunsaturated zoneto be greaterthanin the experiment.
We thereforetriedthe effectof increasing the valueof Dg by a
that the water table was static. Yet the measurednet effiux of CH4
fittedtotheresults in Figure 2bwas280[•molm-2 hr-1, whilein 5.3. Wider Application
the field the effiux from a 10 cm hummockwith temperatureat 10
The values in Figure 7 have been extrapolatedfrom a single
at 20øCwith the watertableat 10 cm depth:caution cmdepthof 14øCwas115•molm-2 hr-1 [ClymoandPearce, measurement 1995]. This differenceis almost exactly that calculablefrom the exponentialeffectof temperatureon net efflux of CH 4 [Daulat and Clymo, 1998] from coressimilar to thoseused in this experiment, which in any case containedonly 5-10% by area of vascular plants,the rest being Sphagnum--covered.We also note that the water tablein raisedpeatlandsis within 2.5 cm of the meanheight for nearly 70% of the time. Theseresultsare consistentwith the view that the experimentalcore behavedmuch as one in natural conditions would
do.
is necessary. In the field the net efflux from 40 cm high hummocks at a mean summertemperatureof 14øCwas 40% of that from hollows [Clymo and Pearce, 1995] implying, if one acceptsthat the productionrate beneathboth is the same [Daulat and Clymo, 1998], that 60% had been oxidized. Figure 7 suggests50% is oxidized.
In the circumstances
this seems to be a reasonable
agreement.Reeburgh et al. [1993] suggestedthat 30% of the CH4 produced in high-latitude wetlands was oxidized before emerginginto the atmosphere:closeto the value in Figure 7 for
20 cm hummocksat a summertemperature of 10øC. Can theseeffectsbe appliedon a largerscale?Supposethat the meantemperature10øCand that the acrotelm(unsaturated layer) The best fit parametervaluesfor the simulation(Table 1) were depthis 30 cm. Supposealso that the CH4 productionin a given determinedwith widely differing sensitivity.The transfercoeffi- time is 100 units, oxidation(Figure 7) is 0.42 x 100 = 42 units, by 1oto cientsof gasesin the gasphaseandin water(Dg,0.8' Dw, 6.4 x givingneteffiuxof 58 units.Now increasethetemperature 10-6 cm2 s-1) arenotdissimilar to theaccepted valuesof the 11øC.Production(Qlo = 4) wouldincreaseby 50% to 150 units, 5.2.
Simulation
molecular diffusion coefficientsobtainedby direct measurement oxidation becomes 0.45 x 150 = 68 units, and net effiux is 82: an
(0.2and1.2 x 10-s cm-2 s-1) andto the0.6cm-2 s-• inferred increase for C3H8in the unsaturated top 7 cm of a peatlandby Fechnerand Hemond [1992]. The transfercoefficientof the containerwall (Oc,
of 24 units but less than half the 50 units it would
have
been without oxidation. Becauseproductionhas an exponential responseto temperature but the oxidationresponseseemsto be near 0.032cm2 s-1) is several orders of magnitude greater thanthe linear (or at least,if exponential,hasa much smallerexponentthan diffusion coefficientof gasesthroughpolythene,but the model productiondoes), any increasein temperaturewill producesome also shows that 18% of the Kr and 19% of the •3C have increasein effiux. If, however,in the exampleabove,the changeof disappearedfrom the systemafter 13 days. These featuresare temperaturewas accompaniedby a drop in water table of 10 cm, consistent with the suggestion that pressuredrivenescapeof gases then the increasesin oxidation causedby higher temperatureand throughthe water seal is causingthe headspaceto behave like a deeperunsaturated zonewouldresultin no overallchangein effiux. Thesecalculationsare quite sensitiveto the depthof the unsatudilution vessel.The gas production(peat decay) coefficients(PM, 0.50yr-• andPc, 0.25yr-•) seemplausible at themeantemper- rated zone and to the mean temperature.We do not know the atureof 20øC:theyseemto indicatethatanaerobic CH4 production distributionof depthof the unsaturated zonefor evena singlesmall is, within its thin zone, an evenmore effectivedecayprocessthan peatland,nor do we have better than a vague idea of how that aerobicCO2 production,a conclusionconsistent with the findings distributionmight changeover 10-50 yearsin responseto a step of Belyea [1996]. However, we note that PM is imprecisely changein precipitation.For thesereasonsit is unhelpful, if not determined. misleading,to try to applytheresultsof thisexperimentto the global TheCH4 oxidation parameter values wereHv = 0.6 nmols-1 scaleat present.This sort of calculationalso ignorespossibilities andHK= 2.1nmoldm-3, butbothwereimprecisely determined,suchasNorthernHemispherepeatlandsat the southernendof their the latter being the most insensitiveof all the parameters.The rangedisappearingaltogether,while new onesform in the north. hyperbolicdefinitionof the oxidationprocesswas formally idenBeforewe beganthiswork, it was widely assumedthat CH4 was tical to that of an enzyme reaction.However, Michaelis-Menten oxidizedduringpassageup throughpeatlandhummocks,but most kinetics assume a well-stirred solution and relatively simple of the evidencewas indirect and qualitativeonly. We now have chemistry,while our experimentand natural conditionsin peat direct evidenceof the processand can calculate,tentatively,the are unstirredand complex.We think that the dynamicsof oxida- proportionof CH4 oxidized to CO2 at realistictemperaturesand tion are probablymuch more affectedby the rate of diffusionof depthsof acrotelm. substratesand productsthan by the propertiesof the enzymes involved,and the insensitivityof determinationof theseoxidation parametersreflectsthis: a wide rangeof valuesproducesalmostas Appendix A: G Span Variability Measure gooda fit becausethe factoryis limitedby transportto and from it not by its machineryand internal organization.Conrad [1996] For reasonsgiven earlier,we neededto calculateproportionlies reviewed the ways in which soil microorganismsmay control (quantiles),i.e., thatvalue of the measuredvariable,which includes
718
PEARCE
AND
CLYMO:
OXIDATION
a specified proportion of the sample or population. Statistics textbooksdeal with this, usuallyfor the 25 and 75% casesneeded for the interquartilerange, but they use a surprisingnumber of nonequivalentrecipesto do this. We devisedthe following. Let n be the numberin the sampleor population.Let p be the proportionilerequired,where [1/(2n)] < [p] < [1 - 1/(2n)]. (For the median,p = 0.5; for the interquartilerange,p = 0.25 and 0.75.) Let a be trunc(np),and a be the valueof the ath memberof the sampleor populationwhen it has been arrangedin ascending orderfrom a = 1. We use linear interpolationbetweenthe value of the ath and (a + 1)th members.We want the value (in the units of
thevariable)for thegivenp. Let thisbeE- Then p - a_+ [np- (a - 0.5)][(a+ 1) - _a]. We define the G spanas that distancewhich, were the sampleor populationdistributedin a Gaussian("normal") fashion,would give the samenumericalvalue as the standarddeviation.Specif-
ically,G span= •0.69- •0.31-
Appendix B:
Details of the Simulation
OF METHANE
IN PEATLAND
Most of this solid matter is in almost unhumified macroscopic pieces,so it was assumedto be physically,but not biologically, inert and without direct influence on transfer processes.In the unsaturatedzone the associatedwater probably does influence transport,so it must be includedin the simulation.Most of the solid matter is Sphagnumcell walls, which presentlittle resistance to diffusion: in effect the tormosityis small. This contrasts with mineral
soils in which most of the solid matter is in small
impermeablepieces causinglarge tortuosityand kinetics dominated by bottlenecks. The saturatedzone containedorganic matter and water only: measurements of wet massand dry masson slicesof accurately known volumefrom coressimilarto the experimentalone [Clymo, 1983, 1984, 1992, unpublishedmanuscript,1995] showno signof an extensivegas phasebelow the water table. Nor did vertical probes attacheddirectly to a mass spectrometer:gas bubbles manifestthemselvesby a large increasein partial pressure(W. Daulat, unpublishedmanuscript,1995). We do not deny that gas bubblesmay be found in the peat below pools (for example),but we think they were unimportantin this experimentso we madeno attemptto simulatethem or their movement. In the unsaturatedzone the proportion of the void volume
occupied by water, pwwasgivenbypw= 10(x/z; - •), wherex is
B1. Physical Conditions
the distance down
The model comprised66 layers representinga horizontalslice through the container and its contents plus a computational sentinellayer at top and bottom. The saturatedand unsaturated zone layers were 0.5 cm thick; the headspacehad a 9 cm layer sandwichedbetweentwo 0.5 cm layers;the lid of the container was 0.3 cm thick (and the area of the headspacesidewallswas added to it). The headspace was entirely gas phase. The saturatedand unsaturatedzoneswere assumedto containorganic
thickness.This functionis a negativeexponentialfrom 10% of the void volumeoccupiedby waterat the top of the top layerto 100% at the bottom of the lowermostunsaturatedlayer. This approximates experimentalmeasurements[Clymo, 1983, 1984, 1992, unpublished,1995]. B2.
into the unsaturated
zone and L is its total
Processes
Masstransferswere madefirst and were simply sumsof ratesin matter of0.05 gcm -3 and of intrinsic --3,sodensity densityat 1.5a gdcWmbUlk a proportion 0.05/1.5 = 0.033 (just over and out multiplied by the time step.After masstransfers,the total
3%) of the spacein theselayers was occupiedby solid matter. gas in the unsaturatedlayers was redistributedbetweengas and
0.10
• D2
0.10
•" D2
'
(a)
(b)
0.08
0.08
0.04
0.04
0.02
0.02
Di-• 0.01
oo
o'.4 Proportion ofD1
o.4 Proportion ofD1
Figure 8. Effectivetransfercoefficient(D) as a functionof the proportionof materialswith two differentvaluesof D combinedin variousways. (a) D2 = 0.1, D• = 0.01. The lowestcurveis for layersof the two materialsin series,and the highestcurve is for the two materialsin parallel (see text and appendixB). Also shown are curvesfor the combinationof seriesand parallel:A indicatesarithmeticmean;G indicatesgeometricmean;and W indicatesmean weightedby the proportion (seeappendixB). All the curvescoincideat the two points0, D2 and 1 D•. The choiceof 2 1
D2,with units cms- , isappropriate forair. D•was chosen toshow theshapes ofthecurves. (b)•)2asinFigure 8a, D• - 1.0x 10-s,appropriate fordiffusion ofgases inwater.Withlargedifferences intheD values, thecurves become very different from each other.
PEARCE
AND
CLYMO:
OXIDATION
waterphasesusingthe solubilitycoefficientsfor 20øC:Kr, 0.067;
CH4,0.033;andCO2,0.880cm3 cm-3. Nine rateswere calculated.Five were fluxes describedformally by zXM/At= D A AC/ZXx,where M is mass, t is time, C is concentration,x is distance,and D is a transfer coefficient. These
OF METHANE
B3.
IN PEATLAND
719
Running the Simulation
The method used is outlined in the main text. At the start of a
run, all concentrationswere set to zero, and there was no Kr or
excess •3Canywhere. Themodelwasthenrunfor 104min,with
incrementsof 0.2 min, or until no layer showedmore than 0.05% fivefluxeswereof Kr, 12CH4, 12CO2, 13CH4, and•3CO 2 between changefrom the previousiteration in concentrationof any gas. adjacentlayers.We used one value of D for all gasesin the gas This establishedthe initial gasconcentrationprofiles.The water in phaseand a secondvalue for all gasesin water. the top 1.5 cm of the saturatedlayerswas thennotionallyremoved There were complicationsin the unsaturatedlayers:the overall andreplaced by watersaturated withKr and13CH4, andtherun (effective)transfercoefficientdependson how the gas and water resumed. are arranged.If a half-thicknesslayer of one follows a halfIn early runswe setthe time incrementto 5 min, but the behavior thicknesslayer of the other in either order (seriesarrangement), was unstablewith alternatelayers building up increasingand then the conductanceis low: only doublewhat it would be if the reversing oscillationsin concentration.We cured this by two whole layer were of low-conductancematerial. If, however, the actions.First we calculatedfull mass changes,but then impletwo materialsare in parallel,then the overall conductance is high: mentedonly half the full changeplusthe half changeleft over from only half that if the whole layer was of high-conductance the previousiteration.This is similarto the partial explicit, partial material.
implicit techniqueusedin finite differencehydrologicalmodeling. Secondwe made the time incrementvery short (0.2 min) and increasedit cautiouslyonly if no concentration was more than 1% differentfrom its value on the previousiteration.If this limit was exceededfor any differencein any layer, the time incrementwas substantially reduced.Theseapproaches requiredfar morecomputing time (a single run took more than an hour on a 100 MHz De = (P•D• + P2D2)/Pt. machine),but the resultswere stable. The criterion to be minimized was similar to a chi-square Figure 8 showsthe effectiveconductivityof differingproportions Y•'[(Yobs,j -- Ycalc,j) / YGS,j] 2,where thesumis overall of the two materials:in seriesat the bottom and (the topmost quantity: timesandj = 1...5 gases, Yobs,j isthemeasured valueof the slopingstraightline) in parallel.Figure8 alsoshowsthe effectsof sample at timet, Yca•c,i is thecorresponding value taking a simplearithmeticor geometricaverageof the two values jth gasin theheadspace Let D• andD2 be the conductivityof the two substances that are in proportionsP• and P2, with Pr = P• + P2, then Ds andDe, the effectiveseriesand parallel conductivity,are
olD.
calculatedin the model, and YGs, i, an inverseweight, is the
errorof Yobs,j assessed by the G span.We applieda The parallel arrangementis not wholly realistic, even though measurement many of the structuralelementsin the unsaturatedlayer, and their further weight to each quantityin the sum becauseobservations associated water, do run vertically.The effectiveconductivityis too were far more frequentin the early part of the experiment.This great (exceptat the endsof the proportionscale).The seriesand weight was the logarithmof the time into the experiment,standsimple averageare wildly unsatisfactorygiving as they do little ardizedso that the mean weight was 1.0. We also applieda third increasein effectiveconductivityuntil the proportionof the low weightthat was the inverseof the meanproportionalerrorfor each conductivitymaterialhasbecomevery small,whenthereis a very gas,standardizedto a meanweight of 1.0. The valuesfor the five large increase.We therefore used a weighted effective mean gasesranged from 0.4 to 2.1. This weighting was to make the importanceproportionalto the precisionof measurementfor the definedby different gases. De = (P•D$ + P2De)/Pr, We optimizedthe parametervalues(minimizedthe criterion)by themethodof Nelder andMead [ 1965]. This is a simpleandrobust where D• < D 2. As Figure 8 shows,when the layer is mostly method,thoughnot the fastest.The model and optimizationwere unsaturated(the proportion of D• is small), the layer behaves programmedin PASCAL. closeto parallel,but by the time the proportionof D• is 90% and the layer is mostly saturated,it behaves close to the series arrangement.
Acknowledgments. We thank P. Cook for making the mass spec-
These rate calculationsrequiredthree parameters:the transfer trometer measurements,four reviewers for comments on drafts of the article, and the Natural Environment Research Council for financial coefficientsin the gasphase,in water,and in the containerlid and support.Bothauthorsdesignedthework;D. M. E. P.madetheexperiments;
headspace walls,Dg, Dw, andDc.
R. S. C. undertookdatareduction,modelbuilding,andthe first draftof this
Two of the other four ratesconcernedthe generationof natural article. CH4 and CO2 by decay.We assumed,for simplicity,that all the CO2 was generatedin the unsaturated layersat a rate proportional to the massin the layer.The CH4 was assumedto be generatedin a References layer 3 cm thick 10 cm below the top of the topmostsaturated Alm, J., CO• and CH4 Fluxes and CarbonBalance in the Atmospheric layer, consistentwith measurements[Daulat and Clymo, 1998, Interaction of Boreal Peatlands,Ph.D. thesis,Publ. in Sci. 44, Univ. of Joensuu,Joensuu,Finland, 1997. unpublishedmanuscript,1996]. The decayprocesses requiredone Alperin, M. J., and W. S. Reeburgh,Inhibitionexperimentson anaerobic parametereach for CH4 and CO2: PM and Pc. methaneoxidation,Appl. Environ.Microbiol., 50, 940-945, 1985. The remainingtwo rateswere of the oxidationof CH4 to CO2 for
•2C andexcess•3C,whichwe supposed to followthe same
Andersen,B. L., G. Bidoglio,A. Leip, andD. Rembges,A new methodto studysimultaneous methaneoxidationand methaneproductionin soils,
hyperbolic relation between rate and concentrationof CH4 in Global Biogeochem.Cycles,12, 587-594, 1998. water. This requiredtwo more parameters:Hr representingthe Bartlett, K. B., and R. C. Harriss, Review and assessmentof methane emissionsfrom wetlands,Chemosphere, 26, 261-320, 1993. maximum rate when concentrationis not limiting and Ha: the concentrationfor half-maximal rate. The oxidation processwas Belyea,L. R., Separatingthe effectsof litter qualityandmicroenvironment on decompositionrates in a petternedpeatland, Oikos, 77, 529-539, restrictedto the unsaturatedlayers:Nedwell and Watson[1995] 1996. reported that CH4 oxidation at Ellergower Moss was entirely Belyea,L. R., and R. S. Clymo, Do hollowscontrolthe rate of peat bog aerobic, though anaerobic oxidation is known to be possible growth?,in PatternedMires and Mire Pools, editedby V. Startden,J. H. [e.g., Alperin and Reeburgh,1985]. Tallis, and R. Meade, pp. 55-65, BritishEcol. Soc.,London, 1998.
720
PEARCE
AND
CLYMO:
OXIDATION
Bircumshaw,L. L., andA. C. Riddiford,Transportcontrolin heterogeneous reactions,Quart. Rev., 6, 157-185, 1952. Briggs, G. E., A. B. Hope, and R. N. Robertson,Electrolytesand Plant Cells, 216 pp., Blackwell Sci., Malden, Mass., 1961. Brumme, R., and W. Borken, Site variationin methaneoxidationas affected by atmosphericdepositionand type of temperateforestecosystem,Global Biogeochem.Cycles,13, 493- 501, 1999. Chanton,J.P., J. E. Bauer,P. A. Glaser,D. I. Siegel, C. A. Kelley, S. C. Tyler, E. H. Romanowicz,and A. Lazrus,Radiocarbonevidencefor the substrates supporting methaneformationwithin northernMinnesotapeatlands, Geochim. Cosmochim.Acta, 59, 3663-3668, 1995. Clymo, R. S., Peat, in Ecosystemsof the World, vol. 4A, Mires: Swamp, Bog,Fen andMoor, editedby A. J.P. Gore,pp. 159-224, Elsevier,New
OF METHANE
IN PEATLAND
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