Journalof Marine Research, 59, 417–452, 2001

Bioirrigationmodeling in experimentalbenthic mesocosms

byYokoFurukawa 1,SamuelJ. Bentley 2 andDawn L.Lavoie 1

ABSTRACT Burrowirrigation by benthic infauna affects chemical mass transfer regimes in marine and estuarinesediments. The bioirrigation facilitates rapid exchange of solutes between oxygenated overlyingwater and anoxic pore water, and thus promotes biogeochemical reactions that include degradationof sedimentary organic matter and reoxidation of reduced species. A comprehensive understandingof chemical mass transfer processes in aquatic sediments thus requires a proper treatmentof bioirrigation. We investigated bioirrigation processes during early diagenesis using laboratorybenthic mesocosms. Bioirrigation was carried out in the mesocosms by Schizocardium sp.,a funnel-feedingenteropneust hemichordate that builds and ventilates a U-shapedburrow. Interpretationof thelaboratory results was aided by atwo-dimensionalmulticomponent model for transportand reactions that explicitly accounts for the depth-dependent distribution of burrows as wellas the chemical mass transfers in theimmediate vicinity of burrow walls. Our study shows that bioirrigationsigniŽ cantly affects the spatial distributions of pore water solutes. Moreover, bioirriga- tionpromotes burrow walls to be the site of steepgeochemical gradients and rapid chemical mass transfer.Our results also indicate that the exchange function, a,widelyused in one-dimensional bioirrigationmodeling, can accurately describe the bioirrigation regimes if itsdepth attenuation is coupledto the depth-dependent distribution of burrows. In addition, this study shows that the multicomponent2D reaction-transport model is ausefulresearch tool that can be used to critically evaluatecommon biogeochemical assumptions such as theprescribed depth dependencies of organic matterdegradation rate and C/ Nratio,as wellas thelackof macrofaunalcontribution of metabolites tothe porewater.

1.Introduction Manymacroinvertebrates inhabit benthic boundary layers in marine and estuarine environments.Some of these animals construct burrows as their habitats, which they ventilatewith O 2-richoverlying water (i.e., bioirrigation). Consequently, O 2 and other electronacceptors are introduced to sediments that are well away from water-sediment interface(WSI), andmetabolites such as dissolved inorganic carbon and ammonium are removedto overlying water. Previous studies have recognized the signiŽ cance of this bioirrigationprocess in sedimentary early diagenesis (e.g., Aller, 1982; Kristensen, 1988; Marinelli,1992; Martin and Banta, 1992; Emerson et al., 1984;Aller and Aller, 1998;

1.Naval Research Laboratory,Sea oor Sciences Branch,Stennis Space Center,Mississippi, 39529, U.S.A. email:yoko.furukawa@ nrlssc.navy.mil 2.Louisiana State University,Coastal StudiesInstitute, Baton Rouge, Louisiana, 70803, U.S.A. 417 418 Journalof MarineResearch [59, 3

Figure1. The schematic model geometry of Aller’s cylindermodel (Aller, 1980), with r1 5 burrow

radius, and r2 5 half-distancebetween burrows.

Furukawa et al., 2000).In these studies, bioirrigation is found to quantitativelyaffect the microbialremineralization reactions and solute  uxes.Comprehensive understanding of thechemical mass transferin marine and estuarine environments thus requires a mechanis- ticand quantitative understanding of thebioirrigation processes. Today,the common quantitative treatment of bioirrigation involves a mathematical expressionof one-dimensionalnonlocal exchange (e.g., Emerson et al., 1984;Boudreau, 1984;Martin and Banta, 1992). The measure for thisexchange, nonlocal exchange function a,isusually described as a simplefunction (e.g., constant, linear decrease, exponentialdecay) of depth. Whereas this modeling strategy often produces agreement betweenmeasured and modeled depth proŽ les of solutes(e.g., Matisof and Wang, 1998; Kristensenand Hansen, 1999; Schlu ¨ter et al., 2000),the mathematical formulae and “best-Žt” parameter values for a donot allow deconvolution of actual mechanistic steps involvedin the bioirrigation processes (Meile et al., 2001).Moreover, this type of 1D treatmentgives little insights to the lateral spatial variability in chemical mass transfer regimesassociated with the burrows. Themost mechanistic model treatment of bioirrigationto datewas establishedby Aller (1980,1982, 1984). In his so-called cylinder model, bioirrigated sediment is idealizedas a collectionof laterallyclose-packed, identical cylinders, each with a cylindricalvoid space (i.e.,burrow) ofan identical geometry in the center (Fig. 1). The outer surface of each microenvironment(i.e., r 5 r2)representsthe midpoint between two adjacent burrows, andthus the point of zero radial  ux.In this model, bioirrigation is mathematically expressedas the radial diffusive exchange of solutesperpendicular to theburrow wall. The concentrationof agivensolute at a givenposition at a giventime, Cx,r,t,canbe determined bythe equation that describes vertical diffusion perpendicular to the water-sediment 2001] Furukawaet al.: Bioirrigation modeling 419 interface(WSI), radialdiffusion perpendicular to the burrow wall, and net rate of productionor consumptionof thesolute due to biogeochemicalreactions:

]Cx,r,t ] Dsw ]Cx,r,t 1 ] Dsw ]Cx,r,t w 5 w 1 rw 1 R (1) ]t ]x X u2 ]x D r ]r X u2 ]r D

(Aller,1980; Boudreau, 1997, p. 63) where w [ porosity, t [ time, Dsw [ diffusion coefŽcient of the solute in seawater, u [ diffusivetortuosity, and R [ overallrate of production/consumptionreactions. The diffusive tortuosity term in the equation can be replacedby aporosityexpression using the following empirical correlation:

u2 5 1 2 ln ~w2! (2)

(Boudreau,1997, p. 132).The model originally presented by Aller(1980) assumes that the burrowwater composition is always the same as that of overlying water (i.e., 100% irrigation).The original model geometry also assumes that all burrows have the identical radiusand depth extent, and are equally spaced. Boudreau and Marinelli (1994) extended themodel to allow periodic, discontinuous irrigation in whichthe burrow water composi- tionstarts to equilibrate with surrounding pore water while the burrows are not actively irrigated.This model re ects the observations that many infauna species go through alternatingventilation and rest cycles (e.g., Kristensen, 2000). Furukawa et al. (2001) incorporatedthe metabolite contribution by burrowingmacrofauna into the discontinuous irrigationmodel. Theadvantage to such a 2Dmodeling approach over the use of simple 1D nonlocal exchangefunctions is that 2D models allow us to quantify the spatial and temporal heterogeneityin sedimentgeochemistry. For example,Aller (1980) showed the widerange oflateralvariability in pore water compositions as a functionof distancefrom themodel burrowwall using the original cylinder model. Marinelli and Boudreau (1996) used the discontinuousirrigation model as well as an idealized laboratory microenvironment to illustratethe steep gradients in redox and pH conditions in the immediate vicinity of burrowwalls. Furukawa et al. (2001)calculated the possible lateral variability in the thermodynamicstabilities of calciumcarbonate minerals due to bioirrigation and infauna metabolismusing the model that incorporated discontinuous irrigation and macrofaunal metaboliteproduction. Whereasthe original cylinder model and its derivatives provide insights to the processes thatoccur in associationwith burrows, their application to actualsediments is limited.This ispartlybecause of theassumption that all burrows are vertical and havethe identical depth extent.In reality, more than one species of burrowing infauna usually inhabit a given sedimentaryarea, creating burrows of variousdepth extents and geometries (e.g., D’ Andrea andLopez, 1997; Levin et al., 1999).Many species of burrowing infauna are known to createburrows with complex geometry that may not be adequately approximated by verticalcylinders (e.g., Davey, 1994; Rowden and Jones, 1995; Ziebis et al., 1996; Scaps et 420 Journalof MarineResearch [59, 3 al., 1998).A bioirrigationmodel would be moreapplicable to actualsediments if itwere ableto account for thevariable depth extents and tilt angles of burrows. Our strategytoward the quantitative and mechanistic understanding of bioirrigationthus involvesthe construction of a2Dbioirrigationmodel, with a simultaneousdata collection inlaboratory benthic mesocosms. The model formulation takes into account the parameters thatwere previouslyconsidered (e.g., burrow radius, number of burrowsper unit area of seabed;Aller, 1980; Boudreau and Marinelli, 1994; Marinelli and Boudreau, 1996). In addition,our model considers other parameters that are important in the adequate descriptionof Želdand laboratory observations, such as the depth-dependent distribution ofburrows and burrow tilt angles. The laboratory experiments provide directly measured datafor constrainingthe model geometry and boundary chemical values. They also supply depthproŽ les of solute species that are used to evaluatethe model outputs. Consequently, thesimulation results demonstrate the quantitative signiŽ cance of depth-dependent bioirri- gationin terms of netchemical mass transfer.Moreover, the model results illustrate the lateralvariability in chemical mass transferregimes especially in the vicinity of burrow walls.This study also demonstrates the model as an evaluation tool for common assumptionsused in biogeochemical studies of early diagenesis, such as the prescribed depthdependencies of organicmatter (OM) degradationrate and C/ Nratio.

2. The model a.Model geometry We haveextended Aller’ s (1980)cylinder model (Fig. 1) to consider sediments with variableburrow depths and tilt angles. Our modelrepresents burrowed sediment using a cylindricalmicroenvironment with a voidspace (i.e., “ modelburrow” ) incenter(Fig. 2a). Thecylinders are arranged in thelateral close packing as inFigure1(a). Whereas the radius ofmicroenvironment ( r2)remainsconstant throughout the depth interval of consideration, theradius of model burrow is a functionof depth (i.e., r1( x)).Thevalue for r2 is determinedby the number of burrow openings at WSI( n (m22))asfollows:

1 r 5 ~m!. (3) 2 Î 2 Î 3 3 n

Eachmicroenvironment has the depth of Ltotal andthe model burrow has the depth of Lburrow. Thefunction and parameters for r1( x)areselected such that the surface area of model burrowwall at the depth interval x ; x 1 dx (Fig.2b andc),

x1dx r x dx E 2p 1~ ! (4) x 2001] Furukawaet al.: Bioirrigation modeling 421

Figure2. The schematic model geometry of the depth-dependent bioirrigation model. The number of burrowsdecreases with depth in natural sediments, and it isrepresented by a microenvironment whoseburrow radius decreases with depth. describesthe surface area of burrowwall interface at the depth interval of x ; x 1 dx for thesediment microenvironment that is being modeled. Thus, the value of r1 at a given depth x reects three factors: (1) theratio of burrowdensity at the given depth to burrow densityat WSI; (2) theburrow radii; and (3) thetilt angles of theburrows. Higher burrow densityyields more burrow wall surface area available for radialdiffusive exchange, and greater r1 value.The larger average burrow radius also translates to thelarger r1 value. The surfacearea of burrowwall interface for averticalburrow within the Ž nitedepth interval

(dx) is 2prburrowdx.Onthe otherhand, the burrow wall interface area of aburrowtilted by angle u isgreater,and given by 2 prburrowdx/cos u (Fig.3). Hence, the greaterthe tilt angle u,thegreater the available burrow wall interface surface area for thegiven depth interval. Figure4 illustrateshow this model geometry can be applied to real sediment. In this example,all burrows have the identical radius ( rburrow).First,the density of burrow 2 2 openingsat WSI ( n (m ))determinesthe outer radius of microenvironment, r2, to be 1 (m) (Eq.3). The burrow wall area for thismicroenvironment within the top dx Î 2Î 3 3 n (m) isgiven by 2 prburrowdx/cos u,whenthe average tilt angle of allburrows at WSIis u. Thesurface area of thisburrow can be representedby a verticalmodel burrow of thesame interfacearea whose radius is r1:

rburrow r 5 . (5) 1,SWI cos u

Similarly,the value of r1 at depth x canbe determinedusing the burrow density at depth x, 22 pn (m ) ( p , 1),andaverage burrow tilt angle at depth x, ux, to be: 422 Journalof MarineResearch [59, 3

Figure3. The wall surface area of atiltedburrow is greater for a unitdepth interval than that of a verticalburrow.

prburrow r1~x! 5 . (6) cos ux Thismodel geometry requires that complex burrow geometry be represented by asingle function, r1( x),usingthe depth-dependent change in burrow wall interface area as a guide. ThissimpliŽ cation is basedon the observations that the primary effect of burrowsin early diageneticchemical mass transferis theincreased amount of diffusiveinterface between oxygenatedwater andanoxic sediments (Forster, 1996; Kristensen, 2000). b.Model equations We considerburrowed sediment with no advection (i.e., no sediment accumulation).

Theno advection assumption is justiŽed when r2 isrelativelysmall compared to Lburrow

Figure4. A schematicdiagram showing how the geometry parameters for the cylinder model ( r2 ,

r1 ( x))aredetermined. 2001] Furukawaet al.: Bioirrigation modeling 423

(Aller,1980). We alsoassume that there is no compaction, and thus porosity ( w) has a constantvalue throughout the sediments. Consequently, we canwrite an equationsimilar toEq.(1) for thenew geometry. The equation for thesolute concentration within sediment

(i.e., 0 # x # Ltotal and 0 # r # r2,excludingthe burrow: 0 # x # Lburrow and 0 # r # r1( x)) is:

2 ]Cx,r,t Dsw ] Cx,r,t Dsw 1 ] ]Cx,r,t 5 1 r 1 R. (7) ]t 1 2 ln ~w2! ]x2 1 2 ln ~w2! r ]r X ]r D

Withinthe burrow (i.e., 0 # x # Lburrow and 0 # r # r1( x)),thesolute concentration is heldat the value of overlying water ( C0)torepresent 100% (continuous) irrigation. Parametervalues and functions needed for thesteady state solution of Eq.(7) are:model burrowradius as a functionof depth( r1( x)(m)), porosity( w),diffusioncoefŽ cient ( Dsw 2 21 21 (m s )), andnet production rate ( R (M s )). Theouter radius of microenvironment, r2 (m) isderived from Eq.(3) usingthe observed burrow opening density at WSI ( n (m22)).

Othergeometry-related parameters include Lburrow and Ltotal.Theburrow parameters (n( x), r1( x), r2, Lburrow)andporosity ( w)canbe determined through direct analysis of sedimentsamples. The net production/ consumptionreaction rate of agivensolute species withinthe sediments ( R)maybe foundin literature(i.e., Van Cappellen and Wang, 1996), estimatedfrom O 2 microproŽles (Marinelli and Boudreau, 1996), or determined by batch incubationexperiments (Aller andYingst, 1980). The diffusion coefŽ cient ( Dsw) can be foundin literature,such as Boudreau(1997, p. 96). c.Boundary conditions Boundaryconditions needed for thenumerical solution of Eq.(7) arethe same as the onesintroduced by Aller (1980), Boudreau and Marinelli (1994) and Marinelli and Boudreau(1996), and include the following. Solute concentration at theWSI (i.e.,at x 5

0)isequalto the bulk solute concentration of theoverlying water ( Cbulk):

Cx50,r,t 5 C0 5 Cbulk (8)

At burrowwall ( r 5 r1( x)),soluteconcentration is also equal to the bulk solute concentrationof theoverlying water (i.e.,100% irrigation):

Cx,r5r1~x!,t 5 C0. (9)

Theexception to the above (8) and(9) isoxygen: due to the diffusive boundary layer (e.g.,

Jørgensen and Revsbech, 1985), the concentration value at WSI andburrow wall ( C0) is typicallyless than the bulk value in the overlying water (i.e., C0 , Cbulk).Thevalue of C0 for oxygenmay be directly determined by inspecting measured O 2 microproŽles (Fu- rukawa et al., 2000).The solute diffusive  uxatthe outer boundary of each sedimentary microenvironment, r2,iszeroin the radial direction, as inAller’s cylindermodel (Aller, 1980): 424 Journalof MarineResearch [59, 3

]C 5 0. (10) ]r U r5r2

Verticalsolute  uxat the bottom boundary (at x 5 Ltotal)canbe set to zero using a sufŽciently large value for Ltotal.Alternatively,when simulating irrigation in anexperimen- taltank with a closedbottom, Ltotal canbe deŽned as the bottom of thetank. In either case, thefollowing equation represents this boundary condition:

]C 5 0. (11) ]x U x5L

Theinitial concentration distribution can be setarbitrarily when solving for steadystate. d.Net production rates and numerical solutions Thenet production rate, R (M s21),for eachspecies is determined through the couplings ofgeochemical reactions that are recognized as important to overall chemical mass 2 transfer.The reactions considered here include OM remineralizationby O 2, NO3 , and 22 1 2 1 SO4 ,reoxidationof NH 4 and SS (5H2S 1 HS ) by O2, rapid NH4 adsorption/ desorptionat mineralsurfaces, and rapid acid-base equilibration reactions among sulŽ de 2 2 22 species (H2S and HS )anddissolved inorganic carbon (CO 2, HCO3 , and CO3 ) (Table 1; VanCappellen and Wang, 1996; Boudreau, 1997; Furukawa et al., 2001).Particle-bound MnandFe areimportant redox species when nonlocal particle mixing due to bioturbation displacesthem across the redox boundaries (Aller, 1994; CanŽ eld et al., 1993).Head-down depositfeeders are one example of bioturbators that displace sediment particles across the redoxboundaries. Our currentmodel assumes contributions of metal oxides to OM remineralizationto be negligible. This is justiŽ ed for theapplication we presentin this paperin which we modelearly diagenesis in laboratorymesocosms inhabited by Schizocar- dium sp.(See Section3a). Eq.(7), the two-dimensional conservation equation, is written for eachof the species 2 22 1 2 consideredin the present study, O 2, NO3 , SO4 , NH4 , SS (5H2S 1 HS ), TCO2 2 22 2 22 2 (5CO2 1 HCO3 1 CO3 ),andtitration alkalinity (Alk t 5 HCO3 1 2CO3 1 HS ). Therate expression for eachof theconservation equations is shownin Table1. AFORTRAN codeis usedto numericallysolve the above conservation equations and boundaryconditions. The assumption of steadystate is valid when r2 issufŽciently small compared to Ltotal (Aller,1980). Locally one-dimensional method (LOD; Boudreau,1997, p.350)with the Crank-Nicholson formula is employedas the numerical solution scheme.

Atwo-dimensional( x and r)gridis appliedto the cylindrical microenvironment, and Cx,r for eachnode is solved as atime-evolutionproblem (Press et al., 1992)until steady state is reached.All conservation equations are coupled and solved simultaneously through the couplingof reactionterms, R (i.e.,Van Cappellen and Wang,1996; Furukawa et al., 2001).

For example,the reaction term for theconservation equation of O 2 at Time Step T is 2001] Furukawaet al.: Bioirrigation modeling 425

Table1. Reactions and rateswithin sediments (after Van Cappellen and Wang, 1996). Primaryredox reactions: 2 2 (CH2 O)x (NH3 )y (H3 PO4 )z 1 (x 1 2y)O2 1 (y 1 2z)HCO3 ® (x 1 y 1 2z)CO2 1 yNO3 1 2 2 zHPO4 1 (x 1 2y 1 2z)H2 O 2 (CH2 O)x (NH3 )y (H3 PO4 )z 1 ((4x 1 3y)/5)NO3 ® ((2x 1 4y)/5)N2 1 ((x 2 3y 1 2 2 2 10x)/5)CO2 1 ((4x 1 3y 2 10z)/5)HCO3 1 zHPO4 1 ((3x 1 6y 1 10z)/5)H2 O 2 2 (CH2 O)x (NH3 )y (H3 PO4 )z 1 (x/2)SO4 1 (y 2 2z)CO2 1 (y 2 2z)H2 O ® (x/2)H2 S 1 (x 1 2 1 2 2 y 2 2z)HCO3 1 yNH4 1 zHPO4 Secondaryredox reactions: 1 2 2 NH4 1 2O2 1 2HCO3 ® NO3 1 2CO2 1 3H2 O 2 2 2 H2 S 1 2O2 1 2HCO3 ® SO4 1 2CO2 1 2H2 O Acid-basereactions (equilibrium): 2 1 CO2 1 H2 O « HCO3 1 H 2 2 2 1 HCO3 « CO3 1 H 2 1 H2 S « HS 1 H Adsorptionreactions (equilibrium) 1 1 NH4 (aq) « NH4 (ads) Reactionrates: D[O ] x 1 2y [O ] 2 2 1 5 ROC 2 2kNH4O2[O2][NH4 ] 2 2kSSO2[O2]@SS# (I-1) Dt x KO2 1 [O2] D[NO2] y [O ] 4x 1 3y [NO2] K9 3 2 3 O2 1 5 2 ROC 1 ROC 2 1 kNH4O2[O2][NH4 ] (I-2) Dt x KO2 1 [O2] 5x KNO3 1 [NO3 ] KO9 2 1 [O2] 22 22 D[SO4 ] 1 [SO4 ] KO9 2 KNO9 3 5 ROC 22 2 1 kS SO2[O2]@SS# (I-3) Dt 2 KSO4 1 [SO4 ] KO9 2 1 [O2] KNO9 3 1 [NO3 ]

D@SCO2# 5 2R (I-4) Dt OC 1 D[NH4 ] y 5 2 R 2 k [O ][NH1] (I-5) Dt x OC NH4O2 2 4 22 D@SS# D[SO4 ] 5 2 (I-6) Dt Dt 2 D@Alkt# y 1 2z [O2] 4x 1 3y 2 10z [NO3 ] KO9 2 5 ROC 2 ROC 2 Dt x K 1 [O ] 5x K 2 1 [NO ] K9 1 [O ] O2 2 NO3 3 O2 2

22 x 1 y 2 2z [SO4 ] KO9 2 KNO9 3 (I-7) 2 ROC 22 2 x KSO4 1 [SO4 ] KO9 2 1 [O2] KNO9 3 1 [NO3 ]

1 2 2kNH4O2[O2][NH4 ] 2 2kS SO2[O2]@SS#

1 determinedby the concentration values of O 2, NH4 , and SSatTime Step T 2 1 (see Table1, I-1).

Inthe end, the model determines the value of Cx,r for eachgrid point for allspecies, as wellas the radially averaged Cx,r for eachof the depth intervals. The radially averaged concentrationsare used as the feedback tool because typical Ž eldmeasurements of pore waterconstituents yield depth proŽ les, in which lateral variability is averaged by the typicalsampling practices (i.e., horizontal slicing of coresamples and long-term deploy- mentof pore water peepers). 426 Journalof MarineResearch [59, 3

Figure5. Body (A) andschematicburrow morphology (B) of Schizocardium sp.(A)Eachincrement onthe scale is 1 mm. (B)Scale is approximate. This organism constructs a U-shapedburrow, ingestingsediment from one burrow opening (creating a feedingpit), and defecating at the other (creatinga fecalmound). Typical burrow depths (in mesocosms and the Ž eld)range from 7 to .15 cm.

3.Experimental methods a.Experimental macrofauna Thisstudy used Schizocardium sp.,a funnel-feedingenteropneust hemichordate, as the bioirrigatorof choicebecause of itsabundance at a nearbyŽ eldstation and adaptability to thelaboratory environment. Each individual Schizocardium sp.creates and inhabits a single U-shapedburrow, whose diameter is approximately 5 mm (Fig.5; Bentley and Richardson,2001). It ingests sediment particles at the feeding pit and egests at theother endof theburrow, creating a fecalmound. Thus, the ingested sediment particles remain withinthe same redox environment in theclose vicinity of WSI, justifyingthe omission of particle-boundMn and Fe inthe reaction couplings for thisparticular application (see Section2d above). The experimental animals were collectedduring several cruises on board R/V Kit Jones ata Želdstation just outside of St.Louis Bay in Mississippi Sound (30° 14.09N, 89° 20.09W). Schizocardium sp.was thenumerically predominant macro- faunacaught in the 0.5mm sievesat this site. The 210Pbgeochronologydata from thesame stationshows that the upper 5 ; 10cmof thesediments are well mixed (Bentley et al., 2000),suggesting that the burrowing activities of Schizocardium sp.extend to these depths.In the Ž eld,active burrows are marked by a few mm-thicktan-colored (i.e., oxidized)halos along the walls, whereas the walls of abandoned burrows exhibit a dark graycolor (i.e., reduced) similar to thematrix sediments. b.Laboratory mesocosms Water-saturated,Ž ne-grainedsediment from St.Louis Bay, Mississippi (30° 17.0 9N, 89° 19.09W)was usedas the experimental substrate. The sediment was Žrst passedthrough the 2001] Furukawaet al.: Bioirrigation modeling 427

Table 2. Schizocardium sp.population in experimental quadrants. Numberin 30 cm 3 Population Burrow Tank Quadrant 30cmquadrant density (m2 2 ) openings (m2 2 ) Tank 3 3B 72 800 1600 3D 9 100 200 Tank 6 6A 32 356 712 6B 28 311 622

0.5mm sievesin order to eliminatemacrofauna. A smallamount of water, whose salinity was adjustedto matchthat of the Schizocardium sp.collection site (18 6 1psu),was added tothe sediment in order to aid sieving. A portionof the sediment was frozenand then thawed,which resulted in the elimination of meiofaunaand sediment compaction due to dewatering. Twoglass tanks (“ Tank3” and “ Tank6” ), 60cm 3 60 cm 3 45cmhigh each, were preparedfor thisstudy. Tank 3 was loadedwith the sediment/ watermixture that had not beenfrozen, which was thenallowed to settlenaturally. Most of sedimentparticles settled withinseven days creating a 13cm-thicksediment column. Tank 6 was loadedwith the sediment/watermixture that had been frozen and thawed. The sediment was alsoallowed tosettlenaturally, and created a 16cm-thicksediment column. After thesettling,Plexiglas dividers(30 cm high)were insertedinto each tank in orderto separate the tank into four equalquadrants (i.e., A, B,CandD) withthe lateral dimension of 30cm 3 30 cm. The waterlevels were maintainedin bothtanks so that there was alwaysapproximately 30 cm ofwater column above WSI. Theoverlying water in the tanks was circulatedthrough externalaragonite-gravel Ž lterchambers for theduration of experiments.

Prior to the Schizocardium sp.introduction, Tank 6 was analyzedusing Clarke-type O 2 microelectrodesto obtain three O 2 microproŽles with the 0.2 mm verticalspatial resolu- tion.The microproŽ les were locatednear the center of Quadrant 6C, and were laterally 5mm apartof eachother. After approximately1.5 months of sediment introduction, all experimental quadrants were populatedwith Schizocardium sp.Animal populations in the experimental quadrants areshown in Table 2. Only two of the quadrants from eachtank were studiedfor the purposeof thispaper (Quadrants 3B, 3D, 6A and6B) andno furtherreplication was made. Withina few days,most of the animals burrowed into the substrate (Fig. 6a). Within a week,the worms visiblyaltered the seabed structure through their tube construction and sedimentingestion/ egestion.The photograph taken after four weeks of animalintroduction inTank 3D (Fig.6b) showsthe magnitude of structuralmodiŽ cation by Schizocardium sp. bioturbation.For theduration of theexperiments, the mesocosms were litfor 10hours per day,salinity and temperature were keptnear constant ( S 5 18 6 1, Ttank3 5 24 6 18C,

Ttank6 5 19 6 1°C), andoverlying waters were circulatedthrough the aragonite Ž lters. Throughoutthe duration of experiments, green algae were allowedto growon WSIaswell asontheinside of tankwalls. On average, 10 –25%oftheWSI was coveredwith the algae, 428 Journalof MarineResearch [59, 3

Figure6. An experimental quadrant (3D) shortly after the Schizocardium introduction(A), and 4 weeksafter the introduction (B). whereasthe tank walls were alwayscompletely covered by the algae. The green algae on wallswere occasionallyremoved by wiping.

Fifty-sixdays after the animal introduction in Quadrant 3B, Clarke-type O 2 microelec- trodeswere usedto measure Ž veO 2 microproŽles at 0.2 mm verticalspatial resolution. Themicroelectrode insertion was arrangedso thatall Ž vemicroproŽles were onalateral straightline near the center of Quadrant3B, withthe lateral spacing between microproŽ les to be 5 mm. Fifty-sevendays after introduction of the animals, the sediments in Quadrants3B and 3Dwere sampledusing two 15 cm-diameterPlexiglas tubes per each quadrant. Quadrant 6Awas sampled26 daysafter the animal introduction, and Quadrant 6B was sampled60 daysafter the animal introduction, using one 15 cm-diametertube for eachquadrant. Large tubeswere necessaryin order to extract enough pore water from each1-cm slices. However,due to the tight Ž ttingof 1 ;215-cmtube(s) plus 17-cm 3 2-cmslab in each 15 3 15-cmquadrant, no samplingcould be duplicated.One core from eachquadrant was thensliced into 1-cm sections, whose pH valueswere determinedby thedirect insertion of apHelectrode calibrated with NBS-traceable buffers. The slices were subsequently centrifugedand Ž lteredto yieldpore water samples. The porewater samples were analyzed 22 for depth-dependentvalues of titration alkalinity (by potentiometric titration), SO 4 (by 1 ionchromatography), and NH 4 (byspectrophotometry). Theremaining cores from 3Band 3D were usedfor physicalproperty (porosity and graindensity) analysis. The method involves the initial determination of bulkdensity and subsequentdetermination of dry density after drying the sediment samples at 105° C overnight.The porosity data were usedto estimate the diffusive tortuosity (Eq. 2). The dryingmethod used here eliminates water trapped within mineral aggregates that may not contributeto diffusivetortuosity (Bourbie ´ et al., 1987).However, we proceededto use the totalporosity in Eq. (2), because the empirical equation correlating porosity to diffusive tortuosityis based on porosity data obtained using a widevariety of dryingmethods for bothclayey and non-clayey sediments (see Boudreau,1997, p. 130, and references therein).The porosity gradients for 6Aand 6B were estimatedfrom acoretaken in the 2001] Furukawaet al.: Bioirrigation modeling 429 quadrantnot used in this study (Quadrant 6C). The Schizocardium sp.population in 6C was 28perquadrant(or 311m 22). Allexperimental quadrants were alsocored using 2.2 cm-thick and 17 cm-wide Plexi- glasslab-shaped corers. The slab cores were X-rayedimmediately after coring in order to characterizethe burrow distribution. The X-radiographs were thenconverted to binary imagesof burrows vs. matrix sediments. These images were subsequentlyoverlaid with horizontallines in 1-cm intervals in order to determine the depth-dependent burrow distributionand burrow tilt angles with 1-cm depth resolution. Transmissionelectron microscope (TEM) was usedto visually inspect the microfabric ofsediments.Samples were takenfrom theimmediate vicinities of WSI andburrow walls, aswell as from thematrix sediments well away from WSI andburrow walls using mini-corers(Lavoie et al., 1996).They were subsequentlytreated with a Žxingagent (Gluteraldehyde-buffersolution; Leppard et al., 1996),embedded in resin, ultramic- rotomed,and imaged under TEM. c.Batch incubation 1 22 Therates for microbialproduction of TCO 2 and NH4 andconsumption of SO 4 were determinedthrough batch incubation experiments in closed systems (Aller andYingst, 1980).After coring,approximately the top5 cmofthe remaining sediments from Tank3D were homogenizedby hand mixing and placed into four centrifuge tubes. Visible fauna were eliminatedprior to placing in the tubes, thus the rates determined herein were consideredto be the microbial reaction rates. The tubes were completelyŽ lledwith sedimentin order to minimize air space, and then placed in a glovebag Ž lledwith ultra highpurity N 2.Thecentrifuge tubes were cappedin the glove bag. All but one of the centrifugetubes were thenplaced in anairtightcontainer with two small openings for N 2 circulation.The container was Žlledwith a faststream of N 2,followedby a slow continuousstream of N 2 inorderto assureno atmosphericO 2 wouldbe incontact with the centrifugebottles. The tubes were takenout of thecontainer one at atimeat 24hours,167 hours,and 384hours after the initial loading, inserted with a pHelectrode,and centrifuged. Thepore water samples were subsequentlyŽ lteredand analyzed for titrationalkalinity, 22 1 SO4 and NH4 concentrationsusing the same methods used above. The remaining sediment-Žlled tube was analyzedfor pHandcentrifuged immediately after Ž llingin order toextract and analyze initial pore water. The time-dependent change in TCO 2 was calculatedusing the measured time-dependent pH and alkalinity data and equilibrium constantsfor thecarbonate system found in Millero (1995). The pH measurement for

24-hoursample failed, thus TCO 2 valuewas notcalculated for thissample.

4.Experimental results and determination of parametervalues a.Porosity, grain density and diffusion coefŽ cients PorosityproŽ les of the experimental quadrants are shown in Figure 7. The mean porosityfor eachquadrant is thusdetermined to be: w3B 5 0.854(range: 0.733 ; 0.928), 430 Journalof MarineResearch [59, 3

Figure7. Depth proŽ les of measuredporosity for Quadrants 3B, 3D, and Tank6.

w3D 5 0.832(range: 0.710 ; 0.896), and w6A 5 w6B 5 0.709(range: 0.660 ; 0.791). The porosityin Tank6 islowerthan that of Tank3 becausethe Tank 6 sedimentwent through freezingbefore loading, which caused dewatering. Themeasured proŽ les (Fig. 7) indicate that the porosity is not constant within each mesocosmtank. The assumption of constantporosity (Section 2b) with the use of mean porosityvalues introduces uncertainty to the tortuosity-corrected diffusion coefŽ cient, DSW .Theestimated uncertainty in diffusioncoefŽ cients is up to23% in Quadrant 1 2 ln ~w2! 3B,up to23% and Quadrant 3D, and up to13%inQuadrant6A and6C. The average grain densityof the mesocosm sediments was determinedto be2.55g cm 23.

b. O2 microproŽles and aerobic OC degradationrate

Figure8 showsthe O 2 microproŽles taken in 6C prior to the Schizocardium sp. introduction,and Figure 9 showsthe O 2 microproŽles taken in 3D prior to the core sampling.The key parameter values for theTank 3 proŽles are also shown in Table 3. The

Figure 8. O2 microproŽles taken in Tank6 priorto the Schizocardium sp.introduction. 2001] Furukawaet al.: Bioirrigation modeling 431

Figure 9. O2 microproŽles taken in Tank3 priorto thecore sampling. ProŽ le (a) exhibits the effect

of lateral O2 diffusionfrom a burrow.

proŽles from 3Dwere usedto calculate the O 2 consumptionrates in all tanks: the 6C proŽles taken before the animalintroduction would yield an O 2 consumptionrate that does notaccount for thepossible change in the microbial activities due to the presence of macrofauna.The procedure outlined below assumes that the observed proŽ les are free from theeffect of lateralO 2 diffusionalong burrow walls. This is a reasonableassumption becausethe radial O 2 penetrationthickness along burrow walls is expected to besimilarto thevertical O 2 penetrationdepth at WSI, whichis approximately2– 3 mm (Table3). Thus, ifthenumber of burrowopenings is 1,600 (m 22)asin Quadrant3B andburrow radius is 1.25(mm), approximately9% oftheWSIsurfaceis under the in uence of radialdiffusion.

Inother words, at WSI, arandomlyinserted O 2 microelectrodehas 91% chance of recordinga verticalO 2 proŽle that is free from theeffect of radialdiffusion. One of the proŽles from 3D(Fig. 9a) exhibits the in uence of radialdiffusion, and thus is excluded from thefollowing calculations. At steadystate, when vertical diffusion is the only transport mechanism, the mass conservationequation describing the pore water proŽ le ofO 2 is,

2 d [O2] D9 1 R 5 0 (12) dx2 O2

Table3. Graphically estimated values of C and L ,andcalculated O consumptionrates R . 0 O 2 2 0 (b) (c) (d) (e) T (°C) 24 2 21 2 9 DS W (m s ) 2.25 3 10 fW S I (%) 89.6 23 23 23 23 C0 (M) .163 3 10 .162 3 10 .171 3 10 .157 3 10 23 23 23 23 LO (m) 2.8 3 10 2.6 3 10 2.4 3 10 2.6 3 10 2 28 28 28 28 R0 (M/s) 27.7 3 10 28.8 3 10 210.9 3 10 28.6 3 10 28 Average R0 (M/s) 29.0 3 10 432 Journalof MarineResearch [59, 3 where D9 isthe molecular diffusion coefŽ cient of O aftertortuosity correction, and R is 2 O2 thenet production rate. For simplicity,we willassume that the rate of consumption of O 2 remainsconstant. The boundary conditions are:

[O2]x50 5 [O2]0 (13)

[O2]x5LO2 5 0 (14) where L is the O penetrationdepth. Consequently, the solution to Eq.(12) is O2 2

0 0 [O ] RO LO RO 2 0 2 2 2 2 [O2]x 5 [O2]0 1 2 1 x 2 x (15) X LO2 2D9 D 2D9

(Bouldin,1968; Cai and Sayles, 1996). By imposingthat the  uxofdissolvedO 2 must be zero at x 5 L , that is, O2

d[O2] 5 0 (16) dx U x5LO2 we obtain

2D9[O ] 0 2 0 RO2 5 2 2 (17) LO2

Eq.(15)predicts depth proŽ les with a quadraticcurvature. An inspection of Figures 8 and9 indicatesthis to betruefor thelowerportions of themeasuredproŽ les. Typically, however, alayerof Žnitethickness separates the upper boundary of thequadratic decay portion of theproŽle from theuniform bulk overlying water O 2 concentration(Fig. 10), indicating the presenceof diffusiveboundary layer above the water-sediment interface (Jø rgensen and

Revsbech,1985). Thus, the concentration [O 2]0 inEq.(17) is not the bulk water value,but L thevalue at the base of boundary layer (Fig. 10). Values of [O 2]0 and O2 areestimated graphicallyfor themeasured proŽ les by settingthe water-sediment interface to bewhere thequadratic decay of theproŽ le begins. These values are combined with an estimate of themeasured porosity values in the upper 1 cmofthesediments (i.e., 89.6% in Quadrant 3D) inEq. (17) to obtain the values for R0 . The DSW valuewas determinedusing the O2 O2 formulagiven in Boudreau(1997, p. 109). The results are shown in Table3. R The O2 valuedetermined here is related to the aerobic OC degradationrate by the followingreaction:

2 (CH2O)x(NH3)y(H3PO4)z 1 ~x 1 2y!O2 1 ~y 1 2z!HCO3 ®

2 22 ~x 1 y 1 2z!CO2 1 yNO3 1 zHPO4 1 ~x 1 2y 1 2z!H2O.

Thus,the ratio of O 2 consumptionrate to aerobicOC degradationrate is ( x 1 2y)/x. If we R Rox assumethe C/ Nratioof labileOC inourexperiments to be 106:16, the O2/ OC ratio is R 3 28 21 determinedto be1.3.Consequently, the average O2 calculatedhere (9.0 10 M s ) 2001] Furukawaet al.: Bioirrigation modeling 433

Figure10. Schematic O 2 microproŽle indicating the parameters necessary for the determination of

O2 consumptionrate.

ox 28 21 ox yields ROC 5 6.9 3 10 M s . This ROC valueis actuallythe upper limit because part of 1 O2 consumedwithin the upper 2– 3 mm isutilizedfor SS and NH4 reoxidationrather than OMremineralization.

1 c.Batch incubation, anaerobic OC degradationrate, and NH 4 adsorptionconstant Thebatch incubation results, shown in Figure 11, were interpretedwith the following 22 1 assumptions:(1) theSO 4 consumptionand TCO 2 and NH4 productionrates remain constantduring the Ž rst ;400hours following the hand mixing; and (2) thechanges in concentrationvalues re ects microbial remineralization reactions only and do notcontain effectsfrom reoxidationby O 2.Underthese assumptions, the slopes of the incubation 22 R 5 2 3 resultsyield the microbial production rates for SO 4 and TCO2 to be SO4 1.29 29 21 R 5 2 3 29 21 10 (M s ) and S CO2 2.94 10 (M s ). Ran R R Theanaerobic OC degradationrate, OC,isrelatedto the above SO4 and S CO2 through 2 Eqs.(I-3) and(I-4) (Table1). In the absence of O 2 and NO3 ,Equations(I-3) and(I-4) can berewritten:

22 D[SO4 ] 1 5 Ran (18) Dt 2 OC

D@SCO2# 5 2Ran (19) Dt OC 434 Journalof MarineResearch [59, 3

Figure11. The results of the batch incubation experiments that were used to determine the microbial 2 2 1 SO4 and TCO2 consumptionrates and NH 4 adsorptioncoefŽ cient of the experimental sedi- ments.

an 29 21 29 21 Eqs.(18) and (19) yield the ROC value to be 12.58 3 10 (M s ) and 12.94 3 10 (M s ), respectively.We takethe average value to be the average anaerobic OC degradationrate within an 29 21 theupper 5 cmof Tank 3 sediments,i.e., ROC 5 12.8 3 10 (M s ). Depthdependency of theanaerobic OC degradationrate in Tank 3 was prescribedas follows.First we assumedthat (1) theanaerobic OC degradationrate is alinearfunction of an depth,and (2) theratevalue reached zero at thebottom of tanks(i.e., ROC 5 a(Ltotal 2 x)). Thevalue of parameter a was thendetermined by solvingthe following equation, because thebatch incubation experiment was carriedout using the upper 0.05 m ofTank 3 sediment:

0.05 a~L 2 x!dx E total 0 5 2.8 3 1029 . (20) 0.05

Thisyields the valueof a for Tank3 tobe 2.7 3 1028.Unfortunately,we didnot conducta batchincubation experiment for Tank6 sediments.The simulation results for 6Aand6B an usingthe Tank 3 ROC value,however, resulted in underestimation of anaerobicproduction 22 of TCO2 andconsumption of SO 4 .Thisindicates that Tank 6 sedimentscontained more labileOC thanthe Tank 3 sediments,possibly because the sediment freezing resulted in deathand decay of meiofauna.The value of a for Tank6 was determinedafter treatment as anadjustable parameter to be5.0 3 1028. 1 1 NH4 intheaqueous phase can be assumedto be inequilibriumwith NH 4 adsorbedonto claymineral surfaces (Mackin and Aller, 1984): 2001] Furukawaet al.: Bioirrigation modeling 435

Figure12. Depth proŽ les of pHdirectlymeasured for the cores from experimental quadrants.

wKN {NH1(ads)} 5 [NH1(aq)] (21) 4 r~1 2 w! 4

1 where KN isthedimensionless adsorption coefŽ cient, {NH 4 (ads)} istheconcentration of 1 1 adsorbed NH4 interms of moles per kg solids, [NH 4 (aq)] (M)isthe concentration of 1 23 aqueous NH4 , r (g cm )isthegrain density, and f isthe porosity. The average grain densityof experimental sediment was 2.55(g cm 2 3),andthe average porosity of sediment 1 inQuadrant 3D was 0.832.The rate of NH 4 productionin anaerobic part of thesediment is an related to ROC throughEq. (I-5) (Table1) by:

1 1 D([NH4 (ads)] 1 [NH4 (aq)]) y 5 2 Ran (22) Dt x OC

1 where x:y isthe C/ Nratioof labileOM and[NH 4 (ads)] istheconcentration of adsorbed 1 3 NH4 interms of moles per dm porewater in contact. Manipulation of Eqs. (20)– (22) yield:

1 D[NH4 (aq)] y ~1 1 K ! 5 2 R . (23) N Dt x OC

1 D@NH4 (aq)] The value of was determinedthrough the batch incubation experiment to be Dt 11.18 3 10210 (M s21).Assumingthe C/ Nratioof x:y 5 106:16,andusing the above w and r values,Eq. (23) yields KN 5 2.5. d.Pore water chemistry Theresults of bulkpore water analyses in the laboratory mesocosms (Figs. 12– 15) as well as the O2 microproŽles (Figs. 8 –9)exhibit depth proŽ les that are typical of Žne-grainedsiliciclastic sediments found in marine and estuarine environment: a rapid 22 consumptionof O 2 withina few mm ofWSI, gradualdepth-dependent depletion of SO 4 , 436 Journalof MarineResearch [59, 3

Figure13. Depth proŽ les of TCO 2 determinedfrom directly measured pH and titration alkalinity usingthe formula in Millero (1995).

1 anddepth-dependent increases in NH 4 and TCO2.Thesebulk pore water proŽles are used toevaluatethe model results in thefollowing sections. e.X-radiography and model geometry TheX-radiography images from allquadrants were convertedto binary images of burrowsvs. matrix sediment in order to characterize the burrow networks (Fig. 16). The geometryof cylindricalmicroenvironment ( r2, r1( x), Lburrow, Ltotal)was determinedusing thebinary images as follows. First,the binary images were overlaidwith horizontal lines in 1-cm intervals, and the numberof burrowsintersected by each horizontal line was recorded(Fig. 17). The burrow numberscaptured in the slab cores were thennormalized to the burrow density per square meterby assumingthat each individual Schizocardium sp.creates two openings at WSI:

n~0! 5 2 3 P (24)

N~x! n~x! 5 n~0! 3 (25) N~0!

1 Figure14. Depth proŽ les of NH 4 directlymeasured for the coresfrom experimental quadrants. 2001] Furukawaet al.: Bioirrigation modeling 437

2 2 Figure15. Depth proŽ les of SO 4 directlymeasured for the cores from experimental quadrants.

Figure16. The x-radiograph images of theexperimental quadrants, and binaryimages of the original x-radiographsthat were used to determine the model geometry. 438 Journalof MarineResearch [59, 3

Figure17. Parameters for model geometry ( r1 ( x), r2 , Lb u rro w )weredetermined by overlaying 1cm-intervalhorizontal lines on the binary burrow image, and counting and examining the burrowsthat intersect with each horizontal line. where n(0)isthe burrow density at WSI (m 2 2), P is the Schizocardium populationdensity for thegiven quadrant (m 22), n( x)isthe burrow density at depth x (m22), N( x) is the numberof burrows intersected by the horizontal line at depth x inthe X-radiography image, and N(0)isthenumber of burrowsat WSI intheX-radiographyimage. The burrow densitydetermined this way assumes that burrows that have been abandoned do not contributeto bioirrigation(Aller, 1984). Thetilt angle expressed in the X-radiographs are the “apparent”tilt angles, u9, which are 2Dprojectionsof thetrue tilt angles, u (Fig.18). Their relationship can be expressed in an equation:

tan u9 p arctan 2 X cos aD u 5 da (26) E p 0 2 where a isthe angle between the vertical plane parallel to X-radiography slab and the verticalplane that contains the burrow (Fig. 18). The angle a hasan equal probability to takeany value between 0 and90 degrees.Subsequently, the arithmetic average of truetilt angle (u)isdetermined for each1-cm interval, and subsequently used in Eqs.(5) and(6) to determinethe model burrow radius ( r1)for each1-cm depth interval. The value of rburrow 23 was assumedto be1.25 3 10 (m). The1-cm interval expression of r1 for eachquadrant was thenŽ ttedto a linearfunction of depth(i.e., r1( x) 5 r1(0) 1 ax)usingthe standard leastsquare Ž ttingprocedure.

Lburrow for eachquadrant was obtainedas the value of x where r1( x)becomesequal to zero. Ltotal for eachquadrant was determinedas thetotal thickness of sedimentsubstrate, 2001] Furukawaet al.: Bioirrigation modeling 439

Figure18. A schematicdiagram showing how apparent burrow tilt angles ( u9)projectedonto the planeof X-radiography are converted to the true tilt angles ( u).Thevertical plane containing the burrow(B) andthe plane of X-radiographyprojection (X) intersectat angle a.

and r2 was determinedusing Eq. (3), in which the value of n was twicethe value of Schizocardium sp.population density (m 22)ineach quadrant. The geometry parameter valuesare summarized in Table 4. f.Electron micrographs TheTEM imagesof samples from WSI, burrowwall, and matrix sediment (Fig. 19) showthat the packing of claymineral particles is differentamong these locations. Mineral particlesare organized into clusters with large inter-cluster pore spaces in sediments from WSIandburrow wall. On the other hand, clay mineral particles in thematrix sediment are distributedmore evenly without large clusters or porespaces. These images indicate that theassumption of uniform diffusive tortuosity (Section 4a., above) may be an oversimpli- Žcationof thediffusive transport processes in thesesediments.

5.The hindcast and discussion a.Summary of parametersand assumptions Modelcalculations were executedusing the parameters determined as described in Section4 (Table4). The determination processes for allmodel parameters required assumptionsin order to keepthe model system simple. The major assumptions include: (1) 440 Journalof MarineResearch [59, 3

Table4. Model parameters.

3B 3D 6A 6B

Sedimentcolumn Ltot (m) 0.13 0.13 0.16 0.16 height (1) Burrowedlayer Lbur (m) 0.09397 0.06106 0.07352 0.1016 thickness(1) Modelcylinder r2 (m) 0.01343 0.03877 0.02014 0.02154 radius (1) Modelburrow r1(x) (m) 0.003137 2 0.002753 2 0.003844 2 0.004583 2 radius (1) 0.03338x 0.04508x 0.05228x 0.04512x Modelnode dimension dx and dr (m) 0.0004 0.0004 0.0004 0.0004 Porosity(2) f 0.854 0.832 0.709 0.709 0 2 3 2 3 2 3 2 3 Bottomwater [O2] (M) 0.223 3 10 0.223 3 10 0.228 3 10 0.228 3 10 2 0 2 3 2 3 2 3 2 3 composition(2) [NO3 ] (M) {0.015 3 10 } {0.015 3 10 } {0.015 3 10 } {0.015 3 10 } 22 0 2 3 2 3 2 3 2 3 [SO4 ] (M) 18.0 3 10 18.0 3 10 15.4 3 10 16.8 3 10 1 0 [NH4 ] (M) 0 0 0 0 [SS]0 (M) 0 0 0 0 0 2 3 2 3 2 3 2 3 [SCO2] (M) 3.25 3 10 3.25 3 10 6.25 3 10 6.17 3 10 [H1 ]0 (M) 6.59 3 102 9 6.59 3 102 9 3.46 3 102 9 5.74 3 102 9 2 9 2 9 2 9 2 9 DiffusioncoefŽ cients D9O2 {1.71 3 10 } {1.64 3 10 } {1.18 3 10 } {1.18 3 10 } 2 9 2 9 2 9 2 9 (3) D9NO32 {1.43 3 10 } {1.38 3 10 } {1.00 3 10 } {1.00 3 10 } 2 10 2 10 2 10 2 10 D9SO422 {7.94 3 10 } {7.64 3 10 } {5.50 3 10 } {5.50 3 10 } 2 9 2 9 2 9 2 9 D9NH41 {1.48 3 10 } {1.42 3 10 } {1.03 3 10 } {1.03 3 10 } 2 9 2 9 2 10 2 10 D9H2S {1.32 3 10 } {1.27 3 10 } {8.99 3 10 } {8.99 3 10 } 2 9 2 9 2 10 2 10 D9HS2 {1.29 3 10 } {1.24 3 10 } {9.24 3 10 } {9.24 3 10 } 2 9 2 9 2 10 2 10 D9CO2 {1.35 3 10 } {1.30 3 10 } {9.37 3 10 } {9.37 3 10 } 2 10 2 10 2 10 2 10 D9HCO32 {8.86 3 10 } {8.52 3 10 } {6.09 3 10 } {6.09 3 10 } 2 10 2 10 2 10 2 10 D9CO322 {6.92 3 10 } {6.66 3 10 } {4.81 3 10 } {4.81 3 10 } C:N:Pratio (4) x:y:z {106:16:1}{106:16:1} {106:16:1} {106:16:1} ox 2 8 2 8 2 8 2 8 AerobicOC oxidation ROC 6.9 3 10 6.9 3 10 6.9 3 10 6.9 3 10 rate (5) an 2 1 2 8 2 8 2 8 2 8 AnaerobicOC ROC(x) (M s ) 2.7 3 10 3 2.7 3 10 3 [5.0 3 10 3 [5.0 3 10 3

oxidationrate (6) (Ltot 2 x) (Ltot 2 x) (Ltot 2 x)] (Ltot 2 x)] 1 Rateconstant for NH 4 kNH41 {0.16} {0.16} {0.16} {0.16} reoxidation(7) 2 3 2 3 2 3 2 3 Rateconstant for SS kS S {5.1 3 10 } {5.1 3 10 } {5.1 3 10 } {5.1 3 10 } reoxidation(8) 1 NH4 adsorption kN 2.5 2.5 2.5 2.5 coefŽcient (9) 2 3 2 3 2 3 2 3 Monodsaturation KO2 {0.02 3 10 } {0.02 3 10 } {0.02 3 10 } {0.02 3 10 } 2 3 2 3 2 3 2 3 constants(10) KNO3 {0.005 3 10 } {0.005 3 10 } {0.005 3 10 } {0.005 3 10 } K 2 3 2 3 2 3 2 3 SO4 {1.6 3 10 } {1.6 3 10 } {1.6 3 10 } {1.6 3 10 } K 2 3 2 3 2 3 2 3 Monodinhibition 9O2 {0.02 3 10 } {0.02 3 10 } {0.02 3 10 } {0.02 3 10 } 2 3 2 3 2 3 2 3 constants(10) K9NO3 {0.005 3 10 } {0.005 3 10 } {0.005 3 10 } {0.005 3 10 } 2 6 2 6 2 6 2 6 Acidityconstants for K1C {1.14 3 10 } {1.14 3 10 } {1.02 3 10 } {1.02 3 10 } 2 10 2 10 2 10 2 10 SCO2 (11) K2C {7.17 3 10 } {7.17 3 10 } {5.89 3 10 } {5.89 3 10 } 2 7 2 7 2 7 2 7 Acidityconstant for KS {3.44 3 10 } {3.44 3 10 } {3.44 3 10 } {3.44 3 10 }

H2S (12) Directlydetermined values are inboldtypes, whereas values determined after treated as adjustable parametersare in []andvalues taken from references are in {}. Remarks:(1) Determined through X-radiographydata analysis (see Section 4e.); (2) Determined through direct measurements; (3) Determinedusing directly measured porosity, salinity, and temperature with formulae given in Boudreau(1997, Chapter 4.2); (4) Typical values for labile organic matter; (5) determinedusing the measured O2 microproŽles (see Section 4b.); (6) the formula for Quadrants 3B and 3D were determinedby assumingthat the incubation experiment results represent the average anaerobic OC degradationrate of upper 5 cmofthe sediment column, whereas the formula for Quadrants 6A and 6Bwere determined after the treatment as an adjustable parameter; (7) from Van Cappellen and Wang(1996); (8) from Van Cappellen and Wang (1996); (9) determined through incubation experiments(see Section 4c.); (10) from Boudreau (1996); (11) calculated from Millero (1995); (12) calculatedfrom Millero (1995). 2001] Furukawaet al.: Bioirrigation modeling 441

Figure19. Transmission electron microscopy (TEM) imagesof the samples from three distinct regionsof the benthic mesocosm sediments. The dark- and medium-grey features represent clay mineralaggregates whereas the  at,light-gray masses are the pore spaces, now Ž lledwith an embeddingmedium. The total volume as wellas thedistribution and geometry of pore spaces are signiŽcantly different between images. This results in spatially heterogeneous diffusive tortuosity forsolute species.

theburrow water composition is equal to the overlying water composition (i.e., 100% irrigation);(2) porosityand diffusive tortuosity are constant throughout the sediments; (3) aerobicOC degradationrate is constant throughout the immediate vicinity of WSI and burrowwalls; (4) anaerobicOC degradationrate is an imposedlinear function of depth and becomeszero at thebottom of sedimentcolumn; (5) thesystem is at steadystate; and (6) thesimple cylinder geometry (Fig. 2) reasonablydescribes the actual burrow network. Theabove assumptions may or maynot be toleratedin thesimulation of our laboratory mesocosmsystems. For example,previous studies on infaunal ventilation patterns show thatthe burrows are usually intermittently ventilated and thus burrow water compositions arenot continuously equal to theoverlying water compositions (Gust and Harrison, 1981; Kristensen,1989; Riisgå rd, 1991; Forster and Graf, 1995).The TEM images(Fig. 19) indicatethat diffusive tortuosity is variablethroughout the sediments, with the values near WSIandburrow walls expected to differ from thevalues in the matrix sediments. The diffusivetortuosity is also affected by organicburrow linings (Aller, 1983). The distribu- tionsof OC andmicro-organisms are expected to be spatially and temporally heteroge- neous,and thus the OC degradationrate is not a constant. Whilethe model is notan exact simulation of theexperimental systems, it allowsus to (1) evaluatethe adequacy of assumptions; and (2) quantitativelydescribe the processes occurringat burrowwalls, which cannot be accomplishedwith the traditional 1D models. b.Calculation results and comparison Modelcalculat ionswere carriedout using parameter values listed in Table4. The resultsare reported here in terms ofvertical(1D) proŽles, which were generatedby 442 Journalof MarineResearch [59, 3

2 2 Figure20. Model-simulated depth proŽ les of SO 4 plottedtogether with actual measured proŽ les fromthe experimental quadrants.

takingthe radial average values of concent rationsfor eachdepth increment .The radiallyaveraged 1D proŽ les allow the visual compariso nbetweenmodel results and measuredproŽ les. 22 Themodel-calculated 1D depth proŽ les of SO 4 arein general agreement with the measuredproŽ les (Fig. 20). For thesimulations of 3Band 3D, no attempt was madeto adjustparameter values in orderto seekbetter Ž t.Theparametervalues determined a priori (Table4) and assumptions (1) through(6) inSection 5a. were theonly constraints. The 22 agreementbetween calculated and measured SO 4 proŽles indicate that the parameter valuesand assumptions used here, including the model geometry, reasonably describe the chemicalmass transferprocesses in these Quadrants. The simulations of 6Aand6B were carriedout similarly: the only difference was that,for 6Aand 6B, the rate of anaerobicOC degradationwas treatedas adjustableuntil a reasonableagreement between measured and 22 modeledproŽ les were met.An underestimation of SO 4 depletionoccurred in thedeeper partsof 6A and 6B. This is probably attributed to errors inthe prescription for depth- an dependencyof ROC.

Themodel-calculated 1D depthproŽ les of TCO 2 arealso in generalagreement with the measuredproŽ les (Fig. 21). However, the overestimation of TCO 2 buildup,especially visiblein 3Band3D, means that there may be additional mechanisms that remove TCO 2 22 from sedimentsat the rates greater than the rates of irrigativeintroduction of SO 4 into sediments.The possible mechanisms include TCO 2 consumptiondue to primary produc- tion,authigenic precipitation of carbonateminerals, and growth of individual Schizocar- dium sp.An underestimation of TCO 2 buildupoccurred in thedeeper parts of 6Aand 6B. 22 Thisphenomenon is coupledto theunderestimationof SO 4 depletionin the same regions, an andprobably also due to the errors inthe assumption for depth-dependencyof ROC.

Theoverestimation of TCO 2 buildupin model results can also be seen in the plots of 22 excess TCO2 Vs. SO4 removed(Fig. 22). The anaerobicOC diagenesisin aclosedsystem isdominatedby the reaction: 2001] Furukawaet al.: Bioirrigation modeling 443

Figure21. Model-simulated depth proŽ les of TCO 2 plottedtogether with actual measured proŽ les fromthe experimental quadrants.

22 (CH2O)x(NH3)y(H3PO4)z 1 ~x/2!SO4 1 ~y 2 2z!CO2 1 ~y 2 2z!H2O ®

2 1 22 ~x/2!H2S 1 ~x 1 y 2 2z!HCO3 1 yNH4 1 zHPO4

22 Consequently,the ratio between TCO 2 increaseand SO 4 decreaseis 2:1. The model calculatedthis ratio for eachdepth increment of all model quadrants, and the resulting slopesare very close to theideal value (0.5). The shallow pore water (i.e., low DTCO2 and

Figure22. For each depth increment, increase in TCO 2 (DTCO2 5 [TCO2 ] 2 [TCO2 ]0 ) is plotted 2 2 2 2 2 2 2 2 againstdecrease in SO 4 (DSO4 5 [SO4 ]0 2 [SO4 ]).Thevalues from model results are plottedin bold lines (top) whereas the values measured in theactual core slices are plotted with 2 2 Žlledcircles (bottom). Lines for the stoichimetric closed system value (see Table 1) of DSO4 /

DTCO2 5 0.5are also shown for comparison. For the laboratory systems, best-Ž t linearlines and theslope values are also shown. 444 Journalof MarineResearch [59, 3

1 Figure23. Model-simulated depth proŽ les of NH 4 plottedtogether with actual measured proŽ les fromthe experimental quadrants.

22 22 DSO4 values)exhibits much lower DSO4 /DTCO2 ratiobecause aerobic OC diagenesis 22 occurringin this region does not deplete SO 4 .Thedifference in diffusion coefŽ cients 22 22 between TCO2 and SO4 andreoxidation of SS cause the DSO4 /DTCO2 ratioto deviate 22 from 0.5slightly. The DSO4 /DTCO2 ratiosobtained from themeasured depth proŽ les of experimentalquadrants, however, differ substantially from theidealclosed system value of

0.5.In the actual experimental systems, diagenetic TCO 2 increaseis not as rapid as the 22 SO4 decrease.Additional TCO 2 sinksnot implemented in the model, such as the primary production,authigenic carbonate mineral formation, and growth of Schizocardium sp. mustbe presentin theseexperimental systems. 1 Themodel-calculated 1D depth proŽ les of NH 4 signiŽcantly underestimate the mea- 1 sured NH4 buildup(Fig. 23). The KN valueestimated from batchincubation experiments 1 maybe too high for theactual NH 4 adsorptionin the mesocosm tanks in which both adsorptionand desorption occur through displacement of clay particles between different porewater environmentsdue to bioturbation.However, simulations using the KN value of 1 zero (KN 5 0.0)stillbarely agree with the measured NH 4 buildup(Fig. 24). There must 1 beadditionalNH 4 sourcesthat were notimplemented in the model. They may include the 1 NH4 excretionby macrofauna, which has been observed and quantitatively reported for othermacrofauna species (e.g., Kristensen, 1984). 1 Inspectionof themeasured DNH4 /DTCO2 ratiodiagrams (Fig. 25) revealsthat the ratio isgreater for mid-depthpore waters thanfor porewaters from deeperparts of the sediments.This is probablycaused by thedepth-dependent C/ Nratioof sourceOM. Inthe mid-depthregion, where freshly produced green algae with low C/ Nratiois consumed by bothmacrofauna and microorganisms, the resulting ratio of OM consumptionproducts, 1 DNH4 /DTCO2,islarge. On the other hand, in deeperparts of thetanks where bioturbation isinfrequentand thus in ux offresh OMisminimal, the OM degradationis dominatedby lesslabile source OM withhigher C/ Nratiothat had been incorporated into the sediments sincethe time of initialtank loading. 2001] Furukawaet al.: Bioirrigation modeling 445

1 Figure24. The depth proŽ le of NH 4 wassimulated using KN 5 0forQuadrant 6A. c.Effect of bioirrigationon 1Dsolutedistributions Thequantitative signiŽ cance of bioirrigation was examinedby comparing the above hindcastresults with model results obtained from a1Ddiffusion-reactionmodel with no radialdiffusion term:

2 ]Cx,r,t Dsw ] Cx,r,t 5 1 R. (27) ]t 1 2 ln ~w2! ]x2 The1D simulationswere carriedout by usingthe same parameter values used in the above hindcasts(see Table4), except for thelack of burrowgeometry terms r1 and r2.

Figure25. For each depth increment, increase in TCO 2 (DTCO2 5 [TCO2 ] 2 [TCO2 ]0 ) is plotted 1 1 1 1 againstincrease in NH 4 (DNH4 5 [NH4 ] 2 [NH4 ]0 ).Thevalues measured in theactual core slicesare plotted with Ž lledcircles. Best-Ž t linearlines and theirslope values are also shown. 446 Journalof MarineResearch [59, 3

2 2 2 2 Figure26. Model-simulated depth proŽ les of SO 4 arecompared with the depth proŽ les of SO 4 calculatedusing the 1D modelwith no irrigation (Eq. 27).

Comparisonof the results (Fig. 26) shows that bioirrigation quantitatively affects the chemicalmass transferregimes in aquatic sediments. When all other parameters including thedepth distribution of anaerobicOM degradationrate are held the same, bioirrigation is thedetermining factor for thedepth distribution of geochemicallyimportant solute species 22 such as SO4 . d.Chemical mass transferin the vicinity of burrowwalls Bioirrigationis quantitatively signiŽ cant not only because it affectsthe vertical distribu- tionof solutespecies as discussedabove, but also because it promotes burrow walls as the interfacebetween oxygenated burrow water and anoxic pore water. In sediment with no burrows,WSI isthe only interface between oxygenated overlying water andanoxic sediments.The interfaceaccommodates steep geochemical gradients due toprocesses such 1 astherapidconsumption of OM andpore water O 2,andrapid production of TCO 2 and H . Whenthe sediments are burrowed, burrow walls become the additional interface to accommodatesuch rapid chemical mass transferprocesses. The addition of burrowwalls astheoxic-anoxic interface is quantitatively signiŽ cant. For example,the model burrow geometryused for thesimulation of Quadrant 3B represents 158% increase in the oxic-anoxicinterface area over the same model cylinder with no burrow,as calculated by thefollowing equation:

SA2 1 Lbur 5 2pr ~x!dx 1 ~pr2 2 pr ~0!2! (28) SA1 r2 1 2 1 p 2 E H 0 J whereSA1 isthe area of WSI for themodel cylinder with no burrow, and SA2 isthe surfacearea of WSI plusburrow wall for themodel cylinder. Similarly, the surface area increasefor theother model quadrants are determined to be11%for 3D,66% for 6A,and 96% for 6B. 2001] Furukawaet al.: Bioirrigation modeling 447

Figure27. Mesh diagrams showing the steep geochemical gradients in theimmediate vicinities of burrowwalls as well as WSI.The relief in thesemesh diagrams indicates the concentration values: whereit is high, the concentration is high, and steep slopes indicate steep gradients in the

concentration.There is a regionof uniformbottom-water O 2 and TCO2 concentrationsalong the burrowaxis, because the burrow is assumed to be100%irrigated.

Themodel-generated gradients of O 2 concentrationsand TCO 2 areillustrated in Figure 27.They show that the immediate vicinities of WSI andburrow wall interface are similar inthat they both are the sites of intensechemical mass transferprocesses, as indicated by thesteep gradients of O 2 and TCO2 concentrations.However, the steady state assumption ofthe model prevents us from usingthe model results to quantitatively discuss the differencesbetween these two types of interfaces.One important difference between the twotypes of interfacesis the temporal dynamics. Chemical mass transferin thevicinity of burrowwalls is temporallydynamic, and less likely to beat steadystate than the chemical mass transferin thevicinity of WSI. Burrowwalls are, in reality, ventilated periodically ratherthan continuously (Kristensen, 1989, 2000), and thus the burrow wall interfaces are subjectto oscillating geochemical parameters including dissolved O 2 concentrationsand pH(Furukawa et al., 2001).A worm mayrapidly build a burrowin thesedimentregion that hasbeen previously fully reduced to create a non-steadystate interface between oxic burrowwater andanoxic sediments. Another difference between the two types of interfacesarises due to biochemical compounds that are excreted by burrowing macro- fauna.For example,some burrowing enteropneusts are known to excrete brominated compounds,which have been found to affect the microbial activities at burrow walls (Jensen et al., 1992;Giray and King, 1997). Hansen et al. (1996)found the increased microbialactivity in thevicinity of Myaarenaria burrowwalls due to OM excretionby the animals.Thus, microbial characteristics in the vicinity of burrowwalls are different from thatin the vicinity of WSI. Inaddition, the diffusive tortuosity at the burrow walls is expectedto bedifferentfrom thatof bulksediments or WSI, becauseburrowing animals oftenstrengthen their burrows by rearrangingŽ ne-grainedparticles (Fig. 19) as well as by excretingorganic lining (Aller, 1983). Thus, from ageochemicalstandpoint, the chemical 448 Journalof MarineResearch [59, 3 mass transferin the vicinity of burrowwalls is notalways analogous to that in thevicinity ofWSI. Themicrobial reaction rates, and all other parameters that are coupled to the microbialreaction rates, are affected by the unique properties of burrow walls. Further geochemical,microbial and microfabric characterizations of burrowwalls are necessary in orderto fullyevaluate the quantitative effect of bioirrigation. e.Comparison with 1D nonlocaltreatment Boudreau(1984) has shown that the radial diffusion term in Aller’s tubemodel (Aller, 1980)can be convertedto a 1-D non-localtransport term using the following relationship:

2D9r1 a~x! 5 2 2 (29) ~r2 2 r1!~r#~x! 2 r1! where a isthenon-local exchange function, and r#( x)istheradial distance from theburrow axiswhose concentration value is equal to the radially averaged concentration for that depth.By usingthe above term in 1Ddiagenetic equation:

d2C D9 2 a~x!~C# 2 C ! 1 R 5 0. (30) dx2 0 the2D tube model becomes equivalent to the 1D nonlocal model. The 1D nonlocal treatmentof bioirrigationhas been widely used: in most cases, a( x)isassigned a simple, depth-dependent a priori functionsuch as exponential decay and linear decay (Martin and Banta,1992; Matisof and Wang, 1998; Kristensen and Hansen, 1999; Schlu ¨ter et al., 2000). The1D nonlocalexchange function, a( x),canbe determinedusing the hindcast results for ourlaboratory mesocosms in the same manner shown by Budreau(1984):

2D9r1~x! a~x! 5 2 2 (31) ~r2 2 r1~x! !~r#~x! 2 r1~x!!

Thisis identical to Eq. (29), except for r1 beinga functionof depth.Detailed derivation stepscan be foundin Boudreau(1984; 1997), p. 75). 1 Theconcentration distributions and horizontally averaged concentrations of NH 4 and 22 SO4 were usedto evaluate the r#( x)asfunctions of depthfor themodel quadrants. The depth-functionfor r#( x)canbe determinedby comparing the radial concentration distribu- tionfor eachdepth interval with the horizontally averaged concentration for thecorrespond- ingdepth interval. All other parameters can be foundin Table4. Thevalues of r#( x) as a functionof depthare shown in Figure 28. 22 1 The r#( x)proŽles derived from theconcentration distributions if SO 4 and NH4 are 2 2 nearlyindependent of depth (Fig. 28). In many cases, r2 .. r1, thus (r2 2 r1( x) ) term in Eq.(31) may be regardedas constant. Thus, using Eq. (31), we derive: 2001] Furukawaet al.: Bioirrigation modeling 449

Figure28. Depth proŽ les of r#( x)calculatedfrom comparing the model-calculated 2D distributions 2 2 1 of SO4 and NH4 concentrationswith the radially-averagedconcentrations.

r1~x! a~x!} . (32) r# 2 r1~x! Theabove expression (32) indicates that, under the assumptions employed in this study, thedepth dependency of 1Dnonlocalexchange coefŽ cient a( x)isdirectlycorrelated to thedepthdependent distribution of burrows.However, the dependency is not linear:rather, thedepth attenuation of a( x)isgreaterthan that of r1( x),asthe denominator in theright sideof (32)increases with depth.

6.Conclusions Thisstudy establishes that the two-dimensional bioirrigation model, in which depth distributionof burrowsis explicitly considered, is anappropriatetool for studyingthe early diagenesisof sediments populated by Schizocardium sp.and other benthic infauna that createand  ushdeep burrows. The model application to ourbenthic mesocosm environ- mentsreveals that the common assumptions used in early diagenetic studies can be criticallyevaluated by examiningthe agreement between measured and model calculated depthproŽ les of pore water species.Such assumptions include the prescribed depth dependencyof OM degradationrate, C/ Nratio,as well as the lack of consideration for macrofaunalmetabolite contributions to the pore water. The steady state model also shows theimportance of burrowwalls as theinterfacebetween oxic and anoxic environments and siteof intense chemical mass transfer.It is evident that more studies are needed to fully characterizethe temporal dynamics of burrow wall environment and its effects on microbialactivities and subsequent chemical mass transfer.Finally, the 1D nonlocal exchangecoefŽ cient for bioirrigationwas foundto be directly correlated with the 450 Journalof MarineResearch [59, 3 depth-dependentdistributio nofburrows through the comparison between model- calculatedradial concentration distributions with the radially averaged concentration values.

Acknowledgments. Wethank J. Watkinsand C. Vaughanfor laboratory assistance and Rick Mang andcrew of R/V Kit Jones forŽ eldassistance. Discussions with C. Meile,M. Richardson,P. Van Cappellenand C. Koretskyhelped the designs of laboratory experiments and calculation schemes. Taxonomicassistance was provided by E. Ruppertand G. King.This study was funded by ONR 322GG(Dr. J. Kravitz,Program Manager, Program Element No. 0601153N). NRL contribution numberJA/ 7431-00-0014.

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Received: 17April,2000; revised: 26April,2001.