Quantifying solute distributions in the bioturbated zone of marine sediments by defining an average microenvironment

0016-7037’80

Gemhimtco et Cosmochimm Acta Vol. 44, pp 1955 lo 1965 0 Pergamon Press Ltd 1980 Prmted m Great Britain

1201-195590200.0

Quantifying solute distributions in the bioturbated zone of marine sediments by defining an average microenvironment ROBERTC. ALLER Department of the Geophysical Sciences, University of Chicago. 5734 South Ellis Avenue, Chicago. IL 60637, U.S.A. (Received

15 April 1980; accepted

in revisedform

29 July 1980)

Abstract-The bioturbated zone of marine sediments is a region having a complex, time-dependent geometry of diffusion and chemical reactions. It is possible to simplify this geometry by postulating an average sediment microenvironment and modelling it as representative of the sediment body as a whole. The microenvironment is assumed to correspond to a single, tube-dwelling animal together with its surrounding sediment and can be represented by a finite hollow cylinder. A transport-reaction model derived from this postulate produces good agreement between observed and predicted pore water profiles using realistic physical constants. The average vertical distributions of pore water solutes and their sediment-water fluxes are influenced by the presence of irrigated burrows to varying degrees depending on the kind of reactions governing their behavior. Pore water profiles of solutes, such as NH;, subject to zero order reaction rates are highly sensitive to the abundance and sizes of burrows while the net flux of the constituent across the sediment-water interface is not. In contrast, profiles of solutes such as Si that are subject to first order reaction rates are less sensitive to the presence of irrigated burrows but net fluxes are greatly affected. Average pore water concentrations, fluxes of solutes like Si, and the apparent one-dimensional diffusion coefficients required to match vertical gradients with measured solute fluxes, are influenced by both the size and spacing of burrows. Because of the range of solute concentrations within the microenvironment at any given depth it is not strictly valid to make detailed solubility calculations on the basis of average pore water concentrations within the bioturbated

INTRODUCTION

NUMEROUSSCIENTISTShave recognized that the activities of large, bottom-dwelling invertebrates must influence the chemical properties of sedimentary deposits (DARWIN, 1894; DAPPLES, 1942; CARRIKER, 1967; RHOADS, 1974; F%TR, 1977; SCHINK and GurNASSO, 1977; ALLER, 1978a). These activities, such as feeding, burrowing, and irrigation, result in particle and fluid transport near the sediment-water interface. This region of a deposit is where diagenetic reactions are often most rapid and where material exchange rates between sediment and overlying water are largely determined. Because of the importance of understanding controls on sediment properties in this boundary zone, recent studies have attempted to extend previous qualitative observations and have tried to specifically document and quantify the effect of macro-infauna on sediment diagenesis and sediment--water solute exchange. With respect to pore water solute distributions, three different transportreaction models have been proposed to describe the effects of bioturbation. One class of models assumes that macrofaunal activities can be accounted for in an increased effective diffusion coefficient of pore water solutes (HAMMONDet ul., 1975; VANDERBORCHTet al., 1977; GOLDHABER et al., 1977; ALLER, 1978b). A second assumes pore water is biogenically advected between discrete well-mixed reservoirs within the sediment and overlying water (GRUNDMANIS and 1955

MURRAY, 1977; HAMMOND and FULLER, 1979; MCCAFFREY er al., 1980). The third assumes that specific changes in the average geometry of molecular diffusion result from the presence of irrigated burrow and tube structures (ALLER, 1977, 1978b, 1980a, b). I think the third type of model, though idealized, is generally the most realistic when tube-dwelling animals are present and provides the most insight into the processes involved. In this paper I present a version of this latter model developed during the last few years and outline its behaviour, advantages, and disadvantages. DISCUSSION The uverage

microenvironment

The bioturbated zone of a sedimentary deposit is characterized by a complex, time-dependent distribution of burrows and tubes most of which are connected to the sediment-water interface (MYERS, 1977). Many of these dwellings are irrigated by their inhabitants and therefore contain solute concentrations close to that of overlying water (MANGUM, 1964; DALES et ul., 1970;

MANGUM and

BURNETT, 1975;

ALLER and YINGST, 1978). At any instant, microenvironment

a typical

in this zone is simply a central irriand its immediately surrounding sedi-

gated burrow ment. The bulk chemical composition of a deposit termined by an average of the compositions

is deof its

R.C. ALLER

1956

(A)

r R

X

(B)

Fig. 1. (A) Sketch of upper region Vertical cross-section of sediments cylinder visualized as the average shown correspond to those used in

of burrowed sediment idealized as packed hollow cylinders. (B) with idealized diffusion geometry of (A). (C) The single hollow microenvironment within the bioturbated zone. The dimensions the transport-reaction model described in the text (after ALLER. 1980a, b).

component microenvironments. Therefore if it is possible to construct a realistic representation of the average microenvironment then the bulk properties will also be known. I postulate that the characteristic microenvironment in the bioturbated zone can be represented by a finite hollow cylinder or annulus of sediment equivalent to a single, average burrow structure. This is similar to the microenvironment assumed by soil scientists to characterize solute transport around roots (COWAN, 1965; NYE and TINKER. 1977) or by physicists to model flow around wells (e.g. MUSKAT, 1934). In order to visualize this mental construction consider first a simple case where all animals inhabiting the sediment are immobile tube-dwellers, are the same size, are oriented vertically, and are uniformly distributed. The bioturbated zone can then be imagined as consisting of finite, hollow cylinders of sediment packed together (Fig. 1). The axial length, (L), and inner radius (rl), of each cylinder is determined by the dimensions of the central tube. The outer radius, (r2), is half the distance between the tube axes corresponding to individual organisms. Only a small portion of sediment lying at the center of any three mutually intersecting cylinders cannot be assigned to a particular tube. This portion corresponds to -99; of the total sediment volume and is unimportant for reasons that will become clear. Because all cylinders are equivalent, to know the composition of a single cylinder is to know the composition of the bulk sediment. When many different kinds of animals are present, individuals will differ in size. mobility, burrow wall construction, irrigation ability, and spacing patterns. In this more complex case it is still possible to imagine a vertically-oriented hollow cylinder as the characteristic microenvironment. The values of L, rl, and r2 are determined in this instance by the @c‘tive population abundance, spatial distribution, and orientation of animals. As an initial approach r1 can be

estimated from the mean width of all or the dominant macrofauna found at a site, L from average burrow or tube length, and rz from l/JiN where N = population abundance of macrofauna (animals retained on a 0.5-1.0 mm mesh sieve). Because of uncertainty in rl, r2, and L due to sampling artifacts and natural patchiness in animal distributions a range of estimated values at any site is both likely and reasonable. These parameters can also be measured directly from X-radiographs (ALLER, 1977; K~ROSEC, 1979). Problems associated with these estimations and assumptions are addressed later. The critical assertion is that an average microenvironment having a simple geometry can be defined for the bioturbated zone of sedimentary deposits. Trunsport-reuction

model

The transport of solutes within the bioturbated zone now becomes equivalent to transport of solutes within a single finite hollow cylinder of sediment. Ignoring advection (justified later). a diffusion-reaction equation describing solute distributions within the microenvironment is given in cylindrical coordinates by:

where:

t = time x = vertical space coordinate, origin at sediment water interface, positive axis into sediment r = radial coordinate measured from cylinder axis C(.x, r, 7) = pore water solute concentration mass;volume pore water D, = solute diffusion coefficient in bulk sediment R = reaction function. For present purposes the diffusion coefficient within the microenvironment is assumed isotropic. Compaction is considered to be insignificant and adsorption is not explicitly included because steady state distributions only will be considered here (BERNER, 1976). To illustrate the behavior of the model, pore water distributions and sediment-water exchange of SO:-. NH:,

Quantifying

solute distributions

in the bioturbated

and Si will be considered. In general, the reaction rate R is known only as a function of depth x. Both NH; production and SO:reduction rates can be described by functions of the form: R,exp( - rx) + R, , where Ro, RI. and 2 are constants (GOLDHABER et ul., 1977; JBRGENSON, 1977; LEKMAN. 1979; ALLER and YIIWST, t980). Assuming solid phase silica is not limiting over the zone of interest, dissolved Si production rates can be approximated by a function: k(C,, - C) where k is a first order reaction rate constant and C,, is an apparent equilibrium Si concentration (HURD. 1973; SCHINK PI al., 1975; KAMATANI and RILEY, lY79). More exact descriptions of Si production require inclusion of solid phase reactive surface areas and allowance for depth dependence in k but this possible complexity is not included here. A useful generalized reaction term for study of interstitial solutes therefore has the form: R = k(C,, Using equation written:

iv

clc - = D,s --- .- + -

(7t

(‘2

23

(3)

where:

I, 2.

n = 0.

i.” = (n + :, ;

- C)

+ Roe-‘” The boundary conditions taken as (r, < rZ):

x

L ,&

term, the transport-reaction interval 0 < .Y < L can be

--

on the imaginary

+ R,.

(2)

cylinder

are

s = 0, C = Cr, r = rr, C = Cr

(a)

r = r2, SC/& = 0

(b)

X = L, c!c/?x

(c)

= 3.

These specify that (a) the solute concentration is held constant along the sediment -water interface by a well-stirred water column and within the burrow by irrigation, (b) concentrations go through a maximum or minimum halfway between any two burrows, and (c) there is continuity of solute flux between the bioturbated and underlying sediment zones. The concentration gradient at the base of the cylinder is fixed at an observed constant value, i?. This value must be specified from direct measurements. Because animal abundances are usually large enough, particularly in nearshore environments, that r2 is relatively small compared to L, the solute distributions within a cylinder microenvironment rapidly attain steady state. This rapid equjlibration is also a justification for ignoring advection. (Biogenic advection of pore water may, how-

G =&CT-C,,) n A,,

-- -

R, :- + (I_!,n!B .7 /“. /.n

The functions i,(z) and K,.(Z) are the modi~ed Bessel functions of the first and second kind respectively of order c (see e.g. ABRAMOWITZ and STEWJM, 1964, for values). The solution (3) gives the radial and vertical pore water distribution around a single burrow or average microenvironment. Measured pore water solute profiles on the other hand are usually average concentrations measured over finite vertical sampling intervals. Assuming a core sample is large enough to average over several burrow microenvironments then the average pore water concentration, C, over any finite vertical interval s1 -.x2 is giv,en by:

(4)

N H4+ imMl 5

19.57

sediments

ever, be important in certain sandy sediments.) Even at low animal densities. if reaction and sedimentation rates are sufficiently slow an assumption of steady state-- no advection is still valid. The steady state (?C/i?t = 0) solution to equation (2) with boundary conditions (a), (b). and (c) can be found by separation of variables and is:

- C) + R,exp( --C(Y) + R,.

this general reaction (I) for the vertical

zone of marme

IO

15

0.1

Si

0.2

0.2

TI

(mbl)

04

- -1-l

06

0.8

2 4 6 8 IO 12 f

14

14

E

16

16

c3

18

18

20

20

Fig. 2. SO:-, NH;, and Si concentration profiles in pore water from Mud Bay. South Carolina used to illustrate behavior of the cylinder microenvironment model. Solid vertical bars-measured concentrations; dashed vertical bars--cylinder model profiles; solid continuous curves-one dimensional model profiles having same diffusion, reaction, and boundary constants used in the cylinder model. The NH: profile predicted by the one-dimensional model is off-scale and not plotted. Model constants given in Table I.

1958

R. C. ALLER

(WOLLAST and GARRELS, 1971; LI and GREC;ORY, 1974). The Si coefficient represents the value in sea water at 25°C modified to 29’C by the StrokessEinstein relation (Ll and GREGORY, 1974) An average Prdicted aoerayr vertical solute profiles porosity of $I = 0.851 in the upper 20 cm based on % Hz0 contents of z 70% and assumed average parVertical profiles of dissolved SO:-, NH:, and Si in ticle density of z 2.5 g/cm3 was used in calculating D, pore water from a station in Mud Bay, a shallow from the D values. extension of the Winyah Bay estuary near GeorgeThe dimensions of a model cylinder microenvirontown. South Carolina, are used here to illustrate the ment were initially determined in this case from behavior of the cylinder model (profiles from Sta. 5 of fauna1 samples (1 mm mesh sieve) taken at the same ALLEK, 1980a; ULLMAN and ALLER, 1980). Summer station as the pore water profiles in Mud Bay. Heteroseason profiles (collection temperature = 29°C) from mastusfiliformis, a tube-dwelling capitellid polychaete, this station are depicted in Fig. 2. These profiles have dominates the fauna numerically although other polymany features in common with pore water solute prochaetes and bivalves are also present but in much tiles from bioturbated sediments reported in other smaller numbers (ALLER, 1980a). The average burrow studies (e.g. SC:HINK et ul., 1975; MARTENS, 1976; radius of Heteromastus in Mud Bay is -0.05 cm. A G~LDHABER et cd., 1977; ALLER, 1980b). SO:- is relareasonable estimate of burrow depth based on tively constant in the top 20 cm despite extensive forX-radiographs and shapes of pore water profiles is mation of solid phase sulfides, NH: has a maximum c 15 cm. Microenvironment dimensions of r, = 0.05 near the sedimenttwater interface, and Si increases and L= 15 cm were therefore assumed. The basal steadily with depth except for a region of relatively gradient, E. at depth L was calculated from the constant concentration between 5511 cm. measured profiles. Values for functions or constants used in evaluation of equations (3) and (4) for a particular pore water With D,, R, rl, L, B, and CT fixed for a given constituent were determined as follows. R(x) for both constituent r2 was varied to obtain the best fit SO$- reduction and NH: production were estimated between predicted and measured profiles. Population by incubation of sediment [temperature _ 22”C] from abundances of Heteromustus and other polychaetes different depth intervals at the same station (MARTENS (mostly nereids) at the sample station range from and BEKNER, 1974; GOLDHABERet al., 1977; ALLER N - 5&500/m2 so that a corresponding range of and YINGST, 1980; ULLMAN and ALLER, 1980). These an initial reasonable estir2 _ 2.555 cm represents data, to be reported in a paper in preparation, give mate of the outer dimension of a cylinder microenvirrates for SOiof R,(x) = -66.1 reaction onment. The NH: profile was modeled first because concentration differences between sediment and overcxp( -0.36.x) - 10.6 mM/yr and for NH: of RN(x) = 46 exp( -0.61x) + I .38 mM/yr. Rates were adjusted lying water, the vertical profile shape, and the lack of upward to equivalent rates at 29°C by multiplying by precipitation reactions make it a particularly sensitive a factor of 2. I2 obtained from an apparent activation indicator of diffusion geometry. The model along with energy of - 19 kcal/mol for SOireduction and measured profiles are plotted in Fig. 2; model values NH; production (JORGENSEN, 1977; ABDOLLAHI and are listed in Table 1. An outer cylinder diameter of NEWELL, 1979; ALLER and YINGST, 1980). The reacr2 = 2.1 cm gives good agreement with the measured tion rates actually used in calculations are therefore (T profile. This is equivalent to an effective population = 29“C):R,(x) = 140 exp(-0.36x) - 22.3 mM/yr abundance of N _ 722/m’. Because a 1 mm rather and R,(x) = 97.5 exp(-0.61x) $ 2.96 mM/yr. than 0.5 mm mesh sieve was used to measure animal abundance the measured N’s may be minimal; this An apparent value of C,, = 577 PM for Si was estieffective value of N may therefore be very close to the mated from asymptotic pore water Si concentrations actual in situ abundance. In any case. it is within a taken from gravity cores (- 1 m long) in Mud Bay. factor of 2 of the average measured value for this This value may not be a true equilibrium concenstation. A one-dimensional model (vertical diffusion tration and is not considered to have general applicaonly) using the same upper and lower boundary conbility to other environments. An estimate for k is ditions (x = 0, x = L) predicts parabolically increasobtained later from modeling after determination of ing NH: concentrations 5-10 times higher than those the size of the cylinder microenvironment. observed and plots offscale on the present Fig. 2. Diffusion coefficients were determined from the reThe SOi- profile predicted by the model was callation D, .. 4*D, where 4 = porosity and D = molecular diffusion coefficient at infinite dilution (LERMAN, culated using the r2 = 2.1 cm value obtained from the NH: fit (Fig. 2). A relatively high Cl~- content of 1978). This is equivalent to assuming a sediment for0.361 M in the upper O-.1 cm causes offset in the top mation factor of l!&3, a reasonable estimate for muds because the average Cl value of (ATKINS and SMITH, 1961; data of KROM and BERNER, centimeter 0.285 f 0.012 M in the interstitial water over l-20 cm 1980; ANDREWS. 1980). Charge coupling is ignored at was used to estimate C, for SO:-. Otherwise the this level of approximation (SAYLES, 1979). Values of correspondence between model and observed data is D at T= 29°C were estimated for NH;, SO:-, and good. For comparison the steady state profile preSi as21.3 x IO-(‘. 11.5 x 10m6 and I1 x 10m6cm/sec

where C is equation (3). The factor 271comes from integrating the incremental sector rdt), where 0 = vectorial angle, around the cylinder.

Quantifying

solute distributions

1959

in the bioturbated zone of marine sediments

Table I. Model values Variable

so4=

cT B

14.7 -

0.1

Si

NH4+

ti

0.0002

mM

0.074

ti

Elwcm

0.011

mM/cm

0.060

r&f/cm

1.33

2 cm /day

0.687

cm2/day

Ds

0.717

a

0.36

cm2/day /cm

0.61

0

/cm

R.

- 0.383

m/day

0.267

&day

0

R1

- 0.061

mM/day

0.0081

&day

0

k

0

0

0.2

C =I

/day

0.577

ti

‘1

0.05

cm

0.05

cm

0.05

cm

=2

2.1

cm

2.1

cm

2.1

cm

L

15

cm

dieted by a one dimensional model [equation (2) with no Ydependence] is also plotted. In this case the same D,. R. and boundary conditions at x = 0 and x = L are used. A poor correspondence between model and observed profiles results when horizontal diffusion is ignored. A model predicted Si profile was calculated by first fixing r = 2.1 cm as before and varying k, the reaction constant. to obtain best fit. A k of 0.2/day gave good agreement between observed and model profiles (Fig. 2, Table I). The corresponding profile obtained with a one dimensional model using the same model parameters is plotted as the continuous solid line for comparison. Si concentrations exceed C,, in the bottom few centimeters in this case because of the specified flux across the lower boundary. The model-derived value of k is not unreasonable when compared with reported opaline Si dissolution rates at lower temperatures. For example, HURD (1973) calculates a mean k - O.Ol/day for deep-sea sediments at 3’C and determined a temperature dependent rate increase of _ 10 times per +2O”C increment. VANDERBORGHT et al. (1977) determined a k - 0.04,lday for nearshore muds at 10°C and KAMATANI and RILEY (1979) report k’s of _ 0.0&2.6/day for decomposing diatoms at 22.9.C. These model profiles demonstrate that good agreement between observed and predicted pore water solute profiles can be obtained using the average microenvironment concept. Manipulation of only one variable, r2, is usually required to bring model and observed data into agreement. In the cases to date in which I have used this model the final value of rZ actually employed corresponded well with initial estimates based on sieve sampling of animal populations. In order to demonstrate how different sizes and abundances of burrows or microenvironments influence pore water composition, the average pore

15

15

cm

cm

water concentration of NH: and Si predicted by equations (3) and (4) for the top &15 cm are plotted as a function of either rl and r2 in Figs 3-6. This is the concentration that would be obtained if the upper CL15 cm of sediment were squeezed as a unit ignoring minor porosity effects. In each case the possible con-

2

r

OverlyIngWater

_____-_-------

0.0001~ ’

’

2

’

’

4

’

’

6

’

’

’

8

’

IO

’

’

I>!

Half Distance Between Burrows km) 31133795 354 199 127 813 65 50 39 32 26 22 Population

Abundance

h?

Fig. 3. Expected average concentration of NH; in C&l 5 cm interval as a function of burrow spacing or abundance (rz) with burrow size fixed (r,). Equivalent population abundances (A’) per mz are indicated beneath r2 values. Possible concentrations are bounded above by the concentration predicted by the one-dimensional model and below by the assumed overlying water concentration. Diffusion and reaction constants are in Table 1.

R. C.

1960

ALLER

No Burrows,_One__------Dimension Vertical Case -

-

-

-

--__

NO

Burrows, One _-___-__--_---_-

- -__

E

_c,L

_-------_--_

---___ :T.: ‘,“E

----._._.

g

6Crn

-‘-....~~=

E

‘,

;

--._

rz=4cm

“’

g

0.5

t 0.4 -

Dimsnslon

-.-._

-.-.-..--_._._ ;---,. .,,,,, -.

... .

”

-

Vertical Case

I =6cm _ _?_ ---.-.-._.. ,... ‘2;

. . . . . -..,,,

4cm

--__

---__

-.

0 k 52

--r2=3cm

.“...,.,,.

0.3 -

-.

s

rz = Zcm

---

z

i r .-

f s

5 e,

0001

z +‘Q

L c

F

2

Overlyiy

_--___

0.00011 ’ 0. I

’

’

’

w_clter_

’

’

_ ---

’

’

’

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Burrow

Radius

’

0.1 0.2 0.3 0.4 0.5 06 0.7 0.8 0.9 1.0 ’

Burrow

’

1.0 I. I 1.2

(cm)

Fig. 4. Expected average concentration of NH; in &15 cm interval as a function of burrow size (rl) with fixed spacing (r*) between burrow axes. centrations are bounded below by the overlying water value and above by the concentration predicted by the one-dimensional case or complete absence of irrigated, permeable burrows. The model behavior of both solutes demonstrates that the build-up of each in pore water is highly sensitive to the size and number of burrows. Concentrations are particularly sensitive to the number or spacing of burrows (Figs 3 and 5). This means that spatial and temporal variation in 06

0.2-

r

Radius km)

Fig. 6. Expected average concentration of Si in pore water from @lS cm interval as a function of burrow size ir,) at fixed burrow spacing (r2).

sediment pore waters will reflect variation in macrobenthic communities. The importance of the kind of reaction term, zero or first order, in determining the effect of horizontal diffusion on solute build-up is also demonstrated by the relative sensitivity of the two solutes to reaction geometry. NH:, having a fixed reaction rate, is more strongly influenced than is Si whose reaction term is dependent on concentration. The plots demonstrate that, even at very low abundance. irrigated burrows can significantly lower the pore water concentrations of solutes. The possible ecological significance of this is discussed in ALLER (1980a). Eflect of burrows on sediment-brtrter

KX+XM~~

The microenvironment model allows examination of how the sediment-overlying flux of solutes can be influenced by the size and abundance of burrow structures. In this case, Fick’s first law of diffusion gives the total flux, J. of a dissolved constituent across the surficial sediment-water interface and the burrow wall as: J = J, + J,

@a)

where : I

t

4

2 Half 0,

Oistance 08

a

6

to

Between Burrows 18

3163 795 354 199 127 68 Papulotion

8

(cm) 0

11

12

11

(5b) I

65 50 39 32 26 22

Abundance

(/I&

Fig. 5. Expected average concentration of Si in pore water from the O-15 cm intervaf as a function of burrow spacing are kz > N) at fixed burrow size (rl). Concentrations bounded above by the one-dimensional model average concentration and below by the assumed overlying water value (C,). The apparent equilibrium concentration is also ._.. plotted.

Model

constants

In Table

1.

(54 Jo

1961

Quantifying solute distributions in the bioturbated zone of marine sediments A, = surface

area

of

rl < r < r2 A, = surface area O
cylinder

of

tube

top wall

at

x = 0; r = rl ;

at

These equations for J, and J, are evaluated at x = 0 and r = rl, respectively. The relative importance of the flux across the burrow wall and the top of the cylinder microenvironment is determined in part by their respective surface areas. Because the flux of solutes across the sediment-water interface is usually measured or calculated relative to the surface area of sediment exposed along the plane normal to the presently defined x-axis at x = 0 and does not include burrow wall surface, the total flux out of the cylinder microenvironment is also normalized here to the cylinder top area for comparative purposes by defining: JT = (A, + A,) J/A,. Fluxes are calculated by performing the appropriate operations on equations (3) and (4). For the present calculations the value of 4 in equations (5b) and (5c), the porosity at x = 0 and r = rl, is taken as C#J-0.851. This is a lower porosity than expected for the sediment-water interface but in the absence of data on porosity near the burrow wall, the average value for the upper 20 cm is used together with the corresponding average bulk sediment diffusion coefficient. The total model flux of NH: out of the sediment at steady state is not affected by the number or size of burrows. This flux is fixed by the defined production rate function to be JT - 4R,/cc + 4L.R,. In reality the production rate of NH: by microorganisms may be sensitive to the build-up of metabolites. Its flux might

Half I

01

Distance Between Burrows km) .

b

3183 795354

c

2

11

199 127 68 65 50

Population

2

0

1

39 32 26

I

22

Abundance t/m*)

Fig. 7. J,/JT for NH; as a function of burrow spacing at fixed burrow size (rl). J, is the flux of NH: across upper surface of the model cylinder; JT is the total flux of the microenvironment as normalized to the upper face area. J,iJ, is a measure of the ratio between the

(r2)

the out

surflux of NH: out of the bottom predicted by molecular diffusion from the vertical pore water concentration gradient at I = 0 and the actual measured flux. It therefore is a measure of the ratio of the molecular diffusion coefficient and the apparent transport coefficient required to match the total flux with the vertical gradient.

0

0.2

0.4 Burrow

0.6 Radius

08

IO

(cm)

Fig. 8. J,/JT for NH: as a function of burrow size fixed burrow spacing or abundance (rz. !V).

(r,)

at

therefore be influenced by tube structures because the resulting lowered concentration of metabolites would stimulate production. Such a stimulatory effect, or other possible effects of macrofauna on microbial activity (YINGST and RHOADS, 1980) remains to be documented in detail and based on flux balance calculations from direct measurements is unlikely to influence the flux by more than a factor of 2 (ALLER. 1980b). Although the total flux of a constituent like NH: which has a zeroth order reaction term is not changed by irrigated burrows, the relative proportion of the flux that escapes across burrow walls compared with that diffusing directly across the surficial sedimentwater interface does change. This change may influence the calculation of fluxes using a vertical pore water gradient close to the sediment surface. ‘The effect will be most dramatic when RI is large relative to Ro. A discrepancy between the total flux of NHf across the sediment-water interface and that calculated from a vertical pore water gradient can be used to define an effective or apparent transport coefficient that balances the vertical gradient with the measured flux (ALLER, 1978b; KOROSEC,1979; MARTENSand KLUMP, 1980). The ratio of J,/JT can be used as a measure of how this effective or apparent diffusion coefficient, derived from a matching between a measured pore water gradient and actual flux, varies with burrow size and density. Figures 7 and 8 illustrate the approximate dependence of an apparent diffusion coefficient, as reflected by J,/JT, on burrow size and abundance for constituents having a fixed reaction rate like NH,. Note that for burrow dimensions and populations such as found in Mud Bay, the apparent diffusion coefficient would be calculated as only about twice the molecular value. For such cases where R. and r are relatively large so that most production occurs near the sediment-water interface, there is httle apparent effect of macrobenthos on the balances within measurement error although the form of the

R. C. ALLER

1962

0.8 t 0.7 0.6

= 1.0 cm

=0.5 cm -0.1 a

Half Distance 11

11

11

Between Burrows (cm) 11

1”

11

-=_ 0.3 iij 0.2

3183 795 354 I99 127 88 65 50 39 32 26 22 Population

Abundance

0. I

(/m2)

Fig. 9. The total flux of Si, JT, out of bottom sediments as a function of burrow spacing (r2, N) at fixed burrow size (r,). The flux is bounded below by the value predicted in the one-dimensional

Half

case.

Distance

I1

Between 11

11

Burrows 0

0

Population

water profile can be dramatically influenced. The ratio J,/JT, like the average concentration, is more sensitive to tube abundance and spacing than to tube size. The total flux, Jr, of Si across the sediment-water interface is shown as a function of burrow size and abundance in Figs 9 and 10. The predicted steadystate flux obtained from the one dimensional mode1 is also plotted to illustrate relative departures from the strictly vertical system. Unlike NH:, the total flux of Si from the sediment is very sensitive to the presence of irrigated burrow structures. This is a direct result of the first order form of the reaction rate. In the present calculations I have assumed for simplicity that solid phase Si is in excess and does not limit dissolved Si production over the modelled depth interval. This assumption should not change the qualitative conclusions inferred from the calculations but will influence the range of fluxes actually possible. An indication that these calculations are reasonable comes from the approximate agreement between directly measured Si fluxes at the Mud Bay station of 5 5 mmol/m’/day and those predicted by the cylinder model (Figs 9 and 10).

Fig. 11. JJ.lT

Abundance

1,

1

3183 795 364 199 127 88 65 pore

km)

50

39 32

(/n?)

for Si as a function of burrow fixed burrow size (r, 1.

spacing

(rZ) at

Figures 11 and 12 illustrate the variation of J,/JT for Si as a function of burrow size and abundance. These graphs indicate that apparent diffusion coefficients approx. 5 times the molecular value would be required to balance the flux with that calculated from a vertical concentration gradient at the Mud Bay station. It is obvious that whereas Si pore water profiles are less sensitive to irrigated burrow structures than those of NH:, Si fluxes from sediment and the resulting apparent transport coefficients are much more influenced than NH: fluxes by diffusion geometry and animal activity. This means that in shallow water where benthic nutrient regeneration is important to plankton, Si-utilizing components of the plankton such as diatoms should be influenced more

_--_--

I.0

No

____

Burrows,

One

---__-

Dimension

Vertical

Case

0.9 0.8 0.7

14r

0.6

\.

\.

‘,\. ‘..

i

5

05 - ‘..,

4

0.4-

;;;r 0.3 -

‘.._

-..

r2 = 6 cm

\

_ _w

‘\\\.

‘2’4Crn .‘..... “.

_ _

“.._,

_._.

- -.-._._

... . .

0.2 0.1 -

“....,, ----___

.‘. . .. -_

I , I I , , , I 0.1 0.2 0.3 0.4 0.5 06 ‘0.7 0.8 0.9 1.0 Burrow

Burrow Radius (cm) Fig. 10. The total flux of Si, JT, out of bottom sediments as a function of burrow size (rl) at fixed burrow spacing (r?).

Fig. 12. J,/JT

Radius

(cm)

for Si as a function of burrow fixed burrow spacing (r2).

size (r,) at

Quantifying

solute distributions

in the bioturbated

zone of marine

1963

sediments

/------..

--__ I/_-Radial

l

r2= 2,l cm r, = 0.05 cm

Position

(cm)

0

Radial

I

Fig. 13. Radial concentration distributions for NH: and Si within average microenvironment vertical depths. Model values in Table 1. than others by the burrow construction benthic communities (ALLER, 1980a). Concentration

variation

within

activities

of

the microenvironment

In addition to evaluation of average sediment properties, the microenvironment model allows examination of possible variation in solute concentration in discrete depth intervals of a deposit. As an example, the radial distributions of both NH: and Si at different depths within the average microenvironment determined for the Mud Bay data are depicted in Fig. 13. Although these profiles may not represent actual radial distributions because of the idealizations made in the model, they serve to illustrate an important point: a range of solute concentrations occurs at all depths within a burrowed sediment interval. This simple illustration has important consequences for solid phase-solute solubility calculations. Strictly speaking, assuming equilibrium controls are important, there will be no single solid phase determining a particular solute concentration at any given depth but rather a range of phases distributed within the microenvironment. This means that although order of magnitude solubility calculations based on average pore water concentration may be valid, it is not generally justified to calculate hypothetical equilibrium solid phase compositions from pore water analyses alone within the bioturbated zone. The microenvironment model can be used together with average pore water analyses and solid phase compositions to help legitimize equilibrium calculations in any given case.

CONCLUSIONS The cylinder microenvironment model is an idealized but comparatively realistic depiction of diffusionreaction geometries within the bioturbated zone. Its advantages are that profiles of pore water solutes having a wide range of chemical behavior can be modeled relatively closely with a minimum of fictitious physi-

2

IF;ition

at discrete

cal variables such as apparent diffusion coefficients. It allows immediate quantitative evaluation of the importance of benthic macrofauna in any given area or time in influencing pore water profiles or sedimentwater exchange. The model also demonstrates that in burrowed sediments pore water can attain rapid steady state distributions because of the small diffusion scales involved. This is in contrast to solid phase distributions which are subject to slower biogenic particle reworking and which take a longer time to reestablish distribution following a disturbance such as a storm. Perhaps most importantly the model demonstrates that where multidimensional diffusion is important, knowledge of reaction rate distribution independent of pore water profiles or fluxes is required for accurate interpretation of sediment composition. A more realistic model would require information on the exact spatial and size distributions of individual animals as well as their residence times at any given depth. Although a model could be constructed in which a random spacing of tubes were allowed this assumption is no closer to reality than assuming an entirely uniform one (JUMARSet al., 1977). In addition, only the upper relatively densely populated zone of sediment has been considered here and deeper, less abundant burrowers such as crustaceans (MYERS, 1979) are ignored. A more complete model would extend continuously to the true base of the bioturbated zone. The present model, however, can be used to check for the effect of deep burrowers on pore water profiles in discrete zones if reaction rates are known. Radial variation in reaction rates around burrows (ALLER and YINGST, 1978), diffusion properties of burrow walls, and irrigation behavior of individual burrow occupants must also be determined for more accurate models. I have attempted to simplify this complexity in the present transport-reaction model so that it would be practically useful with the kinds of information normally available for a deposit and the effort most workers are willing to expend on model

R. C. ALLER

1964

computations. Given the simplicity of the assumptions. the agreement between Dredicted and measured properties obtained by this model is surprisingly good. .4[,krlo\c,lrdy~rnenls~ ~This work was supported by NSF grant OCE-7900971. Fellowship support from the Sloan Research Foundation is also acknowledged. 1 thank V. BARC‘ILON for advice during formulation of the present model. W. ULLMAN aided in the mud and laboratory and critically reviewed the manuscript. 1 thank D.R. SCHINK for his critical comments and review. REFERENCES ABDOLLAHI H. and NEWELL D. B. (1979)

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