U.S. Dept. of Commerce / NOAA / OAR / PMEL / Publications
The sorption and remobilization rates, k
,
and k
, fix the exchange
of Mn between dissolved and fine particulate reservoirs. Cowen
and Li [1991] suggest that only a small fraction of the fine particles,
specifically the metal scavenging capsuled bacteria, are responsible for the
bulk of the dMn scavenging.
The rate k was measured
by Cowen
et al. [1990] using the radioisotope 
Mn
and water samples taken in the vicinity of the JDFR at ridge crest depth. Uptake
of dMn was seen to occur predominately with a time scale of the order of 1 year,
but faster time scales were also evident depending on the population of capsuled
bacteria. In fact, Cowen
and Li s [1991] data suggest that rate coefficients increase with plume
age and perhaps the scavenging efficiency of each capsule increases as well,
so k may be other than a
constant. Such age and efficiency dependence cannot be encompassed at this stage
of model development. Instead k
is here assumed to be constant in space and time (360 days)
.
No direct determinations of the remobilization rate of Mn from capsules, k,
have yet been made. Consequently, Mn data from deep ocean stations removed from
hydrothermal influence are here used to suggest its magnitude. If the similarity
of the scavenging-remobilization process between hydrothermal and nonhydrothermal
regions can be assumed, and if dMn and pMn are nearly in exchange equilibrium
at stations well away from hydrothermal influence, the ratio pMn/dMn (~T
/T
)
at those distal stations may serve to approximate the ratio k/k.
T differs from pMn in that
pMn includes macroaggregate Mn, but macroaggregate Mn should have little effect
on the ratio k/k
because of the relatively low concentration of macroaggregates compared to fine
particles. Of course, strict equilibrium cannot be achieved when particles are
undergoing removal to the seafloor by settling, but partitioning data presently
provide the best available means of narrowing the range of possible values for
k.
Only measurements taken at depths greater than 1500 m are considered here.
Landing
and Bruland [1987], for a station at 15°N and 160°W, present dMn and
pMn data that lead to a average value for k/k
of 0.33. Individual values ranged from 0.17 to 0.66, with the lowest and highest
values occurring at 3000 m and near the seafloor, respectively. For a station
"~2000 km west of central Mexico" and at 1500 m, Martin
and Knauer [1982, p. 1214] report dMn and pMn concentrations that lead
to a k/k
average of 0.29. At 28°N and 155°W, Martin
and Knauer s [1985] data for 2000 m suggest k/k
= 0.13. Samples at 1500-1600 m depth near the JDFR show dMn ranging from 0.7
to 1.6 nmol/L and pMn ranging from 0.2 to 0.5 nmol/L [Cowen
et al., 1990; Cowen
and Li, 1991]. These dMn and pMn values are both slightly above the
background ranges that were inferred from data at more distant stations, as
earlier described, and they lead to k/k
ratios ranging from 0.2 to 0.57. Thus even at these depths on the JDFR there
may normally be some hydrothermal effect. Episodic influence of hydrothermal
activity at 1500 m is certain [Baker
et al., 1989]. In comparison, for points between 500 and 1000 m above
the bottom over the mid-Atlantic ridge, a depth interval which is presumed to
be out of hydrothermal influence, Klinkhammer
et al. [1985] found Mn concentrations that result in an average k/k
ratio of 0.26. All these k/k
estimates are based, of course, on the assumption that chemical exchange equilibrium
prevails.
Taken together, these estimates suggest that the time scale for remobilization
of Mn from fine particles is about 1/3 the length of the time scale for dMn
scavenging. On the other hand, if particles other than metal scavenging bacteria
play an important role in Mn scavenging in these background regions, the k/k
ratios in hydrothermal regions may be somewhat different than 1/3. In the analysis
to follow, we will use separate values of 1/3 and 3 for k/k
in order to examine the model dependence over a range of remobilization rates.
Since k is chosen to be
(360 days), k
then has values of (120 days) and (1080
days), respectively, for the two stated
values of the k/k
ratio.
Estimates for the rate of fine particle scavenging by macroaggregates, k
,
are just beginning to appear in the literature. Nozaki
et al. [1987] used two 
Th profiles
from the western Pacific to infer k
values of (30 days)and (154 days),
though Lavelle
et al. [1991] claim, by reanalyzing the same data, that k
for that data is more likely (320-370 days).
In a deep estuary with particle concentrations much higher than the deep ocean,
k has been estimated to
be (2-6 days) [Lavelle
et al., 1991].
In the Panama Basin, Asper
[1987] measured size, number density, and settling velocity of macroaggregates,
all factors in determining the k
scavenging rate. Consider a unit volume of water in which the number density
of macroaggregates is N. Let the macroaggregates have a common settling
velocity of w
and a common
cross-sectional impact diameter of d. During any time interval dt,
each of N macroaggregates sweeps a volume of water equal to (
/4)d
wdt. If the mass
concentration of fine particles in the same unit volume of water is C,
and if the fine particles encountered by each macroaggregate are scavenged with
a retention efficiency 
(0 
1), then
the rate of fine particle removal by macroaggregate scavenging would be
(12)
The term in brackets represents the scavenging rate k.
The rate depends on d, N, and w,
which Asper
[1987] measured, and the scavenging efficiency .
Asper
[1987] found macroaggregate size classes with diameters 2 and 3.4 mm contributed
89 % of the large particle flux at his Panama Basin site. The smaller size class
(2 mm) settled at an average speed of 36 m/d and had number density of 1.4 particles
per liter. The larger size class (3.4 mm) settled at an average speed of 26
m/d and had a number density of 0.58 particles per liter. If
= 1, these data and equation (12) result in k
values of (6 days) and (5 days),
respectively. For smaller values of , k
is made smaller and the scavenging time scale T(
= 1/k) is lengthened proportionately.
If were 0.2, a k
value of approximately (30 days) would result,
and if were -0.02, a value for k
closer to (360 days) would result. This
uncertainty in assigning a value to is exacerbated
by the likely site-to-site variability of the other factors determining k.
In the absence of appropriate data, no certain value for k
can be assigned for the JDFR region, but it does seem reasonable to assume that
T has a time scale of weeks
to months. Here we have chosen to examine the consequences of k
ranging from (20 days) to (180 days),
using a k of (60 days)
around which to center the analysis.
The final exchange rate, k
,
determines the time scale for release of fine particles from macroaggregates.
The release process is not well defined, but k
must include the effects of total or partial large-particle disaggregation or
other mechanisms of fine particle loss from macroaggregates. The Western Pacific
data of Nozaki
et al. [1987] suggest that an appropriate time scale, T(
= 1/k), is ~6 days [Lavelle
et al., 1991]. Apparently, the scavenging of fine particles occurs
more slowly than does fine particle release. The T
adopted here is 6 days. This time is long compared to the transit time from
a height of 240 m (model source height) to the seafloor if macroaggregates settle
at a speed as high as 100 m/d [e.g.,
Alldredge and Silver, 1988]. Consequently, in this model environment,
the release to the water column below plume depth of capsuled bacteria by macroaggregates
can occur, but the process is not favored.
Observations of currents within the central ridge valley and adjacent regions of the southern JDFR show a spatially complicated and time variable pattern of flow [Cannon et al., 1991]. Tidal, inertial, and atmospherically induced 4-day oscillations dominate the spectra of currents. Mean currents from observations exceeding 6 months in duration for locations below 2100 m (~ ridge crest depth) range from 0.3 to 1.9 cm/s, but the directions are principally northward and southward along the ridge rather than off axis. Occasional divergent off-axis subtidal flow of duration exceeding several weeks is observed.
The evidence on longer term off-axis mean flow is more circumstantial. Reid s [1981] diagrams of phosphate and silica concentrations on an isopycnal surface at approximately 2600 m depth suggest westward mean flow near the JDFR. The patterns of Mn in sediments (Figure 1c), as they do on the EPR [Klinkhammer and Hudson, 1986], suggest long-term off-axis flow as well. Stommel s [1982] model of baroclinic flow caused by hydrothermal heat flux for the EPR suggests a westward mean flow with speeds of -0.2 cm/s. J. Lupton (personal communication, 1991) suggests that a helium plume extends to the southwest of the southern JDFR. Differences in these suggestions and the results of Cannon et al. [1991] may be related to the shorter averaging time and more limited spatial scales of the current meter observations.
The one-dimensional nature and off-axis orientation of the data confine our present analysis to the component of mean flow in the off-axis direction only. Should long-term mean flow actually be directed other than westward in the southern JDFR region, any suggestions of the magnitude of off-axis advection derived here must apply only to the ridge-normal component of that flow. The Mn sediment data and limitations on scavenging time scales restrict the range of possible current speeds allowed that component, however.
Vertical eddy diffusivity, K
,
is given a value of 8 × 10
cm/s,
though values range from 10
to 3-4 × 10
cm/s in the deep ocean away from boundaries,
regions where velocity shears are low [e.g.,
Garrett, 1979; Gargett,
1984]. For our purpose, K
is taken to be vertically uniform. At the seafloor, values for K
10 to 50 times those are more likely appropriate [e.g.,
Garrett, 1979], but the effects of increased benthic boundary layer
turbulence and bathymetry on Mn distributions are both left for later study.
Horizontal diffusivity, K
,
is given a value of 10 m/s [e.g.,
Okubo, 1971]. This diffusivity accounts for the effects on Mn distributions
of unresolved currents including tidal flow, and it permits some upstream presence
of Mn as indicated, for example, by observations of pMn across the width of
the axial valley.
The settling velocity of fine particles, w,
is set to 0.1 m/d in these model realizations. This corresponds to the Stokes
settling speed of, for example, 1.9 µm diameter particles with specific gravity
2.6 or 3.2 µm particles with a specific gravity of 1.55. Particles in this size
range have been documented in hydrothermal plumes of the southern JDFR [Walker
and Baker, 1988]. Furthermore, Cowen
et al. [1986] note that capsuled bacteria from the plumes have diameters
of 1-2 µm. The settling velocity of macroaggregates, w,
is understandably very much larger. The location closest to the JDFR at which
macroaggregate settling speed has been inferred is some 1300 km to the west-northwest
at Ocean Station Papa [Honjo,
1985; Asper,
1986]. Those data suggest that w
is as much as 175 m/d, but the temporal resolution of the data makes the confidence
interval for that estimate large. In other regions the settling speed of macroaggregates
are found to have considerable range [e.g.,
Alldredge and Silver, 1988; Alldredge
and Gotschalk, 1988], with 100 m/d being considered a typical value.
For purpose of our analysis, w
is set to that value.
Particulate concentrations prove useful in evaluating Mn mass fractions. Concentrations
out of the plume and away from the seafloor, the background concentration of
particles, average 15 µg/L [Cowen
et al., 1986; Cowen
et al., 1990]. Within the plume, concentrations are 2-3 times this
[Cowen
et al., 1986]. Only a small fraction of this particulate concentration
is due to macroaggregates. Macroaggregate concentration can be estimated from
settling flux rates and the macroaggregate settling velocity. The reason is
that large particles should comprise the bulk of the vertical flux [e.g.,
McCave, 1975], so the settling flux is nearly equal to w
C. At the Endeavor segment
of the JDFR, Dymond
and Roth [1988] trapped particles over a period of nearly a year; for
sample points away from the effects of resuspension, those flux data average
1.6 g/cm/kyr. Duncan
[1968] measured a sediment accumulation rate of 3 cm/kyr in a core west
of the JDFR. This rate is comparable to that of Dymond
and Roth [1988] assuming a sediment porosity of 0.8 and a sediment density
of 2.6 g/cm
. Dividing flux by w(100
m/d) leads to a C value
of 0.44 µg/L. This is less than 1/30th the concentration of fine particles,
but this is only a crude estimate for C
that awaits better definition by direct field measurement. Model concentrations
C and C
are taken to be spatially uniform.
The rate of erosion of sediment, E, was given a magnitude of 1.7 × 10
g/m/d, a flux rate about 4% that of the settling
flux. This rate is comparable to fine sediment erosion rates in shallower environments
under conditions of low bed stress [Lavelle
et al., 1984]. E, along with vertical diffusivity and settling
velocity, determines gradients of T
and T at the seafloor (equations
(9) and (10)).
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