Role of diatoms in regulating the ocean’s silicon cycle
Andrew Yool and Toby Tyrrell
Southampton Oceanography Centre, Southampton, UK
Received 2 December 2002; revised 16 June 2003; accepted 7 August 2003; published 12 November 2003.
[1] Among phytoplankton the diatoms are strong competitors and contribute
significantly to total global primary production. Aspects of their life history, notably their
high sinking rates, make them important to the export flux of carbon into the ocean
interior. Unlike the majority of other phytoplankton, they utilize silicic acid (=silicate) to
construct their cell walls and are controlled by its availability and distribution. Here a
simple model is developed to study the relationship between the diatoms and the ocean’s
silicon cycle. The ecological component of this model pits the slightly superior diatoms
against all other algae, with both groups competing for phosphate while the diatoms
additionally require silicic acid. The model agrees reasonably with observed distributions
of nutrients and with their biogeochemical fluxes. While theoretically superior, the
diatoms are held in check by the availability of silicic acid, allowing the persistence and
numerical dominance of the other algae. The concentrations of both nutrients are
homeostatically controlled by the phytoplankton, and resist perturbations. Analysis finds
that primary production in the model is ultimately controlled by phosphate, with silicic
acid abundance controlling the fraction of the total produced by diatoms. Sensitivity
analyses using more ecologically detailed variants of the model find that these results are
generally robust. The model’s treatment of the ‘‘silica pump’’ hypothesis [Dugdale and
Wilkerson, 1998] is also examined.
INDEX TERMS: 4805 Oceanography: Biological and
Chemical: Biogeochemical cycles (1615); 4815 Oceanography: Biological and Chemical: Ecosystems,
structure and dynamics; 4842 Oceanography: Biological and Chemical: Modeling; 4845 Oceanography:
Biological and Chemical: Nutrients and nutrient cycling; K
EYWORDS: diatoms, silicic acid, ecosystem model,
competition, homeostasis
Citation: Yool, A., and T. Tyrrell, Role of diatoms in regulating the ocean’s silicon cycle, Global Biogeochem. Cycles, 17(4), 1103,
doi:10.1029/2002GB002018, 2003.
1. Introduction
[2] In a recent modeling study of the relative roles of
nitrogen and phosphorus in controlling phytoplankton abun-
dance, Tyrrell [1999] found that competition between algal
groups that differed in their source of nitrogen for metab-
olism (NO
3
users versus N
2
fixers) was able to produce
a ‘‘thermostat-like’’ effect which controlled the level of
nitrogen in the surface ocean. The competitive interaction
centered on balancing the energetic disadvantage of having
to fix nitrogen, with the advantage of being able to do so
when ambient nitrate levels were low. This model was able
to explain the near-to-origin intercept of nitrate versus
phosphate scatterplots and provided insight into competing
views about which of these two nutrients most limits
phytoplankton production in the ocean.
[
3] Figure 1 shows a scatterplot of nitrate versus phos-
phate, together with a comparable scatterplot of silicic
acid versus phosphate. This latter plot also intercepts close
to the origin, suggesting that silicic acid may be similarly
controlled by the activity of competing algal groups. In
the contemporary ocean the biogeochemical cycle of
silicon is dominated by the activity of the diatoms (class
Bacillariophyceae) [Tre´guer et al., 1995]. This group is
estimated to contribute up to 45% of total oceanic primary
production [Mann, 1999], making them major players in
the cycling of all biological elements. Their primary use
for silicic acid is in the construction of their cell walls
(also known as frustules). This contrasts with other algae
that construct their cell coverings from organic material
(e.g., cyanobacteria, dinoflagellates) or from calcium car-
bonate (e.g., coccolithophorids). Tre´guer et al. [199 5]
estimate that globally the diatoms uptake and process
240 Tmol Si yr
1
.
[
4] In the case of ecologica l interactions controlling the
silicon cycle, the competition may revolve around balancing
the burden of a dependence on silicic acid against the
competitive advantage of using silicic acid to produce
‘‘cheaper’’ cell walls instead of constructing more energet-
ically ‘‘expensive’’ organic cell walls. On a molar basis,
incorporation of silicic acid into a cell wall is calculated to
require only 8% of the energy required for organic carbon
[Raven, 1983]. In addition to this potential energetic advan-
tage, several other facets of diatom physiology are believed
to give them an ecological advantage over their phytoplank-
GLOBAL BIOGEOCHEMICAL CYCLES, VOL. 17, NO. 4, 1103, doi:10.1029/2002GB002018, 2003
Copyright 2003 by the American Geophysical Union.
0886-6236/03/2002GB002018$12.00
14 - 1
ton competitors. Unlike many other algae, whose division
cycles are strongly coupled to the diel light cycle, diatoms
are capable of dividing at any point of the diel cycle
[Martin-Je´ze´quel et al., 2000]. This light independence
extends to their nutrient requirements, with nitrate and
silicic acid uptake and storage continuing during the night
through the use of excess organic carbon synthesized during
the day [Villareal et al. , 1999; Martin-Je´ze´quel et al. , 2000;
Clark et al., 2002]. It has even been suggested that the
presence of biogenic silica acts as an effective pH buffer,
facilitating the conversion of bicarbonate to dissolved CO
2
and enabling more efficient photosynthesis [Milligan and
Morel, 2002]. These features of diatom physiology almost
certainly contribute to the in situ observation that diatoms
have greater maximum growth rates relative to comparable
algae [Furnas, 1990]. Further, so long as silicic acid is
abundant (and other nutrients nonlimiting), diatoms are
found to dominate algal communities [Egge and Aksnes,
1992] (but see Egge [1998] for exceptions).
[
5] Aside from their role in the silicon cycle, the diatoms
have also attracted attention because of their importance to
the export of primary production to the ocean’s interior.
Aggregation and sinking is an important aspect in the life
history of many diatom species [ Smetacek, 1985], and high
sinking velocities, whether as individuals, aggre gates or
mats, allow diatoms to rapidly transport material out of
the surface mixed layer. Additionally, mesozooplankton
grazers which consume diatoms produce large, fast-sinking
faecal pellets. These processes remove nutrients and carbon
from the produ ctive surface waters before they can be
remineralized, making the diatoms crucial to ‘‘new’’ (or
export) production. From studies of diatoms in the equato-
rial Pacific Ocean, Dugdale and Wilkerson [1998] have
suggested that a ‘‘silica pump’’ controls export to the deep
ocean. So long as silicic acid is available, diatoms act as a
conduit for nutrients and carbon to deep waters, contrasting
with the production of other algae which ‘‘traps’’ nutrients
in a regeneration loop at the surface.
[
6] Given these features of diatom ecology, two key
questions are (1) do switches from siliceous phytoplankton
to non-siliceous phytoplankton at low ambient silicic acid
provide a critical feedback which controls the ocean’s silicic
acid content, and (2) if these switches exist, how do they
affect ocean productivity and the export flux? The aim of
this study is to address these questions by constructing a
first-order ecological/biogeochemical model analogous to
that of Tyrrell [1999] but which incorporates the silicon
cycle and diatoms.
2. Model Description
2.1. Framework
[
7] The model described here follows Tyrrell’s [1999]
basic framework of simple representations for both the
ocean and its ecosystem. By stripping away much of the
complexity of real ecosystems, Tyrrell [1999] was able to
focus on, and improve understanding of, the key processes
in the regulation of nitrate and phosphate in the ocean. This
model attempts to do the same for the silicon cycle.
[
8 ] Although the construction of this simple model
requires many simplifications and assumptions, our experi-
ence with sensitivity analyses shows the model to be
relatively insensitive to details of its construction, as will
be described in section 4. For example, the micronutrient
iron is known to play a significant role in regulating primary
production and affecting silicon utilization in diatoms
Figure 1. Plots of nitrate versus phosphate and silicic acid versus phosphate from global climatologies
[Conkright et al., 1994]. Data range from the surface (near the origin) to the seafloor. The dashed lines
represent N:P = 16:1 and Si:P = 16:1, standard Redfield ratios for these nutrients. While active
remineralization processes closely tie nitrate and phosphate concentrations (even at depth), biogenic silica
dissolution is slower and only weakly coupled to these processes; hence the increasing deviation from the
dashed line with depth.
14 - 2 YOOL AND TYRRELL: ROLE OF DIATOMS IN REGULATING OCEANIC Si
[Martin and Fitzwater, 1988; Hutchins and Bruland, 1998].
Although this role is ignored in the base model described in
this section, variants of the model involving both implicit
and semi-explicit treatments of iron biogeochemistry have
been constructed and their significance explored. By build-
ing up the ecological/biogeochemical complexity of a first-
order model, the intention is, in part, to determine the
operational importance of second-order facets of the silicon
cycle.
2.1.1. Physical Model
[
9] The ocean is represented by a standard one-dimen-
sional, two-box model [Broecker, 1971]. The two boxes
resolve the ocean vertically into a surface layer (0 to 500 m)
and a deep layer (500 to 3720 m). A constant amount of
mixing between these two layers is parameterized to repre-
sent ocean overturning, upwelling and diffusion.
2.1.2. Biogeochemical Model
[
10] The ocean’s biogeochemistr y is reduced to only two
nutrients and two phytoplankton groups. Both nutrients are
present in both ocean boxes, but the phytoplankton groups
are confined to t he surface box (which represents the
seasonally mixed zone down to the permanent thermocline).
Figure 2 shows a diagrammatic overview of the model
biogeochemistry. Although it would be more accurate to
include a separate representation of the euphotic zone (e.g.,
the top 100 m), sensitivity analysis (see section 4.2) finds
that this is less important than might be supposed.
[
11] The nutrients included in the model are phosphate
and silicic acid. Because of its important role in genetic and
metabolic machinery, phosphate is required by all algae, but
silicic acid is only a major requirement of siliceous algae.
Both nutrients are supplied to the ocean by rivers, and silicic
acid has additional inputs from aeolian, hydrothermal and
seafloor weathering sources. Both are consumed by algae in
the model’s surface layer and remineralized down the water
column when the algae die and sink into the ocean. The
rates at which the two nutrients are remineralized are
different (phosphate remineralizes faster, and therefore
higher in the water column, than silicic acid), and this is
reflected in the model by different partitioning of reminer-
alization between the two ocean boxes. Small fractions of
the sinking fluxes of both nutrients are lost permanently
from the model system through the sedimentation and burial
of biogenic material on the seafloor. Again, the two
nutrients differ in the fraction of sinking material that is
ultimately buried and lost from the model.
[
12] The two phytoplankton groups modeled are the
diatoms and other algae. More generally these represent
siliceous algae and non-siliceous algae. The diatoms require
both silicic acid and phosphate to grow, and uptake these
nutrients in a variable ratio [Martin-Je´ze´quel et al., 2000].
Their growth rate is controlled by the most limiting of the
two nutrients in a Liebig’s Law formulation. The growth
rate of the other algae is controlled solely by the availability
of phosphate. While only diatoms are modeled here, other
groups, notably the sponges and radiolarians, also utilize
silicic acid. However, although these groups have been
important in the silicon cycle of earlier Eras [Siever,
1991; Kidder and Erwin, 2001], they play relatively minor
roles in the contemporary ocean [ Tre´guer et al., 1995].
[
13] Within the bounds imposed by their differing nutrient
requirements, both algal groups are modeled and param-
eterized in the same way. Both use the same Michaelis-
Menten uptake curve for phosphate, and both algae are
assumed to die at the same rate. However, the maximum
growth rates of the two algal groups are not equal. As
diatoms are generally found to be superior competitors
wherever silicic acid is not limiting, or is less limiting than
other macronutrients [Furnas, 1990; Egge and Aksnes,
1992], their maximum growth rate is set at a value frac-
tionally greater than that of the other algae to give them a
competitive edge. This approach aims to simplify the
ecological model to the assertions that (1) all other things
being equal, diatoms are superior competitors and (2) only
diatoms require (and are potentially limited by) silicic acid.
Other differences between diatoms and the other algae (e.g.,
photosynthesis/nu trient coeffic ients, respiration/mor tality/
sinking rates, etc.) are, for the purposes of clarity, ignored.
The sensitivity of the model to these assumptions is
explored in detail later.
2.2. Equations
[
14] The model has six state variables corresponding to
diatoms, D, other algae, O, surface phosphate, P
s
, surface
silicic acid, S
s
, deep phosphate, P
d
, and deep silicic acid,
S
d
. Since it is the sole common currency, both phytoplank-
Figure 2. Structure of the model’s two nutrient cycles. The
ocean’s biogeochemistry is reduced to two nutrients
(phosphate and silicic acid; surface and deep boxes) and
two competing phytoplankton groups (diatoms and other
algae; surface box only). RP, riverine phosphate; RS,
riverine silicic acid; AS, aeolian silicic acid; HS, hydro-
thermal silicic acid; WS, seafloor weathering silicic acid;
BU, biological uptake; SR, surface phosphate remineraliza-
tion; DR, deep phosphate remineralization; SF, phosphate
sedimentation; SRs, surface silica dissolution; DRs, deep
silica dissolution; SFs, silica sedimentation; K, ocean
mixing. Note that deep remineralization of phosphat e
(DR) and dissolution of silica (DRs) occur both down the
water column and at the sediment-water interface on the
seafloor.
YOOL AND TYRRELL: ROLE OF DIATOMS IN REGULATING OCEANIC Si 14 - 3
ton equations are written in terms of phosphate. Units are
mol m
3
.
dO
dt
¼þ m
O
P
s
P
s
þ K
p
O
|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
growth
M O½
|fflfflffl{zfflfflffl}
mortality
; ð1Þ
dD
dt
¼þ m
D
min
P
s
P
s
þ K
p
;
S
s
S
s
þ K
s
D
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
growth
M D½
|fflfflffl{zfflfflffl}
mortality
; ð2Þ
dP
s
dt
¼ m
O
P
s
P
s
þ K
p
O
|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
O uptake
m
D
min
P
s
P
s
þ K
p
;
S
s
S
s
þ K
s
D
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
D uptake
þ SR M O½
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
O surface P remin
þ SR M D½
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
D surface P remin
þ K
P
d
P
s
SD
|fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl}
ocean mixing
þ
RP
SD
|fflffl{zfflffl}
riverine input
;
ð3Þ
dS
s
dt
¼ m
D
min
P
s
P
s
þ K
p
;
S
s
S
s
þ K
s
D
^
R
org
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
D uptake
þ SR
s
M D
^
R
org
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
D surface Si remin
þ K
S
d
S
s
SD
|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}
ocean mixing
þ
RS þ AS
SD
|fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl}
riverine and aeolian input
;
ð4Þ
dP
d
dt
¼þ DR M O
SD
DD
|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
O deep P remin
þ DR M D
SD
DD
|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
D deep P remin
K
P
d
P
s
DD
|fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl}
ocean mixing
;
ð5Þ
dS
d
dt
¼þ DR
s
M D
^
R
org
SD
DD
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
D deep Si remin
K
S
d
S
s
DD
|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}
ocean mixing
þ
HS þ WS
DD
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
hydrothermal and weathering input
; ð6Þ
where,
^
R
org
¼ R
org
S
s
S
s
þ K
s
min
P
s
P
s
þ K
p
;
S
s
S
s
þ K
s
1
: ð7Þ
[15] Both phytoplankton equations are composed of two
terms. The first is a simple growth term, relating population
increase to the current population, a maximum growth rate
(m
O
or m
D
), and a standard Michaeli s-Menten term for
nutrient uptake. In the diatom equation, the lower of the
two nutrient limitation terms controls the rate of population
increase through a Liebig’s Law formulation. Although
seemingly considerably simpler, these growth terms differ
from those of other plankton models [e.g., Fasham, 1993]
mainly in the reduction of the light-limited portion of the
growth rate to a single parameter. This simplification is
permitted because the model aims to represent the global
nutrient cycles on a mean annual basis. Should the model be
used in a seasonal context, the growth terms would need to
be specified in greater detail .
[
16] The second term in the phytoplankton equations is a
loss rate, removing a constant fraction (M) of the phyto-
plankton populations. This term simplifies all of the possi-
ble loss pathways for phytoplankton (e.g., grazing,
respiration, sinking, disease) down to a single, linear rate.
It is considerably simpler than corresponding terms in other
plankton models. Commonly, loss terms are represented by
explicitly modeling zooplankton populations, which act to
graze down phytoplankton populations. These grazing rela-
tionships are usually modeled in a nonlinear fashion similar
to that of nutrient uptake, and are often further complicated
by parameterizing multiple prey types, grazing thresholds,
or food preferences [Fasham et al., 1990]. The simplifica-
tion used here keeps the model analytically tractable and
concentrates on the most i mportant processes (but see
section 4.2 for relevant sensitivity analyses).
[
17] Phytoplankton growth and loss terms dominate the
fluxes for both modeled nutrients. Growth reduces surface
concentrations of nutrients, while phytoplankton losses are
returned to both ocean boxes by the remineralization of
sinking biogenic material. Remineralization is modeled as
the fractions of the sinking flux of biogenic material t hat are
remineralized within each ocean layer. In reality, these
fractions vary with detrital sinking speed and with reminer-
alization rate, which themselves vary with aggregation /
breakup of particles, and with ambient temperature, pres-
sure, and oxygen concentration. Rather than address this
complexity directly, simple remineralization fractions have
been assumed for both nutrients. Further, as a preliminary
assumption, remineralization of detrital phosphate from
both algal groups is parameterized identically. This assump-
tion ignores the role of sinking in diatom ecology [Smetacek,
1985; Dugdale and Wilkerson, 1998], according to which
one would expect the remineralization profile of diatom-
produced biogenic phosphate to be shifted towards the deep
box. This assumption is examined in section 5.
[
18] Unlike the ratios between the other major elements,
the ratio between silicon and phosphorus (or carbon or
nitrogen) can be extremely variable in diatoms. First, silicic
acid u ptake, unlike that of nitrate and phosphate, is
decoupled from photosynthesis, although it is still ulti-
mately dependent on the energy provided by photosynthesis
[Martin-Je´ze´queletal., 2000]. Further, silicification is
tightly coupled to the cell division cycle, resulting in the
extent of silicification being dependent on the duration of
the division cycle [Ragueneau et al., 2000; Martin-Je´ze´quel
et al., 2000]. The slower a cell grows, the longer a period it
has to uptake silicic acid, and so the more heavily silicified
it becomes (assuming silicic acid is abundant relative to
other limiting factors). For example, the availability of iron,
known to be regionally variable, is widely believed to play a
14 - 4 YOOL AND TYRRELL: ROLE OF DIATOMS IN REGULATING OCEANIC Si
role in the silicic acid utilization in diatoms via its effects on
cell growth rates [Hutchins and Bruland, 1998; Takeda,
1998], with the result that higher Si:P ratios are found
within diatoms growing in iron-limited regions [Pondaven
et al., 1998 ].
[
19] In the equations above, this general relationship is
modeled by relating the Si:P ratio,
^
R
org
, to a function of the
silicic acid uptake rate and the Liebig term. Thus, when
silicic acid most limits the diatoms, the numerator and
denominator in the
^
R
org
equation are equal and a Si:P ratio
of R
org
results (this is assumed to be the minimum Si:P ratio).
However, where silicic acid is more plentiful and phosphate
most limits the diatoms (i.e., extends the duration of the cell
division cycle), the numerator is greater than the denomina-
tor and
^
R
org
> R
org
. The minimum ratio used here should be
viewed as the diatoms’ ideal ratio: When conditions are
good, and both nutrients are nonlimiting, this is the ratio that
will result within actively growing diatom populations.
When under severe silicic acid stress [Martin-Je´ze´quel et
al., 20 00], diat oms may curtail frustule size (either via
reduced thickness or ornamentations such as spines) to lower
their silicic acid requirement and so reduce their Si:P ratio.
Although the model does not represent this response, the
conditions that lead to it are only likely to occur at times and
places when diatoms are less ecologically important, so we
have not included this response. Essentially, while the
relationship used here simplifies a complex process [Flynn
and Martin-Je´ze´quel , 2000], it captures a major facet of the
Si:P ratio and, from a practical point of view, requires no
extra parameters beyond the ideal Si:P ratio.
[
20] Aside from the biologically controlled fluxes, both
nutrients are constantly added to the ocean from terrestrial
or seafloor reservoirs. In the case of phosphate, these are
confined to riverine fluxes entering the surface layer (RP).
Riverine fluxes dominate silicic acid additions to the ocean
[Tre´guer et al., 1995], but these are supplemen ted by
aeolian inputs (also to the surface layer), and hydrothermal
and seafloor weathering inputs which enter the deep layer of
the model (respectively, RS, AS, HS, and WS). Since the
representation of ocean physics is primitive, nutrients in the
two layers are simply mixed at a constant rate (K) between
the two ocean layers.
[
21] An important process only implicit in the equations
above is the burial and permanent loss of material from the
ocean system. As outlined above, sinking biogenic material
is remineralized down the water column, with the two layers
receiving fractions (SR, DR, SR
s
and DR
s
) of the total
biogenic flux. For both nutrients, these fractions sum to
less than 1, and residual quan tities of material leave the
modeled system (SF and SF
s
; see Table 1). Given that there
are constant inputs from riverine and other sources, and that
this burial flux is the only ‘‘exit’’ from the model system, it
is an important pathway in determining the ocean’s equi-
librium state, despite being invisible in the model equations.
2.3. Parameters
[
22] Table 1 lists all of the model’s parameters together
with their descriptions, units and values. All material units
are expressed in moles, spatial dimensions in meters, and
time in years. Remineralization fractions are given as
percentages, although in the model they are used as frac-
tions of unity.
[
23] The majority of the model parameters are derived
from Tyrrell’s [1999] model. Both that model and this one
share the same phosphate cycle submodels, and the param-
eters they have in common are given identical values here.
One slight difference lies in the values assigned to the
phytoplankton maxi mum g rowth r ates. I n the work of
Tyrrell [1999] the other algae are given a slight advantage
over their nitrogen fixing co mpetitors (0.25 d
1
versus
0.24 d
1
), while in this model the diatoms are given a
similarly slight advantage over the other algae (0.26 d
1
versus 0.25 d
1
). Both algae experience the same mortality
rate (M =0.20d
1
).
[
24] These maximum growth and death rates are consid-
erably lower than most values obtained from the field and
Table 1. Model Parameters and Their Values
Symbol Parameter Value Literature
SD depth of surface layer 500 m
DD depth of deep layer 3230 m
Tvol total ocean volume 135 10
16
m
3
Tarea total ocean surface area 362 10
12
m
2
K ocean mixing coefficient 3.0 m yr
1
3.0 [Broecker and Peng, 1982]
SR fraction of P remineralized in surface 95% 92 – 97 [Tyrrell, 1999]
DR fraction of P remineralized in deep 4.8% (100 SR SF)
SF sedimentation fraction of P 0.2% 0.1– 0.2 [Mackenzie et al., 1993]
SR
s
fraction of Si dissolution in surface 50% 50 [Tre´guer et al., 1995]
DR
s
fraction of Si dissolution in deep 47.5% (100 SR
s
SF
s
)
SF
s
sedimentation fraction of Si 2.5% 2.5 [Tre´guer et al., 1995]
RP riverine P input 0.2 mmol P m
2
.yr
1
0.09– 0.21 [Tyrrell, 1999]
RAS riverine Si input 15.0 mmol Si m
2
.yr
1
13.8 ± 2.7 [Tre´guer et al., 1995]
AS aeolian Si input 1.5 mmol Si m
2
.yr
1
1.4 ± 1.4 [Tre´guer et al., 1995]
HS hydrothermal Si input 0.6 mmol Si m
2
.yr
1
0.4 ± 0.3 [Tre´guer et al., 1995]
WS weathering Si input 1.2 mmol Si m
2
.yr
1
1.1 ± 0.8 [Tre´guer et al., 1995]
R
org
minimum Si:P ratio in organic matter 16 mol Si (mol P)
1
16 [Louanchi and Najjar, 2000]
m
O
maximum O growth rate 91.25 yr
1
(= 0.25 d
1
) 36 –1500 [Furnas, 1990]
m
D
maximum D growth rate 94.9 yr
1
(= 0.26 d
1
) 36– 1500 [Furnas, 1990]
K
p
P uptake half-saturation constant 0.03 mmol P m
3
0.03– 0.05 [Tyrrell, 1999]
K
s
Si uptake half-saturation constant 0.5 mmol Si m
3
0.2– 97.4 [Martin-Je´ze´quel et al., 2000]
M mortality rate 73.0 yr
1
(= 0.20 d
1
) 91– 440 [Banse, 1992]
YOOL AND TYRRELL: ROLE OF DIATOMS IN REGULATING OCEANIC Si 14 - 5
![Figure 1. Plots of nitrate versus phosphate and silicic acid versus phosphate from global climatologies [Conkright et al., 1994]. Data range from the surface (near the origin) to the seafloor. The dashed lines represent N:P = 16:1 and Si:P = 16:1, standard Redfield ratios for these nutrients. While active remineralization processes closely tie nitrate and phosphate concentrations (even at depth), biogenic silica dissolution is slower and only weakly coupled to these processes; hence the increasing deviation from the dashed line with depth.](/figures/figure-1-plots-of-nitrate-versus-phosphate-and-silicic-acid-20xa34x1.webp)
