The biological pump of the ocean has changed over Earth's history, from one dominated by prokaryotes to one involving a mixture of prokaryotes
and eukaryotes with trophic structure. Changes in the biological pump
are in turn hypothesized to have caused important changes in the
nutrient and redox properties of the ocean. To explore these hypotheses, we
present here a new box model including oxygen (O), phosphorus (P) and
a dynamical biological pump. Our Biological Pump, Oxygen and
Phosphorus (BPOP) model accounts for two – small and large – organic
matter species generated by production and coagulation,
respectively. Export and burial of these particles are regulated by
a remineralization length (zrem) scheme. We independently
vary zrem of small and large particles in order to study
how changes in sinking speeds and remineralization rates affect the
major biogeochemical fluxes and O and P ocean concentrations.
Modeled O and P budgets and fluxes lie reasonably close to present
estimates for zrem in the range of currently measured
values. Our results highlight that relatively small changes in
zrem of the large particles can have important impacts on
the O and P ocean availability and support the idea that an early
ocean dominated by small particles was nutrient rich due to the
inefficient removal of P to sediments. The results also suggest that
extremely low oxygen concentrations in the shelf can coexist with an
oxygenated deep open ocean for realistic values of zrem,
especially for large values of the small-particle
zrem. This could challenge conventional interpretations
that the Proterozoic deep ocean was anoxic, which are derived from
shelf and slope sediment redox data. This simple and computationally
inexpensive model is a promising tool to investigate the impact of
changes in the organic matter sinking and remineralization rates as
well as changes in physical processes coupled with the biological pump
in a variety of case studies.
Introduction
The “biological pump” describes the production of organic matter at
the surface of the ocean (an oxygen source), its downward export/sinking
flux, remineralization at depth (an oxygen sink) and burial. This set
of processes acts against the homogenization of tracer concentrations
by the ocean circulation, maintaining large-scale tracer gradients
(Sarmiento and Gruber, 2006). In today's world, the biological pump
plays a key role in transferring carbon from the atmosphere/surface
ocean to the deep ocean and in so doing lowers atmospheric
CO2 and creates oxygen demand in deeper waters (Lam et al.,
2011; Kwon et al., 2009). Those deeper waters with the greatest oxygen
demand relative to oxygen supply can be driven hypoxic (O2<60mmolm-3), suboxic (O2<5mmolm-3) or even anoxic – as is being seen in parts
of the ocean today (Keeling et al., 2010). By combining surface oxygen
production and organic carbon burial, the biological pump plays a role
in determining the long-term source of oxygen to the atmosphere. The
biological pump also provides a means of efficiently transferring
organic matter and the nutrients it contains to marine sediments if
sinking through the water column happens fast enough compared to
remineralization for the material to hit the bottom (Sarmiento and
Gruber, 2006). Hence the biological pump plays a key part in balancing
the input of phosphorus to the ocean with a corresponding output flux
of phosphorus buried in marine sediments.
Through Earth's history, the characteristics, efficiency and impact of
the biological pump are thought to have changed dramatically due to
the evolution of increasingly large and complex marine organisms
(Ridgwell, 2011; Logan et al., 1995; Boyle et al., 2018). Life in the
ocean began as just prokaryotes, presumably attacked by viruses, with
slow sinking of the resulting tiny particles. Now the marine ecosystem
is a mix of prokaryotic cyanobacteria and heterotrophs and
size-structured eukaryotic algae, mixotrophs, and heterotrophs all the
way up to large jellyfish, fish, and whales. Some of the resulting
particles sink very fast (McDonnell and Buesseler, 2010).
How changes in the biological pump have affected ocean nutrient and
redox state at different times in Earth history is a subject of active
research and hypothesis generation. Previous work has highlighted the
Neoproterozoic Era, spanning from 1000 to 541 million years ago, as being of
particular interest because it saw a shift of dominance from
prokaryotes to eukaryotes and a series of dramatic shifts in the
climate, biogeochemical cycling and ocean redox state (Katz et al.,
2007; Brocks et al., 2017). A common paradigm has been to assume that
a progressive rise of oxygen in the atmosphere (of uncertain cause)
drove the oxygenation of the deep ocean at this time through air–sea
gas exchange and mixing, but equally, increases in the efficiency of
the biological pump could have lowered ocean phosphorus concentration
and thus oxygenated the ocean (Lenton et al., 2014). Recent data show
a series of transient ocean oxygenation events ∼660–520 Ma, which get more frequent over time, suggesting
a complex interplay of processes on multiple timescales, including
changes in the biological pump and ocean phosphorus inventory (Lenton
and Daines, 2018).
During the Phanerozoic Eon there have been further changes to the
biological pump. In particular, a rise of eukaryotic algae from the
early Jurassic onwards is hypothesized to have increased the
efficiency of the biological pump and thus oxygenated shallow waters
(Lu et al., 2018) but presumably deoxygenated deeper waters, at least
in the short term. In the oceanic anoxic events (OAEs) that occurred
during the Mesozoic Era there were major increases in prokaryotic
nitrogen fixation yet evidence for a eukaryote-dominated biological
pump (Higgins et al., 2012), raising interesting questions as to
whether this reinforced anoxia at depth.
Previous modeling work has examined the impact of changes in the
organic matter remineralization length/depth (zrem) in the
3-D GENIE intermediate complexity model (Meyer et al., 2016; Lu
et al., 2018). Both studies clearly demonstrated the important
control of the zrem on ocean oxygen concentrations – as
it gets larger the oxygen minimum zone shifts to greater
depths. Furthermore, Lu et al. (2018) showed that an increase in
zrem can explain an observed deepening of the oxycline
from the Paleozoic to Meso-Cenozoic in the ocean redox proxy
I/Ca. However, coarse 3-D models such as GENIE do not really resolve
shelf seas and their dynamics, which are distinct from those of the
open ocean. Furthermore, GENIE only accounts for one organic carbon
species, overlooking processes of transformation of organic material,
such as coagulation and fragmentation, which contribute to modulating
the efficiency of the organic matter vertical export and burial
(Wilson et al., 2008; Karakaş et al., 2009; Boyd and Trull, 2007).
In this study, we take a more idealized approach, exploring how
changes in the properties of the biological pump may have affected the
shelf sea and open ocean nutrient and redox state using a new
Biological Pump, Oxygen and Phosphorus (BPOP) box model. This model
combines a box representation of the marine O and P cycles with an
intermediate complexity representation of the biological pump
transformations, including two classes of particulate organic matter
(POM). BPOP allows us to modify the properties of two POM pools, whose
abundance is regulated by the processes of production and
coagulation. We focus on changes in the characteristic depths at which
the two POM pools are remineralized, i.e. the particle
remineralization length scale (zrem), and study the
resulting equilibrium budgets and fluxes. The model has
a deliberately simplified treatment of redox carriers and is designed
to focus on ocean P and ocean redox steady states, not on longer-term
controls on atmospheric oxygen. In the following sections we describe
the model, provide an evaluation of its performance in the context
of modern observations and flux estimates, and finally present and
discuss our model results.
List of the state variables in the model and of their units.
NameDescriptionUnitsPssInorganic phosphorus in surface shelf sea boxmmolm-3PdsInorganic phosphorus in deep shelf sea boxmmolm-3PsoInorganic phosphorus in surface open ocean boxmmolm-3PdoInorganic phosphorus in deep open ocean boxmmolm-3OssMolecular oxygen in surface shelf boxmmolm-3OdsMolecular oxygen in deep shelf boxmmolm-3OsoMolecular oxygen in surface open ocean boxmmolm-3OdoMolecular oxygen in deep open ocean boxmmolm-3OatOxygen mixing ratio in atmosphere (mol per mol)–SedPorgsOrganic phosphorus in the sediments of the shelf seammolm-2SedPorgoOrganic phosphorus in the sediments of the open oceanmmolm-2PTOTDiagnostic variable: total P budget from sources and sinks onlyTmol POTOTDiagnostic variable: total O budget from sources and sinks onlyPmol O2
Parameters set that describes geometry of the box model.
NameDescriptionValueUnitsSourceMolatmoMillimoles of air in atmospheric box1.8×1023mmol–ΔZeuDepth of the euphotic layer in shelf and open ocean100m(1)ΔZdsDepth of the deep shelf sea box100m(2)ΔZdoDepth of the deep open ocean box3500m(3)AoceanTotal area covered by the ocean361×1012m2–PshelfFraction of the total ocean area currently covered0.07–Barrón and Duarte (2015)by the shelf sea (≤200m deep)
Notes: (1) we
assume a constant average euphotic layer depth of 100 m in both shelf and
open sea; (2) the shelf sea is assumed to be 200 m deep in total, in line
with the definition of shelf sea by Barrón and Duarte (2015); and
(3) we assume an average open ocean depth of 3600 m (including euphotic
layer).
Model description
Here we describe the Biological Pump, Oxygen and Phosphorus (BPOP)
model. The model was implemented using MATLAB, and the equations are
solved by the built-in ode15s solver. BPOP can easily run on a single
core, integrating 50 million years of time in less than a minute on an
ordinary machine and is therefore computationally efficient. We refer
to the user manual (see the Supplement) for further information on
how to run the model.
Variables and circulation
The box model resolves explicitly for each relevant box the local
concentrations of three types of tracers: molecular oxygen
O2 (O), inorganic dissolved phosphorus (P) and sediment
organic phosphorus (SedPorg). The total budgets of P and
O, respectively PTOT and OTOT, are also
independently integrated from the net sources and sinks of the two
tracers over the entire model domain, for the purpose of checking mass
conservation. The entire set of state and diagnostic
variables in the model and their units are listed in Table 1. In the following
subsections we describe the geometry of the box model and discuss the
physical and geochemical fluxes that drive the dynamics of the tracers. Box
properties are listed in Table 2, while the set of parameters adopted
for the modeled physical and geochemical fluxes can be found in
Table 3.
Parameter set pertaining to the initial conditions of the model,
circulation mass fluxes and boundary fluxes.
NameDescriptionValueUnitsSourcePiniInitial P concentration for all the ocean boxes2.2mmolm-3Watson et al. (2017)OiniInitial O concentration for all the ocean and atmosphere boxes0mmolm-3–(Porg)iniInitial Porg in all the sediment boxes0mmolm-3–UpwUpwelling cell mass fluxes6Sv (sverdrups)(1)MixvoVertical mixing in the open ocean40Sv(2)MixlsLateral mixing at the surface0.5Sv(3)MixldLateral mixing at depth0.5Sv(3)MixvsVertical mixing in the shelf sea1Sv(4)spySeconds per year conversion factor (Sv to m3yr-1)31 557 600s yr-1–PinTotal P river input92×1012mmol yr-1Slomp and Van Cappellen (2006)PopenFraction of river input delivered to the open ocean0.4–(5)OPRedOxygen to phosphorus Redfield ratio150–Anderson and Sarmiento (1994)TmeanGlobal mean temperature for the Schmidt number of oxygen17.64∘CSarmiento and Gruber (2006)WspeedGlobal mean wind speed for oxygen gas transfer velocity7.5ms-1Sarmiento and Gruber (2006)KHenriHenry's law constant770×10-6m3 atm mmol-1–patAtmospheric pressure at sea level1atm–Omix0Today's oxygen mixing ratio in atmosphere0.21––W0Baseline oxidative weathering flux coefficient9.752×1015mmol yr-1(6)
Notes: (1) Chavez and
Messié (2009) estimate 5.5 Sv (sverdrups) in the four major upwelling systems alone;
(2) compare to 38 Sv (Sarmiento and Gruber, 2006), 17 Sv of mixing flux
in the Southern Ocean alone (Meyer et al., 2015), estimated
open ocean downwelling 38.5 Sv and upwelling 34.5 Sv (Ganachaud and
Wunsch, 2000); (3) cross-shelf mass exchange due to lateral recirculation,
tides and mixing aimed at including exchange processes other than upwelling
(Fennel et al., 2005; Cole et al., 2015; Wollast, 1998); (4) minimal
assumption for vertical mixing in nearshore regions due to seasonal and eddy
mixing; see also Sect. 3.2 Sensitivity to parameter choices; (5) up to
70 % of river outflow reaches the open ocean; see Sharples et al. (2017); and (6) calculated from the equilibrium solution given Pin.
Box properties and physical fluxes of inorganic tracers
The box model includes four ocean boxes, one atmospheric box and two sediment
boxes (Fig. 1a). The ocean and sediment boxes are equally split
between shelf sea and open ocean, both including one surface ocean box
and one deep ocean box.
O and P are exchanged between the four ocean boxes through advection and
mixing, including an upwelling recirculation between shelf sea and
open ocean (Wollast, 1998). For a generic tracer concentration C and
in the ith box, the physical exchange flux (in millimoles per cubic meter per year) is represented by
AdvMix(C)i=∑jMassFluxij/Vi⋅(Cj-Ci),
where MassFluxij represents the volumetric flow between the ith
box and any adjacent box j, while Vi is the volume of the ith
box.
Box model scheme with a representation of the physical and
boundary fluxes affecting inorganic tracers in the water column and
atmosphere, where blue arrows indicate advective and mixing fluxes and
yellow arrows indicate air–sea gas exchange fluxes. The model includes seven
boxes: surface shelf (ss), deep shelf (ds), surface open ocean (so), deep
open ocean (do), atmosphere (at), shelf sediments (s) and open ocean sediments
(o).
Representation of the physical and biogeochemical fluxes affecting
the Porg cycling in the model. Even though some processes (such as burial as Ca–P) are here represented in detail only in one box, the set of
biogeochemical processes regulating the Porg dynamics in shelf sea and
open ocean (both water column and sediments) is the same, as described in
Sect. 2.2.
For each surface box i, air–sea gas exchange allows O fluxes between
the ocean and the atmosphere (at). The flux (in millimoles of O2 per cubic meter per year) is positive when directed into the ocean and depends
on the gas transfer velocity KW, atmospheric pressure
pat (here assumed constant) and Henry's constant
KHenry, as in
AirSeai=KW⋅(Oat⋅pat/KHenry-Oi)⋅Ai/Vi,
where KW (in meter per year) is a function of the prescribed mean
temperature Tmean and wind speed Wspeed
(Sarmiento and Gruber, 2006).
Initialization and boundary fluxes
The model is initialized with an even concentration of P
(Pini) in all the ocean boxes, zero oxygen (Oini) and zero
SedPorg ((Porg)ini). A constant input of P from rivers
(Pin) into the surface ocean replenishes the P ocean
reservoir despite the burial flux (net sink of Porg) into
the sediments. Pin is in part delivered directly to the
surface open ocean (Sharples et al., 2017). At equilibrium, the organic phosphorus
(Porg) burial flux balances Pin. Oxidative
weathering determined by atmospheric oxygen Oat
constitutes a net sink flux for O. The weathering flux (per year)
depends on a constant baseline flux W0, and it
scales like the square root of the oxygen mixing ratio normalized to
present values Omix0 (Lenton et al., 2018), following
OxyWeath=W0⋅Oat/Omix0.
Biological pump details
The modeled tracer cycles are coupled with a set of biological
transformations, i.e. the biological pump, governing the cycle of
production, and remineralization and burial of Porg in the
water column and in the sediments. Porg in the water
column is resolved implicitly; at each time step all the produced
Porg that does not reach the sediments is instantaneously
remineralized. In this sense, in our model no Porg can
accumulate in the ocean water column, and we only calculate fluxes of
water column Porg without treating Porg as a state variable. This scheme is similar to the
one used to represent detrital POM in some modern ocean biogeochemical
models (Moore et al., 2004). P and O biological fluxes are coupled with
a fixed Redfield ratio OPRed. The next few paragraphs
describe the cycle of production, coagulation, export,
remineralization and burial that constitute the biological pump
representation. The full set of parameters used to resolve the
Porg cycle is provided in Table 4.
Parameters set pertaining to the Porg cycle of the model and coupled
biogeochemical fluxes.
NameDescriptionValueUnitsSourcePeffP maximum uptake rate for production0.8yr-1(1)KPMichaelis–Menten constant for P uptake0.2mmolm-3(2)KOsMichaelis–Menten constant for aerobic remineralization in the sediments0.2mmolm-3(3)KOwMichaelis–Menten constant for aerobic remineralization in the water column15mmolm-3(4)cgfCoagulation fraction, determining the portion of small Porg production routed into large Porg0.22–(5)rmrRemineralization rate of sedimented Porg0.36yr-1(6)feanRemineralization enhancement factor under anoxia1.25–Slomp and Van Cappellen (2006)CaPrRate of formation of Ca–P mineral from sedimented Porg0.5(mmolm-2)-1yr-1(7)fsanCa–P formation dampening factor under anoxia0.5–Slomp and Van Cappellen (2006)
Notes: (1) maximum P uptake rate, meant to account for
environmental limitations of phytoplankton growth rate (such as light and
temperature); the magnitude of the rate takes into account that we are not
explicitly resolving phytoplankton concentrations (order of 10-2mmolP); see also production in Gruber et al. (2006) and
Yool and Tyrrell (2003); (2) measured values vary in the range from 0.01 mmolm-3 up to a few millimoles per cubic meter, varying for different phytoplankton
types; see Lomas et al. (2014), Tantanasarit et al. (2013), Krumhardt et al. (2013), Lin et al. (2016) and
Klausmeier et al. (2004); (3) measured half-saturation constant for
oxygen uptake varies in the range of 0.1–3 mmolm-3 (Ploug, 2001);
(4) biogeochemical models commonly switch to anaerobic respiration below 4 mmolm-3 (Paulmier et al., 2009); measurements suggest a value
close to 19 mmolm-3 (DeVries and Weber, 2017); (5) Cavan
et al. (2017) showed that small particles are about 85 % of the total
sinking particles abundance in the coastal region at export depth; the
parameter was further tuned to bring the model closer to modern ocean
conditions; (6) on the same order of magnitude as Gruber et al. (2006); (7) unmeasured – given the analogous adopted functional form, we
assume Ca–P formation to happen on a timescale close to that of Porg
coagulation in the water column in models with explicit particle pools
(Gruber et al., 2006).
Particle classes, production and coagulation
The model includes two Porg classes that get produced,
exported and remineralized in the ocean water column, which are small
Porg (SPorg) and large Porg
(LPorg). The use of two Porg classes is in line with
modern ocean in situ observations, which reveal a bimodal distribution
of the particle sizes and sinking speeds (Riley et al.,
2012; Alonso-González et al., 2010). Moreover, it allows a better
reproduction of the commonly observed Martin power-law decay of the particle
export flux with the use of a remineralization length scheme of export
and burial fluxes (Boyd and Trull, 2007).
Organic matter production happens only in the surface ocean boxes
through the uptake of P. This is regulated by a maximum rate
Peff and a Michaelis–Menten kinetics with constant
KP. Production (in millimoles of P per cubic meter per year) in each
ith box only generates SPorg, according to
Prodi=Peff⋅(Pi/(Pi+KP))⋅Pi.
LPorg is generated via the coagulation of
SPorg at the surface after production. As we do not
explicitly solve for the concentrations of SPorg and
LPorg, we assume that the coagulation (in millimoles of P per cubic meter per year) of SPorg into LPorg in
each box i is proportional to the rate of production of small
particles as follows:
Coagi=cgf⋅Prodi.
This is a necessary simplifying assumption compared to the usual
coagulation models, which define the flux as the square of the particle
concentration (Boyd and Trull, 2007; Gruber et al., 2006), given the
fact that our model does not resolve this variable. Coagulation
impacts the relative contribution of small and large particles to the
export and burial fluxes by subtracting from the local
SPorg pool and adding to the LPorg pool.
Physical fluxes of organic material
The implicit representation of the organic matter in the water column
implies that no organic matter is accumulated in the ocean. In our
baseline version of the model, corresponding to the results presented
in this paper, SPorg and LPorg are
redistributed throughout the water column exclusively by implicitly
modeled gravitational sinking before being buried, accumulated
in the sediments or remineralized. Even though the vertical export by
downwelling and mixing (Stukel and Ducklow, 2017) and the lateral
organic matter redistribution (Lovecchio et al., 2017; Inthorn et al.,
2006) may be important when working with suspended SPorg
(zremS=0), these fluxes are not currently
accounted for in the model.
Remineralization length scheme
The export and sedimentation fluxes of Porg through the
water column are represented by a remineralization length scheme. In
this representation, the vertical fluxes of organic matter f(z) vary
exponentially with depth. The shape of the exponential depends on the
value of the remineralization length (zrem) of each
organic matter species as follows:
fk(z)=f0k⋅e-z-z0zremk,
where f0k is the flux (in millimoles of P per square meter per year) at
the reference depth z0, and the index k indicates the
organic matter pool of reference, either small (S) or large (L). This
representation of the export flux is convenient, as it does not depend
on the specific choice of z0 (Boyd and Trull, 2007).
The remineralization length zrem indicates the distance
through which the particle flux becomes 1/e times (about 36 %) the
flux at the reference depth (Buesseler and Boyd, 2009; Marsay et al.,
2015). This quantity is expressed in meters and can be calculated as
the ratio between the particle sinking speed and the
remineralization rate of the particle (Cavan et al., 2017). Consequently,
zrem implicitly contains information on several particle-inherent properties (among which are density, size, shape and organic matter
liability) as well as information about the surrounding environment,
e.g. the type of heterotrophs that feed upon the organic material
(McDonnell and Buesseler, 2010; Baker et al., 2017). For simplicity,
we assume that the remineralization length of small and large
particles does not vary between shelf sea and open ocean boxes. We
examine the potential impact of this limitation in the Discussion
section of the paper.
Sediments and burial
SPorg and LPorg accumulate in the sediments as SedPorg,
which is calculated as a density per unit of area. The flux
(in millimoles of P per square meter per year) into the sediment box i depends on the
organic matter fluxes into the overlaying deep ocean box j and on
the remineralization length of the two pools as in
SedFlxi=(Flx_SPorgj⋅exp-ΔZj/zremS7+Flx_LPorgj⋅exp-ΔZj/zremL).
The accumulated SedPorg is partially slowly remineralized
and partially irreversibly buried in a mineral form. Phosphorus burial
as mineral Ca–P is modeled as a function of the square of
SedPorg that accumulates in the sediments and is regulated
by a constant rate coefficient CaPr. Ca–P formation
happens at a lower rate under low-oxygen conditions
(CaPr∗=CaPr⋅fsan with fsan<1), in agreement with
observations and previous models (Slomp and Van Cappellen, 2006). The
transition from aerobic and anaerobic conditions is controlled by
a Michaelis–Menten type of function of the oxygen concentration in
the deep ocean box j overlaying the sediment box i. The oxic and
anoxic terms sum to the total formation term (in millimoles per square meter per year) as in
CaPformi=SedPorgi2⋅[CaPr⋅Oj/Oj+KOs8+CaPr⋅fsan⋅1-Oj/Oj+KOs].
This flux is essential to balance the continuous P river input,
therefore preventing the ocean from overflowing with
nutrients.
Remineralization in the water column and sediments
At each time step, remineralization in the water column completely
depletes the Porg that has not reached the sediments. In
the two surface boxes, remineralization of Porg that is
not exported below the euphotic layer uses up part of the oxygen that
was released by production. For this reason, net oxygen production in
each surface box is proportional to the export of Porg
below the euphotic layer. The overall loss of P due to export (in millimoles of P per cubic meter per year) from a surface box i to a deep box j via
gravitational sinking, is calculated as
VExpi=(Flx_SPorgi⋅exp(-(ΔZeu/2)/zremS)+Flx_LPorgi⋅exp(-(ΔZeu/2)/zremL))/ΔZi,
where the fluxes per unit of area of SPorg and LPorg in the surface
boxes depend on production and coagulation as described in
Sect. 2.2.1.
At depth, the remineralization of Porg that does not reach
the sediments happens through both aerobic and anaerobic processes,
completely depleting the remaining Porg. The amount of
inorganic P released in each deep box j by water-column
remineralization (in millimoles of P per cubic meter per year) is
therefore calculated as
WcRemj=(Flx_SPorgj⋅1-exp-ΔZj/zremS10+Flx_LPorgi⋅1-exp-ΔZj/zremL)/ΔZj.
In each deep ocean box i, aerobic remineralization uses some of the
available oxygen and is therefore limited by Michaelis–Menten
kinetics with a half-saturation constant KwO (DeVries and
Weber, 2017). Anaerobic remineralization takes up the entire
remaining Porg that is not remineralized aerobically and
releases a product, which bubbles up to the atmosphere, reacting
with atmospheric oxygen. In our model, the reducing agent produced by
anaerobic remineralization is methane gas, and it is only produced when
the sediments and the deep shelf water column have gone anoxic. As we
do not track other oxidizing agents such as SO4, there is
nothing for the methane to be oxidized by until it reaches the surface
ocean, and as the surface ocean is equilibrated with the atmosphere,
the fact that we assume oxidation in the atmosphere is a reasonable
approximation. In each sediment box i, remineralization of
SedPorg happens in a similar way to remineralization in
the water column, with an aerobic and an anaerobic component. However,
remineralization in the sediments is not instantaneous but rather happens at
a fixed rate which depends on the oxygenation state of the overlaying
water column. Aerobic remineralization takes up oxygen from the
overlaying deep water box j and happens at a rate rmr,
while being limited by a Michaelis–Menten coefficient. Anaerobic
remineralization releases its product to the atmosphere and happens at
a faster rate rmr∗=rmr⋅fean with fean>1, in
agreement with recent observations and previous models (Slomp and Van
Cappellen, 2006). The release of Porg from a sediment box
i into the overlaying ocean box due to sediment remineralization
(in millimoles of P per cubic meter per year) is therefore the sum of the two terms
as in
SedRemi=(rmr⋅SedPorgi⋅Oj/Oj+KOs+(rmr⋅fean)11⋅SedPorgi⋅1-Oj/Oj+KOs)/ΔZd.
Equations summary
The dynamics of the 11 state variables in the model are regulated by just as
many equations. We summarize here the major terms for P, O and
SedPorg in the surface ocean (s), deep ocean (d),
atmosphere (at) and sediments, without distinguishing between coastal
and open ocean boxes and assuming that all terms have been scaled with
dimensions of the reference boxes or number of moles (atmosphere). A full
set of equations including the explicit formulation of all the flux
terms for each box can be found in the Appendix.
12dPsdt=Pin+AdvMix(P)s-VExp13dPddt=AdvMix(P)d+WcRem+SedRem14dOsdt=AdvMix(O)s+VExp⋅OPRed+AirSeadOddt=AdvMix(O)d-WcRemAer⋅OPRed15-SedRemAer⋅OPRed16dSedPorgdt=SedFlx-CaPform-SedRem⋅ΔZddOatdt=-∑AirSea-WcRemAna⋅OPRed17-SedRemAna⋅OPRed-OxyWeath,
where Pin is the river input of P to the surface of the ocean and
AdvMix indicates the advective and mixing physical fluxes of the
variable of interest (which differ for each box according to the
circulation scheme); Exp is the export flux of Porg in P
units; WcRem indicates the water column complete remineralization of
the organic material in P units, which is split into an anaerobic
(Ana) and aerobic (Aer) component; SedRem indicates the sediment
remineralization of SedPorg in P units (also aerobic and
anaerobic); AirSea represents the air–sea flux exchange of O; OxyWeath
is the O weathering flux sink; SedFlx is the SedPorg
accumulation flux as regulated by the remineralization length scheme
at the bottom of the water column; and finally CaPform represents the
sediment burial flux of P in mineral form. For each box, flux terms
are rescaled with the appropriate box geometry.
Strategy: sensitivity studies for varying zrem
In order to characterize the model, we analyze the equilibrium budgets
and fluxes of the state variables for varying zrem values
separately for SPorg and LPorg, respectively
zremS and zremL. We
adopt a range of zrem values that fall close to modern observations
(Cavan et al., 2017; Buesseler and Boyd, 2009; Marsay et al., 2015)
and takes into consideration our future aim to apply the model to
simulate the impact of the time evolution of the early biological pump
(at the Neoproterozoic–Paleozoic transition). For this reason, we
do not push the range as far as what would be needed to consider the
impact of fast sinking rates typical of silicified or calcified small
phytoplankton (McDonnell and Buesseler, 2010; Lam et al., 2011). In
our sensitivity simulations, zremS is in the range of
0–40 m, while zremL varies in the
range of 50–450 m.
EvaluationTimescales
Starting from the initial values listed in Table 3, the modeled state
variables evolve towards equilibrium for any pair of values of
zremS and zremL in the
explored interval. Simple mass conservation checks show no hidden
source or sink of tracers in the boxes of the model. Figure 3 illustrates
an example of evolution of the variables for
zremS and zremL in the
middle of the interval of explored values for both particle types. In
all the ocean boxes, P shows an initial oscillation that evolves on
timescales of tens of thousands of years (Fig. 3a, b), as expected by
the typical timescale of evolution of the tracer (Lenton and Watson,
2000). This is followed by a slower drift, which depends on the
dynamics of the deep water oxygen content, as the release and burial
of P in the sediments depend on the level of oxygenation of the deep
ocean and especially of the deep shelf sea. P reaches complete
equilibrium as soon as the deep ocean boxes become stably
oxygenated. The timescales of the evolution of O are slower and lie on the
order of tens of millions of years (Lenton and Watson, 2000). Oxygen
in the deep shelf overcomes hypoxia after the first few millions of
years and then slowly evolves towards equilibrium on the same
timescale of O in the other ocean boxes. The dynamics of SedPorg are
also strongly driven by level of oxygenation of the deep shelf
sea. The dynamical response of the model to changes in the biological pump
is rapid subsequent to the model equilibrating considering the given
initial conditions. For example, step changes in the
zrem values of the particles result in a transition time to a new equilibrium that
is on the order of a few tens of thousands of years, which is the
typical timescale of the P cycle.
Evolution of the state variables from the initial conditions
listed in Table 2 and remineralization lengths roughly in the middle of the
interval of explored values, zremS=20m and zremL=250m. (a) Evolution of inorganic phosphorus P in the water column (left
axis) and of organic phosphorus in the sediments SedPorg (right axis).
(b) A zoomed-in view of the dynamics of P in the first 200 000 years. (c) Evolution of oxygen in the water column (left axis) and atmosphere (right
axis). In (c) the two lines Oss and Oso are overlapping;
the two variables evolve closely due to the coupling of the surface ocean
with the atmosphere via air–sea gas exchange.
Modern ocean budgets and fluxes
Modern estimates of the zremS and
zremL vary depending on the region of sampling
and on the local community structure, with most of the measurements
focusing on large or heavy particles and most studies focusing on the
open ocean (Iversen and Ploug, 2010; Cavan et al., 2017; Lam et al.,
2011). Furthermore, only a very limited number of measurements
account for both microbial and zooplankton remineralization, the
latter disregarded by lab measurements of zrem (Cavan
et al., 2017). Considering the fundamental role of the shelf sea in
our model (always accounting for >98 % of the total burial), we
evaluate modeled tracer budgets and fluxes for values of
zremL that lie around 76 m, as
measured in situ by Cavan et al. (2017) for a modern shelf sea. We
pose no restrictions on zremS due to the lack
of precise measurements. A summary of our evaluation is provided in
Table 5.
Summary of the model evaluation provided in Sect. 3. Modern
observations and estimates are compared to model results obtained for
zremL in the range of measured values for a modern shelf sea
(Cavan et al., 2017).
QuantityModelModern values or estimatesUnitsSourceTotal ocean P2250–29703100Tmol PWatson et al. (2017)Total ocean O2100–107225–310Pmol O2Duursma and Boisson (1994); Keeling et al. (1993)Pss1.4–21–1.5mmolm-3Garcia et al. (2018a); Sarmiento and Gruber (2006)Pds3.9–4.92.2mmolm-3Garcia et al. (2018a); Watson et al. (2017)Pso0.4–0.90.2–2mmolm-3Garcia et al. (2018a); Sarmiento and Gruber (2006)Pdo1.9–2.51–3mmolm-3Garcia et al. (2018a); Sarmiento and Gruber (2006)Oss273–274200–350mmolm-3Garcia et al. (2018b)Ods3.8–9.20–80mmolm-3Garcia et al. (2018b)Oso273200–350mmolm-3Garcia et al. (2018b)Odo76–8340–200mmolm-3Garcia et al. (2018b)Production (Prod)11–3035–80Gt C yr-1Carr et al. (2006)Export3.4–3.84–20Gt C yr-1Henson et al. (2011)Export production11 %–33 %2 %–20 %of total ProdBoyd and Trull (2007)Burial0.3 %–1 %0.4 %of total ProdSarmiento and Gruber (2006)Shelf sea production16 %–27 %20 %of total ProdBarrón and Duarte (2015); Wollast (1998)Shelf sea export16 %–27 %29 %of total exportSarmiento and Gruber (2006)Shelf sea burial100 %91 %of total burialSarmiento and Gruber (2006)
In the above-mentioned range of zrem, our model predicts
equilibrium budgets of between 2250 and 2970 TmolP for
phosphorus and an oxygen budget of between 100
and 107 PmolO2 in the entire ocean, compared to the
estimated total P reservoir of 3100 TmolP (Watson et al.,
2017) and estimated ocean O2 reservoir of between
225 and 310 PmolO2 (Keeling et al.,
1993; Duursma and Boisson, 1994). Due to the relative size of the
ocean boxes, it is important to underline that total budgets are
strongly driven by the deep open ocean budget and that the low-oxygen
reservoir of our model may be connected to an underestimation of the
deep open ocean oxygenation.
Deep shelf P and O concentrations lie in the ranges of 3.9–4.9 mmolm-3 and 3.8–9.2 mmolm-3,
respectively (Figs. 5 and 6). Deep shelf nutrient concentrations are
higher than expected by about a factor of 2 compared to modern
values, possibly due to the fact that our model does not store any
Porg in the water column or due to an underestimation of
the vertical supply of nutrients to the surface shelf (e.g. via
mixing). Limiting deep P concentrations via lower remineralization or
higher burial rates, however, also results in sensibly lower
production rates. In the deep open ocean, P and O concentrations fall
in the ranges of 1.9–2.5 mmolm-3 and 76–83 mmolm-3, respectively. For any combination of
zremS and zremL, O
levels in surface ocean boxes lie between 273 and
274 mmolm-3, a good approximation of average modern
surface values (Garcia et al., 2018b). In general, the deep shelf
always shows the highest P values and lowest O concentrations compared
to the other ocean regions, while, as expected, the surface shelf sea
is richer in P compared to the surface open ocean.
Total ocean budgets of (a) P and (b) O at equilibrium for
varying zremS and
zremL.
In order to compare the modeled fluxes to modern estimates, we
converted our results into carbon (C) units assuming a C:P Redfield
ratio of 106. However, recent studies found a substantially higher
mean C:P ratio for the modern ocean (Martiny et al., 2014); therefore
our derived C fluxes may be a conservative estimate. Modeled
biological fluxes in C units, such as production and export, fall just
below the low end of present estimates (Fig. 7). Our model predicts
a total primary production of between 11 and 30 GtCyr-1,
and an export below the euphotic layer ranges between 3.4 and
3.8 GtCyr-1. These must be compared to an expected value
of production of between 35 and 80 GtCyr-1 (Carr et al., 2006) and an estimated export flux of at
least 4 TmolCyr-1 (Henson et al., 2011). Despite the
absolute fluxes being at the low end of the present estimates,
modeled export production (the export to production ratio) and the
burial to production ratio compare well to range of present
estimates. The modeled export corresponds to between 11 % and
33 % of total production, strongly depending on
zremS, compared to an expected range of
2 %–20 % (Boyd and Trull, 2007). Buried Porg
corresponds to between 0.3 % and 1 % of total production,
compared to an expected 0.4 % (Sarmiento and Gruber, 2006).
In terms of the shelf contribution to the total fluxes, model results
also fall close to present estimates. Modeled production in the
surface shelf sea represents between 16 % and 27 % of total
production (expected 20 %) (Barrón and Duarte, 2015; Wollast,
1998). The fraction of modeled export and burial that happens in the
shelf region represent, respectively, [16 %, 27 %] and nearly
100 % of the total ocean fluxes, compared to estimated modern
values of 29 % and 91 % (Sarmiento and Gruber, 2006). Our
overestimation of the shelf contribution to the burial fluxes may be
due to the underestimation of the
zrem of open-ocean particles compared to observations (Cavan et al., 2017; Lam
et al., 2011), i.e. our choice of using the same value of
zremS and zremL for
both the coastal and the open ocean box. This simplifying assumption
limits the capacity of Porg to reach the deep sediment
layer in the open ocean. We explore potential limitations of this
choice in the Discussion section.
ResultsBudgets and fluxes sensitivity to changes in zrem
Around the lowest values of zremL adopted in
the present study, i.e. in the range of 50–100 m, our model shows a strong sensitivity of the total and
local ocean P and O budgets to small changes in
zremL (Fig. 4). This is true for any
zremS, with minor differences between low and
high zremS values. For smaller
zremL, the model shows a sharp increase in P
concentrations in all the ocean boxes and a substantial decrease in O
levels at depth (Figs. 5 and 6), which are coupled with high levels of
production and remineralization and low rates of sedimentation
(Fig. 7). Essentially, slow sinking and/or rapid remineralization
results in inefficient removal of P to shelf sea sediments, requiring
the ocean concentration of P to rise considerably for P output to
balance (fixed) P input to the ocean.
Local P concentration in each ocean box for varying
zremS and zremL for the following: (a) surface shelf sea, ss; (b)
surface open ocean, so; (c) deep shelf sea, ds; and (d) deep open ocean, do.
Surface ocean boxes, as well as deep ocean boxes, are plotted on the same
scale.
O concentrations at equilibrium for varying zremS and
zremL for the following: (a) deep shelf sea, ds; (b) deep
open ocean, do. Surface ocean boxes (not shown) have nearly constant values
of O for any set of zrem due to the air–sea gas
exchange, which strongly couples them to the atmosphere.
Our model results show that for any pair of values of
zremS and zremL in the
entire explored range, the biological pump is able to oxygenate the
surface ocean (surface O levels lie close to 273 mmolm-3)
and, for most values, also to maintain the deep ocean above the level
of hypoxia (Fig. 6). The model shows a substantial difference between
the deep shelf and the deep open ocean; while the latter is
substantially oxygenated (O>50mmolm-3) for nearly
any values of zremS and
zremL, the deep shelf is hypoxic or even
suboxic for a broad range of small values of
zremL, especially close to modern shelf
zremL observations. Considering the wide
spatial extension of our boxes, we expect these low oxygen levels to
indicate the development of local anoxia in the deep shelf.
In a limited interval of small zremS values
(roughly zremS<6m), model results
depend only on the LPorg properties due to the rather
irrelevant contribution of SPorg to export and
remineralization. For larger zrem values
(zremS>6m and
zremL>100m), model results show
a strong interdependence of equilibrium budgets and absolute fluxes on
both zremS and
zremL. Interestingly, in this range of values,
export production depends very strongly on the small particle
properties, ranging between 10 % for low
zremS and 30 % for high
zremS, an overall trend that also affects the
ratio of deep remineralization to surface production (Fig. 7).
Biological pump fluxes in P units for the entire ocean for
varying zremS and
zremL in the following cases: (a)Porg surface production;
(b)Porg export through the
euphotic layer depth; (c) export / production, i.e. export to production ratio; and
(d) burial to production ratio.
It is also important to notice that, for any couple of
zremS and zremL,
modeled tracer concentrations and fluxes fall in a range of values
that never exceeds by orders of magnitude the modern observed
values. Considering all of the ocean boxes, P concentrations vary in
the range of roughly 0.2 and 9 mmolm-3, while O levels
lie between 0.5 and 205 mmolm-3. Production in carbon
units lies in the interval [7.6, 70.7 GtCyr-1].
Budgets and fluxes contribution by particle class
The relative role of small and large particles in modeled biological
and physical fluxes depends on a combination of their inherent
properties (zrem) and coagulation. In our simple model,
coagulation of SPorg into LPorg after
production in surface boxes affects a constant fraction
(cgf=0.22) of the produced particles. This
fraction was determined by model tuning to modern ocean conditions
and lies close to modern ocean observations of the large-particle
fraction (15% of the total particles) at export depth (Cavan
et al., 2017).
For zremL>100m, LPorg
efficiently removes P from the water column, limiting production. The
contribution of SPorg to the total export below the
euphotic layer, however, is strongly dominated by the value of
zremS, with a null contribution to export for
all values of zremS<10m and
increasing values above it. This trend is reflected in the deep water
small-particle fraction (Fig. 8c, d). Small particles contribute up to
73 % to export in both ocean boxes and up to 60 % to the
sediment accumulation in the shelf sea, with the highest contribution
to sediment accumulation being reached for large
zremS and low
zremL. Our model highlights therefore the
different role of large and small particles in the determination of
the equilibrium budgets and fluxes. Coagulation into large (fast sinking and less liable) particles is essential to maintain high enough
sedimentation and burial rates, therefore allowing O accumulation in
the system. At the same time, small (slow sinking and more liable)
particles tune the total magnitude of export and remineralization
below the euphotic layer, affecting the distribution of oxygen and
nutrients throughout the water column.
DiscussionModel limitations and robustnessGeneral limitations
BPOP consists of a simple box model with four ocean boxes, two sediment
boxes and one atmospheric box. As with every box model, BPOP only allows
a very rough and fundamental representation of the topography
and circulation of the ocean as well as of the exchange fluxes between ocean,
atmosphere and sediments. Even though this may be a limitation in the
context of the study of the well-known modern (and future) ocean, such
a computationally inexpensive model can be a useful tool to for
a first exploration of a large variety of projected conditions. In the
context of understanding past ocean changes, often characterized by
a limited availability of observational data, the use of such a simple
model constitutes instead an effective and honest approach to
understanding global shifts in budgets and fluxes. Furthermore, BPOP
explicitly distinguishes between the well-sampled shelf sea and the
less known open ocean of deep time; therefore allowing the relation of shelf
data with large-scale open ocean conditions.
The model deliberately simplifies the redox carriers and processes
represented, neglecting denitrification and iron and sulfate
reduction. Including additional oxidants and/or methane consumption
in deeper water column would be expected to intensify anoxia results
at depth. However, our current results suggest that the model is
underestimating the ocean total oxygen budget overall, mostly driven
by the deep open ocean reservoir. This suggests that neglecting these
additional processes in our simple box model does not lead to an
overestimation of oxygen accumulation at depth. Including additional
state variables and processes could also lead to more complex
dynamical behaviors (Wallmann, 2010).
We include anaerobic remineralization of Porg as being faster
than aerobic degradation, but in reality this is not the case for
carbon – which is remineralized at a similar or slower rate under
anoxic vs. oxic conditions (Burdige, 2007; Hedges et al., 1999; Dale
et al., 2015). Hence, in reality, under anoxic conditions, there is
preferential regeneration of phosphorus and organic C:P burial ratios
rise considerably, altering the long-term steady state of atmospheric
oxygen (Van Cappellen and Ingall, 1996). We do not consider these
aspects here because to do so would require adding state variables
for organic carbon (as distinct from organic phosphorus) and because
our focus here is on changes in ocean phosphorus and ocean redox under
an unchanged oxygen steady state. In future work we intend to
elaborate the model in order to explore long-term effects on atmospheric
oxygen.
Limitations connected to the biological pump representation
In our model we adopt a very simplified representation of the
biological pump, including two particle classes, “small” and
“large”, generated by production and coagulation, assuming that, on
average, zremS<zremL. This scheme resembles the one commonly
used in ocean biogeochemical models (Gruber et al., 2006; Jackson and
Burd, 2015). Our model does not include a dissolved organic matter (DOM) pool for reasons mostly
connected to the implicit representation of the biological pump and
the complete remineralization of the non-sedimented organic material
at each integration step. For the same reason, we do not resolve
particle Porg concentrations, and therefore we model the
coagulation flux as a constant fraction of production. A more physical
representation of coagulation would require this flux to scale with
the square of the particle concentrations (Boyd and Trull, 2007). Such
a further development could potentially lead to increase large
particle export for high surface P concentrations leading to high
production and particle concentrations (and vice versa). We reserve
this improvement as our first step for further model developments,
which will include an explicit Porg representation.
Modeled particles get remineralized through the water column
according to their characteristic zrem. Even though for
simplicity we do not use a continuous spectrum of zrem, the
use of two particle classes is in line with observations showing two
distinct peaks in the observed distribution of the sinking
speeds of the particles (Riley et al., 2012; Alonso-González et al.,
2010). Furthermore, this simplification still allows us to closely
approximate the empirical particle flux curve as a function of depth,
also known as Martin's curve (Boyd and Trull, 2007).
We assume that zremS and
zremL do not vary between the shelf sea and
the open ocean. However, modern ocean observations show cross-shore
changes in the phytoplankton community structure and sinking speeds
(Barton et al., 2013). Our simplifying assumption may therefore cause
the overestimation of the relative contribution of the shelf sea to
the total burial flux of Porg. Despite this, we believe
that this choice is still convenient in the context of the current
model, as it allows us to reduce the number of parameters in such
a simple box model representation of the biological pump of the ocean.
Observations suggest that hard-shelled phytoplankton types, especially
calcified cells, contribute substantially to the vertical export and
burial of the organic material thanks to extremely large
zrem despite their small size (Lam et al., 2011; Iversen
and Ploug, 2010). In the present study we focus on an interval of
zremS and zremL values
that are most likely to resemble the biological pump conditions of the
Neoproterozoic–early Paleozoic ocean, before the evolution of such
phytoplankton types. However, the model allows the exploration of different
ranges of zremS and
zremL values and the tuning of the rate of
coagulation in order to explore the influence of these phytoplankton
classes.
Even though bacterial remineralization is thought to be the dominant
pathway for organic matter recycling on a global scale, especially at
low latitudes (Rivkin and Legendre, 2001), modern ocean coastal
environments are also characterized by high grazing rates. The
evolution of zooplankton and increasingly large grazers may have had
a different impact on the effective zremS and
low zremL, given additional Porg
transformations such as particle fragmentation due to sloppy feeding
(Cavan et al., 2017; Iversen and Poulsen, 2007). These processes can
limit the large-particle burial rates, while resulting in the deep
production of small particles, suspended particulate organic matter (s-POM) and DOM. Our model does not
currently account for particle fragmentation, however the process
could be easily considered in future model developments. In this
context, new processes such as the sedimentation and burial of large
grazers should also be considered.
Sensitivity to parameter choices
We discuss here the model sensitivity to changes in a set of
significant parameters adopted to describe its geometry, circulation
and biological processes. Overall, none of the sensitivity experiments
showed significant changes in the model results and conclusions;
trends in budgets and fluxes obtained varying
zremS and zremL and our main results regarding the relative deep shelf and open
ocean oxygenation remain unchanged.
Among the geometrical box model parameters, a key value is represented
by the percentage of shelf sea area (Pshelf). An increase
(e.g. doubling) in Pshelf results in an overall decrease
in the total budget of P and increase in O due to the larger ratio of
burial to production, which is facilitated by a larger extension of
the surface of shallow water. Interestingly, deep shelf anoxia is
enhanced for larger Pshelf; i.e. anoxia is observed for
a wider range of zremS and
zremL values, while the deep ocean tends to be
more oxygenated. Despite a doubling of Pshelf, however,
model results largely remain in the same range of those found for
modern Pshelf.
We explored the effect of varying the physical circulation parameters.
Changes in upwelling (Upw), have an important impact on the budgets of the modeled ocean. An increase in Upw induces a lowering of P levels,
especially in the deep shelf, due to their recirculation towards the
surface and consequent uptake by production. This is coupled with an
overall larger equilibrium O budget due to higher storage in the deep
open ocean and consequent recirculation into the deep shelf. Deep
shelf suboxia is still possible but for a more limited range of
zremL values. Changes in vertical mixing in
the open ocean (Mixvo) affect the overall P and O budgets
mostly for high zremL. For lower
Mixvo, the O budget decreases due to lower O storage at
depth, while P increases. Changes in vertical mixing on the shelf
(Mixvs), instead, have a minor impact on the total
budgets and fluxes of the model, while locally modulating shelf oxygen and nutrient
concentrations. Lateral mixing fluxes (Mixls,
Mixld) were included in our model for means of
generalization and in order to account for the influence of
non-upwelling margins, with a lower value than in previous studies
(Fennel et al., 2005). Changes in Mixls and
Mixld result in significant changes in the deep ocean
storage of tracers and open ocean production, with little impact on
the budget of the other ocean boxes. However, in this case also, our
main conclusions remain unaffected.
We explored the impact of changing the portion of nutrients delivered
directly to the open ocean, Popen. Even large changes in
this parameter do not significantly affect the results of the model,
indicating that the relative levels of P and O at equilibrium are
determined by the internal physical and biogeochemical dynamics of the
model, rather than by boundary conditions.
Lastly, we explored the model sensitivity to the choice of key
biogeochemical parameters representing rates of transformation. Both
increasing coagulation (cgf) and the use of higher rates
of formation of mineral Ca–P (CaPr) result in a general
increase in O levels and decrease in nutrient availability due to
larger sedimentation and burial rates. However, we find again no
substantial change in the model behavior nor in the relative
contribution to budgets and fluxes of each modeled ocean box.
Furthermore, we have tested the impact of having sediment
remineralization rates that vary with the zrem of the particles,
under the assumption that the liability of small and large particles
may be different. In our experiment, we increased the remineralization
rmr rate linearly with zrem by 40 % of
our baseline value (rmr0), with rmr0
being found at the center of the interval of explored values of
zrem=[0, 450 m]. Under these
conditions, we obtained a higher decoupling between the influence of
zremS and zremL on
budgets and fluxes, both being more strongly driven by the small
particle properties for large values of zremL.
Model applicationsPast changes in the biological pump
The evolution of larger and heavier cells during the Neoproterozoic
and across the Neoproterozoic–Paleozoic transition is hypothesized to
have caused significant changes in the nutrient and redox
state of the ocean (Lenton and Daines, 2018). Our new model can be used to assess
the impact of this evolution in both the shelf and the open ocean. Our
first model results highlight that for small
zremL, i.e. for an early biological pump with
reduced capacity of export and burial, nutrient levels and production
rates are particularly high. At the same time, an increase in
zremS alone, fueling higher remineralization
rates at depth, can induce anoxia in the deep shelf while still
maintaining the deep open ocean substantially oxygenated. The
possibility of a coexistence of an anoxic deep shelf with an
oxygenated deep open ocean has important implications for the
interpretation of deep time redox proxy data, which come almost
exclusively from shelf and slope environments yet have been widely
used to infer deep ocean anoxia for most of the Proterozoic Eon
(Lenton and Daines, 2017). We plan to use our model to further explore
these changes from a time-frame perspective, introducing time-varying
boundary conditions (such as changes in Pin) and parameter
properties.
Phytoplankton evolution as well as the development of heavier and
larger marine organisms continued throughout the Phanerozoic (Katz
et al., 2007). BPOP can also be used to explore the role of the
biological pump in the onset of OAEs in the course of the Mesozoic
Era, likely induced by enhanced productivity due to an upwelling
intensification (Higgins et al., 2012). During the Mesozoic Era, the
evolution of dinoflagellates and calcareous and silica-encased
phytoplankton also likely impacted the export and burial rates in
a significant way (Katz et al., 2004). By extending the range of
explored values of zremS and
zremL or possibly including the effect of
grazing and/or an additional heavy POM class for shelled organisms,
BPOP can also be used to study the consequences of such an evolution.
Future changes in the biological pump
Predicted future changes connected to global warming include, among
others, changes in ocean temperature, pH and stratification
(Gruber et al., 2004), with additional repercussions on plankton
community structure, production, remineralization and export rates
(Laufkötter et al., 2017; Acevedo-Trejos et al., 2014; Kwon et al.,
2009). Our results show that around values of
zremL measured for the modern shelf environment
(Cavan et al., 2017), modeled equilibrium budgets and fluxes are very
sensitive to small changes in zrem. This indicates
a potentially high sensitivity of the modern ocean to small changes in
the biological pump, which may be particularly important in the deep
shelf, where the boundary with suboxia is especially close (Keeling
et al., 2010). Our model can be used to get a first assessment of the
large-scale combined effect of predicted changes in the biological
pump with expected shifts in the physical ocean properties.
Exploring past and future changes in geometry, physics and
biogeochemistry
In the present study we have focused on the impact of changes in
zremS and zremL on the
equilibrium budget and fluxes in the ocean. However, BPOP can be used
to explore the effect of global changes in other physical or
biogeochemical processes coupled with the biological pump
dynamics. Aside from testing the robustness of our results, the
sensitivity tests presented in Sect. 5.1.3 serve also as a first
exploration of the possibility to apply the model to these further
studies. We discuss here a few examples of past changes that could be
explored with the present model.
Through Earth's history, variations in the distribution of continents
and in the mean sea level height likely impacted the percentage of
shelf sea area (Pshelf) throughout the global ocean (Katz
et al., 2007). Changes in climate and therefore in the mean
temperature are expected to have affected both the air–sea gas
exchange of oxygen – Schmidt number NSch(Tmean) – and vertical mixing – Mixvo (Petit et al., 1999). Reduced
vertical mixing in warm periods is also expected to be relevant in the
future because of global warming (Gruber et al., 2004). Changes in
temperature are also known to impact biological activity directly,
e.g. by increasing remineralization rates (rmr)
(Laufkötter et al., 2017), and indirectly, e.g. affecting
production and mortality rates through changes in the mixed layer
depth (Polovina et al., 1995). Climatic shifts can also cause changes
in the intensity of alongshore winds and therefore in the upwelling
circulation (Sydeman et al., 2014). Lastly, the model can be used to
test the impact of changes in the biogeochemical cycles, including
shifts in the Redfield ratio as well as global changes in the P input
(Pin) to the ocean (Reinhard et al., 2017; Filippelli,
2008).
Conclusions and outlook
This paper provides a description, evaluation and discussion of the
new BPOP model. BPOP is aimed at exploring the effects of changes in
the biological pump on the shelf and open ocean nutrient and redox
state as well as on P and O fluxes. This model can be adopted for
a large variety of studies aimed at exploring the impact of changes in
the biological pump, i.e. the particle remineralization length scale
zrem, in past and future ocean settings. Furthermore, it
allows us to couple changes in POM properties with changes in the
geometry, circulation and boundary conditions of the ocean.
Despite its simple representation of the ocean circulation and the
biological pump, the model can reasonably simulate values of the
current P and O tracer budgets and biological pump fluxes. The model
predicts potentially large variations in these P and O budgets and
fluxes for past and future changes in the POM remineralization
length. Our preliminary results also indicate that the early ocean may
have been nutrient rich, with high levels of production and
remineralization and that a suboxic deep shelf setting may have been
compatible with an oxygenated deep open ocean.
We plan to apply this model to study the time evolution of the P and O
budgets in both the shelf and the open ocean environment across the
Neoproterozoic–Phanerozoic transition. Further developments of the
model will be aimed at accounting for successive evolutionary
innovations, including particle fragmentation due to grazing.
The code is available for download in the Supplement of the
present publication, which also includes the user manual.
The supplement related to this article is available online at: https://doi.org/10.5194/gmd-13-1865-2020-supplement.
Author contributions
TL and EL conceived the study. EL conceived and implemented the model. EL
and TL evaluated and improved the model. Both authors contributed to the
interpretation of the results and to the writing of the present paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We would like to thank Richard Boyle for his valuable input and
suggestions. We further acknowledge the precious input of the three referees
and the editor, which substantially improved the model and paper. This
research was funded by NERC in the framework of the project Biosphere
Evolution, Transitions and Resilience (BETR).
Financial support
This research has been supported by the Natural Environment Research Council (grant no. NE/P013651/1).
Review statement
This paper was edited by Andrew Yool and reviewed by Klaus Wallmann and one anonymous referee.
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