The reader should be aware that in the following equations, the conversion
ratios between the different elements (Redfield ratios) have been generally
omitted except when particular parameterizations are defined. All
phytoplankton and zooplankton biomasses are in carbon units
(molCL-1) except for the silicon, chlorophyll and iron content
of phytoplankton, which are respectively in Si, Chl and Fe units
(molSiL-1, gChlL-1, and molFeL-1, respectively).
Finally, all parameters and their standard values in PISCES are listed in
Tables a–e at the end of this section.
Phytoplankton
Nanophytoplankton
∂P∂t=(1-δP)μPP-mPPKm+PP-sh×wPP2-gZ(P)Z-gM(P)M
In this equation, P is the nanophytoplankton biomass, and the five terms on
the right-hand side represent growth, mortality, aggregation and grazing by
micro- and mesozooplankton. The mortality term is modulated by
a hyperbolic function of P to avoid extinction of nanophytoplankton at very
low growth rates.
In PISCES, the growth rate of nanophytoplankton
(μP) can be computed according to two different parameterizations:
μP=μPf1(Lday)f2(zmxl)1-exp-αPθChl,PPARPLday(μref+bresp)LlimP,μP=μPf1(Lday)f2(zmxl)1-exp-αPθChl,PPARPLdayμPLlimPLlimP,
where bresp is a small respiration rate and μref
a reference growth rate, independent of temperature. All other terms in these
equations are defined below. The choice between the two different
formulations is made through a parameter in the namelist
(ln_newprod). When ln_newprod is set to true, which is the
default option of PISCES, Eq. () is used. In the previous
equations, Lday is day length (∈[0,1]).
f1(Lday) expresses the dependency of growth rate to the length
of the day . zmxl is the depth of the
mixed layer and f2(zmxl) imposes an additional reduction of the
growth rate when the mixed layer depth exceeds the euphotic depth:
f1(Lday)=1.5Lday0.5+Lday,Δz=max0,zmxl-zeu,tdark=(Δz)2/86 400,f2(zmxl)=1-tdarktdarkP+tdark,
where zeu is the depth of the euphotic zone defined as the depth
at which there is 1 ‰ of surface PAR. tdarkP is set to 3 days
for nanophytoplankton and 4 days for diatoms, as diatoms generally better cope with
prolonged dark periods. tdark is an estimate of the mean residence time of the phytoplankton cells
within the unlit part of the mixed layer, assuming a vertical diffusion coefficient of
1 m2s-1;
86 400 converts tdark from s-1 to day-1. Figure displays f2(zmxl) as a function of Δz.
Reduction of growth rate when the mixed layer depth
exceeds the euphotic depth for nanophytoplankton (continuous line) and
diatoms (dashed line). Depth corresponds to ΔZ.
![]()
μP is defined as follows :
fP(T)=bPT,μP=μmax0fP(T).
In PISCES, vertical penetration of the photosynthetic available radiation (PAR) is based on
a simplified version of the model by , which is described in .
Visible light is split into three wavebands: blue (400–500 nm), green (500–600 nm) and
red (600–700 nm). For each waveband, the chlorophyll-dependent attenuation coefficients are
fitted to the coefficients computed from the full spectral model of (as
modified in ) assuming the same power-law expression. At the sea surface,
visible light is split equally between the three wavebands. PAR can be a constant or
a variable fraction of the downwelling shortwave radiation, as specified in the namelist (ln_varpar).
PAR1(0)=PAR2(0)=PAR3(0)=ρpar3SWPARP(z)=β1PPAR1(z)+β2PPAR2(z)+β3PPAR3(z)
Light absorption by phytoplankton depends on the waveband and on the species. The normalized
coefficients βi have been computed for each phytoplankton group by averaging and
normalizing, for each waveband, the absorption coefficients published in .
In PISCES, the nutrient limitation terms are defined as follows:
LlimP=minLPO4P,LNP,LFeP,LPO4P=PO4PO4+KPO4P,LNP=LNO3P+LNH4P,LNH4P=KNO3PNH4KNO3PKNH4P+KNH4PNO3+KNO3PNH4,LNO3P=KNH4PNO3KNO3PKNH4P+KNH4PNO3+KNO3PNH4,LFeP=min1,max0,θFe,P-θminFe,PθoptFe,P.
As already stated in the introduction, PISCES is a mixed Monod–quota model.
Thus, N and P limitations are based on a Monod parameterization where
growth depends on the external nutrient concentrations, whereas Fe limitation
is modeled according to a classical quota approach. It should be noted here
that for iron, an optimal quota (θoptFe,P) is used in the denominator which
allows luxury uptake as in the model proposed by .
The choice of the half-saturation constants is rather difficult as
observations show that they can vary by several orders of magnitude
e.g.,. However, in general, these
constants increase with the size of the phytoplankton cell as a consequence
of a smaller surface-to-volume ratio (diffusive hypothesis) .
Thus, diatoms will tend to have larger half-saturation constants than
nanophytoplankton. However, in PISCES, phytoplankton are modeled by only two
compartments, each of them encompassing a large range. Experiments performed
with the model have shown that results are sensitive to the choice of these
half-saturation constants.
Following these remarks, it appeared not appropriate to keep the nutrient
half-saturation constants constant. It was then decided to make them vary with
the phytoplankton biomass of each compartment because the observations show that the
increase in biomass is generally due to the addition of larger size
classes of phytoplankton e.g.,:
P1=minP,Pmax,P2=max0,P-Pmax,KiP=KiP,minP1+SratPP2P1+P2,
where SratP is the size ratio of the larger size class over
the smaller size class. KiP,min is the half-saturation
constant of the smaller size class. This parameterization assumes that
half-saturation constants increase linearly with size . The
size dependence of these constants with cell size is not necessarily linear
but has been suggested to follow a power-law function with an exponent lower
than 1 . However, in a recent review,
found an exponent close to 1 for nitrogen (linear relationship) and larger
than 1 for phosphorus. Thus, considering these uncertainties, we decided to
keep a linear relationship, which remains within the estimated range and
which can also be derived from simple volumetric considerations
(surface-to-volume ratio). The three parameters in this equation
(Pmax, KiP,min, and SratP) can be
independently specified for each phytoplankton group. Finally, observations
also suggest that these half-saturation constants should vary with the mean
nutrient concentrations, probably as an acclimation to the local environment
. This acclimation mechanism is not included in
PISCES, except for the case of silicate (see Sect. ).
The distinction between new production based on nitrate and
regenerated production based on ammonium is computed as follows
:
μNO3P=μPLNO3PLNO3P+LNH4PμNH4P=μPLNH4PLNO3P+LNH4P,
where μNO3P and μNH4P are the uptake rates of nitrate and ammonium, respectively.
The nanophytoplankton aggregation term wP depends on the
shear rate (sh), as the main driver of aggregation is the local
turbulence. This shear rate is set to 1 s-1
in the mixed layer and to 0.01 s-1 below. This means that the
aggregation is reduced by a factor of 100 below the mixed layer.
Diatoms
∂D∂t=(1-δD)μDD-mDDKm+DD-sh×wDD2-gZ(D)Z-gM(D)M
In this equation, D is the nanophytoplankton biomass, and the five terms on
the right-hand side represent growth, mortality, aggregation and grazing by
micro- and mesozooplankton.
As for nanophytoplankton, the absorption coefficients of diatoms depend on the
considered waveband:
PARD=β1DPAR1+β2DPAR2+β3DPAR3.
The production terms for diatoms are defined as for nanophytoplankton,
except that the limitation terms also include Si:
LlimD=minLPO4D,LND,LFeD,LSiD,LSiD=SiSi+KSiD.
As for the other nutrients, the half-saturation factor of silicate can vary significantly over
the ocean. In the tropical and temperate regions, this factor is
around 1 µM, whereas values as high as 88.7 µM have been
measured for Antarctic species . In that case,
rather than an effect of the cell size, these variations are a consequence
of an acclimation of the cells to their local environment. When
plotted against maximum local yearly concentration of silicate,
a crude relationship can be inferred :
KSiD=KSiD,min+7Si˘2(KSi)2+Si˘2,
where Si˘ here is the maximum Si concentration over a year (note that during the first year
of a pluriannual simulation, Si˘ is set to a constant). For the other nutrients,
we use the same parameterization as for nanophytoplankton (see Eq. ).
The diatoms aggregation term wpD is increased in case of
nutrient limitation because it has been shown that diatoms cells tend
to excrete a mucus (exocellular polysaccharides, EPS) which increases their stickiness. As a consequence,
collisions between cells yield to a more efficient aggregation process :
wD=wP+wmaxD(1-LlimD).
Furthermore, as for nanophytoplankton, the aggregation is multiplied by the
shear rate. Enhanced aggregation rates when diatoms are stressed result in a
rapid decline of the diatoms blooms when nutrients become exhausted and
produce strong export events.
Chlorophyll in nanophytoplankton and diatoms
Chlorophyll biomass IChl (where I denotes P or D, typical
units are µg Chl L-1 or mgChlm-3) for
both phytoplankton groups is parameterized using the photo-adaptive model of
:
∂IChl∂t=(1-δI)(12θminChl+(θmaxChl,I-θminChl)ρIChl)μII-mIIKm+IIChl-sh×wIIIChl-θChl,IgZ(I)Z-θChl,IgM(I)M,
where I is the phytoplankton group and θChl,I is the
chlorophyll-to-carbon ratio of the considered phytoplankton class;
12 represents the molar mass of carbon; ρIChl
the ratio of energy assimilated to energy absorbed as defined by
:
ρIChl=144μ˘IIαIIChlPARILday,μ˘I=μPf2(zmxl)1-exp-αIθChl,IPARILdayμPLlimILlimI.
In this equation, 144 is the square of the molar mass of C and is used
to convert from mol to mg, as the standard unit for Chl is generally in
mgChlm-3. It should be noted that for chlorophyll synthesis, the second parameterization of phytoplankton growth
is used to compute μ˘I (see Eq. ). This is necessary because of the expression for ρChlI.
Iron in nanophytoplankton and diatoms
The temporal evolution of the iron biomass of phytoplankton IFe
(model units are mol Fe L-1), where I denotes P or D, is
driven by the following equation
∂IFe∂t=(1-δI)μIFeI-mIIKm+IIFe-sh×wIIIFe-θFe,IgZ(I)Z-θFe,IgM(I)M.
Iron in phytoplankton is modeled in PISCES according to a classical quota approach. However, to be consistent
with chlorophyll and silica, we model the iron biomass of phytoplankton (IFe) rather than the iron quota (θFe,I)
directly. Growth rate of the iron biomass of phytoplankton is parameterized according to
μIFe=θmaxFe,ILlim,1IFeLlim,2IFe1-θFe,IθmaxFe,I1.05-θFe,IθmaxFe,IμP.
As in , iron uptake is also downregulated via a feedback from θFe,I using a normalized
inverse hyperbolic function with a small shape factor set to 0.05.
In the former equation, Llim,1IFe is the iron limitation term and is modeled as follows:
Llim,1IFe=bFebFe+KFeIFe,KFeIFe=KFeIFe,minI1+SratII2I1+I2,I2=max0,I-Imax, I1=I-I2,
where bFe is the concentration of bioavailable iron (see
Sect. ).
The half-saturation constant for iron uptake is also increasing with phytoplankton biomass as for the other
half-saturation constants (see Eq. ).
At low iron concentrations, observations suggest that iron uptake might be enhanced, at least for some species
, giving surge uptake. proposed a parameterization of both this surge
uptake and the downregulation of iron uptake at high iron quota (see above) which has been included in the recent
model of . In PISCES, a different parameterization has been chosen since downregulation
is already included in Eq. ():
Llim,2IFe=4-4.5LFeILFeI+0.5.
Llim,2 equals 4 at very low iron concentrations and 1 at high iron concentration. Overall, the downregulation
in Eq. () together with the surge uptake induced by the previous equation results in a behavior
of the system that is qualitatively equivalent to what results from the parameterization of .
The demands for iron in phytoplankton are for photosynthesis, respiration and nitrate/nitrite reduction.
Following , we assume that the rate of synthesis by the cell of new components requiring iron is given
by the difference between the iron quota and the sum of the iron required by these three sources of demand,
which we defined as the actual minimum iron quota:
θminFe,I=0.001655.85θChl,I+1.21×10-5×1455.85×7.625LNP×1.5+1.15×10-4×1455.85×7.625LNO3P.
In this equation, the first right term corresponds to photosynthesis, the
second term corresponds to respiration and the third term estimates nitrate
and nitrite reduction. The parameters used in this equation are directly
taken from . The modeled iron quota in PISCES varies thus
between this minimum quota θminFe,I and the
maximum quota θmaxFe,I , i.e., between about 1
and 40 µmolFe(molC)-1 when using the standard set of
parameters (see Table ).
Silicon in diatoms
∂DSi∂t=θoptSi,D(1-δD)μDD-θSi,DgM(D)M-θSi,DgZ(D)Z-mDDKm+DDSi-sh×wDDDSi
The elemental ratio Si / C (or Si / N) has been observed to vary by
a factor of about 4 to 5 over the global ocean with a mean value around
0.14±0.13 molmol-1 . Light, N, P, or Fe
stress has been demonstrated to lead to heavier silicification
e.g.,. It has been suggested that
these elevated elemental ratios result from the physiological adaptation of
the silicon uptake by the cell depending on the growth rate and on the G2
cycle phase during which Si is incorporated .
Lighter silicification can only result from silicate limitation.
We model the variations of the Si / C ratio following the
parameterization proposed by Bucciarelli et al. (2002, unpublished
manuscript):
θoptSi,D=θmSi,DLlim,1DSimin5.4,4.4exp-4.23Flim,1DSiFlim,2DSi+11+2Llim,2DSi.
Relative to the original parameterization, an additional limitation
term by Si has been added (Flim,2DSi) to produce
a lighter silicification in case of Si exhaustion.
The different terms in Eq. () are defined as follows:
Flim,1DSi=minμDμPLlimD,LPO4D,LND,LFeD,Flim,2DSi=min1,2.2max0,Llim,1DSi-0.5,Llim,1DSi=SiSi+KSi1,Llim,2DSi=Si3Si3+(KSi2)3ifφ<00ifφ>0,
where φ is the latitude. In the Southern Ocean, observations show
that diatoms are very heavily silicified. After correcting for the potential
effects of iron limitation, silicification in the Southern Ocean is at least
3 times stronger than in the tropical regions, which can only be
explained by the diatoms morphological types . To reproduce
those high Si / C ratios, we have introduced the term
Llim,2DSi which increases the Si / C ratio by
a factor of up to 3 when silicate concentrations are high, a specific
characteristics of the Southern Ocean. This increase is restricted to the
Southern Hemisphere and is controlled by the parameter KSi2.
This parameter is set in the namelist and thus, if it is set to a very high
value, then no increase of Si / C at high silicate concentrations is
predicted by the model.
Zooplankton
Microzooplankton
∂Z∂t=eZgZ(P)+gZ(D)+gZ(POC)Z-gM(Z)M-mZfZ(T)Z2-rZfZ(T)ZKm+Z+3Δ(O2)Z
In this equation, Z is the microzooplankton biomass, and the four terms on the right-hand side represent growth, grazing by
mesozooplankton, quadratic and linear mortalities.
The grazing rate depends on temperature according to a typical exponential relationship similar to
what is used for phytoplankton:
gmZ=gmax0,ZfZ(T),fZ(T)=bZT,
where gmax0,Z is the maximum grazing rate at
0 ∘C, bZ is the temperature dependence and T is the
temperature. In their review, have found a Q10
(Q10=bZ10) between 1.7 and 2.2. Lower temperature dependences
were found in laboratory experiments compared to what as been identified in
the field. In PISCES, we have set Q10 to 2.14 which is not only close to the
value found in the field but also close to the value chosen for
mesozooplankton (see below). All terms driving the temporal evolution of
microzooplankton have been assigned the same temperature dependence.
Mortality is enhanced when oxygen is depleted. In other words,
microzooplankton (but also mesozooplankton, see below) are treated as being
unable to cope with anoxic waters. This increased mortality also avoids
respiration in waters devoid of oxygen.
Grazing on each species I is defined as
F=∑JpJZmax0,J-JthreshZFlim=max0,F-min0.5F,FthreshZgZ(I)=gmZFlimFpIZmax0,I-IthreshZKGZ+∑JpJZJ,
where J denotes all the species microzooplankton can graze upon (P, D and POC) and pJZ
is the preference microzooplankton has for each J. In PISCES, we have chosen a Michaelis–Menten parameterization
with no switching and a threshold (FthreshZ) . This choice is rather arbitrary. Another very
popular formulation in models is the Michaelis–Menten parameterization with active switching introduced by
. However, this parameterization exhibits anomalous dynamics such as sub-optimal feeding .
In our parameterization, a threshold for each individual resource (JthreshZ) can be specified in addition
to the global threshold (FthreshZ). For low food abundance, this global threshold is allowed to slowly
decrease to 0 as a function of the total food level to maintain some grazing pressure, in particular in the ocean
interior.
Responses of zooplankton to quality of their preys have been termed
stoichiometric modulation of predation (SMP) by . A complete
review of the different expected responses has been presented by
. For instance, when confronted with poor food quality,
zooplankton can increase their ingestion rate ,
or decrease it as the food can become deleterious . Accounting
for the complexities of these different types of behavior has not been
implemented within PISCES as this would require a model with flexible
stoichiometry. Additionally, it would require a correct parameterization of
the different potential responses and the apparently contradictory nature of
observed responses implies that this task will be very complicated. In
PISCES, food quality is assumed to only affect gross growth efficiency
(eZ): When food quality becomes poor (either the Fe / C ratio
θFe,I or the N / C ratio θN,I of
the preys decreases), eZ decreases:
eNZ=min1,∑IθN,IgZ(I)θN,C∑IgZ(I),∑IθFe,IgZ(I)θFe,Z∑IgZ(I),eZ=eNZminemaxZ,(1-σZ)∑IθFe,IgZ(I)θFe,Z∑IgZ(I).
When the Fe / C ratio of the ingested preys becomes lower than the
zooplankton Fe / C ratio, the excess carbon (and nutrients) is lost as
dissolved inorganic and organic carbon (and nutrients). This is described in
PISCES by a decrease in the carbon gross growth efficiency
(Eq. b). By construction in PISCES, the N / C quota is
constant, so this quota is estimated by solving the classical Droop equation
assuming that it is at steady state (see above the definition of
θN,I).
Mesozooplankton
∂M∂t=eMgM(P)+gM(D)+gM(POC)+gFFM(GOC)+gFFM(POC)+gM(Z)M-mMfM(T)M2-rMfM(T)MKm+M+3Δ(O2)M
In this equation, M is the mesozooplankton biomass, and the three terms on the right-hand side represent growth,
quadratic and linear mortalities. All terms in this equation have been assigned the
same temperature dependence using a Q10 of 2.14 .
Parameterization of mesozooplankton grazing is similar to microzooplankton.
In addition to the “conventional” concentration-dependent grazing
described by Eq. (), flux feeding is also accounted
for in PISCES. This type of grazing has been shown to be potentially
very important for the fate of particles in the water column below the
euphotic zone . Flux feeding depends on
the flux and thus, on the product of the concentration by the
sinking speed. In PISCES, both the small and the large particles experience this type of grazing:
gFFM(POC)=gFFfM(T)wPOCPOC,gFFM(GOC)=gFFfM(T)wGOCGOC.
This importance of flux feeding has been analyzed in PISCES by
. They have shown that flux feeding is the most important
process that controls the flux of particulate organic carbon below the
surface mixed layer.
In Eq. (), the term with a quadratic dependency
to mesozooplankton does not depict aggregation but grazing by the
higher, non-resolved trophic levels. Following , the upper trophic levels are modeled
assuming an infinite chain of carnivores. This assumption permits one to easily compute the production of fecal pellets
as well as the respiration and excretion by these non-resolved carnivores:
PupM=σMfup(emaxM)mMfM(T)M2,RupM=(1-σM-emaxM)fup(emaxM)mMfM(T)M2,
where function fup(x) is
fup(x)=∑i=0∞xi=11-xfor0<x<1.
It should be noted here that a similar quadratic term is also included in the equation for microzooplankton (see Eq. )
despite the fact that their predators are (at least partially) represented in PISCES. In that case, this term
rather represents other density-dependent mortality factors such as viral diseases. As a consequence, the assumption
of an infinite chain of carnivores is not used for microzooplankton and everything is routed to POC.
DOC
The temporal evolution of DOC is driven by the following equation
∂DOC∂t=(1-γZ)(1-eZ-σZ)∑IgZ(I)Z+(1-γM)(1-eM-σM)∑IgZ(I)+gFFM(GOC)M+δDμDD+δPμPP+λPOC⋆POC+(1-γM)RupM-Remin-Denit-Φ1DOC-Φ2DOC-Φ3DOC,
where I includes P, D and POC for microzooplankton and P, D,
Z and POC for mesozooplankton (see Eqs.
and , respectively). In the following, DOM and DOC will be
used indifferently since the stoichiometric ratios in dissolved organic
matter are assumed constant in PISCES.
Marine DOM has traditionally been divided into several fractions
characterized by their lability. DOM, which recycles over timescales of a few
months to a few years, is called semi-labile DOM .
Transport of this pool of dissolved organic matter can make a significant
part of the carbon pump . As a consequence, this
important pool of DOM is modeled in PISCES. The labile and refractory pools
of DOM are not explicitly modeled.
The degradation of semi-labile DOC is parameterized as follows:
Remin=minO2O2ut,λDOCfP(T)1-Δ(O2)LlimbactBactBactrefDOC,Denit=minNO3rNO3⋆,λDOCfP(T)Δ(O2)LlimbactBactBactrefDOC.
Remineralization of DOC can be either oxic (Remin) or anoxic (Denit) depending on the
local oxygen concentration. The distinction between the two types of
organic matter degradation is performed using a factor Δ(O2)
that varies between 0 and 1 (see Sect. for the
formulation of this factor). It is assumed that the
specific rates of degradation (λDOC) specified for respiration and denitrification are identical.
Depending on the quality of the organic matter, bacteria may take up nutrients from seawater
e.g.,, and thus may be limited by their availability.
Of course, bacterial production is also limited by the abundance of dissolved organic matter. Therefore,
we parameterize the regulation of the degradation of DOM by bacterial activity (Lbact) according to
Lbact=LlimbactLDOCbact,LDOCbact=DOCDOC+KDOC,Llimbact=minLNH4bact,LPO4bact,LFebact,LFebact=bFebFe+KFebact,LPO4bact=PO4PO4+KPO4bact,LNbact=LNO3bact+LNH4bact,LNH4bact=KNO3bactNH4KNO3bactKNH4bact+KNH4bactNO3+KNO3bactNH4,LNO3bact=KNH4bactNO3KNO3bactKNH4bact+KNH4bactNO3+KNO3bactNH4.
The half-saturation constants of the P and N limitation terms (Kibact) are set
in the namelist.
In PISCES, bacterial biomass is not explicitly modeled; Instead, we use the following formulation:
zmax=maxzmxl,zeu,Bact=min0.7(Z+2M,4µmolCL-1)ifz≤zmaxBact(zmax)zmaxz0.683Otherwise.
In the previous equation, 0.7(Z+2M) is a proxy for the bacterial
concentration. This relationship has been constructed from an unpublished version
of PISCES (already mentioned in ) that includes an explicit description of the bacterial
biomass. Below a certain depth (zmax), this biomass decreases with depth
via a power-law function .
In Eq. (), the terms ΦDOC denote aggregation processes and are
described hereafter (see Sect. ). For DOM, we consider
turbulence-induced as well as Brownian aggregation processes.
Φ1DOC=sh×(a1DOC+a2POC)DOCΦ2DOC=sh×a3GOC×DOCΦ3DOC=(a4POC+a5DOC)DOC
Particulate organic matter
PISCES includes two different schemes for particulate organic matter:
A simple model based on two different size classes for particulate organic matter. In that case, particulate organic
matter is modeled in PISCES using two tracers corresponding to the two size classes: POC for the smaller class (1–100 µm) and
GOC for the larger class (100–5000 µm).
A more complex model proposed by in which the size spectrum of
the particulate organic matter can be represented by a power-law function. Here, particulate organic matter is
represented by two variables: the first (POC) is the carbon concentration and the second (NUM) is the total
number of aggregates by unit volume of water.
By default, the simplest parameterization is used. The Kriest model is activated by a cpp key key_kriest.
Two-compartment model of Particulate Organic Matter (POM)
The temporal evolution of POC is written:
∂POC∂t=σZ∑gZ(X)Z+0.5mDDD+KmD+rZfZ(T)ZZ+KmZ+mZfZ(T)Z2+(1-0.5RCaCO3)(mPPP+KmP+wPP2)+λPOC⋆GOC+Φ1DOC+Φ3DOC-gM(POC)+gFFM(POC)M-gZ(POC)Z-λPOC⋆POC-Φ-wPOC∂POC∂z,
where wPOC is the vertical sinking speed. For POC, it is
set to a constant value, in general to a small value on the order of a few
meters per day. The fate of mortality and aggregation of nanophytoplankton
depends on the proportion of the calcifying organisms (RCaCO3).
We assume that 50 % of the organic matter of the calcifiers is
associated with the shell. Since calcite is significantly denser than organic
matter, 50 % of the biomass of the dying calcifiers is routed to the
fast sinking particles. The same is assumed for the mortality of diatoms as
a consequence of the denser density of biogenic silica.
The specific degradation rate λPOC⋆ depends on
temperature with a Q10 of about 1.9, the same as for phytoplankton.
Furthermore, observations generally tend to show slower degradation rates
when waters are anoxic . In , the
attenuation coefficient (b) for the flux was found to be about 0.4 instead
of the standard value 0.86 . This corresponds to a
45 % decrease of the degradation rate in anoxic waters relative to
oxic waters, which is implemented as
λPOC⋆=λPOCfP(T)1-0.45Δ(O2).
POC experiences aggregation due to turbulence and differential settling:
Φ=sh×a6POC2+sh×a7POC×GOC+a8POC×GOC+a9POC2.
In this equation, the first two terms correspond to turbulent aggregation,
and the two last terms to differential settling aggregation. The values of
the parameters controlling these processes have been computed offline
assuming a steady-state power-law size spectrum for particles with an
exponent of 3.6. Subsequently, the different coagulation kernels
e.g., have been integrated over the size ranges
corresponding to the different compartments. A constant stickiness of 0.1 has
been chosen.
The temporal evolution of GOC is written
∂GOC∂t=σM∑IgM(I)+gFFM(POC)+gFFM(GOC)M+rMfM(T)MM+KmM+PupM+0.5RCaCO3mPPP+KmP+wPP2+0.5mDDD+KmDwDD2+Φ+Φ2DOC-gFFM(GOC)M-λPOC⋆GOC-wGOC∂GOC∂z.
The equation controlling the temporal evolution of GOC is similar to
that of POC. However, some observations have shown that the mean
sinking speed of particulate organic matter increases with depth
e.g.,. Such an increase is consistent with the power-law formulation proposed by . Such an increase in the
settling speed is parameterized in PISCES for GOC as follows:
zmax=maxzeu,zmxl,wGOC=wGOCmin+(200-wGOCmin)max0,z-zmax5000.
The parameters in this equation have been adjusted using a model of
aggregation/disaggregation with multiple size classes
. The maximum sinking speed is set to 200 md-1
and is reached at about 5000 m depth over most of the ocean since zmax
is generally less than 100 m. We have not included any ballasting effect due
to the higher density of biogenic silica or calcite
. In fact, observations are rather contradictory
on this ballast effect . In particular, the greater efficiency
of the vertical sedimentation of organic matter when associated with calcite
and biogenic silica may be due rather to the protection of an organic matter
fraction by the inorganic matrix .
Kriest model of particulate organic matter
Here we present a brief overview of the model of . The reader
is referred to the literature, where the method has been presented
e.g.,, for more detail. The model
postulates that the carbon content (m(di)), the sinking speed (w(di))
and the abundance of the aggregates (n(di)) can be described by power-law
functions of their diameters (di):
m(di)=Cdiζ,w(di)=Bdiν,n(di)=Adiϵ.
It is also assumed, as in , that aggregates above a certain
size L have a constant sinking speed wL.
The slope of the size spectrum can be computed from the total number of
aggregates (NUM) and the total mass of particles (POC), which are the
two state variables of the model:
ϵ=(ζ+1)POC-mlNUMPOC-mlNUM,
where ml is the mass of the smallest aggregate (of size l).
Having ϵ, the average sinking speed of numbers (wNUM)
and mass (wPOC) can be computed following :
wPOC=wlζ+1-ϵ+(Ll)1+ν+ζ-ϵν1+ν+ζ-ϵ,wNUM=wl1-ϵ+(Ll)1+ν-ϵν1+ν-ϵ.
The number of particles and the mass of particles change independently. For
instance, sinking tends to remove larger particles. As a consequence, the
relationship between the number of particles and their mass evolves with time
and space and so does ϵ. As a result, the sinking speeds for both
mass and number vary with space and time.
Aggregation (ξ) depends on the particle abundance, their size
distribution, rate of turbulent shear and the difference in particle sinking
speeds as well as the stickiness (the probability that two particles stick
together after contact). The approach implemented in PISCES follows that
described in ; see for the term ξ and its
computation. Currently it is assumed that turbulent shear rate is
high in the mixed layer (1 ms-1), and low below
(0.01 ms-1). Summing up the number of collisions due to
turbulent shear and differential settlement, Csh and
Cds, respectively, the decrease of the number of particles due to
aggregation is then:
ξ=Stick×(Csh+Cds).
In PISCES, the stickiness (the efficiency of the collisions) is set to
a constant value in the namelist.
The temporal evolution of the mass of particles is given as
∂POC∂t=σZ∑gZ(X)Z+σM∑IgM(I)+gFFM(POC)M+mPPP+KmP+wPP2+mDDD+KmD+wDD2+rZfZ(T)ZZ+KmZ+mZfZ(T)Z2+rMfM(T)MM+KmM+PupM-gM(POC)M-gZ(POC)Z-λPOC⋆POC+Φ1DOC+Φ3DOC-gM(POC)+gFFM(POC)M-gZ(POC)Z-λPOC⋆POC-wPOC∂POC∂z.
This is exactly equal to the sum of the two equations used for the temporal evolution of POC
and GOC in the two-compartment model of PISCES (see Eqs. and ).
∂NUM∂t=σZ∑gZ(X)Zm¯Z+σM∑IgM(I)+gFFM(POC)Mm¯M+mPPP+KmP+wPP2m¯P+mDDD+KmD+wDD2m¯D+rZfZ(T)ZZ+KmZ+mZfZ(T)Z2m¯Z+rMfM(T)MM+KmM+PupMm¯M-gM(POC)+gFFM(POC)Mm¯M-gZ(POC)Zm¯Z-λPOC⋆POC+Φ1DOC+Φ3DOCml-ξ-wNUM∂NUM∂z
In this equation, each process affecting the mass of the particles is divided by the mean mass (m¯) of the
compartment exerting this process to convert to numbers.
Iron in particles
In this subsection, the description corresponds to the two-compartment
version of the model. To obtain the Kriest version, the equations for both
SFe and BFe, the iron content of the small and big particles,
respectively, should be simply summed.
∂SFe∂t=σZ∑IθFe,IgZ(I)Z+θFe,Z(rZfZ(T)ZZ+KmZ+mZfZ(T)Z2)+λGOC⋆BFe+θFe,P(1-0.5RCaCO3)(mPPP+KmP+sh×wPP2)+θFe,D0.5mDDD+KmD+λFePOCFe′+Cgfe1-λPOC⋆SFe-θFe,POCΦ-θFe,POCgM(POC)+gFFM(POC)M+κBactSFeBactfe-θFe,POCgZ(POC)-wPOC∂SFe∂z,∂BFe∂t=σM∑IθFe,IgM(I)+θFe,POCgFFM(POC)+θFe,GOCgFFM(GOC)M+θFe,M(rMfM(T)MM+KmM+PupM)+θFe,P0.5RCaCO3(mPPP+KmP+sh×wPP2)+θFe,D(0.5mDDD+KmD+sh×wDD2)+κBactBFeBactfe+λFeGOCFe′+θFe,POCΦ+Cgfe2-θFe,GOCgFFM(GOC)M-λPOC⋆BFe-wGOC∂BFe∂z,
where Fe′ is the free form of dissolved iron. Its determination is
detailed in Sect. . Bactfe is the amount of iron taken
up by bacteria which is lost as particulate organic iron. Its computation is
detailed in Sect. .
The free form of dissolved iron Fe′ is the only form of iron
that is assumed to be susceptible to scavenging. The scavenging rate
of iron is made dependent upon the particulate load of the seawater as
follows e.g.,:
λFe⋆=λFemin+λFe(POC+GOC+CaCO3+BSi)+λFedustDust,Scav=λFe⋆Fe′.
Implicitly, in this equation, it is assumed that the affinity of iron for the
different types of biogenic particles is the same. Iron is also scavenged by
lithogenic particles originating from dust deposition as evidenced by
mesocosm experiments . The concentration of lithogenic
particles is estimated as described in Eq. (). Model estimates
suggest a different affinity for these particles compared to
biogenic particles, which justifies the split between biogenic and lithogenic
materials in Eq. (). The amount of iron that is scavenged by
POC (λFePOCFe′) and
GOC (λFeGOCFe′) is then
allocated to SFe and BFe, respectively.
PSi
∂PSi∂t=θSi,DgM(D)M+θSi,DgZ(D)Z+θSi,DmDDKm+DDSi+sh×wDDDSi-λPSi⋆DissSiPSi-wGOC∂CaCO3∂z
The dissolution rate of PSi depends on in situ temperature and on
silicic acid saturation following the parameterization proposed by :
Sieq=106.44-968T+273.15Sisat=Sieq-SiSieqλPSi⋆=λPSi0.2251+T15Sisat+0.7751+T4004Sisat9.
The evolution of λPSi⋆ as a function of Si and of temperature is shown on
Fig. .
Laboratory experiments show that the diatom frustule is made of two biogenic
silica phases which dissolve simultaneously, but at different rates
e.g.,. The first
phase dissolves significantly faster than the second phase. It is associated
with membrane lipids and amino acids and represents about one-third of the
frustule . However, the existence of these two phases is
still a matter of debate as it has been hypothesized to be a result of the
experimental design of the dissolution experiments . In
PISCES, despite this uncertainty, we model silica dissolution using two
phases. The proportion of the most “labile” phase is set to a constant
(χlab) in the upper ocean and is computed in the rest of the
ocean assuming steady state:
zmax=maxzeu,zmxlχlab=χlab0ifz≤zmaxχlab0exp-λPSilab-λPSirefz-zmaxwGOCOtherwise,λPSi=χlabλPSilab+(1-χlab)λPSiref.
Nutrients
Nitrate and ammonium
∂NO3∂t=Nitrif-μNO3PP-μNO3DD-RNH4λNH4Δ(O2)NH4-RNO3Denit∂NH4∂t=γZ(1-eZ-σZ)∑IgZ(I)Z+γM(1-eM-σM)×∑IgM(I)+gFFM(POC)+gFFM(GOC)M+γMRupM+Remin+Denit+Nfix-Nitrif-λNH4Δ(O2)NH4-μNH4PP-μNH4DD
Nitrification (Nitrif) corresponds to the conversion of ammonium to
nitrate due to bacterial activity. It is assumed to be photo-inhibited
e.g., and reduced in suboxic waters:
Nitrif=λNH4NH41+PAR‾1-Δ(O2),PAR‾=PAR1+PAR2+PAR3‾,
where PAR‾ is the PAR averaged over the mixed layer and Δ(O2) varies
between 0 (oxic conditions, O2>O2min,1) and 1 (anoxia) according to
Δ(O2)=min1,max0,0.4O2min,1-O2O2min,2+O2.
When waters become suboxic, nitrate instead of oxygen is consumed during the
remineralization of organic matter, i.e., denitrification (Denit).
The N / C stoichiometric ratio of denitrification RNO3 can
be computed from R-O2/NO3 and is found to be 0.86
. Equation (), implies that denitrification
stops at oxygen concentration above 6 µM . We
further assume complete oxidation by nitrate of the ammonia released from
organic matter during denitrification. This oxidation rate has been
arbitrarily set to the same value as nitrification rate
(λNH4).
Finally, nitrogen fixation is parameterized in PISCES as follows:
LNDz=0.01ifLNP≥0.81-LNPOtherwise,Nfix=Nfixmmax0,μP-2.15LNDzminbFeKFeDz+bFe,PO4KPO4P,min+PO41-e-PAREfix.
This very crude parameterization is based on the following assumptions that have been inferred from studies
of Trichodesmium e.g.,:
Nitrogen fixation is restricted to warm waters above
20 ∘C (μP>μP(20)=2.15).
Nitrogen fixation is restricted to areas with insufficient
nitrogen (LNP<0.8).
Nitrogen fixation requires iron and phosphorus.
Nitrogen fixation needs high light levels, i.e., Efix is high.
The scaling factor Nfixm is set from the namelist and thus, may be chosen by the user.
Phosphate
∂PO4∂t=γZ(1-eZ-σZ)∑IgZ(I)Z+γM(1-eM-σM)∑IgM(I)+∑IgFFM(I)M+γMRupM+Remin+Denit-μPP-μDD
All terms in this equation have been described previously.
Iron
∂Fe∂t=max0,(1-σZ)∑IθFe,IgZ(I)∑IgZ(I)-eNZθFe,Z∑IgZ(I)Z+max0,(1-σM)∑IθFe,IgM(I)+∑IθFe,IgFFM(I)∑IgM(I)+∑IgFFM(I)-eNMθFe,Z∑IgM(I)+∑IgFFM(I)M+γMθFe,ZRupM+λPOC⋆SFe-(1-δP)μPFeP-(1-δD)μDFeD-Scav-Cgfe1-Cgfe2-Aggfe-Bactfe
Iron scavenging (Scav) has been described previously in
Sect. . Iron is present in seawater largely as colloids
e.g.,. These colloids may aggregate with
dissolved organic matter as it forms gels. Thus, they may be transferred to
the particulate pool, and settle to the ocean floor. Very few models have
incorporated this potential important sink of dissolved iron
. In PISCES, we model this process following the approach
chosen for DOM (see Sect. ):
Cgfe1=(a1DOC+a2POC)×sh+a4POC+a5DOC×Fecoll,Cgfe2=a3GOC×sh×Fecoll,
where Fecoll is computed from the iron chemistry model (see below).
When dissolved iron concentration exceeds the total ligand concentration LT,
scavenging is enhanced as it is done in many other biogeochemical models
e.g.,:
Aggfe=1000λFemax0,Fe-LTFe′.
This scavenging loss term is assumed to be definitive, i.e., iron is permanently removed from the ocean by
this process.
Heterotrophic bacteria acquire iron from seawater using siderophore-based
iron transport systems . Observations show that
they have quite elevated Fe / C ratios and account for a significant
fraction of the total biological uptake of iron .
The bacterial uptake of iron is parameterized according to
Bactfe=μPLlimBactθmaxFe,BactFeKFeB,1+FeBact,
where θmaxFe,Bact denotes the maximum Fe / C
ratio of bacteria.
The different iron pools are computed using a chemistry model. Two different chemistry models are
available in PISCES:
A simple chemistry model based on one ligand (L) and two dissolved iron forms: dissolved
inorganic iron (Fe′) and dissolved complexed iron (FeL).
The complex chemistry model of as modified by .
This model is based on two ligands (LW and LS) and five iron forms: free Fe(II) (Fe(II)′) and
Fe(III) (Fe(III)′), Fe(III) bound to the weak ligand (FeLW), Fe(III) bound to
the strong ligand (FeLS) and solid iron (FeP).
The complex iron model is activated in PISCES setting the Boolean variable ln_fechem to true.
Our main purpose is not to provide a fully detailed description of both
chemistry models as they have been described fairly extensively elsewhere.
For the simple chemistry model, the reader should refer to ,
whereas the complex model is detailed in . For the complex
model, all chemical constants have identical values to what was chosen in
and are thus not listed in
Table a–e. Only a very brief description of
both models will be given here, especially for the complex model. Both models
are based on the assumption that chemical reactions are fast enough relative
to the other biogeochemical processes affecting iron (for instance
phytoplankton uptake) that they can be considered at equilibrium.
Simple chemistry model
Dissolved iron is assumed to be in the form of free inorganic iron
Fe′ and of “complexed” iron FeL. Both forms of iron
are assumed to be equally susceptible to consumption by phytoplankton despite
recent observations suggest that this may be not the case
. In other words, the total bioavailable
concentration of iron is equal to the total dissolved iron concentration
(Fe). The chemical speciation of iron is deduced from the three following
equations
LT=FeL+L′Fe=FeL+Fe′KeqFe=FeLL′Fe′.
The chemical equilibrium constant KeqFe is computed from the
formulation proposed by . Solving this set of equations is equivalent to solve
a second-order polynomial equation in Fe′, whose solution is
Δ=1+KeqFeLT-KeqFeFeFe′=-Δ+Δ2+4KeqFeFe2KeqFe.
Colloidal iron is assumed to represent 50 % of FeL:
Fecoll=0.5FeL.
The total ligand concentration LT can be either constant over
the ocean, using a value defined in the namelist or can be variable using the
relationship proposed by :
LT=max0.09(DOC+40-3,0.6),
where LT is in nmol L-1 and DOC in µmol L-1.
Complex chemistry model
The iron chemical system is governed by the following set of four equations
0=klWFe(III)′LW-kbWFeLW-kphWFeLW-kthFeLW,0=klSFe(III)′LS-kbSFeLS-kphSFeLS,0=kphWFeLW+kphSFeLS+kthFe(III)′-koxFe(II)′,0=kpcpFe(III)′-krFeP.
A supplementary reaction has been added relative to the original set of equations. In the Pacific Ocean, thermal (dark)
reduction of Fe(III) organic complexes has been shown to produce the accumulation of a sizeable amount of
Fe(II)′ in the mesopelagic zone .
Additional constraints are given by the conservation of total dissolved iron (Fe), LWT and
LST over the fast timescale:
Fe=Fe(III)′+Fe(II)′+FeLW+FeLS+FeP,LWT=FeLW+LW,LST=FeLS+LS.
Solving this system of equations is equivalent to solving a third-order
polynomial equation in Fe(III)′ (Eq. 16 in
). Because thermal aphotic reduction of
FeLW has been added here, the definition of some
coefficients in the original study has changed:
b=1+kphW+kthkox,KW=kphW+kth+kbWklW,
where kth has been set to 0.0048 h-1.
Then, knowing Fe(III)′, the other four iron species can be computed.
Observations suggest that the weak ligand (LW) is ubiquitous in
the water column and is probably produced by the degradation of organic
matter sinking from the upper layers of the ocean. The strong ligand is
present in the upper ocean and is most probably produced by autotrophic and
heterotrophic bacteria (for instance siderophores) e.g.,.
In PISCES, we assume that two-thirds of the total ligand concentration above
0.6 nmolL-1 is going to LS, the rest is attributed
to LW:
LWT=0.6+13(LT-0.6),LST=23(LT-0.6).
As in the simple chemistry model, the ligand concentration LT
can be either constant over the ocean, using a value defined in the namelist
or can be variable using the relationship proposed by
(see Eq. ).
The rate constants required by the model are identical to those described by
as modified by . Furthermore, we have
slightly changed the formulation of the oxidation rate constant used in the
original model:
kox=kox′maxO2,1µmolL-1O2sat.
This avoids numerical problems in strongly anoxic areas where oxygen
concentration is close to 0. Bioavailable iron can be defined either as
Fe(II)′+Fe(III)′+FeLS or
as Fe(II)′+Fe(III)′+FeLS+FeLW. kth has assigned the value computed
from the observations by , consistent with the data of
. Colloidal iron and dissolved inorganic iron are defined as
Fecoll=0.5(Fep+FeLW+FeLS),Fe′=Fe(III)′+Fe(II)′.
We assumed that 50 % of the iron bound to ligands and of the particulate inorganic iron is colloidal iron.
Si
∂Si∂t=λPSi⋆DissSiPSi-θoptD,Si(1-δD)μDD
All terms in this equation have been already defined previously.
Calcite
∂CaCO3∂t=PCaCO3-λCaCO3⋆CaCO3-wGOC∂CaCO3∂z
In PISCES, calcium carbonate is assumed to exist only in the form of calcite.
Thus, aragonite is not considered, for instance, for the computation of
chemical dissolution in the water column.
The biological production of sinking calcite is defined as
PCaCO3=RCaCO3ηZgZ(P)Z+ηMgM(P)M+0.5(mPPKm+PP+sh×wPP2).
The rain ratio RCaCO3 is variable. We propose the following parameterization
for this ratio:
RCaCO3=rCaCO3LlimCaCO3T0.1+Tmax1,P2×max0,PAR-14+PAR3030+PAR×1+exp-(T-10)225×min1,50zmxl.
This parameterization is based on a set of very simple assumptions, mainly
inferred from the review by :
Coccolithophores are not very abundant in very oligotrophic waters.
Calcification tends to be maximum at intermediate light levels and decrease at either
high and low light levels, around 30 and 4 Wm-2, respectively.
Coccolithophores are not found when the temperature of sea water is below 0 ∘C.
Coccolithophores are found in stratified waters. Their abundance decreases when the mixed layer depth (zmxl) exceeds 50 m.
Maximum levels of coccolithophores are found in the mid-latitudes, where temperature is
around 10 ∘C.
We recognize that this parameterization is quite ad hoc and may seem
arbitrary. But as it will be shown, it simulates reasonable calcification
patterns and alkalinity distribution (yet we recognize that it could be for
the wrong reasons). Furthermore, it avoids an explicit modeling of the
coccolithophores which is far from being trivial.
Only part (ηI) of the grazed shells are routed to sinking calcite. The rest
is taken to dissolve in the acidic guts of zooplankton
. This dissolution is still debated. However,
observations tend to show that a significant proportion of the sinking
shells is lost in the upper ocean, with this being associated with grazing as well as other
mechanisms .
The dissolution of calcite is modeled as in :
ΔCO32-=max0,1-CO32-CO3,sat2-,λCaCO3⋆=λCaCO3(ΔCO32-)nca.
External supply of nutrients
Nutrients are supplied to the ocean from five different sources: atmospheric
dust deposition, rivers, sea ice, sediment mobilization and hydrothermal
vents.
Atmospheric deposition
The model can include the atmospheric supply of Fe, Si, P and N. The former
three sources (Fe, Si and P) are dependent on each other as they are computed
from the same dust input file. They are activated in PISCES by setting the
Boolean ln_dust to true. Otherwise, no atmospheric source of Fe, P
and Si is prescribed. Furthermore, in that case, the dust concentration in
the ocean (used for instance in Eq. ) is set to 0. The iron
content of dust is set to a constant value specified in the namelist. Its
default value is
3.5 % which is the average content of crustal material
e.g.,. The solubility of dust iron in sea water
can be either set to a constant value in the namelist or can be read from a file if ln_solub
is set to true. Once it has left the
surface layer, particulate inorganic iron from dust is still assumed to
experience dissolution. The dissolution rate is computed assuming
that mineral particles sink at a constant speed specified in the
namelist and that about 0.01 % of the particulate iron dissolves in a day . This is
equivalent to a remineralization length scale of 20 000 m if the sinking speed is set to a typical value of
2 mday-1, on the same order as the length scale prescribed for the same process by
. Atmospheric deposition of Si is also considered following
and is restricted to the first layer of the model. Atmospheric deposition
of P is computed from dust deposition assuming that the total phosphorus content of dust
is 750 ppm and that the solubility in surface sea water is
10 % . As for Si, deposition is restricted to the first level
of the ocean model. Atmospheric deposition of N is treated separately from the deposition of the other nutrients
and can be activated in the model by the Boolean ln_ndepo. All nitrogen deposited at the
ocean surface is assumed to dissolve. We made the quite strong assumption for all nutrients that sea ice does not alter the
deposition fluxes.
The dust (Dust) concentration in the ocean is modeled in a very
simplistic way in PISCES. It is computed from dust deposition assuming
a constant sinking speed (the same as the sinking speed used to compute iron
dissolution from dust in the interior of the ocean). Furthermore, dust is not
transported by the ocean currents. This assumption is made in PISCES to avoid
adding another prognostic tracer in the model. As a consequence, the
concentration of dust is computed as
Dust=Ddustwdust,
where Ddust is dust deposition at the surface and wdust is the prescribed sinking
speed of dust.
River discharge
River discharge is activated by setting the Boolean variable ln_river to
true in the namelist. The river discharge of the different elements is then
read from a file that must be provided in that case by the user. The river
supply of DIN, DIP, DON, DOP, Si, DIC, alkalinity and DOC need
to be provided. As DON, DOC and DOP are not separately modeled in
PISCES (fixed stoichiometry), dissolved organic matter is assumed to
remineralize instantaneously at the river mouth and thus, DON, DOP and
DIC are added to DIN, DIP and DIC, respectively. As a default
in PISCES, river supply of all elements but DIC and alkalinity is
taken from the GLOBAL-NEWS2 data sets . For DIC and
alkalinity, we use results from the Global Erosion Model (GEM) of
, neglecting the POC delivery as most of it is lost in
the estuaries and in the coastal zone . All fields are
interpolated onto the ORCA grid and co-localized with the river runoff
prescribed in the physical model. Iron is also delivered to the ocean by
rivers. The amount of supplied iron is computed from the river supply of
inorganic carbon, assuming a constant Fe / DIC ratio. This ratio
is determined so that the total Fe supply equals 1.45 TgFeyr-1
as estimated by .
Reductive mobilization of iron from marine sediments
Reductive mobilization of iron from marine sediments have been
recognized as a significant source to the ocean
. Fe concentrations in the sediment
pore waters are often several orders of magnitude larger than in the
seawater. A large part of the iron released to the ocean either by
diffusion or by resuspension is likely to be oxidized in insoluble
forms and trapped back to the sediments, at least in oxygenated waters
. Yet, some of this iron should escape as observations
clearly show increasing concentration gradients of particulate and
dissolved iron toward the coastal zones. Unfortunately, almost no
quantitative information is available to parameterize this potentially
important source. Observations from benthic chambers indicate that this source
may be controlled by the oxygen concentrations overlying the sediments and
perhaps the magnitude of the organic carbon export to the sediments . Such
potential relationships are not yet embedded in PISCES.
In a way similar to , we apply a maximum constant iron
source from the sediments. Since anoxic sediments are more likely to
release iron to the seawater, we have modulated this source by
a factor (Fsed) computed from the metamodel of :
zFsed=min8,z500m-1.5,ζFsed=-0.9543+0.7662ln(zFsed)-0.235ln(zFsed)2,Fsed=min1,exp(ζFsed)/0.5.
From this metamodel, it is possible to estimate the relative contribution of
anaerobic processes to the total mineralization of organic matter in
the sediments, and thus to have an indication on how well the sediment
is oxygenated . Our modulation factor is simply set
equal to this relative contribution. The maximum iron flux from the
sediments has been set by default to 2 µmolFem-2d-1 by adjusting
the modeled iron distribution to the few iron observations available
over the continental margins. This value is identical to that used by
in their model. The maximum
iron flux constant can be specified in the namelist and thus, may be changed from the
default value by the user.
Unfortunately, as a consequence of the relatively coarse resolution of ORCA2, the model
bathymetry is not able to correctly represent the critical spatial
scales of the ocean bathymetry. An example is the continental
shelves, which typically have a width scale of 10–30 km, which can be
approximately an order of magnitude less than the horizontal
resolution of the model. In order to take sub-model grid scale
bathymetric variations into account in the Fe source function, the
model grid structure has been compared with the high-resolution ETOPO5
data set. An algorithm was developed whereby for each and every
horizontal grid cell, the corresponding region in the ETOPO5 data set
is considered. For each vertical level in the model corresponding to
a particular horizontal grid point, the corresponding ocean-bottom area
from ETOPO5 (in fractional units) is saved, with the end result being
a three-dimensional array containing an equivalent area for the bottom
bathymetry of the ocean for the ETOPO5 data set. The iron flux
computed as described above is then multiplied by this fractional area %sed (which varies
between 0 and 1):
FFesed=FFe,maxsed×Fsed×%sed.
This corresponds to a global flux
of 34 Gmol Fe yr-1.
Iron from hydrothermalism
Recent studies have shown that hydrothermalism may deliver to the deep ocean
a significant amount of dissolved iron
e.g.,. Despite very large
uncertainties, this source has been estimated, based on discrete data and
a model, to 3 to 9×108 mol Fe yr-1 globally
. In PISCES, this source is included following
the modeling study by and may be activated by setting the
Boolean ln_hydrofe to true. The hydrothermal flux of iron has been
computed based on observed correlations between 3He and dFe
and using a data compilation of dFe / 3He (see
the Supplement of ). Then, the spatial distribution of
this flux has been derived from previous modeling works on 3He, which
relate the 3He flux to the ridge-spreading rates ;
0.2 % of the delivered iron is assumed to be soluble.
θoptSi,D as a function of
Si concentration
and Flim,1DSi. The vertical axis corresponds to log(Si).
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Iron from sea ice
The last external source of nutrients which is taken into account in PISCES
is the exchange of iron between the ocean and the sea ice associated with
formation and melting. This source is activated by setting the Boolean
variable ln_ironice to true. The receding ice edge is often
characterized by intense phytoplankton abundance which can be explained by
ocean stratification promoted by the melting of sea ice as
well as the releases of iron accumulated in sea ice during winter
. Measurements
in sea ice have found iron concentrations of more than 1 order of magnitude
higher than in adjacent sea water . About 90 % of this
iron has been shown to be of oceanic origin . Thus, iron is taken up
from sea water when ice forms and is released back to the ocean when it melts.
have studied the impact of this source in the Southern Ocean and shown that it is of primary importance
in the seasonal ice zone. Their approach relies on the modeling of iron concentration within sea ice.
In PISCES, we have simplified this model by assuming that iron concentration in sea ice is constant.
In that case, the iron fluxes between the ocean and the sea ice can be computed from the
water fluxes between these two reservoirs:
FFeice,-=min0,-EPoi×Fe,FFeice,+=max0,-EPoi×Feice,FFeice=FFeice,-+Ficeice,+,
where EPoi is the water flux (in kg m-2s-1) from the ice to the ocean and
Feice is the iron concentration in sea ice which has been found to be on the order of 10 nmolL-1.
In this equation, FFeice,- is thus the loss of iron from the ocean when sea ice forms and
FFeice,+ is the release of iron to ocean when sea ice melts. It should be noted here that since
we do not model iron in sea ice, the exchange of iron between both reservoirs is not conservative. In the model configuration
presented here, ice represents a net source of iron of 0.024 Gmol Fe yr-1.
Dissolution rate of PSI
(λPSi⋆)
normalized to its value at 0 ∘C with no silicate. Temperature is in ∘C.
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Bottom boundary conditions
At the bottom of the ocean, the exchange between the sediments and the ocean
can be represented either with or without a sediment model. The sediment
model is activated by using the cpp key key_sed. This model will
not be described in this document. It is basically identical to the model of
with some modifications as described by .
The main modification is the addition of denitrification to the set of early
diagenetic reactions. Parameter values are identical to those in
.
When the sediment model is not activated, very basic but different treatments
are applied at the bottom of the ocean depending on the tracer considered.
For biogenic silica, the amount of particulate material that is permanently
buried in the sediments is assumed to exactly balance the external input from
dust deposition and river discharge, described in the previous section. Then,
we assume that the part of biogenic silica that is not permanently buried
redissolves back to the water column instantaneously.
For particulate organic carbon, we first determine the proportion of organic
matter reaching the seafloor that is permanently buried. The burial
efficiency is computed using the algorithm proposed by :
Eburial=0.013+0.53FOC2(7.0+FOC)2,
where Eburial is the burial efficiency and FOC is the
flux of organic carbon at the bottom (in mmol C m-2d-1). We
then use the metamodel by to determine the proportion of
degradation of the remaining organic matter that is due to denitrification:
log(Pdenit)=-2.2567-1.185log(FOC)-0.221log(FOC)2-0.3995log(NO3)log(O2)+1.25log(NO3)+0.4721log(O2)-0.0996log(z)+0.4256log(FOC)log(O2),
where the tracer concentrations are in µmol L-1 and
FOC is the flux of organic carbon at the bottom (in µmol cm-2d-1). In this equation, oxygen and nitrate
concentrations are not allowed to be below 10 µmol L-1
and 1 µmol L-1, respectively. Then, the fluxes of
nitrate and oxygen to the sediment as a consequence of denitrification and
oxic degradation, respectively, can be computed:
FNO3denit=RNO3PdenitFOC,FO2oxic=O2ut(1-Pdenit)FOC.
Particulate organic carbon which has been degraded by denitrification and
oxic processes is released in the bottom box as ammonium.
A specific treatment of calcite at the sediment interface is embedded in PISCES. The preservation of
calcite in the sediments is represented as a function of the saturation level
of the overlying waters:
%CaCO3=min1,1.30.2-Ω0.4-Ω,
where Ω is the calcite saturation level. This relationship has been deduced from the study
by . The permanent burial of calcite is modulated by %CaCO3. The amount of
calcite that is not buried, instantaneously dissolves back to the ocean.
Boolean variables in the namelist. These variables activate
functionalities of PISCES.
Boolean name
Description
ln_co2int
Read atmospheric pco2 from a file (T) or constant (F)
ln_presatm
Constant atmospheric pressure (F) or from a file (T)
ln_varpar
PAR made a variable fraction of shortwave (T) or not (F)
ln_newprod
Use Eq. () (T) or Eq. () for phytoplankton growth
ln_dust
Dust input from the atmosphere (T)
ln_solub
Variable solubility of iron in dust (T)
ln_river
River discharge of nutrient (T)
ln_ironsed
Sedimentary source of iron (T)
ln_ironice
iron input from sea ice (T)
ln_hydrofe
iron input from hydrothermalism (T)
ln_pisdmp
Relaxation of some tracers to a mean value (T) *
ln_check_mass
Check mass conservation (T)
* The frequency at which the restoring technique is applied is specified by the parameter nn_pisdmp.