We describe the third version of Minnesota Earth System Model for Ocean
biogeochemistry (MESMO 3), an Earth system model of intermediate complexity,
with a dynamical ocean, dynamic–thermodynamic sea ice, and an energy–moisture-balanced atmosphere. A major feature of version 3 is the flexible
C:N:P ratio for the three phytoplankton functional types represented in the
model. The flexible stoichiometry is based on the power law formulation with
environmental dependence on phosphate, nitrate, temperature, and light.
Other new features include nitrogen fixation, water column denitrification,
oxygen and temperature-dependent organic matter remineralization, and
CaCO3 production based on the concept of the residual nitrate potential
growth. In addition, we describe the semi-labile and refractory dissolved organic
pools of C, N, P, and Fe that can be enabled in MESMO 3 as an optional
feature. The refractory dissolved organic matter can be degraded by
photodegradation at the surface and hydrothermal vent degradation at the
bottom. These improvements provide a basis for using MESMO 3 in further
investigations of the global marine carbon cycle to changes in the
environmental conditions of the past, present, and future.
Introduction
Here we document the development of the third version of the Minnesota Earth
System Model for Ocean biogeochemistry (MESMO 3). As described for the first
two versions
(Matsumoto
et al., 2008, 2013), MESMO is based on the non-modular version of the Grid
ENabled Integrated Earth (GENIE) system model
(Lenton
et al., 2006; Ridgwell et al., 2007). The computationally efficient
ocean–climate model of Edwards and Marsh (Edwards
and Marsh, 2005) forms the core of GENIE's physical model. MESMO is an Earth
system model of intermediate complexity (EMIC), which occupies a midpoint in
the continuum of climate models that span high-resolution, comprehensive
coupled models on one end and box models on the other
(Claussen et al., 2002).
MESMO has a 3D dynamical ocean model on a 36 × 36 equal-area horizontal grid
with 10∘ increments in longitude and uniform in the sine of
latitude. There are 16 vertical levels. It is coupled to a 2D energy
moisture-balanced model of the atmosphere and a 2D dynamic and thermodynamic
model of sea ice. Thus, MESMO retains important dynamics that allow for
simulations of transient climate change, while still being computationally
efficient.
Since the first version, MESMO has continued to be developed chiefly for
investigations of ocean biogeochemistry (Table 1). Briefly, in MESMO 1 the
main improvements over the predecessor GENIE focused on the biological
production and remineralization, as well as on the uptake of natural
radiocarbon (14C) and anthropogenic transient tracers
(Matsumoto et al., 2008).
The net primary production (NPP) in MESMO 1 occurred in the top two vertical
levels, representing the surface 100 m, and depended on temperature,
nutrients, light, and mixed-layer depth (MLD). The nutrient dependence was
based on the Michaelis–Menten uptake kinetics of phosphate (PO4),
nitrate (NO3), and aqueous CO2. The limiting nutrient was
determined by Liebig's rule of the minimum relative to the fixed uptake
stoichiometry of C:N:P=117:16:1. A single generic phytoplankton functional
type (PFT) carried out NPP, which was split between particulate organic
matter (POM) and dissolved organic matter (DOM) in a globally constant ratio
of 1:2. The semi-labile form of the dissolved organic carbon (DOC) was the
only form of DOM simulated in MESMO 1. The POM flux across the 100 m level
defined the export production. The vertical flux of POM was driven by a
fixed rate of sinking and a temperature-dependent, variable remineralization
rate.
Summary of MESMO development.
Model (run ID)Biogeochemical featuresPhysical featuresMESMO 33 PFTs: Eu, Cy, and Dz(210310d)Uptake C:N:P=f(PO4, NO3, T, PAR) by power lawN cycle (N fixation, denitrification)OM remineralization=f(O2, T)CaCO3 production by EuRNPG: competition w/in single Eu PFTfDOM =f(T)Optional: alternative uptake C:N:P by cell quotaOptional: DOC, DOP, DON, DOFe (semi-labile)Optional: DOCr, DOPr, DONr (refractory)MESMO 2Nutrients = PO4, NO3, CO2, Fe, SiSeasonal winds(120531a)2 PFTs: LG, SMSi cycle (Si, 30Si)Fe cycle (Fe′, FeL)Uptake C:Fe=f(FeT)Uptake Si:N=f(FeT) by LGCaCO3 production by SMMESMO 1Jprod= (PAR, nutrients, T, MLD)16 vertical levels(090309a)Nutrients = PO4, NO3, CO2(aq)Arctangent Kv(z)DOC (semi-labile)Seasonal PARfDOM = 0.67
PFT stands for phytoplankton functional types. MESMO 2 PFTs are as follows: LG stands for large (diatoms) and
SM stands for small. MESMO 3 PFTs are as follows: Eu stands for eukaryotes, Cy stands for cyanobacteria, and
Dz stands for diazotrophs. OM stands for organic matter. RNPG stands for residual nitrate potential
growth. T stands for temperature. PAR stands for photosynthetically available radiation.
fDOM stands for the fraction of NPP routed to dissolved organic matter (DOM). The two
types of DOM are semi-labile (DOC, DOP, DON, and DOFe) and refractory (DOCr,
DOPr, and DONr). Carbon isotopes (12C, 13C, and 14C) are
calculated separately for DOC and DOCr. The run ID is 210310m for the MESMO
3 experiment LVR and 210310o for the experiment LVR with
fDOMr=0.2 %.
The main aim of MESMO 2 was a credible representation of the marine silica
cycle (Matsumoto et al., 2013). To this end,
the set of limiting nutrients (P, N, and C) in MESMO 1 was augmented to
include iron (Fe) and silicic acid (Si(OH)4) in MESMO 2 (Table 1). The
stable isotope of Si (30Si) was also added as a state variable. The Fe
cycle included an aeolian flux of Fe, complexation with organic ligand, and
particle scavenging of free Fe. The scavenged Fe that reached the seafloor
was removed from the model domain. This burial flux of Fe balanced the
aeolian flux at steady state. In addition, a new PFT was added in MESMO 2 chiefly to
represent diatoms. This new “large” PFT was limited by Si and
characterized by a high maximum growth rate and large half-saturation
constants for the nutrient uptake kinetics. It represented fast and
opportunistic phytoplankton that do well under nutrient replete conditions.
In comparison, the “small” PFT was characterized by a lower maximum
growth rate and smaller half-saturation constants and outperformed the large
PFT in oligotrophic subtropical gyres. CaCO3 production was associated
with the “small” PFT in MESMO 2. The addition of Fe, Si, and the large PFT in
MESMO 2 allowed it to have a Fe-dependent, variable Si:N uptake ratio
(Hutchins and Bruland, 1998; Takeda, 1998), which is
critical for simulating important features of the global ocean Si distribution.
MESMO 1 and 2 were assessed and calibrated by multi-objective tuning and
extensive model–data comparisons of transient tracers (anthropogenic carbon,
CFCs), deep ocean Δ14C, and nutrients
(Matsumoto
et al., 2008, 2013). These versions have been employed successfully in a
number of studies of global distributions of carbon and carbon isotopes
under various conditions of the past, present, and future
(Cheng
et al., 2018; Lee et al., 2011; Matsumoto et al., 2010, 2020; Matsumoto and
McNeil, 2012; Matsumoto and Yokoyama, 2013; Sun and Matsumoto, 2010; Tanioka
and Matsumoto, 2017; Ushie and Matsumoto, 2012). In addition, MESMO 1 and 2 have
participated in model intercomparison projects
(Archer
et al., 2009; Cao et al., 2009; Eby et al., 2013; Joos et al., 2013; Weaver
et al., 2012; Zickfeld et al., 2013).
In this contribution, we describe the third and latest version of MESMO with
a number of substantial biogeochemical model modifications and new features
that bring MESMO up to date with the evolving and accumulating knowledge of
the ocean biogeochemical cycle (Table 1). There is no change in the physical
model between MESMO 3 and MESMO 2. The most significant new feature of MESMO
3 over the previous versions is the power law formulation of flexible
phytoplankton C:N:P ratio. Other new features include additional PFT
diazotrophs that carry out N fixation, water column denitrification, the
dependence of organic matter remineralization on the dissolved oxygen
(O2) and temperature, and CaCO3 production based on the concept of
the residual nitrate potential growth. In addition, we describe the semi-labile DOM
for P, N, and Fe (DOPsl, DONsl, and DOFesl) and the
refractory DOM for C, P, and N (DOCr, DOPr, and DONr), which
can be activated as an optional feature in MESMO 3. Some of these features
have been described separately in different publications
(Matsumoto et al., 2020; Matsumoto
and Tanioka, 2020; Tanioka and Matsumoto, 2017, 2020a). This work
consolidates the descriptions of all these features in a single publication.
Model description
Here we present the full set of biogeochemical equations of MESMO 3 and the key model parameters (Table 2). We describe only the biogeochemical
source and sink terms and omit the physical (advective and diffusive)
transport terms that are calculated by the ocean circulation model. We
discuss the production terms first, followed by remineralization terms,
and finally the conservation equations that incorporate both terms.
MESMO 3 biogeochemical model parameters values: (a) phytoplankton nutrient uptake; (b) power law model of flexible C:N:P stoichiometry;
(c) iron uptake stoichiometry; (d) parameters related to POM, DOM, CaCO3, and opal; (e) nitrogen and iron cycles.
(a)ParameterDescriptionUnitMESMO 2MESMO 3LP/Eukaryotes τOptimal uptakeyr-10.010.002KPO4PO4 half-saturation constµmol kg-10.390.120KNO3NO3 half-saturation constµmol kg-15.002.0KCO2CO2 (aq) half-saturation constµmol kg-10.9250.925KFeFeT half-saturation constnmol kg-10.100.30KSi(OH)4Si(OH)4 half-saturation constµmol kg-11.01.0SM/Cyanobacteria τOptimal uptakeyr-10.160.04KPO4PO4 half-saturation constµmol kg-10.030.012KNO3NO3 half-saturation constµmol kg-10.500.4KCO2CO2 (aq) half-saturation constµmol kg-10.0750.075KFeFeT half-saturation constnmol kg-10.010.008Diazotrophs τOptimal uptakeyr-1–0.2KPO4PO4 half-saturation constµmol kg-1–0.300KCO2CO2 (aq) half-saturation constµmol kg-1–0.075KFeFeT half-saturation constnmol kg-1–0.030(b)*ParameterDescriptionUnitMESMO 2MESMO 3[PO4]0Reference [PO4]µmol kg-1–0.57[NO3]0Reference [NO3]µmol kg-1–5.7T0Reference temperature∘K–291I0Reference light levelW m-2–70Eukaryotes [P:C]0Reference P:C molar ratio‰–11.6[N:C]0Reference N:C molar ratio‰–151.0sPO4P:CSensitivity of P:C to [PO4]––0.58sNO3N:CSensitivity of N:C to [NO3]––0.22sIN:CSensitivity of N:C to light––-0.05Cyanobacteria [P:C]0Reference P:C molar ratio‰–6.3[N:C]0Reference N:C molar ratio‰–151.0sPO4P:CSensitivity of P:C to [PO4]––0.28sNO3N:CSensitivity of N:C to [NO3]––0.22sTP:CSensitivity of P:C to temperature––-8.0sIN:CSensitivity of N:C to light––-0.05Diazotrophs [P:C]0Reference P:C molar ratio‰–6.3[N:C]0Reference N:C molar ratio‰–151.0sPO4P:CSensitivity of P:C to [PO4]––0.28sTP:CSensitivity of P:C to temperature––-8.0sIN:CSensitivity of N:C to light––-0.05
* Sensitivity factors not listed in Table 2b have a value of zero (e.g.,
sPO4N:C=0; thus, the environmental driver PO4 does not drive
the N:C ratio). The reference ratios are in ‰ so that
[P:C]0=11.6 ‰ (i.e., C:P= 86.2) for eukaryotes,
and [P:C]0= 6.3 ‰ (i.e., C:P= 158.7) for
cyanobacteria and diazotrophs. The reference ratio
[N:C]0= 151.0 ‰ for all PFTs (i.e., C:N:=106:16) is the Redfield ratio.
Phytoplankton nutrient uptake
NPP occurs in the top two vertical levels of the ocean domain above the
fixed compensation depth (zc) of 100 m. Key parameter values are given
in Table 2a. Nutrient uptake by phytoplankton type i (Γi) depends on the optimal nutrient uptake timescale (τi), nutrients, temperature (T), irradiance (I), and mixed-layer depth
(zml):
Γi=1τi⋅FN,i⋅FT⋅FI⋅max1,zczml.
Subscript i refers to PFT (i=1: eukaryotes; i=2: cyanobacteria; i=3: diazotrophs). The nutrient dependence FN,i is given by Liebig's law
of minimum combined with Michaelis–Menten uptake kinetics of limiting
nutrients: PO4, NO3, CO2 (aq), total dissolved iron (sum of
free iron and ligand-bound iron: FeT= Fe′+FeL), and Si(OH)4:
FN,i=minPO4PO4+KPO4,i⋅PO4,NO3NO3+KNO3,i⋅NO3⋅QN,i-1,CO2aqCO2aq+KCO2,i⋅CO2aq⋅QC,i-1,FeTFeT+KFeT,i⋅FeT⋅QFe,i-1,SiOH4SiOH4+KSiOH4⋅SiOH4⋅QSi-1,
where KX,i is the half-saturation concentration of nutrient X for PFT
i. Only eukaryotes (i=1) are limited by Si(OH)4. Diazotrophs (i=3) are not limited by NO3. Nutrient uptake Γ is based
on the master nutrient variable P, and all other nutrient uptake is related
to Γ by the uptake stoichiometry
QX,i, where X is N, Fe, Si, or C. For example,
QC,i=1P:Ci for PFT i. Thus, QC,i is numerically equivalent
to C:P for PFT i, but we write the equations in terms of P:C for numerical
stability and convenience. The QX,i ratios represent
the flexible phytoplankton uptake stoichiometry and are described more fully in Sect. 2.2.
The temperature dependence FT of Eq. (1) is
given by
FT=T∘C+2T∘C+10,
which is analogous to the commonly used Q10=2 relationship. Light
limitation FI of Eq. (1) is described by a
hyperbolic function:
FT=II+20,
where I is the seasonally variable solar short-wave irradiance in W m-2. Light is attenuated exponentially from the ocean surface with a 20 m depth scale.
Nutrient uptake in Eq. (1) has a dependence on
zml, which is diagnosed using the σt density gradient
criterion (Levitus, 1982). Following the Sverdrup (1953) model of the spring bloom, Eq. (1) allows for the
shoaling of zml relative to zc to enhance nutrient uptake.
Phytoplankton uptake stoichiometry
As noted above, all nutrients and O2 are related to the main model
currency P by QX,i. We describe three different,
mutually exclusive formulations in this section. The standard formulation is
the power law model (Matsumoto et al., 2020;
Tanioka and Matsumoto, 2017). The other two (linear model and
optimality-based model of stoichiometry) are alternative formulations that
have been coded, and the user can activate them (one at a time) in place of
the power law formulation. However, the alternative formulations are not
calibrated. Key parameter values are given in Table 2b for the power law
formulation.
Power law model of stoichiometry
The uptake P:C and N:C ratios are calculated using the power law formulation
as a function of ambient concentrations of phosphate [PO4], nitrate
[NO3], temperature (T), and irradiance (I).
5P:Ci=P:C0,i⋅PO4PO40sPO4,iP:C⋅NO3NO30sNO3,iP:C⋅TT0sT,iP:C⋅II0sI,iP:C6N:Ci=N:C0,i⋅PO4PO40sPO4,iN:C⋅NO3NO30sNO3,iN:C⋅TT0sT,iN:C⋅II0sI,iN:C
Equations (5) and (6) are the
power law equations that calculate the change in P:C and N:C for fractional
changes in environmental drivers relative to the reference P:C and N:C,
respectively (Matsumoto et al., 2020;
Tanioka and Matsumoto, 2017). The exponents are the sensitivity factors
determined by a meta-analysis (Tanioka and Matsumoto, 2020a).
Subscript “0” indicates the reference values (Table 2b). We have hard bounds
for the calculated P:C and N:C ratios to be within 26.6 <C:P< 546.7 and 2 <C:N< 30 as observed
(Martiny et al., 2013).
The P:C and N:C ratios from Eqs. (5) and
(6) can then be converted to
QN,i and QC,i for use in
Eq. (2).
7QC,i=1P:Ci8QN,i=1P:Ni=N:CiP:Ci
Linear model of stoichiometry by Galbraith and Martiny
A much simpler, alternative formulation for P:C and N:C is the model of
Galbraith and Martiny (2015), where P:C is a
linear function of [PO4] (in µM) and N:C is a Holling type 2
functional form with a frugality behavior only at very low [NO3] (in
µM). The same P:C and N:C values are applied to all three PFTs.
9P:C=6.9⋅PO4+6.0100010N:C=0.125+0.03⋅NO30.32+NO3
Optimality-based model of stoichiometry
The optimality-based model of phytoplankton growth is based on the chain
model, which connects the cellular P, N, and C acquisition via a chain of
limitations, where the P quota limits N assimilation and the N quota drives
carbon fixation
(Pahlow et
al., 2013; Pahlow and Oschlies, 2009, 2013). Resource allocations of cellular
P, N, and C among different cellular compartments are derived from balancing
energy gain from gross carbon fixation and energy loss due to nutrient
acquisition and light harvesting. The optimality-based model by Pahlow et
al. (2013) computes C:N and C:P as a function of nutrient availability
(PO4 and NO3), irradiance, and day length. Temperature dependence
was added by Arteaga et al. (2014)
following the simple logarithmic temperature dependence on maximum nutrient
uptake rate of Eppley (1972).
Different versions of this optimality-based model have previously been
successfully implemented in global ocean biogeochemical models, such as the
Pelagic Interactions Scheme for Carbon and Ecosystem Studies (PISCES)
(Kwiatkowski
et al., 2018, 2019) and the University of Victoria Earth System Model (UVic)
(Chien
et al., 2020; Pahlow et al., 2020). However, as we are not describing any
results in this paper, we will only mention here that there is an option to
calculate C:N:P using this stoichiometry model in MESMO 3. The full
description of the optimality-based stoichiometry model and its parameter
calibration is presented specifically for the UVic model elsewhere
(Chien
et al., 2020; Pahlow et al., 2020).
Stoichiometry of iron and silica
Iron uptake stoichiometry QFe,i is calculated as a
function of FeT following the power law formulation of
Ridgwell (2001). Key parameter values are given in
Table 2c.
11QFe,i=Fe:Pi=Fe:Ci⋅QC,i12Fe:Ci=1.0/(C:Femin,i+C:Feref,i⋅FeT-sFe:Ci)
For all PFTs, the power law exponent sFe:C in Eq. (12) is -0.65. The allowable Fe:C ratio is bounded at
the low end by the hard-bound minimum Fe:C of 1:220 000. The scaling
constant or [C:Fe]ref,i is set differently for PFTs, with eukaryotes
having a higher base [C:Fe]ref,i than cyanobacteria and diazotrophs
(115 623:1 and 31 805:1, respectively). The high end of the allowable Fe:C
ratio is bounded by [C:Fe]min,i (i.e., maximum Fe:C) of 15 000:1 for
eukaryotes and 20 000:1 for cyanobacteria or diazotrophs. These parameters
directly follow Ridgwell (2001), who fitted power law functions to the
experimental data (Sunda and Huntsman, 1995).
Silica uptake stoichiometry by eukaryotes QSi is a
power law of FeT concentration and increases with a decrease in
[FeT] (Brzezinski, 2002).
The power law exponent sSi:N is set to 0.7. The Si:N ratio is limited
to a maximum of 18 and a minimum of 1.
13QSi=Si:P=Si:N⋅QN,114Si:N=minSi:Nmax,maxSi:Nmin,FeT0.5nmolkg-1-sSi:N
O2 liberated by phytoplankton during photosynthesis per PO4 consumed (Q-O2,i) is
calculated from the uptake C:P and N:P ratios (Tanioka and
Matsumoto, 2020b):
Q-O2,i=1.1QC,i+2QN,i.
Production of POM and DOM
In the top 100 m of the model domain, where phytoplankton P uptake occurs
(i.e., Γi>0, see Sect. 2.1), NPP
is immediately routed to POM and DOM pools (Fig. 1). The production fluxes
of POM, DOMsl, and DOMr from NPP are given as Jprod. Here we write
the equations in terms of the master nutrient variable P:
16JprodPOPi=1-fDOM⋅Γi,17JprodDOPsl=∑i(1-fDOMr)⋅fDOM⋅Γi,18JprodDOPr=∑ifDOMr⋅fDOM⋅Γi.
Schematic diagram of DOM cycling in MESMO 2 vs. MESMO 3. In the
new model, DOMr can be activated. DOMr is produced from POM
breakdown, which can occur in the production layer or throughout the water
column in the “deep POC split”. Possible DOMr remineralization
mechanisms are the slow background degradation that occurs everywhere,
thermal degradation in hydrothermal vents, and photodegradation at the
surface. See the text for details.
The term fDOM denotes the fraction of NPP that is routed to DOM as opposed
to POM. Likewise, fDOMr is the fraction of DOM that is routed to
DOMr as opposed to DOMsl. The value of fDOMr is not well
known but estimated to be ∼ 1 % (Hansell, 2013),
which we tentatively adopt in MESMO 3. If DOMr is not selected in the
model run, fDOMr=0. In previous versions of MESMO, fDOM was
assigned a constant value of 0.67. In reality, a large variability is
observed locally for this ratio, ranging from 0.01–0.2 in temperate waters
to 0.1–0.7 in the Southern Ocean
(Dunne
et al., 2005; Henson et al., 2011; Laws et al., 2000). In MESMO 3, fDOM is
calculated as a function of the ambient temperature following Laws et al. (2000):
fDOM=1.0-min0.72,max0.04,0.62-0.02⋅T∘C.
This formulation gives low export efficiency (i.e., high fDOM) in the warmer
regions compared to the colder high-latitude regions. Locally, we impose
fixed fDOM upper and lower bounds of 0.96 and 0.28, respectively, as
estimated from a previous study (Dunne et
al., 2005).
In MESMO 3, a new DOM production pathway below the production layer is
available as an option. In previous MESMO versions, sinking POM was respired
in the water column with the loss of O2 directly to the dissolved
inorganic forms (i.e., POC→ DIC, POP → PO4,
and PON
→ NO3). In the new “deep POC split” pathway,
sinking POM is simply broken down into DOM without the loss of O2 as in
the production layer (Fig. 1). If DOMr is selected in the model, the
broken-down POM is further routed to both DOMsl and DOMr according
to fDOMr. If not, all of the broken down POM is converted to
DOMsl. Thus, when the deep POC split is activated, the presence of DOM
in the deep ocean can be accounted for by in situ production of DOM and DOMr
in addition to DOM transport from the surface. Thus, the deep POC split
pathway offers an alternative means to control deep ocean DOM distribution.
Production of CaCO3 and opal by eukaryotes
In MESMO 2, opal production was associated with the “large” PFT, and CaCO3
production was associated with the “small” PFT. We recognize that
coccolithophorids and diatoms, which are the producers of these biogenic
tests, are both eukaryotes. Therefore, in MESMO 3, we associate both
CaCO3 and opal production with the POP production by the same eukaryote
PFT (JprodPOP1):
20JprodCaCO3=rCaCO3:POC⋅JprodPOP1⋅QC,1,21Jprodopal=JprodPOP1⋅QSi.
The concept of the residual nitrate potential growth (RNPG)
(Balch et al., 2016) is useful in
allowing competition between diatoms and non-siliceous phytoplankton within
the same PFT (Matsumoto et al., 2020).
Typically, in the real ocean, non-Si phytoplankton are able to grow faster
and dominate the community if Si concentration is low and diatom growth is
Si limited. Otherwise, diatoms are more competitive, as they have higher
intrinsic growth rates. The RNPG index recasts the ambient concentrations of
NO3 and Si(OH)4 into potential algal growth rates:
RNPG=NO3NO3+KNO3,1-SiOH4SiOH4+KSiOH4.
If RNPG is more positive, the index indicates that nitrate-dependent growth
exceeds silica-dependent growth. Thus, non-Si phytoplankton are more
competitive, and this leads to higher CaCO3 production. On the other
hand, a more negative RNPG implies that silica limitation for diatoms is
relieved, leading to enhanced diatom growth and reduced CaCO3
production. The RNPG index is incorporated in the calculation of the rain
ratio rCaCO3:POC
presented in Eq. (20) as follows:
rCaCO3:POC=r0CaCO3:POC⋅Ω-1η⋅min1,max0.1,RNPG⋅kT,CaCO3.
Equation (23) indicates the base rain ratio
r0CaCO3:POC
(set to 0.30) is also modified by the carbonate ion saturation state Ω by η (set to 1.28) and temperature (see
Ridgwell
et al., 2007, and references therein):
24Ω=Ca2+CO32-Ksp,25kT,CaCO3=min1.0,T∘C+2T∘C+8.
Ksp is the solubility product of CaCO3. The temperature dependency
of CaCO3 formation
(kT,CaCO3) is similar to that of
Moore et al. (2004) where warmer
temperatures favor the growth of carbonate-bearing phytoplankton.
Remineralization of POM and DOM
Once produced, both POM and DOM undergo remineralization throughout the
water column. Key remineralization parameter values are given in Table 2d.
Previously, POM remineralization had a temperature dependence and decayed
exponentially with depth (Yamanaka et
al., 2004). In MESMO 3, we incorporate an additional dependency on dissolved
oxygen following Laufkötter et
al. (2017):
RPOMi=VPOM⋅ekR⋅T⋅O2[O2]+KO2⋅POMi.
VPOM is the base remineralization rate,
kR expresses the temperature sensitivity of
remineralization, and KO2 is
half-saturation constant for oxygen-dependent remineralization. When the
sediment model is not coupled, any POM that reaches the seafloor dissolves
completely to its inorganic form and is returned to the overlying water.
In MESMO 3, all forms of semi-labile DOM remineralize at the same rate. It
is represented by τsl, the inverse of the timescale of
DOMsl decay, which has been estimated previously to be ∼ 1.5 years (Hansell, 2013):
RDOMsl=τsl⋅DOMsl.
All forms of DOMr also remineralize at the same rate in MESMO 3. In
total, there are three optional, additive sinks of DOMr in the model:
slow background decay, photodegradation, and degradation via hydrothermal
vents (Fig. 1). Observations clearly indicate that the 14C age of
deep-ocean DOCr is 103 years (e.g.,
Druffel et al., 1992), much older than DI14C. In addition, the deep ocean
DOCr concentration decreases modestly along the path of the deep water
from the deep North Atlantic to the deep North Pacific
(Hansell and Carlson, 1998). Thus, it is
understood that there is a slow DOMr background decay in the deep
ocean. We represent this ubiquitous process with τbg, which is
the inverse of the background decay timescale, estimated to be
∼ 16 000 years (Hansell, 2013).
Observations to date indicate that photodegradation is a major sink of
DOMr (e.g., Mopper et al.,
1991). This process is believed to convert DOMr that is upwelled from
the ocean interior into the euphotic zone into more labile forms of DOM. We
represent photodegradation with τphoto, the inverse of the decay
timescale, estimated to be ∼ 70 years
(Yamanaka and Tajika, 1997). This occurs only in the
surface.
Finally, observations of DOM emanating from different types of hydrothermal
vents indicate that they have variable impacts on the deep-sea DOMr
(Lang et al., 2006).
However, the off-axis vents circulate far more seawater through the
fractured oceanic crust than the high-temperature and diffuse vents and are thus
believed to determine the overall impact of the vents on the deep-sea
DOMr as a net sink
(Lang et al., 2006). Here
we assume simply that seawater that circulates through the vents loses all
DOMr (i.e., 1/τvent<Δt, where Δt
is the biogeochemical model time step of 0.05 year). This means that the
more seawater circulates through the vents, the more DOMr is removed:
the total removal rate depends on the vent flux of seawater Hflux. We
implement the vent degradation of DOMr in MESMO 3 by first identifying
the wet grid boxes located immediately above known mid-ocean ridges. We then
distribute the annual global Hflux of 4.8×1016 kg yr-1
(Lang et al., 2006)
equally among those ridge-associated grid boxes. The grid cells contain a
mass of seawater much greater than the mass that circulates through vents in
Δt (1021 kg vs. 1013 kg). Therefore, the seawater mass
in the vent grid cells that does not circulate through the vents in Δt is subject only to background degradation in MESMO 3.
The three DOMr sinks are not mutually exclusive. They can thus be
combined to yield the total DOMr remineralization rate:
RDOMr=τbg+τphoto+τvent⋅SWflux_localSWgrid⋅DOMr,
where SWflux_local is the mass of seawater that
circulates through the vents in each grid box in Δt, and SWgrid
is the total mass of seawater in the same grid box.
The amount of O2 respired as a result of these POM and DOM
remineralization processes is related to the organic carbon pools by the
respiratory quotients of POC and DOC,
r-O2:POC and
r-O2:DOC, respectively.
These are molar ratios of O2 consumed per unit organic carbon respired.
They are variable and calculated from the ambient POM and DOM concentration
(Tanioka and Matsumoto, 2020b):
29r-O2:POC=1.1+2PONPOC,30r-O2:DOC=1.1+2DONDOC.
Remineralization of CaCO3 and opal
Remineralization of CaCO3 and opal particles occurs as they sink
through the water column and remains the same as in MESMO 2. Key parameter
values are given in Table 2d. Remineralization of CaCO3 is a function
of temperature similar to that of particulate organic matter
remineralization but without oxygen dependency. The temperature-dependence
term kR modifies the base remineralization rate
VCaCO3:
RCaCO3=VCaCO3⋅ekR⋅T⋅CaCO3.
Opal remineralization in the water column follows
Ridgwell et al. (2002). The rate of opal
remineralization Ropal is given by the product of
normalized dissolution rate (ropal), base opal
dissolution rate (kopal), and opal concentration
[opal].
32Ropal=ropal⋅kopal⋅opal33ropal=0.16⋅1+T∘C15⋅uopal+0.55⋅1+T∘C4004⋅uopal9.2534uopal=SiOH4eq-SiOH4SiOH4eqropal is a function of temperature (T) and the degree
of under-saturation (uopal), which in turn is
calculated from the ambient SiOH4 and SiOH4 at equilibrium. The equilibrium concentration
is a function of ambient temperature:
log10SiOH4eq=6.44-968TK.
Without the sediment module of MESMO activated, both CaCO3 and opal
particles that reach the seafloor are completely dissolved back to inorganic
forms.
Conservation of organic matter and biogenic tests
The time rate of change of the biogenic organic matter and tests are given
by the sum of the production terms (i.e., sources) and the remineralization
terms (i.e., sinks). The circulation-related transport terms are omitted as
noted above, but the vertical transport due to particle sinking is included
here. The sinking speed w is the same for all particles. The sum of
POMi of all the PFTs give the total POM concentrations.
36∂POPi∂t=JprodPOPi-∂∂zwPOPi-RPOP,i37∂POCi∂t=JprodPOPi⋅QC,i-∂∂zwPOCi-RPOC,i38∂PONi∂t=JprodPOPi⋅QN,i-∂∂zwPONi-RPON,i39∂POFei∂t=JprodPOPi⋅QFe,i-∂∂zwPOFei-RPOFe,i40[POM]=∑iPOMi
The time rate of change of CaCO3 and opal is expressed in much the same
way as POM.
41∂CaCO3∂t=JprodCaCO3-∂∂zwCaCO3-RCaCO342∂opal∂t=Jprodopal-∂∂zwopal-Ropal
The DOM pools have the production and remineralization terms without the
particle sinking term.
43∂DOPsl∂t=JprodDOPsl-RDOPsl44∂DONsl∂t=JprodDONsl-RDONsl45∂DOCsl∂t=JprodDOCsl-RDOCsl46∂DOFesl∂t=JprodDOFesl-RDOFesl47∂DOPr∂t=JprodDOPr-RDOPr48∂DONr∂t=JprodDONr-RDONr49∂DOCr∂t=JprodDOCr-RDOCr
Conservation of inorganic nutrients
The time rate of change of the inorganic nutrients have organic carbon
production as sink terms and remineralization as source terms. The
production terms (Jprod) are zero below the upper-ocean production
layer. Nutrients have a unit of mol element kg-1 in the model.
50∂PO4∂t=-∑iΓi+∑iRPOP,i+RDOPsl+RDOPr51∂NO3∂t=-∑iΓi⋅QN,i+∑iRPON,i+RDONsl+RDONr+FixN-DenN52∂DIC∂t=-∑iΓiQC,i+JprodCaCO3+∑iRPOC,i+RDOCsl+RDOCr+RCaCO3+Fgas,CO253∂ALK∂t=-2⋅JprodCaCO3-∑iΓiQN,i-∑iRPON,i-RDONsl-RDONr-FixN+DenN+2⋅RCaCO354∂FeT∂t=-∑iΓiQFe,i+∑iRPOFe,i+RDOFesl+RPOMFe+AeolianFe55∂SiOH4∂t=-Jprodopal+Ropal56∂O2∂t=∑iΓi⋅Q-O2,i-(r-O2:DOC⋅RDOCsl+RDOCr+∑ir-O2:POC,i⋅RPOC,i)+1.25DenN+Fgas,O2
In Eq. (51), FixN is the N fixation
carried out by diazotrophs, and DenN is the water column
denitrification. There is an air–sea gas exchange term Fgas in
Eqs. (52) and (56) for
gaseous CO2 and O2, respectively. In Eq. (53), alkalinity increases with decreasing nitrate
concentrations and increasing CaCO3 dissolution. Equation (54) contains RPOMFe, which is an iron source
that represents remineralization of the Fe′ scavenged by sinking particles.
These terms are explained in the following sections.
Prognostic nitrogen cycle
Biological production by diazotrophs is stimulated when the ambient NO3
is low. Nitrogen fixed by diazotrophs during their growth is added to the
marine NO3 pool. The prognostic nitrogen fixation model employed here
is similar to that used in the HAMOCC biogeochemical module
(Paulsen et al., 2017):
57FixN=Γ3⋅QN,3⋅INO3,58INO3=1.0-NO32KNO3_Nfix2+NO32,
where FixN is the nitrogen fixation rate and
INO3 is the nitrate dependency
term in quadratic Michaelis–Menten kinetics form with the half-saturation
constant KNO3_Nfix. See Table 2e for the values
related to the N cycle.
Water column denitrification is formulated in an approach similar to that of
the original GENIE model
(Ridgwell
et al., 2007), in which 2 mol of NO3 are converted to 1 mol of
N2 and liberating 2.5 mol of O2 as a byproduct:
2NO3-+2H+→2.5O2+N2+H2O.
Denitrification takes place in grid boxes, in which O2 concentration
is below a threshold concentration (O2,def) and is
stimulated if the total global inventory of NO3 relative to PO4 is
high. In other words, denitrification can effectively act as negative
feedback to nitrogen fixation. The threshold O2 concentration
(O2,def) takes the minimum of the hard-bound O2 threshold concentration (O2,crit) and the NO3
to PO4 ratio, scaled by a parameter kD. The parameters O2,crit and
kD are calibrated to give the global denitrification
rate of roughly 100 Tg N yr-1, which balances the total nitrogen
fixation rate in the model.
60DenN=0.8yr-1⋅maxO2def-O2,061O2def=minO2,crit,kD⋅NO3inventoryPO4inventory
Prognostic iron cycle
The iron cycle in MESMO 3 remains the same as in MESMO 2. Key parameter
values are given in Table 2e. The two species of dissolved iron (Fe′ and
FeL) are partitioned according to the following equilibrium relationship:
Kligand=FeLFe′⋅L,
where [L] is the ligand concentration and Kligand is
the conditional stability constant. The sum of ligand and FeL is set at a
constant value of 1 nmol kg-1 everywhere. Iron is introduced into the
model domain by a constant fraction (3.5 wt %) of aeolian dust
deposition at the surface (Fin) following the
prescribed modern flux pattern (Mahowald et
al., 2006) with constant solubility (β):
SFe=β⋅Fin.
Particle-scavenged iron POMFe (note the difference from POFe) is
produced below the productive layer when sinking POM scavenges Fe′ to sinking POM:
JFe=-τsc⋅Ko⋅POC0.58⋅Fe′,
where τsc and Ko are
empirical parameters that determine the strength of scavenging.
Remineralization of Fe scavenged to POM (POMFe) is identical in form to
that of POM remineralization:
RPOMFe=VPOM⋅ekRT⋅O2[O2]+KO2⋅POMFe.
The conservation equation of the particle scavenged iron is thus expressed
as follows:
∂POMFe∂t=JFe-∂∂zwPOMFe-RPOMFe.
Any scavenged iron that escapes remineralization in the water column
reaching the seafloor is removed from the model domain in order to keep the
total Fe inventory at a steady state.
Air–sea gas exchange
The air–sea gas exchange formulation remains the same as in MESMO 2 and
follows
Ridgwell
et al. (2007). It is the function of gas transfer velocity, the ambient
dissolved gas concentration, and saturation gas concentration. The flux of
CO2 and O2 gases across the air–sea interface is given by
67Fgas,CO2=k⋅CO2sat-CO2⋅1-A,68Fgas,O2=k⋅O2sat-O2⋅1-A,
where k is the gas transfer velocity, CO2sat and O2sat are saturation
concentrations, and A is the fractional ice-covered area that is calculated
by the physical model. Gas transfer velocity k is a function of wind speed
(u) following Wanninkhof (1992) where Sc is the Schmidt
number for a specific gas:
k=0.31⋅u2⋅Sc660-0.5.
Results and discussion
All new results from MESMO 3 presented here are from the steady state. On a
single computer core at the Minnesota Supercomputing Institute, it takes
approximately 1 h to complete 1000 years of MESMO 3 simulation. The
“standard” MESMO 3 has the power law model of flexible stoichiometry but no
DOMr. The results from the standard model (hereafter just MESMO 3) are
presented in Sect. 3.1, and the results from the DOMr-enabled model
are presented in Sect. 3.2. In Table 3, we summarize and compare key
biogeochemical diagnostics from MESMO 3 against those from MESMO 2 and
available observational constraints. The global NPP, as well as global
export production of POC and opal, are comparable or somewhat lower in MESMO
3 than MESMO 2.
Key Biogeochemical diagnostics
DiagnosticsUnitConstraintMESMO 2MESMO 3(120531a)(210310d)Phytoplankton community/bulk NPPPg C yr-130–7036.0a31.3POC exportPg C yr-14–1011.99.1DOC exportPg C yr-10.4–20.41.4Opal exportTmol Si yr-170–185130130CaCO3 exportPg C yr-10.4–1.81.00.6fDOM%0.670.69N fixationTg N yr-180-200–101DenitrificationTg N yr-160–150–101Uptake C:N:Pmolar ratio146:20:1117:16:1146:20:1Export C:N:Pmolar ratio117:16:1117:16:1113:17:1Deep O2µmol kg-1169179155LP/eukaryotes Uptake C:N:Pmolar ratio117:16:1103:15:1POC exportPg C yr-18.73.6Abundance%73b42SM/cyanobacteria Uptake C:N:Pmolar ratio117:16:1196:23:1POC exportPg C yr-13.24.8Abundance%27b51Diazotrophs Uptake C:N:Pmolar ratio–213:33:1POC exportPg C yr-1–0.7Abundance%–7RMSE PO4µmol kg-10.430.52NO3µmol kg-15.76.9Si(OH4)µmol kg-18.510.6O2µmol kg-137.536.2
a NPP for MESMO 2 was unavailable as a model output and is therefore
estimated from POC and fDOM = 0.67. b NPP (in terms of C) is needed in
the calculation of the PFT abundance. The root-mean-square error (RMSE) of
the simulated P, N, Si, and O2 distributions from MESMO 2 and 3 was
calculated relative to the World Ocean Atlas 2018 (WOA18) gridded data
(Garcia
et al., 2018, 2019). The model–data comparison is made in the top 100 m for
nutrients and below 100 m for O2. WOA18 was regridded to the MESMO 3
grid to calculate the RMSE.
References for independent constraints are as follows: (1) global NPP
(Carr et al., 2006), (2) global
POC export (DeVries and Weber, 2017),
(3) global DOC export assumed to be 20 % of total carbon export
(Hansell et al., 2009;
Roshan and DeVries, 2017), (4) global opal
(Dunne et al., 2007), (5) global CaCO3
export
(Berelson
et al., 2007), (6) global N fixation and denitrification rates
(Landolfi et al., 2018), (7) uptake C:N:P ratio is
based on POM measurements (Martiny et al., 2013),
(8) export C:N:P ratio is assumed to equal the subsurface remineralization
ratio (Anderson and Sarmiento, 1994), and (9) deep O2
from WOA18 below 100 m (Garcia et al., 2019).
We relied on experience to calibrate MESMO 3 with the primary goal of
reasonably simulating the phytoplankton community composition and C:N:P
ratio (e.g., abundant cyanobacteria and high ratio for all PFTs in
oligotrophic gyres). We tried to improve or at least preserve the gains that
we achieved in earlier versions of MESMO in terms of the global
distributions of PO4, NO3, O2, Si(OH)4, and FeT
(Supplement Figs. S1, S2, S3, S4, and S5). Overall, there is a stronger
nutrient depletion in the new model. For example, the surface PO4 and
NO3 in MESMO 3 are now sufficiently depleted in the subtropical gyres
but are too low in the eastern equatorial Pacific when compared to the World
Ocean Atlas (Fig. S1; see RMSE in Table 3). It is a challenge for MESMO
and other coarse-resolution models to simulate narrow dynamical features
such as equatorial upwelling and reproduce biogeochemical features with
sharp gradients. The spatial pattern of POC export that drives this surface
nutrient pattern is similar in the two models (Fig. S2). In the 1D global
profile, there is a marked improvement in the subsurface distribution of
O2 in MESMO 3 over MESMO 2. Whereas the depth of the oxygen minimum was
∼ 300 m in MESMO 2, it is ∼ 1000 m in both MESMO
3 and the World Ocean Atlas (Fig. S3). At 1000 m, the O2 minimum is
located in the far North Pacific in MESMO 3, whereas in the World Ocean
Atlas it occurs in both the Northeast Pacific and the Arabian Sea. In
contrast, the world ocean at 1000 m is too well oxygenated in MESMO 2. We
believe that the improved match in the O2 minimum depth would help
simulate denitrification in the correct depth range, and there is a modest
improvement in the data–model O2 mismatch in terms of RMSE in MESMO 3
over MESMO 2 (Table 3). The deepening of the O2 minimum was achieved
largely by increasing the particle sinking speed, which tends to strengthen
the biological pump and deplete the surface nutrients. This also helps MESMO
3 preserve MESMO 2's surface Si(OH)4 depletion in much of the world
ocean except in the North Pacific and Southern Ocean (Fig. S4). This is a
feature captured by Si*< 0 (Si*=[Si(OH)4]-[NO3]) in
observations (Sarmiento et al., 2004) and
simulated previously by MESMO 2 and now MESMO 3. Finally, surface FeT is also
depleted more strongly in MESMO 3 over MESMO 2, except the North Atlantic,
where aeolian deposition of dust from the Sahara maintains a steady Fe
supply (Fig. S5).
In MESMO 3, we made no effort to calibrate all the semi-labile pools of DOM:
DOCsl, DOPsl, DONsl, and DOFesl. We note only that the
surface DOCsl concentration of 58 µmolkg-1 and DOC export
production of 1.4 Pg C yr-1 in MESMO 3 are higher than in MESMO 2 (24 µmolkg-1 and 0.4 Pg C yr-1, respectively). The higher
surface concentration is due to the longer τsl in MESMO 3 (Table 2d). The global average of the temperature-dependent fDOM in MESMO 3 is
0.69, which is slightly higher than the spatially uniform value of 0.67 in
MESMO 2.
Novel features of MESMO 3
An important new feature of MESMO 3 is the representation of the primary
producers by three PFTs (Fig. 2). The eukaryotes are characterized by the
highest maximum growth rate and high half-saturation constants. Thus, the
eukaryotes are more dominant than the other PFTs in the more eutrophic
waters of the equatorial and polar regions (Fig. 2a). The cyanobacteria
have smaller half-saturation constants and thus are more dominant in the
oligotrophic subtropical gyres (Fig. 2c). The diazotrophs do not have
NO3 limitation but have the lowest maximum growth rate. Thus it is much
lower in abundance than the other two PFTs generally, and out-competed in
transient blooms and thus excluded in higher latitudes (Fig. 2e).
NPP-based surface phytoplankton functional type (PFT) abundance
and nutrient limitation in MESMO 3. Fractional abundance and nutrient
limitation for eukaryotes (a, b), cyanobacteria (c, d), and diazotrophs (e, f).
Figure 2 also indicates that all three PFTs show Fe limitation in the
Southern Ocean. Outside the Southern Ocean, the eukaryotes are primarily
limited by Si(OH)4 (Fig. 2b). As far as organic carbon is concerned,
we consider the eukaryotes to basically represent diatoms, which are
arguably the most important agent of organic carbon export. In this context,
the widespread silica limitation for eukaryotes would be consistent with the
notions that silica uptake by diatoms should be limited in ∼ 60 % of the world surface ocean (Ragueneau et al., 2000) and that much the
world ocean thermocline is filled with silica-depleted water (Si*< 0
as noted above). On the other hand, the cyanobacteria are largely limited by
NO3 outside the Southern Ocean (Fig. 2d). The diazotrophs are limited
by iron in much of the world ocean except in the Atlantic basin (Fig. 2f),
where surface PO4 is strongly depleted in both observations
(Mather et al., 2008) and in our model
(Fig. S1).
Figure 3 illustrates the influence of the RNPG index, which was implemented
in MESMO 3 to allow for the effect of competition between diatoms and
coccolithophores within the same PFT (Eqs. 22
and 23). The eukaryote NPP (Fig. 3a) is
effectively split into two parts: one is associated with diatoms and opal
production (Fig. 3b), and the other is associated with coccolithophores
and CaCO3 production (Fig. 3c). According to the RNPG index, opal
production is simulated more in the higher latitudes of the Southern Ocean
and the North Pacific, where surface [Si(OH)4] is abundant. Elsewhere,
CaCO3 production is relatively large. The decoupling is prominent in
the North Indian Ocean. Note that the spatial pattern of CaCO3 production is
quite different in MESMO 3 (Fig. 3c) and MESMO 2 (Fig. 3d) because
CaCO3 production was associated in MESMO 2 with the “small” PFT, which
corresponds to the cyanobacteria PFT in MESMO 3.
Eukaryote production in MESMO 3 and CaCO3 export in MESMO 2.
In MESMO 3, eukaryote NPP (a) is linked to both opal export (b) and
CaCO3 export (c) but the two export productions are differentiated by
the residual nitrate potential growth (RNPG). Compare CaCO3 export in
MESMO 3 (c) to MESMO 2 (d) (unit: mol m-2 yr-1).
The global pattern of the mean C:P uptake ratio in the production layer is
shown in Fig. 4. Consistent with observations
(Martiny et al., 2013), the simulated
C:P ratio of the phytoplankton community is elevated in the oligotrophic
subtropical gyres and low in the eutrophic polar waters (Fig. 4a). The
community C:P ratio exceeds 200 in the gyres and reaches as low as 40–50 in
the Southern Ocean. The community C:P has contributions from both
physiological effects (i.e., environmental drivers acting on each PFT's C:P
ratio) and taxonomic effects (i.e., the shift in the community composition
changes the weighting of each PFT's C:P ratio). Figure 4b shows that the
community C:P is high in oligotrophic gyres because cyanobacteria and to a
lesser extent diazotrophs dominate the community and their C:P ratio is
high. Conversely, the community C:P is low in the polar waters because the
eukaryotes dominate and their C:P ratio is low. For both eukaryotes and
cyanobacteria, their C:P is high in oligotrophic subtropical gyres because
PO4 is low (Fig. 4c and d). This physiological effect is larger in
eukaryotes than cyanobacteria because the former has greater sensitivity
(i.e., larger sensitivity factor sPO4P:C; see Eq. 5 and Table 2b). However, the cyanobacteria PFT's C:P
ratio has an additional sensitivity to temperature (i.e., sTP:C≠0) that elevates their C:P in the lower latitudes. We do not show the C:P
ratio for diazotrophs because it is very similar to that of cyanobacteria
(Fig. 4b, d).
Uptake C:P ratio in the top 100 m in MESMO 3: (a) phytoplankton
community C:P, (b) zonal mean C:P of all three PFTs and phytoplankton
community, (c) eukaryote C:P, and (d) cyanobacteria C:P. The colors in (b)
indicate community C:P (black), eukaryote C:P (red),
cyanobacteria C:P (green), and diazotroph C:P (blue). In addition, (b) shows the mean range of
observed C:P ratio binned by latitude
(Martiny et al., 2013).
In order to gain more insights into the spatial patterns of the C:P ratio
(Fig. 4), we examined the relationships between the C:P and C:N ratios and
the four possible environmental drivers for eukaryotes and cyanobacteria
(Fig. 5; again, diazotrophs are not shown). The red plots show that there
is a causal relationship between the ratios and the drivers as formulated by
the power law model (Eqs. 5 and
6). The black plots show the absence of a causal
relationship. For example, the C:P ratio of both eukaryotes and
cyanobacteria is strongly correlated with PO4 because there is a
causal relationship (Fig. 5a, b, shown in red). Similarly, the C:N ratio of
the same two PFTs have a strong correlation with PO4 (Fig. 5c, d in
black), but there is actually not a causal relationship (i.e.,
sPO4N:C=0, Table 2b). The C:N-PO4 correlation exists simply
because the nutrients are well correlated. Similarly, because temperature
and photosynthetically active radiation (PAR) tend to be correlated via
latitude, the stoichiometry has a similar correlation to the two drivers.
For example, cyanobacteria C:P has a strong correlation with both
temperature and PAR (Figs. 5j, 4n), but only the temperature is a real
driver. Figure 5 indicates which are the dominant drivers of the C:N:P ratio
in MESMO 3. For the eukaryote C:P ratio, it is PO4. For the
cyanobacteria C:P ratio, the important drivers are temperature and PO4.
For the C:N ratio for both eukaryotes and cyanobacteria, NO3 is more
important than PAR. Figure 5 also serves to remind us that correlation does
not indicate causation.
Scatterplots of surface ocean eukaryote and cyanobacteria C:P and
C:N vs. environmental drivers in MESMO 3. Columns show the following data, from left to right, eukaryote C:P, cyanobacteria C:P, eukaryote C:N, and cyanobacteria C:N.
Rows show the following data, from top to bottom, PO4, NO3, temperature, and PAR. Red
indicates the causal relationship according to the power law formulation of
flexible C:N:P ratio. PAR stands for photosynthetically active radiation in W m-2.
Figure 6 shows the community C:P and C:N ratios plotted against the four
environmental drivers. Unlike Fig. 5, which reflected the individual PFT's
physiological response, Fig. 6 includes the effect of taxonomy as well.
Still, the effects of PO4 and temperature are clearly visible on the
community C:P ratio. Both low [PO4] and warmer waters are found in the
lower latitudes, so the P frugality and temperature effects are additive.
The effect of NO3 on the community C:N ratio is also very clear, but
the effect of PAR is not as clear. Thus, the overall physiological effects
seen in the PFT-specific C:N:P are obvious in the community C:N:P ratio.
Scatterplots of surface ocean community C:P and C:N vs.
environmental drivers in MESMO 3.
DOMr-enabled MESMO 3
In MESMO 2, DOCsl was a standard state variable. In MESMO 3, other
forms of DOM are available as options. They are the semi-labile forms of
DOM, i.e., DOPsl, DONsl, and DOFesl, and the refractory forms of
DOM, i.e., DOCr, DOPr, and DONr. MESMO 3 is not yet calibrated with
respect to all the DOM variables, but here we demonstrate their potential
use in future biogeochemical investigations by presenting steady state DOM
results from the model experiment LV (experiment ID: 210310m). In this run,
all three sinks of DOMr are activated: slow background decay,
photodegradation, and degradation in hydrothermal vents.
The experiment name LV stands for “literature values”. In LV, we use the
literature values for the key DOM remineralization model parameters (Table 2d) and fDOMr=0.01 (Hansell, 2013). All other model
parameter values in the LV run are identical to the standard MESMO 3 model
(Table 2). The black lines in Fig. 7 show the global mean vertical
profiles of the total DOC (DOCt= DOCsl+ DOCr) with solid lines and DOCr with a dashed line. Qualitatively, the simulated
profiles are consistent with the observations, showing a near-uniform
DOCr concentration and a DOCsl profile that rapidly attenuates with depth in
the top few hundred meters (Hansell, 2013). However, the
simulated values reach 130 µmolkg-1 at the surface, which is
approximately twice the observations. More typically, the observed DOCr
is 30–40 µmolkg-1, and the observed DOCsl
attenuates with depth from 30–40 µmolkg-1 near the
surface. So their sum, which is represented by DOCt, is approximately
60–80 µmolkg-1 at the surface in observations.
Global mean vertical profiles of DOC from the DOMR-enabled
MESMO 3. DOCt (DOCsl+DOCr, black line) and DOCr (dashed black
line) from the LV run. The red line is DOCt after reducing fDOMr
from 1 % in LV to 0.2 % (Experiment 210310o) (unit: µmol kg-1).
Figure 8 adds a lateral perspective to Fig. 7. The rapid DOCt
attenuation in the vertical is strong in the lower latitudes where
stratification is generally stronger. The transport of DOCsl from the
surface to deeper waters is evident in the high latitudes of the North
Atlantic and the Southern Ocean. The DOCt change in the deep ocean is
limited.
Global depth–latitude transect of DOCt from the
DOMR-enabled MESMO 3 LV run. Transects are north–south along 25∘ W in
the Atlantic, east–west along 60∘ S in the Southern Ocean, and north–south along
165∘ E in the Pacific (unit: µmol kg-1).
Observations of deep-ocean DOCt indicate a reduction by 29 % or 14 µmolkg-1 from the deep North Atlantic to the deep North Pacific
(Hansell and Carlson, 1998). Figure 8 shows
that the deep-ocean DOCt gradient in LV is approximately 10 µmolkg-1 from 70–75 µmolkg-1 in the North Atlantic to < 65 µmolkg-1 in the North Pacific.
The horizontal DOCt distributions from the LV run can also be compared to
a global extrapolation based on an artificial neural network (ANN) of the
available DOCt data (Roshan and DeVries,
2017). At the surface, the extrapolation indicates higher DOCt
concentrations in the subtropical gyres (Fig. 9a), while our simulation
does not clearly delineate the gyres (Fig. 9c). In our model, fDOM is
temperature-dependent and strongly controls the production of DOM. The
surface DOCt is thus more elevated in the lower latitudes.
Interestingly, the ANN study diagnosed higher rates of DOM production in the
subtropical gyres. Since the oligotrophic subtropical gyres have low NPP,
the diagnosis would thus suggest that somehow fDOM is higher in the gyres.
At depth, both the extrapolated and simulated DOCt show a gradual
decline in concentrations from the North Atlantic to the North Pacific
(Fig. 9b, d). The highest deep DOCt in the LV run is seen just south of
Greenland, where convection occurs in the model.
Assessment of surface and deep-ocean DOCt from the
DOMR-enabled MESMO 3 LV run. Data-derived DOCt distributions in the
top 100 m (a) and 2500–4000 m (b). Model-simulated DOCt distributions
in the top 100 m (c) and 2500–4000 m (d). Data-derived DOCt are from
Roshan and DeVries (Roshan and DeVries, 2017)
(unit: µmol kg-1).
Finally, we show that the deep-ocean radiocarbon aging is larger in DIC than
in DOCt in the model (Fig. 10). The North Pacific–North Atlantic
Δ14C gradient is roughly -100 ‰ for DIC and
-70 ‰ for DOCt. The oldest DOCtΔ14C is approximately -430 ‰ in the North Pacific.
If 14C decay were the only mechanism of change along the path of the
deepwater circulation, the Δ14C gradient should be quite
similar between DIC and DOCt, which are both dissolved phases and
transported passively by the same circulation. The one potentially important
difference is that the addition of the relatively young DI14C and
DO14C to the deep ocean by the “deep POC split” (see Sect. 2.3).
The addition impacts DOCtΔ14C more than DIC Δ14C because
DOCt is 2 orders of magnitude lower in concentration than DIC.
Δ14C of deep-ocean DIC (a) and DOCt(b) from
the DOMR-enabled MESMO 3 LV run. Vertical average over 2500–4000 m water
depth (unit: ‰).
In observations, the aging of DIC and DOCt is reportedly similar in the
Antarctic Bottom Water (below 4000 m) of the deep Pacific
(Druffel et al., 2019). This may be
explained by the fact that there would not be much deep POC split occurring
so deep in the ocean. The North Pacific–North Atlantic Δ14C
gradient, accounting for thermonuclear bomb 14C, may be as large as
-100 ‰ for DOCt (about -550 ‰ in
the deep Pacific and -456 ‰ in the deep Atlantic)
(Druffel et al., 2019). This gradient is
not rigorously determined because there is not enough data to do an
objective analysis. Therefore, the equivalent Δ14C gradient for
DIC cannot be determined. However, the DIC Δ14C endmember
values by inspection (about -250 ‰ in the deep Pacific
and -70 ‰ in the deep Atlantic)
(Matsumoto and Key, 2004) indicate a clearly
larger Δ14C gradient for DIC than DOCt as simulated by the
experiment LV.
One lesson from the data–LV run mismatch in the overall DOCt
concentration (Fig. 7) and surface DOCt pattern (Fig. 9) is that
the parameter values from the literature do not fully capture the DOC cycle
and/or that MESMO 3 is still lacking some important DOC process. In LV, the surface
DOCt is too high because DOCr is too high, while DOCsl is not
unreasonable (Fig. 7). DOCr is too high because there is too much
DOCr production (e.g., fDOMr=1 % is too large), there is too
little DOCr degradation (e.g., one of the DOM decay mechanisms is too
slow; Eq. 28 and Table 2d), or some combination of both. For example,
fDOMr is a key parameter that is not well constrained by observations.
Had we used 0.2 % instead of 1 % for fDOMr, the global mean surface
DOCt drops to 76 µmolkg-1 (red line, Fig. 7), consistent
with observations. For achieving a better surface DOCt pattern, we may
need a different formulation of fDOM that is, for example, negatively
related to nutrient concentrations so that fDOM increases in the
oligotrophic subtropical gyres (Roshan and
DeVries, 2017).
Another lesson from the DOM modeling exercise is that it is important to
simulate DOPr reasonably well in order to preserve the favorable
results we achieved in MESMO 3 with respect to biological production and the
phytoplankton C:N:P ratio. We find that in the experiment LV, the global mean
DOPr concentration becomes steady at 0.45 µmol-P kg-1. In
observations, the mean DOCr is about 40 µmol-C kg-1 and the
DOCr:DOPr ratio is estimated to be ∼1370:1
(Letscher and Moore, 2015), so DOPr concentration should
only be roughly 0.03 µmol-P kg-1. Thus, the simulated
DOPr=0.45 µmol-P kg-1 is an order of magnitude too high.
Because there is more P in the form of DOPr in LV, the oceanic inventory
of PO4 declines, causing a nearly 10 % drop in export production
compared to the standard MESMO 3. In LV, the decline in the surface ocean
PO4 that accompanies the change in the PO4 inventory acts on the
phytoplankton physiology (i.e., P effect on C:P in Eq. 5), which leads to a large rise in the global mean
phytoplankton community C:P export ratio from 113:1 to 127:1. The
implementation of preferential remineralization of DOP (and DON) over DOC
(Letscher and Moore, 2015) is one way to deal with the
problem of too high DOPr concentrations.
Large-scale patterns of N2 fixation and denitrification
The modeled habitat of diazotrophs is concentrated in tropical and
subtropical waters between 40∘ S and 40∘ N and limited
by iron (Fig. 1e, f). Most noticeably in the North Pacific subtropical gyre,
diazotrophs constitute ∼ 40 % of total NPP. The latitudinal
extent of diazotrophs is mainly determined by surface nitrate availability
and physical factors such as surface temperature and irradiance. Low nitrate
availability in subtropical gyres gives diazotrophs a competitive advantage
over small cyanobacteria. Warm temperature and high irradiance are also critical
physical factors that drive the growth of diazotrophs in the model.
The modeled global depth-integrated N2 fixation is 101 Tg N yr-1
(Table 3), and this value falls well within the range of observational and
geochemical constraints of 80–200 Tg N yr-1
(Landolfi et al., 2018). In MESMO 3, N2
fixation occurs in the North Pacific and mid-to-low latitudes of the
Atlantic basin (Supplement Fig. S6), where diazotrophs are generally
more abundant (Fig. 2e). The elevated N2 fixation rate in the North
Pacific, where nitrate limits eukaryotes and cyanobacteria (Fig. 2b, d),
can be explained by the healthy growth of diazotrophs, which is not limited
by N. In the subtropical and tropical Atlantic and the Indian Ocean, high
N2 fixation is driven by a elevated C:P and N:P ratio (Fig. 4),
exemplified by low phosphate availability and warm surface temperature. This
spatial pattern agrees with a recent inverse model study
(Wang et al., 2019), which showed an
elevated N2 fixation rate in subtropical gyres.
Global water column denitrification is 101 Tg N yr-1 (Table 3) and is
equal to the global N2 fixation because the model has reached steady
state. Denitrification is restricted to the subpolar North Pacific (Fig. S6), where sub-surface oxygen concentration is significantly depleted
(Fig. S3d). Enhanced denitrification in this region is in qualitative
agreement with a previous modeling study
(Bianchi et al., 2018), which showed the
anaerobic niche due to particle microenvironments can significantly expand
the hypoxic expanses in the North Pacific. However, the extent of
denitrification in our model does not include the eastern equatorial Pacific
and northern Indian oceans, which are important hotspots for denitrification
(Codispoti, 2007; Deutsch et
al., 2007). This issue is typical of coarse-resolution global ocean
biogeochemistry models that lack spatial resolution in reproducing intense
upwelling
(Marchal
et al., 1998; Najjar et al., 1992; Yamanaka and Tajika, 1997).
Finally, the ratio of the global inventories of NO3 and PO4 in
MESMO 3 is just about 16 at steady state, consistent with observations
(Gruber and Sarmiento, 1997). One key
model parameter in this regard is the nitrate uptake half-saturation
constant of diazotrophs, KNO3_Nfix
in Eq. (58).
A large value of KNO3_Nfix
will make it hard for diazotrophs to obtain
fixed N from NO3, which would facilitate N2 fixation and pushes up
the global N/P ratio. With a smaller value of KNO3_Nfix, diazotrophs will
more easily uptake NO3, thus depressing N2 fixation and lowering the
global N/P ratio.
Conclusions
MESMO 3, the third and latest version of MESMO, is comprehensively described
here. With a fully flexible C:N:P ratio in three PFTs, a prognostic N cycle,
and more mechanistic schemes of organic matter production and
remineralization, MESMO 3 reflects the evolving and accumulating knowledge
of the ocean biogeochemistry. The model thus remains an effective tool for
investigations of the global biogeochemical cycles, especially over long timescales, given the model's computational efficiency. In particular, MESMO 3
holds promise for studying the marine DOM cycle. The optional features of
MESMO 3 include the semi-labile and refractory pools of C, P, N, and Fe. The
fact that the literature values regarding the present marine DOM cycle are
unable to simulate key observations indicates an opportunity for MESMO 3 to
contribute to an improved understanding of the marine DOM cycle.
Code and data availability
Model results presented in this study are archived and available with the code. The complete code of MESMO version 3.0 and the results presented here are
available at GitHub https://github.com/gaia3intc/mesmo.git (last access: 26 April 2021) and have the following DOI:
10.5281/zenodo.4403605 (Matsumoto, 2020).
The supplement related to this article is available online at: https://doi.org/10.5194/gmd-14-2265-2021-supplement.
Author contributions
KM, TT, and JZ developed the model code. KM performed the simulations,
carried out the analyses, and archived the model code and results. KM and TT
wrote the paper.
Acknowledgements
Numerical modeling and analysis were carried out using resources at the
University of Minnesota Supercomputing Institute.
Financial support
This research has been supported by the National Science Foundation (grant no. OCE-1827948).
Review statement
This paper was edited by Andrew Yool and reviewed by two anonymous referees.
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