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**Geoscientific Model Development**
An interactive open-access journal of the European Geosciences Union

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- About
- Editorial board
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- About
- Editorial board
- Articles
- Special issues
- Highlight articles
- Manuscript tracking
- Subscribe to alerts
- Peer-review process
- For authors
- For editors and referees
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- Abstract
- Introduction
- CSIRO Mk3L-COAL v1.0
- Carbon and nitrogen isotope equations
- Model performance
- Ecosystem effects
- Conclusions
- Data availability
- Code availability
- Appendix A: Ecosystem component of the OBGCM
- Appendix B: Parameterisation of the OBGCM ecosystem component
- Author contributions
- Competing interests
- Acknowledgements
- Review statement
- References
- Supplement

GMD | Articles | Volume 12, issue 4

Geosci. Model Dev., 12, 1491–1523, 2019

https://doi.org/10.5194/gmd-12-1491-2019

© Author(s) 2019. This work is distributed under

the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/gmd-12-1491-2019

© Author(s) 2019. This work is distributed under

the Creative Commons Attribution 4.0 License.

Special issue: The CSIRO Mk3L climate system model

**Model description paper**
16 Apr 2019

**Model description paper** | 16 Apr 2019

Ocean carbon and nitrogen isotopes in CSIRO Mk3L-COAL version 1.0: a tool for palaeoceanographic research

^{1}Institute for Marine and Antarctic Studies, University of Tasmania, Hobart, Tasmania, Australia^{2}CSIRO Oceans and Atmosphere, CSIRO Marine Laboratories, G.P.O. Box 1538, Hobart, Tasmania, Australia^{3}ARC Centre of Excellence in Climate System Science, Hobart, Tasmania, Australia^{4}Antarctic Climate and Ecosystems Cooperative Research Centre, Hobart, Tasmania, Australia^{a}now at: the Department of Earth, Ocean and Ecological Sciences, University of Liverpool, Liverpool, UK

^{1}Institute for Marine and Antarctic Studies, University of Tasmania, Hobart, Tasmania, Australia^{2}CSIRO Oceans and Atmosphere, CSIRO Marine Laboratories, G.P.O. Box 1538, Hobart, Tasmania, Australia^{3}ARC Centre of Excellence in Climate System Science, Hobart, Tasmania, Australia^{4}Antarctic Climate and Ecosystems Cooperative Research Centre, Hobart, Tasmania, Australia^{a}now at: the Department of Earth, Ocean and Ecological Sciences, University of Liverpool, Liverpool, UK

**Correspondence**: Pearse J. Buchanan (pearse.buchanan@liverpool.ac.uk)

**Correspondence**: Pearse J. Buchanan (pearse.buchanan@liverpool.ac.uk)

Abstract

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The isotopes of carbon (*δ*^{13}C) and nitrogen
(*δ*^{15}N) are commonly used proxies for understanding the ocean.
When used in tandem, they provide powerful insight into physical and
biogeochemical processes. Here, we detail the implementation of
*δ*^{13}C and *δ*^{15}N in the ocean component of an
Earth system model. We evaluate our simulated *δ*^{13}C and
*δ*^{15}N against contemporary measurements, place the model's
performance alongside other isotope-enabled models and document the response
of *δ*^{13}C and *δ*^{15}N to changes in ecosystem
functioning. The model combines the Commonwealth Scientific and Industrial
Research Organisation Mark 3L (CSIRO Mk3L) climate system model with the
Carbon of the Ocean, Atmosphere and Land (COAL) biogeochemical model. The
oceanic component of CSIRO Mk3L-COAL has a resolution of 1.6^{∘}
latitude × 2.8^{∘} longitude and resolves multimillennial
timescales, running at a rate of ∼400 years per day. We show that this
coarse-resolution, computationally efficient model adequately reproduces
water column and core-top *δ*^{13}C and *δ*^{15}N
measurements, making it a useful tool for palaeoceanographic research.
Changes to ecosystem function involve varying phytoplankton stoichiometry,
varying CaCO_{3} production based on calcite saturation state and
varying N_{2} fixation via iron limitation. We find that large changes
in CaCO_{3} production have little effect on *δ*^{13}C and
*δ*^{15}N, while changes in N_{2} fixation and phytoplankton
stoichiometry have substantial and complex effects. Interpretations of
palaeoceanographic records are therefore open to multiple lines of
interpretation where multiple processes imprint on the isotopic signature,
such as in the tropics, where denitrification, N_{2} fixation and
nutrient utilisation influence *δ*^{15}N. Hence, there is
significant scope for isotope-enabled models to provide more robust
interpretations of the proxy records.

How to cite

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How to cite.

Buchanan, P. J., Matear, R. J., Chase, Z., Phipps, S. J., and Bindoff, N. L.: Ocean carbon and nitrogen isotopes in CSIRO Mk3L-COAL version 1.0: a tool for palaeoceanographic research, Geosci. Model Dev., 12, 1491–1523, https://doi.org/10.5194/gmd-12-1491-2019, 2019.

1 Introduction

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Elements that are involved in reactions of interest, such as exchanges of
carbon and nutrients, experience isotopic fractionation. Typically, the
heavier isotope will be enriched in the reactant during kinetic
fractionation, in more oxidised compounds during equilibrium fractionation
and in the denser form during phase state fractionation (i.e. evaporation).
Because fractionation against one isotope relative to the other is minuscule,
the isotopic content of a sample is conventionally expressed as a *δ*
value (*δ*^{h}*E*), where the ratio of the heavy to light element
in solution (^{h}*E*:^{l}*E*) is compared to a standard ratio
(^{h}*E*_{std}:^{l}*E*_{std}) in units of per mille
(‰).

$$\begin{array}{}\text{(1)}& {\mathit{\delta}}^{\mathrm{h}}E=({\displaystyle \frac{{}^{\mathrm{h}}E\phantom{\rule{0.125em}{0ex}}:{}^{\mathrm{l}}E}{{}^{\mathrm{h}}{E}_{\mathrm{std}}\phantom{\rule{0.125em}{0ex}}:{}^{\mathrm{l}}{E}_{\mathrm{std}}}}-\mathrm{1})\cdot \mathrm{1000}\end{array}$$

The strength of fractionation against the heavier isotope during a given
reaction, *ϵ*, is also expressed in per mille notation. Fractionation
with an *ϵ* equal to 10 ‰, for example, will involve 990
units of ^{h}*E* for every 1000 units of ^{l}*E* at a
hypothetical standard ratio
(^{h}*E*_{std}:^{l}*E*_{std}) of 1:1. At more
realistic standard ratios *⋘*1:1, say 0.0112372:1 for a
*δ*^{13}C value of 0 ‰, a fractionation at 10 ‰
would involve $\sim \mathrm{0.0111123}(\mathrm{0.010}\cdot \frac{\mathrm{0.0112372}}{\mathrm{1.0112372}})$ units of ^{13}C per unit of
^{12}C. Slightly greater preference of one isotope over another in
this case involves a preference for the lighter carbon isotope
(^{12}C) over the heavier (^{13}C), which enriches the
remaining dissolved inorganic carbon (DIC) in ^{13}C and depletes the
product. Certain isotopic preferences, or strengths of fractionation,
therefore allow certain reactions to be detected in the environment.

The measurement of the stable isotopes of carbon (*δ*^{13}C) and
nitrogen (*δ*^{15}N) have been fundamental for understanding how these
important elements cycle within the ocean (e.g. Schmittner and Somes, 2016; Menviel et al., 2017a; Rafter et al., 2017; Muglia et al., 2018). We will now briefly introduce each
isotope in turn.

The distribution of *δ*^{13}C is dependent on air–sea gas exchange,
ocean circulation and organic matter cycling. These contributions make the
*δ*^{13}C signature difficult to interpret, and several modelling
studies have attempted to elucidate their roles (Tagliabue and Bopp, 2008; Schmittner et al., 2013). These studies have shown that preferential uptake of
^{12}C over ^{13}C by biology in surface waters enforces strong
horizontal and vertical gradients in *δ*^{13}C of DIC
(*δ*^{13}C_{DIC}), greatly enriching surface waters, particularly
in subtropical gyres where vertical exchange with deeper waters is restricted
(Tagliabue and Bopp, 2008; Schmittner et al., 2013). Meanwhile, air–sea gas exchange and
carbon speciation control the *δ*^{13}C_{DIC} reservoir over longer
timescales (Schmittner et al., 2013). Because air–sea and speciation
fractionation are temperature dependent, such that cooler conditions tend to
elevate the *δ*^{13}C_{DIC} of surface waters, they also tend to
smooth the gradients produced by biology by working antagonistically to them.
Despite this smoothing, biological fractionation drives strong gradients at
the surface, which imparts unique *δ*^{13}C signatures to the water
masses that are carried into the interior. These insights have provided clear
evidence of reduced ventilation rates in the deep ocean during glacial
climates (Tagliabue et al., 2009; Menviel et al., 2017a; Muglia et al., 2018).

*δ*^{15}N is determined by biological processes that add or remove
fixed forms of nitrogen. It therefore records the relative rates of sources
and sinks within the marine nitrogen cycle (Brandes and Devol, 2002). Dinitrogen
(N_{2}) fixation is the largest source of fixed nitrogen to the ocean,
the bulk of which occurs in warm, sunlit surface waters and introduces
nitrogen with a *δ*^{15}N of approximately −1 ‰
(Sigman et al., 2009). Denitrification is the largest sink of fixed nitrogen and
occurs in deoxygenated water columns and sediments. Denitrification
fractionates strongly against ^{15}N at ∼25 ‰
(Cline and Kaplan, 1975). Fractionation during denitrification is most strongly
expressed in the water column where ample nitrate (NO_{3}) is available,
making water column denitrification responsible for elevating global mean
*δ*^{15}N above the −1 ‰ of N_{2} fixers
(Brandes and Devol, 2002). Meanwhile, denitrification occurring in the sediments
only weakly fractionates against ^{15}N (Sigman et al., 2009), providing
only a slight enrichment of *δ*^{15}N above that introduced by
N_{2} fixation. Variations in *δ*^{15}N can therefore tell us
about global changes in the ratio of sedimentary to water column
denitrification, with increases in *δ*^{15}N associated with
increases in the proportion of denitrification occurring in the water column
(Galbraith et al., 2013), but it can also reflect regional changes in N_{2}
fixation and denitrification (Ganeshram et al., 1995; Ren et al., 2009; Straub et al., 2013).

However, nitrogen isotopes are also subject to the effect of utilisation,
which makes the interpretation of *δ*^{15}N more complicated.
Basically, when nitrogen is abundant, the preference for ^{14}N over
^{15}N increases but when nitrogen is limited this preference
disappears (Altabet and Francois, 2001). Complete utilisation of nitrogen therefore
reduces fractionation to 0 ‰. While this adds complexity, it also
imbues *δ*^{15}N as a proxy of nutrient utilisation by
phytoplankton. As nitrogen supply to phytoplankton is controlled by physical
delivery from below, changes in *δ*^{15}N can be interpreted as
changes in the physical supply (Studer et al., 2018). Phytoplankton fractionate
against ^{15}N at ∼5 ‰ (Wada, 1980) when
bioavailable nitrogen is abundant. If nitrogen is utilised to completion,
which occurs in much of the low to midlatitude ocean, then no fractionation
will occur and the *δ*^{15}N of organic matter will reflect the
*δ*^{15}N of the nitrogen that was supplied (Sigman et al., 2009).
However, in the case where nitrogen is not consumed towards completion, which
occurs in zones of strong upwelling/mixing near coastlines, the Equator and
high latitudes, the bioavailable nitrogen pool will be enriched in
^{15}N as phytoplankton preferentially consume ^{14}N. As the
remaining bioavailable N is continually enriched in ^{15}N, the organic
matter that settles into sediments beneath a zone of incomplete nutrient
utilisation will bear this enriched *δ*^{15}N signal. In
combination with modelling (Schmittner and Somes, 2016), the *δ*^{15}N
record is able to provide evidence for a more efficient utilisation of
bioavailable nitrogen during glacial times (Martinez-Garcia et al., 2014; Kemeny et al., 2018) and a less efficient one during the Holocene (Studer et al., 2018).

Complimentary measurements of *δ*^{13}C and *δ*^{15}N
provide powerful, multi-focal insights into oceanographic processes.
*δ*^{13}C is largely a reflection of how water masses mix away the
strong vertical and horizontal gradients enforced by biology, while
*δ*^{15}N simultaneously reflects changes in the major sources and
sinks of the marine nitrogen cycle and how effectively nutrients are consumed
at the surface. However, the interpretation of these isotopes is often
difficult. They are subject to considerable uncertainty because there are
multiple processes that imprint on the measured values. Our goal is to equip
version 1.0 of the Commonwealth Scientific and Industrial
Research Organisation Mark 3L (CSIRO Mk3L) climate system model with the
Carbon of the Ocean, Atmosphere and Land (COAL) Earth system model with oceanic
*δ*^{13}C and *δ*^{15}N such that this model can be used
for interpreting palaeoceanographic records. First, we introduce CSIRO
Mk3L-COAL. Second, we detail the equations that govern the implementation of
carbon and nitrogen isotopes. Third, we assess our simulated isotopes against
contemporary measurements from both the water column and sediments and
compare the model performance against other isotope-enabled models. Finally,
as a first test of the model, we take the opportunity to document how changes
in ecosystem functioning affect *δ*^{13}C and *δ*^{15}N.

2 CSIRO Mk3L-COAL v1.0

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The CSIRO Mk3L-COAL couples a computationally efficient climate system model (Phipps et al., 2013) with biogeochemical cycles in the ocean, atmosphere and land. The model is therefore based on the CSIRO Mk3L climate system model, where the “L” denotes that it is a low-resolution version of the CSIRO Mk3 model that contributed towards the third phase of Coupled Model Intercomparison Project (Meehl et al., 2007) and the Fourth Assessment Report of the Intergovernmental Panel on Climate Change (Solomon et al., 2007). See Smith (2007) for a complete discussion of the CSIRO family of climate models. The land biogeochemical component represents carbon, nitrogen and phosphorus cycles in the Community Atmosphere Biosphere Land Exchange (CABLE) (Mao et al., 2011). The ocean component currently represents carbon, alkalinity, oxygen, nitrogen, phosphorus and iron cycles. The atmospheric component conserves carbon and alters its radiative properties according to changes in its carbon content. For this paper, we focus on the ocean biogeochemical model (OBGCM).

Previous versions of the OBGCM have explored changes in oceanic properties
under past (Buchanan et al., 2016), present (Buchanan et al., 2018) and future
scenarios (Matear and Lenton, 2014, 2018). These studies demonstrate that the
model can reproduce observed features of the global carbon cycle, nutrient
cycling and organic matter cycling in the ocean. The OBGCM offers highly
efficient simulations of these processes at computational speeds of
∼400 years per day when the ocean general circulation model (OGCM) is
run offline (compared to ∼10 years per day in fully coupled mode). The
ocean is made up of grid cells of 1.6^{∘} in latitude by 2.8^{∘} in
longitude, with 21 vertical depth levels spaced by 25 m at the surface and
450 m in the deep ocean (Table 1). The OGCM time step is 1 h,
while the OBGCM time step is 1 d. The ability of the OBGCM to reproduce
large-scale dynamical and biogeochemical properties of the ocean coupled with
its fast computational speed makes the OBGCM useful as a tool for
palaeoceanographic research.

The OBGCM is equipped with 13 prognostic tracers (Fig. 1).
These can be grouped into carbon chemistry fields, oxygen fields, nutrient
fields, age tracers and nitrous oxide (N_{2}O). Carbon chemistry fields
include DIC, alkalinity (ALK), DI^{13}C
and radiocarbon (^{14}C). Radiocarbon is simulated according to
Toggweiler et al. (1989). Oxygen fields include dissolved oxygen (O_{2})
and abiotic dissolved oxygen (${\mathrm{O}}_{\mathrm{2}}^{\mathrm{abio}}$), a purely physical tracer
from which true oxygen utilisation (TOU) can be calculated
(Duteil et al., 2013). Nutrient fields include phosphate (PO_{4}),
dissolved bioavailable iron (Fe), nitrate (NO_{3}) and ^{15}NO_{3}.
Although we define the phosphorus and nitrogen tracers as their dominant
species, being PO_{4} and NO_{3}, these tracers can also be thought
of as total dissolved inorganic phosphorus and nitrogen pools.
Remineralisation, for instance, implicitly accounts for the process of
nitrification from ammonium (NH_{4}) to NO_{3} (Paulmier et al., 2009)
and therefore implicitly includes NH_{4} and nitrite (NO_{2})
within the NO_{3} tracer. Age tracer fields include years since
subduction from the surface (Age_{gbl}) and years since entering a
suboxic zone where O_{2} concentrations are less than 10 mmol m^{−3}
(Age_{omz}). Finally, N_{2}O in µmol m^{−3} is
produced via nitrification and denitrification according to the
temperature-dependent equations of Freing et al. (2012). All air–sea gas
exchanges (CO_{2}, ^{13}CO_{2}, O_{2} and N_{2}O)
and carbon speciation reactions are computed according to the Ocean Modelling
Intercomparison Project phase 6 protocol (Orr et al., 2017).

Because the isotopes of carbon and nitrogen are influenced by biological
processes and there is as yet no accepted standard for ecosystem model
parameterisation in the community (see Hülse et al., 2017, for a more detailed
discussion), we provide a thorough description of the ecosystem
component of the OBGCM in Sect. A in the Appendix. Default parameters for the
OBGCM are further provided in Sect. B in the Appendix. Briefly, the
ecosystem model simulates the production, remineralisation and stoichiometry
(elemental composition) of three types of primary producers: a general
phytoplankton group, diazotrophs (N_{2} fixers) and calcifiers.

3 Carbon and nitrogen isotope equations

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The OBGCM explicitly simulates the fractionation of ^{13}C from the
total DIC pool, where for simplicity we make the assumption that the total
DIC pool represents the light isotope of carbon and is therefore
DI^{12}C. Fractionation occurs during air–sea gas exchange,
equilibrium reactions and biological consumption in the euphotic zone.

The air–sea gas exchange of ^{13}CO_{2} is calculated as
the exchange of CO_{2} with additional fractionation factors applied to
the sea–air and air–sea components (Zhang et al., 1995; Orr et al., 2017). The flux of
^{13}CO_{2} across the air–sea interface,
*F*(^{13}CO_{2}), therefore takes the form of CO_{2} with
additional terms that convert to units of ^{13}C in both environments.
Without any isotopic fractionation, the equation requires the gas piston
velocity of carbon dioxide in m s^{−1} (${k}_{{\mathrm{CO}}_{\mathrm{2}}}$), the
concentration of aqueous CO_{2} in both mediums at the air–sea interface
in mmol m^{−3} (${\mathrm{CO}}_{\mathrm{2}}^{\mathrm{air}}$ and ${\mathrm{CO}}_{\mathrm{2}}^{\mathrm{sea}}$) and the ratios
of ^{13}C:^{12}C in both mediums (*R*_{atm} and
*R*_{sea}):

$$\begin{array}{ll}\text{(2)}& {\displaystyle}& {\displaystyle}F\left({}^{\mathrm{13}}{\mathrm{CO}}_{\mathrm{2}}\right)={k}_{{\mathrm{CO}}_{\mathrm{2}}}\cdot (\phantom{\rule{0.125em}{0ex}}{\mathrm{CO}}_{\mathrm{2}}^{\mathrm{air}}\cdot {R}_{\mathrm{atm}}\phantom{\rule{0.125em}{0ex}}-\phantom{\rule{0.125em}{0ex}}{\mathrm{CO}}_{\mathrm{2}}^{\mathrm{sea}}\cdot {R}_{\mathrm{DIC}}\phantom{\rule{0.125em}{0ex}}),{\displaystyle}& {\displaystyle}\text{where}\\ {\displaystyle}& {\displaystyle}{R}_{\mathrm{DIC}}={\displaystyle \frac{{\mathrm{DI}}^{\mathrm{13}}\mathrm{C}}{{\mathrm{DI}}^{\mathrm{13}}\mathrm{C}+{\mathrm{DI}}^{\mathrm{12}}\mathrm{C}}}\\ {\displaystyle}& {\displaystyle}{R}_{\mathrm{atm}}={\displaystyle \frac{{}^{\mathrm{13}}{\mathrm{CO}}_{\mathrm{2}}}{{}^{\mathrm{13}}{\mathrm{CO}}_{\mathrm{2}}+{}^{\mathrm{12}}{\mathrm{CO}}_{\mathrm{2}}}}=\mathrm{0.011164381}.\end{array}$$

A transfer of ^{13}C into the ocean is therefore positive and an
outgassing is negative. The *R*_{atm} is set to a preindustrial
atmospheric *δ*^{13}C of −6.48 ‰ (Friedli et al., 1986).

The fractionation of carbon isotopes during air–sea exchange involves three
components. These are (${\mathit{\u03f5}}_{\mathrm{k}}^{{}^{\mathrm{13}}\mathrm{C}}$), a kinetic
fractionation that occurs during transfer of gaseous CO_{2} into or out
of the ocean; (${\mathit{\u03f5}}_{\mathrm{aq}\leftarrow \mathrm{g}}^{{}^{\mathrm{13}}\mathrm{C}}$), a fractionation
that occurs as gaseous CO_{2} becomes aqueous CO_{2} (is dissolved
in solution); and (${\mathit{\u03f5}}_{\mathrm{DIC}\leftarrow \mathrm{g}}^{{}^{\mathrm{13}}\mathrm{C}}$), an
equilibrium isotopic fractionation as carbon speciates into DIC constituents (H_{2}CO_{2} ⇔
${\mathrm{HCO}}_{\mathrm{3}}^{-}$ ⇔ ${\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}$). The kinetic fractionation
during transfer, ${\mathit{\u03f5}}_{\mathrm{k}}^{{}^{\mathrm{13}}\mathrm{C}}$, is constant at 0.99912, thus
reducing the *δ*^{13}C of carbon entering the ocean by
0.88 ‰. Conversely, carbon outgassing increases the
*δ*^{13}C of the ocean. The fractionations during dissolution
(${\mathit{\u03f5}}_{\mathrm{aq}\leftarrow \mathrm{g}}^{{}^{\mathrm{13}}\mathrm{C}}$) and speciation
(${\mathit{\u03f5}}_{\mathrm{DIC}\leftarrow \mathrm{g}}^{{}^{\mathrm{13}}\mathrm{C}}$) are both dependent on
temperature. Fractionation during speciation is also dependent on the
fraction of ${\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}$ relative to total DIC (${f}_{{\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}}$).
These fractionation factors are parameterised as

$$\begin{array}{}\text{(3)}& {\displaystyle}& {\displaystyle}{\mathit{\u03f5}}_{\mathrm{aq}\leftarrow \mathrm{g}}^{{}^{\mathrm{13}}\mathrm{C}}={\displaystyle \frac{\mathrm{0.0049}\cdot T-\mathrm{1.31}}{\mathrm{1000}}}+\mathrm{1}\text{(4)}& {\displaystyle}& {\displaystyle}{\mathit{\u03f5}}_{\mathrm{DIC}\leftarrow \mathrm{g}}^{{}^{\mathrm{13}}\mathrm{C}}={\displaystyle \frac{\mathrm{0.0144}\cdot T\cdot {f}_{{\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}}-\mathrm{0.107}\cdot T+\mathrm{10.53}}{\mathrm{1000}}}+\mathrm{1}.\end{array}$$

Dissolution of CO_{2} into seawater (${\mathit{\u03f5}}_{\mathrm{aq}\leftarrow \mathrm{g}}^{{}^{\mathrm{13}}\mathrm{C}}$) therefore preferences the lighter isotope and lowers
*δ*^{13}C by between 1.32 ‰ and 1.14 ‰, while the
speciation of gaseous CO_{2} into DIC instead prefers the heavier
isotope and raises *δ*^{13}C by between 10.7 ‰ and
6.8 ‰ for temperatures between −2 and 35 ^{∘}C.

These fractionation factors are applied to the gaseous exchange of
CO_{2} (Eq. 2) to calculate carbon isotopic fractionation.

$$\begin{array}{ll}{\displaystyle}F\left({}^{\mathrm{13}}{\mathrm{CO}}_{\mathrm{2}}\right)=& {\displaystyle}\phantom{\rule{0.25em}{0ex}}k\cdot {\mathit{\u03f5}}_{\mathrm{k}}^{{}^{\mathrm{13}}\mathrm{C}}\cdot {\mathit{\u03f5}}_{\mathrm{aq}\leftarrow \mathrm{g}}^{{}^{\mathrm{13}}\mathrm{C}}\\ \text{(5)}& {\displaystyle}& {\displaystyle}\cdot (\phantom{\rule{0.125em}{0ex}}{\mathrm{CO}}_{\mathrm{2}}^{\mathrm{air}}\cdot {R}_{\mathrm{atm}}\phantom{\rule{0.125em}{0ex}}-\phantom{\rule{0.125em}{0ex}}{\displaystyle \frac{{\mathrm{CO}}_{\mathrm{2}}^{\mathrm{sea}}\cdot {R}_{\mathrm{DIC}}}{{\mathit{\u03f5}}_{\mathrm{DIC}\leftarrow \mathrm{g}}^{{}^{\mathrm{13}}\mathrm{C}}}}\phantom{\rule{0.125em}{0ex}})\end{array}$$

Because fractionation to aqueous CO_{2} from DIC
(${\mathit{\u03f5}}_{\mathrm{aq}\leftarrow \mathrm{DIC}}^{{}^{\mathrm{13}}\mathrm{C}}$) is equal to
$\frac{{\mathit{\u03f5}}_{\mathrm{aq}\leftarrow \mathrm{g}}^{{}^{\mathrm{13}}\mathrm{C}}}{{\mathit{\u03f5}}_{\mathrm{DIC}\leftarrow \mathrm{g}}^{{}^{\mathrm{13}}\mathrm{C}}}$, a strong preference to
hold the heavy isotope in solution exists (${\mathit{\u03f5}}_{\mathrm{aq}\leftarrow \mathrm{DIC}}^{{}^{\mathrm{13}}\mathrm{C}}=-\mathrm{11.9}$ ‰ to −7.9 ‰ between −2 and
35 ^{∘}C). Aqueous carbon that is transferred to the atmosphere is
hence depleted in ^{13}C. It is therefore the equilibrium
fractionation associated with carbon speciation that is largely responsible
for bolstering the oceanic *δ*^{13}C signature above the
atmospheric signature, as it tends to shift ^{13}C towards the
oxidised species (${\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}$), a tendency that strengthens under cooler
conditions.

In the default version of CSIRO Mk3L-COAL v1.0, the fractionation of carbon
during biological uptake (${\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}$) is
set at 21 ‰ for general phytoplankton, 12 ‰ for diazotrophs
(e.g. Carpenter et al., 1997) and at 2 ‰ for the formation of
calcite (Ortiz et al., 1996). However, a variable fractionation rate for the
general phytoplankton group may be activated and depends on the aqueous
CO_{2} concentration (CO_{2}(aq) in mmol m^{−3}) and the growth
rate (µ in d^{−1}, as a function of temperature and limiting
resources) following Tagliabue and Bopp (2008):

$$\begin{array}{}\text{(6)}& {\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}=(\mathrm{0.371}-{\displaystyle \frac{\mathit{\mu}}{{\mathrm{CO}}_{\mathrm{2}\left(\mathrm{aq}\right)}}})/\mathrm{0.015}.\end{array}$$

An upper bound of 25 ‰ exists within Eq. (6) when $\frac{\mathit{\mu}}{{\mathrm{CO}}_{\mathrm{2}\left(\mathrm{aq}\right)}}$ approaches zero but a lower bound does not. We chose to limit ${\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}$ to a minimum of 15 ‰ given the reported variations of ${\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}$ from culture studies (e.g. Laws et al., 1995).

$$\begin{array}{}\text{(7)}& {\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}=max(\mathrm{15},{\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}})\end{array}$$

Biological fractionation of ^{13}C is then applied to the uptake and
release of organic carbon.

$$\begin{array}{}\text{(8)}& {\displaystyle}{\displaystyle}\mathrm{\Delta}{\mathrm{DI}}^{\mathrm{13}}\mathrm{C}={R}_{\mathrm{DIC}}\cdot {\mathrm{C}}_{\mathrm{org}}\cdot (\mathrm{1}-{\displaystyle \frac{{\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}}{\mathrm{1000}}})\end{array}$$

Because biological fractionation is strong for the general phytoplankton
group, which dominates export production throughout most of the ocean, this
imparts a negative *δ*^{13}C signature to the deep ocean.
Subsequent remineralisation releases DIC with no fractionation. Finally, the
concentration of DI^{13}C is converted into a *δ*^{13}C via

$$\begin{array}{}\text{(9)}& {\mathit{\delta}}^{\mathrm{13}}\mathrm{C}=({\displaystyle \frac{{\mathrm{DI}}^{\mathrm{13}}\mathrm{C}}{\mathrm{DIC}}}\cdot {\displaystyle \frac{\mathrm{1}}{\mathrm{0.0112372}}}-\mathrm{1})\cdot \mathrm{1000},\end{array}$$

where 0.0112372 is the Pee Dee Belemnite standard (Craig, 1957).

The OBGCM explicitly simulates the fractionation of ^{15}N from the
pool of bioavailable nitrogen. For simplicity, we treat this bioavailable pool
as nitrate (NO_{3}), where total NO_{3} is the sum of
^{15}NO_{3} and ^{14}NO_{3}. We therefore chose to ignore
fractionation during reactions involving ammonium, nitrite and dissolved
organic nitrogen, which can vary in their isotopic composition independent of
NO_{3} but represent a small fraction of the bioavailable pool of
nitrogen.

The isotopic signatures of N_{2} fixation and atmospheric deposition,
and the fractionation during water column denitrification
(${\mathit{\u03f5}}_{\mathrm{wc}}^{{}^{\mathrm{15}}\mathrm{N}}$) and sedimentary denitrification
(${\mathit{\u03f5}}_{\mathrm{sed}}^{{}^{\mathrm{15}}\mathrm{N}}$) determine the global *δ*^{15}N of
NO_{3} (Brandes and Devol, 2002). Biological assimilation
(${\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{15}}\mathrm{N}}$) and remineralisation are internal exchanges
of the oceanic nitrogen cycle and affect the distribution of
*δ*^{15}NO_{3}. N_{2} fixation and atmospheric deposition
introduce ^{15}NO_{3} to the ocean with *δ*^{15}N values of
−1 ‰ and −2 ‰, respectively, while biological
assimilation, water column denitrification and sedimentary denitrification
fractionate against ^{15}NO_{3} at 5 ‰, 20 ‰ and
3 ‰, respectively (Sigman et al., 2009, Fig. 1).

The accepted standard ^{15}N:^{14}N ratio used to measure variations
in nature is the average atmospheric ^{15}N:^{14}N ratio of 0.0036765.
To minimise numerical errors caused by the OGCM, we set the atmospheric
standard to 1. This scales up the ^{15}NO_{3} such that a
*δ*^{15}N value of 0 ‰ was equivalent to a
^{15}N:^{14}N ratio of 1:1.

Because we simulate NO_{3} and ^{15}NO_{3} as tracers, our
calculations require solving for an implicit pool of ^{14}NO_{3} during
each reaction involving ^{15}NO_{3}. The introduction of NO_{3} at
a fixed ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ of −1 ‰ due to remineralisation
of N_{2} fixer biomass provides a simple example with which we can begin
to describe our equations. Setting the isotopic value of newly fixed
NO_{3} to −1 ‰ is simple because it removes any complications
associated with fractionation. We note, however, that in reality the
nitrogenase enzyme does fractionate during its conversion of aqueous
N_{2} (+0.7 ‰) to ammonium and the biomass that is
subsequently produced can vary substantially depending of the type of
nitrogenase enzyme used (vanadium versus molybdenum based)
(McRose et al., 2019). However, we choose to implicitly account for these
transformations and considerably simplify them by setting the
*δ*^{15}N of N_{2} fixer biomass equal to −1 ‰,
which reflects the biomass of N_{2} fixers associated with the more
common Mo-nitrogenase.

A ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ of −1 ‰ is equivalent to a
^{15}N:^{14}N ratio of 0.999 in our approach, where 0 ‰ equals
a 1:1 ratio of ^{15}N:^{14}N. If the amount of NO_{3} being
added is known alongside its ^{15}N:^{14}N ratio, in this case 0.999
for N_{2} fixation, we are able to calculate how much ^{15}NO_{3}
is added. We begin with two equations that describe the system.

$$\begin{array}{}\text{(10)}& {\displaystyle}& {\displaystyle}{\mathrm{NO}}_{\mathrm{3}}={}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{3}}+{}^{\mathrm{14}}{\mathrm{NO}}_{\mathrm{3}}\text{(11)}& {\displaystyle}& {\displaystyle}{\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}=({\displaystyle \frac{{}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{3}}{/}^{\mathrm{14}}{\mathrm{NO}}_{\mathrm{3}}}{{}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{std}}/{}^{\mathrm{14}}{\mathrm{N}}_{\mathrm{std}}}}-\mathrm{1})\cdot \mathrm{1000}\end{array}$$

Ultimately, we need to solve for the change in ^{15}NO_{3} associated
with an introduction of NO_{3} by N_{2} fixation. Our known variables are
the change in NO_{3}, the *δ*^{15}N of that NO_{3} and
the ^{15}N_{std}∕^{14}N_{std}. Our two unknowns are ^{15}NO_{3}
and ^{14}NO_{3}. We must solve for ^{14}NO_{3} implicitly by
describing it according to ^{15}NO_{3} by rearranging
Eq. (11).

$$\begin{array}{}\text{(12)}& {\displaystyle}{\displaystyle}{}^{\mathrm{14}}{\mathrm{NO}}_{\mathrm{3}}={}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{3}}/\left(\right({\displaystyle \frac{{\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}}{\mathrm{1000}}}+\mathrm{1})\cdot {}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{std}}{/}^{\mathrm{14}}{\mathrm{N}}_{\mathrm{std}})\end{array}$$

This allows us to replace the ^{14}NO_{3} term in Eq. (10),
such that

$$\begin{array}{}\text{(13)}& {\displaystyle}{\mathrm{NO}}_{\mathrm{3}}={}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{3}}+{}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{3}}/\left(\right({\displaystyle \frac{{\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}}{\mathrm{1000}}}+\mathrm{1})\cdot {}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{std}}{/}^{\mathrm{14}}{\mathrm{N}}_{\mathrm{std}}).\end{array}$$

In our example of N_{2} fixation, we know the *δ*^{15}N of the
newly added NO_{3} as being −1 ‰. We also know
^{15}N_{std}∕^{14}N_{std} as equal to 1:1, or 1. Our equation is
simplified.

$$\begin{array}{}\text{(14)}& {\displaystyle}{\displaystyle}{\mathrm{NO}}_{\mathrm{3}}={}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{3}}+{}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{3}}/\mathrm{0.999}\end{array}$$

We can now solve for ^{15}NO_{3} by rearranging the equation.

$$\begin{array}{}\text{(15)}& {\displaystyle}{\displaystyle}{}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{3}}={\displaystyle \frac{\mathrm{0.999}\cdot {\mathrm{NO}}_{\mathrm{3}}}{\mathrm{1}+\mathrm{0.999}}}\end{array}$$

The same calculation is applied to NO_{3} addition via
atmospheric deposition, except at a constant fraction of 0.998
(*δ*^{15}N $=-\mathrm{2}$ ‰), and can be applied to any addition
or subtraction of ^{15}NO_{3} relative to NO_{3} where the isotopic
signature is known.

Fractionating against ^{15}NO_{3} during biological
assimilation (${\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{15}}\mathrm{N}}$), water column
denitrification (${\mathit{\u03f5}}_{\mathrm{wc}}^{{}^{\mathrm{15}}\mathrm{N}}$) and sedimentary
denitrification (${\mathit{\u03f5}}_{\mathrm{sed}}^{{}^{\mathrm{15}}\mathrm{N}}$) involves more
considerations because we must account for the preference of ^{14}NO_{3}
over ^{15}NO_{3}. We begin with an *ϵ* of 5 ‰ for
biological assimilation. This is equivalent to a ^{15}NO_{3}:^{14}NO_{3}
ratio of 0.995 when our atmospheric standard is equal to 1:1 using the
following equation.

$$\begin{array}{}\text{(16)}& {\displaystyle}{\displaystyle}\mathit{\u03f5}=({\displaystyle \frac{{}^{\mathrm{15}}\mathrm{N}{/}^{\mathrm{14}}\mathrm{N}}{{}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{std}}{/}^{\mathrm{14}}{\mathrm{N}}_{\mathrm{std}}}}-\mathrm{1})\cdot \mathrm{1000}\end{array}$$

Note that a positive *ϵ* value returns a ^{15}NO_{3}:^{14}NO_{3}
ratio <1, while a negative *δ*^{15}N in the previous example
with N_{2} fixation also returned a ^{15}NO_{3}:^{14}NO_{3} ratio <1. This works because the reactions are in opposite directions. N_{2}
fixation adds NO_{3}, while assimilation removes NO_{3}. This means
that 0.995 units of ^{15}NO_{3} are assimilated per unit of
^{14}NO_{3}. As we have seen, a more useful way to quantify this is per
unit of NO_{3} assimilated into organic matter. Using
Eq. (15), we find that ∼0.4987 units of ^{15}NO_{3}
and ∼0.5013 units of ^{14}NO_{3} are assimilated per unit (1.0) of
NO_{3} when *ϵ* equals 5 ‰. Biological assimilation
therefore leaves slightly more ^{15}N in the unused NO_{3} pool
relative to ^{14}N, which increases the *δ*^{15}N of
NO_{3} while creating more ^{15}N-deplete organic matter
(*δ*^{15}N_{org}).

However, we must also account for the effect that NO_{3} availability
has on fractionation. The preference of ^{14}NO_{3} over
^{15}NO_{3} strongly depends on the availability of NO_{3}, such
that when NO_{3} is abundant the preference for the lighter isotope will
be strongest. This preference (fractionation) becomes weaker as NO_{3}
is depleted because cells will absorb any NO_{3} that is available
irrespective of its isotopic composition (Mariotti et al., 1981). Thus, as
NO_{3} is utilised, *u*, towards 100 % of its availability (*u*=1),
the fractionation against ^{15}NO_{3} decreases to an *ϵ* of
0 ‰. This means that when *u* is equal to 1, no fractionation occurs
and equal parts ^{15}N and ^{14}N (0.5:0.5 per unit
NO_{3}) are assimilated. As we are interested in long timescales, we
chose the accumulated product equations (Altabet and Francois, 2001) to approximate
this process, where

$$\begin{array}{}\text{(17)}& {\displaystyle}& {\displaystyle}u=min(\mathrm{0.999},max(\mathrm{0.001},{\displaystyle \frac{{\mathrm{N}}_{\mathrm{org}}}{{\mathrm{NO}}_{\mathrm{3}}}}\left)\right)\text{(18)}& {\displaystyle}& {\displaystyle}{\mathit{\u03f5}}_{\mathrm{u}}=\mathit{\u03f5}\cdot {\displaystyle \frac{\mathrm{1}-u}{u}}\cdot \mathrm{ln}(\mathrm{1}-u).\end{array}$$

For numerical reasons, we limited the domain of *u* to (0.001,0.999) rather
than (0,1), such that the utilisation-affected *ϵ*_{u} has a
range of −4.997 to −0.035 ‰ for an *ϵ* of 5 ‰.
*ϵ*_{u} is then converted into ratio units by dividing by 1000
and added to the ambient ^{15}N:^{14}N of NO_{3} in the reactant
pool to determine the ^{15}N:^{14}N of the product. In this case, it
is the ^{15}N:^{14}N of newly created organic matter but could also
be unused NO_{3} effluxed from denitrifying cells in the case for
denitrification.

$$\begin{array}{}\text{(19)}& {\displaystyle}{\displaystyle}{}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}{:}^{\mathrm{14}}{\mathrm{N}}_{\mathrm{org}}={}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{3}}{:}^{\mathrm{14}}{\mathrm{NO}}_{\mathrm{3}}+{\mathit{\u03f5}}_{\mathrm{u}}\end{array}$$

We then solve for how much ^{15}NO_{3} is assimilated into organic
matter using Eq. (15) because we now know the change in
NO_{3} (ΔNO_{3}) and the ^{15}N:^{14}N of the product,
which is ^{15}N_{org}∕^{14}N_{org} in our example of biological
assimilation.

$$\begin{array}{}\text{(20)}& {\displaystyle}{\displaystyle}{\mathrm{\Delta}}^{\mathrm{15}}{\mathrm{NO}}_{\mathrm{3}}={\displaystyle \frac{{}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}{/}^{\mathrm{14}}{\mathrm{N}}_{\mathrm{org}}\cdot \mathrm{\Delta}{\mathrm{NO}}_{\mathrm{3}}}{\mathrm{1}+{}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}{/}^{\mathrm{14}}{\mathrm{N}}_{\mathrm{org}}}}\end{array}$$

Here, the change in ^{15}NO_{3} is equivalent to that assimilated into
organic matter. Following assimilation into organic matter, the release of
^{15}NO_{3} through the water column during remineralisation occurs with
no fractionation, such that the same *δ*^{15}N signature is
released throughout the water column.

We apply these calculations to each reaction in the nitrogen cycle that
involves fractionation (assimilation, water column denitrification and
sedimentary denitrification). They could be applied to any form of
fractionation process with knowledge of *ϵ*, the isotopic ratio of the
reactant, the amount of reactant that is used and the total amount of
reactant available.

4 Model performance

Back to toptop
CSIRO Mk3L-COAL adequately reproduces the large-scale thermohaline properties
and circulation of the ocean under preindustrial conditions in numerous prior
studies (Phipps et al., 2013; Matear and Lenton, 2014; Buchanan et al., 2016, 2018). Rather
than reproduce these studies, we concentrate here on how the biogeochemical
model performs relative to measurements of *δ*^{13}C and
*δ*^{15}N in the water column (Eide et al., 2017, ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$
data courtesy of the Sigman Lab at Princeton University) and in the
sediments (Tesdal et al., 2013; Schmittner et al., 2017). We make these model–data
comparisons alongside other isotope-enabled ocean general circulation models
(Table 1).

All analyses of model performance were undertaken using the default parameterisation of the biogeochemical model, which is summarised in the tables of Sect. B in the Appendix. Each experiment was run towards steady state under preindustrial atmospheric conditions over many thousands of years. All results presented in this paper therefore reflect tracers that have achieved an equilibrium solution. We present annual averages of the equilibrium state in the following analysis.

The recent reconstruction of preindustrial *δ*^{13}C_{DIC} by
Eide et al. (2017) provides a large dataset for comparison. We chose this
dataset over the compilation of point location water column data of
Schmittner et al. (2017) because it offers a gridded product where short-term
and small-scale variability are smoothed, making for more appropriate
comparison with model output.

Predicted values of *δ*^{13}C_{DIC} from CSIRO Mk3L-COAL broadly
replicated the preindustrial distribution. The predicted global mean of
0.41 ‰ reflected that of the reconstructed mean of 0.42 ‰
(Table 2). Spatial agreement was acceptable with a global
correlation of 0.80 (G marker in Fig. 2). Regionally, the
Southern Ocean performed well with the lowest root mean square (rms) error of 0.42 ‰,
while a greater degree of disagreement in the values of
*δ*^{13}C_{DIC} existed in the middle and lower latitudes of each
major basin, particularly in the Atlantic where model–data agreement
(correlation, rms error and normalised standard deviation) was poorest.
Subsurface *δ*^{13}C_{DIC} was too low in the tropics of the major
basins by ∼0.2 ‰ and too high in the North Pacific and North
Atlantic by 0.4 ‰ to 0.6 ‰ (Fig. 3).

These inconsistencies were likely related to physical and biological
limitations of CSIRO Mk3L-COAL. *δ*^{13}C_{DIC} in subsurface
tropical waters was too low because restricted horizontal mixing and high
carbon export drove very negative *δ*^{13}C_{DIC} values. The very
negative *δ*^{13}C values were associated with very large oxygen
minimum zones and were thus a product of poorly represented, fine-scale
equatorial dynamics. Coarse-resolution OGCMs are known to have weak
equatorial undercurrents that lead to oxygen minimum zones that are too large
(Matear and Holloway, 1995; Oschlies, 2000) and CSIRO Mk3L-COAL is no exception.
Alternatively, the large oxygen minimum zones could be due to our
conservative treatment of organic matter remineralisation
(Sect. A in the Appendix), where remineralisation is prevented when O_{2}
and NO_{3} are unavailable. Organic matter therefore falls deeper into
the interior through oxygen-deficient zones, leading to their vertical
expansion. Almost certainly, however, it was the poorly represented dynamics
within the Pacific basin that were responsible for high
*δ*^{13}C_{DIC} in the subsurface North Pacific, which contains low
O_{2} and low *δ*^{13}C_{DIC} water due to northward transport
from the tropics.

Another inconsistency was a positive bias in the upper 200–500 m, with
values exceeding 2 ‰ in many areas of the lower latitudes. However,
values as high as 2 ‰ have been measured in the upper 500 m of the
Indo-Pacific (Schmittner et al., 2017). Given the difficulties associated with
accounting for the Suess effect (invasion of isotopically light fossil fuel
CO_{2}), it is possible that the upper ocean values of Eide et al. (2017)
underestimate the preindustrial *δ*^{13}C_{DIC} surface field.
It is also equally possible that a fixed biological fractionation
(${\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}$) of 21 ‰ may have driven
unrealistic enrichment in the simulated field. High growth rates are thought to lower the strength of
fractionation during carbon fixation (Laws et al., 1995). To explore the
possibility of model–data mismatch caused by our choice to fix
${\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}$ at 21 ‰, we implemented biological
fractionation that is dependent on phytoplankton growth rate and aqueous
CO_{2} concentration (Eq. 6). We found the implementation
of a variable ${\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}$ reduced high values in the
upper part of the low-latitude ocean but that this reduction was small
(Fig. 4). The overwhelming effect was an increase in
*δ*^{13}C_{DIC} throughout the interior, itself caused by weaker
fractionation in the tropical ocean. Global mean *δ*^{13}C_{DIC}
subsequently increased by 0.25 ‰. Meanwhile, model skill was
unaffected (see CSIRO Mk3L-COAL (vary-${\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}$)
in Fig. 2). Neither fixed nor variable biological
fractionation could reproduce the low upper ocean values of the data.

It is helpful to place our predicted *δ*^{13}C_{DIC} alongside
those of other global ocean models (Fig. 2;
Table 2), both for skill assessment and to further understand the
cause of the positive bias in the upper ocean. We take annually averaged,
preindustrial *δ*^{13}C_{DIC} distributions from the UVic-MOBI,
PISCES, LOVECLIM and iCESM-low biogeochemical models, most of which have been
used in significant palaeoceanographic modelling studies (Menviel et al., 2017a; Tagliabue et al., 2009; Schmittner and Somes, 2016). Predicted *δ*^{13}C_{DIC} performs
adequately in CSIRO Mk3L-COAL relative to these state-of-the-art models.
LOVECLIM showed good fit in terms of global and regional means
(Table 2) but had lower correlations (Fig. 2),
suggesting that its values were accurate but its distribution biased.
UVic-MOBI had high correlations, but it consistently overestimated the
preindustrial field by ∼0.2 ‰. Interestingly, the bias of
UVic-MOBI, which treats biological fractionation as a function of growth rate
and aqueous CO_{2}, is similar to CSIRO Mk3L-COAL when this form of
fractionation was activated (vary-${\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}$).
PISCES and iCESM-low were the best performing models, equally demonstrating
high correlations, low biases, accurate regional and global means and the
lowest rms errors. This is perhaps not surprising considering the
significantly finer vertical resolutions of these OGCMs and their more
complex horizontal grid structure that enables an improved representation of
ocean dynamics (Table 1). However, all models performed most
poorly in the Atlantic Ocean, with poor correlations, high variability and
greater biases.

Returning to the consistent positive bias in the upper ocean, most models
(except iCESM-low) predicted upper ocean
*δ*^{13}C_{DIC} ≥ 2.0 ‰ (Figs. S1, S2,
S3 and S4 in the Supplement) similar to CSIRO Mk3L-COAL. As each model has a unique
representation of the marine ecosystem and consequently a unique treatment of
biological fractionation, the common prediction of high upper ocean
*δ*^{13}C once more suggests that the upper ocean values between
200 and 500 m of Eide et al. (2017) may be too low. The underestimation of
*δ*^{13}C_{DIC} may be due to a neglect of biology introducing
anthropogenic, isotopically depleted carbon to surface and subsurface layers
via remineralisation (the biological Suess effect). This would in turn
suggest that a higher global mean of 0.73 ‰ generated from a global
compilation of foraminiferal *δ*^{13}C (Schmittner et al., 2017) is
perhaps a more accurate representation of preindustrial *δ*^{13}C
values.

Overall, CSIRO Mk3L-COAL performed acceptably in terms of its mean values and
correlations but had consistently greater rms errors in major basins outside
of the Southern Ocean. This indicates that CSIRO Mk3L-COAL exaggerated
regional minima and maxima as discussed. Despite the regional biases of CSIRO
Mk3L-COAL, the comparison demonstrates that all models have strengths and
weaknesses. Given its low resolution and computational efficiency, CSIRO
Mk3L-COAL performs adequately among other biogeochemical models in its
simulation of *δ*^{13}C_{DIC}.

We extended our assessment of modelled *δ*^{13}C_{DIC} by comparing
it to a compilation of benthic *δ*^{13}C measured within the
calcite of foraminifera from the genus *Cibicides*
(Schmittner et al., 2017), a genus on which much of the palaeoceanographic
*δ*^{13}C records are based. For this comparison, we adjusted our
predicted *δ*^{13}C_{DIC} to predicted *δ*^{13}C_{Cib}
using the linear dependence on carbonate ion concentration and depth
suggested by Schmittner et al. (2017):

$$\begin{array}{ll}{\displaystyle}{\mathit{\delta}}^{\mathrm{13}}{\mathrm{C}}_{\mathrm{Cib}}=& {\displaystyle}\phantom{\rule{0.25em}{0ex}}\mathrm{0.45}+{\mathit{\delta}}^{\mathrm{13}}{\mathrm{C}}_{\mathrm{DIC}}-\mathrm{2.2}\times {\mathrm{10}}^{-\mathrm{3}}\\ \text{(21)}& {\displaystyle}& {\displaystyle}\cdot {\mathrm{CO}}_{\mathrm{3}}-\mathrm{6.6}\times {\mathrm{10}}^{-\mathrm{5}}\cdot z.\end{array}$$

This adjustment accounts for slight fractionation during incorporation of DIC
into foraminiferal calcite and is found to be partly explained by the
concentration of ${\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}$ ions and pressure. A one-to-one comparison
between *δ*^{13}C_{DIC} and *δ*^{13}C_{Cib} hence
introduces some degree of error since this fractionation is not accounted
for. Because we are interested in applying simulated
*δ*^{13}C_{DIC} to a palaeoceanographic context, we must first be
able to convert our simulated *δ*^{13}C_{DIC} to
*δ*^{13}C_{Cib} in an effort to make better comparisons,
particularly as the distribution of ${\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}$ is subject to change. By
adjusting our three-dimensional *δ*^{13}C_{DIC} output using
Eq. (21), we attain predicted *δ*^{13}C_{Cib} (see
inset titled “calibration” in Fig. 5). For good
measure, we also computed measures of statistical fit for a traditional one-to-one
comparison between *δ*^{13}C_{DIC} and
*δ*^{13}C_{Cib} to assess the benefit of the calibration.

Measured *δ*^{13}C_{Cib} data from Schmittner et al. (2017) were
binned into model grid boxes and averaged for the comparison. Those
measurements that fell within the OGCM's land mask were excluded. Transfer
and averaging onto the coarse-resolution OGCM grid reduced the number of
points for comparison from 1763 to 690, lowered the mean of measured
*δ*^{13}C_{Cib} from 0.76 ‰ to 0.52 ‰ and reduced
the absolute range from $-\mathrm{0.9}\to \mathrm{2.1}$ to $-\mathrm{0.7}\to \mathrm{2.1}$.

Adjusted *δ*^{13}C_{Cib} using Eq. (21) showed
good fit to measured *δ*^{13}C_{Cib} given the sparsity of data,
with a global correlation of 0.64, a mean of 0.57 ‰ and an rms error
of 0.63 ‰ (Table 3). If a one-to-one relationship
between *δ*^{13}C_{DIC} and *δ*^{13}C_{Cib} was used, the
global correlation was not affected and only slightly worse skill was
detected in mean, rms error and standard deviation. Accounting for the
regional influence of carbonate ion concentration and depth was therefore
beneficial, likely because very negative and positive values were slightly
adjusted towards the mid-range (inset in Fig. 5), but
this was not necessary for an adequate comparison. This conclusion was also
reached by Schmittner et al. (2017). Likewise, implementing variable
fractionation by phytoplankton (${\mathit{\u03f5}}_{\mathrm{bio}}^{{}^{\mathrm{13}}\mathrm{C}}$) had
little effect except to increase values and slightly improve measures of
skill (Table 3). Of the 690 data points used in the
comparison, 419 fell within the error around what could be considered a good
fit (shaded red area in Fig. 5). The error was taken as
0.29 ‰ and represents the standard deviation associated with the
relationship between *δ*^{13}C_{DIC} and *δ*^{13}C_{Cib}
measurements (Schmittner et al., 2017).

Some notable over and underestimation occurred in the adjusted
*δ*^{13}C_{Cib} output that more or less mirrored those
inconsistencies previously discussed for *δ*^{13}C_{DIC}. Values as
low as −1.9 ‰, well below measured *δ*^{13}C_{Cib}
minima of −0.7 ‰, existed in the equatorial subsurface Pacific and
Indian oceans (i.e. where the oxygen minimum zones existed). This can be seen
in Fig. 5, where some values in the equatorial band are
well below the shaded region of good fit. Meanwhile, very high values of
*δ*^{13}C_{Cib} were predicted in Arctic surface waters. The
exaggeration of these local minima and maxima reflects those found in the
modelled *δ*^{13}C_{DIC} distribution. Despite these local
inconsistencies, CSIRO Mk3L-COAL shows good potential for direct comparisons
to palaeoceanographic data sets of foraminiferal *δ*^{13}C with or
without calibration.

We produced univariate measures of fit by comparing measurements of ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ with equivalent values from CSIRO Mk3L-COAL at the nearest point (Fig. 6; Table 4). Measured ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ values were collected over a 30-year period using a variety of collection and measurement methods with a distinct bias towards the Atlantic Ocean. To try and remove some temporal and spatial bias, we binned and averaged measurements into equivalent model grids.

CSIRO Mk3L-COAL adequately reproduced the global patterns of
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$. We found excellent agreement in the
volume-weighted means of ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ (Table 4).
Tight agreement in the means was a consequence of reproducing similar values
where the majority of observed data existed. Most ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$
measurements have been taken from the upper 1000 m in the North Atlantic
where values cluster at just under 5 ‰ (see Fig. 7a, c, e). Closer inspection of the Atlantic using depth
and zonally averaged sections (Figs. 8
and 9) revealed that the model adequately reproduced the low
*δ*^{15}N signature of ∼4 ‰ caused by N_{2}
fixation occurring in the tropical Atlantic (Marconi et al., 2017). A basin-wide
rate of Atlantic N_{2} fixation equal to ∼33 Tg N yr^{−1}
lowered Atlantic values below 5 ‰ and was fundamental for
reproducing the observations. Outside the Atlantic, where data are more sparse,
the model successfully reproduced the meridional gradients across the
Antarctic, Subantarctic and subtropical zones, the subsurface
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ maxima in the tropics of all major basins and the
tongues of high and low values in surface waters of the Pacific consistent
with changes in nitrate utilisation (Figs. 8
and 9).

Some important regional inconsistencies between the simulated and measured
values did exist (refer to Figs. 8 and 9)
and degraded the correlation. Much like the high values of
*δ*^{13}C_{DIC} that were transported too deeply into the North
Atlantic interior, a low ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ signature was transported
too far into the deep North Atlantic. CSIRO Mk3L-COAL therefore
underestimated deep ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ before mixing through to the
South Atlantic restored values towards the measurements. Subsurface values in
the North Pacific were also underestimated, which can be attributed to the
inability of the coarse-resolution OGCM to transport low O_{2}, high
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ water northwards from the eastern tropical
Pacific. Simulated values in the Indian Ocean, specifically near the
Arabian Sea, significantly underestimated the data because the suboxic zone
was misrepresented in the Bay of Bengal. Misrepresentation of the northern Indian
Ocean was responsible for very poor model–data fit in the Indian Ocean
(Fig. 6). Meanwhile, the deep (>1500 m) eastern tropical
Pacific tended to overestimate the data, due to a large, deep, unimodal
suboxic zone. These physically driven inconsistencies in the oxygen field are
common to other coarse-resolution models (Oschlies et al., 2008; Schmittner et al., 2008) and, like the *δ*^{13}C distribution, were the main
cause of the misfit between simulated and observed
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$. The correlations reflected these regional under-
and overestimations, particularly in the Indian Ocean.

Finally, we placed CSIRO Mk3L-COAL in the context of other isotope-enabled
global models: UVic-MOBI, PISCES and iCESM-high (Table 1).
This comparison demonstrated that the modelled distribution of
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ was adequately placed among the current generation
of models. The global and regional means were more accurately reproduced by
CSIRO Mk3L-COAL than for UVic-MOBI, PISCES and iCESM-high
(Table 4; also see shading in Fig. 6). Atlantic
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ was best reproduced by CSIRO Mk3L-COAL. Meanwhile,
correlations tended to be slightly lower for CSIRO Mk3L-COAL than UVic-MOBI
and iCESM-high, and consistently lower than PISCES (Fig. 6).
UVic-MOBI underestimated the data but produced high correlations in the
Southern Ocean and globally. Regionally, PISCES was best correlated to the
measurements of ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ of the three models, although it
had a consistent positive bias. iCESM-high was acceptably correlated with the
data in the global sense but was highest in rms errors, particularly in the
Pacific. CSIRO Mk3L-COAL therefore showed an acceptable measure of fit to the
noisy and sparse ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ data and reproduced most regional
patterns, albeit with misrepresentation in the Indian Ocean and some
exaggerations of local minima/maxima as discussed. Future model–data
comparisons with CSIRO Mk3L-COAL should therefore take these limitations into
account. Overall, however, we find that CSIRO Mk3L-COAL broadly reproduced
the ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ data. Annual rates of N_{2} fixation,
water column denitrification and sedimentary denitrification at roughly 122,
52 and 78 Tg N yr^{−1}, respectively, produced this agreement.

An important caveat to the ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ routines of CSIRO
Mk3L-COAL should be noted. CSIRO Mk3L-COAL underwent significant tuning of
water column and sedimentary denitrification parameterisations in order to
reproduce known values of ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ during development. One
important parameter is the lower threshold of NO_{3} concentration at
which point water column denitrification is shut off (Sect. A2.3).
In CSIRO Mk3L-COAL, this is set at 30 mmol m^{−3}, which is an arbitrary
limit that was implemented to prevent water column denitrification from
reducing NO_{3} to zero in the large suboxic zones. Hence, a caveat of
the current model is an inability for water column and sedimentary
denitrification to realistically adjust as suboxia changes. However, the
parameterisation does allow for targeted experiments where the ratio of water
column to sedimentary denitrification can be controlled if, for instance, it
is unclear how water column and sedimentary denitrification respond to
certain conditions. This is currently the case during the Last Glacial
Maximum, where expansive suboxic zones in the Pacific (Hoogakker et al., 2018)
were counter-intuitively associated with reduced rates of water column
denitrification (Ganeshram et al., 1995). We have, in this version, chosen to
keep this parameterisation and note that future developments will focus on
dynamic responses to variations in suboxia.

CSIRO Mk3L-COAL tracks the *δ*^{15}N signature of organic matter
(*δ*^{15}N_{org}) that is deposited in the sediments. We compared
the simulated *δ*^{15}N_{org} to the core-top compilation of
Tesdal et al. (2013) with 2176 records of *δ*^{15}N_{org}. These
records were binned and averaged onto the CSIRO Mk3L-COAL ocean grid, such
that the 2176 records became 592. When comparing sediment core-top
measurements of *δ*^{15}N to that of the model, it is necessary to
consider how *δ*^{15}N_{org} is altered by early burial. As records
in the compilation of Tesdal et al. (2013) are from bulk nitrogen, we can
assume that the “diagenetic offset” as described by Robinson et al. (2012) is
active. The diagenetic offset involves an increase in the *δ*^{15}N
of sedimentary nitrogen of between 0.5 ‰ and 4.1 ‰ relative to that of
sinking particulate organic matter and appears to be related to pressure
(Robinson et al., 2012), although the reasoning behind this relationship remains
to be defined.

In light of the diagenetic offset, we make three comparisons with the compilation of Tesdal et al. (2013). A raw comparison is made, alongside an attempt to account for the diagenetic offset using two depth-dependent corrections (Table 5 and Fig. 10):

$$\begin{array}{}\text{(22)}& {\displaystyle}& {\displaystyle}{\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}^{\mathrm{cor}:\mathrm{1}}=\left\{\begin{array}{ll}{\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}},& \text{if}\phantom{\rule{0.25em}{0ex}}z\left(\mathrm{km}\right)<\mathrm{1}\phantom{\rule{0.125em}{0ex}}\mathrm{km}\\ {\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}+(\mathrm{1}\cdot z(\mathrm{km})+\mathrm{1}),& \text{if}\phantom{\rule{0.25em}{0ex}}z\left(\mathrm{km}\right)\ge \mathrm{1}\phantom{\rule{0.125em}{0ex}}\mathrm{km}\end{array}\right.\text{(23)}& {\displaystyle}& {\displaystyle}{\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}^{\mathrm{cor}:\mathrm{2}}={\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}+\mathrm{0.9}\cdot z\left(\mathrm{km}\right).\end{array}$$

The first correction (${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}^{\mathrm{cor}:\mathrm{1}}$) is taken from
Robinson et al. (2012), while the second (${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}^{\mathrm{cor}:\mathrm{2}}$)
originates from how Schmittner and Somes (2016) treated sedimentary nitrogen
isotope data in their study of the Last Glacial Maximum. Both are based on
the observation that the diagenetic offset increases with pressure, in this
case represented by depth (*z*) in kilometres (km).

Following binning and averaging onto the model grid, the raw comparison
immediately showed a consistent underestimation of the core-top data, with a
predicted mean of 2.7 ‰ well below the observed mean of
4.7 ‰. Our correlation was 0.27, which indicates a limited ability
to replicate regional patterns. This underestimation and low correlation is
easily seen when predicted values are compared directly to the core-top data
in Fig. 10. Like the nitrogen isotope model of
Somes et al. (2010), we find that the offset between simulated and observed
core-top bulk *δ*^{15}N_{org} is roughly equivalent to the observed
average diagenetic offset of $\sim \mathrm{2.3}\pm \mathrm{1.8}$ ‰. This indicates that
diagenetic alteration of *δ*^{15}N_{org} is active during early
burial in the core-top data.

Including a diagenetic offset therefore improved agreement between our
predicted *δ*^{15}N_{org} and the core-top data considerably
(Table 5 and Fig. 10). Both corrections
accounted for the enrichment of *δ*^{15}N in deeper regions and the
minor diagenetic alteration in areas of high sedimentation that typically
occurs in shallower sediments. The average *δ*^{15}N_{org} increased
to 4.5 ‰ for ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}^{\mathrm{cor}:\mathrm{1}}$ and 5.2 ‰
for ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}^{\mathrm{cor}:\mathrm{2}}$. Correlations increased from 0.27 to
0.47 and 0.53, respectively. The improvement was clearly observed in the
Southern Ocean, where both the magnitude and spatial pattern of
*δ*^{15}N_{org} were well replicated by the model. Changes in the
Southern Ocean over glacial–interglacial cycles reflect shifts in the global
marine nitrogen cycle and nutrient utilisation (Martinez-Garcia et al., 2014; Studer et al., 2018), and the ability of CSIRO Mk3L-COAL to account for these patterns
in the core-top data is encouraging for future study. We suggest that future
palaeoceanographic model–data comparisons of *δ*^{15}N_{org} use
the depth correction of Schmittner and Somes (2016) as it provided the best
correlations and reproduced Southern Ocean *δ*^{15}N_{org} at
0.5 ‰ greater than the global mean (see Table 5).

5 Ecosystem effects

Back to toptop
As a first test of the isotope-enabled ocean model, we undertook simple
ecosystem experiments to assess the effect on *δ*^{13}C and
*δ*^{15}N. For reference, the assessment of model performance
described above used model output with variable stoichiometry activated, a
fixed 8 % rain ratio of CaCO_{3} to organic carbon and a strong iron
limitation of N_{2} fixers that enforced a low degree of spatial
coupling between N_{2} fixers and denitrification zones. A summary of
the biogeochemical effects of the different experiments is provided in
Table 6.

Enabling variable stoichiometry (see Sect. A3 in the Appendix) of the general
phytoplankton group (${\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}$) over a Redfieldian ratio
($\mathrm{C}:\mathrm{N}:\mathrm{P}:{\mathrm{O}}_{\mathrm{2}}^{\mathrm{rem}}:{\mathrm{NO}}_{\mathrm{3}}^{\mathrm{rem}}$ $=\mathrm{106}:\mathrm{16}:\mathrm{1}:-\mathrm{138}:-\mathrm{94.4}$) altered
the rate and distribution of organic matter export. Organic matter had more
carbon and nitrogen per unit phosphorus in regions with low PO_{4}, such
as the Atlantic Ocean (Fig. 11a), which elevated O_{2}
and NO_{3} demand during oxic and suboxic remineralisation
(denitrification), respectively. Lower ratios were produced in eutrophic
regions such as the subarctic Pacific, Southern Ocean and tropical zones of
upwelling. Overall, global mean C:P increased from the Redfieldian
106:1 to 117:1 and caused an increase in carbon export from 7.6 to
8.0 Pg C yr^{−1}. Approximately 0.1 Pg C yr^{−1}, or 25 % of the
increase, was attributed purely to organic carbon export from N_{2}
fixation, which increased from 107 to 122 Tg N yr^{−1} as higher
N:P ratios in the tropics broadened their competitive niche. The total
contribution of N_{2} fixation to the increase in carbon export was
likely greater than 25 %, as NO_{3} also became more available to
NO_{3}-limited ecosystems in the lower latitudes (Moore et al., 2013). The
increase in carbon export under variable stoichiometry as compared to a
Redfieldian ocean was therefore felt largely in the lower latitudes between
40^{∘} S and 40^{∘} N (Fig. 11b). Export
production decreased poleward of 40^{∘}, particularly in the Southern
Ocean, because C:P ratios were lower than the 106:1 Redfield ratio
(Fig. 11a).

Distributions of both isotopes were affected by the change in carbon export
and the marine nitrogen cycle. Global mean *δ*^{13}C_{DIC}
increased from 0.47 ‰ to 0.51 ‰ and
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ increased from 5.1 ‰ to 5.6 ‰.
These are not great changes on the global scale and they had little influence
on model–data measures of fit. However, the spatial distribution of these
isotopes was significantly altered. Intermediate waters leaving the Southern
Ocean were depleted in *δ*^{13}C_{DIC} by up to 0.1 ‰ and
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ by up to 1 ‰, while the deep ocean,
particularly the Pacific, was enriched in both isotopes to a similar degree
(Fig. 12). Depletion of both isotopes in waters subducted
between 40 and 60^{∘} S reflected the local loss in export production
as a result of lower C:P and N:P ratios, such that biological
fractionation was unable to enrich DIC and NO_{3} in the heavier isotope
to the same degree as surface waters travelled north. Enrichment of
*δ*^{13}C in the deep ocean was the result of reduced carbon export
in the Antarctic zone due to low C:P ratios, while enrichment of
*δ*^{15}N in the deep ocean was the result of increased tropical
production that increased water column denitrification
(${\mathit{\u03f5}}_{\mathrm{wc}}^{{}^{\mathrm{15}}\mathrm{N}}$ =20 ‰). Lower C:P and
N:P ratios in both the Antarctic and Subantarctic zones therefore
elicited divergent isotope effects in deep and intermediate waters leaving
the Southern Ocean.

Meanwhile, each isotope showed a different response in the suboxic zones of
the tropics where variable stoichiometry increased the volume of suboxia
(O_{2}<10 mmol m^{−3}) by 0.5 %. The increase in water column
denitrification caused by the expansion of suboxia increased
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$, while the local increase in carbon export that
drove the increase in water column denitrification reduced
*δ*^{13}C_{DIC} in the same waters (Fig. 12).
Overall, the increase in low-latitude carbon export caused an expansion of
water column suboxia and elicited diverging behaviours in the isotopes,
whereby ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ increased and *δ*^{13}C_{DIC}
decreased.

The rate of calcification of planktonic foraminifera and coccolithophores is
dependent on the calcite saturation state (Zondervan et al., 2001). In previous
experiments, the production of CaCO_{3} was fixed at a rate of 8 % per
unit of organic carbon produced in accordance with the modelling study of
Yamanaka and Tajika (1996) and produced 0.54 Pg CaCO_{3} yr^{−1}. Now we
investigate how spatial variations in the CaCO_{3}:C_{org} ratio
(${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$ in Eq. A17) affected
*δ*^{13}C_{DIC} and *δ*^{13}C_{Cib} (see
Sect. A1.3 in the Appendix). We applied three different values of *η* to
Eq. (A18) to alter the quantity of CaCO_{3} produced per
unit of organic carbon (${\mathrm{C}}_{\mathrm{org}}^{\mathrm{G}}$) given the calcite saturation
state (Ω_{ca}). The *η* coefficients were 0.53, 0.81 and
1.09. These numbers are equivalent to those in the experiments of
Zhang and Cao (2016).

Mean ${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$ was 4.5 %, 6.6 % and 9.5 %, and annual CaCO_{3}
production was 0.32, 0.47 and 0.68 Pg CaCO_{3} yr^{−1} in the three
experiments. Although different in total CaCO_{3} production, the three
experiments shared the same spatial patterns. Low-latitude waters were high
in ${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$, particularly the oligotrophic subtropical gyres, while
high latitudes were low, particularly the Antarctic zone where mixing of old
waters into the surface depressed the calcite saturation state
(Fig. 13). These regional patterns in ${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$
therefore had the largest effect in areas of high export production.
Productive, high-latitude areas like the Southern Ocean, subpolar Pacific and
North Atlantic waters all produced less CaCO_{3} when compared to an
enforced 8 % rain ratio, while CaCO_{3} production between
40^{∘} S and 40^{∘} N relative to a fixed ${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$ of
8 % was dependent on *η*. The highest *η* coefficient of 1.09
achieved greater export of CaCO_{3} in the mid- to lower-latitude regions
of high export production (Fig. 13). The consequence of
increasing CaCO_{3} production in the middle–lower latitudes was a loss of
upper ocean alkalinity, subsequent outgassing of CO_{2} and losses in
the DIC inventory. Losses in global DIC were 95 and 130 Pg C as
${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$ increased from $\mathrm{4.6}\to \mathrm{6.6}\to \mathrm{9.5}$ %
(Table 6), equivalent to one-fifth of the glacial increase in
oceanic carbon (Ciais et al., 2011).

Despite the significant changes associated with the implementation of
Ω_{ca}-dependent CaCO_{3} production, effects were
negligible on both *δ*^{13}C_{DIC} and *δ*^{13}C_{Cib}.
Global mean *δ*^{13}C_{DIC} was 0.51 ‰, when
${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$ was fixed at 8 %, and this changed to 0.52 ‰,
0.50 ‰ and 0.48 ‰ under *η* coefficients of 0.53, 0.81
and 1.09 (Table 6). Likewise, global mean
*δ*^{13}C_{Cib} was 0.59 ‰, when ${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$ was
fixed at 8 %, and this changed to 0.60 ‰, 0.58 ‰ and
0.55 ‰. Minimal change in *δ*^{13}C_{Cib} indicated
minimal change in the ${\mathrm{CO}}_{\mathrm{3}}^{\mathrm{2}-}$ concentration (see
Eq. 21), which varied by ≤2 mmol m^{−3} between
experiments. Visual inspection of the change in *δ*^{13}C_{DIC} and
*δ*^{13}C_{Cib} distributions showed an enrichment of these
isotopes in the upper ocean north of 40^{∘} S. Subsequent increases in
*η*, which increased low-latitude CaCO_{3} production, magnified the
enrichment. Enrichment of *δ*^{13}C_{DIC} and
*δ*^{13}C_{Cib} was caused by outgassing of CO_{2} as surface
alkalinity decreased in response to greater CaCO_{3} production
(Fig. 14). The change, however, was at most 0.1 ‰,
which lies well within 1 standard deviation of variability known in the
proxy data (Schmittner et al., 2017). We therefore find little scope for
recognising even large variations in global CaCO_{3} production (0.32 to
0.68 Pg CaCO_{3} yr^{−1}) in the signature of carbon isotopes
despite considerable effects on the oceanic inventory of DIC.

However, we stress that version 1.0 of CSIRO Mk3L-COAL does not include
CaCO_{3} burial or dissolution from the sediments according the calcite
saturation state of overlying water (Boudreau, 2013). To neglect
ocean–sediment CaCO_{3} cycling is to neglect of an important aspect of
the global carbon cycle active on millennial timescales (Sigman et al., 2010).
Changes in CaCO_{3} burial and dissolution could have a non-negligible
effect on *δ*^{13}C through altering whole ocean alkalinity and
thereby air–sea gas exchange of CO_{2}, which would in turn affect
surface *δ*^{13}C as we have seen. While we do not address these
effects here, we aim to do so in upcoming versions of the model equipped with
carbon compensation dynamics.

The degree to which N_{2} fixers are spatially coupled to the tropical
denitrification zones is controlled by altering the degree to which
N_{2} fixers are limited by iron (${K}^{{\mathrm{D}}_{\mathrm{Fe}}}$) in
Eq. (A12) (see Sect. A1.2 in the Appendix). Decreasing
${K}^{{\mathrm{D}}_{\mathrm{Fe}}}$ ensures that N_{2} fixation becomes less dependent
on iron supply and as such is released from regions of high aeolian
deposition, such as the North Atlantic, to inhabit areas of low
NO_{3}:PO_{4} ratios. Areas of low NO_{3}:PO_{4} exist in the tropics
proximal to water column denitrification zones. Releasing N_{2} fixers
from Fe limitation therefore increases the spatial coupling between
N_{2} fixation and water column denitrification and increases the global
rate of N_{2} fixation.

We steadily decreased iron limitation (${K}^{{\mathrm{D}}_{\mathrm{Fe}}}$) to increase the
strength of spatial coupling between N_{2} fixers and the tropical
denitrification zones (Fig. 15). As N_{2} fixers
coupled more strongly to regions of low NO_{3}:PO_{4}, the rate of
N_{2} fixation increased from 122 to 144 to 154 Tg N yr^{−1}
(Table 6). An expansion of suboxia from 2.1 % to 2.5 % to
2.7 % of global ocean volume in the tropics accompanied the increase in
N_{2} fixation, as did a decrease in global mean
*δ*^{13}C_{DIC} of 0.06 ‰ and 0.1 ‰, since
greater rates of N_{2} fixation stimulated tropical export production.
Due to the expansion of the already large suboxic zones, which occurred in
both horizontal and vertical directions, the amount of organic carbon that
reached tropical sediments (20^{∘} S to 20^{∘} N) increased from
0.35 to 0.46 to 0.51 Pg C yr^{−1}.

The overarching consequence for ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ due to an
expansion of the suboxic zones was an increase in the sedimentary to water
column denitrification ratio from 1.5 to 1.9 to 2.2, which decreased mean
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ from 5.6 ‰ to 5.2 ‰ to
5.0 ‰ (Table 6). The increase in N_{2} fixation
(${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{\mathrm{org}}=-\mathrm{1}\phantom{\rule{0.125em}{0ex}}\mathrm{\u2030}$) and sedimentary denitrification
(${\mathit{\u03f5}}_{\mathrm{sed}}^{{}^{\mathrm{15}}\mathrm{N}}=\mathrm{3}\phantom{\rule{0.125em}{0ex}}\mathrm{\u2030}$) in the tropics was felt
globally for ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ (Fig. 16). Lower
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ by 0.5 ‰ and 0.9 ‰ permeated
water columns in the Southern Ocean and tropics, respectively. Meanwhile,
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ was up to 10 ‰ lower in surface waters of
the tropical and subtropical Pacific, which is where the greatest increase in
N_{2} fixation and sedimentary denitrification occurred. The dramatic
reduction in surface ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ was subsequently conveyed to
the sediments as *δ*^{15}N_{org}±1 ‰–2 ‰.

These simple experiments demonstrate that the insights garnered from
sedimentary records of *δ*^{15}N are open to multiple lines of
interpretation. An expansion of the suboxic zones, normally associated with
an increase in ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ (Galbraith et al., 2013), could
instead cause a decrease in ${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ if more organic matter
reached the sediments to stimulate sedimentary denitrification. There is good
evidence that the suboxic zones might have undergone a vertical expansion
(Hoogakker et al., 2018) and that more organic matter reached the tropical
sediments under glacial conditions (Cartapanis et al., 2016). The glacial
decrease in bulk *δ*^{15}N_{org} recorded in the eastern tropical
Pacific (Ganeshram et al., 1995; Liu et al., 2008) therefore does not necessarily mean a
decrease in suboxia. Rather, our experiments show that lower
*δ*^{15}N_{org} might also be caused by an increase in local
N_{2} fixation and sedimentary denitrification. The decrease in
${\mathit{\delta}}^{\mathrm{15}}{\mathrm{N}}_{{\mathrm{NO}}_{\mathrm{3}}}$ associated with more sedimentary denitrification
and local N_{2} fixation demonstrates the complexity of interpreting
sedimentary *δ*^{15}N_{org} records in the lower latitudes.

6 Conclusions

Back to toptop
The stable isotopes of carbon (*δ*^{13}C) and nitrogen
(*δ*^{15}N) are proxies that have been fundamental for
understanding the ocean. We have included both isotopes into the ocean
component of an Earth system model, CSIRO Mk3L-COAL, to enable future studies
with the capability for direct model–proxy data comparisons. We detailed how
these isotopes are simulated, how to conduct model–data comparisons using
both water column and sedimentary data and some basic assessment of changes
caused by altered ecosystem functioning. We made three overall findings.
First, CSIRO Mk3L-COAL performs well alongside a number of isotope-enabled
global ocean GCMs. Second, alteration of *δ*^{13}C during formation
of foraminiferal calcite does not jeopardise simple one-to-one comparisons
with simulated *δ*^{13}C of DIC, while diagenetic alteration of
bulk organic *δ*^{15}N during early burial must be accounted for in
model–data comparisons. Third, changes in how marine ecosystems function can
have significant and complex effects on *δ*^{13}C and
*δ*^{15}N. Our idealised experiments hence showed that the
interpretation of palaeoceanographic records may suffer from multiple lines
of interpretation, particularly records from the lower latitudes where
multiple processes imprint on the isotopic signatures laid down in sediments.
Future work will involve palaeoceanographic simulations of CSIRO Mk3L-COAL
that seek to understand how the oceanic carbon and nitrogen cycles respond to
and influence important climate transitions.

Data availability

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Data availability.

All model output is provided for download on Australia's National Computing Infrastructure (NCI) at https://geonetwork.nci.org.au/geonetwork/srv/eng/catalog.search\#/metadata/f3048_7378_3224_4737 (last access: 12 April 2019) and is citable with https://doi.org/10.25914/5c6643f64446c (Buchanan et al., 2019). Nitrogen isotope data are available by request to Dario M. Marconi and Daniel M. Sigman at Princeton University. LOVECLIM data are freely available for download at https://doi.org/10.4225/41/58192cb8bff06 (Menviel et al., 2017b). UVic-MOBI data were provided by Christopher Somes, PISCES data by Laurent Bopp, iCESM-high data from Simon Yang and iCESM-low data by Alexandra Jahn.

Code availability

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Code availability.

The source code for CSIRO Mk3L-COAL is shared via a
repository located at
http://svn.tpac.org.au/repos/CSIRO_Mk3L/branches/CSIRO_Mk3L-COAL/ (last access: 12 April 2019). Access to the repository may be obtained by following
the instructions at
https://www.tpac.org.au/csiro-mk3l-access-request/ (last access: 12 April 2019). Access to the source code is subject to a bespoke
license that does not permit commercial usage but is otherwise unrestricted.
An “out-of-the-box” run directory is also available for download with all
files required to run the model in the configuration used in this study,
although users will need to modify the *runscript* according to their
computing infrastructure.

Appendix A: Ecosystem component of the OBGCM

Back to toptop
The production of organic matter by the general phytoplankton group
(${\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}$) is measured in units of mmol phosphorus (P)
m^{−3} d^{−1} and is dependent on temperature (*T*), nutrients
(PO_{4}, NO_{3} and Fe) and irradiance (*I*):

$$\begin{array}{ll}\text{(A1)}& {\displaystyle}& {\displaystyle}{\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}={{\mathrm{S}}^{\mathrm{G}}}_{\mathrm{E}:\mathrm{P}}\cdot \mathit{\mu}(T{)}^{\mathrm{G}}\cdot min({\mathrm{P}}_{\mathrm{lim}}^{\mathrm{G}},{\mathrm{N}}_{\mathrm{lim}}^{\mathrm{G}},{\mathrm{Fe}}_{\mathrm{lim}}^{\mathrm{G}},F\left(I\right)),{\displaystyle}& {\displaystyle}\text{where}\\ {\displaystyle}& {\displaystyle}{{\mathrm{S}}^{\mathrm{G}}}_{\mathrm{E}:\mathrm{P}}=\mathrm{0.005}\phantom{\rule{0.25em}{0ex}}\mathrm{mmol}\phantom{\rule{0.125em}{0ex}}{\mathrm{PO}}_{\mathrm{4}}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{\mathrm{3}}\\ \text{(A2)}& {\displaystyle}& {\displaystyle}\mathit{\mu}(T{)}^{\mathrm{G}}=\mathrm{0.59}\cdot {\mathrm{1.0635}}^{T}\text{(A3)}& {\displaystyle}& {\displaystyle}F\left(I\right)=\mathrm{1}-{e}^{L\left(I\right)}\text{(A4)}& {\displaystyle}& {\displaystyle}L\left(I\right)={\displaystyle \frac{I\cdot \mathit{\alpha}\cdot \mathrm{PAR}}{\mathit{\mu}\left(T\right)}}.\end{array}$$

In the example above, S_{E:P} converts growth rates in units of d^{−1} to
mmol PO_{4} m^{−3} d^{−1}. S_{E:P} conceptually
represents the export to production ratio, and for simplicity we assume it
does not change. *μ*(*T*) is the temperature-dependent maximum daily growth
rate of phytoplankton (doubling per day), as defined by
Eppley (1972). The light limitation term (*F*(*I*)) is the productivity
versus irradiance equation used to describe phytoplankton growth defined by
Clementson et al. (1998) and is dependent on *I*, the daily averaged shortwave
incident radiation (W m^{−2}), *α*, the initial slope of the
productivity versus radiance curve (d^{−1} (W m^{−2})^{−1}) and PAR, the fraction of shortwave radiation
that is photosynthetically active.

The nutrient limitation terms (${\mathrm{P}}_{\mathrm{lim}}^{\mathrm{G}}$, ${\mathrm{N}}_{\mathrm{lim}}^{\mathrm{G}}$ and ${\mathrm{Fe}}_{\mathrm{lim}}^{\mathrm{G}}$) may be calculated in two ways.

If the option for static nutrient limitation is true, then Michaelis–Menten kinetics (Dugdale, 1967) is used:

$$\begin{array}{}\text{(A5)}& {\displaystyle}& {\displaystyle}{\mathrm{P}}_{\mathrm{lim}}^{\mathrm{G}}={\displaystyle \frac{{\mathrm{PO}}_{\mathrm{4}}}{{\mathrm{PO}}_{\mathrm{4}}+K{}_{{\mathrm{PO}}_{\mathrm{4}}}^{\mathrm{G}}}}\text{(A6)}& {\displaystyle}& {\displaystyle}{\mathrm{N}}_{\mathrm{lim}}^{\mathrm{G}}={\displaystyle \frac{{\mathrm{NO}}_{\mathrm{3}}}{{\mathrm{NO}}_{\mathrm{3}}+K{}_{{\mathrm{NO}}_{\mathrm{3}}}^{\mathrm{G}}}}\text{(A7)}& {\displaystyle}& {\displaystyle}{\mathrm{Fe}}_{\mathrm{lim}}^{\mathrm{G}}={\displaystyle \frac{\mathrm{Fe}}{\mathrm{Fe}+K{}_{\mathrm{Fe}}^{\mathrm{G}}}}.\end{array}$$

Half-saturation coefficients (${K}^{{\mathrm{G}}_{\mathrm{nutrient}}}$) show a large range
across phytoplankton species (e.g. Timmermans et al., 2004), and so for
simplicity, we set ${K}^{{\mathrm{G}}_{{\mathrm{PO}}_{\mathrm{4}}}}=\mathrm{0.1}$ mmol PO_{4} m^{−3}
(Smith, 1982), ${K}^{{\mathrm{G}}_{{\mathrm{NO}}_{\mathrm{3}}}}=\mathrm{0.75}$ mmol NO_{3} m^{−3}
(Eppley et al., 1969; Carpenter and Guillard, 1971) and ${K}^{{\mathrm{G}}_{\mathrm{Fe}}}=\mathrm{0.1}$ µmol Fe m^{−3} (Timmermans et al., 2001).

If the option for variable nutrient limitation is true (default), then optimal uptake kinetics (Smith et al., 2009) is used:

$$\begin{array}{ll}\text{(A8)}& {\displaystyle}& {\displaystyle}{\mathrm{P}}_{\mathrm{lim}}^{\mathrm{G}}={\mathrm{PO}}_{\mathrm{4}}\phantom{\rule{0.125em}{0ex}}/\phantom{\rule{0.125em}{0ex}}({\displaystyle \frac{{\mathrm{PO}}_{\mathrm{4}}}{\mathrm{1}-{f}_{A}}}+{\displaystyle \frac{V/A}{{f}_{A}\cdot \mathrm{N}:\mathrm{P}}})\text{(A9)}& {\displaystyle}& {\displaystyle}{\mathrm{N}}_{\mathrm{lim}}^{\mathrm{G}}={\mathrm{NO}}_{\mathrm{3}}\phantom{\rule{0.125em}{0ex}}/\phantom{\rule{0.125em}{0ex}}({\displaystyle \frac{{\mathrm{NO}}_{\mathrm{3}}}{\mathrm{1}-{f}_{A}}}+{\displaystyle \frac{V/A}{{f}_{A}}})\text{(A10)}& {\displaystyle}& {\displaystyle}{\mathrm{Fe}}_{\mathrm{lim}}^{\mathrm{G}}={\displaystyle \frac{\mathrm{Fe}}{\mathrm{Fe}+{K}_{\mathrm{Fe}}}},{\displaystyle}& {\displaystyle}\text{where}\\ {\displaystyle}& {\displaystyle}{f}_{A}=max\left[\right(\mathrm{1}+\sqrt{{\displaystyle \frac{\left[{\mathrm{NO}}_{\mathrm{3}}\right]}{V/A}}}{)}^{-\mathrm{1}},\\ \text{(A11)}& {\displaystyle}& {\displaystyle}\phantom{\rule{1em}{0ex}}(\mathrm{1}+\sqrt{{\displaystyle \frac{\left[{\mathrm{PO}}_{\mathrm{4}}\right]\cdot \mathrm{N}:\mathrm{P}}{V/A}}}{)}^{-\mathrm{1}}].\end{array}$$

Optimal uptake kinetics varies the two terms in the denominator of the
Michaelis–Menten form according to the availability of nutrients. It
therefore accounts for different phytoplankton communities with different
abilities for nutrient uptake and does so using the *f*_{A} term. The *V*∕*A*
term represents the maximum potential nutrient uptake, *V*, over the cellular
affinity for that nutrient, *A*, and is set at 0.1.

Organic matter produced by diazotrophs (${\mathrm{P}}_{\mathrm{org}}^{\mathrm{D}}$) is also
measured in units of mmol phosphorus (P) m^{−3} d^{−1} and is
calculated in the same form of Eq. (A1), but using the maximum
growth rate *μ*(*T*)^{D} of Kriest and Oschlies (2015), notable changes in the
limitation terms and minimum thresholds that ensure the nitrogen fixation
occurs everywhere in the ocean, except under sea ice. ${\mathrm{P}}_{\mathrm{org}}^{\mathrm{D}}$ is
calculated via

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\mathrm{P}}_{\mathrm{org}}^{\mathrm{D}}={{\mathrm{S}}^{\mathrm{D}}}_{\mathrm{E}:\mathrm{P}}\cdot \mathit{\mu}(T{)}^{\mathrm{D}}\cdot max(\mathrm{0.01},\phantom{\rule{0.125em}{0ex}}min({\mathrm{N}}_{\mathrm{lim}}^{\mathrm{D}},{\mathrm{P}}_{\mathrm{lim}},{\mathrm{Fe}}_{\mathrm{lim}}^{\mathrm{D}}))\\ \text{(A12)}& {\displaystyle}& {\displaystyle}\phantom{\rule{1em}{0ex}}\cdot (\mathrm{1}-\mathrm{ico}),{\displaystyle}& {\displaystyle}\text{where}\\ \text{(A13)}& {\displaystyle}& {\displaystyle}\mathit{\mu}(T{)}^{\mathrm{D}}=max(\mathrm{0.01},\phantom{\rule{0.125em}{0ex}}-\mathrm{0.0042}{T}^{\mathrm{2}}+\mathrm{0.2253}T-\mathrm{2.7819})\text{(A14)}& {\displaystyle}& {\displaystyle}{\mathrm{N}}_{\mathrm{lim}}^{\mathrm{D}}={e}^{-{\mathrm{NO}}_{\mathrm{3}}}\text{(A15)}& {\displaystyle}& {\displaystyle}{\mathrm{P}}_{\mathrm{lim}}^{\mathrm{D}}={\displaystyle \frac{{\mathrm{PO}}_{\mathrm{4}}}{{\mathrm{PO}}_{\mathrm{4}}+{K}^{{\mathrm{D}}_{{\mathrm{PO}}_{\mathrm{4}}}}}}\text{(A16)}& {\displaystyle}& {\displaystyle}{\mathrm{Fe}}_{\mathrm{lim}}^{\mathrm{D}}=max(\mathrm{0.0},\phantom{\rule{0.125em}{0ex}}\mathrm{tanh}(\mathrm{2}\mathrm{Fe}-{K}^{{\mathrm{D}}_{\mathrm{Fe}}}\left)\right).\end{array}$$

The half-saturation values for PO_{4} and Fe limitation are set at
0.1 mmol m^{−1} and 0.5 µmol m^{−1}, respectively, in the
default parameterisation. The motivation for making N_{2} fixers
strongly limited by Fe was the high cellular requirements of Fe for
diazotrophy (see Sohm et al., 2011, and references therein). A dependency on
light is omitted from the limitation term when ${\mathrm{P}}_{\mathrm{org}}^{\mathrm{D}}$ is
produced. The omission of light is justified by its strong correlation with
sea surface temperature (Luo et al., 2014) and its negligible effect on nitrogen
fixation in the Atlantic Ocean (McGillicuddy, 2014). Finally, the
fractional area coverage of sea ice (ico) is included to ensure that cold
water N_{2} fixation (Sipler et al., 2017) does not occur under ice, since
a light dependency is omitted.

The calcifying group produces calcium carbonate (CaCO_{3}) in units of
mmol carbon (C) m^{−3} d^{−1}. The production of CaCO_{3} is
always a proportion of the organic carbon export of the general phytoplankton
group (${\mathrm{C}}_{\mathrm{org}}^{\mathrm{G}}$), according to

$$\begin{array}{}\text{(A17)}& {\displaystyle}{\displaystyle}{\mathrm{CaCO}}_{\mathrm{3}}={\mathrm{C}}_{\mathrm{org}}^{\mathrm{G}}\cdot {R}_{{\mathrm{CaCO}}_{\mathrm{3}}}.\end{array}$$

The ratio of CaCO_{3} to ${\mathrm{C}}_{\mathrm{org}}^{\mathrm{G}}$ (${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$) can be
calculated in two ways.

If the option for fixed ${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$ is true (default), then
${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$ is set to 0.08 as informed by the experiments of
Yamanaka and Tajika (1996). The production of CaCO_{3} is thus 8 % of
${\mathrm{C}}_{\mathrm{org}}^{\mathrm{G}}$ everywhere.

If the option for variable ${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$ is true, then
${R}_{{\mathrm{CaCO}}_{\mathrm{3}}}$ varies as a function of the saturation state of calcite
(Ω_{ca}) according to Ridgwell et al. (2007), where

$$\begin{array}{}\text{(A18)}& {\displaystyle}{\displaystyle}{R}_{{\mathrm{CaCO}}_{\mathrm{3}}}=\mathrm{0.022}\cdot ({\mathrm{\Omega}}_{\mathrm{ca}}-\mathrm{1}{)}^{\mathit{\eta}}.\end{array}$$

The exponent (*η*) is easily modified consistent with the
parameterisations of Zhang and Cao (2016) and controls the rate of CaCO_{3}
production at a given value of Ω_{ca}.

Organic matter produced by the general phytoplankton group (in units of
phosphorus: ${\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}$) at the surface is instantaneously
remineralised each time step at depth levels beneath the euphotic zone using a
power law scaled to depth (Martin et al., 1987). This power law defines the
concentration of organic matter remaining at a given depth
(${\mathrm{P}}_{\mathrm{org}}^{\mathrm{G},z}$) as a function of organic matter at
the surface (${\mathrm{P}}_{\mathrm{org}}^{\mathrm{G},\mathrm{0}}$) and depth itself (*z*).
Its form is as follows:

$$\begin{array}{}\text{(A19)}& {\displaystyle}{\displaystyle}{\mathrm{P}}_{\mathrm{org}}^{\mathrm{G},z}={\mathrm{P}}_{\mathrm{org}}^{\mathrm{G},\mathrm{0}}\cdot ({\displaystyle \frac{z}{{z}_{\mathrm{rem}}}}{)}^{b},\end{array}$$

where *z*_{rem} in the denominator represents the depth at which
remineralisation begins and is set to be 100 m everywhere. The OBGCM
therefore does not consider sinking speeds or an interaction between
organic matter and physical mixing. However, variations in the *b* exponent
affect the steepness of the curve, thereby emulating sinking speeds and
affecting the transfer and release of nutrients from the surface to the deep
ocean.

Remineralisation of ${\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}$ through the water
column is therefore dependent on the exponent *b* value in
Eq. (A19). The *b* exponent is calculated in two ways.

If the option for static remineralisation is true, then *b* is set
to −0.858 according to Martin et al. (1987).

If the option for variable remineralisation is true (default), then
*b* is dependent on the component fraction of picoplankton
(*F*_{pico}) in the ecosystem. The *F*_{pico} shows a strong
inverse relationship to the transfer efficiency (*T*_{eff}) of organic
matter from beneath the euphotic zone to 1000 m depth (Weber et al., 2016).
Because *F*_{pico} is not explicitly simulated in OBGCM, we estimate
*F*_{pico} from the export production field in units of carbon
(${\mathrm{C}}_{\mathrm{org}}^{\mathrm{G}}$), calculate *T*_{eff} using the parameterisation
of Weber et al. (2016) and subsequently calculate the *b* exponent:

$$\begin{array}{}\text{(A20)}& {\displaystyle}& {\displaystyle}{F}_{\mathrm{pico}}=\mathrm{0.51}-\mathrm{0.26}\cdot {\displaystyle \frac{{\mathrm{C}}_{\mathrm{org}}^{\mathrm{G}}\phantom{\rule{0.25em}{0ex}}\left(\mathrm{mg}\phantom{\rule{0.125em}{0ex}}\mathrm{C}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{\mathrm{h}}^{-\mathrm{1}}\right)}{{\mathrm{C}}_{\mathrm{org}}^{\mathrm{G},\mathrm{max}}\phantom{\rule{0.25em}{0ex}}\left(\mathrm{mg}\phantom{\rule{0.125em}{0ex}}\mathrm{C}\phantom{\rule{0.125em}{0ex}}{\mathrm{m}}^{-\mathrm{2}}\phantom{\rule{0.125em}{0ex}}{\mathrm{h}}^{-\mathrm{1}}\right)}}\text{(A21)}& {\displaystyle}& {\displaystyle}{T}_{\mathrm{eff}}=\mathrm{0.47}-\mathrm{0.81}\cdot {F}_{\mathrm{pico}}\text{(A22)}& {\displaystyle}& {\displaystyle}b={\displaystyle \frac{\mathrm{log}\left({T}_{\mathrm{eff}}\right)}{\mathrm{log}\left(\frac{\mathrm{1000}}{\mathrm{100}}\right)}}=\mathrm{log}\left({T}_{\mathrm{eff}}\right).\end{array}$$

Remineralisation of diazotrophs (${\mathrm{P}}_{\mathrm{org}}^{\mathrm{D}}$) is calculated in the
same way as the general phytoplankton group
(${\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}$), with the exception that the depth at
which remineralisation occurs is raised from 100 to 25 m in
Eq. (A19). This alteration emulates the release of NO_{3}
from N_{2} fixers well within the euphotic zone, which in some cases can
exceed the physical supply from below (Capone et al., 2005). Release of their N-
and C-rich organic matter (see stoichiometry Sect. A3.2) therefore
occurs higher in the water column than the general phytoplankton group.

The remineralisation of ${\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}$ and
${\mathrm{P}}_{\mathrm{org}}^{\mathrm{D}}$ will typically require O_{2} to be removed, except
for in regions where oxygen concentrations are less than a particular
threshold (Den${}^{{{\mathrm{O}}_{\mathrm{2}}}_{\mathrm{lim}}}$), which is set to
7.5 mmol O_{2} m^{−3} and represents the onset of suboxia. In these
regions, the remineralisation of organic matter begins to consume NO_{3}
via the process of denitrification. We calculate the fraction of organic
matter that is remineralised by denitrification (*F*_{den}) via

$$\begin{array}{}\text{(A23)}& {\displaystyle}{\displaystyle}{F}_{\mathrm{den}}=(\mathrm{1}-{e}^{-\mathrm{0.5}\cdot {\mathrm{Den}}_{\mathrm{lim}}^{{\mathrm{O}}_{\mathrm{2}}}}+{e}^{{\mathrm{O}}_{\mathrm{2}}-\mathrm{0.5}\cdot {\mathrm{Den}}_{\mathrm{lim}}^{{\mathrm{O}}_{\mathrm{2}}}}{)}^{-\mathrm{1}},\end{array}$$

such that *F*_{den} rises and plateaus at 100 % in a sigmoidal
function as O_{2} is depleted from 7.5 to 0 mmol m^{−3}.

Following this, the strength of denitrification is reduced if the ambient
concentration of NO_{3} is deemed to be limiting. Denitrification within
the modern oxygen minimum zones only depletes NO_{3} towards
concentrations between 15 and 40 mmol m^{−3} (Codispoti and Richards, 1976; Voss et al., 2001). Without an additional constraint that weakens denitrification as
NO_{3} is drawn down, here defined as *r*_{den}, NO_{3}
concentrations quickly go to zero in simulated suboxic zones
(Schmittner et al., 2008). We weaken denitrification by prescribing a lower
bound at which NO_{3} can no longer be consumed via denitrification,
${\mathrm{Den}}_{\mathrm{lim}}^{{\mathrm{NO}}_{\mathrm{3}}}$, which is set at 30 mmol NO_{3} m^{−3}.

$$\begin{array}{}\text{(A24)}& {\displaystyle}& {\displaystyle}{r}_{\mathrm{den}}=\mathrm{0.5}+\mathrm{0.5}\cdot \mathrm{tanh}(\mathrm{0.25}\cdot {\mathrm{NO}}_{\mathrm{3}}-\mathrm{0.25}\cdot {\mathrm{Den}}^{{{\mathrm{NO}}_{\mathrm{3}}}_{\mathrm{lim}}}-\mathrm{2.5})\text{(A25)}& {\displaystyle}& {\displaystyle}\text{if}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{1em}{0ex}}{F}_{\mathrm{den}}>{r}_{\mathrm{den}},\phantom{\rule{1em}{0ex}}\text{then}\phantom{\rule{1em}{0ex}}{F}_{\mathrm{den}}={r}_{\mathrm{den}}\end{array}$$

*F*_{den} is therefore reduced if NO_{3} is deemed to be
limiting and subsequently applied against both ${\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}$ and
${\mathrm{P}}_{\mathrm{org}}^{\mathrm{D}}$ to get the proportion of organic matter to be
remineralised by O_{2} and NO_{3}.

If the availability of O_{2} and NO_{3} is insufficient to
remineralise all the organic matter at a given depth level, *z*, then the
unremineralised organic matter will pass into the next depth level.
Unremineralised organic matter will continue to pass into lower depth levels
until the final depth level is reached, at which point all organic matter is
remineralised by either water column or sedimentary processes. This version
of CSIRO Mk3L-COAL does not consider burial of organic matter.

The dissolution of CaCO_{3} is calculated using an *e*-folding
depth-dependent decay, where the amount of CaCO_{3} at a given depth *z*
is defined by

$$\begin{array}{}\text{(A26)}& {\displaystyle}{\displaystyle}{{\mathrm{CaCO}}_{\mathrm{3}}}^{z}={{\mathrm{CaCO}}_{\mathrm{3}}}^{\mathrm{0}}\cdot {e}^{\frac{-z}{{z}_{\mathrm{dis}}}},\end{array}$$

where *z*_{dis} represents the depth at which *e*^{−1} of
CaCO_{3} (∼0.37) produced at the surface remains undissolved.

Calcifiers are not susceptible to oxygen-limited remineralisation or the
concentration of carbonate ion because the dissolution of CaCO_{3}
depends solely on this depth-dependent decay. All CaCO_{3} reaching
the final depth level is remineralised without considering burial. Future
work will include a full representation of carbonate compensation.

The elemental constitution, or stoichiometry, of organic matter affects the
biogeochemistry of the water column through uptake (production) and release
(remineralisation). The general phytoplankton group and diazotrophs both
affect carbon chemistry, O_{2} and nutrients (PO_{4}, NO_{3}
and Fe), while the calcifiers only affect carbon chemistry tracers (DIC,
DI^{13}C and ALK).

Alkalinity ratios for both the general and nitrogen-fixing groups are the
negative of the N:P ratio, such that for a loss of 1 mmol of
NO_{3}, alkalinity will increase at 1 mmol eq m^{−3}
(Wolf-Gladrow et al., 2007).

The stoichiometry of the general phytoplankton group is calculated in two ways.

If the option for static stoichiometry is true, then the $\mathrm{C}:\mathrm{N}:\mathrm{Fe}:\mathrm{P}$ ratio is set according to the Redfield ratio of $\mathrm{106}:\mathrm{16}:\mathrm{0.00032}:\mathrm{1}$ (Redfield et al., 1937).

If the option for variable stoichiometry is true (default), then the $\mathrm{C}:\mathrm{N}:\mathrm{P}$ ratio of ${\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}$ is made dependent on the ambient nutrient concentration according to Galbraith and Martiny (2015):

$$\begin{array}{}\text{(A27)}& {\displaystyle}& {\displaystyle}\mathrm{C}:\mathrm{P}=({\displaystyle \frac{\mathrm{6.9}\cdot \left[{\mathrm{PO}}_{\mathrm{4}}\right]+\mathrm{6}}{\mathrm{1000}}}{)}^{-\mathrm{1}}\text{(A28)}& {\displaystyle}& {\displaystyle}\mathrm{N}:\mathrm{C}=\mathrm{0.125}+{\displaystyle \frac{\mathrm{0.03}\cdot \left[{\mathrm{NO}}_{\mathrm{3}}\right]}{\mathrm{0.32}+\left[{\mathrm{NO}}_{\mathrm{3}}\right]}}\text{(A29)}& {\displaystyle}& {\displaystyle}\mathrm{N}:\mathrm{P}=\mathrm{C}:\mathrm{P}\cdot \mathrm{N}:\mathrm{C}.\end{array}$$

Thus, the stoichiometry of ${\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}$ varies across the ocean
according to the nutrient concentration, and the uptake and release of
carbon, nutrients and oxygen (see Sect. A3.4) are dependent on the
concentration of surface PO_{4} and NO_{3}. The ratio of iron to
phosphorus (Fe:P) remains fixed at 0.00032, such that 0.32 µmol of Fe is consumed per mmol of PO_{4}. We chose to maintain a fixed
Fe:P ratio because phytoplankton communities from subtropical to
Antarctic waters appear to show similar iron content (Boyd et al., 2015),
despite changes in $\mathrm{C}:\mathrm{N}:\mathrm{P}$. However, the ratio of $\mathrm{C}:\mathrm{N}:\mathrm{Fe}$ does
change as a result of varying $\mathrm{C}:\mathrm{N}:\mathrm{P}$ ratios, with higher C:Fe in
oligotrophic environments and lower C:Fe in eutrophic regions.

The stoichiometry of diazotrophs is fixed at a $\mathrm{C}:\mathrm{N}:\mathrm{P}:\mathrm{Fe}$ ratio of
$\mathrm{331}:\mathrm{50}:\mathrm{1}:\mathrm{0.00064}$, which represents values reported in the literature
(Kustka et al., 2003; Karl and Letelier, 2008; Mills and Arrigo, 2010). Diazotrophs do not consume
NO_{3}; rather, they consume N_{2}, which is assumed to be of
unlimited supply, and release NO_{3} during remineralisation.

Calcifying organisms produce CaCO_{3}, which includes DIC,
DI^{13}C and ALK, and these tracers are consumed and released at a
ratio of $\mathrm{1}:\mathrm{0.998}:\mathrm{2}$, respectively, relative to organic carbon. Thus, the
ratio of $\mathrm{C}:{\mathrm{DI}}^{\mathrm{13}}\mathrm{C}:\mathrm{ALK}$ relative to each unit of phosphorus consumed
by the general phytoplankton group is equal to the rain ratio of
CaCO_{3} to organic phosphorus multiplied by $\mathrm{106}:\mathrm{105.8}:\mathrm{212}$. This group
has no effect on nutrient tracers or oxygen values.

The requirements for oxygen (${\mathrm{O}}_{\mathrm{2}}^{\mathrm{rem}}:\mathrm{P}$) and nitrate
(${\mathrm{NO}}_{\mathrm{3}}^{\mathrm{rem}}:\mathrm{P}$) during oxic and suboxic remineralisation, respectively,
are calculated from the $\mathrm{C}:\mathrm{N}:\mathrm{P}$ ratios of organic matter via the
equations of Paulmier et al. (2009). Additional knowledge of the hydrogen and
oxygen content of the organic matter is also required to calculate
${\mathrm{O}}_{\mathrm{2}}^{\mathrm{rem}}:\mathrm{P}$ and ${\mathrm{NO}}_{\mathrm{3}}^{\mathrm{rem}}:\mathrm{P}$. However, the hydrogen and oxygen
content of phytoplankton depends strongly on the proportions of lipids,
carbohydrates and proteins that constitute the cell. As there is no empirical
model for predicting these physiological components based on environmental
variables, we continue Redfield's legacy by assuming that all organic matter
is a carbohydrate of the form CH_{2}O. Future work, however, should
address this obvious bias.

To calculate ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{rem}}:\mathrm{P}$ and ${\mathrm{NO}}_{\mathrm{3}}^{\mathrm{rem}}:\mathrm{P}$, we therefore need to first calculate the amount of hydrogen and oxygen in organic matter via

$$\begin{array}{}\text{(A30)}& {\displaystyle}& {\displaystyle}\mathrm{H}:\mathrm{P}=\mathrm{2}\mathrm{C}:\mathrm{P}+\mathrm{3}\mathrm{N}:\mathrm{P}+\mathrm{3}\text{(A31)}& {\displaystyle}& {\displaystyle}\mathrm{O}:\mathrm{P}=\mathrm{C}:\mathrm{P}+\mathrm{4}.\end{array}$$

Once a $\mathrm{C}:\mathrm{N}:\mathrm{P}:\mathrm{H}:\mathrm{O}$ ratio for organic matter is known, we calculate
${\mathrm{O}}_{\mathrm{2}}^{\mathrm{rem}}:\mathrm{P}$ and ${\mathrm{NO}}_{\mathrm{3}}^{\mathrm{rem}}:\mathrm{P}$ in units of
mmol m^{−3} P^{−1} using the equations of Paulmier et al. (2009):

$$\begin{array}{ll}{\displaystyle}{\mathrm{O}}_{\mathrm{2}}^{\mathrm{rem}}:\mathrm{P}=& {\displaystyle}\phantom{\rule{0.25em}{0ex}}-(\mathrm{C}:\mathrm{P}+\mathrm{0.25}\mathrm{H}:\mathrm{P}-\mathrm{0.5}\mathrm{O}:\mathrm{P}-\mathrm{0.75}\mathrm{N}:\mathrm{P}\\ \text{(A32)}& {\displaystyle}& {\displaystyle}+\mathrm{1.25})-\mathrm{2}\mathrm{N}:\mathrm{P}{\displaystyle}{\mathrm{NO}}_{\mathrm{3}}^{\mathrm{rem}}:\mathrm{P}=& {\displaystyle}-(\mathrm{0.8}\mathrm{C}:\mathrm{P}+\mathrm{0.25}\mathrm{H}:\mathrm{P}-\mathrm{0.5}\mathrm{O}:\mathrm{P}-\mathrm{0.75}\mathrm{N}:\mathrm{P}\\ \text{(A33)}& {\displaystyle}& {\displaystyle}+\mathrm{1.25})+\mathrm{0.6}\mathrm{N}:\mathrm{P}.\end{array}$$

The calculation of ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{rem}}:\mathrm{P}$ accounts for the oxygen that is also needed to oxidise ammonium to nitrate.

From these calculations, we find the following requirements of oxic and suboxic remineralisation, assuming the static stoichiometry option for the general phytoplankton group:

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\mathrm{O}}_{\mathrm{2}}^{\mathrm{rem}}:{\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}=\mathrm{138}\\ {\displaystyle}& {\displaystyle}{\mathrm{NO}}_{\mathrm{3}}^{\mathrm{rem}}:{\mathrm{P}}_{\mathrm{org}}^{\mathrm{G}}=\mathrm{94.4}\\ {\displaystyle}& {\displaystyle}{\mathrm{O}}_{\mathrm{2}}\mathrm{rem}:{\mathrm{P}}_{\mathrm{org}}^{\mathrm{D}}=\mathrm{431}\\ {\displaystyle}& {\displaystyle}{\mathrm{NO}}_{\mathrm{3}}^{\mathrm{rem}}:{\mathrm{P}}_{\mathrm{org}}^{\mathrm{D}}=\mathrm{294.8}.\end{array}$$

These numbers change dynamically alongside $\mathrm{C}:\mathrm{N}:\mathrm{P}$ ratios when the stoichiometry of organic matter is allowed to vary.

The remineralisation of organic matter within the sediments is provided as an
option in the OBGCM. Sedimentary denitrification, and its slight preference
for the light isotopes of fixed nitrogen (${\mathit{\u03f5}}_{\mathrm{sed}}^{{}^{\mathrm{15}}\mathrm{N}}$ =3 ‰), is an important component of the marine nitrogen cycle and
its isotopes. It acts as an additional sink of NO_{3} and reduces the
*δ*^{15}N value of the global ocean by offsetting the strong
fractionation of water column denitrification (${\mathit{\u03f5}}_{\mathrm{wc}}^{{}^{\mathrm{15}}\mathrm{N}}$
=20 ‰).

If sedimentary processes are active, the empirical model of
Bohlen et al. (2012) is used to estimate the rate of sedimentary
denitrification, where the removal of NO_{3} is dependent on the rate of
particulate organic carbon (${\mathrm{C}}_{\mathrm{org}}^{\mathrm{G}}$ + ${\mathrm{C}}_{\mathrm{org}}^{\mathrm{D}}$)
arriving at the sediments and the ambient concentrations of oxygen and
nitrate. In the following, we assume that the concentrations of NO_{3}
and O_{2} that are available in the sediments are two-thirds of the
concentration in the overlying water column based on observations of transport
across the diffusive boundary layer (Gundersen and Jorgensen, 1990).

$$\begin{array}{}\text{(A34)}& {\displaystyle}\mathrm{\Delta}{\mathrm{NO}}_{\mathrm{3}}\left(\mathrm{sed}\right)=& {\displaystyle}\phantom{\rule{0.25em}{0ex}}(\mathit{\alpha}+\mathit{\beta}\cdot {\mathrm{0.98}}^{({\mathrm{O}}_{\mathrm{2}}-{\mathrm{NO}}_{\mathrm{3}})})\cdot ({\mathrm{C}}_{\mathrm{org}}^{\mathrm{G}}+{\mathrm{C}}_{\mathrm{org}}^{\mathrm{D}})\text{(A35)}& {\displaystyle}& {\displaystyle}\text{where}\phantom{\rule{1em}{0ex}}\mathit{\alpha}=\mathrm{0.04}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathit{\beta}=\mathrm{0.1}\end{array}$$

In the example above, both the *α* and *β* values were halved from the
values of Bohlen et al. (2012) to raise global mean NO_{3} concentrations
and lower the sedimentary to water column denitrification ratio to between 1
and 2. If NO_{3} is not available, the remaining organic matter is
remineralised using oxygen if the environment is sufficiently oxygenated. An
additional limitation is set for sediments underlying hypoxic waters
(O_{2}<40 mmol m^{−3}), where oxic remineralisation is weakened
towards zero according to a hyperbolic tangent function $(\mathrm{0.5}+\mathrm{0.5}\cdot \mathrm{tanh}(\mathrm{0.2}\cdot {\mathrm{O}}_{\mathrm{2}}-\mathrm{5}\left)\right)$. If oxygen is also limiting, the remaining organic
matter is remineralised via sulfate reduction. As sulfate is not explicitly
simulated, we assumed that sulfate is always available to account for the
remaining organic matter.

Thus, sedimentary denitrification is heavily dependent on the rate of organic
matter arriving at the sediments. However, a large amount of sedimentary
remineralisation is not captured using only these parameterisations because
the coarse resolution of the OGCM enables it to resolve only the largest
continental shelves, such as the shallow Indonesian seas. Many small areas of
raised bathymetry in pelagic environments are also unresolved by the OGCM. To
address this insufficiency and increase the global rate of sedimentation and
sedimentary denitrification, we coupled a subgrid-scale bathymetry to the
coarse-resolution OGCM following the methodology of Somes et al. (2013) using
the Earth topography 5 min grid (ETOPO5) 1/12^{∘} dataset. For each latitude-by-longitude grid
point, we calculated the fraction of area that would be represented by
shallower levels in the OGCM if this finer-resolution bathymetry were used.
At each depth level above the deepest level, the fractional area represented
by sediments on the subgrid-scale bathymetry can be used to remineralise all
forms of exported matter (${\mathrm{C}}_{\mathrm{org}}^{\mathrm{G}}$, ${\mathrm{C}}_{\mathrm{org}}^{\mathrm{D}}$ and
CaCO_{3}) via sedimentary processes.

Also following the methodology of Somes et al. (2013), we included an option to
amplify sedimentary denitrification in the upper 250 m to account for narrow
continental shelves that are not resolved by the OGCM. Narrow shelves
experience strong rates of upwelling and productivity, and hence high rates
of sedimentary denitrification (Gruber and Sarmiento, 1997). To amplify shallow rates
of sedimentary denitrification, we included an optional acceleration factor
(Γ_{sed}), set to 3.0 in the default parameterisation, dependent on
the total fraction of shallower depths not covered by the subgrid-scale
bathymetry:

$$\begin{array}{}\text{(A36)}& {\displaystyle}{\displaystyle}\mathrm{\Delta}{\mathrm{NO}}_{\mathrm{3}}\left(\mathrm{sed}\right)=\mathrm{\Delta}{\mathrm{NO}}_{\mathrm{3}}\left(\mathrm{sed}\right)\cdot \left(\right(\mathrm{1}-{F}_{\mathrm{sgb}})\cdot {\mathrm{\Gamma}}_{\mathrm{sed}}+\mathrm{1}).\end{array}$$

For those grids with a low fraction covered by the subgrid-scale bathymetry
(*F*_{sgb}), the amplification of sedimentary denitrification is
therefore greatest.

Appendix B: Parameterisation of the OBGCM ecosystem component

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Supplement

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Supplement.

The supplement related to this article is available online at: https://doi.org/10.5194/gmd-12-1491-2019-supplement.

Author contributions

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Author contributions.

PJB designed the study, undertook model development, ran the experiments, analysed model output and wrote the manuscript. RJM designed the study, provided instruction on development, aided in analysis and edited the manuscript. ZC designed the study, aided in analysis and edited the manuscript. SJP aided in model development and edited the manuscript. NLB aided in interpretation of results and edited the manuscript.

Competing interests

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Competing interests.

The authors declare that there is no conflict of interest.

Acknowledgements

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Acknowledgements.

The Australian Research Council's Centre of Excellence for Climate System Science and the Tasmanian Partnership for Advanced Computing (TPAC) were instrumental for this research. This research was supported under the Australian Research Council's Special Research Initiative for the Antarctic Gateway Partnership (project ID SR140300001). The authors wish to acknowledge the use of the Ferret programme for the analysis undertaken in this work. Ferret is a product of NOAA's Pacific Marine Environmental Laboratory (information is available at http://ferret.pmel.noaa.gov/Ferret/, last access: 12 April 2019). The Matplotlib package (Hunter, 2007) and the cmocean package (Thyng et al., 2016) were used for producing the figures. We are indebted to Kristen Karsh, Daniel Sigman, Dario Marconi and Eric Raes for discussions that focussed this work. Special thanks are given to Christopher Somes for correspondence in some development steps and revisions that improved the manuscript. Finally, the lead author is indebted to an Australian Fulbright postgraduate scholarship, which supported him at the Princeton Geosciences department during the writing of the manuscript.

Review statement

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Review statement.

This paper was edited by Andrew Yool and reviewed by Christopher Somes and two anonymous referees.

References

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Special issue

Short summary

Oceanic sediment cores are commonly used to understand past climates. The composition of the sediments changes with the ocean above it. An understanding of oceanographic conditions that existed many thousands of years ago, in some cases many millions of years ago, can therefore be extracted from sediment cores. We simulate two chemical signatures (^{13}C and ^{15}N) of sediment cores in a model. This study assesses the model before it is applied to reinterpret the sedimentary record.

Oceanic sediment cores are commonly used to understand past climates. The composition of the...

Geoscientific Model Development

An interactive open-access journal of the European Geosciences Union