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\DOI{10.5802/crgeos.271}
\datereceived{2024-03-29}
\daterevised{2024-07-10}
\dateaccepted{2024-07-11}
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\begin{noXML}

\CDRsetmeta{articletype}{research-article}

\title{Unaccountable counting: the folly of incorporating open ocean
carbon sinks in Nationally Determined Contributions}

\alttitle{Compter sans rendre de compte : les limites \`a
l'int\'egration du puit de carbone oc\'eanique dans les contributions
d\'etermin\'ees au niveau national}

\author{\firstname{Manon} \lastname{Berger}\IsCorresp}
\address{LMD/IPSL, ENS, PSL University, \'Ecole Polytechnique, Institut Polytechnique de Paris, Sorbonne Universit\'e, CNRS, Paris, France}
\email[M. Berger]{manon.berger@lmd.ipsl.fr}

\author{\firstname{Adrien} \lastname{Comte}\CDRorcid{0000-0001-9895-0669}}
\address{IRD, Univ Brest, CNRS, Ifremer, LEMAR, Plouzan\'e, France}

\author{\firstname{Lester} \lastname{Kwiatkowski}\CDRorcid{0000-0002-6769-5957}}
\address{LOCEAN/IPSL, Sorbonne Universit\'e, CNRS, IRD, MNHN, Paris, France}

\author{\firstname{Laurent} \lastname{Bopp}\CDRorcid{0000-0003-4732-4953}}
\addressSameAs{1}{LMD/IPSL, ENS, PSL University, \'Ecole Polytechnique, Institut Polytechnique de Paris, Sorbonne Universit\'e, CNRS, Paris, France}

\shortrunauthors

\begin{abstract} 
The national climate action plans to cut greenhouse gas emissions,
referred to as Nationally Determined Contributions (NDCs), currently
include anthropogenic land-based carbon fluxes but typically exclude
open ocean carbon sinks within Exclusive Economic Zones (EEZs). Here,
we utilise a high-resolution global ocean biogeochemical model
alongside available observations to illustrate why including EEZ carbon
sinks in NDCs would be both conceptually and practically highly
problematic. 

To demonstrate this, we focus on the case of the French EEZ, where we
simulate an anthropogenic carbon sink of 0.21 GtCO\textsubscript{2}\textperiodcentered{}yr\textsuperscript{--1} over
the past decade, representing nearly 50\% of France's territorial
greenhouse gas emissions over the same period. However, it should be
noted that this anthropogenic carbon uptake results from the physical
and biogeochemical properties of water masses, rather than from human
management practices. Additionally, the EEZ oceanic carbon sink is
already considered in estimates of remaining carbon budgets to meet the
goals of the Paris Agreement. Therefore, integrating these fluxes into
NDCs would lead to inconsistency between national objectives and global
climate goals.

We argue that to identify the additionality of management measures
aimed at enhancing the anthropogenic carbon sink in EEZ waters, robust
assessments of the baseline carbon sink and how it would have evolved
without intervention will be needed. As we show, this is complicated by
the spatially and temporally dynamic nature of ocean carbon fluxes.
More fundamentally, there is no colocalization between air--sea fluxes
and the subsequent sequestration of carbon in the ocean due to
circulation and mixing. Consequently, the measurement, reporting, and
verification requirements for national stocktakes would be highly
challenging. Moreover, as fluxes predominantly occur in the high
latitude oceans and sequestration in the subtropics, the national
allocation of credits would involve contentious issues of equity and
justice.
\end{abstract}

\begin{altabstract} 
Les plans d'action nationaux pour le climat, connus sous le nom de
contributions d\'etermin\'ees au niveau national (CDN), int\`egrent les
flux de carbone anthropiques continentaux, mais excluent
g\'en\'eralement le puit de carbone oc\'eanique des zones \'economiques
exclusives (ZEE). Dans cette \'etude, nous utilisons un mod\`ele
biog\'eochimique oc\'eanique global \`a haute r\'esolution ainsi que les
observations disponibles pour illustrer les raisons pour lesquelles
l'int\'egration du puits de carbone des ZEE dans les CDN serait
conceptuellement et concr\`etement probl\'ematique. 
Pour le d\'emontrer, nous nous penchons sur le cas de la ZEE
fran\c{c}aise, pour laquelle nous simulons un puits de carbone anthropique
de 0,21 GtCO\textsubscript{2}\textperiodcentered{}yr\textsuperscript{--1} au cours des dix derni\`eres ann\'ees.

Nous argumentons que pour identifier l'additionnalit\'e de mesures
d'att\'enuation, des \'evaluations solides du puits de carbone de r\'ef\'erence
sont n\'ecessaires. Cette t\^ache est rendu complexe, comme nous le
d'emontrons, en raison de la nature dynamique des flux de carbone
oc\'eaniques.
\end{altabstract}

\keywords{\kwd{Ocean carbon sink}
\kwd{Nationally Determined Contributions}
\kwd{Exclusive Economic Zones}
\kwd{Climate change}
\kwd{Mitigation}}

\altkeywords{\kwd{Puit de carbone oc\'eanique}
\kwd{Contributions d\'etermin\'ees au niveau national}
\kwd{Zones \'economiques exclusives}
\kwd{Changement climatique}
\kwd{Att\'enuation}}

\maketitle

\twocolumngrid

\end{noXML}

\section{Introduction}

Under the Paris Agreement, global efforts to address climate change and
achieve climate goals have led nations to explore various strategies to
reduce carbon emissions and enhance carbon sinks. The Global Stocktake
evaluates progress towards the goals of the Paris Agreement, including
mitigation, adaptation, and means of implementation and support. This
assessment aims to determine the effectiveness of existing climate
policies, identify gaps in climate\break action and support, and accelerate
efforts to combat climate change. As part of this effort, Nationally
Determined Contributions (NDCs) have become an important framework for
countries to outline their commitments to limit global warming. While
terrestrial ecosystems have traditionally been the focus of carbon sink
accounting and carbon removal initiatives
\citep{powis_quantifying_2023}, the role of oceanic ecosystems has
gained attention \citep{pendleton_estimating_2012}.

To date, the only ocean-related pathways that are included as a
mitigation strategy in NDCs are those mediated by blue carbon
(mangroves, seagrasses, and salt marshes) or other carbon-rich
ecosystems such as kelp forests  \citep{picourt_l_coastal_2021}.
These ecosystems are recognized for their critical role in carbon
sequestration and other ecosystem services, acting as natural buffers
against storms and erosion, and providing essential habitats for marine
biodiversity  \citep{barbier_value_2011, friess_ecosystem_2020}.
Conservation and restoration of blue carbon ecosystems is emerging not
only as a climate change mitigation strategy, but also as an adaptation
tool for biodiversity conservation and the well-being of marine and
human communities. Nevertheless, the global-scale mitigation potential
of blue carbon ecosystems is limited, likely amounting to less than 2\%
of current CO$_{2}$ emissions
\citep{bindoff_changing_nodate}, primarily due to the restricted
surface area available for the growth of these ecosystems.

In contrast, nations' Exclusive Economic Zones (EEZs) are vast,
covering 41\% of the Earth's ocean surface, and potentially
representing a significant portion of the world's ocean carbon sink.
Including these extensive oceanic areas in NDCs has been debated
\citep{geomar59991}, particularly when comparing coastal states with
large EEZs to landlocked states. This comparison raises questions about
feasibility and the potential impact on global carbon accounting
\citep{mcneil_significance_2006,karstensen_valuing_2021}. As climate
change mitigation efforts intensify under the Paris Agreement, the role
of oceanic ecosystems is gaining attention. The vast areas of EEZs
present both an opportunity and a challenge for carbon accounting.

The ocean differs from terrestrial carbon sinks in that oceanic carbon
fluxes and subsequent storage are delocalized. The mixing of water
masses in the ocean hinders the validation of local changes in stock
measurements. Ocean carbon fluxes are inorganic, unlike terrestrial
biosphere fluxes, which occur directly between the atmosphere and the
organic carbon pool. Instead carbon fluxes between the atmosphere and
the ocean are determined by the CO$_{2}$ partial pressure
(\textit{p}CO$_{2}$) gradient at the air--sea interface and physical
properties like turbulence and bubbles.  Another distinction is that,
in the ocean,  discrimination must be made between total carbon fluxes
and anthropogenic carbon fluxes. The preindustrial ocean is
estimated to have degassed approximately 0.6 PgC per year to the
atmosphere due to imbalances in natural river inputs and sediment
losses of carbon \citep{regnier_land-ocean_2022}. This estimated
preindustrial natural carbon degassing and its distribution must be
subtracted from the total ocean carbon flux that is measured today in
order to estimate the residual anthropogenic ocean carbon flux. In
contrast with the land biosphere, the circulation of water masses and
biogeochemical processes in the ocean result in regions of natural
atmospheric carbon uptake (e.g.\ deep-water formation regions) and loss
(e.g.\ equatorial upwelling regions). Consequently, ocean anthropogenic
carbon uptake can manifest as both an enhancement in total carbon
ingassing, and counterintuitively, a reduction in total carbon
outgassing.  The resulting anthropogenic carbon sink is generally
quantified with a combination of global ocean biogeochemical models and
observation-based products. Global ocean biogeochemical models show
relatively good agreement with the observed spatial and temporal
variability of surface ocean \textit{p}CO$_{2}$ over large spatial and
annual scales \citep{hauck_consistency_2020,
friedlingstein_global_2023}. However, they are subject to biases,
notably in the transport of carbon from the surface to the deep ocean
\citep{bourgeois_stratification_2022}, and potentially underestimate
the mean ocean carbon sink \citep{masson2021ipcc}. Measurements are
therefore essential for estimating the total carbon flux from observations
and for evaluating models. However, while the number of observations
has increased considerably, sampling is not evenly distributed both
spatially and temporally, leading to significant biases
\citep{hauck_sparse_2023}.

{France's EEZ covers about 10 million km$^{2}$, second only to the
United States in global extent.  It includes overseas territories
spread across all ocean basins with the exception of the Arctic, making
it a major contributor to the ocean carbon cycle. Here, we use the
French EEZ as a case study to highlight the\break potential pitfalls of
incorporating the open ocean carbon sink in NDCs. Using a
high-resolution ocean biogeochemical model forced with a recent
atmospheric reanalysis, as well available \textit{p}CO$_{2}$
observations, we assess the French EEZ anthropogenic carbon sink over
the last forty years. Our analysis illustrates the multiple challenges
associated with monitoring and assessing the dynamics of this carbon
sink and highlights the conceptual complexities and incompatibilities
surrounding the incorporation of the open ocean carbon sink into NDCs.
We do not address the inclusion of coastal blue carbon ecosystems in
NDCs, which is already taking place and is beyond the scope of this
paper.

{\vspace*{2pt}}

\section{Methods}

{\vspace*{2pt}}

We use a high-resolution ocean biogeochemical model forced 
with atmospheric reanalyses. The model is therefore
closely aligned to recent climate change and variability. The use of a
model allows us to explicitly compute anthropogenic carbon fluxes in
space and time, providing a comprehensive view of the underlying
mechanisms and variability. 

{\vspace*{2pt}}

\subsection{NEMO-PISCES ocean biogeochemical model}

{\vspace*{2pt}}

Historical ocean-only simulations were performed using version 3.6 of
the Nucleus for European Modelling of the Ocean (NEMO). This
comprehensive framework includes version 3 of the Louvain-La-Neuve Sea
Ice Model (LIM) \citep{fichefet_sensitivity_1997} and version 2 of
the Pelagic Interaction Scheme for Carbon and Ecosystem Studies
(PISCES) biogeochemical model \citep{aumont_pisces-v2_2015}. The
PISCES ocean biogeochemical model  \citep{aumont_pisces-v2_2015}
includes key elements for the assessment of air--sea carbon fluxes and
oceanic sequestration of anthropogenic carbon. This includes carbon in
various non-living forms (dissolved inorganic carbon, dissolved organic
carbon, particulate inorganic carbon (calcite), and particulate organic
carbon) and living compartments (nanophytoplankton, diatoms,
microzooplankton, and mesozooplankton). It also includes total
alkalinity and essential marine macro/micro nutrients (nitrate,
ammonium, phosphate, silicate and iron). No vegetated coastal
ecosystems, such as blue carbon ecosystems, are\break explicitly represented
in the model. Air--sea CO$_{2}$ fluxes follow Ocean Model
Intercomparison Project protocols \citep{orr_biogeochemical_2017},
with gas exchange dependent on the air--sea partial pressure gradient
and a parameterization of the instantaneous gas transfer velocity that
depends on 10 m atmospheric wind speed
\citep{wanninkhof_relationship_1992,ho_measurements_2006}. We
implemented the widely used ``eddy-permitting'' (0.25\textdegree{} horizontal grid)
global ocean configuration eORCA025, which contains 75 vertical levels,
including 7 levels in the top 10 m. The same model configuration
has previously been used to assess the efficacy of marine carbon
dioxide removal (mCDR) interventions, including macroalgae
afforestation \citep{berger_ocean_2023} and ocean alkalinity
enhancement \citep{kwiatkowski_contrasting_2023} and has been shown
to simulate total and anthropogenic ocean carbon fluxes in broad
agreement with data-based estimates
\citep{kwiatkowski_contrasting_2023}. The simulated estimate of the
global oceanic carbon sink for 2011--2020 is\break 9.59
GtCO$_{2}{\cdot}$yr$^{-1}$, consistent with the multi-model global carbon
budget estimate of 10.3 GtCO$_{2}{\cdot}$yr$^{-1}$\break (9--12 GtCO$_{2}{\cdot}$yr$^{-1}$) 
\citep{friedlingstein_global_2023}.

{\vspace*{3pt}}

\subsection{Simulations}

{\vspace*{3pt}}

Simulations were initiated in 1958, based on data-derived climatologies
and a coarser resolution NEMO-PISCES historical simulation of the
anthropogenic ocean carbon stock \citep{terhaar_model_2019}. The model
was then run from 1958 to 2015 using atmospheric forcings provided by
the Drakkar forcing set 5.2 (DFS5) \citep{dussin_making_2016}, based
on the ERA-Interim reanalysis over 1979--2015.  A historical simulation
was forced with yearly averaged historical atmospheric CO$_{2}$
concentrations reconstructed from ice cores and atmospheric records
\citep{le_quere_global_2015}. A parallel preindustrial control run
(PI control) was also performed, in which the atmospheric forcings were
identical but the atmospheric CO$_{2}$ mole fraction was held constant
at the preindustrial level, defined as 287 ppm in 1870. Total air--sea
CO$_{2}$ fluxes were derived from the historical simulation while
anthropogenic fluxes were calculated as the difference between fluxes
in the historical simulation and the parallel PI control.

An additional set of simulations (historical and PI control) was
performed, incorporating atmospheric forcings from JRA55-do v1.5
\citep{tsujino_jra-55_2018} which cover the period from 1958 to near
present. These simulations were run from 2006 to 2020,\break initiated from
DFS5 simulations. The DFS5 and JRA55-do v1.5 forced simulations were
finally merged in January 2014 to form two coherent historical and PI
control simulations that cover the period 1958 to 2020.

\subsection{Observations}

Robust \textit{p}CO$_{2}$ measurements are critical for estimating
total carbon fluxes from observations. In this context, we used the
latest version of the Surface Ocean CO$_{2}$ Atlas (SOCAT,
\url{https://www.socat.info}), 
which contains about 43 million observations of
surface \textit{p}CO$_{2}$. We characterized the temporal and spatial
coverage of observations in the French EEZ  using the gridded product
on a 1\textdegree{} $\times$ 1\textdegree{} grid. This was compared to
EEZ boundaries projected on the same grid using the Python
\textit{shapefile} function.

EEZ boundaries, including the French territories, were defined using
the Maritime Boundaries Geodatabase, version 11 (Flanders Marine
Institute (2019), \url{https://www.marineregions.org}). This analysis
included certain disputed areas, including those contested by New
Caledonia and Vanuatu, and by Tromelin and Mauritius.

\section{Results}

\subsection{The anthropogenic open ocean carbon sink of the French EEZ}

The simulated anthropogenic ocean carbon sink in the French EEZ over
the period  2011--2020 was\break 0.21 GtCO$_{2}{\cdot}$yr$^{-1}$ 
(Figure~\ref{fig:donut}). This is 7.5\% of the global EEZ anthropogenic
carbon sink and 2\% of the total global oceanic anthropogenic carbon
sink.  Due to extensive overseas territories, notably in the Pacific
and Indian Oceans, French waters were the third largest EEZ carbon
sink, after the United Kingdom and Australia, absorbing the equivalent
of about 50\% of the 418 million tonnes of 
CO$_{2,\mathrm{eq}}{\cdot}$yr$^{-1}$
emissions of France over 2011--2020 (territorial annual greenhouse gas
emissions in 2011--2022) \citep{jones_national_2023,
friedlingstein_global_2023}.

\begin{figure*}
\vspace*{7pt}
\includegraphics{fig01}
\vspace*{3pt}
\caption{\label{fig:donut}{The extent of Exclusive Economic Zones and their
associated anthropogenic carbon sink.} (a)~Surface area 
(million km$^{2}$) of the world's oceans, the high seas, the global Exclusive
Economic Zone (EEZ), and the 19 largest EEZs (color bar), each
identified by its ISO 3166 code.  (b) Corresponding anthropogenic carbon
sink values (in GtCO$_{2}{\cdot}$yr$^{-1}$) for the same
geographical entities: the global ocean, the high seas, the global EEZ
(indicated by a numerical value), and the 19 largest EEZs sorted by
extent. The anthropogenic carbon sink is averaged  over the period
2011--2020 for each country. (c) Map of the mean global anthropogenic
carbon sink over 2011--2020 in gCO$_{2}{\cdot}$m$^{-2}{\cdot}$yr$^{-1}$.} 
\vspace*{7pt}
\end{figure*}

\subsection{Variable regional contributions to the French ocean carbon sink}

The model simulations indicate significant regional disparities in the
French EEZ anthropogenic carbon sink. Southern Ocean territories
exhibited the highest fluxes per unit area, with mean anthropogenic
carbon fluxes ranging from 20 to 
60~gCO$_{2}{\cdot}$m$^{-2}{\cdot}$yr$^{-1}$ (Figure~\ref{fig:flux}), 
up to 160~gCO$_{2}{\cdot}$m$^{-2}{\cdot}$yr$^{-1}$ in winter. Notably, the
Atlantic and Mediterranean coastal areas of mainland France also
demonstrated relatively high area-specific anthropogenic carbon fluxes,
ranging from 10 to 50~gCO$_{2}{\cdot}$m$^{-2}{\cdot}$yr$^{-1}$,
reaching 100~gCO$_{2}{\cdot}$m$^{-2}{\cdot}$yr$^{-1}$ in winter.
In contrast, the tropical and subtropical regions of the French EEZ
displayed lower area-specific anthropogenic carbon fluxes, ranging from
5 to 30~gCO$_{2}{\cdot}$m$^{-2}{\cdot}$yr$^{-1}$. Despite lower
area-specific fluxes, the areal extent of some of these tropical
regions, notably in the Pacific territories, means that they are major
drivers of the anthropogenic carbon sink in the French EEZ. For
instance, the total uptake for French Polynesia and New Caledonia in
2020 was 83.7 MtCO$_{2}{\cdot}$yr$^{-1}$ and 31.8 MtCO$_{2}{\cdot}$yr$^{-1}$,
respectively. The combined anthropogenic carbon sequestration capacity
of these two regions exceeded that of all other French territories
combined.

\begin{figure*}
\includegraphics{fig02}
\caption{\label{fig:flux}{Distribution of the French EEZ anthropogenic carbon
flux across territories.} The mean anthropogenic carbon flux 
(gCO$_{2}{\cdot}$m$^{-2}{\cdot}$yr$^{-1}$) 
over 2011--2020 in French territories of the (a)
Pacific (New Caledonia, Matthew and Hunter Island, Wallis and Futuna,
French Polynesia, and Clipperton), (b) Caribbean (Martinique,
Guadeloupe, Saint-Martin, Saint-Barth\'elemy, (c) South America  (French
Guiana), (d) Indian Ocean (Juan de Nova, Bassas da India, Europa,
R\'eunion and Tromelin) and Southern Ocean (Crozet, Kerguelen and
Amsterdam and Saint Paul Islands), and (e) mainland France. All maps are
on the same scale. Saint-Pierre and Miquelon has been omitted.}
\end{figure*}

\subsection{Historical trends in the French ocean carbon sink}

Our simulations show that over the last 40 years the French EEZ sink
increased from 140 MtCO$_{2}{\cdot}$yr$^{-1}$ to about 225
MtCO$_{2}{\cdot}$yr$^{-1}$  (Figure~\ref{fig:evol}a). The largest
increases occurred in French Polynesia, New Caledonia, the Southern
Ocean Islands and Clipperton, with the increase near proportional to the
initial sink ($R^{2}=0.96$).  The observed increase of the French EEZ
carbon sink corresponds to that of the global EEZ carbon sink,
indicative of a response to the atmospheric carbon dioxide growth rate
(Figure~\ref{fig:evol}a). However, our simulations revealed a 
decline in the growth of the French carbon sink since 2013 with a
particularly low carbon sink in 2016 observed in 7 out of 21
territories. This slowdown is distinct from a slowdown of the global
EEZ carbon sink  (Figure~\ref{fig:evol}b). As a result, the French EEZ
share of the global EEZ carbon sink declined from 
7.3\% to 6.4\%, with French Polynesia, New Caledonia, and Amsterdam
and St Paul Islands territories being the main contributors to this\break
decline.}

\begin{figure*}
{\vspace*{4pt}}
\includegraphics{fig03}
{\vspace*{4pt}}
\caption{\label{fig:evol}{Evolution of the anthropogenic carbon sink in the
territories of the French EEZ.} The annual mean anthropogenic carbon
sink presented as (a) absolute values and (b) percentages of the global
EEZ anthropogenic carbon sink. The carbon sink values for each
territory are stacked, and the cumulative total is the globally
integrated French carbon sink.}
{\vspace*{4pt}}
\end{figure*}

\subsection{Disentangling anthropogenic and total ocean carbon fluxes
and stocks}

Analysis of the anthropogenic carbon sink using the French EEZ
territories as a case study, highlights a number of features that are
consistent across other EEZs. 

\subsubsection{Net air--sea fluxes of anthropogenic carbon into an
EEZ (or EEZ region) are not indicative of the change in anthropogenic
carbon stocks within that EEZ}

For all of the French EEZ territories, there is an imbalance between
the net air--sea anthropogenic carbon flux and the change in the
ocean anthropogenic carbon stock (Figure~\ref{fig:stockvsflux}a). Some
EEZ territories are net exporters of anthropogenic carbon to other EEZs
and the high seas. For example, roughly 25\% (3
gC${\cdot}$m$^{-2}{\cdot}$yr$^{-1}$) of the net-air sea
anthropogenic carbon flux in Kerguelen is not retained in its waters.
While in Guadeloupe, the increase in the integrated anthropogenic
carbon stock is approximately 4 times what it receives in net air--sea
fluxes, with\break 12 gC${\cdot}$m$^{-2}{\cdot}$yr$^{-1}$ supplied by
waters that are transported into the Guadeloupe region. Ocean dynamics,
therefore, lead to significant disparities between the carbon stocks
within EEZ waters and the anthropogenic carbon uptake from the
atmosphere.

\begin{figure*}
\vspace*{5pt}
\includegraphics{fig04}
\vspace*{3pt}
\caption{\label{fig:stockvsflux}{The relationship between total and 
anthropogenic carbon fluxes and anthropogenic carbon storage across French 
EEZ territories.} (a) Comparison of the mean air--sea anthropogenic carbon
flux (gC${\cdot}$m$^{-2}{\cdot}$yr$^{-1}$) and the change in depth
integrated anthropogenic carbon stock in each French EEZ territory
(gC${\cdot}$m$^{-2}{\cdot}$yr$^{-1}$). In the area identified as
``importers'', the increase in the anthropogenic carbon stock exceeds the
air--sea flux, indicating a net horizontal transport of carbon into
territorial waters. Conversely, in the area identified as ``exporters'',
the air--sea anthropogenic carbon flux exceeds the increase in the
inventory, indicating a net export of anthropogenic carbon to other
EEZs or the high seas. (b) The mean anthropogenic carbon flux and mean
total carbon flux in each French EEZ territory. The total carbon flux
is the sum of the anthropogenic carbon flux and the natural carbon
flux. A negative total carbon flux indicates a net flux of carbon to
the atmosphere (outgassing). A positive total carbon flux indicates a
net flux of carbon to the ocean (ingassing/uptake).}
\vspace*{10pt}
\end{figure*}


\subsubsection{Anthropogenic carbon uptake occurs in regions of
carbon ingassing and outgassing}

The French EEZ case study highlights the disconnect between total
air--sea carbon fluxes and\break anthropogenic carbon fluxes
(Figure~\ref{fig:stockvsflux}b). All territories of the French EEZ are
anthropogenic carbon sinks with fluxes ranging from 2--11
gC${\cdot}$m$^{-2}{\cdot}$yr$^{-1}$. However, the total air--sea carbon
fluxes for the same EEZ territories range from ${-}$10 to 20
gC${\cdot}$m$^{-2}{\cdot}$yr$^{-1}$. French EEZ territories can,
therefore, exhibit net ingassing or outgassing of  total carbon while
still exhibiting anthropogenic carbon uptake. The French EEZ territory
with the highest anthropogenic carbon fluxes (Kerguelen,
C$_{\mathrm{ant}}$: 11 gC${\cdot}$m$^{-2}{\cdot}$yr$^{-1}$) 
has actually total carbon fluxes near zero.



\subsection{Observational coverage}

The NEMO-PISCES model permits the calculation of anthropogenic carbon
fluxes in space and time, providing insight into carbon flux trends and
the mismatch between carbon fluxes and carbon stocks. However, given
the persistence of large discrepancies between data and models
\citep{friedlingstein_global_2023}, robust \textit{p}CO$_{2}$
measurements are essential for estimating total carbon fluxes from
observations. Therefore, good observational coverage is crucial, as
under-sampling could lead to significant biases in fluxes reconstructed
from observations \citep{hauck_sparse_2023}. A review of the
available SOCATv2023 \textit{p}CO$_{2}$ measurements in French EEZ
waters, showed that observational coverage  remains limited 
(Figure~\ref{fig:socat_map}). Compiled measurements for 2011--2021 are
patchy in \mbox{several} French territories. This is particularly striking in
French Polynesia where spatial coverage is notably low. Large portions
of the territory either have no observations at all or only one month
of observations. Specifically, on a 1\textdegree{} $\times$
1\textdegree{} grid, only 14\%   of the French Polynesia EEZ grid cells have at least
one observation, and a mere 1\% has at least 2 months of observations
available. The southern Indian Ocean also has limited data, with 35\%
of Crozet, 73\% of Amsterdam and Saint Paul and 83\% of Kerguelen
Island covered by at least one observation. However, this coverage
drops to 0\%, 5.5\% and 7\% for those three islands,
respectively, when the criterion is at least 4 months of observations
per year. This lack of data is particularly problematic as this region
plays an important role in carbon uptake, but only a fraction of the
seasonal cycle is present in the observations. On the contrary, the
Atlantic territories have good spatial and temporal coverage, with
75\% of French Guiana territory covered with at least 6 months of
data and 66\% for both mainland France and Martinique.

\begin{figure*}
{\vspace*{-3pt}}
\includegraphics{fig05}
{\vspace*{-3pt}}
\caption{\label{fig:socat_map}{The scarcity of ocean carbon observations 
in the French EEZ.} Spatial and temporal resolution of \textit{p}CO$_2$
measurements (gridded SOCATv3) in the French EEZ during the period
2011--2021. Central map: Calendar months with available data in the
French EEZ, where 12 indicates full coverage of the seasonal cycle and
light gray indicates no measurements available for the period
2011--2021. Surrounding time series: Number of \textit{p}CO$_2$
measurements for each French EEZ territory from 2011 to 2021. The grey area below
the lines indicates continuous observations with at least one
measurement per month.}
{\vspace*{-3pt}}
\end{figure*}

\section{Discussion}

{\vspace*{2pt}}

\subsection{The French EEZ case study}

{\vspace*{2pt}}

Our study reveals a significant anthropogenic carbon sink in the
world's EEZs, accounting for 3.55~GtCO$_{2}{\cdot}$yr$^{-1}$ or 35\%
of the global ocean CO$_{2}$ sink in 2020. The anthropogenic carbon
sink in EEZs can be a similar order of magnitude to national emissions:
for example, the French EEZ sink corresponds to around 50\% of French
CO$_{2,\mathrm{eq}}$ territorial emissions, while the two largest EEZ
sinks, Australia and the UK, both absorb the equivalent of around
40\% of their emissions. Even more absurd, the waters of 34 countries
absorb more than their own emissions, up to 1640 times more for Tuvalu.
We estimate an increase in the anthropogenic carbon sink within the
French EEZ over the last 40 years, from 140
MtCO$_{2}{\cdot}$yr$^{-1}$ in 1980 to about 225
MtCO$_{2}{\cdot}$yr$^{-1}$ in 2020. This is driven by the increase
in the global ocean carbon sink in response to rising atmospheric 
CO$_{2}$ levels \citep{masson2021ipcc, friedlingstein_global_2023}.
However, we have identified a recent decrease in the French EEZ
that is not reflected in the global EEZ carbon sink. This decrease
may be attributable to changes in atmospheric forcing in our
simulations that affect ocean dynamics and redistribute air--sea fluxes.

Using the French EEZ as a case study, we highlight the considerable
diversity among EEZ territories in terms of total air--sea carbon
fluxes, anthropogenic air--sea carbon fluxes and changing oceanic
C$_{\mathrm{ant}}$ stocks. French EEZ territories exhibit both total
uptake of carbon from the atmosphere (ingassing) and total loss of
carbon to the atmosphere (outgassing). Yet despite this, over the
simulated period, all EEZ territories are net absorbers of
anthropogenic carbon, albeit with the magnitude of the area-specific
air--sea C$_{\mathrm{ant}}$ flux differing by a factor of 6 between
territories. Moreover, territories show wide disparities in the
accumulation of C$_{\mathrm{ant}}$ in their waters, and this
accumulation is not equivalent to the cumulative air--sea
C$_{\mathrm{ant}}$ flux. This disparity is a consequence of the
advection and mixing of C$_{\mathrm{ant}}$ within the ocean, which
results in certain EEZ territories being net exporters of
C$_{\mathrm{ant}}$ to adjacent waters, while others are net
importers. Despite the temptation to incorporate ocean carbon fluxes
into NDCs due to the magnitude of associated anthropogenic carbon
sinks, the drivers and properties of ocean carbon fluxes, as well as
the wider context of the remaining carbon budget, make this highly
inadvisable.

\subsection{Pitfalls of including EEZ carbon fluxes in NDCs}

One of the principal issues with including EEZs in NDCs, is that ocean
anthropogenic carbon uptake is already accounted for when estimating
the remaining carbon budget \citep{lamboll_assessing_2023,
rogelj_differences_2016, damon_matthews_integrated_2021}.
Consequently, the only rationale for including EEZs in NDCs lies in
demonstrating that human interventions have enhanced the anthropogenic
carbon sink. The transient climate warming response to cumulative
CO$_{2}$\break emissions (TCRE) is central to remaining carbon budget
estimates and can be derived from both models and observations using a
variety of methodologies. TCRE estimates invariably account for
unmanaged ocean anthropogenic carbon uptake, including that which is
projected to occur in EEZs. As such, our best estimates of permissible
emissions to stay within 1.5~\textdegree{}C or 2~\textdegree{}C global warming targets already
assume that ocean anthropogenic carbon uptake in EEZs will continue in
response to biogeophysical forcing.  Including total anthropogenic
fluxes, as opposed to any managed additional flux, into NDCs would
therefore break the coherence between the remaining carbon budget and
the global stocktake.

Moreover, for consistency, any management
practices found to have diminished EEZ C$_{\mathrm{ant}}$ uptake,
would equally need to be declared \citep{bach_testing_2021}. The
concept of additionality requires a standardized definition applicable
across all contexts. For instance, notable disparities exist in
estimating anthropogenic land-use carbon fluxes between the model-based
Global Carbon Budget (GCB) and the inventories submitted by countries
to the United Nations Framework Convention on Climate Change (UNFCCC).
The former includes only direct anthropogenic effects, while the
inventories reported by countries generally include indirect removals
on that land, such as the fertilization effect caused by increasing
atmospheric CO$_{2}$ concentrations \citep{grassi_harmonising_2023,
gidden_aligning_2023}. Similarly, the anthropogenic ocean carbon sink
operates independently of human management, primarily in response to
increased atmospheric CO$_{2}$. Although ocean C$_{\mathrm{ant}}$
uptake is nearly ubiquitous, the magnitude of this flux at the air--sea
interface is highly regionally variable (Figure~\ref{fig:donut}) and
strongly determined by ocean dynamics and carbonate chemistry. In
particular, cold deep-water formation regions such as the North
Atlantic and Southern Ocean are major hotspots of anthropogenic carbon
uptake (Figure~\ref{fig:donut}) as water masses containing
C$_{\mathrm{ant}}$ are subducted. As such, both historical and future
C$_{\mathrm{ant}}$ uptake in an EEZ is almost entirely determined by
the natural ocean dynamics and carbonate chemistry of the waters, and
the impact of climate change on these properties (in conjunction with
global CO$_{2}$ emissions). Crucially, these oceanic properties are
almost entirely independent of human intervention and presently beyond
the control of any nation state.\looseness=-1

Furthermore, integrating EEZ carbon fluxes into NDCs presents a
challenge to  fairness and equity, and  may raise climate justice
concerns. C$_{\mathrm{ant}}$ uptake at the air--sea interface is
higher in high latitude regions, such as the Southern Ocean and the
North Atlantic (Figure~\ref{fig:donut}c), coincident with the EEZs of
a small number of developed countries that have historically high
emissions. The potential for human enhancement of C$_{\mathrm{ant}}$
uptake may additionally be greater in these regions due to generally
lower sea surface temperatures (i.e., higher CO$_{2}$ solubility,
\citep{berger_ocean_2023, feng_model-based_2017, he_limits_2023}.
Conversely, interior ocean C$_{\mathrm{ant}}$ storage is higher in
subtropical regions \citep{gruber_trends_2023}, coincident with the
EEZs of developing countries that have historically low emissions. The
question of which nation could rightfully claim credit for Ocean
C$_{\mathrm{ant}}$ would arise because of large differences between
where uptake initially occurs and where C$_{\mathrm{ant}}$ is
subsequently stored. The functioning of the ocean is global and cannot
be divided into administrative units.

The  transboundary nature of oceanic carbon also presents a heightened
risk of potential double counting. Many EEZs are located near multiple
borders; EEZ territories may be net importers or exporters of
C$_{\mathrm{ant}}$ to adjacent waters,  regardless of whether they
ingas or outgas total carbon (Figure~\ref{fig:stockvsflux}).
This situation exacerbates the risks of potential double counting
\citep{luisetti_climate_2020}. Moreover, interventions in the waters
of one EEZ can cause harm in another, particularly in the context of
carbon dioxide removal (CDR) projects \citep{tagliabue_ocean_2023,
boyd_potential_2022}. Thus, the emergence of ocean CDR poses novel
risks that require specific policies and legislation
\citep{boettcher_navigating_2021}. The development of such a
comprehensive legal framework is imperative, but is challenging and
necessitates an arduous process due to the ocean's status as a shared
resource requiring extensive international cooperation. Although
existing international treaties, such as the London Protocol, have
addressed transboundary environmental risks, focusing on ocean
fertilization \citep{dixon2014update}, there remains a notable
absence of a comprehensive legal framework dedicated to marine
CDR research \citep{NAP26278}. However various legal norms exist as
well as codes of conduct to help guide responsible decisions in marine
CDR \citep{boettcher2023code}.

\subsection{Enhancing monitoring and estimation of oceanic carbon
sinks: imperatives for climate mitigation and reporting}

Although the inclusion of EEZs in NDCs is misguided, an accurate
estimate of the EEZ carbon sink is highly desirable given its
significant contribution to the global ocean carbon sink (up to 35\%
in our simulations). Enhanced monitoring of EEZ carbon fluxes is
essential to track long-term trends and variability, as the ocean
carbon sink is vulnerable to shifts caused by both direct and indirect
anthropogenic drivers. Climate change exerts a diverse and multifaceted
influence on ocean carbon fluxes and storage, via temperature
increases, reduced buffering capacity, and changes in circulation and
marine productivity. In addition, anthropogenic impacts on runoff and
river inputs \citep{regnier_land-ocean_2022}, bottom trawling
\citep{atwood_atmospheric_2024, sala_protecting_2021}, coastal
development, and deep-sea mining can also have substantial impacts on
carbon fluxes and stocks. Predicting future changes in carbon fluxes
and storage is therefore a considerable challenge, requiring the
establishment of an efficient observational network to accurately
constrain these dynamics. Moreover, monitoring the changes and
variability is critical to delivering accurate carbon budgets to the
parties to the UNFCCC, and to providing a comprehensive global
understanding of carbon stocks and fluxes. This understanding assists
parties in formulating mitigation targets consistent with the
temperature goals of the Paris Agreement. Similar concerns have been
raised for terrestrial ecosystems, highlighting the need for improved
monitoring of natural and anthropogenic carbon fluxes
\citep{gidden_aligning_2023, nabuurs_reporting_2023}.

Recent improvements in observational capabilities and developments in
machine-learning based interpolation methods have facilitated the
generation of global gap-filled, high-resolution data products of
oceanic \textit{p}CO$_{2}$ and ocean air--sea CO$_{2}$ fluxes
\citep{fay_seaflux_2021}. These developments have improved our
understanding of long-term trends in coastal air--sea carbon fluxes
\citep{roobaert_novel_2024} and enabled model-data combination to
estimate global coastal fluxes \citep{resplandy_synthesis_2024}.
However, despite this progress, the quantification of coastal CO$_{2}$
flux trends from observations remains severely constrained by limited
spatial coverage and/or relatively short time series duration, while
large discrepancies between data and models persist
\citep{hauck_southern_2023, resplandy_synthesis_2024}. Additionally,
the anthropogenic component of the air--sea carbon flux cannot be
directly observed. While local estimates of DIC$_{\mathrm{ant}}$ are
possible (e.g.\ though the $\Delta C^*$ method
\citep{gruber1996improved} or the transient time distribution method
\citep{hall2002inferring}, data-based methods can only estimate
global anthropogenic carbon uptake. Furthermore, model estimates
generally do not account for anthropogenic impacts unrelated to
atmospheric CO$_{2}$ and climate change. 

In the context of reporting on potential CDR projects,
establishing a baseline is critical as it is the starting point against
which emission reductions or additional sinks are measured. Accurate
monitoring helps avoid errors in establishing this baseline and ensures
that it reflects carbon fluxes and storage in the absence of human
intervention \citep{ho_monitoring_2023}. Accurate monitoring of
carbon fluxes will allow for better accounting of managed carbon fluxes
and avoiding methodological errors in setting baseline emissions in
reporting of carbon projects, within NDCs or elsewhere
\citep{cooley_sociotechnical_2023}. In addition, a poorly defined
baseline can lead to inaccurate accounting. This can be particularly
detrimental if emission reductions are overestimated, creating a
discrepancy between the remaining emissions allowed to meet climate
change targets and the actual remaining emissions. 

\section*{Declaration of interests}
The authors do not work for, advise, own shares in, or receive funds
from any organization that could benefit from this article, and have
declared no affiliations other than their research organizations.

\section*{Dedication}

The manuscript was written through contributions of all authors. All
authors have given approval to the final version of the manuscript.

\def\textdegrees{{\textdegree}s}

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