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# Jigsaw puzzle of the interwoven biologically-driven ocean carbon pumps

Louis Legendre

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## To cite this version:

Louis Legendre. Jigsaw puzzle of the interwoven biologically-driven ocean carbon pumps. Progress in Oceanography, 2024, 229, 10.1016/j-pocean.2024.103338. insu-04786609

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Submitted on 30 Nov 2024

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Review

# Jigsaw puzzle of the interwoven biologically-driven ocean carbon pumps

Louis Legendre

Sorbonne Université, CNRS, Laboratoire d'Océanographie de Villefranche, LOV, F-06230 Villefranche-sur-Mer, France

ARTICLE INFO

Keywords:

Ocean carbon pumps

Biological pump

Carbonate pump

Microbial pump

Carbon sequestration

Jigsaw puzzle

A B S T R A C T

The biological pumping of carbon in the ocean and its effects on ocean carbon sequestration are being studied by researchers from several disciplines. These studies address the biological carbon pump (also called organic, soft-tissue, or biogeochemical carbon pump), the carbonate pump (or counter-pump) and the microbial carbon pump, which are most often treated separately. In the present study, the three pumps are treated together for the first time, under the generic name of "biologically-driven ocean carbon pumps", in short, "bio-pumps". The interactions among the carbon fluxes of three interwoven bio-pumps are summarized in the bio-pump jigsaw puzzle.

The bio-pump literature presents a wide range of approaches to the nature and processes of carbon pumps and the ensuing carbon sequestration in the ocean, approaches that often differ significantly. It is shown that sequestration fluxes from all three bio-pumps can occur throughout the water column, albeit in different forms, and this "continuous vertical sequestration" concept is used to propose a target framework to simplify the research on bio-pumps, and unify the studies carried out by researchers from different disciplines. The review of the wide range of approaches to ocean biologically-driven carbon pumping and sequestration in the literature includes both a look back at the initial ocean carbon pump concept and an analysis of current approaches. It also includes estimates of century-scale (≥100 years) global sequestration fluxes in the water column by the three bio-pumps, which are about 1–3, 0.7 and 0.2 Pg C y⁻<fnref n="1" /> for the biological, carbonate and microbial pumps, respectively. The value of 0.7 Pg C y⁻<fnref n="1" /> appears to be the first ever published for the carbonate pump. The review is followed by detailed analysis of the functioning of the bio-pumps and their carbon sequestration processes, which is organized around four common components, i.e. downward fluxes of biogenic carbon from the upper ocean (i. e. export), transformation fluxes of the exported biogenic carbon in the lower ocean, carbon sequestration fluxes throughout the water column, and upward flux of dissolved inorganic carbon. It is recommended that future carbon-pump publications use representations that include these four components. This leads to a synthetic description of the processes involved in the three bio-pumps and their carbon sequestration, and a proposed unification of research on the interwoven bio-pumps.

# 1. The jigsaw puzzle of the interwoven biologically-driven ocean carbon pumps

During the last decades, the biologically-driven pumping of carbon in the ocean and its effects on carbon sequestration in the ocean have been studied by researchers from a variety of disciplines, including biological, chemical and physical oceanography, marine biogeochemistry and ecology, and climate-oriented oceanography. These studies addressed the biological carbon pump (also called organic, soft-tissue, or biogeochemical carbon pump), the carbonate pump (or counter-pump<fnref n="1" />) and/or the microbial carbon pump. The expression biological carbon pump is sometimes used to encompass the biological and carbonate pumps (e.g.

Passow and Carlson, 2012). In a departure from the current literature where the three pumps are most often investigated separately, I treat the three pumps together for the first time in this study, and I call them biologically-driven ocean carbon pumps, in short, bio-pumps. In the existing bio-pump literature, one finds a wide range of approaches concerning the nature and processes of the three pumps and the ensuing ocean carbon sequestration, for which references are provided below. The acronyms and symbols used in this study are summarized in Table 1.

In general, readers of bio-pump papers (including myself until recently) look at only one or, at best, a few publications at any one time, and may thus not realize that different studies often refer, explicitly or implicitly, to different concepts or definitions of the pumps under

<footnote>E-mail address: legendre@imev-mer.fr</footnote>

<footnote n="1">¹ The origin of the qualifier "counter" for this pump is explained in Section 2.3.</footnote>
<caption>**Table 1**</caption>

Quantities used or mentioned in the text: acronyms and symbols, definitions, areal dimensions, and units often used in oceanography. N/A: not applicable.

<table><thead><tr><th>Acronym or symbol</th><th>Definition</th><th>Dimensions (areal)</th><th>Units (areal)</th></tr></thead><tbody><tr><td>C<sub>T</sub></td><td>Total dissolved inorganic carbon (i.e. DIC)</td><td>N/A</td><td>N/A</td></tr><tr><td>DIC</td><td>Dissolved inorganic carbon (CO<sub>2</sub> + H<sub>2</sub>CO<sub>3</sub> + HCO<sub>3</sub><sup>-</sup> + CO<sub>3</sub><sup>2-</sup>)</td><td>N/A</td><td>N/A</td></tr><tr><td>DOC</td><td>Dissolved organic carbon</td><td>N/A</td><td>N/A</td></tr><tr><td>DOC<sub>100</sub></td><td>Century-scale recalcitrant DOC (lifetime ≥ 100 years)</td><td>N/A</td><td>N/A</td></tr><tr><td>DOC (DOC<sub>100</sub>)</td><td>DOC including DOC<sub>100</sub></td><td>N/A</td><td>N/A</td></tr><tr><td>F<sub>dissPIC</sub></td><td>Dissolution flux of PIC</td><td>ML<sup>-2</sup>T<sup>-1</sup>, NL<sup>-2</sup>T<sup>-1</sup></td><td>g C m<sup>-2</sup> year<sup>-1</sup>, mol C m<sup>-2</sup> year<sup>-1</sup></td></tr><tr><td>F<sub>DOC100</sub></td><td>Flux of DOC<sub>100</sub> in the water column</td><td>ML<sup>-2</sup>T<sup>-1</sup>, NL<sup>-2</sup>T<sup>-1</sup></td><td>g C m<sup>-2</sup> year<sup>-1</sup>, mol C m<sup>-2</sup> year<sup>-1</sup></td></tr><tr><td>F<sub>exp</sub></td><td>Export flux of biogenic carbon (DOC, DOC(DOC<sub>100</sub>), PIC, and/or POC)</td><td>ML<sup>-2</sup>T<sup>-1</sup>, NL<sup>-2</sup>T<sup>-1</sup></td><td>g C m<sup>-2</sup> year<sup>-1</sup>, mol C m<sup>-2</sup> year<sup>-1</sup></td></tr><tr><td>F<sub>org</sub></td><td>Downward flux of organic carbon (DOC and/or POC) in the water column</td><td>ML<sup>-2</sup>T<sup>-1</sup>, NL<sup>-2</sup>T<sup>-1</sup></td><td>g C m<sup>-2</sup> year<sup>-1</sup>, mol C m<sup>-2</sup> year<sup>-1</sup></td></tr><tr><td>F<sub>remin</sub></td><td>Remineralization flux of organic carbon (DOC and/or POC) in the water column</td><td>ML<sup>-2</sup>T<sup>-1</sup>, NL<sup>-2</sup>T<sup>-1</sup></td><td>g C m<sup>-2</sup> year<sup>-1</sup>, mol C m<sup>-2</sup> year<sup>-1</sup></td></tr><tr><td>F<sub>sedim</sub></td><td>Flux of biogenic particles (PIC and/or POC) into the sediment</td><td>ML<sup>-2</sup>T<sup>-1</sup>, NL<sup>-2</sup>T<sup>-1</sup></td><td>g C m<sup>-2</sup> year<sup>-1</sup>, mol C m<sup>-2</sup> year<sup>-1</sup></td></tr><tr><td>F<sub>seq</sub></td><td>Sequestration flux in the form of DIC or DOC<sub>100</sub> in the water column</td><td>ML<sup>-2</sup>T<sup>-1</sup>, NL<sup>-2</sup>T<sup>-1</sup></td><td>g C m<sup>-2</sup> year<sup>-1</sup>, mol C m<sup>-2</sup> year<sup>-1</sup></td></tr><tr><td>F<sub>up</sub></td><td>Upward flux of carbon-pump DIC in the water column</td><td>ML<sup>-2</sup>T<sup>-1</sup>, NL<sup>-2</sup>T<sup>-1</sup></td><td>g C m<sup>-2</sup> year<sup>-1</sup>, mol C m<sup>-2</sup> year<sup>-1</sup></td></tr><tr><td>F<sub>wc</sub></td><td>Flux of carbon-pump DIC into the water column</td><td>ML<sup>-2</sup>T<sup>-1</sup>, NL<sup>-2</sup>T<sup>-1</sup></td><td>g C m<sup>-2</sup> year<sup>-1</sup>, mol C m<sup>-2</sup> year<sup>-1</sup></td></tr><tr><td>F'<sub>seq</sub></td><td>F'<sub>seq</sub> = F<sub>seq</sub> - F<sub>sedim</sub></td><td>ML<sup>-2</sup>T<sup>-1</sup>, NL<sup>-2</sup>T<sup>-1</sup></td><td>g C m<sup>-2</sup> year<sup>-1</sup>, mol C m<sup>-2</sup> year<sup>-1</sup></td></tr><tr><td>f<sub>100</sub></td><td>Fraction of water that remains in the ocean's interior for ≥ 100 years</td><td>Dimension-less</td><td>N/A</td></tr><tr><td>mCDR</td><td>Marine carbon dioxide removal (method)</td><td>N/A</td><td>N/A</td></tr><tr><td>pCO<sub>2</sub></td><td>Partial pressure of CO<sub>2</sub></td><td>ML<sup>-1</sup>T<sup>-2</sup></td><td>atm, bar, kP</td></tr><tr><td>PIC</td><td>Particulate inorganic carbon (CaCO<sub>3</sub>)</td><td>N/A</td><td>N/A</td></tr><tr><td>POC</td><td>Particulate organic carbon</td><td>N/A</td><td>N/A</td></tr><tr><td>TA</td><td>Total alkalinity</td><td>NM<sup>-1</sup></td><td>μmol kg<sup>-1</sup></td></tr><tr><td>t<sub>seq</sub></td><td>Sequestration time of carbon</td><td>T</td><td>year</td></tr><tr><td>z<sub>eu</sub></td><td>Depth of euphotic zone</td><td>L</td><td>m</td></tr><tr><td>z<sub>exp</sub></td><td>Depth of carbon export</td><td>L</td><td>m</td></tr><tr><td>τ<sub>seq</sub></td><td>Mean residence time of carbon in the water column</td><td>T</td><td>year</td></tr><tr><td>ΣCO<sub>2</sub></td><td>Total carbon dioxide (same as DIC)</td><td>N/A</td><td>N/A</td></tr><tr><td>Σz<sub>exp</sub>F</td><td>Cumulative flux between z<sub>exp</sub> and depth z in the water column</td><td>ML<sup>-2</sup>T<sup>-1</sup>, NL<sup>-2</sup>T<sup>-1</sup></td><td>g C m<sup>-2</sup> year<sup>-1</sup>, mol C m<sup>-2</sup> year<sup>-1</sup></td></tr></tbody></table>

consideration and their carbon sequestration. These initial differences, which can be quite significant, contribute to variability in the results and the conclusions of published studies.

The differences in approaches to the bio-pumps and their ocean carbon sequestration could be seen as an irritating problem caused by the multiplicity of disciplines involved, each of which investigates different pump processes from different angles. Alternatively, one can consider that the variety of approaches provides a deeper understanding of the processes thanks to the range of methods used by the different

disciplines. In addition, bio-pumps provide a common focus for studies that would otherwise have little or no connection with each other, e.g. air-sea gas exchanges, vertical mixing of the water column, vertical distributions of chemical properties in the ocean, biological production in the upper ocean,<fnref n="2" /> grazing and respiration by the pelagic food web in the upper and lower oceans, vertical migrations of organisms, formation and dissolution of calcium carbonate, formation of recalcitrant dissolved organic carbon, and sinking of particles collected in sediment traps in the lower ocean.

I propose here a framework to unify studies carried out on the three bio-pumps by biological, chemical and physical oceanographers, marine biogeochemists and ecologists, and climate-oriented oceanographers. The framework is illustrated in the form of the bio-pump jigsaw puzzle (Fig. 1), the concept of which is developed progressively throughout this study. Briefly, the jigsaw puzzle summarizes the following elements: Biogenic carbon moves in the ocean through a complex network of carbon fluxes, which make up the three bio-pumps (Section 2); the different bio-pumps have some carbon fluxes in common, which belong to four carbon-pump components, i.e. export,<fnref n="3" /> transformation, water-column sequestration and upward fluxes (Sections 3.1–3.6); each bio-pump has some distinct characteristics, such as the production of particulate and dissolved organic carbon (POC and DOC, respectively), particulate inorganic carbon (PIC, i.e. calcium carbonate, CaCO<sub>3</sub>) and century-scale recalcitrant DOC<fnref n="4" /> (DOC<sub>100</sub>) by the biological, carbonate and microbial pumps, respectively (Sections 2.3–2.5, and 4.1); all three pumps sequester carbon in the water column, in the form of dissolved inorganic carbon (DIC; biological and carbonate pumps) or DOC<sub>100</sub> (microbial pump) (Section 3.4); and the biological and carbonate pumps also sequester carbon in the seafloor (Section 3.7). The five different forms of carbon cited here (DIC, DOC, DOC<sub>100</sub>, PIC, and POC) are explained below.

The following discussion will show the advantage of the framework proposed here for research on bio-pumps and their ocean carbon sequestration. In addition, this approach should be useful not only for fundamental environmental research, but also for such ongoing developments as marine carbon dioxide removal (mCDR) deployments in offshore waters (NASEM, 2022; Boyd et al., 2023).

## 2. Wide range of approaches to the biological pumping of carbon and the associated carbon sequestration

### 2.1. The initial ocean carbon pump concept

A key quantity in ocean carbon-pump studies cited in the previous section is DIC, which is also called total carbon dioxide (ΣCO<sub>2</sub>) or total dissolved inorganic carbon (C<sub>T</sub>).<fnref n="5" /> It comprises four dissolved chemical species, i.e. free carbon dioxide (CO<sub>2</sub>), carbonic acid (H<sub>2</sub>CO<sub>3</sub>), and bicarbonate (HCO<sub>3</sub><sup>-</sup>) and carbonate (CO<sub>3</sub><sup>2-</sup>) ions:

$$DIC = C_{T} = \sum CO_{2} = CO_{2} + H_{2}CO_{3} + HCO_{3}^{-} + CO_{3}^{2-} \quad (1)$$

In the ocean, there is a vertically increasing gradient in DIC concentra-

<footnote n="2">² In this work, the expressions upper ocean and surface layer are used as synonyms. In the literature, these expressions refer, depending on the study, to the upper 100 m of the ocean or to the euphotic zone. The depth of the latter varies geographically and seasonally, from a few metres in turbid waters to around 200 m in the clearest ocean waters.</footnote>

<footnote n="3">³ In the context of bio-pumps, export refers to downward fluxes of biogenic carbon from the upper ocean.</footnote>

<footnote n="4">⁴ Recalcitrant DOC and refractory DOC are sometimes used as synonyms. In this study, recalcitrant refers to DOC that is resistant to rapid microbial degradation and as a result has accumulated and is observable in the ocean (Hansell, 2013), and refractory is used for DOC that sequesters carbon for a period longer than the ocean transit time under in situ conditions (Baltar et al., 2021).</footnote>

<footnote n="5">⁵ In some publications, CO<sub>2</sub> is used to mean DIC.</footnote>
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Bio-pump jigsaw puzzle. Biogenic carbon moves through the network of fluxes (arrows) of the three interwoven bio-pumps (colours) and their four components, i.e. export, transformation, water-column sequestration and upward fluxes (patterns). The biological and carbonate pumps also sequester carbon in the seafloor. The combination of carbon fluxes, pumps and components makes up the puzzle. The network of carbon fluxes is illustrated in Fig. 5 for each pump individually and for the three pumps together.</figcaption></figure>

tion (Fig. 2), with average ocean-basin values varying from about 2,000 to 2,150 µmol kg⁻¹ at surface and 2,150 to 2,350 µmol kg⁻¹ at 3,000 m (Zeebe and Wolf-Gladrow, 2009, their Fig. 3a). In order to explain the maintenance of this gradient against the destructive effect of diffusive ocean mixing, Volk and Hoffert (1985) proposed the existence of ocean

carbon pumps. The objective of the initial carbon-pump publication was therefore different from that of current studies which target ocean carbon sequestration, a topic that was not addressed in the literature of the 1980s.

Volk and Hoffert (1985) defined carbon pumps as “processes that create or maintain a concentration gradient, such as the sodium ion pump in the membrane of a cell”. In their study, these authors ascribed the maintenance of the vertical gradient in DIC concentration in the ocean to two biological and one physical ocean carbon pumps, which they called *soft-tissue pump*, *carbonate pump* and *solubility pump*, respectively.<fnref n="6" />

Volk and Hoffert (1985) described the three pumps as follows. On the one hand, the soft-tissue and carbonate pumps were “due to the action of organisms at the ocean’s surface removing ∑CO₂ and incorporating it into organic and calcium carbonate [CaCO₃] particles, respectively”. These particles were “transported into the depths through gravitational settling and active bio transport (Redfield et al., 1963) where the carbon and other components are returned to their dissolved, inorganic forms”. On the other hand, the solubility pump was “driven by the CO₂ solubility differences of warm and cold water, i.e., the surface and deep-water”, and resulted “from the increased CO₂ solubility in downwelling cold water”. Given that the present study focuses on biologically-driven pumps, it does not consider the solubility pump further, apart from a few occasional brief mentions.

In summary (Fig. 3a), the two biologically-driven carbon pumps defined by Volk and Hoffert (1985) included downward fluxes of POC and PIC, but these authors did not take into account possible fluxes of DOC. They considered two mechanisms of particle export in their two biologically-driven pumps, i.e. gravitational settling and active bio transport (i.e. vertical migrations of organisms). They did not invoke

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Average vertical distribution of DIC in the world ocean: pre-industrial and modern values, and anthropogenic contribution (C<sub>anth</sub>). Credit: NOAA Pacific Marine Environmental Laboratory (https://www.pmel.noaa.gov/feature-d-publication/new-study-shows-larger-human-released-co2-increases-subsur-face-waters-north).</figcaption></figure>

<footnote n="6">⁶ Volk and Hoffert (1985) did not use the well-known expression *biological pump* in their study, but they applied the qualifier “biological” to the soft-tissue pump in one instance, when discussing the possible global effect of this pump on the solubility pump.</footnote>
<figure><img src="image_6.png" /><figcaption>Fig. 3. Carbon fluxes from atmospheric CO₂ to (a) water-column DIC through the carbonate pump (left) and the biological pump (right) as described in Volk and Hoffert (1985), and (b) to water-column DIC and seafloor POC through the biological pump (left) and to water-column DOC₁₀₀ through the microbial pump (right) as described in Jiao et al. (2010). The biological pump is called soft-tissue pump in Volk and Hoffert (1985). Export mechanisms: (a) gravitational and migrant, and (b) gravitational and mixing. The differences in biological-pump carbon fluxes between the two panels reflect the shift of ocean carbon-pump studies from (a) the vertical DIC gradient in the 1980s to (b) carbon sequestration later (see also Fig. 5). Boundary between the upper and the lower oceans: (a) 100 m (i.e. mixed-layer depth in the model of Hoffert et al., 1981) and (b) zₑu (Jiao et al., 2010).</figcaption></figure>

physical transport of particles for the two biologically-driven pumps, but identified downwelling as the main transport mechanism of DIC in the physical, solubility pump. In addition, as their study focused on the water-column vertical DIC gradient, they did not consider the fate of carbon reaching the seafloor. The latter influenced the treatment of ocean carbon pumps in the subsequent literature which, following Volk and Hoffert (1985), has often not included sediment burial in carbon sequestration (Section 2.7).

Volk and Hoffert (1985) recognized that the biological and carbonate pumps have different effects on CO₂ concentration in the upper ocean, i. e. the first decreases the partial pressure of CO₂ (pCO₂) in the upper ocean, whereas the net effect of the second is to increase the upper-ocean pCO₂. These effects are examined in Section 2.3.

## 2.2. Names of the three bio-pumps in the literature and in this study

In the current literature, the soft-tissue pump of Volk and Hoffert (1985) is generally called biological carbon pump, but two other names are also found, i.e. organic carbon pump and biogeochemical carbon pump.<fnref n="7" /> In IPCC (2019, 2021b), biological carbon pump refers to the organic (or soft-tissue) component of ocean carbon pumping, and I use this name in the present study in the abbreviated form of biological pump to avoid numerous repetitions of the word carbon.

Volk and Hoffert's (1985) carbonate pump focuses on the PIC component of ocean carbon pumping. It is often called carbonate counter-pump in the literature, for the reason explained in Section 2.3. In this study, I use carbonate pump, which is the primary name in IPCC (2019, 2021b), where counter-pump is also mentioned.

The microbial carbon pump (Section 2.5) deals with the sequestration of carbon in the form of refractory DOC (IPCC, 2019). This form of biogenic carbon was not considered by Volk and Hoffert (1985), who were addressing the ocean's vertical DIC gradient. I generally use the abbreviated form microbial pump to avoid numerous repetitions of the word carbon.

The following carbon-pump acronyms are found in the literature: BCP for biological carbon pump or biogeochemical carbon pump (Section 2.6), CCP for carbonate counter-pump (Section 2.3), MCP for microbial carbon pump (Section 2.5) and SCP for solubility carbon pump (Section 2.1). Jiao et al. (2023, 2024) proposed combining BCP, CCP, MCP and SCP into BCMS for an ecoengineering approach. For the sake of clarity, I do not use these acronyms in the present text.

## 2.3. Effects of the biological pumping of carbon on free CO₂, DIC and total alkalinity in the water column

The co-existence of four different DIC species in seawater (eq. (1)) results from the fact that dissolved free CO₂ gas combines with water (H₂O) to produce H₂CO₃, which rapidly dissociates into HCO₃⁻ and CO₃²⁻ as follows:

$$CO_2 + H_2O \rightleftharpoons H_2CO_3 \rightleftharpoons HCO_3^- + H^+ \rightleftharpoons CO_3^{2-} + 2H^+ \quad (2)$$

Equation (2) describes the seawater carbonate system. The chemical equilibria (double arrows) among the four carbon species depend on environmental factors that include temperature, pH and hydrostatic pressure. The fact that the pH of seawater is slightly above 8.0 in most of the ocean has the following consequences on the carbonate system (Fig. 4): HCO₃⁻ ions are dominant; free CO₂ gas and CO₃²⁻ ions are in very small concentrations; and there is almost no H₂CO₃, as the lifetime of this compound in seawater is very short.

<footnote n="7">⁷ Different meanings of the expression biogeochemical carbon pump are discussed in Section 2.6.</footnote>
<figure><img src="image_7.png" /><figcaption>Fig. 4. Bjerrum plot of the carbonate system: concentrations of the chemical forms of dissolved inorganic carbon in water as a function of pH (here, for seawater with a temperature of 20 °C, and a salinity of 35). Shaded band: current pH of seawater, between 8.1 and 8.2. Bertrand and Legendre (2021, their Fig. 9.7; used under CC BY-SA 4.0).</figcaption></figure>

Depending on the environmental conditions, eq. (2) operates from left to right, transforming free CO₂ gas into HCO₃⁻ and CO₂⁻ ions, or from right to left, transforming HCO₃⁻ and/or CO₂⁻ ions into free CO₂ gas. When conditions are such that eq. (2) operates from left to right, as is currently the case in most of the ocean due to the dissolution of increasing atmospheric CO₂ into seawater, the resulting increase in dissolved H⁺ ions lowers the pH of seawater, causing ocean acidification.<fnref n="8" />

In addition, Fig. 4 shows that when pH is high, only a small fraction of DIC in surface waters is under the form of CO₂ gas, and therefore the ocean can absorb much atmospheric CO₂, and that when pH is lower, a larger fraction of DIC in surface waters is in the form of CO₂, and therefore the ocean can absorb less atmospheric CO₂. Hence, the net effect of the current increase in atmospheric CO₂ concentration of is to slow down the uptake of this gas by the ocean, which is called the *Revelle effect* in the literature. As a consequence, while the ocean will likely continue to take up more CO₂ in the future as a result of the increasing atmospheric CO₂ concentration, the ocean's role in absorbing *anthropogenic CO₂* – i.e. the fraction of total CO₂ corresponding to emissions resulting from human activities – will gradually decrease in the future (Jiang et al., 2019).

The concentration of free CO₂ in the ocean's surface layer is affected by the action of the biological and carbonate pumps. However, the effects of these two pumps on free CO₂ are different because, in the *biological pump*, the synthesis of organic matter by phytoplankton *removes free CO₂* from the ambient water, whereas in the *carbonate pump*, the formation of CaCO₃ *releases free CO₂* in the ambient water. The biochemical processes in the two pumps are as follows:

* In the *biological pump*, phytoplankton photosynthesis uses the carbon in the CO₂ taken from the surrounding water to produce organic matter:

$$CO_2 + 2H_2S + \text{energy carried by solar photons} \rightarrow [CH_2O] + 2S + H_2O \quad (3)$$

$$CO_2 + 2H_2O + \text{energy carried by solar photons} \rightarrow [CH_2O] + O_2 + H_2O \quad (4)$$

where [CH₂O] is the generalized chemical formula for sugar, which is the first step in the synthesis of organic matter. Equation (3) describes

anoxygenic photosynthesis, where the substances providing the electrons (e⁻) and protons (H⁺) used in the photosynthetic process can be H₂S or other chemicals. This type of reaction, which is performed by phototrophic bacteria, does not produce free oxygen (O₂). In *oxygenic photosynthesis* (eq. (4)), which is dominant in the upper ocean, the electrons (e⁻) and protons (H⁺) are provided by H₂O, from which photosynthetic O₂ is derived. This type of photosynthesis is performed by a wide variety of phytoplankton that includes cyanobacteria and diatoms. Photosynthesis of the two types requires the energy from solar photons, and thus only takes place in the lighted upper water column.

Phytoplankton photosynthesis takes up free CO₂ from the ambient seawater (eqs. (3) and (4)), and produces both particulate and dissolved organic matter, i.e. POC and DOC in the present study. The release of photosynthetic DOC is called *exudation*, which can exceed 30 % and even 40 % of the total production of organic carbon (POC+DOC) by phytoplankton (Thornton, 2014). The photosynthetic formation of organic carbon in the lighted upper ocean decreases the concentration of DIC in surface waters, which contributes to maintain the vertical difference in DIC with the deeper ocean (Fig. 2).

Organic matter is also produced by the process of *chemosynthesis*, in which chemoautotrophic bacteria fix carbon from CO₂ using chemical energy instead of light energy, hence the term *dark carbon fixation*. The organic matter produced in this way enters the marine food web and thus contributes to the biological carbon pump. The production of organic matter by water-column chemosynthesis corresponds to only < 0.5 % of euphotic-zone photosynthesis, but can be significant in sediments where it corresponds to 5, 4, 2 and 0.01 % of euphotic-zone photosynthesis near shore, on the shelf, on the slope and in the open ocean, respectively (Middelburg, 2011; his Table 1). The possible effect of chemosynthesis on carbon sequestration is discussed briefly in Section 3.7, which deals with seafloor carbon sequestration fluxes.

In both the upper ocean and lower water column, POC and DOC are progressively *remineralized* to CO₂ through the process of *respiration*:

$$[CH_2O] + O_2 \rightarrow CO_2 + H_2O + \text{energy} \quad (5)$$

There are different types of respiration, which all produce CO₂. The most frequent in the ocean's water column uses dissolved O₂ (eq. (5)) and is thus called *aerobic respiration*. It is performed by a wide range of organisms that include phytoplankton, heterotrophic bacteria and archaea, microzooplankton, copepods, fish and whales. The release of CO₂ in deeper water by the respiration of heterotrophic organisms (mainly microbial; Robinson, 2019) increases its DIC concentration (eq. (2)), contributing to maintain the ocean's vertical DIC gradient (Fig. 2).

* In the *carbonate pump*, the formation of solid CaCO₃ from dissolved

<footnote n="8">⁸ The simplified definition of pH is: pH = log([H⁺]), where [H⁺] is the concentration of H⁺ ions. Hence, an increase in seawater [H⁺] (eq. (2)) decreases the pH and thus acidifies the water.</footnote>
$HCO_3^-$ and calcium ($Ca^{2+}$) ions releases free $CO_2$ from $HCO_3^-$:

$$Ca^{2+} + 2HCO_3^- \rightleftharpoons CaCO_3(\text{solid}) + H_2O + CO_2(\text{free}) \quad (6)$$

When eq. (6) is read from left to right, it describes the process of formation (or precipitation<fnref n="9" />) of solid $CaCO_3$, which is known as calcification. Pelagic calcifying organisms include phytoplankton (coccolithophores), protozoans (foraminifers), crustaceans (ostracods, of which only some planktonic forms have $CaCO_3$ shells) and molluscs (pteropods; most of the Thecosomata have some form of $CaCO_3$ shell, while the Gymnosomata do not; the first are also called sea butterflies, and the second sea angels). Because calcification releases $CO_2$ into the ambient water, the carbonate pump is often called counter-pump (for simplicity, it is called pump in this study).

The increasing $pCO_2$ in the upper ocean leads to the efflux of free $CO_2$ into the atmosphere,<fnref n="10" /> not necessarily locally (where $pCO_2$ may be lower in the ocean than in the atmosphere) but globally. This lowers the concentration of DIC in the upper ocean and thus contributes to maintain the vertical difference in DIC between the upper and deeper ocean, which explains why Volk and Hoffert (1985), who were considering the vertical DIC gradient and not $CO_2$ fluxes, called this process pump (Fig. 2). When the focus of studies later shifted to the exchange of $CO_2$ between the ocean and the atmosphere, the process was renamed counter-pump (e.g. Heinze et al., 1991; Zeebe, 2012).

The chemical equilibrium between the two sides of eq. (6) (double arrow) depends on environmental factors that include temperature and hydrostatic pressure, and when eq. (6) is read from right to left, it describes the process of dissolution of solid $CaCO_3$. In the water column, hydrostatic pressure increases and temperature decreases with depth, leading to the progressive dissolution of solid $CaCO_3$ formed in the surface layer as it sinks. This increases the concentration of DIC in deep waters, which contributes to maintain the vertical DIC gradient (Fig. 2).

It follows from eqs. 3–6 that the two pumps contribute similarly to maintain the vertical DIC gradient, i.e. they both decrease the concentration of DIC in the upper ocean and increase it below. It is thought that the DIC gradient is maintained to 70 % by the biological pump, 20 % by the carbonate pump, and 10 % by the physical solubility pump mentioned in Section 2.1 (Neukermans et al., 2023).

However, the two bio-pumps have different effects on the concentration of free $CO_2$ (not DIC) in the upper ocean. On the one hand, the biological pump decreases $pCO_2$ in the upper ocean (eqs. (3) and (4)), which causes a flux of $CO_2$ from the atmosphere into the ocean and thus contributes to decrease atmospheric $pCO_2$. On the other hand, the net effect of the carbonate pump is to increase the upper-ocean $pCO_2$ (eq. (6)), which causes a flux of $CO_2$ from the ocean into the atmosphere and thus contributes to increase atmospheric $pCO_2$. It is thus important to clearly distinguish between $CO_2$ and DIC when examining the global biogeochemical effects of the two pumps.

In addition, the two pumps have different effects on total alkalinity (TA), which is a measure of the balance of electric charges in seawater:

$$TA = [HCO_3^-] + 2[CO_3^{2-}] + [B(OH)_4^-] + [OH^-] - [H^+] + \text{minor compounds} \quad (7)$$

In eq. (7), $[CO_3^{2-}]$ is counted twice because this ion bears two electric charges.

• The carbonate pump creates a vertical gradient in TA. Indeed, the formation of $CaCO_3$ (calcification) in the upper ocean decreases TA by consuming $HCO_3^-$ (eq. (6) read from left to right), which is accompanied by a reduction in the ability of surface waters to absorb atmospheric $CO_2$ (eq. (2) read from right to left). Conversely, the dissolution of $CaCO_3$ at depth releases $HCO_3^-$ (eq. (6) read from right to left), which increases both TA and the ability of deep water to absorb atmospheric $CO_2$ (eq. (2) read from left to right) when this water is brought back to the surface at the timescale of the ocean circulation (up to 1,000 years). Because of these processes, the carbonate pump is also called alkalinity pump.

• In the biological pump, the addition (or removal) of $CO_2$ to seawater has no direct effect on TA because the net reaction produces one $H^+$ ion for each $HCO_3^-$ ion formed, and two $H^+$ ions for each $CO_3^{2-}$ ion formed (eq. (2)). Consequently, TA is not affected by photosynthesis and respiration (eqs. (3) to (5); biological pump), nor by the exchange of $CO_2$ between the atmosphere and the ocean (solubility pump, cited in Section 2.1).

## 2.4. Effects of the biological pump on the concentration of $O_2$ in the ocean interior

Studies focused on the biological pump seldom examine the effect of this pump on the concentration of free $O_2$ in the ocean's interior. Oxygenic photosynthesis in the upper ocean releases $O_2$ gas in the ambient water, most of which outgasses into the atmosphere. In contrast, the oxidation of organic matter into DIC in the lower ocean consumes dissolved $O_2$, this consumption being largely fuelled by the export of organic matter produced by photosynthesis in the upper ocean (Engel et al., 2022). As a consequence, the oxidation of one mole of organic matter in the lower ocean corresponds to the prior transfer of one mole of $O_2$ to the atmosphere. In other words, although it may not be intuitively obvious, the transfer of carbon from the upper to the lower ocean by the biological pump is accompanied by what amounts to a net transfer of $O_2$ from the ocean's interior to the atmosphere.

Despite the loss of dissolved $O_2$ in the lower ocean that accompanies the functioning of the biological pump, the $O_2$ concentration in most of the ocean's interior remains relatively constant over time. This is because $O_2$ in deep and intermediate waters is regularly replenished by large- and meso-scale thermohaline convection of $O_2$-rich surface water. However, in some areas of the global ocean, the loss of $O_2$ associated to the biological pump in the ocean's interior is larger than its replenishment by convection, thus causing large-scale water-column deoxygenation (Schmidtko et al., 2017). This situation, which is detrimental to the aerobic inhabitants of the ocean's interior, could increase in the coming decades as a consequence of two different types of event, both related to the ongoing climate change.

The first type of event could be the collapse of the Atlantic meridional overturning circulation (AMOC), which would cause deoxygenation of the ocean's interior during at least 500 years before an eventual recovery of $O_2$ concentrations (Yamamoto et al., 2015). According to IPCC (2021a), such a dramatic event should not take place before the 21st century, but a collapse of the AMOC may perhaps occur around the middle of this century under the current scenario of future $CO_2$ emissions (Ditlevsen and Ditlevsen, 2023). If this were to happen, the evil of ocean deoxygenation would have resulted from the collapse of the AMOC, which would itself have been caused by human-made global warming.

The second type of event could result from marine carbon dioxide removal (mCDR) deployments in offshore waters based on long-term geoengineered enhancement of biological carbon pumping in the ocean. One such scheme could be the regular artificial enrichment of surface waters in iron, the aim of which would be to remove $CO_2$ from the atmosphere and store its carbon in the form of DIC in the water

<footnote n="9">⁹ The term precipitation is commonly used in the chemical and geological literature for the process of $CaCO_3$ formation. However, I do not use it in this text because precipitation could be confused with the sinking of $CaCO_3$ particles in the water column.</footnote>

<footnote n="10">¹⁰ In fact, the amount of free $CO_2$ produced by calcification in the upper ocean is only about 60% of that predicted by eq. (6) (read from left to right). This is because part of the $CO_2$ released in the ambient water during calcification (eq. (6)) is transformed into $HCO_3^-$ and $CO_3^{2-}$ (eq. (2)), which are not exchanged with the atmosphere. Conversely, $CaCO_3$ dissolution in the lower ocean causes the transfer back to $HCO_3^-$ of about 90% of the dissolved free $CO_2$ predicted by eq. (6) (read from right to left) (Smith and Gattuso, 2011).</footnote>
column over the long term (NASEM, 2022). Such sustained biological pumping of carbon would be accompanied by sustained loss of O₂ in the ocean's interior, which may not be (or may be) compensated by the replenishment of O₂ by thermohaline circulation depending on location, and could thus increase deoxygenation. In such a case, human societies would have to choose between two human-made evils, i.e. global warming or ocean deoxygenation.

## 2.5. The third bio-pump

In addition to the biological and carbonate pumps, the bio-pumps include the microbial pump already mentioned in Sections 1 and 2.2 and called microbial carbon pump by Jiao et al. (2010). The key difference between this pump and the biological pump is the fate of the exported organic matter in the lower ocean (Fig. 3b). Indeed, the biological pump considers the remineralization of organic matter to CO₂ (eq. (5)) and ultimately DIC (eq. (2)), but part of the organic matter in the water column ends up as DOC. The latter is a complex mixture of different organic compounds (Cai and Jiao, 2023; Mitschke et al., 2023), with a wide range of lifetimes, i.e. labile, semi-labile, semi-refractory, refractory and ultra-refractory DOC. Definitions of DOC fractions vary between studies, e.g. the average lifetimes for labile, semi-labile, semi-refractory, refractory and ultra-refractory DOC are about 0.001, 1.5, 20, 16,000 and 40,000 years, respectively, in the review of Hansell (2013), and mineralization rates for labile, semi-labile, semi-refractory and refractory DOC are 0.05, 2, 20 and 5,000 years⁻¹, respectively, in modelling studies by DeVries and Weber (2017) and Nowicki et al. (2022).

The microbial pump focuses on the generation of recalcitrant DOC, and is called microbial because the generation of recalcitrant DOC is attributed to the action of microbial heterotrophs (Jiao et al., 2010). The organisms responsible for the production and transformation of this DOC are progressively being identified (Jiao et al., 2024). The present study specifically considers century-scale recalcitrant DOC, which has a lifetime ≥ 100 years (DOC₁₀₀), whereas in many studies the adjective recalcitrant is used for DOC with lifetimes much shorter than 100 years, e.g. days, weeks, months or years. One example of the latter is surface-layer DOC that was recalcitrant over 9 to 14 days when exposed to the surface-layer microbial communities, but was consumed by microbial communities from the upper mesopelagic layer (Letscher et al., 2015).

Fig. 3b illustrates the microbial pump as described and compared to the biological pump by Jiao et al. (2010). This schematic representation shows that the two pumps share the same processes of POC and DOC production in the upper ocean, with the addition of DOC₁₀₀ for the microbial pump, and the same gravitational and mixing export mechanisms into the lower ocean. The migrant mechanism was not invoked by Jiao et al. (2010) and is thus not present in Fig. 3b, contrary to Fig. 3a where its presence reflects the mention of “active bio transport” in Volk and Hoffert (1985). The two pumps are characterized by different fates of the exported organic matter, i.e. the biological pump deals with the remineralization of POC and DOC to water-column DIC, which sooner or later returns to the atmosphere, and the burial of PIC in the seafloor, whereas the microbial pump focuses on the generation of DOC₁₀₀, which remains in the water column for > 100 years.

The DOC characteristics responsible for recalcitrance remain largely unknown. Some studies invoke intrinsic recalcitrance, whereby DOC stability would be due to inherent molecular properties, whereas others put forward emergent recalcitrance, by which DOC would be continuously transformed by marine microheterotrophs and recalcitrance would emerge on an ecosystems level (Dittmar et al., 2021). Depending of the production mechanisms considered, e.g. abiotic photochemical reactions at the sea surface or biotic activity in the water column, recalcitrant DOC may be formed mainly in the surface layer or throughout the water column (Wagner et al., 2020; Dittmar et al., 2021; Cai and Jiao, 2023). In this study, I do not further address the type of recalcitrance, and I assume that DOC₁₀₀ generation can occur in both the upper and lower ocean without specifying which environment may be the most

favourable.

The carbonate, biological and microbial pumps are all biologically-driven, but despite this common characteristic, these pumps are generally treated separately in the literature, both for historical and disciplinary reasons. Indeed, the processes of carbonate formation and dissolution are mostly treated by marine chemists and geochemists, those of photosynthesis and respiration by marine biological and biogeochemical oceanographers, and those pertaining to recalcitrant DOC by marine microbiologists and chemical oceanographers. Contrary to these usual studies, I treat here the three bio-pumps together, and stress the potential benefits of doing so.

## 2.6. Differences in the literature concerning the definitions and processes of the three bio-pumps

The three bio-pumps are driven by biological processes, i.e. the organic matter involved in the biological and microbial pumps is synthesized and transformed by the pelagic food web, and almost all the CaCO₃ involved in the carbonate pump is formed by marine organisms.<fnref n="11" /> However, the three bio-pumps are treated very differently in the literature, and differences in the definitions and processes of these pumps are summarized in the left column of Table 2.

Different bio-pump studies often address different carbon fluxes (Table 2, item 1.1):

* Studies on the biological pump focus on carbon fluxes fed by the production of POC and sometimes DOC. These studies do not take DOC100 fluxes into account, as Jiao et al. (2010) defined the microbial pump in contrast to the biological pump (Section 2.5). I explain in Section 2.7 why this approach was appropriate when the microbial pump was initially proposed and also why the microbial pump is treated along with the biological and carbonate pumps in the present work.

* Most biological-pump studies do not include (even implicit) the carbonate pump. In other words, most of these studies consider only the organic (soft-tissue) component of biological pumping.

* A few biological-pump studies address both the organic (soft-tissue) and carbonate components of biological pumping. However, in most of these studies, the carbonate pump is only briefly mentioned at the beginning of the publication (or is not even mentioned, but included implicitly) and the remainder of the study deals exclusively with biological-pump fluxes.

In fact, very few carbon-pump studies address the carbonate pump, either with the biological pump or independently. The reasons for this likely include the difficulty of obtaining field data on the processes of CaCO₃ formation and dissolution (eq. (6)), the complexity of including such processes in numerical models, and the (perhaps) implicit assumption that this pump contributes little to water-column carbon fluxes. Section 2.8 shows that the latter assumption would be incorrect.

In addition to the biological, carbonate and microbial pumps, some publications refer to the biogeochemical carbon pump. Some of these papers only consider the organic (or soft-tissue) component of biological pumping (Hartmann, 2019; Flynn, 2010), while others also include the carbonate component (Moreau et al., 2016). The expression biogeochemical pumps can also designate the three bio-pumps together (Hense et al., 2017). To avoid any confusion, I do not use this expression in the

<footnote n="11">¹¹ Almost all the formation of CaCO₃ in the modern ocean is done by marine organisms using the process of calcification, but some CaCO₃ in the water column can be produced chemically. Indeed, in warm, shallow waters supersaturated in calcium carbonate, there is chemical formation of small CaCO₃ grains called oolites. In addition, there is spontaneous formation of authigenic carbonate on and within the seafloor (Sun and Turchyn 2014).</footnote>
<caption>**Table 2**</caption>

Differences in published studies on bio-pumps concerning the pumps' concepts and processes and their modes of carbon sequestration. A single example from the literature is provided for each characteristic cited.

<table><thead><tr><th colspan="2">Differences in published studies on bio-pumps</th></tr><tr><th>Differences concerning the definition and functioning of the pumps</th><th>Differences concerning the ocean carbon sequestration by the pumps</th></tr></thead><tbody><tr><td>1.1. The definition of the biological pump takes into account the production of POC (and sometimes DOC) in the upper ocean<sup>a</sup>; in some studies, the definition also includes the production of CaCO<sub>3</sub> (PIC)<sup>b</sup>, but most of these studies do not take PIC into account when estimating carbon fluxes<sup>c</sup>, although a few do it<sup>d</sup>.</td><td>2.1. The definition of sequestration refers to carbon fluxes in some studies<sup>e</sup>, or carbon inventories in others<sup>w</sup>.</td></tr><tr><td>1.2. The export mechanisms include the gravitational settling of POC<sup>e</sup> and/or PIC<sup>d</sup> in all studies<sup>e</sup> and also, in some studies, the vertical migrations of organisms<sup>f</sup> and/or physical injection or mixing<sup>g</sup>.</td><td>2.2. Sequestration flux estimates are calculated throughout the water column in some studies<sup>x</sup>, or only below a given depth horizon in others<sup>y</sup>.</td></tr><tr><td>1.3. Studies include the export fluxes of POC<sup>h</sup> and/or PIC<sup>l</sup> and also sometimes DOC<sup>j</sup>.</td><td>2.3. The sources of water-column carbon sequestration in the form of DIC include the remineralization of POC in all studies<sup>z</sup>, the remineralization of DOC in some studies<sup>aa</sup>, and/or the dissolution of PIC in a few studies<sup>bb</sup>.</td></tr><tr><td>1.4. The fluxes of DIC production in the water column are taken into account in most studies<sup>k</sup>, but not in those that focus exclusively on export fluxes<sup>l</sup>.</td><td>2.4. Some studies focus on water-column carbon sequestration in the form of DOC<sup>cc</sup><sub>100</sub>, whereas others consider it together with sequestration in the form of DIC fluxes throughout the water column<sup>dd</sup>.</td></tr><tr><td>1.5. The studies that address the release of DIC production in the water column take into account the remineralization of POC in all cases<sup>m</sup>, the remineralization of DOC in some cases<sup>n</sup>, and/or the dissolution of PIC in a few cases<sup>o</sup>.</td><td>2.5. Some estimates of carbon sequestration fluxes specifically include the burial of carbon in the seafloor<sup>ee</sup>, and others do not<sup>ff</sup>.</td></tr><tr><td>1.6. Some of the studies that consider the generation of recalcitrant DOC in the water column focus on this process<sup>g</sup>, whereas others consider it together with remineralization to DIC<sup>q</sup>.</td><td>2.6. Contrary to studies that estimate carbon sequestration fluxes including carbon burial in the seafloor<sup>gg</sup>, studies that estimate carbon sequestration inventories do not include such burial<sup>hh</sup>.</td></tr><tr><td>1.7. Some studies consider the upward flux of DIC<sup>f</sup>, but not others<sup>g</sup></td><td></td></tr><tr><td>1.8. The regions considered are mostly offshore waters<sup>g</sup> but sometimes inshore<sup>u</sup>.</td><td></td></tr></tbody></table>

<sup>a</sup> Chisholm (2000); <sup>b</sup> Knor et al. (2023); <sup>c</sup> Boscolo-Galazzo et al. (2018); <sup>d</sup> Passow and Carlson (2012); <sup>e</sup> Henson et al. (2012); <sup>f</sup> Longhurst (1991); <sup>g</sup> Boyd et al. (2019); <sup>h</sup> Siegel et al. (2021); <sup>i</sup> Honjo et al. (2008); <sup>j</sup> Kwon et al. (2009); <sup>k</sup> Legendre et al. (2015); <sup>l</sup> Clements et al. (2023); <sup>m</sup> Giering and Humphreys (2018); <sup>n</sup> Siegel et al. (2023); <sup>o</sup> Sulpis et al. (2021); <sup>p</sup> Jiao et al. (2010); <sup>q</sup> Nowicki et al. (2022); <sup>r</sup> Wilson et al. (2022); <sup>s</sup> Guidi et al. (2015); <sup>t</sup> Knor et al. (2023); <sup>u</sup> Stukel et al. (2023); <sup>v</sup> Iversen (2023); <sup>w</sup> Wilson et al. (2022); <sup>x</sup> Siegel et al. (2021); <sup>y</sup> Guidi et al. (2015); <sup>z</sup> Boscolo-Galazzo et al. (2018); <sup>aa</sup> Kwon et al. (2009); <sup>bb</sup> Legendre et al. (2015); <sup>cc</sup> Jiao et al. (2010); <sup>dd</sup> Nowicki et al. (2022); <sup>ee</sup> Ricour et al. (2023); <sup>ff</sup> Boyd et al. (2019); <sup>gg</sup> Sigman and Hain (2012); <sup>hh</sup> Siegel et al. (2023).

present study.

The downward transport of carbon in the three pumps can involve up to three biological and three physical mechanisms<fnref n="12" /> (Boyd et al. 2019), which are detailed in Section 3.2. In short, the biologically-driven export mechanisms are the gravitational sinking of biogenic particles (POC and PIC) and daily and seasonal vertical migrations of animals, while the physical export mechanisms are driven by three different types of physical injection. These are sometimes grouped, for simplicity, into the three gravitational, migrant and mixing (or physical injection) mechanisms, to which I refer below rather than the six original mechanisms. All bio-pump studies take into account the gravitational settling of biogenic particles, and some also include the vertical migrations of organisms and/or physical injection (Table 2, item 1.2).

Very few bio-pump studies consider the export of both POC and PIC, and as mentioned above for item 1.1, few of the studies that initially mention the carbonate pump actually take into account the export of PIC and its fate in the water column (Table 2, item 1.3). Furthermore, all three export mechanisms contribute to the downward transport of particles but only mixing can also transport DOC, which means that only studies that include the mixing mechanism take into account the export of DOC and its fate in the water column (Table 2, item 1.3).

A key effect of the three transport mechanisms is the release of DIC in the water column. However, many carbon-pump studies do not explicitly treat DIC fluxes (Table 2, item 1.4). Indeed, as indicated above (Section 1.1), many studies are focused on the downward transport of carbon from the surface ocean towards deep waters, and do not pay much attention to the accompanying release of DIC in the water column.

All the studies that explicitly address the release of DIC in the water column take into account the remineralization of POC. However, only some of them also consider the remineralization of DOC and/or the dissolution of PIC (Table 2, item 1.5). These two processes are examined

in turn:

* First, the sources of DOC in the lower water column are both export from surface waters by the mixing mechanism and *in situ* production resulting from the consumption of POC by zooplankton and bacteria, i.e. DOC is released from faecal pellets, and attached bacteria hydrolyze POC to DOC which is then assimilated by both free and attached bacteria (refs. in Legendre et al., 2015). As a result, there are different types of DOC in the water column with very different lifetimes (Section 2.5). The various types of DOC are remineralized to CO₂ at different depths depending on their sources and lifetimes, and the biological processing of some of the DOC may generate DOC₁₀₀. There are only few biological pump studies that take into account the different lifetimes of DOC fractions (e.g. DeVries and Weber, 2017; Nowicki et al. 2022).

* Second, a variable fraction of the exported PIC dissolves to HCO₃⁻ during its downward journey, depending on the type of CaCO₃ mineral (aragonite or calcite) and the environmental conditions and depth in the water column (Section 3.3). Dissolution of this PIC in the water column increases the concentration of DIC in the lower ocean.

The generation of DOC₁₀₀ is the special focus of microbial-pump studies, which seldom combine the effects of this pump with those of the two other bio-pumps (Table 2, item 1.6). Very few previous studies attempted such combination, which is a central purpose of the present work.

Most of the DIC released in the water column by the carbon pumps is returned quite rapidly to the upper ocean, from where CO₂ may be lost to the atmosphere. However, the upward flux of DIC is seldom quantified in bio-pump studies, and only a few publications explicitly consider it (Table 2, item 1.7). The lack quantification of the upward flux of DIC is an additional consequence of the focus, noted above, of many bio-pump studies on the downward transport of carbon without consideration of the accompanying water-column DIC fluxes.

Finally, most ocean bio-pump studies are dedicated to offshore waters, explicitly or implicitly, and only a few publications address these pumps in inshore, coastal waters (Table 2, item 1.8). This is because the carbon pump concept was initially developed for the open ocean (Section 2.1), and the presence of the seafloor in shallow areas

<footnote n="12">¹² The downward transport mechanisms and their associated carbon fluxes are sometimes called “pumps” in the literature (Boyd et al. 2019, Nowicki et al. 2022). In the present study, I do not use the word “pump” for these mechanisms to avoid confusion with the carbonate, organic, microbial and solubility pumps.</footnote>
complicates the calculation of vertical fluxes in models. The present study does not examine the specific characteristics of ocean carbon pumps in shallow waters.

## 2.7. Differences in the literature concerning ocean carbon sequestration by the three bio-pumps

In the decades following the seminal paper of Volk and Hoffert (1985), the focus of ocean carbon-pump publications shifted from the vertical DIC gradient to the role of the ocean in sequestering atmospheric $CO_2$ (Table 2, right column). Ocean carbon sequestration was not mentioned by Volk and Hoffert (1985), who had created the concept of ocean carbon pumps to explain the ocean's vertical DIC gradient (Section 2.1).

The expression carbon sequestration usually refers to the long-term storage of carbon, i.e. "the long-term removal of $CO_2$ or other forms of carbon from the atmosphere, with secure storage on climatically significant time scales (decadal to century)" (IPCC, 2019). There is a major difference in the literature between two approaches to ocean carbon sequestration, i.e. some studies investigate carbon sequestration fluxes whereas others target the inventory of sequestered carbon (Table 2, item 2.1). In studies that investigate sequestration fluxes, the units of the sequestration metric (flux) are: locally, mass per unit area and per unit time; and globally (i.e. whole ocean), mass per unit time. Studies that target the inventory of carbon sequestered below the euphotic zone irrespective of the retention time assume instantaneous equilibration of the ocean and atmosphere, and the units of the sequestration metric are: locally, mass per unit area; and globally, mass. The present study considers carbon storage of $\ge$ 100 years, called century-scale sequestration (Ricour et al., 2023).

The original definition of ocean carbon pumps in Volk and Hoffert (1985) focused on the gradient in DIC concentration between the surface and the deep ocean (Fig. 3a), whereas a large part of the subsequent carbon-pump literature focused on a different gradient, i.e. the decreasing concentration of particles (POC and PIC) from surface to deep waters. Because it was thought until recently that the long-term storage of carbon in the form of DIC only took place in deep waters, most of the carbon-pump literature was devoted to mechanisms carrying biogenic carbon downwards without considering DIC fluxes in the mid-water column. This had the following four consequences concerning the estimation of ocean carbon sequestration.

* First, many publications focused on the estimation of the carbon flux down to some deep horizon, e.g. 2,000 m (Honjo et al., 2008; Henson et al., 2012), 1,000 m (Passow and Carlson, 2012; Legendre et al., 2015; Iversen, 2023), or a deep isopycnal (Guidi et al., 2015) (Table 2, item 2.2). Such estimates implicitly assumed that all the carbon reaching the targeted depth would be sequestered as DIC in the underlying waters (and also, in some studies, as biogenic carbon buried in the sediment). These estimates also implicitly assumed that the carbon that did not reach this depth returned rapidly to the surface layer and the atmosphere, and was thus not sequestered in the ocean.

Many of the ocean sequestration concepts are largely derived from the high-quality dataset resulting from the deployment of 134 deep sediment traps in the global ocean between 1976 and 2004, synthesized by Honjo et al. (2008). However, the particles collected at depth are in fact the remnants of transport, transformation and sequestration processes that took place in the overlying water column, which explains why there may be little relationship between the magnitude and variability of fluxes recorded by deep sediment traps and those of the water-column bio-pumps (Emerson et al., 2014).

Most of the above studies focused on the decrease in carbon flux with depth, and not on the fate of DIC resulting from the remineralization of organic matter in the water column. However, it is now known that DIC can be physically sequestered at all depths of the water column, in proportions that differ depending on location and depth (Siegel et al. 2021), leading to the concept of continuous vertical sequestration of DIC

(CONVERSE; Ricour et al., 2023) (Table 2, item 2.2). Accordingly, some recent studies estimate carbon sequestration throughout the water column, as either inventories (Nowici et al., 2022; Wilson et al., 2022; Siegel et al., 2023) or fluxes (Ricour et al., 2023) (Section 3.4).

* Second, even in studies that include the carbonate pump in their definition, the DIC resulting from the partial or complete dissolution of $PIC$ to $HCO_3$ in the water column is generally not included in carbon sequestration estimates (Table 2, item 2.3). The reasons for this are likely the same as those invoked above to explain why most carbon-pump studies did not investigate the carbonate pump (Section 2.6). Another reason may be that the carbonate pump acts as a counter-pump for $CO_2$ (Section 2.3), which may lead one to think that this pump does not cause net carbon sequestration. However, this would be incorrect for at least two reasons. Firstly, some of the $CO_2$ released by calcification in the upper ocean is retained in the water column and may eventually be sequestered (Note 10). Secondly, the carbonate-pump process sequence of $CaCO_3$ formation in the upper ocean, export of $PIC$, dissolution of $PIC$ to $HCO_3$ in the lower ocean, and storage of some of this $HCO_3$ for $\ge$ 100 years in the ocean's interior (Section 2.3) results in net century-scale sequestration of carbon in the form of DIC. The resulting DIC sequestration flux is estimated in Section 2.8.

The carbonate pump moves carbon from $HCO_3$ from the surface ocean to the lower water column where part of it is sequestered as DIC, similar to the biological pump which moves carbon from $CO_2$ from the surface ocean to the lower water column where part of it is sequestered as DIC. Given that the sequestration flux of the carbonate pump is far from negligible (Section 2.8), efforts should be made, at least in models, to assess the spatio-temporal variability of carbon sequestration by this pump together with that of the biological pump.

* Third, carbon-pump studies had not considered the possibility of sequestration in the form of $DOC_{100}$ in the water column until the seminal publication of Jiao et al. (2010) proposing the microbial pump, although it had been known previously that $DOC_{100}$ could biochemically sequester carbon in the water column (Legendre and Le Fèvre 1991, 1995; Legendre and Rassoulzadegan, 1996; Legendre and Michaud, 1998). Since the paper of Jiao et al. (2010), water-column sequestration of carbon resulting from the generation of $DOC_{100}$ has been investigated by microbial pump studies, but only few have considered the microbial pump together with the other bio-pumps (e.g. Legendre et al., 2015, their Fig. 1; Nowicki et al., 2022; Jiao et al., 2023, 2024; Table 2, item 2.4).

Until recently, it was thought that only $DOC_{100}$ fluxes could sequester carbon throughout the water column, and it was therefore reasonable to treat the microbial pump separately from the other bio-pumps. However, as it is now known that DIC sequestration fluxes from the biological and carbonate pumps can also take place throughout the water column (first point above), three bio-pumps are treated together in the present study and the possibility of combining their sequestration fluxes is examined in Section 3.4 (eq. (23)).

* Fourth, many publications do not include in their sequestration estimates the very small fraction of organic carbon that escape remineralization in the water column and is buried in the sediments (Table 2, item 2.5). The carbon flux into sediments is very small on an annual basis, but biogenic carbon can be sequestered in the seafloor for thousands and even millions of years,<fnref n="13" /> so these long residence times lead to the creation of huge reservoirs of inorganic and organic carbon in the form of $CaCO_3$ (limestone and other rocks) and fossil organic carbon (including kerogen, from which natural gas and petroleum formed in the past), respectively (Bertrand and Legendre 2021). The shift in focus of carbon-pump studies from the vertical DIC gradient (Volk and Hoffert 1985; Section 2.1) to carbon sequestration (right side of Table 2) should perhaps be accompanied by the incorporation of sedimented carbon into

<footnote n="13">¹³ According to Seton et al. (2020), the mean age of the oceanic crust, on which carbon deposits build up, is 64.2 million years.</footnote>
the estimates of sequestration fluxes by bio-pumps.

As explained above, some ocean carbon sequestration studies target the inventory of sequestered carbon, whereas others investigate the carbon sequestration flux (Table 2, item 2.1). This difference has an effect on whether or not carbon burial in the seafloor is included in estimates of sequestered carbon. Indeed, this inclusion is possible for sequestration fluxes but not for sequestration inventories for reasons explained in Section 3.4 (Table 2, item 2.6).

The differences in publications described in Sections 2.6 and 2.7 should be taken into account by readers of carbon-pump publications in order to understand the results of these studies and use them correctly. The carbon fluxes of the three bio-pumps described above are summarized in Fig. 5a-c for each pump individually and in Fig. 5d for the three pumps together, as a step in the construction of the bio-pump jigsaw puzzle (Fig. 1). The different fluxes are examined in detail in Section 3.

## 2.8. Estimates of century-scale global carbon sequestration fluxes by the three bio-pumps

Before examining the functioning of the three bio-pumps and their carbon sequestration processes in the following sections, it is useful to have in mind the orders of magnitude of global carbon sequestration fluxes by the bio-pumps in the literature. The values cited here are for century-scale sequestration fluxes (Section 2.7). There are several values of sequestration fluxes for the biological pump in the literature, but surprisingly very few for the two other pumps.

**Biological pump.** Historical estimates for the biological pump are provided by the flux of organic particles in deep sediment traps, i.e. 0.4 Pg C y⁻¹ at 2,000 m (Honjo et al., 2008). Flux values from models based on these data combined with estimates of carbon export are up to 0.66 Pg C y⁻¹ at 2,000 m (Henson et al., 2012) and 0.72 Pg C y⁻¹ at the top of the permanent pycnocline (Guidi et al., 2015). It is now known that DIC can be physically sequestered throughout the water column (Siegel et al., 2021; Section 2.7), and corresponding estimates for the century-scale global carbon sequestration flux involving the three export mechanisms of the biological pump range between 0.9 and 2.6 Pg C y⁻¹ (Ricour et al., 2023).

In addition, Hayes et al. (2021) report a global flux of total organic carbon in the sediment of 20 Tg C y⁻¹ (0.02 Pg C y⁻¹). This value may seem low compared with the water-column DIC sequestration flux of 0.9 to 2.6 Pg C y⁻¹, but it should be remembered that the lifetime of water-column DIC sequestration ranges between centuries and a millennium (i.e. the residence time of deep waters in the ocean), whereas that of seafloor POC sequestration can be millions of years, which affects the Earth System significantly in the long term.

**Carbonate pump.** There do not seem to be any estimates in the literature of the global DIC sequestration flux from the water-column dissolution of PIC. However, Sulpis et al. (2021, their Fig. 5) provide vertical profiles of the global flux of DIC from the dissolution of PIC for two depths intervals in the water column. This information is summarized in Table 3, where I calculate a first-order century-scale global DIC sequestration flux from PIC throughout the water-column of about 0.7 Pg C y⁻¹. This may be the first value ever published for this major bio-pump sequestration flux.

In addition, Sulpis et al. (2021, their Fig. 5) provide a value for the burial flux of PIC in the seafloor of 10 ± 2 Tmol y⁻¹ = 0.1 Pg C y⁻¹. This value is consistent with the carbonate burial values of 11.5 and 18 Tmol y⁻¹ for the open ocean and the ocean margin, respectively, from Middelburg et al. (2020).<fnref n="14" /> It is also consistent with the global-ocean value of 136 Tg C y⁻¹ (i.e. 0.1 Pg C y⁻¹) for the seafloor burial of CaCO₃ in the deep sea from Hayes et al. (2021). Comparing these

values to the global PIC flux in sediment traps at 2,000 m of 0.4 Pg C y⁻¹ (Honjo et al., 2008) indicates a dissolution flux of about 0.3 Pg C y⁻¹ below 2000 m, which is roughly consistent with the value of 0.3 Pg C y⁻¹ between 3,000 and 6,000 m cited in Table 3 (i.e. 29 Tmol y⁻¹).

As was already the case for the biological pump above, it should not be forgotten that the lifetime of water-column DIC sequestration ranges between centuries and a millennium, whereas that of seafloor PIC sequestration can be millions of years. The limestone deposits found on continents comes from CaCO₃ sequestered in the seafloor over very long periods.

**Microbial pump.** There appears to be only one estimate of the century-scale global DOC₁₀₀ sequestration flux in the literature, i.e. 0.2 Pg C y⁻¹ (Legendre 2015). This estimate was derived from production rates of labile, semi-labile, semi-refractory and refractory DOC (Section 2.5) from Hansell (2013). The lifetime of recalcitrant DOC in the water column can reach several millennia (Section 2.5), which is longer than the turnover time of the ocean.

**Seafloor sequestration.** The above sequestration fluxes of biogenic carbon in the seafloor, i.e. 0.02 and 0.1 Pg C y⁻¹ for POC and PIC, respectively, are consistent with the net carbon burial flux based on a global reconstruction of carbon burial in deep-sea sediments, of the order of 0.1 Pg C y⁻¹ prior to the rapid input of carbon during the industrial period (Cartapanis et al., 2018). However, the present study focuses on water-column sequestration fluxes, and only marginally addresses carbon sequestration in the seafloor.

**The three bio-pumps together.** The existing estimates of global water-column sequestration fluxes driven by the three bio-pumps are thus quite different, i.e. 0.9–2.6, 0.7 and 0.2 Pg C y⁻¹ for the biological, carbonate and microbial pumps, respectively. The estimates for the carbonate and microbial pumps are both based on a single study, and are therefore uncertain. The three values are nevertheless consistent with the annual global CO₂ uptake by the ocean of 3.0 ± 0.5 Pg C y⁻¹ (not counting the Arctic Ocean) during the period 2011–2017 (Watson et al., 2020, their Supplementary Table 2).

The lifetime of water-column sequestration of DIC by the biological and carbonate pumps ranges between centuries and a millennium, and that of DOC₁₀₀ by the microbial pump can be several millennia. In addition, the organic and carbonate pumps can both sequester carbon in the seafloor for millions of years in the form of POC and PIC, respectively, this sequestration timescale being much longer than those of water column DIC and DOC₁₀₀. The three bio-pumps therefore each make a significant, but different, contribution to ocean carbon sequestration.

# 3. Functioning of the bio-pumps and their processes of ocean carbon sequestration

## 3.1. The four common components of the three bio-pumps

The three bio-pumps share the following four components:

* downward fluxes of biogenic carbon exported from the surface layer in the form of POC, DOC (without or with DOC₁₀₀) or PIC (FexpPOC, FexpDOC, FexpDOC(DOC₁₀₀) or FexpPIC, respectively);

* transformation fluxes of exported biogenic carbon, i.e. POC and/or DOC remineralization into CO₂ or PIC dissolution into HCO₃⁻ (FreminPOC, FreminDOC or FdissPIC, respectively), or in situ production of DOC₁₀₀;

* sequestration fluxes of biogenic carbon in the water column in the form of DIC or DOC₁₀₀ (FseqDIC and FseqDOC₁₀₀, respectively), or contribution to the inventory of carbon sequestered in the form of DIC in the water column; and.

* upward fluxes of non-sequestered DIC to the surface layer (FupDIC).

In addition, the carbonate and biological pumps share a fifth component:

* sequestration fluxes of biogenic carbon into the seafloor in the form of PIC or POC, respectively (Fsedim, examined in Section 3.7).

The implementation of the Fseq concept requires the definition of a

<footnote n="14">¹⁴ These values correspond to 23 and 36 Tmol y⁻¹ in Fig. 6 and Table 3 of Middelburg et al. (2020), which are alkalinity fluxes, i.e. sinks of two moles of alkalinity per mole of CaCO₃ buried.</footnote>
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Carbon fluxes in (a-c) each of the three bio-pumps individually, and (d) the three pumps together. The export depth is $z_{exp} = 100$ m or $z_{eu}$. Panel d is the basis of the bio-pump jigsaw puzzle (Fig. 1).</figcaption></figure>

<caption>**Table 3**</caption>

Flux of DIC from PIC dissolution for different depth intervals in the water column, fraction (%) of water remaining in the global ocean's interior for ≥ 100 years ($f_{100}$; Fig. 7), and century-scale (≥100 years) DIC sequestration flux calculated as the product of the previous two values. The DIC fluxes for 400 to 5,000 m (pelagic dissolution) and 3,000 to 6,000 m (seafloor dissolution) are from Fig. 4 of Sulpis et al. (2021).

<table><thead><tr><th>Depth interval (m)</th><th>DIC flux (Tmol y<sup>-1</sup>)</th><th>% retention for 100 years ($f_{100}$)<sup>b</sup></th><th>100-year DIC sequestration flux (Tmol y<sup>-1</sup>)</th></tr></thead><tbody><tr><td>400-700<sup>a</sup></td><td>4</td><td>30</td><td>1</td></tr><tr><td>700-5,000<sup>a</sup></td><td>32</td><td>90</td><td>29</td></tr><tr><td>3,000-6,000</td><td>30</td><td>99</td><td>30</td></tr><tr><td>Water column</td><td>66</td><td></td><td>60 = 0.7 Pg C y<sup>-1</sup></td></tr></tbody></table>

sequestration time ($t_{seq}$) corresponding to the duration of carbon storage in the ocean, i.e. carbon is sequestered when it is stored for a period ≥ $t_{seq}$. The most frequent value found in the literature is $t_{seq} = 100$ years (whose origin is discussed in Legendre et al., 2015; see also NASEM, 2022), but any other time could be used without changing the generality of the following text. When sequestration is estimated in terms of carbon inventory and not carbon flux, each $I_{seqDIC}$ value is accompanied by the mean residence time of the carbon in the water column ($\tau_{seq}$; e.g. DeVries et al., 2012; Nowicki et al., 2022; Wang et al., 2023).

The carbon fluxes underlying the four common carbon-pump components are summarized in Fig. 5 for (a) the three bio-pumps individually and (d) together. In the next sections, each carbon-pump component is first examined for the three bio-pumps (Sections 3.2 to 3.5), after which the four components are combined (Section 3.6), and finally the fifth component is discussed for the carbonate and biological pumps (Section 3.7).

<footnote><sup>a</sup> The DIC flux between 400 and 5,000 m from Sulpis et al. (2021), 36 ± 8 Tmol y<sup>-1</sup>, is subdivided here as follows: 10% above 700 m and 90% below.</footnote>

<footnote><sup>b</sup> Median value in each depth interval corresponding to Fig. 7.</footnote>
## 3.2. First common carbon-pump component: Export fluxes of biogenic carbon

In the surface layer, phytoplankton synthesizes POC and DOC using free CO₂ (eqs. (3) and (4)), and a large part of this organic matter is rapidly consumed by heterotrophic organisms and thus remineralized to CO₂ (eq. (5)) (Fig. 5c). Some of the DOC is transformed into DOC₁₀₀ by the activity of the food web (Section 2.5; Fig. 5b). The primary source of free CO₂ in the upper ocean is the dissolution of atmospheric CO₂ in surface waters, and secondary sources include heterotrophic respiration, the chemical transformation of HCO₃⁻ and CO₂⁻ into free CO₂ (eq. (2)), and the biological production of free CO₂ from HCO₃⁻ by the calcification process (eq. (6)). Part of the respiratory CO₂ as well as free CO₂ from calcification in the surface ocean can be used by phytoplankton to synthesize POC and DOC, thus contributing to the upper-ocean carbon cycle, but most of this CO₂ generally returns to the atmosphere depending on the location and the time of the year (Fig. 5).

The HCO₃⁻ present in seawater results both from the chemical reaction of free CO₂ with H₂O (eq. (2)), and from the geochemical weathering (chemical dissolution) of two types of rocks on continents by CO₂-laden water, which can be represented as follows:

$$CaCO_{3(\text{solid})} + H_2O + CO_{2(\text{diss})} \rightleftharpoons Ca^{2+}_{(\text{diss})} + 2HCO_{3(\text{diss})} \quad (8)$$

$$CaSiO_{3(\text{solid})} + 3H_2O + 2CO_{2(\text{diss})} \rightarrow Ca^{2+}_{(\text{diss})} + 2HCO_{3(\text{diss})}^{-} + Si(OH)_4(\text{diss}) \quad (9)$$

where dissolution eqs. (8) and (9) are read from left to right. The solid compounds in these equations are limestone (CaCO₃; eq. (8)) and the silicate mineral wollastonite (CaSiO₃; eq. (9)). In eq. (9), CaSiO₃ represents a wide variety of rock minerals, including feldspars which are the main constituents of basalt rocks and make up more than 50 % of the volume of the Earth's crust (Bertrand and Legendre 2021). The products resulting from the above two weathering reactions – HCO₃⁻ and calcium (Ca²⁺) ions and orthosilicic acid (Si(OH)₄) – are transported into the ocean in dissolved form by river waters. In the ocean, the combination of Ca²⁺ and HCO₃⁻ ions forms solid CaCO₃ (PIC, Fig. 5a), mainly through the process of calcification (eq. (6)).

It should be noted that the weathering of CaCO₃ rocks on continents (eq. (8)) followed by the formation of CaCO₃ in the upper ocean (eq. (6)) and export of this CaCO₃ does not modify the long-term global concentration of atmospheric CO₂, since the CO₂ taken up from the atmosphere by the weathering of CaCO₃ on continents (eq. (8)) is globally released into the atmosphere in the long term by the formation of CaCO₃ in the ocean (eq. (6)); see also Note 10). Indeed, the net result of this process is to move CaCO₃ from continental surfaces to the deep ocean and the seafloor. On the contrary, the net long-term effect of the weathering of one mole of continental CaSiO₃ rock (eq. (9)) followed by the formation of one mole of CaCO₃ in seawater (eq. (6)) and its export is to remove one mole of CO₂ from the atmosphere, since only one of the two moles of CO₂ taken up from the atmosphere by the weathering of CaSiO₃ on continents (eq. (9)) is globally released to the atmosphere in the long term by the formation of CaCO₃ in the upper ocean (eq. (6)), resulting in the net sequestration of one mole of atmospheric carbon in the ocean. This process stores carbon over the long term (i.e. sequesters) in deep waters in the form of DIC and in the seafloor in the form of PIC. As a consequence, the weathering of CaSiO₃-type rocks is part of a global feedback loop that stabilizes the Earth's temperature over the long term, on a timescale of about 400,000 years (Bertrand and Legendre, 2021).

The ultimate source of carbon for the ocean carbon pumps is thus the atmosphere. This carbon comes from the atmosphere both directly through the dissolution of atmospheric CO₂ in the surface ocean and indirectly through the weathering of continental rocks by CO₂-laden water. Biogenic carbon that is not recycled within the surface layer can be exported in various forms. As explained in Section 2.6, export can involve up to three biological and three physical mechanisms (Boyd et al. 2019), which are briefly described here.

• The first biological mechanism is the gravitational sinking of biogenic particles, i.e. POC and PIC. Organic particles (POC) consist mostly of phytoplankton cells and aggregates, zooplankton faecal pellets, food-web debris and transparent exopolymer particles (Mari et al., 2017). Biogenic inorganic particles (PIC) mostly include debris of pelagic protozoa (foraminifers) and molluscs (pteropods), and coccoliths which only sink when incorporated into larger aggregates because they are too small to sink by themselves. Most POC is remineralized in the water column and most PIC dissolves there, but some of the sinking particles reach the seafloor.

• The two other biological export mechanisms are driven by animals that migrate vertically, either daily or seasonally. These migrants include zooplankton, fish, and jellies. During their vertical migrations, animals that ingest PIC and POC in the upper ocean defecate, excrete DOC, dissolve some PIC in their guts and release respiratory and gut DIC deeper in the water column. Migrants also include marine mammals, but these do not release respiratory CO₂ at depth because they only breathe at surface; the mechanisms of their possible contribution to carbon pumping are discussed in Boyd et al. (2024).

• The three physical injection mechanisms are driven by the seasonal shoaling and deepening of the mixed layer, the subduction of water masses along mesoscale to sub-mesoscale fronts associated with eddies, and the large-scale advection and overturning of the ocean, respectively (Boyd et al. 2019). These mix down dissolved organic products resulting from the activity of the food web in the upper water column (DOC and DOC₁₀₀) and also suspended particles.

As also explained in Section 2.6, the six export mechanisms are grouped, for simplicity, into the gravitational, migrant and mixing (or physical injection) mechanisms, which are illustrated in Fig. 5a-c for each bio-pump and in Fig. 5d for the three bio-pumps together. All three mechanisms contribute to export POC ($F_{expPOC}$; Fig. 5b,c):

$$F_{\text{exp}} = F_{\text{expPOC}} \quad (10)$$

Of the three mechanisms, mixing can export not only POC but also DOC ($F_{expDOC}$), including DOC₁₀₀ (Fig. 5c):

$$F_{\text{exp}} = F_{\text{expPOC}} + F_{\text{expDOC(\text{DOC}100)}} \quad (11)$$

The three mechanisms can also export PIC ($F_{expPIC}$; Fig. 5a):

$$F_{\text{exp}} = F_{\text{expPOC}} + F_{\text{expPOC(\text{DOC}100)}} + F_{\text{expPIC}} \quad (12)$$

It follows that, depending on publications, $F_{exp}$ be calculated in three different ways (eqs. (10) to (12)). In the literature, the ratio $F_{expPIC}/F_{expPOC}$ is called rain ratio, and based on published estimates of the two fluxes (i.e. 0.45–1.8 and 4–12 Pg C y⁻¹, respectively), this ratio ranges by over an order of magnitude between 0.04 and 0.45 (Neukermans et al., 2023).

In addition, the depth at which $F_{exp}$ is calculated varies among studies. In some publications, the export depth ($z_{exp}$) is fixed, and is often set at 100 m (e.g. Ricour et al., 2023):

$$z_{\text{exp}} = 100 \text{ m} \quad (13)$$

In other publications, $z_{exp}$ is the depth of the euphotic zone ($z_{eu}$; e.g. DeVries and Weber, 2017; Wang et al., 2023), which varies with location in the ocean and time of the year:

$$z_{\text{exp}} = z_{\text{eu}} \quad (14)$$

Most studies using eq. (14) only consider spatial variations in $z_{eu}$, i.e. they do not include its temporal variability during the year. In practice, choosing one $z_{exp}$ or another may not change much the estimates of water-column fluxes and carbon sequestration. However, this choice strongly modifies the values of the transfer efficiency calculated in many carbon-pump studies, as this metric measures the ratio of the sinking POC flux at a given depth (typically 1,000 m) to $F_{exp}$. The estimates of
transfer efficiency calculated at 1,000 m relative to $F_{exp}$ at $z_{eu}$ are generally around 0.15 globally, with considerable geographic variation (Devries and Weber, 2017, Cram et al., 2018).

Finally, different studies may consider different export mechanisms. Indeed, many models in the past only considered gravitational export, whereas some recent models incorporate the different mechanisms described above. For example, Wang et al. (2023) modelled two broad types of export flux, i.e. advective-diffusive (mixing mechanism) and non-advective-diffusive (gravitational and migrant mechanisms), and found a global flux of total organic carbon at the base of the euphotic zone of $15.0 \pm 1.1$ Pg C/year, of which $10.6 \pm 0.1$ Pg C/year was driven by the non-advective-diffusive mechanism. The latter value is much higher than that obtained by the $^{234}$Th method used at sea to estimate the downward POC flux, i.e. $4 \pm 2.2$ Pg C/year (Henson et al., 2011), a value used as $F_{exp}$ in some models (e.g. Henson et al., 2012; Guidi et al., 2015; Ricour et al., 2023).

Overall, export fluxes are not easy to observe or model because of the myriad of interconnected processes involved in the biological pump. Indeed, export fluxes are influenced by processes such as climate-driven changes in water-column stratification or in the depth at which organic matter remineralization takes place, which influences nutrient replenishment in the surface ocean with feedbacks to climate. Greater understanding of these feedbacks would contribute to improved model representation of carbon remineralization and sequestration fluxes (Henson et al., 2022). The same applies to the two other bio-pumps.

As a consequence of the above differences, the meaning and values of $F_{exp}$ may vary among publications, not only because they take into account different forms of biogenic carbon (eqs. (10) to (12)) but also because they use different $z_{exp}$ (eqs. (13) and (14)) and consider different export mechanisms. In addition, the algorithms used to estimate $F_{expPOC}$, $F_{expIDOC}$ and/or $F_{expPIC}$ can vary quite considerably among publications. Readers of ocean carbon-pump studies should be aware of the many methodological differences that affect $F_{exp}$ estimates in the carbon-pump literature.

Because the ultimate source of the carbon used by phytoplankton to synthesize organic matter and by various organisms to form $CaCO_3$ is the atmosphere (eq. (2)), $F_{exp}$ causes a net influx of $CO_2$ from the atmosphere into the ocean. This way, the bio-pumps contribute to the global influx of atmospheric $CO_2$ into the ocean, in addition to the solubility pump mentioned in Section 2.1. However, the influx of atmospheric $CO_2$ may occur in different areas and at different times to those in which the pumps operate (e.g. weathering of rocks on continents, followed by $CaCO_3$ formation far away and much later in the ocean; Section 3.2), and may be offset by efflux of $CO_2$ from the ocean to the atmosphere in other areas and at other times (Section 3.5).

One should not confuse here the total flux of $CO_2$ from the atmosphere into the ocean with the flux of anthropogenic $CO_2$, which is a component of the total flux (Section 3.2). The difference between the two fluxes is important because although bio-pumps currently take up some atmospheric carbon, they do not affect its anthropogenic component. Indeed, photosynthesis in the upper ocean is generally limited by the supply of nutrients, not $CO_2$, so the current increase in dissolved $CO_2$ does not enhance phytoplankton production and thus the biological pump. Given that phytoplankton production is not increasing, nor is $DOC_{100}$ production, it is likely that the microbial pump is not responding to the current increase in upper-ocean dissolved $CO_2$. In addition, the current ocean acidification resulting from the increase in dissolved $CO_2$ in the upper ocean and global warming are predicted to lead to a decrease in calcification, so although the observed effects range from decreases to increases in calcification (Raven and Beardall, 2021), the carbonate pump is unlikely to be enhanced by the present-day increase in dissolved $CO_2$. It follows that only the physical solubility pump (Section 2.1) currently takes up anthropogenic $CO_2$. The roles of the different pumps in this respect may change in the future as the ocean environment is progressively affected by climate change.

### 3.3. Second common carbon-pump component: Transformation fluxes of the exported biogenic carbon in the lower water column

Most of the POC, DOC (except $DOC_{100}$) and DIC exported from the upper ocean is transformed into biogenic DIC below the export depth during its downward journey in the water column. The processes of this transformation are remineralization of POC and DOC, and dissolution of PIC ($CaCO_3$). There is also production of $DOC_{100}$ in the lower water column.

Remineralization of organic carbon and production of $DOC_{100}$ in the lower water column (Fig. 5b,c). There is progressive remineralization of $F_{expPOC}$ and $F_{expDOC}$ into biogenic $CO_2$, and transformation of some of particulate $F_{expPOC}$ into dissolved $F_{DOC}$. As explained in Section 2.6, the food-web mechanisms involved in the formation of $F_{DOC}$ in the lower ocean include the release of DOC from faecal pellets and the hydrolysis of POC to DOC by attached bacteria, this DOC being then assimilated by both free and attached bacteria. The *in situ* DOC flux adds up to $F_{expDOC}$, and most of the combined DOC is rapidly respired to $CO_2$ (eq. (5)).

A small fraction of DOC in the lower water column is transformed *in situ* into $DOC_{100}$, which resists remineralization to $CO_2$ (Section 2.5). The *in situ* $DOC_{100}$ flux ($F_{DOC_{100}}$) adds up to $F_{expDOC}(DOC_{100})$ from the upper water column (Fig. 5c).

The $CO_2$ resulting from remineralization of POC and DOC reacts with water (eq. (2)), causing a flux of DIC into the water column ($F_{wCDIC}$):

$$F_{wCDIC} = F_{wC}(CO_2 + H_2CO_3 + HCO_3 + CO_3) \quad (15)$$

Studies that only take into account the downward flux of POC use the flux of DIC from POC remineralization ($F_{reminPOC}$) to calculate $F_{wCDIC}$ at various water-column depths $z$:

$$F_{wCDIC}(z) = F_{reminPOC}(z) \quad (16)$$

Studies that also take into account the downward flux of DOC combine $F_{reminPOC}(z)$ and the flux of DIC from DOC remineralization ($F_{reminDOC}$) to calculate $F_{wCDIC}$:

$$F_{wCDIC}(z) = F_{reminPOC}(z) + F_{reminDOC}(z) \quad (17)$$

The downward flux of organic carbon in the water column ($F_{org}$; POC and DOC) decreases with depth, and its value at any depth $z$ reflects cumulative $F_{wCDIC}$ from the export depth ($z_{exp}$) down to $z$ ($\sum_{z}^{z_{exp}} F_{wCDIC}$):

$$F_{org}(z) = F_{exp} - \sum_{z}^{z_{exp}} F_{wCDIC}(z) \quad (18)$$

where $F_{exp}$ is calculated with either eq. 10 or 11. For simplicity, it is assumed here that the fraction of $F_{exp}$ transformed into $DOC_{100}$ below $z_{exp}$ is very small compared to $F_{org}$, i.e. $F_{DOC_{100}}(z) \ll F_{org}(z)$ at $z > z_{exp}$, and consequently eq. (18) does not include a term for $F_{DOC_{100}}(z)$.

Fig. 6a,b provides a simplified illustration of the changes in $F_{org}(z)$ and $\sum_{z}^{z_{exp}} F_{wCDIC}(z)$ with depth. The calculations only take gravitational POC export into account, i.e. $F_{org}(z)$ is calculated using eqs. (10) and (18). The vertical profiles in panels a and b show that $F_{org}(z)$ decreases with increasing depth $z$, and that $\sum_{z}^{z_{exp}} F_{wCDIC}(z)$ increases correspondingly. The other panels of Fig. 6 are examined in Sections 3.4 and 3.5.

For simplicity, Fig. 6 uses only the gravitational export mechanism and thus does not take into account vertical migrations or mixing. As a result, carbon fluxes in the water column below $z_{exp}$, including $F_{org}(z)$ and $\sum_{z}^{z_{exp}} F_{wCDIC}(z)$, are lower than they would have been if vertical migrations and mixing had been taken into account. Nevertheless, Fig. 6 captures most of the sequestration fluxes as the gravitational mechanism accounts for 66–79 % of total $F_{seq}$ in the ocean (Ricour et al., 2023).

It should be noted that many studies compare water-column heterotrophic carbon demand (i.e. the carbon flux required to sustain heterotrophic production and respiration) to the magnitude of phytoplankton production, often leading to the conclusion that the latter is too small to
support the former. Legendre and Rivkin (2008) explained that this comparison is incorrect because any one carbon atom can be recycled many times, numerically causing carbon demand to exceed supply, and they recommended to compare instead the respiration flux (i.e. $\sum_{z}^{z_{exp}} F_{wcDIC}$), which is additive, to phytoplankton production. This approach was shown to be correct by Giering et al. (2014), who used it to reconcile the carbon budget in the ocean's twilight zone (or mesopelagic layer) at the Porcupine Abyssal Plain site in the eastern North Atlantic Ocean.

Dissolution of PIC (CaCO₃) in the lower water column (Fig. 5a). Part of the exported CaCO₃ dissolves to DIC in the lower ocean, causing the progressive transformation of F<sub>expPIC</sub> into F<sub>dissPIC</sub>. Depending on water depth and environmental conditions, a variable fraction of the PIC can escape dissolution in the water column and reach the seafloor, where this residual F<sub>expPIC</sub> can cause carbon to be buried for millions of years (see Section 3.8).

As explained in Section 2.6, most bio-pump studies do not take into account the fate of CaCO₃ in the lower column in their calculations, and the resulting F<sub>wcDIC</sub> estimates therefore do not include F<sub>dissPIC</sub>. Hence, most studies implicitly assume that F<sub>dissPIC</sub> does not contribute much to F<sub>wcDIC</sub>, which is not correct as clearly shown in Section 2.8.

Equations (16) and (17) can be transformed as follows to include F<sub>dissPIC</sub>:

$$F_{wcDIC}(z) = F_{reminPOC}(z) + F_{dissPIC}(z) \quad (19)$$

$$F_{wcDIC}(z) = F_{reminPOC}(z) + F_{reminDOC}(z) + F_{dissPIC}(z) \quad (20)$$

An expression similar to eq. (18) can be written to describe the decreasing flux of exported CaCO₃ (F<sub>PIC</sub>) with increasing depth, in which the value at any depth z in the water column reflects the cumulative F<sub>dissPIC</sub> from the export depth (z<sub>exp</sub>) down to z:

$$F_{PIC}(z) = F_{expPIC} - \sum_{z}^{z_{exp}} F_{dissPIC}(z) \quad (21)$$

The solubility of CaCO₃ in the ocean depends on a number of interacting factors (Adkins et al., 2021), and generally increases with increasing depth. It also depends on the mineral involved, i.e. solid CaCO₃ occurs in the natural environment in two major crystalline forms, called aragonite and calcite, which are chemically similar but have different crystal structures and thus different solubility. The solubility of aragonite is higher than that of calcite, with the consequence that the calcareous parts of calcifying organisms made of aragonite dissolve more easily than those made of calcite. In particular, the shells of planktonic pteropods (molluscs) are made of aragonite and thus dissolve more rapidly in the water column than the tests of planktonic coccolithophores (phytoplankton), foraminifers (protozoa) and ostracods

<figure><img src="image_9.png" /><figcaption>Fig. 6. Depth variations of biological-pump components considering only gravitational POC export (i.e. F<sub>org</sub> calculated using eqs. (10) and (18) and eq (1) of Martin et al., 1987, with b = 0.86): (a,c,e) carbon fluxes at different depths z, and (b,d,f) cumulative carbon fluxes from z<sub>exp</sub> to z.</figcaption></figure>
(crustaceans), whose primary constituent is calcite.

Because the aragonite shells of planktonic pteropods dissolve faster than the calcite tests of coccolithophores, foraminifers and ostracods, the aragonite shells of pteropods are less abundant in marine sediments than calcite tests. On the seafloor, pteropod-rich ooze is restricted to water depths shallower than 2,500 and 1,500 m in the Atlantic and Pacific Oceans, respectively, whereas calcite sediments can be found down to about 5,000 m in the two oceans.

### 3.4. Third common carbon-pump component: Water-column carbon sequestration

As explained in Section 2.7, carbon-pump studies in the literature estimate ocean carbon sequestration in term of either carbon flux ($F_{seq}$) or carbon inventory ($I_{seq}$). The two approaches are now examined in turn, considering in a first step only carbon sequestration in the water column, i.e. excluding sequestration in the sediment, which is discussed in Section 3.7.

Carbon sequestration fluxes. Depending on location in the ocean and depth in the water column, a variable fraction of the water will remain in the ocean's interior for a long period (Siegel et al., 2021), this fraction being called $f_{100}$ for periods ≥ 100 years by Ricour et al. (2023). Geographically variable $f_{100}$ generally increases with depth, as shown by Siegel et al. (2021; their Supplementary Fig. S2) and also illustrated by Ricour et al. (2023; their Extended Data Fig. 2). Fig. 7 displays the vertical changes in median $f_{100}$ values in the global ocean.

The values of $f_{100}(z)$ are used together with those of the above $F_{WCDIC}(z)$ (eqs. (16), (17), (19) or (20)) to compute the century-scale carbon sequestration flux at any depth (z) throughout the water column:

$$F_{seqDIC}(z) = F_{WCDIC}(z) \times f_{100}(z) \qquad (22)$$

The actual $F_{seqDIC}(z)$ calculations are not performed with the median values for the global ocean (Fig. 7), but instead with the $F_{WCDIC}(z)$ and $f_{100}(z)$ values in the different ocean pixels (Ricour et al., 2023). Because $f_{100}(z)$ in eq. (22) is dimensionless, the units of $F_{seqDIC}(z)$ are the same as those of $F_{WCDIC}(z)$, i.e. mass (or amount) of carbon sequestered per unit area and per unit time, or when considering the whole ocean, mass (or amount) of carbon sequestered per unit time.

In most studies, the carbon sequestration flux ($F_{seqDIC}$) reflects the sequestration of DIC from remineralization of POC or that of POC and DOC, i.e. $F_{WCDIC}(z)$ is calculated with eq. (16) or (17). However, $F_{seq}$ should also reflect DIC sequestration from PIC dissolution (eqs. (19) and (20)) (Fig. 5a), with the resulting estimates being necessarily higher than those obtained with eq. (16) or (17).

Fig. 6c,d illustrates, considering only POC export (i.e. $F_{org}(z)$ calculated using eqs. (10) and (18), the changes in $F_{seqDIC}(z)$ and $\sum_z^{z_{exp}} F_{seqDIC}$ with depth. It shows that the combination of the vertical profiles of $F_{WCDIC}(z)$ (Fig. 6b) and $f_{100}$ (Fig. 7) creates a maximum in $F_{seqDIC}(z)$ at relatively shallow depth, i.e. at 1,000 m in Fig. 6c. It also shows that about half of the cumulative $\sum_z^{z_{exp}} F_{seqDIC}$ occurs in the upper water column, i.e. above 1,100 m in Fig. 6d. Calculations for the global ocean indicate that this shallow maximum is of general occurrence (Ricour et al., 2023, their Fig. 4).

As explained in Section 2.5, the remineralization time of DOC$_{100}$ to CO$_2$ is much longer than $t_{seq}$ (i.e. 100 years), meaning that DOC$_{100}$ geochemically sequesters carbon in the water column. Hence, $F_{DOC100} = F_{seqDOC100}$. As suggested in Section 2.7, $F_{seq}(z)$ could combine the fluxes of carbon sequestered in the form of both DIC and DOC$_{100}$:

$$F_{seq}(z) = F_{seqDIC}(z) + F_{DOC100}(z) \qquad (23)$$

However, given that the global carbon sequestration flux driven by the microbial pump is quite small relative to those of the two other bio-pumps (Section 2.8), it remains to be seen whether using eq. (23) instead of eq. (22) would change the $F_{seq}$ estimates significantly in the global ocean or in some specific areas.

<figure><img src="image_10.png" /><figcaption>Fig. 7. Fraction of water remaining in the ocean's interior for ≥ 100 years ($f_{100}$): median values for the world ocean at different depths (Ricour et al., 2023, Fig. 2b; original values from Siegel et al., 2021).</figcaption></figure>

Carbon sequestration inventory. A different concept of ocean carbon sequestration considers the inventory of DIC from *remineralized* (respired) organic carbon ($F_{WCDIC}$) that the ocean stores at steady state, assuming instantaneous equilibration of respired CO$_2$ with the atmosphere (Nowicki et al., 2022). The above $F_{WCDIC}(z)$ values (eqs. (16) or (17)) can be used together with those of the mean residence time of carbon at any depth z in the water column ($\tau_{seq}(z)$) to compute the corresponding carbon-pump carbon sequestration inventory as follows:

$$I_{seqDIC}(z) = F_{WCDIC}(z) \times \tau_{seq}(z) \qquad (24)$$

Because the unit of $\tau_{seq}(z)$ is time, those of $I_{seqDIC}(z)$ are the mass (or amount) of carbon sequestered per unit area or, when considering the whole ocean, the mass (or amount) of carbon sequestered. It is thus important for readers of carbon-pump publications to know if the metric used for carbon sequestration in a given study is $I_{seqDIC}$ or $F_{seqDIC}$ as that these two quantities are very different.

The above, very specific definition of $I_{seqDIC}(z)$ only includes the DIC inventory from *remineralized* (respired) organic carbon stored in the ocean at steady state and not the corresponding DIC inventory from dissolved CaCO$_3$ (PIC). Hence, eq. (24) corresponding to this definition is calculated with $F_{WCDIC}(z)$ from POC remineralization (eq. (16)) or POC and DOC remineralization (eq. (17)). However, the definition could be extended to also take into account DIC from PIC dissolution, which would lead to calculating eq. (24) with $F_{WCDIC}(z)$ that includes the dissolution of PIC (eq. (19) or (20)). This would generate estimates of the inventory of carbon stored in the ocean by the carbonate and biological pumps, and not only by the latter.

Similarly, $I_{seqDIC}(z)$ could possibly include the inventory of DOC$_{100}$ generated by the microbial pump (Section 2.5). However, because $\tau_{seq}$ of water-column DOC$_{100}$ can reach several thousand years (Section 2.5), which is much longer than the $\tau_{seq}$ of water-column DIC (centuries to a
millennium), the inclusion of DOC100 in eq. (24) could swamp the total Iseq estimates. In order to resolve this problem, a published study on carbon sequestration inventory taking DOC100 into account considered that all DOC100 was eventually remineralized to CO2 in the water column (eq. (5)), and incorporated it in this way into the calculation of water-column IseqDIC (Nowicki et al., 2022).

### 3.5. Fourth common carbon-pump component: Upward fluxes of dissolved inorganic carbon

The fraction of water that does not remain in the ocean for a period ≥ tseq returns relatively rapidly to the upper ocean, driving an upward carbon-pump flux of DIC (FupDIC; Fig. 5). In the case of century-scale sequestration, the fraction of water that does not remain in the ocean for ≥ 100 years is (1 − f100), and FupDIC at any depth z can be computed as follows:

$$F_{\text{upDIC}}(z) = F_{\text{wcDIC}}(z) \times (1 - f_{100}(z)) = F_{\text{wcDIC}}(z) - F_{\text{seqDIC}}(z) \quad (25)$$

The rightmost expression is obtained using eq. (22). The values of FwcDIC(z) in eq. (25) can be computed with either eq. (16), (17), (19) or (20). Using eq. (25), FwcDIC(z) can be expressed in term of its two “daughter” fluxes FseqDIC(z) and FupDIC(z):

$$F_{\text{wcDIC}}(z) = F_{\text{seqDIC}}(z) + F_{\text{upDIC}}(z) \quad (26)$$

and the same can be done for $\sum_{z}^{z_{\text{exp}}} F_{\text{wcDIC}}$:

$$\sum_{z}^{z_{\text{exp}}} F_{\text{wcDIC}}(z) = \sum_{z}^{z_{\text{exp}}} F_{\text{seqDIC}}(z) + \sum_{z}^{z_{\text{exp}}} F_{\text{upDIC}}(z) \quad (27)$$

This expression will be used in Section 3.6.

Fig. 6e,f illustrates, considering only POC export (i.e. Forg(z) calculated using eqs. (10) and (18), the changes in FupDIC(z) and $\sum_{z}^{z_{\text{exp}}} F_{\text{upDIC}}$ with depth. It shows that FupDIC(z) increases rapidly from around 500 m towards the surface (Fig. 6e). It also shows that, correspondingly, the cumulative upward flux $\sum_{z}^{z_{\text{exp}}} F_{\text{upDIC}}(z)$ is almost constant below 500 m, indicating that most of the upward flux occurs above this depth (Fig. 6f).

The global upward flux of remineralized DIC is mostly driven by the upwelling of deep waters in some regions of the ocean (Kwon et al., 2009), and this flux also carries DOC100 upwards. Once remineralized DIC and DOC100 reach the surface, they may, depending on the environmental conditions, be partially or completely converted into CO2, and this CO2 may be partially or completely degassed into the atmosphere. The conversion mechanisms of DIC and DOC100 into CO2 are different. On the one hand, the conversion of DIC into CO2 follows eq. (2) operating from right to left. On the other hand, the main process converting DOC100 into CO2 in surface waters may be photodegradation by solar UV radiation, which could alter the DOC and make it available for remineralization by bacteria (eq. (5); refs. in Legendre et al., 2015, and in Cai and Jiao, 2023).

The upward fluxes of DIC and the efflux of CO2 from the upper ocean into the atmosphere are not generally quantified in bio-pump publications. However, quantifying these fluxes would be useful because the efflux of CO2 from the ocean driven by the bio-pumps contributes to the global release of CO2 from the ocean into the atmosphere, for which the role of bio-pumps is poorly known. Together, the upward bio-pump component and the bio-pump influx of CO2 into the ocean resulting from the downward fluxes of POC, DOC and PIC (Section 3.2) are important factors that contribute to different regions of the ocean acting as sinks or sources of atmospheric CO2 at different times of the year.

### 3.6. Combined four common carbon-pump components

Combining eqs. (18) and (27) shows that, at any depth z in the water column, the sum of downward Forg(z) and the cumulative values of sequestration and upward fluxes between zexp and z is equal to Fexp,

where Fexp is calculated with either eq. 10 or 11. Indeed, eq. (18) can be rewritten as follows:

$$F_{\text{org}}(z) + \sum_{z}^{z_{\text{exp}}} F_{\text{wcDIC}}(z) = F_{\text{exp}} \quad (28)$$

and replacing $\sum_{z}^{z_{\text{exp}}} F_{\text{wcDIC}}(z)$ in eq. (28) by its value from eq. (27) gives:

$$F_{\text{org}}(z) + \sum_{z}^{z_{\text{exp}}} F_{\text{seqDIC}}(z) + \sum_{z}^{z_{\text{exp}}} F_{\text{upDIC}}(z) = F_{\text{exp}} \quad (29)$$

Even if Forg(z) is not written with the $\sum$ symbol, it is cumulative given that Forg(z) cumulates the losses of exported organic carbon between zexp and z, so the left side of eq. (29) is the sum of three cumulative terms. The above equations could also be rewritten to include PIC (not done here, for simplicity).

Equations (28) and (29) state a fundamental property of carbon-pump fluxes, namely that the three cumulative carbon-pump fluxes are complementary, as the sum of their values remains constant with depth. Fig. 8 illustrates that this sum is equal to Fexp at all depths in the water column.

In Fig. 8a, the values of Forg(z), $\sum_{z}^{z_{\text{exp}}} F_{\text{seqDIC}}$ and $\sum_{z}^{z_{\text{exp}}} F_{\text{upDIC}}$ – and Forg(z) and $\sum_{z}^{z_{\text{exp}}} F_{\text{wcDIC}}$ – from Fig. 6 are added together from left to right. The distances between the depth-axis and the green and black curves correspond to Fexp(z) and Forg(z), respectively; the distance between the green and black curves corresponds to $\sum_{z}^{z_{\text{exp}}} F_{\text{wcDIC}}(z)$; the distance between the red and black curves corresponds to $\sum_{z}^{z_{\text{exp}}} F_{\text{seqDIC}}(z)$; and the distance between the green and red curves correspond to $\sum_{z}^{z_{\text{exp}}} F_{\text{upDIC}}(z)$.

The vertical profiles in Fig. 8a may appear quite different from schematic representations of the biological pump concept in the literature where the decrease in sinking POC with increasing depth z is represented as a “funnel” (e.g. Boscolo-Galazzo et al., 2018; Iversen, 2023; Jiao et al., 2024). However, when the areas from Fig. 8a are distributed equally to the left and right of the centre of the diagram, the decrease in Forg(z) with increasing z forms a funnel, as is the case in these conceptual representations (Fig. 8b). In addition to illustrating the decrease in Forg(z) with depth that is common to all biological-pump representations, Fig. 8 shows that this decrease is accompanied by sequestration and upward DIC fluxes, i.e. FseqDIC(z) and FupDIC(z) (eqs. (22) and (25)).

Even if many conceptual carbon-pump schemes correctly represent the decrease in Forg with increasing depth (i.e. the decrease with depth in Fig. 8a, or the “funnel” in Fig. 8b), they generally do not adequately represent the vertical changes in $\sum_{z}^{z_{\text{exp}}} F_{\text{wcDIC}}$, $\sum_{z}^{z_{\text{exp}}} F_{\text{seqDIC}}$ and $\sum_{z}^{z_{\text{exp}}} F_{\text{upDIC}}$, and the fact that $[F_{\text{org}}(z) + \sum_{z}^{z_{\text{exp}}} F_{\text{seqDIC}} + \sum_{z}^{z_{\text{exp}}} F_{\text{upDIC}}] = [F_{\text{org}} + \sum_{z}^{z_{\text{exp}}} F_{\text{wcDIC}}] = F_{\text{exp}}$. I therefore recommend that future carbon-pump publications use representations similar to those in Fig. 8a or 8b, which would have the advantage of accounting for all the exported carbon, whereas in the usual conceptual or even numerical representations of bio-pumps, some of the exported carbon seems to “disappear into thin air” (or “into thick water”).

### 3.7. Fifth carbon-pump component: Carbon sequestration fluxes into the seafloor

The historical reason why the flux of carbon into the sediment is often not included in the calculation of Fseq or Iseq is explained in Section 2.1. Briefly, the ocean carbon pumps were proposed by Volk and Hoffert (1985) to explain the maintenance of the vertical DIC gradient in the ocean’s water-column, and thus did not consider the sediment. When, in the years that followed, the focus of carbon-pump studies shifted from the vertical DIC gradient to ocean carbon sequestration, most studies retained Volk and Hoffert’s (1985) water-column definition of the carbon pumps and did not take into account the fluxes of POC or PIC into the sediment when estimating carbon sequestration.

Should the Fseq estimates take into account Fsedim in carbon-pump studies? This would seem appropriate for the carbonate and biological
<figure><img src="image_11.png" /><figcaption>Fig. 8. The three cumulative biological-pump fluxes from Fig. 6 are added together showing that $[F_{org}(z) + \sum_{z}^{z_{exp}} F_{seqDIC} + \sum_{z}^{z_{exp}} F_{upDIC}] = [F_{org}(z) + \sum_{z}^{z_{exp}} F_{wcDIC}] = F_{exp}$. The different curves are added together (a) from left to right, and (b) from the centre to the left and the right.</figcaption></figure>

pumps, but not for the microbial pump which sequesters carbon only in the form DOC$_{100}$ in the water-column (Fig. 5a-c). However, including $F_{sedim}$ in the calculations could have the following effects on the $F_{seq}$ and $I_{seq}$ estimates.

* Including $F_{sedim}$ in the calculation of $F_{seq}$ would not really change the values usually found in the literature because of the way water-column sequestration is generally estimated. Indeed, in studies that do not explicitly take $F_{sedim}$ into account, it is generally assumed that all POC, DOC (except DOC$_{100}$) and/or PIC reaching bottom waters is either mineralized or dissolved there, and that the resulting DIC is stored in deep waters for periods longer than $t_{seq}$. This assumption can be implemented as follows using eq. (22):

$$F_{seqDIC}(\text{bottom water}) = F_{wcDIC}(\text{bottom water}) \times [f_{100}(\text{bottom water}) = 1.0] \qquad (30)$$

In these studies, the calculations include in the carbon sequestered in the form of DIC in deep waters the component of $F_{org}$ that would be sequestered in sediments.

In some studies (e.g. Ricour et al., 2023), values of $F_{sedim}$ (e.g. available in Hayes et al., 2021) are subtracted from the value calculated with eq. (30) to distinguish between bottom-water and seafloor $F_{seq}$:

$$F'_{seqDIC}(\text{bottom water}) = F_{seqDIC}(\text{bottom water}) - F_{sedim} = F_{wcDIC}(\text{bottom water}) - F_{sedim} \qquad (31)$$

Because the carbon buried in the sediment is stored there for $> t_{seq}$, which is also the case for the DIC sequestered in the water column, calculating total $F_{seq}$ with eq. (31) plus $F_{sedim}$ leads to the same value as with eq. (30):

$$F'_{seqDIC}(\text{bottom water}) + F_{sedim} = F_{wcDIC}(\text{bottom water}) \qquad (32)$$

Although $F_{sedim}$ only represents 1–3 % of the global water-column $F_{seqDIC}$ (Ricour et al., 2023), it may be interesting to use eq. (31) instead of eq. 30 when calculating sequestration fluxes. This is because eq. (31) makes it possible to distinguish between long-time carbon sequestration fluxes into the water column ($>t_{seq}$) and very-long-time sequestration fluxes into the seafloor ($>t_{seq}$), whereas eq. (30) does not.

In addition, chemoautotrophic bacteria can fix significant amount of CO$_2$ carbon into organic matter in nearshore, shelf and slope sediments (Section 2.3). It follows that carbon-pump studies in areas containing such sediments could take into account the contribution of dark carbon

fixation in sediment when estimating carbon sequestration. This could be significant in relatively shallow waters where $F_{seqDIC}$ is quite low (Fig. 6c) and where dark carbon fixation could create a flux from short-term water-column PIC to longer-term sediment POC and/or DOC.

* Including $F_{sedim}$ in the calculation of $I_{seq}$ may not be appropriate. Indeed, the mean residence time of DIC sequestered in the water column is not more than 500 years at best,<fnref n="15" /> whereas that of carbon sequestered in the seafloor is millions of years. Assuming that the ratio of $F_{sedim}$ (POC and PIC) to $F_{wcDIC}$ in the water column ($\sum_{bottom}^{z_{exp}} F_{DBCwcDIC}$) is 1/100 = 0.01, and that $\tau_{seq}$ is 500 years for $F_{wcDIC}$ and 1,000,000 years for $F_{sedim}$, the ratio of sequestration in the sediment to the water column would be 20 (eq. (24)):

$$\frac{I_{seq}(\text{seafloor})}{I_{seqDIC}(\text{water column})} = \frac{(1 \times 1,000,000\text{y})}{(100 \times 500\text{y})} = 20 \qquad (33)$$

In other words, because the very small fraction of biogenic carbon sequestered in the seafloor is stored there for a very long time, including the value of $I_{seq}(\text{seafloor})$ in total $I_{seq}$ would swamp the latter’s estimate (e.g. by a factor of 20 in eq. (33)). Accordingly, the modelling exercise of Nowicki et al. (2022) provided an estimate of ~0.4 g C y⁻¹ for $F_{sedim}$, but the authors did not take this value into account when they calculated $I_{seq}$, which they strictly defined as the inventory of DIC from the mineralization of POC and DOC in the water column (Section 3.4).

The three largest reservoirs of carbon on Earth are, in descending order, the crust and sediments, the ocean, and fossil organic matter.<fnref n="16" /> One would thus expect that at least some of the carbon-pump studies would devote efforts to estimate the sequestration fluxes of both organic carbon and $CaCO_3$ by the bio-pumps into the seafloor, where biogenic carbon is stored for very long times in the form of fossil organic matter and carbonate rocks. However, for the reasons explained above, most carbon-pump studies focus on sequestration fluxes in the sole water column and even on the sole organic carbon component of these fluxes.

<footnote n="15">¹⁵ Nowicki et al. (2022) report average sequestration times of 140 years for the gravitational mechanism, 150 years for the migrant mechanism, and 50 years for the mixing mechanism.</footnote>

<footnote n="16">¹⁶ Legendre (2014, Table 4.3) reports the following values (Pg C) for the three main carbon reservoirs: crust and sediments, $1 \times 10^8$; ocean, $3.9 \times 10^4$; fossil organic matter, $4 \times 10^3$. The value he reports for the amount of carbon in the atmosphere is much smaller, i.e. $7.2 \times 10^2$ Pg C.</footnote>
### 3.8. Carbon effluxes from the seafloor relevant to the three bio-pumps

Carbon sequestration in seawater can be affected by different types of efflux from the seafloor. Three such effluxes, which are relevant to the biological, carbonate and microbial pumps, respectively, are briefly examined here.

The first efflux affects organic carbon sequestered in the seafloor as a result of the long-term action of the biological pump. The processes described here involve the production and destabilization of deposits of solid methane hydrate (also called methane clathrate, or fire ice) in the seafloor. This substance is thought to be formed in situ by microbial decomposition of organic matter (POC and DOC) previously accumulated in the sediment by the biological pump during very long periods. Depending on temperature and pressure conditions, methane hydrate is stable or not. Destabilization can result from the warming of bottom water, for example at the end of an ice age or in the foreseeable future due to the ongoing global warming. It can also result from a decrease in hydrostatic pressure, for example during an ice age when sea level falls (sea level dropped by ≥ 100 m during the last ice ages).

Destabilized methane hydrate deposits release methane gas ($CH_4$), most of which is used by two different types of methanotrophic bacteria (De La Fuente et al., 2022). On the one hand, anaerobic bacteria consume most of the released $CH_4$ within the seafloor, resulting in a net production of $HCO_3^-$ ions:

$$CH_4 + SO_4^{2-} \rightarrow HCO_3^- + HS^- + H_2O \quad (34)$$

Some of the $HCO_3^-$ ions escape from the seafloor, where some can be used by organisms to form $CaCO_3$ structures on the seafloor, this process (calcification) releasing $CO_2$ in the surrounding water (eq. (6)). On the other hand, a small fraction of the $CH_4$ released from methane hydrates may escape into the water column where it is mainly consumed by aerobic bacteria, leading to the oxidation of $CH_4$ into $CO_2$ via a series of two-electron steps in which methanol, formaldehyde and formate act as intermediates. The net effect of this water-column process is as follows:

$$CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \quad (35)$$

The combined release of $HCO_3^-$ escaping from the seafloor (eq. (34)) and of $CO_2$ in the water column (eq. (35)), where most of it combines with water molecules (eq. (6)), increases water-column DIC (eq. (1)). The net effect of this suite of processes is to transfer carbon from the seafloor reservoir, where it was sequestered in the form of very-long-time POC and DOC, to the water-column reservoir, where it is sequestered in the form of shorter-time DIC.

The second efflux affects carbon sequestered in the form of $CaCO_3$ deposited on the seafloor by the carbonate pump. It was explained in Section 2.3 that the increasing concentration of atmospheric $CO_2$ and the corresponding dissolution of $CO_2$ in the upper ocean causes an increase in seawater DIC (eq. (2)). When the deep oceanic circulation brings DIC-enriched surface seawater into contact with $CaCO_3$ sediments, there is dissolution of solid $CaCO_3$:

$$CaCO_{3(\text{solid})} + CO_{2(\text{aqueous})} + H_2O \rightleftharpoons Ca^{2+}_{(\text{aqueous})} + 2HCO_{3(\text{aqueous})}^- \quad (36)$$

The dissolution of one mole of solid sedimented $CaCO_3$ consumes one mole of seawater $CO_2$ and store the carbon from $CaCO_3$ and $CO_2$ as dissolved $HCO_3^-$ ions.

Some dissolution of $CaCO_3$ sediments has already been observed in the western North Atlantic Ocean, and the phenomenon has also been reported at various sites in the Southern Atlantic, Indian and Pacific Oceans (Sulpis et al., 2018). A net effect of the process is to transfer carbon from very-long-time solid carbonates in the seafloor to shorter-time dissolved DIC in the water column.

The third efflux affects carbon sequestered in the water column by the microbial pump in the form of $DOC_{100}$. It is known that part of the ocean's bottom water circulates in hydrothermal systems of the oceanic

crust. A study found that approximately 70 % of the DOC entering such systems is removed during the circulation of seawater in the crustal reservoir, one of the possible fates of this DOC being thermal degradation into $CO_2$ or $CH_4$ (Lang et al., 2006).

It has been suggested that the crustal circulation mechanism may remove $DOC_{100}$ from deep waters (Hansell 2013; Legendre et al. 2015), and it can be assumed that some of the $CO_2$ and possibly $CH_4$ resulting from the thermal degradation of $DOC_{100}$ is returned to the ocean in hydrothermal waters. The net effect of these processes would be to transfer carbon from the $DOC_{100}$ pool, in which it was sequestered for a long time, to the biogenic DIC pool, in which it is sequestered for a shorter time.

Each of the above three effluxes transforms into water-column DIC some carbon that had been sequestered for long times in other chemical forms by one of the three bio-pumps, i.e. POC and DOC sequestered in the seafloor by the biological pump, PIC ($CaCO_3$) sequestered in the seafloor by the carbonate pump, and $DOC_{100}$ sequestered in the water-column by the microbial pump. These fluxes potentially decrease the sequestration times of four carbon compounds, i.e. POC, DOC, PIC and $DOC_{100}$. For simplicity, carbon effluxes from the seafloor are not represented in Fig. 5 or in the bio-pump jigsaw puzzle (Fig. 1).

### 4. Towards a unified approach to research on the three bio-pumps

#### 4.1. Processes involved in the three bio-pumps and their ocean carbon sequestration

The analysis of the bio-pump literature in Section 2 showed that most individual carbon-pump studies address only one of the three bio-pumps, and often only one or a few components of that pump. The analysis also showed that almost all aspects of the various pumps and their carbon sequestration are often treated differently in different studies. An important result of the analysis was that the sequestration fluxes of the three bio-pumps, although very different, are quantitatively significant. In Section 3, it was shown that the three pumps contribute in various ways to the different carbon-pump components, which are additive.

The information from the previous sections is organized in analytical Table 4 to compare key characteristics of the three bio-pumps. The pumps in Table 4 are listed in the same order as in Fig. 5a-c, and their characteristics are in the same order as in Sections 3.2 to 3.5, 3.7 and 3.8.

All three carbon pumps (see also Fig. 5d). In the surface layer, the combination of dissolved $CO_2$ with water leads to the formation of DIC ($CO_2 + H_2CO_3 + HCO_3^- + CO_3^{2-}$; eq. (1), with the resulting carbonate system (eq. (2)) governing the chemistry of dissolved $CO_2$ in seawater (eq. (2)). This affects the three bio-pumps and also to the physical solubility pump mentioned in Section 2. All three export mechanisms (gravitational, migrant and mixing) contribute to each of the three bio-pumps, albeit in different ways (below), and the mixing mechanism also exports DIC in the solubility pump.

Carbonate pump (see also Fig. 5a). In surface waters, different organisms use dissolved $HCO_3^-$ ions to form $CaCO_3$ body parts (PIC, eq. (6)). These organisms include coccolithophores, foraminifers, pteropods and ostracods (Sections 2.1 and 3.3). Most of the resulting PIC is eventually exported to the lower water column by the gravitational mechanism, and also as part of the body or in the guts of vertically migrating organisms (eq. (12)). The mixing mechanism could also contribute to exporting PIC, but this has not yet been documented. At depth, depending on the crystal nature of the $CaCO_3$ (i.e. aragonite or calcite; Section 3.3) and water temperature and pressure, part of the exported PIC dissolves back to $HCO_3^-$ (eq. (6)), and some of the resulting DIC is sequestered in the water column. Although most previous studies considered that sequestration fluxes only took place in deep waters, it is
<caption>**Table 4**</caption>

Comparison of key characteristics of the three bio-pumps. The three pumps are described in Section 2, and their components are examined in Section 3. The horizontal arrows (⇒) represent changes in carbon form. In brackets: numbers of the equations describing the processes. N/A: Not applicable. The three pumps (columns) are in the same order as in Fig. 5a-c.

<table><thead><tr><th>Characteristics</th><th>Carbonate pump</th><th>Biological pump</th><th>Microbial pump</th></tr></thead><tbody><tr><td>Surface layer</td><td>CO<sub>2</sub> + H<sub>2</sub>O ⇌ H<sub>2</sub>CO<sub>3</sub> ⇌ HCO<sub>3</sub><sup>-</sup> + H<sup>+</sup> ⇌ CO<sub>3</sub><sup>2-</sup><br/>HCO<sub>3</sub><sup>-</sup> ⇌ PIC &amp; CO<sub>2</sub><br/>(6)</td><td>CO<sub>2</sub> ⇌ POC &amp; DOC<br/>(3, 4)<br/>POC &amp; DOC ⇌ CO<sub>2</sub><br/>(5)</td><td>+ H<sup>+</sup> (2)<br/>Same as the<br/>biological<br/>pump &amp; DOC ⇌<br/>DOC<sub>100</sub><br/>Microbial<br/>heterotrophs</td></tr><tr><td>Examples of<br/>organisms</td><td>Coccolithophores,<br/>foraminifers,<br/>pteropods</td><td>Cyanobacteria,<br/>diatoms,<br/>heterotrophic<br/>bacteria, copepods</td><td></td></tr><tr><td>Exported substances</td><td></td><td></td><td></td></tr><tr><td>• Gravitational</td><td>PIC (11)</td><td>POC (9)</td><td>POC (9)</td></tr><tr><td>• Migrant</td><td>PIC (11)</td><td>POC (9)</td><td>POC (9)</td></tr><tr><td>• Mixing<sup>a</sup></td><td>PIC (11)</td><td>POC &amp; DOC (10)</td><td>POC, DOC &amp;<br/>DOC<sub>100</sub> (10)</td></tr><tr><td>Water-column<br/>processes</td><td>PIC ⇌ HCO<sub>3</sub><sup>-</sup> (7)</td><td>POC ⇌ DOC ⇌ CO<sub>2</sub><br/>⇒ DIC (5, 2)<br/>POC ⇌ CO<sub>2</sub> ⇌ DIC<br/>(5, 2)<br/>DOC ⇌ CO<sub>2</sub> ⇌ DIC<br/>(5, 2)</td><td>POC ⇌ DOC ⇌<br/>DOC<sub>100</sub><br/>DOC ⇌ DOC<sub>100</sub></td></tr><tr><td>Sequestration flux</td><td></td><td></td><td></td></tr><tr><td>• Water column</td><td>DIC (22)</td><td>DIC (22)</td><td>DOC<sub>100</sub> (23)</td></tr><tr><td>• Seafloor</td><td>PIC</td><td>POC</td><td>N/A</td></tr><tr><td>Water-column<br/>sequestration<br/>inventory</td><td>DIC (24)</td><td>DIC (24)</td><td>DIC (24)</td></tr><tr><td>Upward fluxes</td><td>DIC ⇌ CO<sub>2</sub> (25)</td><td>DIC ⇌ CO<sub>2</sub> (25)</td><td>DOC<sub>100</sub> ⇌ CO<sub>2</sub><br/>(5)</td></tr><tr><td>Seafloor effluxes</td><td>CaCO<sub>3</sub> ⇌ HCO<sub>3</sub><sup>-</sup> (36)</td><td>Seafloor POC &amp;<br/>DOC ⇌ CH<sub>4</sub> ⇌ CO<sub>2</sub><br/>(34, 35)</td><td>DOC<sub>100</sub> ⇌ CO<sub>2</sub></td></tr></tbody></table>

now known for the biological pump that these fluxes can occur throughout the water column, their magnitude depending on location and depth (Sections 2.7 and 3.4). The same should be true for the carbonate-pump DIC sequestration fluxes, but this calculation does not appear to have been carried out in the literature prior to the estimate provided in Section 2.8.

The estimates of carbon sequestration fluxes (eq. (22)) can explicitly include or not the fraction of sinking PIC that does not dissolve in the water column and is buried in the sediment, whereas carbon sequestration inventories (eq. (24)) are restricted to water-column DIC. The DIC resulting from PIC dissolution that is not sequestered in the lower ocean returns relatively rapidly to the surface layer, where it may be partially or completely converted into CO₂, and this CO₂ be partially or completely degassed into the atmosphere.

The long-term fate of sedimented PIC is incorporation into calcareous deposits in the seafloor, leading to the formation of limestone and other rocks. However, during high-CO₂ periods, as is currently the case, some of the PIC sedimented on the seafloor can be transformed into water-column DIC by CO₂-enriched seawater (eq. (36)) and thus lost to very-long-term sequestration.

**Biological pump** (see also Fig. 5b). In the surface layer, phytoplankton synthesize POC and DOC (eqs. (3) and (4)), and most of this organic matter is remineralized back to CO₂ by the upper-ocean pelagic food web (eq. (5)). Photosynthetic plankton include phototrophic bacteria, cyanobacteria and diatoms (Section 2.1). The remaining organic carbon can be exported, i.e. POC by the three mechanisms (eq. (10)), and DOC by mixing (eq. (11)). In the water column below the export depth, some POC is transformed into DOC by the food web, most of the POC and DOC is remineralized back to CO₂, and some of the resulting DIC is

sequestered in the water column. As explained above for the carbonate pump, it is now known that that carbon sequestration fluxes in the form of DIC can occur throughout the water column, and not only in deep waters as previously thought. Ricour et al. (2023) applied this continuous vertical sequestration approach to the calculation of DIC sequestration fluxes by the biological pump throughout the ocean.

Estimates of carbon sequestration fluxes (eq. (22)) may or not explicitly include the small fraction of the sinking POC that is not remineralized in the water column and is buried in the sediment, whereas carbon sequestration inventories (eq. (24)) only take into account water-column DIC. Remineralized DIC resulting from organic matter remineralisation that is not sequestered in the lower ocean returns, along with the non-sequestered DIC from PIC dissolution (above), relatively rapidly to the surface layer. There, CO₂ may be partially or completely degassed into the atmosphere.

The usual long-term fate of sedimented POC is incorporation into seafloor organic matter, including fossil organic carbon. In the shorter term, some of the POC and DOC buried in the seafloor can be transformed into deposits of solid methane hydrate. Destabilization of these deposits, which depends on bottom-water temperature and hydrostatic pressure, produces CH₄ gas which is largely transformed into shorter-time water-column DIC (eqs. (34) and (35)) and is thus lost to long-term sequestration.

**Microbial pump** (see also Fig. 5c). The microbial pump focuses on the generation of DOC₁₀₀ in the surface layer and in the lower water column. In the surface layer, the formation of DOC₁₀₀ accompanies the synthesis of POC and DOC by phytoplankton (eqs. (3) and (4)) and the remineralization of this organic matter back to CO₂ (eq. (5)) described above for the biological pump. The specific mechanisms leading to the formation of DOC₁₀₀ in the surface layer and deeper remain poorly characterized, but they likely involve microbial heterotrophs (Jiao et al., 2010; Dittmar et al., 2021; Cai and Jiao, 2023; Jiao et al., 2024). The DOC₁₀₀ fraction in the surface layer is exported by the mixing mechanism (eq. (11)). In the water column below the export depth, there is additional generation of DOC₁₀₀ from POC and DOC carried downwards by the three export mechanisms. Given that the lifetime of DOC₁₀₀ exceeds t<sub>seq</sub> (i.e. 100 years), fluxes of this recalcitrant DOC fraction biochemically sequester carbon at any depth in the water column. Sequestration inventories may consider the DIC resulting from the long-term remineralization of DOC₁₀₀.

The sequestration time of DOC₁₀₀ is affected by the residence time of water at various depths. Indeed, it was explained in Section 2.6 that some DOC₁₀₀ can be photodegraded by solar UV radiation when brought close to the ocean surface, so the sequestration time of DOC₁₀₀ partly depends on the residence time of water below the surface layer. In addition, some of the DOC₁₀₀ in bottom water may be remineralized to CO₂ when this water circulates in hydrothermal systems of the ocean crust, and then transformed into shorter-time water-column DIC, i.e. lost to long-term sequestration.

## 4.2. Unifying research on the interwoven bio-pumps

The analysis of Table 2 has shown that the concepts and/or calculations concerning the bio-pumps and their carbon sequestration can be very different in the literature (Sections 2.6 and 2.7). These fundamental differences may be responsible for some of the discrepancies among published ocean carbon sequestration estimates and among the conclusions drawn from these estimates. On the one hand, the readers of publications on bio-pumps and their carbon sequestration should be aware of the different approaches used in different studies. On the other hand, it would be useful for the bio-pump research community to agree on a minimum number of common approaches for future studies.

The above analysis also showed that the bio-pumps share several characteristics, so that the three pumps are closely interwoven both in their functioning and in their carbon sequestration mechanisms. These characteristics are listed in Table 5. A key component of bio-pump

<footnote><sup>a</sup> The mixing mechanism also exports DIC as part of the physical *solubility* pump (Section 2.1).</footnote>
<table><caption>**Table 5**

Characteristics shared by two or all three bio-pumps (Table 4), showing their interweaving.</caption><thead><tr><th>Characteristics</th><th>Carbonate pump</th><th>Biological pump</th><th>Microbial pump</th></tr></thead><tbody><tr><td>Biologically-driven</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Source of carbon: DIC</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Production of DOC</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td>Three export mechanisms</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Sequestration throughout the water column</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Sequestration in the form of DIC</td><td>Yes</td><td>Yes</td><td>No</td></tr><tr><td>Sequestration fluxes into the sediment</td><td>Yes</td><td>Yes</td><td>No</td></tr><tr><td>Upward flux of DIC</td><td>Yes</td><td>Yes</td><td>No</td></tr><tr><td>Effux of CO<sub>2</sub> to the atmosphere</td><td>Yes</td><td>Yes</td><td>Yes</td></tr></tbody></table>

interweaving is that sequestration fluxes from all three bio-pumps can occur throughout the water column, albeit in different forms, i.e. DIC or DOC₁₀₀. The interweaving of the three bio-pumps is illustrated in Fig. 1, in which the carbon fluxes are represented in the form of a global jigsaw puzzle where biogenic carbon moves through the network of fluxes of the three interwoven bio-pumps and their four components.

Given the interweaving of the three bio-pumps, one might expect them to be investigated together, or at least two at a time, in theoretical studies and modelling exercises and, even more so, in the field, but this is seldom the case. On the one hand, one of the reasons why most field studies focus on a single pump, and often on only some aspects of a pump, may be the multiplicity and complexity of the processes involved in the three pumps. On the other hand, the reasons why most modelling studies do not take all three bio-pumps into account likely include the lack of field measurements of variables pertaining to the three pumps. This may also be due to the conceptual difficulty of combining processes from different disciplines, such as the various processes that govern carbon sequestration in the water column, i.e. remineralization of different forms of POC and DOC, dissolution of different forms of CaCO₃, and formation of chemically complex DOC₁₀₀. A starting point for progress towards integrating the three bio-pumps in models and in field studies could be to improve the joint theoretical treatment of the pumps, as attempted here.

A real possibility for integrated field investigations of the bio-pumps arises from the rapidly expanding deployment at sea of biogeochemical Argo floats (BGC-Argo) and other autonomous platforms equipped with biogeochemical sensors (e.g. gliders and saildrones). The sensors already carried by such platforms provide data on carbon fluxes driven by different export mechanisms of the biological pump (Claustre et al., 2021; Henson et al., 2022). In addition, a miniaturized PIC sensor deployed on autonomous platforms (Neukermans et al., 2023) could be used to estimate carbonate-pump variables at the same time as biological-pump variables. Also, sensors measuring fluorescence emission at different wavelengths could distinguish between different types of DOC (e.g. “protein-like” and “humic-like” components), which could be used to quantify microbial-pump characteristics (Xiao et al., 2023). The combined deployment on autonomous platforms of sensors measuring variables pertaining to the three bio-pumps could make it possible to acquire at sea the data needed to implement the concept of interwoven bio-pumps illustrated in the form of a jigsaw puzzle in Fig. 1.

Despite advances in BGC-measurements at sea and associated numerical models, it is likely that most future bio-pump studies will continue to target a single pump, or even a single component of a pump. One typical example of the latter is the export of organic carbon in the biological pump, which is a popular topic in the literature. However, these studies could now be carried out in the context of the three interwoven bio-pumps, where each study would be seen as a piece of the global jigsaw puzzle (Fig. 1). Explicitly linking each study to the whole

picture would enhance its scientific relevance, which would be a step towards unifying research on the interwoven bio-pumps.

Understanding the functioning of the bio-pumps and their contributions to carbon sequestration in the ocean is of fundamental interest for marine carbon biogeochemistry. This understanding is also important from a practical point of view, for predicting changes in ocean carbon and sequestration fluxes in the context of the globally changing environment and also their ecological effects (e.g. ocean deoxygenation, Section 2.4). Furthermore, this understanding could become crucially needed if (or when) mCDR schemes currently under consideration are deployed in the ocean. Indeed, some of the mCDRs planned for offshore waters would be large-scale manipulations of bio-pumps, e.g. to enhance the biological pump (nutrient fertilization), and all mCDR deployments could have unexpected side-effects on ecosystems in the affected ocean areas (NASEM, 2022; Boyd et al., 2023). Hence the high relevance of conducting studies on bio-pumps and their carbon sequestration processes in an integrated manner.

## Credit authorship contribution statement

**Louis Legendre:** Writing – original draft, Formal analysis, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data availability

No data was used for the research described in the article.

The data used to draft Figs. 6 and 8 are publicly available at https://zenodo.org/records/13142409

## Acknowledgements

I thank Philip Boyd, Hervé Claustre, Jean-Pierre Gattuso, Emanuele Organelli, Lars Stemmann and Douglas Wallace for suggestions on topics discussed in this study and/or for comments on drafts of the manuscript. I also thank Florian Ricour for providing the f₁₀₀ data used in Table 3.

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