# Inorganic carbon dynamics and their relation to autotrophic community regime shift over three decades in a large, alkaline river

Jacob S Diamond, An Nguyen Truong, Gwenaël Abril, Enrico Bertuzzo, Vincent Chanudet, Raphael Lamouroux, Florentina Moatar

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Jacob S Diamond, An Nguyen Truong, Gwenaël Abril, Enrico Bertuzzo, Vincent Chanudet, et al. "Inorganic carbon dynamics and their relation to autotrophic community regime shift over three decades in a large, alkaline river." Limnology and Oceanography, 2025, 10.1002/lno.70016. hal-05101281

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Distributed under a Creative Commons Attribution 4.0 International License
LIMNOLOGY
and
OCEANOGRAPHY

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Limnol. Oceanogr. 70, 2025, 1122–1136
© 2025 The Author(s). Limnology and Oceanography published by Wiley Periodicals LLC
on behalf of Association for the Sciences of Limnology and Oceanography.
doi: 10.1002/ino.70016

RESEARCH ARTICLE

# Inorganic carbon dynamics and their relation to autotrophic community regime shift over three decades in a large, alkaline river

Jacob S. Diamond ID,¹,²* An Nguyen Truong ID,¹ Gwenaël Abril ID,³,⁴ Enrico Bertuzzo ID,²
Vincent Chanudet ID,⁵ Raphael Lamouroux ID,⁶ Florentina Moatar ID¹

¹RiverLy, INRAE, Centre de Lyon-Grenoble Auvergne-Rhône-Alpes, Lyon, France; ²Department of Environmental Sciences, Informatics and Statistics, University of Venice Ca' Foscari, Venice, Italy; ³Laboratoire de Biologie des Organismes et Ecosystèmes Aquatiques (BOREA), UMR 8067, Muséum National d'Histoire Naturelle, CNRS, IRD, SU, UCN, UA, Paris, France; ⁴Programa de Geoquímica, Universidade Federal Fluminense, Niterói, Rio de Janeiro, Brazil; ⁵EDF HYDRO, Centre d'Ingénierie Hydraulique, Savoie Technolac, Le Bourget-du-Lac, France; ⁶EDF Recherche et Développement, Laboratoire National d'Hydraulique et Environnement, Chatou, France

## Abstract

How much of the excess CO₂ in running waters comes from in-stream respiration of organic carbon? To answer this, we developed a 30-yr metabolism-carbonate system database at an hourly resolution for the Loire River, France, a large, alkaline river. We asked the following questions: what are the intra-annual patterns of in-stream (“internal”) CO₂ production, what processes drive these patterns, and how do these patterns depend on autotrophic community composition? We estimated internal CO₂ production as the ratio of net ecosystem production to CO₂ water-to-air flux (FCO₂). We also estimated the daily ecosystem quotient (EQ, O₂ released: dissolved inorganic carbon [DIC] consumed) and the prevalence of non-CO₂ autotrophic DIC uptake pathways under CO₂ depletion. Median internal CO₂ production was 49% of FCO₂ in the Loire from 1990 to 2022. The river predictably shifted from a heterotrophic, CO₂ source to an autotrophic, CO₂ sink as a function of discharge, leading to four trophic-flux (“trophlux”) states: autotrophic-sink, autotrophic-source, heterotrophic-sink, and heterotrophic-source. During autotrophic states (41% of the time), CO₂ depletion (FCO₂ ≤ 0, median pCO₂ = 135 µatm) led to the use of HCO₃⁻ and of CO₂ released by CaCO₃ precipitation as alternative DIC sources to autotrophs to support their high rates of primary production (occurring on average for 33% of the growing season). Finally, during a period of phytoplankton dominance, the median EQ was 1.3, which was reduced to 1.0 under macrophyte dominance. This work describes a dynamic coupling among autotrophic communities, calcium carbonate equilibria, and discharge-controlled FCO₂ that together imply lower-than-predicted FCO₂ magnitude and greater-than-predicted internal CO₂ production for the Loire River.

Closing the freshwater carbon budget remains an important goal in the context of global change. Budget closure reduces uncertainty in the amount of carbon leaked from terrestrial systems to inland waters (Battin et al. 2023) and thus constrains estimates of terrestrial net productivity (Turner et al. 2013). A large uncertainty in the budget is the origin of excess CO₂ in running waters (Duvert et al. 2018). This uncertainty is made critical as streams and rivers are the dominant source of CO₂ to the atmosphere among freshwater systems (Regnier et al. 2013; Drake et al. 2018). Excess riverine CO₂ is sourced from two carbon forms delivered by lateral transport from the terrestrial landscape and floodplains (Abril and Borges 2019). The first is dissolved inorganic carbon (DIC = CO₂ + HCO₃⁻ + CO₂²⁻) derived from soil

<footnote>*Correspondence: j.diamond@unesco.org</footnote>

<footnote>This is an open access article under the terms of the [Creative Commons Attribution License](https://creativecommons.org/licenses/by/4.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited.</footnote>

<footnote>Associate editor: Robert Hall Jr.</footnote>

<footnote>**Data Availability Statement:** Raw data must be requested by the authors as they are proprietary from the Electricité de France, but some analyzed data (e.g., metabolism estimates) are already available (http://www.hydroshare.org/resource/b1547a02846b4a88a8273aa229454eb0), and code is presented to replicate all analyses (https://github.com/jakediamond/MetaCalc/).</footnote>
respiration or mineral weathering (Johnson et al. 2006). The second form is organic carbon that is respired to CO₂ in-stream (Cole and Caraco 2001). The latter is often indirectly estimated using stream net ecosystem production (NEP = GPP - ER, the balance between gross primary production [GPP] and ecosystem respiration [ER]). A negative NEP indicates in-stream respiration of organic carbon that was not produced locally—the subsequent CO₂ release is referred to as “internal production” (Battin et al. 2008; Hotchkiss et al. 2015). Despite previous efforts, this internal CO₂ production remains a poorly constrained link in our understanding of carbon cycling in running waters.

The implicit, and well-documented, assumption of using NEP to estimate the terrestrial organic matter input to running waters is that most rivers are heterotrophic (NEP < 0) (Bernhardt et al. 2022). Under heterotrophic conditions, –NEP is a fraction of the total CO₂ emitted (FCO₂), and this fraction defines the internal CO₂ production (and by difference the terrestrial CO₂ inputs). Moreover, it is generally expected, though relatively untested, that the –NEP : FCO₂ fraction increases with river size, and that the majority of CO₂ comes from internal production in large rivers (> 100 m³ s⁻¹) (Hotchkiss et al. 2015). Complicating this accounting is the fact that large rivers can be autotrophic (NEP > 0; Lynch et al. 2010; Aho et al. 2021), yielding negative internal production. Furthermore, most conceptual models and estimates of internal CO₂ production are biased toward growing season conditions, and there is a paucity of interannual deployments (but see Marescaux et al. 2018; Haque et al. 2022). There is thus a clear need for studies of inter- and intra-annual internal production, particularly in large rivers exhibiting autotrophy (Lynch et al. 2010; Hotchkiss et al. 2015).

Importantly, aquatic NEP is almost always estimated from O₂ measurements, which are transformed into estimates of C or CO₂ using the 1 : 1 stoichiometry of glucose photosynthesis and respiration. The true O₂ : CO₂ stoichiometries of photosynthesis and respiration can vary widely, however (e.g., 0.5–3.5, Williams and Robertson 1991), though they are regularly assumed to be 1–1.2 (Aho et al. 2021; Kirk and Cohen 2023). The ratio of mol O₂ produced to mol CO₂ consumed is referred to as the photosynthetic quotient (PQ), and its inverse analogue (mol CO₂ produced to mol O₂ consumed) as the respiratory quotient (RQ). Both can vary, among other controls, according to organismal stoichiometry, nitrogen and light availability, pH, and O₂ and CO₂ concentrations (Kliphuis et al. 2011; Sand-Jensen et al. 2018). Specifically, PQ decreases proportionally with increasing C : N of autotrophic biomass (Raine 1983) and further decreases from photorespiration under high O₂, low CO₂ (see Trentman et al. 2023 for a full discussion). Likewise, RQ appears to decrease under high O₂ conditions and with abundant planktonic algae (Berggren et al. 2012). Practically, it is difficult to separately estimate PQ and RQ in river metabolism studies, and it is more convenient to consider their joint effect—and the effect of unmeasured processes (Pathak et al. 2022)—in an ecosystem quotient (EQ: apparent mol O₂ produced to mol DIC consumed by all ecosystem processes; cf. Vachon et al. 2020). Changing EQ

under dynamic organismal stoichiometry may occur regularly in large rivers, with measurable yet hitherto undiscussed implications for internal CO₂ production.

Less still is known regarding the influence of community effects on metabolism and its subsequent control on CO₂. For example, the well-observed stable states of phytoplankton or macrophyte dominance in lakes (Capon et al. 2015), and recently in rivers (Ibáñez et al. 2022) have unique ecosystem metabolism signals (e.g., mode, magnitude, and timing; Carpenter and Lodge 1986; Lynch et al. 2010; Diamond et al. 2021) and differing autotrophic stoichiometry. Moreover, at high rates of primary production, CO₂ may become depleted. Under low CO₂ conditions, aquatic autotrophs may utilize CO₂-concentrating mechanisms (CCMs) based on the active uptake of HCO₃⁻ as their DIC source (Maberly and Madsen 1998; Giordano et al. 2005; Morales-Williams et al. 2017). Indeed, most phytoplankton and half of all studied freshwater macrophyte species use CCM, and the evidence is clear that HCO₃⁻ uptake supports photosynthesis even at zero CO₂ (Maberly and Gontero 2017). Thus, riverine autotrophic community composition controls DIC levels through primary production but is also selected for based on its adaptation to DIC supply. However, the extent to which autotrophic community structure may influence both internal CO₂ production and CO₂ consumption has not yet been quantified.

Finally, in rivers with total alkalinity (A_T) greater than ca. 1 mmol L⁻¹, there is a potential for calcite (CaCO₃) precipitation (McConnaughey and Whelan 1997), and its subsequent sediment storage, transport as particulate inorganic carbon, or dissolution. Calcification—CaCO₃ precipitation accompanied by CO₂ release—is an autotrophic strategy to meet inorganic carbon demands for photosynthesis (Rupp and Adams 1981), a phenomenon well studied in lakes (McConnaughey et al. 1994; Sand-Jensen et al. 2018; Andersen et al. 2019). Indeed, CO₂ generated by calcification can support up to half of lake GPP (McConnaughey et al. 1994). Hence, calcification is an internal production of CO₂ that is ultimately derived from external DIC, not organic carbon, complicating carbon accounting in alkaline rivers. As the majority (ca. 60%) of riv-ers with Strahler order > 3 are alkaline (Hartmann et al. 2014), calcification may be an important yet understudied aspect of internal CO₂ production in running waters.

Here, we develop a 30-yr hydrochemistry dataset in a large, alkaline river to address the questions: what are the intra-annual patterns of internal CO₂ production, what processes drive these patterns, and how do these patterns depend on autotrophic community composition (phytoplankton vs. macrophytes)? We hypothesized (H1) that extended periods of net autotrophy (i.e., negative internal production of CO₂) would deplete CO₂ and lead to regular CO₂ sink behavior for the river. Based on this hypothesis, we predicted (P1.1) that CO₂ depletion would instigate autotrophs to remove HCO₃⁻ from the water column as a DIC source, leading to continued GPP despite near-zero CO₂. We likewise predicted (P1.2) that biologically induced CaCO₃
precipitation would arise during these CO₂-depleted periods to support GPP. Finally, we hypothesized (H2) that a measured shift from a planktonic, algal to a benthic, macrophytic auto-troph community would lead to systematic reductions in EQ, internal CO₂ production, and non-CO₂-supported photosynthesis. We predicted (P2) that planktonic regime EQ would be 1.2 (Ryther 1956; Raine 1983), but that benthic regime EQ would be reduced by ca. 0.2 due to the doubled biomass C:N ratio of macrophytes relative to phytoplankton (Williams and Raine 1979).

# Methods

## Study site

The ca. 10-km study reach is located on the Loire River, France (47.6°N, 2.6°E), with a catchment area of 35,500 km², a mean discharge of 300 m³ s⁻¹ (median = 200 m³ s⁻¹), a mean width of 250 m, and a mean depth of 1.3 m. Calcareous bedrock (Baratelli et al. 2016) leads to high A_T (1770 µmol L⁻¹) and calcium (Ca²⁺ = 780 µmol L⁻¹) (Grosbois et al. 2000, 2001). As a result, seasonal calcite precipitation comprised up to 80% of the suspended particulate matter mass before ca. 2005 (Néglér and Grosbois 1999; Néglér et al. 2000). Since 2005, the river has undergone re-oligotrophication (sensu Ibáñez et al. 2022), which is well described in the literature (Floury et al. 2013; Minaudo et al. 2015). Prior to 2005, the autotrophic community was planktonic (i.e., dominated by phytoplankton) whereas after 2005 it has been predominantly benthic (i.e., dominated by rooted macrophytes), leading to reductions in O₂-based GPP and ER magnitudes and their weaker temporal coupling (Diamond et al. 2021). We refer to these differing periods of autotrophic community dominance as the planktonic (1990–2004) and benthic regimes (2005–2022).

## Data acquisition and processing

We obtained hourly dissolved oxygen (mg O₂ L⁻¹), water temperature (°C), specific conductance at 25°C (C₂₅; µS cm⁻¹), and pH data (Supporting Information Fig. S1) for 1990–2022 from a regulatory dataset maintained and collected by Électricité de France and partly described by Diamond et al. (2021). Additional specifics on data cleaning and processing of O₂, pH, and C₂₅ are detailed in the Supporting Information.

From June 29, 2007 to April 25, 2022, A_T and Ca²⁺ concentrations were provided by Électricité de France at varying frequencies (from 2 to 8 d) and we supplemented these with nearby monthly grab samples from a French database (http://www.naiades.eaufrance.fr/) and the Loire-Brittany Water Agency. We estimated daily Ca²⁺ with a random forest model (root mean square error [RMSE] = 70 µmol L⁻¹; Supporting Information), and we subsequently estimated hourly A_T from hourly C₂₅, and daily mean Ca²⁺, discharge, and temperature with multiple regression (R²ₐ₉₆ = 0.80; RMSE = 133 µmol L⁻¹; Supporting Information Table S1). Daily mean discharge was obtained from HydroPortail (https://hydro.eaufrance.fr;

site = K4180010). Daily mean depth (z) was calculated as the mean of four modeled rating curves (Camenen et al. 2016) for four equally spaced locations in the 10 km upstream of the sampling site (approximately equal to the O₂ integration length; Diamond et al. 2021).

## Data analysis

### Metabolism

An existing river metabolism model (Diamond et al. 2021) based on measured O₂, temperature, solar radiation, and discharge was used to estimate daily mean GPP, ER, and NEP (mmol O₂ m⁻² d⁻¹) in addition to the gas exchange coefficient, K₆₀₀ (d⁻¹; Supporting Information Fig. S2). Hourly NEP (NEPₜₚ) was estimated according to the O₂ balance (Hall and Hotchkiss 2017). We summed daily mean NEP to get estimates of annual NEP, where annual refers to the water year (September–August). By convention, NEP is positive (GPP > ER) when DIC is removed from the water column to build biomass, and NEP is negative (ER > GPP) when organic carbon is respired into the water column as CO₂. With no prior evidence for PQ and RQ, we assumed a 1:1 correspondence between O₂ and CO₂ for metabolism. Additional details on metabolism models are available in the Supporting Information.

### Carbonate equilibria and trophlux states

We calculated the hourly carbonate system equilibrium from pH and A_T while accounting for temperature-dependent and ionic strength-dependent activity effects (see Supporting Information Fig. S3). Code is provided to calculate the system (Diamond 2024). To improve the interpretation of stoichiometric relations between CO₂ and O₂, we expressed their concentrations as molar excesses relative to atmospheric equilibrium as exCO₂ = CO₂ – CO₂,atm and exO₂ = O₂ – O₂,atm (µmol L⁻¹). We also defined the excess DIC relative to atmospheric equilibrium at the measured A_T and atmospheric pCO₂, exDIC = DIC – DICₐ₉₆ (Stets et al. 2017). This metric was useful to partition the varying trophic (autotrophic vs. heterotrophic) and air-water CO₂ flux (source vs. sink) states. We grouped these two state types together and refer to their four products as “trophlux” states, that is, autotrophic sink, autotrophic source, heterotrophic sink, and heterotrophic source.

### Air-water CO₂ flux and internal CO₂ production

Fluxes of CO₂ between atmosphere and water (FCO₂ [mmol m⁻² d⁻¹]) were calculated with Fick's Law, using the gas transfer velocity of CO₂ (kCO₂ [m d⁻¹]) and deviation from atmospheric equilibrium (see Supporting Information for details, Fig. S4). By convention, FCO₂ is positive when CO₂ is emitted from the river to the atmosphere (i.e., the river is a net source of CO₂), and FCO₂ is negative when there is an influx of CO₂ to the river from the atmosphere (i.e., the river is a net sink of CO₂). We used the median as the measure of the central tendency for FCO₂ (see Supporting Information Fig. S5; Table S2).
We estimated internal CO₂ production as –NEP : FCO₂. A negative NEP is used to align the direction of these carbon fluxes as they are in opposite directions by convention. For all analyses, we used R (R Core Team 2023). Where appropriate for visual aid, we used a generalized additive model with a cubic spline smoother (R package mgcv, Wood 2011; function gam() with y ~ s[x]).

## Calcite precipitation and dissolution

Calcification, in general, produces 1 mol of CO₂ and removes 2 mol of A_T per mole of CaCO₃ formed, leading to a net removal of 1 mol of DIC (Eq. 1; Kₛₚ is the calcite solubility product constant) (Wolf-Gladrow et al. 2007). However, when calcification is biologically mediated and CO₂ is used for photosynthesis (Eq. 2), there is a net removal of 2 mol of DIC.

$$Ca^{2+} + 2HCO_3^- \underset{K_{sp}}{\overset{K_{sp}}{\rightleftharpoons}} CaCO_{3(s)} + CO_2 + H_2O \quad (1)$$

$$Ca^{2+} + 2HCO_3^- \xrightarrow{\text{energy}} CaCO_{3(s)} + CH_2O + O_2 \quad (2)$$

Under biologically mediated calcification (Eq. 2), there is a 1 : 1 correspondence of photosynthesis and calcification (McConnaughey and Whelan 1997), but a 1 : 2 molar ratio of O₂ to DIC. To estimate calcification and dissolution rates on a benthic area basis (Qₐₗc; mmol m⁻² h⁻¹), we follow work from lake studies that used half the hourly A_T rate of change (Qₐₗc = -0.5 dA_T/dt) (Andersen et al. 2019; Escoffier et al. 2023), following the stoichiometry of Eq. 2. We further calculated the calcite saturation index (SI, [-]) to evaluate the potential for CaCO₃ precipitation (Plummer and Busenberg 1982). If |SI| > 0.4, we assumed precipitation or dissolution was possible (Escoffier et al. 2023).

## Primary autotrophic C uptake pathway

To differentiate CO₂ uptake from HCO₃⁻ uptake or biologically induced CaCO₃ precipitation for photosynthesis, we used a simple decision tree approach (cf. Perolo et al. 2023). To be conservative, we calculated the possibility of non-CO₂ autotrophic DIC uptake when hourly GPP was twice the available CO₂ (=CO₂ - ER/z dt - FCO₂/z dt; dt = 1 h; note sign conventions) for at least half the photoperiod. These conditions ensured at least 50% of the required CO₂ for photosynthesis was unavailable. We thus use the word “primary” to imply confidence that a particular pathway (i.e., CO₂ uptake, HCO₃⁻ uptake, or CaCO₃ precipitation) supplied greater than 50% of DIC for photosynthesis. If CO₂ limiting conditions were not met, we assumed CO₂ as the primary autotrophic uptake pathway. If CO₂ limiting conditions were met, we inferred either primary HCO₃⁻ uptake or primary CaCO₃ precipitation. We used a criterion, described below, based on changes in C₂₅ to determine if CaCO₃ precipitation was the primary DIC pathway; if this criterion was not met, we assumed primary HCO₃⁻ uptake.

Specific conductance (C₂₅) is predominantly determined by HCO₃⁻ and Ca²⁺ in the Loire (Supporting Information

Table S3; Figs. S6, S7), and thus C₂₅ is strongly linked to processes controlling CaCO₃ precipitation and dissolution (see Supporting Information). Critically, diel C₂₅ oscillations in the Loire only emerge under high GPP, strongly implying their link to biologic CaCO₃ precipitation. Diel C₂₅ patterns may also be controlled by diel discharge and groundwater A_T contributions (Wilcock and Chapra 2005), but these do not appear to be the most plausible explanations in the Loire (Supporting Information Figs. S8, S9). We thus modeled how hourly changes in C₂₅ (ΔC₂₅) vary according to hourly NEP under different CaCO₃ precipitation scenarios (Supporting Information Figs. S10, S11). A simple and robust metric emerged that could differentiate varying contributions of biologic CaCO₃ precipitation to GPP: the slope of hourly ΔC₂₅ – NEP (βₐₗNEP). A βₐₗNEP ≤ -0.1 implies that at least 50% of GPP is supported by biologic CaCO₃ precipitation. We therefore used βₐₗNEP ≤ -0.1 (p < 0.01) as our criterion to determine CaCO₃ as a primary pathway for autotrophic DIC. We report the primary DIC pathway as its growing season (April 1 to September 31) occurrence frequency.

## Ecosystem quotient

We use the slope of exO₂ vs. DIC (βₐₗDIC) to evaluate daily EQ. For example, a βₐₗDIC = -1.2 suggests that 1.2 mol of O₂ is released per mole of DIC uptake on average, and EQ = 1.2. We estimated EQ for each day (n = 24 hourly points) with βₐₗDIC (n = 11,820 d). To avoid periods without clear diel signals in both exO₂ and DIC (e.g., high discharge when rapid gas exchange occludes biologic signals), we only examined days with robust βₐₗDIC (p < 0.05 and R² > 0.66; n = 7214 d). We relied on this large dataset to develop well-populated distributions of EQ from βₐₗDIC and we interpret the median βₐₗDIC as the typical EQ of the system.

## Results

### Regular, but small negative internal CO₂ production

There was clear support for the hypothesis (H1) that extended autotrophic periods (NEP > 0) resulted in negative internal CO₂ production (–FCO₂) in the Loire River (Fig. 1a). Indeed, from 1990 to 2022, the river was a CO₂ sink 27% of the time based on hourly data with median CO₂ = 48 µmol L⁻¹ (pCO₂ = 915 µatm; Supporting Information Table S2).

Internal CO₂ production, FCO₂, and NEP varied widely over time in the Loire River. Median daily FCO₂ was 91 mmol C m⁻² d⁻¹ (interquartile range = 6.6–262 mmol m⁻² d⁻¹) and median daily NEP was -29 mmol C m⁻² d⁻¹ (-130–53 mmol C m⁻² d⁻¹). Median daily internal CO₂ production was 49% (24–90%) for heterotrophic-source states. Across all trophlux states, median daily internal CO₂ production was 42% (0.21–130%). At the annual scale, internal production ranged from 1.5% in 2006 (NEP = -1.4 mol C m⁻² yr⁻¹; FCO₂ = 91 mol m⁻² yr⁻¹) to 74% in 2016 (NEP = -35 mol C m⁻² yr⁻¹; FCO₂ = 48 mol m⁻² yr⁻¹). There were also 8 yr with
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Trophic-flux (trophlux) states and internal CO₂ production in the middle Loire from 1990 to 2022. (a) All daily estimates of net ecosystem production (NEP) and CO₂ water-to-air flux (FCO₂). The four quadrants of this space partition the trophlux states. The contours indicate the percentage of data contained within them. (b) Daily fluxes of carbon as a function of discharge with smoothed generalized-additive models shown for visual aide. Net ecosystem production (NEP) is converted from O₂ units to C on a 1 : 1 basis. (c) Daily evolution of trophlux state occurrence probabilities across the water year (September–August), where colors of stacked bars refer to trophlux states as defined in (a, d). The mean pattern of annual discharge (without units) is shown as a dark blue line for visual reference. (d) Mean annual (water year) contribution of trophlux states to atmospheric CO₂ flux according to log₁₀ discharge bins. Dashed vertical line indicates overall mean discharge from 1990 to 2022.</figcaption></figure>

positive annual NEP ranging from 1.4 ± 1 mol C m⁻² yr⁻¹ in 1993 (mean ± SD) to 21 ± 0.86 mol m⁻² yr⁻¹ in 1995. Thus, for 24% of yearly estimates, the total annual NEP was in the opposite direction to FCO₂, and both fluxes cumulatively removed CO₂ from the river (into biomass and atmosphere, respectively). In these years, there was an annual net negative internal production of CO₂.

Negative internal production was small in magnitude relative to overall FCO₂, which was largely controlled by discharge (Fig. 1b,c). Discharge explained 45% of the variation in FCO₂ and 33% of the variation in NEP (Fig. 1b). By contrast, NEP

explained 28% of the variation in FCO₂ (Fig. 1a). Most (75%) FCO₂ occurred at discharges greater than the mean (300 m³ s⁻¹) and 90% of FCO₂ occurred at discharges greater than the median (200 m³ s⁻¹). Nearly all negative FCO₂ occurred at discharges less than the mean (Fig. 1d). On average, 80% of annual FCO₂ occurred in the 5–10% of the water year that delivers 70% of the discharge; this majority of FCO₂ was emitted from the river by April 7 each water year. Above mean discharge (35% of time), heterotrophic states dominated (70% of time), contributing 80% of cumulative annual FCO₂ (~40 mol C m⁻² yr⁻¹).
## Trophlux state timing and characteristics

The middle Loire River predictably shifted between trophic (autotrophic and heterotrophic) and $FCO_2$ states (source and sink), or trophlux states (Fig. 1c). Hence, the river could be in one of four trophlux states, with each trophlux state exhibiting a typical annual occurrence and contribution to the river's atmospheric carbon emissions (Fig. 1c,d; Table 1).

Nearly all positive $FCO_2$ occurred during the heterotrophic-source state, predominately in winter (Fig. 1c; Supporting Information Fig. S1). During winter, NEP was a minor component of $FCO_2$, but its contribution was 50% greater in the benthic (56%) compared to the planktonic regime (36%; Table 1). We attribute this difference to a decrease in external $CO_2$ inputs as evidenced by increasing winter pH over time (Supporting Information Fig. S1; A.T. Nguyen et al. unpubl.). During the three other trophlux states, NEP magnitude was 1.2–10 times greater than $FCO_2$ and was frequently in the opposite direction (as indicated by a negative value for –NEP : $FCO_2$). The opposite direction of –NEP and $FCO_2$ occurs during the “autotrophic source” and “heterotrophic sink” trophlux states.

Of the heterotrophic-sink events, 76% were preceded by the autotrophic-sink state, indicating that these were temporary events (lasting an average of $4.7 \pm 4.1$ d) as the river shifted from autotrophic-sink to autotrophic-source states (50% of time) or from autotrophic-sink states to heterotrophic-source states (50% of time).

Each trophlux state exhibited distinct diel biogeochemical signals. The signatures of the autotrophic-sink (black in Fig. 2) were large amplitudes for $exO_2$ (Fig. 2a), $C_{25}$ (Fig. 2b), and pH (Fig. 2c), with $C_{25}$ anti-phase with $exO_2$ and pH. The mean diel range of $C_{25}$ was $15 \mu S \text{ cm}^{-1}$ (ca. 6% daily change) in the autotrophic-sink state and was greatest ($21.3 \mu S \text{ cm}^{-1}$, ca. 9% daily change) in the benthic regime (Supporting Information Fig. S9).

Supporting our prediction (P1.1), there were clear signals of continued DIC drawdown in the absence of $CO_2$. Indeed, in all trophlux states except the heterotrophic-source, $CO_2$ could

become depleted, yet DIC uptake supported continued photosynthesis (Fig. 3d,e,g from 12 : 00 to 18 : 00). Autotrophic-sink states exhibited the strongest evidence of $CO_2$ depletion, but autotrophic-source states (gold in Fig. 2) could also exhibit depletion, though their pH was typically an entire unit lower than autotrophic-sinks (Fig. 2c), and $exCO_2$ was consistently positive and greater in amplitude (Fig. 2d).

There was clear support for our prediction that $CO_2$ depletion would instigate $CaCO_3$ precipitation (P1.2; Fig. 2f,i). Elevated saturation index values indicative of conditions suitable for $CaCO_3$ precipitation were evident in all trophlux states except heterotrophic-source. $CaCO_3$ precipitation rates were greatest in the autotrophic-sink state, with typical peak hourly fluxes ranging from 1 to $5 \text{ mmol m}^{-2} \text{ h}^{-1}$ (Fig. 2i), approximately 5–10% of maximal hourly GPP.

## Strong evidence of continued photosynthesis in $CO_2$-depleted conditions

In further support of our hypothesis (H1), $CO_2$ was regularly depleted relative to autotrophic demand in the Loire River. For 1937 d (33%) of the growing seasons from 1990 to 2022, hourly GPP was more than twice the available $CO_2$ for at least half of the photoperiod. During these $CO_2$-depleted days (Fig. 3a), we estimated that $HCO_3^-$ was the primary uptake pathway 34% of the time and $CaCO_3$ 2.2% of the time. Hence, $CO_2$ was not the primary source of photosynthesis in approximately 2 months out of each year.

In line with predictions, regular $HCO_3^-$ uptake (P1.1) and $CaCO_3$ precipitation (P1.2) comprised sizeable fractions of DIC sources to autotrophs as $CO_2$ became depleted. Based on our theoretical framework (Fig. 3b; Supporting Information Figs. S10, S11), we estimate that calcification as a primary pathway was uncommon regardless of regime or year, often relegated to a few days per year (1–5% of the growing season; Fig. 3d). However, as indicated by $\beta_{NEP}$, calcification may be commonplace (Fig. 3b,c). We estimate that calcification

<table><caption>**Table 1.** Summary of occurrence frequency of trophlux states according to the autotrophic regime, their contribution to total $FCO_2$, their median daily NEP, $FCO_2$, and that median ratio.</caption><thead><tr><th>Autotrophic regime</th><th>Trophic state</th><th>FCO<sub>2</sub> state</th><th>Freq. (%)</th><th>FCO<sub>2</sub> (%)</th><th>NEP* (mmol m<sup>-2</sup> d<sup>-1</sup>)</th><th>FCO<sub>2</sub><sup>†</sup> (mmol m<sup>-2</sup> d<sup>-1</sup>)</th><th>-NEP : FCO<sub>2</sub><sup>‡</sup></th></tr></thead><tbody><tr><td rowspan="4">Planktonic (1990–2004)</td><td rowspan="2">Autotrophic</td><td>Source</td><td>19</td><td>9.7</td><td>37</td><td>45</td><td>-1.1</td></tr><tr><td>Sink</td><td>29</td><td>-2.6</td><td>140</td><td>-19</td><td>7.4</td></tr><tr><td rowspan="2">Heterotrophic</td><td>Source</td><td>47</td><td>93</td><td>-120</td><td>290</td><td>0.36</td></tr><tr><td>Sink</td><td>5</td><td>-0.35</td><td>-37</td><td>-17</td><td>-2.3</td></tr><tr><td rowspan="4">Benthic (2005–2022)</td><td rowspan="2">Autotrophic</td><td>Source</td><td>24</td><td>7.5</td><td>51</td><td>37</td><td>-1.4</td></tr><tr><td>Sink</td><td>10</td><td>-0.56</td><td>110</td><td>-9.9</td><td>11</td></tr><tr><td rowspan="2">Heterotrophic</td><td>Source</td><td>65</td><td>93</td><td>-110</td><td>190</td><td>0.56</td></tr><tr><td>Sink</td><td>1</td><td>-0.14</td><td>-75</td><td>-13</td><td>-4.6</td></tr></tbody></table>

$FCO_2$, $CO_2$ water-to-air flux; NEP, net ecosystem production.

*Net ecosystem productivity from the river perspective, calculated with [O<sub>2</sub>] data.

†Flux of $CO_2$ from the river to the atmosphere.

‡–NEP is used to align with atmospheric perspective.
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Diel signals of calcium-carbonate system variables for the four trophic-flux (trophlux) states. All variables show mean behavior (1990–2022) as the central line with uncertainty shading depending on the variable type. (a–c) Measured variables: uncertainty shows 25–75% distribution; (d–f) calculated variables based on carbonate equilibria; uncertainty shows ± standard error; (g–i) calculated fluxes; uncertainty shows ± standard error. For calculated variables (d–i), standard errors are derived using Gaussian propagation of uncertainty throughout all calculation steps.</figcaption></figure>

supported at least 25% of GPP for 14% of the growing season from 1993 to 2022 (Fig. 3b, central light blue band).

There was clear support for our hypothesis (H2) of a systematic reduction in non-CO₂ supported photosynthesis under the benthic autotrophic regime. When comparing across water years, primary CO₂ uptake was 60% less common in the planktonic (45% ± 11%, mean ± SD) compared to the benthic regime (74% ± 20%) (Fig. 3d). Likewise, primary HCO₃⁻ uptake was 60% more common in the planktonic (53% ± 12%) compared to the benthic regime (20% ± 15%). Primary DIC uptake varied considerably across years, and HCO₃⁻ as a dominant DIC source ranged from 2% in 2007 (median Q=246 m³ s⁻¹ and median pCO₂=2300 µatm) to 76% in 1997 (median Q=92 m³ s⁻¹ and median pCO₂=120 µatm).

### Ecosystem quotients decrease under a shift from phytoplankton to macrophytes

Hourly data tended to follow the -1 : 1 line expected of EQ = 1 in exO₂ – exDIC space (Fig. 4a). This alignment with EQ = 1 was not observed in exO₂ – exCO₂ space (Fig. 4a, inset; Supporting Information Fig. S12), which exhibited a hockey-stick shape at the equilibrium limits for CO₂ at a given temperature and A_T.

Supporting our hypothesis (H2), there was a clear distinction in EQ (as evidenced by daily exO₂ – DIC slopes, β_DIC) between the two autotrophic regimes, with the planktonic regime exhibiting a far greater range of slopes than the benthic regime (Fig. 4b). The median β_DIC in the planktonic regime was -1.3, whereas it was -1.0 in the benthic regime, implying a difference in EQ of 0.3, close to predictions
<figure><img src="image_5.png" /></figure>

**Fig. 3.** Evidence of alternative CO₂ pathways as the primary autotrophic dissolved inorganic carbon (DIC) source. (a) Six randomly chosen examples (three from each autotrophic regime) where CO₂ became depleted during a day. Each curve shows the available CO₂ (CO₂ – ERhr – FCO₂) over time, colored according its value relative to hourly gross primary production (GPP) (white indicates GPPhr is twice CO₂avail). (b) Six examples of hourly differences in C₂₅ (ΔC₂₅) vs. hourly Net ecosystem production (NEP) from the same dates as in (a); end points in (a) match colors here. Three ΔC₂₅ – NEP curves with slopes representative of predicted CaCO₃ precipitation as 25–50% of GPP (light blue; theoretical slope, βNEP = -0.04) and three curves with slopes indicative of CaCO₃ with supplying at least 50% of GPP (dark blue; βNEP ≤ -0.1). (c) Smoothed daily median βNEP with 25–75% interquartile range bands (gray) over the year. Theoretical slopes for varying CaCO₃ precipitation contribution to GPP shown as colored bands. (d) Estimates of the primary autotrophic DIC source by autotrophic regime (colors) shown as mean (± SE) percentage of growing season days.

<figure><img src="image_6.png" /></figure>

(P2) due to stoichiometric differences between plankton (C : N = 20 : 1) and macrophytes (C : N = 8 : 1). The planktonic regime also exhibited a greater proportion of steep βDIC (e.g., < -1.5) than the benthic regime. Both the planktonic and benthic regimes exhibited a similar temporal distribution of βDIC (Fig. 4b, inset): near 0 in the winter with a gradual increase to a βDIC aligning with their median EQ in the summer. Note that slopes were more likely to be indistinguishable from zero in the heterotrophic-source state, potentially implying decoupling between metabolism and FCO₂ (green dots in Fig. 4a).

Discussion

Internal CO₂ production was half of total FCO₂ to the atmosphere in the Loire River from 1990 to 2022. However, this estimate, using –NEP:FCO₂, only considers the heterotrophic-source trophlux state (NEP and FCO₂ directed to the atmosphere). When also considering the autotrophic-sink state (NEP and FCO₂ directed into the river) this number increases to 72%, supporting our hypothesis (H1) that extended periods of autotrophy led to regular negative internal production of CO₂. In other words, the atmosphere
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Variation in excess O₂ vs. dissolved inorganic carbon as an indicator of the photosynthetic quotient. (a) Hourly exO₂ vs. exDIC from 1990 to 2022, colored by hourly trophic-flux (trophlux) state, with dashed line indicating -1 : 1. Inset presents the same data, but with exCO₂ on the x-axis; a sharp barrier exists for exCO₂ at -24 µM leading to a hockey stick shape. (b) Kernel densities of daily slopes (β_DIC; n = 24) of hourly exO₂ vs. DIC, colored by the autotrophic regime of the river with dashed vertical lines indicating the median slope and thus ecosystem quotient (EQ) for each autotrophic regime. Inset shows the mean annual time series of the same data smoothed using a generalized additive model.</figcaption></figure>

is an additional source of CO₂ in the Loire River during periods of autotrophy, adding approximately 1.2 mol C m⁻² yr⁻¹. Although this is a small percentage of the total CO₂ budget (Fig. 1d; Table 1), this observation suggests that positive NEP can regularly reverse FCO₂ in large rivers.

Still, the heterotrophic-source state was the dominant trophlux state of the Loire River, and its occurrence controlled

annual FCO₂ magnitudes. Overall, annual FCO₂ in the middle Loire River (920 ± 540 g C m⁻² yr⁻¹; mean ± SD) was highly variable, but within the range of other major rivers (Richey et al. 2002; Butman and Raymond 2011; Mwanake et al. 2022) despite its mean pCO₂ (1200 ± 1100 µatm) being half to one-third the average from similarly sized rivers (Cole and Caraco 2001; Butman and Raymond 2011). The high inter-annual variability in FCO₂ and in its CO₂ source is further complicated by the additional questions of (1) whether the organic matter fueling respiration is of terrestrial or aquatic origin (Bertuzzo et al. 2022)—as was the case in the planktonic regime in the Loire (Moatar 1997)—and (2) whether that biomass is ultimately derived from terrestrial DIC (Cole and Caraco 2001).

## Trophlux states depend on discharge

The distinct trophlux states exhibited by the Loire River provide insight into the processes controlling internal CO₂ sources from large rivers (and see A.T. Nguyen et al. unpubl.). As seen elsewhere (Abril et al. 2014; Hotchkiss et al. 2015; Mwanake et al. 2022), FCO₂ increased with increasing discharge through several potential mechanisms: (1) increased external inputs, (2) increased gas exchange, and (3) decreased NEP. Discharge conditions can thus be used to predict the timing and magnitude of NEP, FCO₂, and NEP: FCO₂ (Bernhardt et al. 2022; Mwanake et al. 2022).

One of the predictions of discharge-controlled trophlux states is that riverine FCO₂ exhibits a non-normal distribution. Thus, point measurement extrapolation to annual fluxes or use of mean values from limited field campaigns may underestimate true fluxes (Supporting Information Fig. S13). We broadly caution against the interpretation of average values in the context of FCO₂ as they are rife with uncertainty—the median is likely more appropriate in most cases (Supporting Information Table S2). It is a truism that the aggregation of errors in non-stationary and heterogeneous systems will result in large biases in estimated average system behavior (Kirchner 2016), and thus estimates of river FCO₂ and NEP will depend strongly on the scale of analysis and the discharge conditions at that scale.

Still, even after accounting for discharge, seasonal variability, and uncertainty, the most comprehensive synthesis (Hotchkiss et al. 2015) estimated double our mean daily values for FCO₂ (1.9 vs. 1.1 g C m⁻² d⁻¹) and NEP (−0.75 vs. −0.37 g C m⁻² d⁻¹) for large rivers (i.e., > 100 m³ s⁻¹). The most recent mean annual NEP estimates for temperate rivers (−0.71 g C m⁻² d⁻¹) are also double our values (Battin et al. 2023). Our internal production estimates were also approximately 50% greater (0.49 vs. 0.32) than those from Hotchkiss et al. (2015) for large rivers. These discrepancies are likely attributed to the small number of samples (n = 5) and the lack of paired CO₂ and metabolism data used in Hotchkiss et al. (2015) for estimating these fluxes from large rivers. Expanding multiseason and inter-annual datasets from large rivers thus is a critical aspect toward upscaling measurements.
A complex, but predictable carbonate system

Characteristic solute signatures of the four trophlux states in the Loire River revealed a complex, but predictable pattern of interactions between autotrophs, metabolism, FCO₂, and the carbonate system. The heterotrophic-source state was the least dynamic at the hourly scale, but a clear diel signature and predictable duration (i.e., winter; Fig. 2a) suggest it as a useful heuristic for future modeling efforts. Indeed, this temporally dominant trophlux state was also the only real contributor to FCO₂, reinforcing the hypothesis that internal CO₂ production is a large source of CO₂ excess in large rivers (Hotchkiss et al. 2015). It was surprising that the heterotrophic-sink state (3% samples during 32 years of observation) was physically possible as it indicates that although NEP is adding CO₂, the river is still under-saturated. This phenomenon may be explained by the buffering capacity of the calcium carbonate system in the Loire, which can create lags in responses of CO₂ to biological processes (Stets et al. 2017).

Solute signatures of the autotrophic trophlux states implied widespread and regular non-CO₂ photosynthesis, in line with our predictions (P1.1 and P1.2). Indeed, our results suggest that both CCM and CaCO₃ precipitation are common in the Loire, regardless of phytoplankton or macrophyte dominance. The autotrophic state predictably emerged each year at the start of the growing season, and as GPP gradually removed excess CO₂ from the water, the river shifted from CO₂ source to sink. The shift to a CO₂ sink state was strongest and of the longest duration in the previous phytoplankton regime but continued to occur even in recent years.

The regularity of CO₂ sink conditions revealed that external CO₂ can be a limited resource in the Loire River. Indeed, growing season demand for DIC was an order of magnitude or greater than the atmospheric CO₂ influx during periods with low gas exchange and high GPP (cf. Maberly and Madsen 1998). As CO₂ became limiting, autotrophs adopted HCO₃⁻ uptake to support their DIC needs. Our estimates of HCO₃⁻ uptake align well with those from a large river in Connecticut, USA, where approximately 30%, and up to 58% of GPP was supported by HCO₃⁻ (Aho et al. 2021). Indeed, as CCM is a common strategy in most alkaline aquatic systems (Giordano et al. 2005; Raven et al. 2008; Maberly and Gontero 2017), HCO₃⁻ may be underestimated as an autotrophic DIC source in large rivers, even in those that are not CO₂ depleted.

Our work is one of the few studies examining CaCO₃ precipitation as a DIC source for photosynthesis in rivers, at times accounting for over 50% of carbon for GPP (Fig. 3). Although there is a large body of literature on calcification in streams (Neal et al. 2002; de Montety et al. 2011; Nimick et al. 2011), there is a paucity of its analysis with respect to a DIC source for autotrophs (but see Green and Smeck 1979). In lakes, by contrast, calcification as a driver of photosynthesis is well known (Groleau et al. 2000; Andersen et al. 2019; Escoffier et al. 2023). Our estimates of Qₐₑₐᵣₐₑₐ during CO₂-depleted periods

(ca. 13 mmol m⁻² d⁻¹) align with lake studies (e.g., ca. 20 mmol m⁻² d⁻¹, Groleau et al. 2000; ca. 10–30 mmol m⁻² d⁻¹, Escoffier et al. 2023). Contrary to lakes, however, where calcification can regularly make up at least 50% of GPP (Groleau et al. 2000; Andersen et al. 2019; Escoffier et al. 2023) calcification in the Loire River was a more typically 10–25% of total GPP. We note that more accuracy is needed to isolate calcification signals from C₂₅ variation in rivers (Supporting Information Figs. S8, S9), but our approach (with β<sub>NEP</sub>) may be a useful tool going forward.

In alkaline lakes, daytime removal of A<sub>T</sub> during calcification can return to the water column at night by respiration and carbonate dissolution in the bottom waters, leading to a “carbon [ate] pump” (sensu Andersen et al. 2019). In flowing waters, this removed A<sub>T</sub> may be transported downstream on phytoplankton or diatom particles (Négrel and Grosbois 1999; Négrel et al. 2000), temporarily buried, or dissolved back to the water column from the leaves of macrophytes. While reoligotrophicication in the Loire has led to a marked decrease in planktonic calcite transported downstream (Grosbois et al. 2001), our results show no major difference in CaCO₃ precipitation between the two autotrophic regimes. It is thus likely that calcification is now taking place on macrophyte leaves (Supporting Information Fig. S14), which is well documented for the main genera (*Myriophyllum* spp., *Potamegaton* spp., *Ranunculus* spp.; McConnaughey and Whelan 1997; Rott et al. 2004) that occur in the middle Loire (Diamond et al. 2021).

To aid in understanding the complex processes described above, we provide a conceptual diagram of the calcium carbonate system and its associated trophlux states (Fig. 5) for the Loire River. We believe this diagram is likely representative of many large, productive rivers with high alkalinity (e.g., 1.5 mmol L⁻¹), which represent most rivers with Strahler order > 3 (Hartmann et al. 2014).

Ecosystem quotients are linked to autotrophic
stoiichiometry

In line with our predictions, EQ decreased from 1.3 to 1.0 as the autotrophic community shifted from phytoplankton to macrophytes. As C : N ratios increase under macrophyte dominance and demand for N (typically as NO₃⁻) decreases, less O₂ is released, leading to a lower PQ. Changing nitrification rates can also affect EQ, but nitrate (mean = 133 µmol L⁻¹; Supporting Information Table S3) is approximately 97% of total dissolved inorganic nitrogen in the Loire River, and this ratio did not vary over the study period. Instead, the doubling of autotrophic stoichiometry (C : N from 8 to 20) under re-oligotrophicication and the subsequent change in autotrophic nitrate assimilation (Diamond et al. 2021) is a more plausible explanation for a changing PQ and thus EQ over time.

The reduction in EQ alters the interpretation of recent ana-
lyses, where GPP in terms of oxygen decreased ca. 20% under
macrophyte dominance compared to phytoplankton
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** Conceptual model of the Loire River’s coupled metabolism-carbonate system. Annual evolution of the four trophic-flux (trophlux) states observed in the Loire with their relative temporal occurrence indicated by the pie chart in the middle, with colors and position aligned. Gray arrows indicate the typical progression among trophlux states, whereas black arrows indicate relative quantities and directions of C flux.</figcaption></figure>

dominance (Diamond et al. 2021). This GPP decrease is almost exactly the EQ shift measured here, implying that GPP in terms of carbon remained quite stable in the Loire over 30 years, despite a massive reduction in nutrient availability and a dramatic change in autotrophic community. We caveat this interpretation with the understanding that EQ integrates both PQ and RQ, and the plethora of other processes that affect oxygen in the river (Pathak et al. 2022). Moreover, our approach to EQ is different from most typical freshwater applications as it considers changes to the DIC pool (DeGrandpre et al. 1997; Cotovicz Jr et al. 2015), not just CO₂ (cf. Vachon et al. 2020). Additional analysis is clearly warranted here, but shifting EQ due to changing nutrients and C : N may explain additional GPP trends from re-oligotrophied rivers (Arroita et al. 2019).

Despite the broad trend in decreasing EQ, there was large inter-day variability in EQ estimates derived from β_DIC, particularly under phytoplankton dominance (Fig. 4b). High O₂ saturation—predicted to reduce PQ due to photorespiration (Trentman et al. 2023)—resulting from elevated GPP was not linked to EQ < 1. Perhaps CCMs, which are most needed during high GPP periods, suppress or reduce the expected photorespiration effect (Maberly and Gontero 2017). Additional insights may be gained by accounting for the carbon costs of CCMs (Maberly and Gontero 2017), which should predictably affect both the PQ and RQ, and thus be evident in the slope of exO₂ – DIC. Finally, apparent EQ may be diminished by “missing” stream metabolic signals due to O₂ ebullition via bubble formation and direct O₂–CO₂ exchange with the atmosphere for non-submerged plants

(Koschorreck et al. 2017; Long et al. 2020). The relative importance of these processes is unknown in the Loire, but they provide a potential rationale for decreasing EQ under the macrophyte regime.

## Future directions

This work motivates an ambitious research agenda for understanding the links among carbonate equilibria, external DIC, biota and their metabolism, and changing drivers of hydrology and hydrochemistry due to management and global change. Future efforts should seek to elucidate the proportional co-fixation of CO₂ vs. HCO₃⁻, which is occluded by the current practice of comparing exCO₂ or exDIC with exO₂. Isotopic analysis of C and O may also be used to this end and may also be used to partition CCM fixation from CaCO₃ precipitation. In addition to the new perspectives that coincident CO₂ and O₂ measurements can provide (Aho et al. 2021), we suggest that future work account for diel fluctuations in A_T, as such methods become less labor-intensive (Shangguan et al. 2021). It will also be critical to account for network transport of DIC, as the definition of what is considered “external” DIC often depends on the integration length of analysis, which is highly dependent on discharge (Diamond et al. 2023). We suggest that modeling studies may help disentangle the fate of upstream autochthonous DIC and its relative contribution to “external” vs. “internal” DIC. Finally, evaluation of long-term NEP:FCO₂ evolution is a fundamental next step toward understanding changing dynamics of external vs. internal sources as a function of global change.
## Author Contributions

Jacob S. Diamond led the manuscript effort. Jacob S. Diamond, An Nguyen Truong, Gwenaël Abril, and Florentina Moatar came up with the research question and designed the study approach. Jacob S. Diamond and An Nguyen Truong conducted the data curation and preparation, and Jacob S. Diamond conducted the statistical analyses. Jacob S. Diamond wrote the paper with contributions from all authors.

## Acknowledgments

Funding was provided by the Électricité de France under the project MetaCalc. We further acknowledge the helpful conversations with Dr. Dieter Wolf-Gladrow on understanding $HCO_3^-$ uptake, carbonate kinetics, and equilibria/disequilibria. We additionally thank two anonymous reviewers and the Associate Editor for their comments, which improved the clarity and rigor of this work. Open access publishing facilitated by Universita Ca' Foscari, as part of the Wiley - CRUI-CARE agreement. [Correction added on 16 May 2025, after first online publication: CRUI-CARE funding statement has been included in this version.]

## Conflicts of Interest

None declared.

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**Supporting Information**

Additional Supporting Information may be found in the online version of this article.

Submitted 01 May 2024
Revised 22 November 2024
Accepted 16 February 2025