# An empirical assessment of dissolved organic carbon fluxes to oceans under climate change

Clément Fabre, Sabine Sauvage, Michelle T.H. van Vliet, Amandine Pastor, José-Miguel Sánchez-Pérez

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Clément Fabre, Sabine Sauvage, Michelle T.H. van Vliet, Amandine Pastor, José-Miguel Sánchez-Pérez. An empirical assessment of dissolved organic carbon fluxes to oceans under climate change. Global and Planetary Change, 2025, 253, pp.104971. 10.1016/j.gloplacha.2025.104971. hal-05184493

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# An empirical assessment of dissolved organic carbon fluxes to oceans under climate change

Clément Fabre<sup>a, *,</sup> Sabine Sauvage<sup>a</sup>, Michelle T.H. van Vliet<sup>b</sup>, Amandine V. Pastor<sup>c,d,e</sup>,
José-Miguel Sánchez-Pérez<sup>a, *</sup>

## ARTICLE INFO

Editor: Dr. Jed O Kaplan

Keywords:

DOC
Global
Climate change
Riverine exports

## ABSTRACT

Climate change is a primary concern in the coming decades, affecting temporal and spatial patterns in temperature and hydrology worldwide. These variations will undoubtedly affect the global carbon balance. The export of riverine dissolved organic carbon (DOC) to the oceans is crucial for maintaining the carbon balance and sustaining the oceanic food web. Recent modelling quantified historical DOC exports and future daily discharges delivered to the oceans. We intend to compare historical (1971–2000) and future (2071–2100) DOC deliveries from large rivers using an easy-to-use equation that integrates future air temperatures, soil organic carbon contents, and hydrological dynamics under a changing climate. On a set of 338 large rivers, we found future global DOC exports to the oceans of 136.9 ± 35.8 and 148.1 ± 38.9 TgC y⁻¹ in the RCPs 2.6 and 8.5. Compared to the historical flux of 126.1 ± 32.6 TgC y⁻¹, global variations are not significant. However, regional trends were found. Among all watersheds, cold catchments returned the most significant rises of +0.07 ± 0.02 and +0.13 ± 0.03 TgC y⁻¹, resulting in increases of +28 % and + 55 % for RCPs 2.6 and 8.5, respectively. Moreover, the usual spring freshet in these catchments, which delivers most of the DOC, occurs earlier (10 and 18 days, respectively). This paper highlights the high variability in future dissolved organic carbon (DOC) deliveries to the oceans, particularly in high latitudes. These increases might affect the local and global sustainability of aquatic ecosystems.

## 1. Introduction

Climate change will impact water quality by altering global river discharge patterns, which will have a significant and non-negligible effect on freshwater and oceanic ecosystems. A mean annual increase in river discharge is expected in high-latitude rivers, while water release is expected to decrease in Europe, Africa, and Central America (Milliman et al., 2008; Schewe et al., 2014). At a daily time step, van Vliet et al. (2013) highlighted an increase in the seasonal variations of river discharge globally.

Organic carbon (OC) exported by rivers to the oceans is essential for many biological processes (Cole et al., 2007; Drake et al., 2017). For example, riverine OC influences denitrification in rivers, coastal areas (Taylor and Townsend, 2010), and floodplains (Fabre et al., 2020a).

Riverine OC exports are also directly used by the oceanic food web (Follett et al., 2014; Steinberg and Landry, 2017; Ward et al., 2017). Besides, riverine OC is a primary source of freshwater and oceanic greenhouse gas emissions (IPCC, 2023) and interacts with different biogeochemical cycles (Cole et al., 2007; Drake et al., 2017) and various pollutants such as mercury (Lavoie et al., 2019). Thus, climate change will affect global OC and other nutrient and contaminant dynamics.

Riverine OC flows in rivers in two forms: the particulate organic carbon (POC) and the dissolved organic carbon (DOC; Hope et al., 1994). By modifying the water cycle, climate change will reshape POC and DOC dynamics. Estimating riverine DOC transport is of primary importance as its labile part is microbially or photochemically degraded in rivers and estuaries (Raymond and Bauer, 2001; Jones et al., 2016), and the receiving ecosystems' functioning relies on the properties of

<footnote><sup>a</sup> Université de Toulouse, Toulouse INP, CNRS, IRD, CRBE, Toulouse, France</footnote>

<footnote><sup>b</sup> Department of Physical Geography, Utrecht University, P.O. Box 80.115, 3508 TC Utrecht, the Netherlands</footnote>

<footnote><sup>c</sup> ITAP, Univ Montpellier, INRAE, Institut Agro, Montpellier, France</footnote>

<footnote><sup>d</sup> Elsa, Research Group for Environmental Lifecycle and Sustainability Assessment, Montpellier, France</footnote>

<footnote><sup>e</sup> cE3c, Faculty of Sciences, University of Lisbon, Lisbon, Portugal</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: clement.fabre@univ-tlse3.fr (C. Fabre), jose.sanchez@univ-tlse3.fr (J.-M. Sánchez-Pérez).</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 1. Representation of the modelling structure used in this study. The daily discharges come from the VIC hydrological model (van Vliet et al., 2016a). The daily DOC fluxes for the two RCP scenarios are calculated from 2005 to 2100 using the equation of Fabre et al. (2020b). A focus on the historical period (1971–2000) was done to compare with future fluxes. Q stands for discharge, and F<sub>DOC</sub> stands for DOC fluxes.</figcaption></figure>

POC and DOC. Moreover, the refractory part feeds the DOC pool in oceans, a tremendous reservoir of OC (Schlesinger, 1991; Catalán et al., 2016). DOC originates mainly from soil leaching (Meybeck, 1993), and a substantial part of the DOC reaching the oceans is labile (Ittekkot and Laane, 1991; Søndergaard and Middelboe, 1995; Zhou et al., 2021), which means that it is subjected to different biogeochemical processes in aquatic ecosystems (Drake et al., 2017). This lability varies in space and time and could reach a large part of the total DOC export, e.g. during high freshets (Holmes et al., 2008; Mann et al., 2012).

Based on various modelling methods, past research evaluated his-
torical yearly global DOC exports to the oceans between 130 and 360
TgC y⁻¹ (1 Tg = 10¹² gC; Meybeck, 1993; Ludwig et al., 1996; Aitken-
head and McDowell, 2000; Seitzinger et al., 2010; Dai et al., 2012; Li
et al., 2017; Fabre et al., 2020b; Nakayama, 2020). Moreover, Tian et al.
(2023) showed that historical riverine DOC fluxes increased from 246 ±
31 TgC y⁻¹ to 262 ± 33 TgC y⁻¹ from the 1800s to the 2010s. Therefore,
studying future DOC dynamics would help improve our understanding
of the impacts of climate change on future food web dynamics and
global carbon dynamics (Nakhavali et al., 2024).

Daily river discharges are necessary to detail DOC fluxes seasonality (Fabre et al., 2020b). In this paper, we employed an easy-to-use equation (Fabre et al., 2020b) to estimate future daily DOC fluxes based on future daily discharges (van Vliet et al., 2013). The objectives of the study are: 1) to predict future DOC exports from large rivers based on simulated future water releases (RCPS 2.6 and 8.5 scenarios) and an equation with adapted parameters, and 2) to highlight the differences in the seasonality of DOC fluxes to the oceans under historical and future climates.

## 2. Materials and methods

2.1. Selected equation

The equation used in this study was developed by Fabre et al. (2019;
2020b; 2021). This equation calculates DOC concentrations ([DOC] in
mg L⁻¹) based on the daily specific discharge (Qs in mm day⁻¹), and α
and β are two parameters specific to each watershed:

$$
[DOC] = \frac{\alpha^* Q_s}{\beta + Q_s} \qquad (1)
$$

where [DOC] is the riverine DOC concentration in milligrams per litre (mg L⁻¹). Fabre et al. (2019, 2020b, 2021) developed this equation by compiling multiple datasets for 74 exorheic catchments, which included daily data from 1990 to 2015 covering approximately 35 % of the continental surface. According to their dominant Köppen-Geiger climate classification, these large exorheic catchments represent a range of environmental conditions and are distributed as follows: nine tropical, 11 dry, 31 temperate, and 23 continental catchments (Rubel and Kottek,

2010).

Fabre et al. (2020b) correlated the two parameters α and β to the soil organic carbon content (SOC in kg m⁻³), the mean annual precipitation amount (P in mm y⁻¹) and the air temperature (T in °C):

$$
\begin{cases}
\alpha = a^* \frac{\text{SOC}}{12} + b \ (2) \\
\beta = \frac{12.6}{T + 16.1} - 0.03 \ (3)
\end{cases}
$$

The original determination of α in Fabre et al. (2020b) uses SOC in % weight. We adapted the parameters by recalibrating the equation with SOC in kg m⁻³ to match units from the CMIP5 project. Moreover, Fabre et al. (2020b) mentioned that α is the most sensitive parameter, mainly due to SOC. Todd-Brown et al. (2013) showed that SOC contents vary widely between the different Global Circulation Models (GCMs) of the CMIP5 project. Therefore, we decided to recalibrate eq. 2 for each GCM selected in the study. The resulting a and b values are detailed in the following section.

Finally, the resulting daily DOC fluxes are calculated as:

$$
F_{\text{DOC},i} = [\text{DOC}]_i * Q_i \qquad (4)
$$

where [DOC]<sub>i</sub> is the riverine DOC concentration in milligrams per litre (mg L<sup>-1</sup>) for river i, and Q<sub>i</sub> is the daily discharge in m<sup>3</sup> s<sup>-1</sup> for river i. Yearly fluxes in TgC y<sup>-1</sup> for each river i.

With eqs. 1, 2, and 3, we obtain for each river i:

$$
F_{\text{DOC},i} = \frac{\left( a^{*} \frac{\text{SOC}_i}{T_i} + b \right) * Q_{si}}{\left( \frac{12.6}{T_i + 16.1} - 0.03 \right) + Q_{si}} * Q_i \quad (5)
$$

2.2. Climate change scenarios and variables needed

Fig. 1 details the modelling framework of this study. Two Repre-
sentative Concentration Pathways (RCP 2.6 and RCP 8.5) were selected
to capture a broad range of uncertainties in future projected climate
change and account for the maximum variations in future DOC dy-
namics. The RCP 2.6 scenario assumes maximal global GHG emissions
between 2010 and 2020, followed by a slight decrease. On the contrary,
the RCP 8.5 scenario depicts a continuous rise in GHG emissions
throughout the 21st century. The resulting increases in temperature at
the global scale are 1.3–2.4 °C and 3.3–5.7 °C for the Shared Socio-
economic Pathways 1–2.6 and 5–8.5 corresponding to RCPs 2.6 and 8.5,
respectively (IPCC, 2023).

The eqs. 2 and 3 mentioned in section 2.1 were forced with average
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Re-calibration of Eq. 2, determining the parameter α for each Global Circulation Model with 10,000 Monte Carlo simulations. Standard deviations of α come from Fabre et al. (2020), while errors related to precipitation amount and SOC contents estimated by each GCM were set to ±10 %. The frequency of resulting a and b parameters and their respective standard deviations (dashed lines) are shown.</figcaption></figure>

air temperature, precipitation, and SOC contents for the period 1971–2100 for five GCMs, i.e., GFDL-ESM2M (Dunne et al., 2012), HadGEM2-ES (Collins et al., 2011; Martin et al., 2006), IPSL-CM5A-LR (Dufresne et al., 2013), MIROC-ESM-CHEM (Watanabe et al., 2011), and NorESM1-M (Bentsen et al., 2013). For each model, the needed variables were downloaded from the Coupled Model Intercomparison Project 5 (CMIP5) databases available at https://esgf-node.llnl.gov/sear ch/cmip5/. In the models that separate the contents of litter and soil (IPSL-CM5A-LR, MIROC-ESM-CHEM, and NorESM1-M), the two compartments are added to obtain the SOC contents, as proposed by Todd-Brown et al. (2013).

Concerning Eq. 2, new values for a and b were determined for each GCM based on their respective average precipitation amount and SOC contents for the historical period. Monte Carlo simulations (10,000) were performed to link α with the related variables simulated by each GCM, considering their respective uncertainties. Standard deviations for α were extracted from Fabre et al. (2020), while errors related to

<figure><img src="image_5.png" /><figcaption>**Table 1**</figcaption></figure>

Re-calibrated parameters a and b determining the parameter α for each Global Circulation Model.

<table><thead><tr><th>Model</th><th>GFDL-ESM2M</th><th>HadGEM2-ES</th><th>IPSL-CM5A-LR</th><th>MIROC-ESM-CHEM</th><th>NorESM1-M</th></tr></thead><tbody><tr><td>a</td><td>21.7 ± 4.5</td><td>30.9 ± 10.9</td><td>32.0 ± 7.0</td><td>12.4 ± 2.8</td><td>16.5 ± 21.7</td></tr><tr><td>b</td><td>4.1 ± 0.7</td><td>2.5 ± 1.7</td><td>2.1 ± 1.2</td><td>3.5 ± 0.9</td><td>6.3 ± 1.3</td></tr></tbody></table>

precipitation amount and SOC contents estimated by each GCM were set to ±10 %. The resulting regressions and associated coefficients are shown in Fig. 2 and Table 1.

Concerning discharges, global gridded daily discharge simulations were produced with the VIC hydrological model (Liang et al., 1994; Lohmann et al., 1998), which was forced with the bias-corrected output of the five GCMs for the RCPs 2.6 and 8.5 from 1971 to 2100 (van Vliet
<figure><img src="image_6.png" /><figcaption>Fig. 3. Yearly global DOC a) export and b) difference with initial flux (TgC y⁻¹) for RCP 2.6 and 8.5 averaged from five GCMs. The historical period extends from 1971 to 2000, while the future period stands for the 2071–2100 period. P-values for Mann-Kendall tests, Student tests and Sen’s slope are shown for c) RCP 2.6 and d) RCP 8.5. The dashed lines in c and d represent the 0.05 significance limit.</figcaption></figure>

et al., 2016a, 2016b). Discharges were extracted for the outlets of the main exorheic catchments to model DOC fluxes.

Appendix A presents the discharge simulations per watershed for the historical period (1971–2000) and anomalies in the two RCP scenarios for the future period (2071–2100). Similarly, Appendix B outlines the expected variations in SOC contents, average air temperatures, and mean annual precipitation amounts for RCPS 2.6 and 8.5 at the global scale.

## 2.3. Quantification of uncertainties

The uncertainties related to the determination of $F_{DOC}$ are assessed as follows. First, a 10 % error was considered for the variables extracted from the VIC model (daily discharges) and each GCM (precipitation amount and SOC). Second, a 1 °C error was considered acceptable for air temperatures. The uncertainties for the parameters a and b were included (Table 1). Finally, for each river i, we estimated future daily and yearly DOC fluxes and their resulting standard deviations with 1000 Monte Carlo simulations considering the standard deviations of α, β, and Q previously determined (eq. 5):

$$F_{DOC,i} \pm \Delta_{F_{DOC},i} = \frac{\sum \left( \frac{(a \pm \Delta_a)^{\frac{SOC_i + \Delta_{SOC_i}}{12}}}{\frac{P_i - \Delta_{P_i}}{12}} + (b \pm \Delta_b) \right) * (Q_{i1} \pm \Delta_{Q_{i1}})}{\frac{\left( \frac{12.6}{(\bar{r}_i \pm \Delta_{r_i})} + 0.03 \right)}{\left( \frac{16.1}{(\bar{r}_i \pm \Delta_{r_i})} \right)^{16.1}} + (Q_{i1} \pm \Delta_{Q_{i1}})} * (Q_i \pm \Delta_{Q_i})} \quad (6)$$

with n the number of years in the historical period (1971–2000) and the future period (2071–2100). Finally, average fluxes are calculated at

global scale, for each Köppen-Geiger climate group and for each ocean:

$$F_{DOC} \pm \Delta_{F_{DOC}} = \sum_{i=1}^{338} F_{DOC,i} \pm \Delta_{F_{DOC,i}} \quad (7)$$

## 2.4. Trend evaluation

To assess whether a trend emerges in the two RCP scenarios between the historical and future periods, 10,000 Monte Carlo simulations on annual DOC fluxes and their associated standard deviations were performed. Then, Mann-Kendall tests and Sen’s slope evaluations were performed on the entire dataset, and Student t-tests were conducted to compare the evolution of the means between the historical and future periods.

# 3. Results

## 3.1. Historical and future DOC exports

Fig. 3 shows the temporal evolution of DOC fluxes at the global scale. Future fluxes in both RCPs tend to be slightly higher than in the historical period (Fig. 3a & b). In the historical period 1971–2000, the average DOC flux is 126.1 ± 32.6 TgC y⁻¹ (Table 2). In the future period (2071–2100), we found global DOC fluxes of 136.9 ± 35.8 and 148.1 ± 38.9 TgC y⁻¹ in the RCPs 2.6 and 8.5, respectively. Mann Kendall trends, Student tests and Sen’s slopes return insignificant results in both RCPs (p-values of 0.32, 0.33, and 0.32 for RCP 2.6, and 0.07, 0.09, and 0.07 for RCP 8.5, respectively), even though most Monte Carlo simulations (~4000 out of 10,000) show significant trends for RCP 8.5 (Fig. 3c & d). Semi-arid, cold, and polar catchments returned increasing trends (Fig. 4
<caption>**Table 2**</caption>

Modelled global DOC fluxes (TgC y⁻¹) exported to the oceans in the three scenarios during the 1971–2000 period (historical) and the 2071–2100 period (future). These values are based on a dataset of 338 large rivers. The significance of change was tested using Mann Kendall trend tests, Sen's slopes, and paired t-tests. Significant trends and changes are bold.

<table><thead><tr><th></th><th>Control</th><th>Future (RCP 2.6)</th><th>Mann Kendall tau (p-values)</th><th>Sen's slopes (p-values)</th><th>t-tests p-values</th><th>Rel change (% change; RCP 2.6)</th><th>Future (RCP 8.5)</th><th>Mann Kendall tau (p-values)</th><th>Sen's slopes (p-values)</th><th>t-tests p-values</th><th>Rel change (% change; RCP 8.5)</th></tr></thead><tbody><tr><td rowspan="2">Global</td><td>126.1 ± 32.6</td><td>136.9 ± 35.8</td><td>0.07 ± 0.06<br>(0.32 ± 0.07)</td><td>0.1 ± 0.08<br>(0.32 ± 0.29)</td><td>0.32 ± 0.29</td><td>10.7 ± 34.2<br>(+9 %)</td><td>148.1 ± 38.9</td><td>0.15 ± 0.06<br>(0.07 ± 0.14)</td><td>0.22 ± 0.09<br>(0.07 ± 0.14)</td><td>0.09 ± 0.17</td><td>22 ± 35.9<br>(+17 %)</td></tr><tr><td>20.5 ± 5.2</td><td>26.2 ± 6.7</td><td>0.22 ± 0.05<br>(0.01 ± 0.03)</td><td>0.06 ± 0.01<br>(0.01 ± 0.03)</td><td>0.01 ± 0.04</td><td>5.8 ± 6<br>(+28 %)</td><td>31.7 ± 8.1</td><td>0.37 ± 0.05<br>(0 ± 0)</td><td>0.11 ± 0.02<br>(0 ± 0)</td><td>0 ± 0</td><td>11.3 ± 6.8<br>(+55 %)</td></tr><tr><td rowspan="6">Ocean</td><td>72.6 ± 18.9</td><td>74.6 ± 19.4</td><td>0.02 ± 0.06<br>(0.5 ± 0.29)</td><td>0.01 ± 0.05<br>(0.5 ± 0.29)</td><td>0.48 ± 0.29</td><td>2 ± 19.2<br>(+3 %)</td><td>76.3 ± 19.7</td><td>0.05 ± 0.06<br>(0.42 ± 0.3)</td><td>0.04 ± 0.05<br>(0.42 ± 0.3)</td><td>0.42 ± 0.3</td><td>3.7 ± 19.3<br>(+5 %)</td></tr><tr><td>14.6 ± 3.9</td><td>16.4 ± 4.6</td><td>0.1 ± 0.06<br>(0.2 ± 0.24)</td><td>0.02 ± 0.01<br>(0.2 ± 0.24)</td><td>0.22 ± 0.26</td><td>1.8 ± 4.3<br>(+13 %)</td><td>18.8 ± 5.5</td><td>0.2 ± 0.06<br>(0.01 ± 0.05)</td><td>0.04 ± 0.01<br>(0.01 ± 0.05)</td><td>0.02 ± 0.06</td><td>4.2 ± 4.7<br>(+29 %)</td></tr><tr><td>18.5 ± 4.8</td><td>19.5 ± 5.2</td><td>0.06 ± 0.06<br>(0.38 ± 0.3)</td><td>0.01 ± 0.01<br>(0.38 ± 0.3)</td><td>0.41 ± 0.3</td><td>1.1 ± 5<br>(%)</td><td>21.2 ± 5.7</td><td>0.13 ± 0.06<br>(0.12 ± 0.2)</td><td>0.03 ± 0.01<br>(0.12 ± 0.2)</td><td>0.14 ± 0.21</td><td>2.7 ± 5.3<br>(+15 %)</td></tr><tr><td>61.6 ± 16.1</td><td>62.6 ± 16.5</td><td>0.01 ± 0.06<br>(0.51 ± 0.29)</td><td>0 ± 0.04<br>(0.51 ± 0.29)</td><td>0.5 ± 0.29</td><td>1 ± 16.3<br>(+2 %)</td><td>67.8 ± 17.6</td><td>0.09 ± 0.06<br>(0.25 ± 0.27)</td><td>0.06 ± 0.04<br>(0.25 ± 0.27)</td><td>0.27 ± 0.28</td><td>6.2 ± 16.9<br>(+10 %)</td></tr><tr><td>3.7 ± 1</td><td>4.7 ± 1.3</td><td>0.17 ± 0.05<br>(0.03 ± 0.09)</td><td>0.01 ± 0.09</td><td>0.04 ± 0.1</td><td>0.9 ± 1.2<br>(+25 %)</td><td>5.6 ± 1.6</td><td>0.31 ± 0.05<br>(0 ± 0)</td><td>0.02 ± 0<br>(0 ± 0)</td><td>0 ± 0</td><td>1.9 ± 1.3<br>(+51 %)</td></tr><tr><td>25.5 ± 6.6</td><td>26.9 ± 7.2</td><td>0.05 ± 0.06<br>(0.41 ± 0.3)</td><td>0.01 ± 0.02<br>(0.41 ± 0.3)</td><td>0.42 ± 0.3</td><td>1.4 ± 6.9<br>(+6 %)</td><td>26.3 ± 7.4</td><td>0.02 ± 0.06<br>(0.48 ± 0.29)</td><td>0.01 ± 0.02<br>(0.48 ± 0.29)</td><td>0.47 ± 0.3</td><td>0.8 ± 7<br>(%)</td></tr><tr><td rowspan="2">Climate</td><td>34.1 ± 8.6</td><td>41.2 ± 10.4</td><td>0.17 ± 0.06<br>(0.03 ± 0.09)</td><td>0.07 ± 0.02<br>(0.03 ± 0.09)</td><td>0.05 ± 0.11</td><td>7.1 ± 9.5<br>(+21 %)</td><td>46.8 ± 11.8</td><td>0.28 ± 0.05<br>(0 ± 0)</td><td>0.13 ± 0.03<br>(0 ± 0)</td><td>0 ± 0.01</td><td>12.7 ± 10.4<br>(+37 %)</td></tr><tr><td>1.2 ± 0.3</td><td>1.5 ± 0.4</td><td>0.17 ± 0.06<br>(0.03 ± 0.09)</td><td>0 ± 0<br>(0.03 ± 0.09)</td><td>0.05 ± 0.11</td><td>0.3 ± 0.3<br>(+21 %)</td><td>1.7 ± 0.4</td><td>0.29 ± 0.05<br>(0 ± 0.01)</td><td>0 ± 0<br>(0 ± 0.01)</td><td>0 ± 0.01</td><td>0.5 ± 0.4<br>(+38 %)</td></tr></tbody></table>

& Table 2), with relative changes of +25 % and +51 %, +21 % and +27 %, and +21 % and +38 % for RCP 2.6 and RCP 8.5, respectively. For cold catchments, these relative changes correspond to important increases in fluxes with 0.07 ± 0.02 and 0.13 ± 0.03 TgC y⁻¹, which gives a significant increasing trend for the Arctic Ocean (+28 % for RCP 2.6 and +55 % for RCP 8.5; Fig. 4 & Table 2) where most of the cold basins discharge.

Appendix C provides details of the predicted DOC fluxes for each GCM. The fluxes range between 113.1 ± 40.8 and 140.8 ± 35.3 TgC y⁻¹ for the historical period, between 132.3 ± 20.7 and 150.9 ± 37.1 TgC y⁻¹ for RCP 2.6 and between 139.5 ± 21.9 and 155.2 ± 38.0 TgC y⁻¹. The lowest fluxes are calculated by HadGEM2-ES for the historical period and by GFDL-ESM2M for both RCPs while the highest fluxes are calculated by NorESM1-M.

By focusing on future daily trends, the spring freshet occurring in catchments delivering DOC to the Arctic Ocean peaks at Julian day 162 during the historical period (Fig. 5). In RCPs 2.6 and 8.5, the peak is slightly higher and occurs at Julian day 152 and 144, respectively.

## 3.2. Catchment-scale DOC exports

The two RCP scenarios returned different DOC flux variations at the global scale (Fig. 6). In the RCP 2.6 scenario, no trends appear except for high latitudes and west Africa. Regarding RCP 8.5, high-latitude catchments exhibit a more pronounced rise, while watersheds in Europe and the Southern Hemisphere show mostly significant decreasing trends.

# 4. Discussion

## 4.1. Future DOC exports

This paper provides estimates of future global daily DOC exports from lands to the oceans in a climate change context using a simplified approach. No significant increases in global DOC fluxes appear in both RCPs. Spatial variations are observed. The main changes occur in Arctic Rivers, where we found substantial increases in DOC fluxes of +28 % for RCP 2.6 and +55 % for RCP 8.5 (Table 2). This is mainly explained by an increase in discharge (+29 % for RCP 8.5; Appendix D). This increase occurs between November and May, which is linked to an earlier arrival of the spring freshet in these streams (van Vliet et al., 2013).

## 4.2. Comparison with previous estimates

Few previous studies estimated future DOC exports at various scales. At the global scale, Seitzinger et al. (2010) estimated a slight decrease of 1.5 % ± 0.3 % by 2030 and of 2.1 % ± 0.6 % by 2050. These decreases are associated with variations in the extent of wetlands and river discharges. Several factors may explain the differences in the results obtained by our method. Seitzinger et al. (2010) integrate multiple sources of DOC from natural and anthropogenic origins. It also considers anthropogenic impacts on river connectivity. In this study, we approach the DOC fluxes using easily obtainable variables, such as SOC stocks, precipitation amounts, and air temperatures and do not consider complex land and in-stream processes that affect DOC dynamics. Similarly, Nakhavali et al. (2024) predicted increases of +10 % and +42 % in DOC leaching globally under RCP 2.6 and 8.5, respectively, with substantial contributions from high latitudes. Our study supports their assertion that high latitudes may exhibit the highest increases in DOC exports.
<figure><img src="image_7.png" /><figcaption>Fig. 4. DOC exports by each Köppen-Climate group (top), and to each ocean (bottom). p-values for Mann-Kendall trends, Student tests, and Sen's slopes for the 10,000 Monte-Carlo simulations are displayed.</figcaption></figure>

### 4.3. Validity of the estimated DOC fluxes

#### 4.3.1. Agreement between modelled and observed water and DOC fluxes in the historical period

Fig. 7 shows the comparison of simulated and observed discharge data. Modelled water releases are slightly higher than observations in many latitude classes, except in high latitudes. The resulting water discharge going to the oceans for the 338 rivers is around 19,500 km³ y⁻¹ for the observations and about 25,500 ± 2700 km³ y⁻¹ (Appendix D) for the two RCPs scenarios. Details on the agreement between observed and simulated discharges can be found in van Vliet et al. (2013, 2016a).

Concerning DOC exports, Fig. 7 shows that modelled exports correspond well to the observations. However, simulations slightly overestimate the annual deliveries in some groups: 30-40S, 10-20S, and from 10 to 20 N to 70-80 N. Fabre et al. (2020b) already discussed possible underestimations by their model, which could reduce the discrepancies with our results.

#### 4.3.2. Global discharge

We showed that the VIC model could represent the past hydrological dynamics of numerous exorheic catchments globally. However, the model overestimates water releases in most latitude groups, as detailed

in Fig. 7. As mentioned in van Vliet et al. (2013, 2016a), these overestimates are due to the neglect of water extractions by the global models and the difficulties of representing wetlands dynamics (Haddeland et al., 2011). On the other hand, the VIC model underestimates the water exports in high-latitude rivers. Modelling tools show difficulties fitting the observations in these high latitudes, even if recent efforts at the watershed scale could help refine large-scale estimates of exports to the Arctic Ocean (Fabre et al., 2019).

Furthermore, spatial differences between the two RCP scenarios have already appeared in the historical period (Fig. 7), leading to more uncertainty in predicting future discharge. Finally, the observed water releases are not always available at the outlet of the catchments. Indeed, the observed data used in this study are derived from monitoring stations that do not cover the entire area of the corresponding catchment. As a result, the total observed water flux of 19,500 km³ y⁻¹ may be underestimated, implying that the water exports simulated by the VIC model might not be as inaccurate as suggested by Appendix D.

#### 4.3.3. GCMs heterogeneity

This study proposes an estimation of future flows using several GCMs. The use of several GCMs allows to reduce the uncertainties on the estimates. However, since the input data were different, it was necessary to redefine the factors a and b to estimate the α parameter of the DOC
<figure><img src="image_8.png" /><figcaption>Fig. 5. Future daily DOC fluxes (TgC d⁻¹) in each Köppen-Climate group (top) and to each ocean (bottom), in the two RCPs 2.6 and 8.5 scenarios during the historical period (1971–2000) and the future period (2071–2100; top). The graphs at the bottom show the relative change of DOC fluxes (%) between the future (2071–2100) and the historical period (1971–2000).</figcaption></figure>

model (Fig. 2). Appendix C shows quite similar results in the fluxes estimated by each GCM for the historical period after this recalibration but disparities emerge. HadGEM2-ES underestimates fluxes relative to the others, particularly in high latitudes. In contrast, NorESM1-M overestimates them overall. It also underestimates high latitudes but compensates by overestimating other groups relative to the other models. Moreover, these two models are the ones that return the least significant regressions between α and the ratio between SOC and precipitation (Fig. 2). Thus, the results returned by these two GCMs should be taken with more caution than the other three.

### 4.3.4. Determination of α and β

Fabre et al. (2020b) demonstrated that α is the most sensitive parameter, particularly due to variations in SOC. By forcing the original equation with GCMs outputs, we found that the alpha parameter needed to be recalibrated (Fig. 2). The resulting DOC fluxes in the historical period are in the range of past studies. Nevertheless, the ratio between SOC content and precipitation amount may not be the best predictor for α. Indeed, it simplifies DOC processes in catchments as the result of soil leaching but does not consider important parameters such as anthropogenic disturbance or in-stream processes. Other variables available at high resolution and on a global scale could make it possible to better

approach α and refine the estimates of DOC concentrations and therefore of DOC fluxes at catchment and global scales.

Moreover, the empirical calibration of α and β values relies on a set of 74 exorheic catchments. While these catchments represent large DOC providers, their limited number compared to the total number of catchments considered in our study (338) may restrict its applicability to unmonitored regions. The resulting deviations between observed and simulated DOC fluxes in the historical period for smaller watersheds may lead to misestimates in the final global DOC flux.

Moreover, the regressions presented in Fig. 2 tend to suggest that the SOC to precipitation ratio would not be a good predictor of α. Several explanatory factors of DOC dynamics such as land use or vegetation type are not considered in the model. Fabre et al. (2020b) did not find simple links between α and variables like the percentages of forests or wetlands in each basin. Nevertheless, it would be interesting to update the datasets used in their study and re-explore these links with more complex methods such as neural networks to bring out more robust correlations and therefore better estimates of DOC fluxes to the oceans.

### 4.3.5. Temporal validity of the equation

The equation used in this study was validated for spatial predictions of DOC fluxes with historical data (Fabre et al., 2020b). To use it for
<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Spatial distribution of DOC flux variations (%) between the historical period (1971–2000) and the future period (2071–2100). Non-significant trends at the catchment scale are set to 0.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 7.** Comparison in the different latitude classes of the annual discharges in the historical period 1971–2000 for the scenarios RCPs 2.6 and 8.5 with observed water releases from various datasets on the left side and the annual DOC fluxes exported on the historical period 1971–2000 for the scenarios RCPs 2.6 and 8.5 with fluxes estimated by Fabre et al. (2020b) on the right side.</figcaption></figure>

future trends, we checked if the relation between DOC concentration and discharge behaves the same throughout multiple decades at monitoring stations where long-term observed data are available. The variations of the equation predictions in multiple decades were assessed in the Solimoes River, a tributary of the Amazon River, the Murray River in Australia, the Garonne River in France, and the Yenisei River in Russia (Appendix E). Observed data for at least two decades are available on these rivers. Moreover, these rivers present different climatic conditions with tropical, sub-arid, temperate, and cold climates for the Solimoes, the Murray, the Garonne, and the Yenisei, respectively.

The equation returns α and β values in the same range for multiple decades, except for the α and β values on the Murray River in 2010–2019 and the β value on the Garonne River (Appendix F). Fabre et al. (2020b) mention that when the equation does not fit, it returns an α value close to the yearly average DOC concentration when the β value is close to 0, a method that may not capture daily variations but is satisfactory for estimating global DOC fluxes. On the one hand, the issue concerning the Murray River, or the Garonne River could be due to sampling troubles or to a non-representativeness of the whole hydrological cycle by the available data. On the other hand, these issues could be due to anthropogenic inputs of DOC that could alter the relation between DOC and discharges in relatively small catchments.

Nevertheless, Fabre et al. (2020b) demonstrated that minor modifications of α and β values change the simulated DOC concentrations only slightly. Therefore, as the shape of the relation between the discharge and the DOC concentration seems to behave the same through decades, we could assume that this relation will remain valid for the future period by integrating the variations of precipitation amounts, air temperature and SOC contents within the coefficients α and β.

### 4.3.6. SOC contents under climate change

Past studies used various models to estimate the future SOC stocks at global scale. However, models return different distributions of the stocks depending on the processes they consider. Todd-Brown et al. (2014) compared future SOC stocks from 11 models. They found an average variation of +65 ± 113 Pg C in SOC, going from -72 Pg with the MIROC-ESM model to +253 Pg in HadGEM2-ES. Concerning regional variations, the models also returned drastically different results. Indeed,

HadGEM2-ES or BNU-ESM showed a significant increase in high-latitude SOC stocks, while GFDL-ESM2G or MIROC-ESM estimated decreases in these areas.

In the same way, Crowther et al. (2016) estimated the influence of warming on SOC losses and found a significant decrease in high-latitude SOC stocks. Ito et al. (2020) showed a global increase in SOC with CMIP6-LUMIP models by considering land use changes. Finally, Wieder et al. (2013) focused on the microbial role in SOC variations. They showed a much wider range of soil C responses to climate change depending on the adaptation of microbial diversity to warming. SOC accumulates in soils if microbial growth efficiency declines with warming, while if growth efficiency adapts to warming, the microbial model projects significant SOC losses at global scale. Therefore, as our DOC estimates depend on these uncertainties regarding future variations of SOC stocks, reducing these uncertainties may improve our results.

### 4.3.7. Quantification of uncertainties

In this study, uncertainty was calculated at each step of the cascade of models using Monte Carlo simulations. However, our method considers a linear propagation of uncertainties through the different steps and treats uncertainties associated with each variable independently. These variables might be interdependent, and their combined effect could differ from our estimates. Considering assessing potential nonlinearities and interdependencies could strengthen the robustness of our estimates.

## 4.4. Future directions

These future daily DOC exports based on the equation of Fabre et al. (2020b) could help improve our understanding of the role of the main rivers in deltaic and oceanic biogeochemistry. This equation estimates the DOC concentrations at the outlet of exorheic basins. As Fabre et al. (2020b) mention, this approach may oversimplify the estimation of DOC exports to the oceans by not considering the transformation of DOC along the stream due to microbial processes or temperature (Taylor and Townsend, 2010; O'Donnell et al., 2016), as well as the impacts of land use changes or vegetation dynamics on DOC exports. This equation can help in empirically representing the evolution of DOC fluxes at large
scale but should not be used for comprehensive long-term studies, especially at the catchment scale.

Nevertheless, the current equation version approaches several in-stream processes, such as allochthonous production, within the α parameter, by determining it with the SOC content. However, it overlooks in-stream primary production from either phytoplankton or periphyton, which affects the amount and lability of riverine DOC (Raymond and Bauer, 2001). The in-stream distribution between allochthonous and autochthonous sources of DOC varies among rivers. Moreover, anthropogenic contributions are ignored even though they can have a considerable influence in certain areas. It might explain the differences in performance of the equation from Fabre et al. (2020b) for each river. Considering the impact of autochthonous and anthropogenic inputs of DOC, in addition to the decomposition of DOC, might improve the estimates. It would also help to model organic carbon quality characteristics such as lability, which is essential to refine the future DOC fluxes impact on ecosystems.

Moreover, the spatial transition between the passive pipe and the reactor conditions, as mentioned in Casas-Ruiz et al. (2020), is implicitly considered in our equation. The first part of the curve, showing increasing DOC concentrations with discharge, represents non-storm conditions. The second step shows a saturation of the DOC concentration during high-flow periods.

Riverine DOC exports are also directly used by the oceanic food web (Follett et al., 2014; Steinberg and Landry, 2017; Ward et al., 2017) and could be responsible for recent ecosystem disturbances (Wang et al., 2019). This study may help in understanding the future distribution of the coastal food web based on future nutrient deliveries from the main exorheic catchments. Still, like many others, our study does not consider the role of deltas in connecting rivers to oceans. DOC interacts with other elements in deltas and may be altered before being delivered to the oceans. Considering this role is not trivial, as many biotic and abiotic changes occur in these areas. However, estimating the final export of DOC to the oceans is essential.

Modifications in the exports of DOC may also affect the ratio between dissolved and particulate organic carbon (POC). It would be interesting to use this work to study how the changes in DOC exports will affect this distribution at the outlet of the main exorheic catchments. This ratio is already affected by human activities. For example, damming decreases POC export (Maavara et al., 2017). Therefore, combining the drop in POC delivery with the increase in DOC exports suggested by our study might lead to an imbalance in deltas and coastal areas.

Finally, this study provides DOC exports for RCPs 2.6 and 8.5. Applying the equation to the other RCP scenarios would help capture a clearer picture of the different future trends. A recent debate exists regarding the likelihood of the RCP 8.5 scenario (Hausfather and Peters, 2020). According to numerous studies, a global temperature increase of 3 °C by 2100 is more likely to occur (Hausfather and Peters, 2020). Therefore, estimating future DOC exports from rivers under new climatic scenarios would help the scientific community capture future trends in carbon balance. In the same way, the model could also be used under Shared Socioeconomic Pathways (SSPs) developed within the Coupled Model Intercomparison Project Phase 6 (CMIP6) of the World Climate Research Programme (IPCC, 2023).

# 5. Conclusion

This study highlights climate change effects on riverine DOC fluxes. Variations in SOC contents, precipitation, and temperature distribution due to climate change will affect DOC exports in the main river basins worldwide. We showed no significant increases at the global scale. However, regional trends are significant with the largest rises in Arctic catchments (0.07 ± 0.02 and 0.13 ± 0.03 TgC y⁻¹, for RCPs 2.6 and 8.5, respectively), mainly due to increases in discharges. These results will help us understand the fate of future OC fluxes to the oceans. As OC exports play a crucial role in the sustainability of aquatic ecosystems, this study will help predict more accurate future nutrient dynamics in riverine, coastal, and marine environments and their impact on trophic chains. Nevertheless, given that some factors that may affect the dynamics of DOC concentrations are not considered in the model (deforestation, changes in DOC production/mobilisation/consumption processes in watercourses, melting glaciers and permafrost), the overall fluxes proposed here are uncertain, and the changes could be more significant.

## CRediT authorship contribution statement

**Clément Fabre:** Visualization, Methodology, Formal analysis, Writing – original draft, Validation, Investigation, Conceptualization.
**Sabine Sauvage:** Validation, Methodology, Writing – original draft, Supervision.
**Michelle T.H. van Vliet:** Writing – original draft, Supervision, Validation.
**Amandine V. Pastor:** Writing – original draft, Supervision, Validation, Conceptualization.
**José-Miguel Sánchez-Pérez:** Validation, Methodology, Writing – original draft, Supervision, Conceptualization.

## Statements and declarations

This work is part of the Spatial, in situ and modelling hydrology (HYDROSIM) project. MTHvV was financially supported by the NWO Vidi grant (VI.Vidi.193.019).

## 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.

## Acknowledgements

We thank the Global Runoff Data Center, the International Center for Water Resources and Global Change, the Observation Service SO HYBAM and the Arctic Great Rivers Observatory for sharing their daily discharge data. We acknowledge the World Climate Research Programme, which, through its Working Group on Coupled Modelling, coordinated and promoted CMIP6. We thank the climate modelling groups for producing and making available their model output, the Earth System Grid Federation (ESGF) for archiving the data and providing access, and the multiple funding agencies that support CMIP6 and ESGF.
<figure><img src="image_11.png" /><figcaption>Appendix A. Yearly discharge for the historical period (km³ y⁻¹) and future discharge anomalies (%) for RCP 2.6 and RCP 8.5</figcaption></figure>
## Appendix B. Yearly precipitation amounts (mm) and average air temperature (°C) for the historical period and resulting anomalies for the RCPs 2.6 and 8.5. Datasets come from the WorldClim databases

<figure><img src="image_12.png" /></figure>

## Appendix C. DOC fluxes in TgC y⁻¹ estimated by each Global Circulation Model

<table><thead><tr><th></th><th></th><th>GFDL-ESM2M</th><th>HadGEM2-ES</th><th>IPSL-CM5A-LR</th><th>MIROC-ESM-CHEM</th><th>NorESM1-M</th></tr></thead><tbody><tr><td rowspan="2">Historical</td><td>Total</td><td>126.0 ± 19.8</td><td>113.1 ± 40.8</td><td>121.8 ± 33.0</td><td>129.0 ± 25.5</td><td>140.8 ± 35.3</td></tr><tr><td>Arctic</td><td>25.6 ± 5.1</td><td>14.1 ± 4.9</td><td>27.2 ± 6.8</td><td>23.8 ± 5.2</td><td>11.5 ± 3.7</td></tr><tr><td rowspan="5">Ocean</td><td>Atlantic</td><td>68.2 ± 10.0</td><td>67.2 ± 25.9</td><td>63.5 ± 17.7</td><td>73.3 ± 14.1</td><td>90.9 ± 22.2</td></tr><tr><td>Indian</td><td>14.0 ± 2.0</td><td>14.0 ± 5.4</td><td>14.2 ± 4.0</td><td>13.2 ± 2.5</td><td>17.5 ± 4.1</td></tr><tr><td>Pacific</td><td>18.2 ± 2.7</td><td>17.8 ± 6.6</td><td>16.8 ± 4.6</td><td>18.7 ± 3.5</td><td>20.8 ± 5.4</td></tr><tr><td>Tropical</td><td>60.1 ± 8.8</td><td>53.6 ± 21.7</td><td>50.8 ± 15.0</td><td>60.6 ± 11.8</td><td>82.9 ± 19.4</td></tr><tr><td>Dry</td><td>3.8 ± 0.6</td><td>3.7 ± 1.5</td><td>3.3 ± 0.9</td><td>3.5 ± 0.7</td><td>4.4 ± 1.0</td></tr><tr><td rowspan="3">Climate</td><td>Temperate</td><td>22.3 ± 3.1</td><td>26.7 ± 7.4</td><td>25.0 ± 6.5</td><td>25.1 ± 4.7</td><td>28.5 ± 7.4</td></tr><tr><td>Cold</td><td>37.7 ± 6.9</td><td>28.6 ± 10.0</td><td>41.2 ± 10.2</td><td>38.5 ± 8.0</td><td>24.4 ± 7.3</td></tr><tr><td>Polar</td><td>2.1 ± 0.4</td><td>0.5 ± 0.2</td><td>1.5 ± 0.4</td><td>1.3 ± 0.3</td><td>0.6 ± 0.2</td></tr><tr><td rowspan="2">RCP 2.6</td><td>Total</td><td>132.3 ± 20.7</td><td>134.7 ± 49.8</td><td>132.8 ± 33.7</td><td>133.6 ± 26.3</td><td>150.9 ± 37.1</td></tr><tr><td>Arctic</td><td>31.8 ± 6.1</td><td>22.7 ± 7.8</td><td>32.3 ± 8.0</td><td>30.5 ± 6.4</td><td>13.8 ± 4.2</td></tr><tr><td rowspan="5">Ocean</td><td>Atlantic</td><td>68.8 ± 10.1</td><td>71.7 ± 26.9</td><td>68.4 ± 18.9</td><td>70.0 ± 13.5</td><td>94.4 ± 22.6</td></tr><tr><td>Indian</td><td>13.5 ± 1.9</td><td>19.4 ± 7.4</td><td>15.4 ± 4.3</td><td>14.0 ± 2.7</td><td>19.8 ± 4.5</td></tr><tr><td>Pacific</td><td>18.2 ± 2.7</td><td>21.0 ± 7.7</td><td>16.6 ± 4.5</td><td>19.1 ± 3.6</td><td>22.8 ± 5.7</td></tr><tr><td>Tropical</td><td>60.5 ± 8.8</td><td>58.2 ± 22.9</td><td>53.5 ± 15.7</td><td>55.2 ± 10.8</td><td>85.9 ± 19.8</td></tr><tr><td>Dry</td><td>3.6 ± 0.5</td><td>5.1 ± 2.0</td><td>3.9 ± 1.1</td><td>5.3 ± 1.0</td><td>5.3 ± 1.2</td></tr><tr><td rowspan="3">Climate</td><td>Temperate</td><td>21.2 ± 3.0</td><td>31.7 ± 11.1</td><td>25.8 ± 4.7</td><td>25.0 ± 4.7</td><td>30.9 ± 7.8</td></tr><tr><td>Cold</td><td>44.6 ± 7.9</td><td>38.7 ± 13.4</td><td>47.9 ± 11.8</td><td>46.6 ± 9.5</td><td>28.1 ± 8.1</td></tr><tr><td>Polar</td><td>2.4 ± 0.5</td><td>1.0 ± 0.4</td><td>1.7 ± 0.4</td><td>1.5 ± 0.3</td><td>0.7 ± 0.2</td></tr><tr><td rowspan="2">RCP 8.5</td><td>Total</td><td>139.5 ± 21.9</td><td>145.1 ± 53.2</td><td>150.6 ± 41.4</td><td>150.4 ± 29.4</td><td>155.2 ± 38.0</td></tr><tr><td>Arctic</td><td>36.1 ± 6.8</td><td>29.9 ± 10.2</td><td>39.3 ± 9.7</td><td>37.2 ± 7.5</td><td>16.2 ± 4.7</td></tr><tr><td rowspan="5">Ocean</td><td>Atlantic</td><td>68.8 ± 10.0</td><td>70.0 ± 25.9</td><td>73.1 ± 21.0</td><td>78.5 ± 15.4</td><td>91.2 ± 22.0</td></tr><tr><td>Indian</td><td>14.9 ± 2.1</td><td>22.6 ± 8.7</td><td>20.1 ± 5.8</td><td>15.1 ± 2.9</td><td>21.5 ± 4.8</td></tr><tr><td>Pacific</td><td>19.5 ± 2.9</td><td>22.8 ± 8.4</td><td>18.0 ± 5.1</td><td>19.7 ± 3.7</td><td>26.1 ± 6.4</td></tr><tr><td>Tropical</td><td>64.6 ± 9.4</td><td>56.3 ± 21.9</td><td>65.4 ± 19.8</td><td>63.8 ± 12.7</td><td>89.0 ± 20.6</td></tr><tr><td>Dry</td><td>4.3 ± 0.6</td><td>5.8 ± 2.3</td><td>5.8 ± 1.7</td><td>6.8 ± 1.3</td><td>5.5 ± 1.2</td></tr><tr><td rowspan="3">Climate</td><td>Temperate</td><td>19.0 ± 2.7</td><td>34.4 ± 12.3</td><td>24.1 ± 6.3</td><td>24.6 ± 4.6</td><td>29.2 ± 7.4</td></tr><tr><td>Cold</td><td>49.1 ± 8.7</td><td>47.2 ± 16.2</td><td>53.5 ± 13.2</td><td>53.5 ± 10.5</td><td>30.6 ± 8.6</td></tr><tr><td>Polar</td><td>2.5 ± 0.5</td><td>1.4 ± 0.5</td><td>1.8 ± 0.4</td><td>1.7 ± 0.3</td><td>0.9 ± 0.2</td></tr></tbody></table>
<table><caption>Appendix D. Modelled global discharges (km³ y⁻¹) exported to the oceans in the three scenarios during the 1971–2000 period (historical) and the 2071–2100 period (future). These values are based on a dataset of 338 large rivers. The significance of change was tested using Mann Kendall trend tests, Sen's slopes, and paired t-tests. Significant trends and changes are bold</caption><thead><tr><th></th><th>Historical</th><th>Future<br>(RCP<br>2.6)</th><th>Mann<br>Kendall tau<br>(p-values)</th><th>Sen's<br>slopes (p-<br>values)</th><th>t-tests<br>p-<br>values</th><th>Rel change<br>(% change;<br>RCP 2.6)</th><th>Future<br>(RCP<br>8.5)</th><th>Mann<br>Kendall tau<br>(p-values)</th><th>Sen's<br>slopes (p-<br>values)</th><th>t-tests<br>p-<br>values</th><th>Rel change<br>(% change;<br>RCP 8.5)</th></tr></thead><tbody><tr><td rowspan="2">Global</td><td>25,228 ±<br>2535</td><td>26,201<br>± 2634</td><td>0.08 ±<br>0.06 (0.31<br>± 0.29)</td><td>8.2 ± 6.3<br>(0.31 ±<br>0.29)</td><td>0.27 ±<br>0.28</td><td>973 ± 301<br>(+4 %)</td><td>27,666<br>± 2786</td><td>0.2 ± 0.05<br>(0.01 ±<br>0.04)</td><td>23.6 ±<br>6.4 (0.01<br>± 0.04)</td><td>0.02<br>± 0.05</td><td>2438 ±<br>2664 (+10<br>%)</td></tr><tr><td>3256 ±<br>326</td><td>3762 ±<br>378</td><td>-0.02 ±<br>0.05 (0.51<br>± 0.29)</td><td>-1.28 ±<br>3.18 (0.51<br>± 0.29)</td><td>0.54 ±<br>0.28</td><td>506 ± 41<br>(+16 %)</td><td>4192 ±<br>422</td><td>0.18 ±<br>0.05 (0.03<br>± 0.07)</td><td>10.92 ±<br>3.34 (0.03<br>± 0.07)</td><td>0.04<br>± 0.09</td><td>936 ± 377<br>(+29 %)</td></tr><tr><td rowspan="2">Ocean</td><td>15,201 ±<br>1528</td><td>15,258<br>± 1534</td><td>0.22 ±<br>0.05 (0 ±<br>0.02)</td><td>1.4 ± 0.3<br>(0 ± 0.02)</td><td>0 ±<br>0.01</td><td>56 ± 178<br>(+0 %)</td><td>15,598<br>± 1568</td><td>0.39 ±<br>0.04 (0 ±<br>0)</td><td>2.86 ±<br>0.31 (0 ±<br>0)</td><td>0 ± 0</td><td>397 ± 1548<br>(+3 %)</td></tr><tr><td>3054 ±<br>310</td><td>3350 ±<br>341</td><td>0.05 ±<br>0.05 (0.41<br>± 0.3)</td><td>1.1 ± 1.21<br>(0.41 ±<br>0.3)</td><td>0.42 ±<br>0.3</td><td>296 ± 38<br>(+10 %)</td><td>3783 ±<br>387</td><td>-0.05 ±<br>0.06 (0.41<br>± 0.3)</td><td>-1.09 ±<br>1.21 (0.41<br>± 0.3)</td><td>0.45 ±<br>0.3</td><td>729 ± 350<br>(+24 %)</td></tr><tr><td rowspan="2">Arctic</td><td>3716 ±<br>373</td><td>3831 ±<br>384</td><td>0.24 ±<br>0.05 (0 ±<br>0.02)</td><td>6.74 ±<br>1.55 (0 ±<br>0.02)</td><td>0.01 ±<br>± 0.03</td><td>115 ± 44<br>(+3 %)</td><td>4092 ±<br>411</td><td>0.35 ±<br>0.05 (0 ±<br>0)</td><td>10.47 ±<br>1.6 (0 ±<br>0)</td><td>0 ± 0</td><td>376 ± 393<br>(+10 %)</td></tr><tr><td>13,007 ±<br>1310</td><td>13,006<br>± 1310</td><td>0.27 ±<br>0.05 (0 ±<br>0.01)</td><td>0.2 ±<br>0.04 (0 ±<br>0.01)</td><td>0 ±<br>0.01</td><td>-1 ± 153<br>(+0 %)</td><td>14,115<br>± 1421</td><td>0.47 ±<br>0.04 (0 ±<br>0)</td><td>0.41 ±<br>0.04 (0 ±<br>0)</td><td>0 ± 0</td><td>1109 ±<br>1367 (+9<br>%)</td></tr><tr><td rowspan="2">Atlantic</td><td>1099 ±<br>112</td><td>1249 ±<br>128</td><td>0.31 ±<br>0.05 (0 ±<br>0)</td><td>5.05 ±<br>0.85 (0 ±<br>0)</td><td>0 ± 0</td><td>150 ± 14<br>(+14 %)</td><td>1410 ±<br>145</td><td>0.48 ±<br>0.04 (0 ±<br>0)</td><td>9.22 ±<br>0.92 (0 ±<br>0)</td><td>0 ± 0</td><td>311 ± 129<br>(+28 %)</td></tr><tr><td>4966 ±<br>499</td><td>5087 ±<br>511</td><td>-0.02 ±<br>0.06 (0.51<br>± 0.29)</td><td>-0.99 ±<br>3.72 (0.51<br>± 0.29)</td><td>0.53 ±<br>0.28</td><td>121 ± 59<br>(+2 %)</td><td>4873 ±<br>492</td><td>0.05 ±<br>0.06 (0.39<br>± 0.3)</td><td>3.62 ±<br>3.76 (0.39<br>± 0.3)</td><td>0.39 ±<br>0.3</td><td>-93 ± 496<br>(+ - 2 %)</td></tr><tr><td rowspan="2">Polar</td><td>6007 ±<br>602</td><td>6690 ±<br>670</td><td>0.17 ±<br>0.05 (0.02<br>± 0.06)</td><td>2.96 ±<br>0.8 (0.02<br>± 0.06)</td><td>0.03 ±<br>± 0.07</td><td>684 ± 74<br>(+11 %)</td><td>7077 ±<br>710</td><td>0.37 ±<br>0.04 (0 ±<br>0)</td><td>7.11 ±<br>0.85 (0 ±<br>0)</td><td>0 ± 0</td><td>1071 ± 658<br>(+18 %)</td></tr><tr><td>149 ± 15</td><td>169 ± 17</td><td>0.08 ±<br>0.06 (0.26<br>± 0.27)</td><td>1.39 ±<br>0.92 (0.26<br>± 0.27)</td><td>0.34 ±<br>0.29</td><td>19 ± 2<br>(+13 %)</td><td>191 ± 19</td><td>0.21 ±<br>0.05 (0.01<br>± 0.03)</td><td>3.8 ±<br>0.96 (0.01<br>± 0.03)</td><td>0.01 ±<br>0.05</td><td>42 ± 17<br>(+28 %)</td></tr></tbody></table>
## Appendix E. Fitting of the DOC equation for the selected rivers and each decade

<figure><img src="image_13.png" /></figure>

## Appendix F. α and β values on the selected rivers for each decade and the respective simulated (Fsim), observed (Fobs), and simulated fluxes. The deviation is estimated using the equation calibrated with the entire dataset

<table><thead><tr><th>Catchment</th><th>Decade</th><th>n</th><th>α</th><th>β</th><th>RMSE</th><th>R<sup>2</sup></th><th>p-value</th></tr></thead><tbody><tr><td rowspan="6">Garonne</td><td>Full period (Fabre et al., 2020b)</td><td></td><td>2.79 ± 0.10</td><td>0.020 ± 0.014</td><td>3.3 e-4</td><td>0.004</td><td>0.13</td></tr><tr><td>1970–1979</td><td>35</td><td>3.11 ± 0.29</td><td>0.001</td><td>4.7 e-6</td><td>4.1 e-3</td><td>0.49</td></tr><tr><td>1980–1989</td><td>41</td><td>2.86 ± 0.33</td><td>0.001</td><td>8.5 e-7</td><td>6.8 e-5</td><td>0.49</td></tr><tr><td>1990–1999</td><td>62</td><td>2.32 ± 0.09</td><td>0.001</td><td>3.3 e-6</td><td>2.4 e-3</td><td>0.48</td></tr><tr><td>2000–2009</td><td>79</td><td>2.71 ± 0.15</td><td>0.030 ± 0.023</td><td>7.8 e-5</td><td>0.03</td><td>0.09</td></tr><tr><td>2010–2019</td><td>109</td><td>3.00 ± 0.20</td><td>0.021 ± 0.021</td><td>6.7 e-5</td><td>0.01</td><td>0.22</td></tr><tr><td rowspan="5">Murray</td><td>Full period (Fabre et al., 2020b)</td><td></td><td>22.2 ± 1.97</td><td>0.021 ± 0.003</td><td>4.69</td><td>0.50</td><td>1.7 e<sup>-12</sup></td></tr><tr><td>1980–1989</td><td>87</td><td>13.6 ± 1.44</td><td>0.010 ± 0.002</td><td>1.09</td><td>0.52</td><td>1.6 e<sup>-5</sup></td></tr><tr><td>1990–1999</td><td>115</td><td>13.5 ± 1.37</td><td>0.008 ± 0.002</td><td>0.91</td><td>0.42</td><td>4.4 e<sup>-6</sup></td></tr><tr><td>2000–2009</td><td>224</td><td>7.94 ± 0.92</td><td>0.004 ± 0.001</td><td>0.84</td><td>0.15</td><td>5.8 e<sup>-5</sup></td></tr><tr><td>2010–2019</td><td>30</td><td>2.04 e<sup>10</sup></td><td>2.62 e<sup>7</sup></td><td>1.92</td><td>0.87</td><td>0.99</td></tr><tr><td rowspan="3">Solimoes</td><td>Full period (Fabre et al., 2020b)</td><td></td><td>4.67 ± 0.50</td><td>0.568 ± 0.568</td><td>0.001</td><td>0.004</td><td>0.28</td></tr><tr><td>2000–2009</td><td>61</td><td>5.76 ± 1.08</td><td>2.002 ± 2.002</td><td>6.00 e-4</td><td>0.03</td><td>0.17</td></tr><tr><td>2010–2019</td><td>67</td><td>4.14 ± 0.55</td><td>0.064</td><td>2.50 e-5</td><td>6.1 e-5</td><td>0.48</td></tr><tr><td rowspan="3">Yenisei</td><td>Full period (Fabre et al., 2020b)</td><td></td><td>13.98 ± 0.46</td><td>0.967 ± 0.085</td><td>0.24</td><td>0.74</td><td>1.1 e<sup>-24</sup></td></tr><tr><td>2000–2009</td><td>40</td><td>12.3 ± 0.75</td><td>0.757 ± 0.161</td><td>5.0 e-4</td><td>0.71</td><td>1.7 e<sup>-5</sup></td></tr><tr><td>2010–2019</td><td>214</td><td>14.5 ± 0.56</td><td>1.030 ± 0.099</td><td>0.30</td><td>0.74</td><td>5.2 e<sup>-21</sup></td></tr></tbody></table>

## Data availability

SOC data set is available at https://www.fao.org/soils-portal/data-hub/soil-maps-and-databases/harmonized-world-soil-database-v12/

en/. Climate data sets are available at https://worldclim.org/data/index.html. The code and the data used in this study can be found in the following GitHub repository: https://github.com/fabrecle/Future_DOC_fluxes, except for future discharge data that
should be asked to MTHvV. Correspondence and requests for materials
should be addressed to CF.

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