Main

River networks form a crucial link between the terrestrial, atmospheric and marine carbon cycles, storing, transforming and exporting inorganic and organic carbon3,4. Globally, rivers and streams emit an estimated 2.0 (1.6–2.2) Pg C year−1 to the atmosphere as CO2, along with 28 (16.7–39.7) Tg of CH4 per year (refs. 1,2,4,5). These carbon emissions are equivalent to 59% of net terrestrial carbon uptake (net ecosystem exchange)7 or about 1.8% of terrestrial gross primary production (GPP)6. Export of carbon by rivers is often the second largest component of ecosystem carbon loss after soil respiration8. The age of the carbon fuelling river emissions to the atmosphere—whether supplied by rapid, sub-decadal or much older sources—is a notable knowledge gap in pre-industrial, contemporary and future carbon cycles5.

Rivers are at the interface of carbon cycling across timescales. A large part of river CO2 emissions is generated by a combination of terrestrial respiration of organic carbon recently fixed by photosynthesis and within-river production and respiration9,10,11. Thus, river CO2 emissions are generally considered a component of the contemporary carbon cycle fuelled by annual to decadal carbon turnover3,5,6. However, rivers also transport older carbon, such as organic matter in particulate12,13 and dissolved forms14,15,16, whereas aged riverine DIC17,18, CO2 (refs. 19,20) and CH4 (ref. 21) have all been directly observed.

River DIC, CO2 and CH4 ages vary based on the source of carbon delivered to rivers. The oldest carbon stores in river catchments are rock-derived (‘petrogenic’ or geologic) carbon in carbonate minerals and rock organic matter. Chemical weathering and erosion can mobilize these carbon sources and route them into rivers22,23,24,25,26. By contrast, heterotrophic respiration of soil organic matter can produce CO2 and CH4 ranging in age from several years to millennia27,28. These gases can be dissolved in water and moved from soils and sediments into stream and river waters. Older carbon, which can be sourced from deeper in soil profiles29, represents a reintroduction of previously stored soil carbon to the contemporary carbon cycle and, where associated with anthropogenic perturbations such as land-use change, may represent a source of anthropogenic greenhouse gas emissions15,18,30,31. We define these three potential river carbon sources as ‘decadal’ (fixed into the biosphere through photosynthesis since 1955), ‘millennial’ (biospheric carbon that is hundreds to several thousands of years old) and ‘petrogenic’ (older than about 55,000 years)3,32. To understand the role of global river carbon emissions in the climate system, it is essential to determine the relative contributions of decadal inputs versus these ‘old’ (millennial-aged and petrogenic) carbon sources.

Here we constrain the age and source of river carbon emissions at the global scale using the radiocarbon composition (reported as fraction modern, F14C (ref. 33)) of river DIC, CO2 and CH4 (Fig. 1 and Supplementary Information section 1). The F14C value of DIC provides a surrogate for the isotope composition of river CO2 emissions owing to the fast equilibration times between DIC and CO2 relative to water flow path lengths (Supplementary Information section 2). We provide an extra subset of paired DIC and CO2 F14C measurements to show that these values are generally within 0.02 of one another (for F14C of 1.0 versus 0.98, this equates to 162 14C years), which, although higher than analytical uncertainty, is 5–20 times smaller than the variability we find across the entire database assembled here (Extended Data Table 1 and Supplementary Fig. 1). As such, the large DIC component of our database allows us to robustly assess the radiocarbon content of river CO2 emissions. The assembled database contains 1,141 published observations and 54 new measurements (1,195 total from 67 distinct studies; Supplementary Table 1) and includes observations across most of the main land masses, biomes and lithologies, including North and South America, Iceland, Europe, Scandinavia, East Africa, China, Southeast Asia, Australia and Antarctica (Fig. 1a, Supplementary Figs. 2 and 3 and Supplementary Information section 1). Overall, the distribution of sample locations captures global proportions of the main lithologies and biomes (Supplementary Information section 1 and Supplementary Fig. 4).

Fig. 1: Global 14C patterns in river DIC, CO2 and CH4.
figure 1

a, Map of sampling locations. b, All F14C values assembled in the database separated by compound. The dashed horizontal line shows F14C = 1.0 (atmospheric CO2 in 1955 CE, panel c), mean age in uncalibrated 14C years is indicated on the right axis, values in parentheses indicate percentage of observations for which F14C > 1.0 (younger than 1955 CE, for which no 14C age can be calculated and are considered ‘modern’); lines in the middle of the boxes represent the median, box limits represent the upper and lower quartiles and whiskers extend to 1.5 times the interquartile range. c, All F14C values assembled in the database plotted by year of sample collection and shown in the context of atmospheric 14CO2 (1950 to 2019 CE; black line; data from ref. 34). The dashed horizontal line shows F14C = 1.0; F14C values are shown separated by compound.

Full size image

Age of river CO2 and CH4 emissions

The mean F14C of all river DIC and CO2 measurements were 0.914 ± 0.184 (±1σ) and 0.961 ± 0.074, respectively, equivalent to radiocarbon ages of 722 ± 1,264 and 320 ± 483 14C years. The mean F14C for CH4 was 0.879 ± 0.167 (1,036 ± 1,364 14C years), but because we found a more limited number of available 14CH4 observations, we focus our analysis on DIC and CO2 measurements (Extended Data Table 1). There is notable variability in atmospheric 14CO2 content over the past 70 years, driven by nuclear weapons testing (increasing F14C values to above 1.0 since 1955 CE), dilution by fossil fuel emissions (lowering F14C values) and variability in rates of natural 14C production in the troposphere34 (Fig. 1c). River CO2 and CH4 with F14C values > 1.0 are thus expected if the degradation of organic matter formed through photosynthesis since 1955 is generating these greenhouse gases.

Most F14C observations were less than 1.0 (62–74% for DIC, CO2 and CH4; Fig. 1b and Supplementary Fig. 5), indicating that carbon older than 1955 is contributing to river emissions. The remaining 26–38% of F14C observations were greater than 1.0, which can be explained by inputs from decadal carbon sources. To further explore the youngest carbon sources to river systems independent of atmospheric 14CO2 variability, we calculated F14Catm, which represents the fraction modern for each observation after normalizing to atmospheric 14CO2 in the year of sample collection35. The database reveals 430 (36%) F14Catm values that are greater than 1.0 (Extended Data Fig. 1). In many terrestrial ecosystems, the residence time of carbon is very short, on the order of less than 20 years (refs. 36,37). The highest river F14Catm values suggest an efficient route for ecosystem respiration into some streams and rivers. Otherwise, the F14Catm values suggest a declining trend from 1991 to 2023 (R2 = 0.04, P ≪ 0.001; Extended Data Fig. 1).

Low (old) F14Catm values were prevalent in catchments of all sizes (Fig. 2a and Extended Data Fig. 2). We would expect larger catchments to be less affected by specific processes that mobilize old carbon (for example, localized erosion or groundwater inputs) and therefore be more likely to find older carbon in smaller catchments. By contrast, we found that F14Catm values were lower (older) as catchments got larger (Extended Data Fig. 2), suggesting that contributions of old carbon to river CO2 from deeper hydrologic flow paths or exposed old carbon stores are occurring across large scales.

Fig. 2: Influence of catchment size, river-reach biome and lithology on 14C in river DIC, CO2 and CH4.
figure 2

a, Normalized F14Catm values for DIC, CO2 and CH4 separated by catchment size, either ≤10 km2 or >10 km2 (Methods and Supplementary Fig. 6); statistical difference is indicated by the P value (shown at the top) derived from an unpaired two-sample Wilcoxon test. b, F14Catm values separated by lithology of the river reach (within a 1-km2 radius of the sampling location) as defined in HydroATLAS and binned for comparison (Methods and Supplementary Fig. 3); statistically significant differences are indicated by P values when comparing across all three lithologies using a Kruskal–Wallis test (shown at the top) and unpaired two-sample Wilcoxon tests (P values and horizontal bars). c, F14Catm values separated by the biome of the river reach (Methods and Supplementary Fig. 2); lowercase letters indicate statistically significant differences (P < 0.05) using a Kruskal–Wallis test (P value shown at the top) and Conover–Iman post hoc. The horizontal black line in each panel represents the mean-normalized F14Catm for all samples; box and whisker dimensions follow Fig. 1b.

Full size image

An important spatial predictor of F14Catm was lithology (Fig. 2b), with catchments underlain by sedimentary lithologies, including carbonates, having a lower mean F14Catm (0.848 ± 0.159, median = 0.873 for DIC, CO2 and CH4) compared with igneous (0.903 ± 0.156, median = 0.959; P = 4.5 × 10−5) and metamorphic (0.957 ± 0.092, median = 0.983; P = 3.9 × 10−15) lithologies. Weathering of carbonate minerals and rock organic carbon in sedimentary lithologies contributes petrogenic carbon (F14C ≈ 0) to rivers from weathering processes38,39 (Supplementary Information section 2); these petrogenic contributions from rock weathering and oxidation would be unlikely in igneous or metamorphic lithologies. Therefore, other 14C-depleted carbon contributions are required to explain the prevalence of F14Catm values of less than 1.0 across all lithologies.

The variability of river F14Catm values across biomes was statistically significant (Fig. 2c), but there were no clear trends based on differences between biomes. The lowest F14Catm values (oldest) were collected from the montane grassland and tropical grassland and shrubland biomes. In high-elevation zones, climatic and geomorphic conditions can promote erosion (for example, steep channel slopes, landslides), which could increase petrogenic inputs from the underlying sedimentary lithologies and thus lower F14Catm values. In other more productive temperate and tropical biomes, decadal-aged to millennial-aged carbon inputs could be supplied from recently fixed organic carbon and older soil carbon pools27 such as peat19,40, particularly where soils have been affected by drainage31 or agriculture15.

To further explore the potential drivers of river DIC F14Catm, we applied a random forest model to determine which parameters could explain the F14Catm DIC dynamics in the database41. For large catchments (>10 km2 in area), the most important parameters (in descending order of importance) were: mean annual precipitation, mean elevation, mean annual air temperature, karst percentage cover and forest percentage cover of the catchment (Extended Data Fig. 3). For small catchments (≤10 km2), these were slightly different: mean elevation, soil organic carbon content, soil sand content and mean annual air temperature of the river reach (within a 1-km2 radius; Extended Data Fig. 4). Mean elevation (large and small catchments) and karst area (large catchments only) had a negative relationship with F14Catm, indicating that catchments with higher elevations and carbonate lithologies released more 14C-depleted (older) DIC. Mean annual precipitation (large catchments) and temperature (large and small catchments) were generally positively related to F14Catm, although there was an upper limit to this influence in large catchments: above 2,000 mm rainfall and above 20 °C, F14Catm tended to decrease (Extended Data Fig. 3b,d). This suggests that catchments receiving higher precipitation and with warmer temperatures tended to release less 14C-depleted (younger) DIC, although the limit to this mechanism indicates that more arid or especially warm and wet regions may store more carbon and/or release older carbon. In small catchments, the high (>15) increase in the mean square error values from the random forest model for soil organic carbon and sand content demonstrate the potential importance of small-scale controls on the age of DIC released by rivers, influencing organic carbon mobilization and hydrologic flow paths. These results, and the influence of lithology and biome, highlight that river DIC and CO2 are driven by more than just recently fixed carbon, with important contributions from millennial and petrogenic carbon sources.

Old CO2 emitted from global rivers

To better constrain the origin of river CO2 emissions, we modelled the potential contributions from decadal and millennial carbon sources after accounting for published estimates of river petrogenic inputs from carbonate mineral and rock organic matter weathering. Owing to limited data availability, it is not possible to correlate our F14C data with catchment-specific weathering information (for example, solute export22), so we take a global view using our mean F14C DIC values and assess the petrogenic inputs using global estimates of carbonate and rock organic carbon weathering rates. Using the global river CO2 emission flux of 2.0 ± 0.2 Pg C year−1 (refs. 5,6), a lateral export of DIC to the oceans of 0.5 Pg C year−1 (ref. 42), we then account for the estimated range of petrogenic inputs by rock weathering of 0.150–0.218 Pg C year−1 (refs. 22,39). The non-petrogenic flux of river CO2 and DIC is thus 2.28–2.35 Pg C year−1 and has an F14C value of 0.978–1.007 (Methods; equation (7)).

The remaining total DIC flux, having accounted for petrogenic carbon inputs, must be some mixture of: (1) DIC supplied from soil or atmospheric CO2 during carbonate and silicate weathering; (2) CO2 derived from ecosystem respiration supplied by hydrological flow paths through shallow and deeper soils; (3) CO2 derived from within-river heterotrophic and autotrophic respiration; and (4) invasion of atmospheric CO2 if rivers are undersaturated with respect to the atmosphere. We note that (1) and (2) may be supplied concurrently in some systems, whereas (2) and (3) include direct soil respiration plus soil decomposition products that can be respired within rivers, such as dissolved and particulate organic carbon43,44. Carbon inputs (1) to (4) can be decadal in age (F14C value similar to the atmosphere; Fig. 1c), whereas (1) to (3) can be millennial in age if derived from deeper soil respiration flushed to rivers laterally by hydrological flow paths.

Using the non-petrogenic component of the river DIC pool (vertical CO2 emission plus lateral DIC export) of 2.28–2.35 Pg C year−1 and its F14C value of 0.978–1.007, we use a two-endmember isotope mixing model and Monte Carlo simulation to estimate the remaining proportional contributions of carbon inputs from decadal and millennial carbon sources (Methods and Extended Data Fig. 5). The mean modelled proportional contribution to global river CO2 from decadal carbon sources was 0.41 ± 0.16 (±1σ), equivalent to a vertical emission flux of 0.9 ± 0.3 Pg C year−1; for millennial sources, the mean proportional contribution was 0.52 ± 0.16, or 1.1 ± 0.3 Pg C year−1 (Table 1). When petrogenic and millennial soil carbon inputs are combined, we estimate that these old carbon sources (millennial or greater in age) could be contributing as much as 1.2 ± 0.3 Pg C year−1 to the atmosphere from global river systems. To independently assess the outputs of this petrogenic-constrained, two-endmember isotope mixing model, we also ran a Bayesian isotope mixing model (Supplementary Information section 3), which quantified potential contributions from three carbon sources (decadal, millennial and petrogenic) without any priors other than F14C ranges for each endmember (Extended Data Fig. 6 and Supplementary Table 2). The two-endmember Monte Carlo simulation and three-endmember Bayesian analysis outputs were in agreement with one another (Table 1). Altogether, these findings suggest that across both biome and lithological variability, a third to two-thirds of river CO2 emissions are derived from old carbon sources (Table 1 and Supplementary Table 2).

Table 1 Modelled source contributions to global river CO2 emissions
Full size table

A new conceptual model of river CO2

Widespread contribution of old carbon to river CO2 emissions challenges existing models (Fig. 3a). River CO2 emissions are commonly assumed to be dominated by the lateral routing of terrestrial GPP, alongside within-river production3,4,5,6. Some estimates of global river CO2 emissions state that petrogenic carbon sources are minor, based on a limited number of 14C-DIC observations6. Other inland water CO2 emission syntheses have noted that millennial and petrogenic inputs are a substantial knowledge gap32, and where these old sources are included in analyses, they are not considered a direct contributor to river CO2 release3,8. Also, the influence of deeper soil (millennial) and groundwater (millennial/petrogenic) inputs of CO2 to river carbon emissions is assumed to be less important as river size increases5,6,10, affecting only relatively short river reaches5,45. This relative decrease in terrestrial and groundwater inputs is thought to be offset by increased within-river CO2 production and, potentially, riparian wetland inputs5,6,10,46. These conceptual models, in which within-river production offsets groundwater inputs as river size increases and/or terrestrial GPP dominates, cannot account for the sizeable contribution of old carbon to river CO2 emissions evident in our analysis across biome, lithology and catchment size. As a result, current numerical models of river carbon transport and emission also fail to account for inputs from old carbon sources.

Fig. 3: The importance of river CO2 emission age for the global carbon cycle.
figure 3

a, Existing model in which river CO2 is only derived from young, rapid-cycling carbon (decadal-aged = green); lateral DIC export to the coast is considered a mixture of decadal and petrogenic inputs (grey). By accounting for these river carbon losses, it is estimated that 1.7 Pg C year−1 of anthropogenic carbon emitted to the atmosphere may be accumulating in the rapid-cycling terrestrial carbon pools3; anote that this estimate is based on a lower estimate of vertical river CO2 emissions of 1.51 Pg C year−1. b, Revised conceptual model based on the assembled F14C values of river DIC, CO2 and CH4 presented here; millennial carbon inputs are needed from organic matter degradation in soils or river sediments (orange) as well as petrogenic carbon from rock weathering to explain the observed F14C values in our database. This revised conceptual model indicates a loss of carbon from an old (millennial) store on land through vertical river CO2 emissions; a first-order estimate of the impact on the partitioning of carbon in the biosphere and soils is provided (b).

Full size image

On the basis of our findings, we propose a new conceptual model of river CO2 emissions that accounts for a mixture of decadal-aged and millennial-aged inputs from the biosphere and their impacts on and response to carbon cycle perturbations (Fig. 3b). There are further contributions from petrogenic sources (carbonate weathering, rock oxidation) that may or may not be vulnerable to catchment perturbations in the same way as the biosphere (Extended Data Fig. 7).

The second largest proportion (41 ± 16%) of the CO2 emitted by rivers is attributed to rapid, decadal carbon cycling through ecosystems (Fig. 3b). Most of this decadal-aged proportion of river CO2 is probably produced at the near surface through root respiration and/or surface litter decomposition. Some of this CO2 may be used during chemical weathering of carbonate and silicate minerals to generate DIC and some carried as dissolved CO2 laterally to rivers and streams. Within-river aquatic metabolism is likely to supplement these rapid-cycling river CO2 emissions10 alongside degradation of young and reactive river dissolved and particulate organic carbon44,47. This fraction of river CO2 emissions is a loss pathway from ecosystem respiration, whose transit time for carbon is typically on the order of years to decades37.

The largest proportion (52 ± 16%) of river CO2 emissions is sourced from millennial-aged carbon on the basis of the global-scale assessment presented here (Fig. 3b). Hydrological flow paths can mobilize dissolved CO2 and DIC produced by soil respiration from deeper in the soil profile. This depth may coincide with the production of CO2 through root respiration, linking decadal-aged to millennial-aged CO2 sources. However, inputs of older CO2 from deeper in soil profiles, recently eroded or degraded soil surfaces, hyporheic zones and degradation of older river dissolved and particulate organic carbon could all contribute13,48.

The remaining 7 ± 1% of river CO2 emissions is derived from petrogenic carbon (Fig. 3b). Hydrological flow paths can also readily reach deeper into the bedrock underlying soils, supplying rivers49, soils26 and plants50, and connectivity can also occur where bedrock is exposed or soil coverage is minimal. The petrogenic carbon contained within carbonate rocks and rock organic matter can thus be mobilized by chemical weathering and erosion and delivered to river systems (Fig. 3).

The last two old (millennial and petrogenic) components of river CO2 may not necessarily have contributed to local ecosystem respiration. Instead, they represent a leak of older terrestrial carbon that escapes to the atmosphere through river surfaces (Extended Data Fig. 7).

Implications for global carbon budget

River CO2 emissions represent a mirror of ecosystem processes liberating DIC and CO2 from organic and mineral carbon stores (Extended Data Fig. 7). Having shown that more than 50% of river CO2 emissions are derived from these old organic or mineral sources, we assess their impact on relevant terrestrial carbon stores and budgets.

Decadal-aged river CO2 emissions are about 1% of global terrestrial GPP (109 Pg C year−1 (ref. 6)). As such, our findings suggest that 0.9 ± 0.3 Pg C year−1 may be leaving this rapid carbon loop from river surfaces. Although this is a relatively small annual flux compared with global GPP, over decadal to centennial timescales, these losses are large and mean that river CO2 emissions need to be accounted for in terrestrial carbon budgets.

The millennial-aged river CO2 emissions identified here are 2–3% of global soil heterotrophic respiration rates (39 to 51 Pg C year−1 (refs. 8,51)). River CO2 emissions therefore act as a loss term from older soil organic carbon reservoirs. When compared with the total stock of soil organic carbon (roughly 840 ± 280 Pg C (ref. 27)), river CO2 loss from this store (1.1 ± 0.3 Pg C year−1; Table 1) would suggest soil carbon residence times of about 400–1,400 years at steady state. This is within the range of soil age values from bulk 14C activity27 and could suggest that hydrological flow paths are an important carbon loss pathway from deeper soil storage49.

Our insight into the age of river CO2 emissions can be used to reassess an existing mass balance of land to ocean carbon transfers and their impact on the carbon cycle3 (Fig. 3). With no constraint on river carbon age, this previous analysis3 calculates that terrestrial ecosystems take up about 2.3 Pg C year−1 of anthropogenic carbon (26% of fossil fuel emissions), but only store about 1.7 Pg C year−1, with the remaining approximately 0.6 Pg C year−1 released back to the atmosphere by rivers, transported to coastal oceans or stored in sediments3. Here we suggest that only 41 ± 16% of river CO2 emissions (0.9 ± 0.3 Pg C year−1) could contain recent anthropogenic-derived carbon (decadal-aged or younger). This means that the riverine loss from this decadal carbon store is approximately half of the total flux used in this previous mass balance3. This budget adjustment suggests that the decadal-aged biosphere is storing more anthropogenic carbon than previously suggested3, whereas the remaining river CO2 leak is from soil and geologic carbon stores that predate widespread anthropogenic fossil fuel CO2 emissions (Fig. 3b). This fundamentally changes our inference of where anthropogenic carbon resides within the main Earth system carbon reservoirs.

Whether or not anthropogenic perturbation has increased the leak of old carbon to the atmosphere through rivers that we observe here remains a notable knowledge gap. The dataset shows a trend of increasing age of F14Catm in river DIC, CO2 and CH4 during the observation period (Extended Data Fig. 1). This could indicate increasing emissions of old carbon through time owing to destabilization of global soil carbon stocks14,15,31,48,52 and changes to weathering, erosion and rock oxidation rates22,38,53 as a result of climate and anthropogenic perturbations. Anthropogenic climate change may increase CO2 supply to rivers as soils warm and/or get wetter and microbial respiration increases54, whereas the delivery of DIC and CO2 from rock weathering may also increase as landscapes warm22,53. However, we do not know whether the trend in Extended Data Fig. 1 is because of increased perturbation (Extended Data Fig. 7), the declining atmospheric 14CO2 signal moving through the biosphere (Fig. 1c), sampling bias (Supplementary Information section 4) or a combination of these. Regardless, our analysis indicates that river CO2 emissions are responsive to inputs from old carbon sources and could increase under direct anthropogenic disturbance regimes such as landscape drainage, clearance, burning and agricultural soil cultivation, as well as because of anthropogenic climate change.

Knowledge of how the source of river CO2 emissions has changed through time is at present data-limited—we lack time series samples of river 14C-DIC and 14C-CO2—and we have no way as yet to reconstruct the source of river carbon emissions in the past. These observations are crucial for improving our ability to partition and explain the drivers of this substantial global carbon flux55. Nevertheless, we provide evidence for a previously unrecognized, planetary-scale release of old, pre-industrial-aged carbon from land to the atmosphere through rivers. River emissions are thus vulnerable to perturbations of short-term carbon cycling (GPP), millennial soil carbon stocks and geologic carbon cycling, which can route carbon from catchments to the atmosphere through river surfaces (Extended Data Fig. 7).

Methods

Study approach and methods summary

Our aim was to analyse global-scale patterns of the age and source of river carbon emissions. Radiocarbon studies of river DIC, CO2 and CH4 have been conducted from ecological to geochemical perspectives and varying degrees in between. As a result, widely differing sets of variables are available from each study, making river to river comparisons difficult. Here we instead focus on a global approach to compare the 14C content of river CO2 emissions and the probable carbon source components within this flux to the atmosphere.

We first assembled a database of measurements of the radiocarbon content of river DIC, CO2 and CH4 from the literature and then added a subset of unpublished data. Radiocarbon content is presented here as F14C. In conventional 14C dating, F14C = 1.0 represents 1950 CE; however, in relation to carbon cycling and the atmospheric 14CO2 record (Fig. 1c), F14C < 1.0 indicates carbon older than 1955 CE and F14C > 1.0 is carbon younger than 1955 CE (Fig. 1b). The database was dominated by DIC measurements, so we demonstrated that DIC and CO2 are probably in isotopic equilibrium (Supplementary Information section 1), allowing us to explore the F14C content of global river CO2 emissions from the database.

Owing to inconsistencies in how catchment characteristics were reported in the literature from which we assembled the radiocarbon measurements (if they were reported at all), we used a global database of hydrological-environmental characteristics (HydroATLAS56) to extract key catchment information for each sampling location in a consistent manner (for example, catchment size, lithology, biome).

The resolution limits of HydroATLAS mean that, for catchments <10 km2 in size, it was difficult to ensure that the correct catchment characteristics were extracted. Further, not all data in HydroATLAS are available at the catchment scale. For this reason, we extracted data from HydroATLAS at both the reach (1-km radius from the sampling location) and the catchment scale and use the reach characteristics for small catchments ≤10 km2 and the catchment characteristics for large catchments >10 km2.

We used the HydroATLAS information to explore the potential underlying drivers of the F14C content of river DIC, CO2 and CH4, first through mapping key characteristics such as catchment size, lithology and biome (Fig. 2) and then using a random forest model to explore a wide range of catchment characteristics (such as climate and soil properties). Owing to the catchment size issue identified above, we ran the model separately for catchments ≤10 km2 and >10 km2 to ensure that we did not incorporate anomalous catchment characteristics into the model.

To determine the potential contributions of different carbon sources, defined here as decadal, millennial and petrogenic carbon sources, we used a two-endmember isotope mixing model with Monte Carlo simulations, constrained by known inputs of petrogenic carbon to river DIC from weathering. To independently assess this approach, we also independently used an unconstrained three-endmember Bayesian isotope mixing model. We then used these estimates of the proportional contribution of different carbon sources to global river DIC to estimate the magnitude of river CO2 emissions to the atmosphere derived from old carbon (millennial or older).

New data

We include data from three unpublished works in our analysis. These include dissolved CO2, CH4 and DIC data from the UK, Taiwan, Cambodia and China.

Eight dissolved CO2 and three dissolved CH4 samples were collected for 14C analysis from a range of urban rivers and canals in London in September 2021. Paired CO2 and CH4 samples were collected from the River Brent, Regent’s Canal and the River Thames; CO2 samples were collected from Bow Creek and more sites on Regent’s Canal and the River Thames (Supplementary Table 1). CO2 samples were collected using the super headspace method57, with samples collected by equilibrating 3 l of water with 1 l of CO2-free headspace for three minutes and the headspace injected into a molecular sieve cartridge for transport to the National Environmental Isotope Facility (NEIF) Radiocarbon Laboratory in East Kilbride, UK. CH4 samples were collected with the coiled membrane method21, in which water was slowly pumped through a hydrophobic, gas-permeable membrane into a headspace containing ambient air. The vessel was left to collect CH4 overnight and recovered after 12–18 h; the headspace was collected into foil gas bags and transported by land to the NEIF Radiocarbon Laboratory. CH4 samples were corrected for the ambient air in the headspace following refs. 21,52.

River water DIC samples from Taiwanese rivers and the Mekong River in Cambodia were collected using the methods outlined in refs. 18,58. In Taiwanese rivers, 1-l sampling bottles were submerged into the middle of the channel using a weighted Teflon sampler. On the Mekong River, near-surface samples were collected using a horizontally mounted Niskin-type sampler. River water was then filtered directly into preweighed 1-l foil bags (FlexFoil PLUS) through polyethersulfone filters (0.22 μm) using syringe-mounted filtration, with care to avoid any atmospheric air mixing. The foil bag was filled with approximately 200–500 ml of filtered river water (depending on expected DIC concentration) and then gently squeezed before closing to ensure that no air was trapped. The filled bag was reweighed and stored at 4 °C during fieldwork, before shipping to the UK, in which the sample was frozen within about a week of collection58.

The UK, Taiwan and Cambodia samples were processed at the NEIF Radiocarbon Laboratory. CO2 samples were retrieved from the molecular sieve cartridges by heating to 425 °C. CH4 samples were passed through soda lime and molecular sieve filters to remove residual CO2 and then combusted to CO2 using platinum bead catalyst at 950 °C. For the DIC samples, orthophosphoric acid was added to the defrosted, filtered water sample in the foil bag and the degassed CO2 collected, isolated and purified using cryogenic traps58. The CO2 for 14C analysis was then cryogenically recovered and graphitized using Fe–Zn reduction and analysed for 14C content by Accelerator Mass Spectrometry (AMS) at the Scottish Universities Environmental Research Centre in East Kilbride. For quality assurance, standard materials of known 14C content were processed alongside the samples.

We collected 14C samples for DIC from 19 river sites on or draining the Qinghai–Tibet Plateau. Samples were collected in 2017, 2018 and 2023, with five sites visited in both 2018 and 2023 (MD, NQ, TNH, XD and ZMD; Supplementary Table 1). River water samples were filtered to 0.45 μm using polyethersulfone filters and collected in acid-washed (10% HCl v/v, 24 h) 1-l HDPE Nalgene bottles rinsed three times with filtered river water before collection. Samples were kept refrigerated between collections and analysis. DIC was processed to CO2 for 14C analysis within 2–3 weeks of collection.

Samples collected in 2017 and 2018 were processed and analysed at the Peking University AMS facility (PKU_AMS) in Beijing, China, following ref. 59. Water samples were acidified with phosphoric acid and shaken and heated to 75 °C for 2 h to convert all DIC to CO2. The CO2 was then purified cryogenically on a vacuum line and graphitized using zinc reduction. Samples collected in 2023 were processed and analysed at the Beta Lab AMS facility in Miami, Florida, USA. Samples were acidified using phosphoric acid and stripped from the water by bubbling pure N2 or Ar gas through the sample. The resulting CO2 was collected cryogenically and graphitized using hydrogen reduction of the CO2 sample over a cobalt catalyst. In both the PKU and Beta labs, reference standards, internal QA samples and backgrounds were processed alongside the samples.

F 14C data assembly from the literature

We initially compiled our database using the 209 DIC values available in ref. 17. We then searched for further studies of river DIC, CO2 and CH4 14C values from the peer-reviewed literature. We searched and compiled studies published before 2023 using Web of Science and Google Scholar60 (Supplementary Fig. 7). The following string terms were used in the search: (dissolved inorganic carbon OR DIC OR carbon dioxide OR CO2 OR methane OR CH4) AND (14C OR radiocarbon) AND (stream OR river); (dissolved inorganic carbon OR DIC OR carbon dioxide OR CO2 OR methane OR CH4) AND (14C OR radiocarbon). We undertook the search several times to ensure completeness. Measurements from groundwater seeps or similar extreme endmembers were excluded, extracting only data from flowing, open water streams and rivers. We augmented these search results with our own knowledge of the literature for which studies were missed in the above searches. Ultimately, we were able to obtain 1,195 observations of fluvial DIC, CO2 and CH4 14C from 67 studies, including our own data collection outlined above.

From each study, we collected the following information when available (Supplementary Table 1):

  • Site identifier (ID)

  • Date and year of sample collection

  • Brief site description

  • Catchment name

  • Compound (DIC, CO2 or CH4)

  • DIC concentration (converted to µmol l−1)

  • δ13C (‰ VPDB) and associated uncertainty

  • δ2H-CH4 (‰) and associated uncertainty

  • Radiocarbon publication code

  • Radiocarbon content in F14C (fraction modern) and Δ14C (‰) and associated uncertainty

  • Radiocarbon age (14C years) and associated uncertainty

  • Sample water pH

  • Sample water temperature (°C)

  • Latitude and longitude, country and hemisphere of sampling location

  • Water type (river, stream and so on)

  • Brief method outlines for sample collection and processing

  • Exact watershed size (km2)

We then provided flags for the coordinates and data uncertainties collected from the literature.

For the coordinates flags:

  • Exact sampling location from the original study

  • General but not exact location provided in the original study (for example, centre of catchment)

  • Estimated on the basis of the map in the original study in conjunction with Google Earth Pro

For the uncertainty flags:

  • Uncertainties provided in the original study

  • Average uncertainties from the facility in which samples were analysed

When data were reported in Δ14C, we also calculated F14C and vice versa:

$${\Delta }^{14}{\rm{C}}=\mathrm{1,000}\times ({F}^{14}{\rm{C}}\times {\exp }^{-\lambda (y-1950)}-1)$$
(1)
$${F}^{14}C=\left(\left(\frac{{\Delta }^{14}{\rm{C}}}{\mathrm{1,000}}\right)+1\right){\times \exp }^{\lambda (y-1950)}$$
(2)

in which λ = 1/8,267 year−1 and y is the year of sample collection.

Some locations in the database were sampled more than once. This is because of a combination of experimental approaches, for example, repeat sampling, exploration of temporal variations and method development. When a sample location was repeat sampled more than four times in a calendar year (that is, more than 0.5% of all observations), we took the average of the F14C observations at that location for that year and recalculated a new radiocarbon age and uncertainty61. This removal left n = 1,020 observations (Extended Data Table 1).

Normalization of F 14C values to atmospheric 14CO2

We normalized the F14C values in the database for each measurement to the F14C-CO2 content in the atmosphere in the year of sample collection, defined as F14Catm:

$${F}^{14}{{\rm{C}}}_{{\rm{atm}}}=\frac{F{m}_{{\rm{sample}}}}{F{m}_{{\rm{atmosphere}}}}$$
(3)

in which F14Catm is the normalized F14C value of the sample (Fmsample in fraction modern) divided by the F14C value of the atmosphere in the year of sampling (Fmatmosphere in fraction modern)35.

The atmospheric F14C-CO2 values used in equation (3) were compiled from 1950 to 2023. Atmospheric 14CO2 is from ref. 34 for 1950 to 2019. For 2020 to 2023, annual 14CO2 was estimated by extrapolating the declining annual trend of 14CO2 observed between 2014 and 2019. This period was chosen because the curve seemed to be flattening during this period relative to the steeper decline seen earlier in the data (Fig. 1c). Although we note that the relative contributions of contemporary biomass and soil respiration to river carbon emissions are probably not globally consistent and cannot be captured by normalizing to a single year atmospheric 14CO2 value, this method allows a consistent normalization of the entire database irrespective of individual river catchment characteristics.

Paired DIC–CO2 14C measurements

To explore the relationship between F14C in DIC and CO2 emissions, we compiled 15 paired F14C measurements of DIC and CO2 (Supplementary Fig. 1, Supplementary Table 3 and Supplementary Information section 2). These paired samples cover 11 distinct sites and a river pH range of 4.2–7.7, indicative of the range of pH found in natural waters. Six of these paired observations come from ref. 19, collected from two peatland headwater streams, one in north England (Moor House) and one in southern Scotland (Auchencorth Moss). Eight unpublished paired measurements were also obtained from headwater streams in the north of Scotland, four in the Flow Country and four on the Isle of Lewis. Another unpublished paired measurement was obtained from Peru, from the Manu River. Sample 14C collection and processing for the new Scotland and Peru measurements were the same as for the London, Taiwan and Cambodia samples outlined above.

Data extraction from HydroATLAS

For each data point in the radiocarbon database, we collected information on the catchment characteristics of the sampled river. Unfortunately, this information was reported in a highly inconsistent manner and, in many cases, not at all, in the published literature. Therefore, for consistency in our analysis, we extracted catchment and hydrological characteristics from HydroATLAS56. HydroATLAS provides catchment and reach characteristics for rivers across the globe at 15-arcsecond resolution and includes parameters on hydrology, physical catchment settings, climate, land cover and use, soils and geology and anthropogenic influences. We extracted selected parameters at both the reach and catchment scale where possible and added these to our database (Supplementary Tables 1 and 4).

To ensure that we were extracting catchment characteristics for the correct river in HydroATLAS, we collected the details of catchment area for each sampling point from the original study; when this was not available, we estimated catchment size based on indicative values in the original study, published catchment sizes found in other studies of the same rivers or through order of magnitude estimates from visual assessment on Google Earth Pro (for example, 1 km2, 10 km2, 100 km2, 1,000 km2 and so on; Supplementary Table 1). Exact catchment sizes and combined exact/estimated catchment sizes are provided separately in the database. We compared the exact or estimated catchment size with the extracted catchment size from HydroATLAS (Supplementary Fig. 6). For most catchments greater than 10 km2 in size, the values matched well. For catchments less than 10 km2, the relationship broke down because of the resolution of HydroATLAS. For further analysis, we only used reach characteristics (extracted for the nearest river reach within 1 km2 of the sampling point) for sampling points with exact or estimated catchment size ≤10 km2. For catchments greater than 10 km2, we used the catchment characteristics. Note that, for some parameters, only catchment or reach characteristics were available (Supplementary Table 4).

From the catchment size information, we produced two sets of classifications. (1) A binary ‘small’ (≤10 km2) and ‘large’ (>10 km2) classification—this classification was chosen owing to the lower river basin size limit of the HydroATLAS (10 km2) and was based on the exact/estimated catchment size information extracted from the original studies. This binary size class was used primarily for QA/QC checks in the database and also in defining whether to use reach or catchment parameters from HydroATLAS in the random forest model (Extended Data Figs. 3 and 4). (2) A multiclass exponential classification of 0–10 km2, 100 km2 (10 to 100), 1,000 km2 (100 to 1,000) 10,000 km2 (1,000 to 10,000) 100,000 km2 (10,000 to 100,000), 1,000,000 km2 (>100,000)—this classification was based on binary class (1) above for the 0–10-km2 class and catchment size extracted from HydroATLAS for the other classes and was used in the analysis presented here. Both size classifications were created manually and are provided in Supplementary Table 1.

From the biomes provided in HydroATLAS, we simplified these into eight classes (Supplementary Fig. 2):

  1. 1.

    Temperate grasslands and shrublands, which was the same as HydroATLAS biome ‘8. Temperate Grasslands, Savannas & Shrublands’.

  2. 2.

    Tropical grasslands and shrublands, which included HydroATLAS biomes ‘7. Tropical & Subtropical Grasslands, Savannas & Shrublands’ and ‘9. Flooded Grasslands & Savannas’ (which occur mostly in tropical regions62).

  3. 3.

    Temperate conifer and boreal forests, which included HydroATLAS biomes ‘5. Temperate Conifer Forests’ and ‘6. Boreal Forests/Taiga’.

  4. 4.

    Tropical broadleaf and conifer forests, which included HydroATLAS biomes ‘1. Tropical & Subtropical Moist Broadleaf Forests’, ‘2. Tropical & Subtropical Dry Broadleaf Forests’ and ‘3. Tropical & Subtropical Coniferous Forests’.

  5. 5.

    Temperate and Mediterranean broadleaf mixed forest, which included HydroATLAS biomes ‘4. Temperate Broadleaf & Mixed Forests’ (although no samples in the database come from this biome) and ‘12. Mediterranean Forests, Woodlands & Scrub’.

  6. 6.

    Tundra, which was the same as HydroATLAS biome ‘11. Tundra’.

  7. 7.

    Montane grass and shrubs, which was the same as HydroATLAS biome ‘10. Montane Grasslands & Shrublands’.

  8. 8.

    Deserts, which included HydroATLAS biome ‘13. Deserts & Xeric Shrublands’ and also a further classification ‘15. Polar Desert’ added here to include the samples in the database from the Antarctic.

From the lithology classifications provided in HydroATLAS, we simplified these into three classes (Supplementary Fig. 3):

  1. 1.

    Metamorphic, which was the same as HydroATLAS class ‘8. Metamorphic Rocks (MT)’.

  2. 2.

    Igneous, which included the HydroATLAS classes ‘2. Basic Volcanic Rocks (VB)’, ‘4. Basic Plutonic Rocks (PB)’, ‘7. Acid Volcanic Rocks (VA)’, ‘9. Acid Plutonic Rocks (PA)’, ‘10. Intermediate Volcanic Rocks (VI)’, ‘12. Pyroclastics (PY)’ and ‘13. Intermediate Plutonic Rocks (PI)’.

  3. 3.

    Sedimentary, which included the HydroATLAS classes ‘1. Unconsolidated Sediments (SU)’, ‘3. Siliciclastic Sedimentary Rocks (SS)’, ‘5. Mixed Sedimentary Rocks (SM)’ and ‘6. Carbonate Sedimentary Rocks (SC)’.

One data point returned ‘No Data (ND)’ from the HydroATLAS lithology classes and was excluded from the lithology analysis. Data from Antarctica were also excluded from the analysis owing to a lack of lithology data (returning ‘Ice and Glaciers (IG)’ from the HydroATLAS lithology classes).

Statistical analyses

Statistical analyses were carried out in R version 4.1.1 (ref. 63). We used nonparametric Kruskal–Wallis tests with the kruskal.test function in R, supplemented by post hoc analyses consisting of Conover–Iman tests using the conover.test function and unpaired two-sample Wilcoxon tests using the wilcox.test function. We undertook linear regression analyses using the lm function. The details of where each analysis is applied are provided in the Figures in the main text, Extended Data and Supplementary Information.

Random forest model

We explored potential drivers of the age of river carbon emissions using a random forest model. Random forests are a machine learning model that integrate numerous regression trees to make predictions. Owing to its capacity to capture nonlinear relationships, and mitigate the risk of data overfitting, this approach has proved to be successful in numerous environmental studies for unravelling the interplay among variables64,65,66. In this study, we use random forest models to investigate the relationships between key catchment characteristics extracted from HydroATLAS and F14Catm values in the database. We aimed to identify which variables have the strongest control on F14Catm of river carbon emissions.

To select the input variables for the model, we first removed variables that correlated significantly with other potential input variables based on a Spearman correlation greater than 0.6 to avoid the results being influenced by correlated input variables. The remaining variables are shown in Supplementary Table 5 and includes the year of sample collection (‘year’).

We split the model runs by catchment size (Extended Data Figs. 3 and 4) using whole catchment characteristics for rivers with catchments greater than 10 km2 and reach characteristics for rivers with catchments ≤10 km2. Owing to limits on the number of data points, we only applied the model to DIC data, in which observations were n > 100 when separated by size.

We conducted the random forest analysis using the randomForest 4.6-14 package in R (ref. 41). Random forest models were built for the F14Catm-DIC (having removed repeat sampled locations in a calendar year) using all 19 variables from all of the 673 large catchments. We assessed the performance of the random forest model prediction by calculating the coefficient of determination (Rd2) and determining the importance of each variable through the increase in the mean square error. A tenfold cross-validation was used to enhance the robustness of the results. The dataset was randomly divided into ten equal-sized samples, with 90% of the data used for training the random forest model, whereas the remaining 10% was used to assess model performance. This process was iterated ten times until each 10% sample was used and the final model performance was computed as the mean of the ten evaluation results. Following the same approach, random forest models were also built for F14Catm-DIC using all 18 variables across all of the 211 small catchments.

We assessed the association between predictor variables and F14Catm with partial dependence plots using the pdp R package67. The partial dependence plots show how F14Catm changes when a given input variable (Supplementary Table 5) varies but all other variables are held constant in the random forest model. We performed the partial dependence analysis ten times (mirroring the ten iterations of random forest models from using tenfold cross-validation) and plotted the mean values from these ten runs, with the variability across the runs indicated by the shaded area (Extended Data Figs. 3 and 4).

Endmember isotope mixing model and Monte Carlo simulation

We used an endmember isotope mixing model and Monte Carlo approach to constrain the role of decadal versus centennial and older carbon inputs to river DIC and its contribution to river CO2 emissions. To do this, we sought to account for petrogenic inputs from carbonate mineral and rock organic matter weathering and calculate an F14C value for the non-petrogenic residual. This non-petrogenic residual is a combination of: (1) the DIC supplied from soil or atmospheric CO2 during carbonate weathering; (2) DIC supplied by silicate mineral weathering from soil or atmospheric CO2; (3) CO2 derived from ecosystem respiration and delivered by water flowing through catchments; (4) CO2 derived from within-river respiration of dissolved and particulate organic carbon by aquatic flora and fauna; and (5) the potential invasion of atmospheric CO2 if rivers are undersaturated with respect to atmospheric concentrations.

In an ideal world, it would be possible to account for petrogenic inputs to DIC and CO2 for each watershed in the database (and potentially for each sampling point). To do this, we would need to use dissolved cation (Na+, Ca2+, Mg2+, K+) and anion (Cl−, SO42+, Re) data to assess the weathering acids and contributions from carbonate and rock organic matter weathering18,38,39. Unfortunately, most of the studies reporting river DIC and CO2 F14C measurements do not report dissolved ion data, or if they do, do not report the necessary range of cation and anion measurements to complete a weathering-source inversion. As such, we take a global view using our mean F14C DIC values and assess the petrogenic inputs using global estimates of carbonate and rock organic carbon weathering rates.

We can express total river DIC–CO2 export as a mass balance of the known lateral and vertical fluxes (concentrations per unit area per unit time):

$$\begin{array}{l}{\rm{Total\; river\; DIC\; flux}}\,=\,{\rm{lateral\; DIC\; export\; to\; ocean}}\\ +\,{{\rm{vertical\; CO}}}_{2}\,{\rm{emission\; flux}}+{\rm{carbonate\; precipitation}}\end{array}$$
(4)

in which DIC is the sum of dissolved CO2, HCO3− and CO32− (Supplementary Information section 2), we express all fluxes at the global scale in Pg C year−1 and we assume that carbonate precipitation is negligible at the global scale68. Lateral DIC export from rivers to the global oceans is estimated to be 0.52 ± 0.17 Pg C year−1 (ref. 42), and global vertical CO2 emissions from rivers are estimated to be 2.0 ± 0.2 Pg C year−1 (ref. 6), producing a total river DIC flux of 2.5 ± 0.4 Pg C year−1.

We can also express global river F14C of DIC and CO2 (F14Criver) as the mass balance of the three main carbon sources defined in this study, for which the proportional contributions from all three carbon sources (a + b + c) sum to 1:

$${F}^{14}{{\rm{C}}}_{{\rm{river}}}=a\times {F}^{14}{{\rm{C}}}_{{\rm{decadal}}}+b\times {F}^{14}{{\rm{C}}}_{{\rm{millennial}}}+c\times {F}^{14}{{\rm{C}}}_{{\rm{petro}}}$$
(5)

We can then combine these two mass balances to provide a first-order estimate of the contributions of these sources to the global river DIC flux:

$${\rm{Total\; river\; DIC\; flux}}\times {F}^{14}{{\rm{C}}}_{{\rm{river}}}=({\rm{lateral\; DIC\; export\; to\; ocean}}+{{\rm{vertical\; CO}}}_{2}\,{\rm{emissions\; flux}})\times (a\times {F}^{14}{{\rm{C}}}_{{\rm{decadal}}}+b\times {F}^{14}{{\rm{C}}}_{{\rm{millennial}}}+c\times {F}^{14}{{\rm{C}}}_{{\rm{petro}}})$$
(6)

To further constrain equation (6), we account for published estimates of petrogenic DIC inputs to the global river DIC flux derived from weathering of carbonate and rock organic matter. Global carbonate mineral weathering rates are relatively well constrained at an input of 0.15 Pg C year−1 to DIC from petrogenic carbon in the CaCO3 mineral22. If driven by carbonic acid weathering, this carbon flux is likely to be delivered by hydrological flow paths from weathering zones to streams and rivers. However, if sulfuric acid weathering is operating in landscapes, some of this petrogenic carbon may be released to the atmosphere as CO2 and not enter the DIC pool53. This fate of carbon is not well constrained globally. Also, rock organic carbon oxidation has been estimated to contribute 0.068 Pg C year−1 in the weathering zone39. Again, it is not known what proportion of this carbon enters the DIC pool53,69 and may contribute to the global river DIC flux. We thus considered the full range between two scenarios of petrogenic carbon inputs. First, a 0.15 Pg C year−1 scenario, which may represent a lower bound. Second, we consider 0.218 Pg C year−1, which is likely to be an upper bound, summing both carbonate and rock organic matter weathering (we incorporate this as 0.18 ± 0.034 for consistency with other fluxes and uncertainties). Incorporating this ‘weathering input’ flux constraint into equation (6) gives:

$$\begin{array}{l}{\rm{Total\; river\; DIC\; flux}}\times {F}^{14}{{\rm{C}}}_{{\rm{river}}}\\ =\,(({\rm{Lateral\; DIC\; export\; to\; ocean}}+{{\rm{vertical\; CO}}}_{2}\,{\rm{emissions\; flux}}\\ \,-\,{\rm{weathering\; inputs}})\times (a\times {F}^{14}{{\rm{C}}}_{{\rm{decadal}}}+b\times {F}^{14}{{\rm{C}}}_{{\rm{millennial}}}))\\ \,+\,(c\times {F}^{14}{{\rm{C}}}_{{\rm{petro}}}\times {\rm{weathering\; inputs}})\end{array}$$
(7)

Using the mean F14C value for DIC, CO2 and CH4 across all rivers in our database of F14Criver = 0.919 (Extended Data Table 1) and subtracting petrogenic C inputs (0.150–0.218 Pg C year−1) from the sum of lateral DIC export to the ocean and vertical river CO2 emissions (2.5 ± 0.4 Pg C year−1), we can simplify equation (7) to:

$$\begin{array}{l}{F}^{14}{{\rm{C}}}_{{\rm{river}}}\,\times \,2.5={F}^{14}{{\rm{C}}}_{{\rm{decadal}}+{\rm{millennial}}}\,\times \,(2.28\,{\rm{to}}\,2.35)\\ \,\,\,\,\,\,\,+\,{F}^{14}{{\rm{C}}}_{{\rm{petro}}}\times (0.15\,{\rm{to}}\,0.218)\end{array}$$
(8)

We can then calculate the non-petrogenic F14C value (F14Cdecadal+millennial), because the petrogenic source is assumed to contain no radiocarbon (that is, F14C = 0.0). This provided an estimate of the F14Cdecadal+millennial = 0.978 to 1.007.

We then assumed that this residual non-petrogenic carbon was a mixture of a decadal-aged carbon source (using mean ± 1σ F14C content of atmospheric CO2 between 1950 and 2023, F14C = 1.226 ± 0.216 (ref. 34)) and a millennial-aged carbon source (using the carbon-weighted mean (±1σ) age of global mineral soil carbon in the upper 0–30 cm, F14C = 0.841 ± 0.033 (ref. 27)). The conceptual model of this carbon source partitioning, decadal and millennial (and petrogenic; see Bayesian isotope mixing model methods in Supplementary Information section 3), follows refs. 14,32. The decadal source endmember captures annual to decadal carbon cycling through biomass and soils, including the decomposition of dissolved organic carbon, which tends to have an F14C value indicative of annual-decadal terrestrial residence times17. The millennial source endmember captures carbon in soil stores of 0–30 cm depth (and deeper in some regions27), which includes the potential decomposition of older dissolved14,17,48 and particulate12 organic matter. To estimate the most probable composition and its uncertainty, we use a Monte Carlo simulation to generate 10,000 model runs, varying the petrogenic flux (0.150–0.218 Pg C year−1) and the F14C values of the decadal (1.011–1.442) and millennial (0.808–0.874) inputs to equation (8). We report the mean proportional contributions of the decadal and millennial contributions ±1σ of the 10,000 model runs (Extended Data Fig. 5). We then convert these to proportions of the vertical river CO2 flux by first quantifying the proportional contribution of petrogenic carbon: 0.180 ± 0.034 Pg C year−1 of 2.5 Pg C year−1 (total river DIC flux) = 0.07 ± 0.03 (Table 1) and then subtracting the petrogenic proportion from the total to give 0.93 and multiplying this by the mean decadal and millennial contributions to give 0.41 ± 0.16 and 0.52 ± 0.16, respectively (Table 1). We then multiplied estimated vertical CO2 emissions from global rivers (2.0 ± 0.2 Pg C year−1) from ref. 6 by these proportional carbon source contributions (Table 1). We note that there may be some equilibration of the DIC/CO2 pool with the atmosphere during river transport and emission, which adds young carbon to the CO2 pool70, meaning that our estimates of old carbon contributions may be conservative.

We were not able to collect consistent, site-specific concentration or emission flux data alongside the F14C data extracted from the literature. This means that we were not able to scale the F14C values in the database with local and regional emission fluxes (Supplementary Information section 4).