Deep CO₂ release and the carbon budget of the central Apennines modulated by geodynamics

Abstract

Recent studies increasingly recognize the importance of critical-zone weathering during mountain building for long-term CO₂ drawdown and release. However, the focus on near-surface weathering reactions commonly does not account for CO₂ emissions from the crust, which could outstrip CO₂ drawdown where carbonates melt and decarbonize during subduction and metamorphism. We analyse water chemistry from streams in Italy’s central Apennines that cross a gradient in heat flow and crustal thickness with relatively constant climatic conditions. We quantify the balance of inorganic carbon fluxes from near-surface weathering processes, metamorphism and the melting of carbonates. We find that, at the regional scale, carbon emissions from crustal sources outpace near-surface fluxes by two orders of magnitude above a tear in the subducting slab characterized by heat flow greater than 150 mW m^–2 and crustal thickness of less than 25 km. By contrast, weathering processes dominate the carbon budget where crustal thickness exceeds 40 km and heat flow is lower than 30 mW m^–2. The observed variation in metamorphic fluxes is one to two orders of magnitude larger than that of weathering fluxes. We therefore suggest that geodynamic modulations of metamorphic melting and decarbonation reactions are an efficient process by which tectonics can regulate the inorganic carbon cycle.

Main

Global plate motions impact Earth’s carbon cycle by modulating both the release of CO₂ from the crust and mantle¹ and the emission or sequestration of CO₂ from rock weathering². In uplifting mountains, near-surface (critical-zone) chemical weathering reactions are particularly efficient³, resulting in timescale-dependent changes in the CO₂ content of the atmosphere through silicate and carbonate mineral weathering with carbonic acid (H₂CO₃) and sulfuric acid (H₂SO₄). Thus, orogenesis is proposed to impact global climate by increasing the weatherability of Earth’s surface^4,5. However, mountain building can also generate large volumes of ‘metamorphic’ CO₂ from the decarbonation or melting of carbonate in the crust and mantle^1,6,7,8, where orogenesis involves the collision and subduction of carbonate rock. This release of CO₂ ultimately reflects the conversion of carbonate to weatherable silicate minerals that completes the global silicate weathering cycle⁹. However, the different timescales required for metamorphic CO₂ release and silicate weathering suggest mountain building may impact global climate through the modulation of these deep CO₂ emissions^10,11.

Determining the role of orogenesis in the global carbon cycle requires direct comparisons of its impact on both deep processes and chemical weathering. To our knowledge, such comparisons exist for only two locations. In the New Zealand Southern Alps, collision of mostly siliceous rocks results in degassing-related CO₂ emission fluxes, which are an order of magnitude smaller than inferred CO₂ drawdown fluxes from silicate weathering¹². In the Himalaya, the subduction and collision of carbonates lead to CO₂ degassing that outpaces silicate weathering fluxes^13,14. These studies estimate metamorphic CO₂ degassing directly from samples in springs, aquifers and gas vents, whereas weathering fluxes are estimated from riverine fluxes. Therefore, these datasets cannot constrain how deep, crustal or mantle-derived CO₂ fluxes interact with the critical zone and may be buffered by carbonate and silicate weathering. Moreover, it remains unclear how geodynamics—the influence of mantle convection on tectonics—impact the relative spatial importance of degassing and weathering fluxes across a mountain range.

To address this important knowledge gap in the inorganic carbon cycle, we investigate the relationship between deep CO₂ release and chemical weathering in the critical zone along a geodynamic gradient in the central Apennines (Italy), an active mountain range that exposes and subducts large volumes of carbonate. We present major riverine element and isotope data from two large catchments that straddle a gradient in crustal thickness and heat flow above a tear and area of retreat within the subducting slab and assess inorganic CO₂ emission and sequestration fluxes associated with critical zone and deep processes. We use an inverse approach to apportion the solute flux to the weathering of carbonates, silicates and sulfide and to distinguish atmospheric, lithologic and metamorphic CO₂ sources. The results of this study demonstrate that the inorganic carbon budget of the central Apennines is controlled primarily by metamorphic release that varies strongly across the regional geodynamic gradient. Hence, the impact of regional tectonics on CO₂ sources may be substantially larger than tectonic modulation of CO₂ sinks.

Tectonic setting of the central Apennines

The Apennine chain is a fold-and-thrust belt characterized by an accretionary wedge to the east and a back-arc extensional basin to the west¹⁵ (Fig. 1 and Supplementary Text 1), which developed through syn-convergent extension, due to the subduction and rollback of the Adriatic slab beneath Eurasia¹⁶. This dynamic has produced a tectonic gradient expressed by an increase in extension from east to west, resulting in lower crustal thickness (~20 km) and higher heat flow (>200 mW m^–2) in the west relative to thicker crust (>40 km) and lower heat flow (<30 mW m^–2) in the east^8,17,18 (Fig. 1d). In the central Apennines, the absence of intermediate seismicity and the presence of anomalously low P-wave velocities have been interpreted as a slab window^8,19,20 formed due to progressive east-directed rollback and tearing of the Adriatic slab. By contrast, intermediate and deep seismicity beneath the northern Apennines and Calabria illustrate an intact, subducting slab²⁰.

Fig. 1: Overview of the sampling locations and the geologic and geodynamic setting.

a, Location of studied catchments (pink outlines) and location of the cross-section shown in e. b, Sample distribution (black circles) and river networks. Networks for the studied rivers are shown in blue, and adjacent river networks are shown in black. c, Simplified geologic map. d, Geodynamic setting for the central Apennines. Moho depth is illustrated as a colour gradient. Heat-flow isotherms are illustrated as contour lines for a 10 mW m^–2 contour interval (dashed lines) or a 50 mW m^–2 contour interval (solid line) unless otherwise noted. e, Geologic cross-section through the Italian peninsula. The cross-section illustrates the ages, lithologies and major tectonic structures in the upper 20 km of the crust. Layers in b–d are overlain on a Shuttle Radar Topography Mission (SRTM) 90 m hillshade and digital elevation model. All individual sample points are shown in Extended Data Fig. 1. Panels adapted with permission from: c, refs. ^22,23 under a Creative Commons license CC BY 3.0; d, ref. ⁴⁶, Oxford University Press; ref. ¹⁷, Springer; ref. ⁸, Elsevier; e, ref. ¹⁵, The Virtual Explorer Pty Ltd.

Water chemistry of the Tevere and Aterno-Pescara rivers

We present 104 water samples collected during winter 2021 (55) and summer 2020 (49) from these catchments (Fig. 1 and Extended Data Fig. 1), which were selected to maximize areal coverage and to sample different lithologies and water bodies (for example, river, springs/groundwater, lakes), to understand the potential sources of dissolved ions to the river channels. For all samples, we measured concentrations of dissolved major elements as well as isotopes of inorganic carbon (δ¹³C, F¹⁴C (fraction modern carbon)) and sulfur and oxygen in sulfate (δ³⁴S, δ¹⁸O(SO₄)). On the basis of these measurements, we can unmix the contributions to the dissolved load of carbonate, silicate and evaporite mineral sources (Methods). In addition, we distinguish the acid sources for weathering, including sulfuric acid (H₂SO₄), carbonic acid (H₂CO₃) derived from biogenic or atmospheric CO₂ and H₂CO₃ derived from metamorphic carbon.

Because the weathering of carbonate versus silicate rocks can have different implications for the inorganic carbon cycle, we broadly categorize the lithology at each sampling location as ‘carbonate’, ‘siliciclastic’ or ‘mixed’ (a carbonate-siliciclastic mix)²¹ on the basis of the distribution of surface lithologies in refs. ^22,23. The weathering of silicate or carbonate rock by H₂CO₃ or H₂SO₄ co-determines the resulting production of ions and dissolved inorganic carbon (DIC)²⁴. In the absence of a gypsum contribution, the ratios of [SO₄²⁻]/[Σ⁺] and [Ca²⁺]/[Σ⁺] (where Σ⁺ is the sum of cations) reflect the balance of carbonate and silicate weathering with a mixture of H₂CO₃ and H₂SO₄ sources. Most river samples have ratios of [SO₄²⁻]/[Σ⁺] below 0.45 and [Ca²⁺]/[Σ⁺] ratios between ~0.3 and 0.9 (Fig. 2a,b). The siliciclastic samples and a subset of numbered Tevere samples collected at or near springs display the lowest [Ca²⁺]/[Σ⁺] ratios. Cations in these samples are dominated by Na⁺, rather than Ca²⁺, and the similarity between [Na⁺] and [Cl⁻] in these samples suggests that halite is probably the primary source of [Na⁺] (ref. ²¹). Overall, the high [Ca²⁺]/[Σ⁺] and low [SO₄²⁻]/[Σ⁺] values of the samples suggest that the study area is dominated by H₂CO₃ weathering of carbonate and silicate rock.

Fig. 2: Water chemistry in relation to the expected chemical signatures of critical-zone weathering and metamorphic carbon.

a,b, Ratios of [Ca²⁺]/[Σ⁺] plotted against ratios of [SO₄²⁻]/[Σ⁺] for winter samples (a) and summer samples (b). c,d, δ¹³C plotted against F¹⁴C for winter samples (c) and summer samples (d). Samples are coloured by the dominant lithology in the upstream area²¹: carbonate, mixed carbonate and siliciclastic, or siliciclastic. Bars represent ion or isotopic endmember compositions²¹. Annotated samples in a and b are samples with low [Ca²⁺]/[Σ⁺] that have higher [Na⁺] than [Ca²⁺] and reflect evaporite δ³⁴S and δ¹⁸O(SO₄) signatures.

Carbon isotopes and major element geochemistry yield insights into the proportions of DIC sourced from modern carbon (F¹⁴C = 1; for example, biogenic or atmospheric carbon) and from rock-derived, radiocarbon dead sources (F¹⁴C = 0; for example, from carbonate weathering or metamorphic carbon). Both δ¹³C and F¹⁴C values are highly variable and reflect these different carbon sources (Fig. 2c,d). Most samples lie between the biogenic (modern) carbon and the carbonate–H₂CO₃ endmembers, while approximately 30% of samples lie beyond the carbonate–H₂CO₃ endmember. These low F¹⁴C and enriched δ¹³C values could be explained by H₂SO₄ dissolution of carbonates²⁵; however, major element chemistry is inconsistent with such large contributions of H₂SO₄ to the weathering budget (Extended Data Fig. 2). Hence, the low F¹⁴C and enriched δ¹³C values require that a substantial proportion of the H₂CO₃ is derived from upwelling of deeper, rock-derived CO₂-rich fluids⁸.

Studies in the central Apennines from the past two decades have identified δ¹³C-enriched sources of CO₂ at cold and thermal mineralized springs^26,27,28 and in the regional aquifers²⁹, as well as CO₂ degassing from localized gas vents. The geochemical (⁴He/³He) signature of CO₂ emissions suggests that degassing fluxes are sourced predominantly from melting of the carbonate sedimentary cover on the subducting Adriatic slab within the mantle lithosphere^8,30,31, producing carbonate-rich melts that upwell through the mantle⁸. Additional CO₂ derives from decarbonation of carbonates in the overriding Eurasian plate³⁰. Localized metamorphic CO₂ outgassing has been linked with periods of high seismicity^16,32,33, suggesting that widespread normal faults and fractures are effective conduits for CO₂-rich fluids that migrate through the crust³⁴ (Fig. 1c,e). On reaching the surface, the CO₂ either is outgassed at vents²⁸ or mixes with meteoric water in the regional carbonate aquifers and can be released at springs^8,35,36. Our chemical analysis of the stream waters suggests that CO₂ not only is directly degassed but effectively interacts with the critical zone by providing H₂CO₃ that can weather carbonate and silicate rocks near the surface.

A CO₂ budget for the central Apennines

To quantitatively deconvolve the sources of DIC and contributions of lithologic endmembers to central Apennine rivers, we use a recent inverse model, Mixing Elements and Dissolved Isotopes in Rivers (MEANDIR)³⁷. We quantify the fraction of major ions (Ca²⁺, Na⁺, Mg²⁺, SO₄²⁺, Cl⁻) contributed from silicates, carbonates, evaporites, pyrite oxidation and meteoric water, as well as the fraction of DIC from biogenic carbon, rock-derived carbon, and atmospheric carbon and meteoric water (Methods). The pyrite oxidation endmember allows us to quantify the proportion of weathering by H₂SO₄. Together with the relative proportions of biogenic and rock-derived carbon, it further allows us to constrain the fraction of carbon derived from deep sources. Where possible, we convert ion concentrations to fluxes by multiplying molar masses of the respective ion with ion concentrations and available run-off estimates averaged over the months of data collection (Methods). We note that our model inputs of Ca²⁺, HCO₃⁻ and δ¹³C are corrected for the effects of secondary carbonate precipitation, which accounts for the loss of 45% of [Ca²⁺] for locations included in our carbon budget²¹. After this correction, estimates of [DIC] increase by 0–181% ([DIC]_Corr) and metamorphic CO₂ fluxes are 0–45% higher²¹.

We follow previous work³⁸ and infer CO₂ sequestration and release from our fluxes on timescales longer than the compensation of alkalinity fluxes to the ocean by carbonate precipitation (1–10 kyr) (ref. ³⁹) but shorter than the timescales for sulfur reduction in the ocean (>10 Myr)³⁹. We find that the solute and carbon budget of the main rivers in the study area are variable in space and related to the geomorphic setting. In the Aterno-Pescara River, CO₂ fluxes (reported in tons of carbon (tC) per area per time) are dominated by silicate weathering (−0.4–0 tC km^–2 yr^–1), with minor fluxes from coupled pyrite oxidation and carbonate weathering (0–0.1 tC km^–2 yr^–1) but no measurable metamorphic carbon fluxes (Fig. 3), with the exception of springs or small tributaries near or along faults (Extended Data Figs. 3–6). CO₂ fluxes from pyrite oxidation (0–0.2 tC km² yr^–1) and silicate weathering (−1.1–0 tC km² yr^–1) in the Tevere River are of similar magnitude to the Aterno-Pescara River. However, the net CO₂ fluxes in the Tevere are 1–2 orders of magnitude higher than in the Aterno-Pescara River due to large CO₂ fluxes inferred from metamorphic carbon (Fig. 3). In the largest Tevere tributaries, the flux of metamorphic CO₂ is consistently 1−2 orders of magnitude higher than fluxes from silicate weathering and pyrite oxidation, respectively (Fig. 3)²¹. While smaller tributaries that drain siliciclastic-rich lithologies are dominated by silicate weathering (Extended Data Figs. 3–6), the regional inorganic carbon budget shows that the central Apennines are a net carbon source.

Fig. 3: CO₂ sinks and sources inferred from the Tevere and Aterno-Pescara River chemistry.

Regional inorganic CO₂ fluxes from five sampling locations with the largest upstream drainage area. a, The sampling locations, site numbers²¹ and closest discharge stations. Upstream catchment areas from each sampling location are outlined in black and coloured in grey, and the corresponding drainage network (blue lines) is shown. Note that the upstream area for site 45 also includes the area encompassed by site 42. b, Enlarged image of Aterno-Pescara sampling locations and discharge stations. c, CO₂ exchange with the atmosphere, shown as fluxes associated with mechanisms that result in long-term CO₂ drawdown (silicate weathering) or CO₂ release (pyrite oxidation and metamorphic carbon). The sum of the fluxes is illustrated as the total CO₂ exchange with the atmosphere. Data bars represent mean values ± 1σ (ref. ²¹).

Our field seasons broadly reflect the hottest and driest or wettest and coldest times of the year⁴⁰, allowing us to estimate minimum (summer) and maximum (winter) yearly CO₂ fluxes. We calculate a minimum net CO₂ flux of 7.9 ± 2.4 tC km^–2 yr^–1 over an area of 18,243 km² (Sites 5, 45 and 46) and a maximum estimate of 16.4 ± 6.3 tC km^–2 yr^–1 over an area of 18,655 km² (Sites 1, 5, 8, 45 and 46). Overall, the weighted yearly average net CO₂ flux is 12.3 ± 4.1 tC km^–2 yr^–1 (Sites 5, 45 and 46). Relative to a yearly metamorphic CO₂ flux upscaled from spring data (28 tC km^–2 yr^–1) (ref. ²⁹), our estimate of CO₂ fluxes is about a factor of 2 lower. These two values probably constitute minimum and maximum estimates, respectively, and their difference could be due to two reasons. First, our river estimates may underestimate CO₂ fluxes because they miss rapid, diffusion-controlled CO₂ degassing that is not associated with secondary precipitation of carbonate and has a negligible effect on the carbon isotopic composition of the water⁴¹. Second, upscaled fluxes from springs to the entire watersheds could overestimate the regional flux of CO₂, because they miss diffuse inputs of water across the catchments that can represent between ~20% and 100% of riverine major ion concentrations⁴². Despite these uncertainties, we can conclude that CO₂ fluxes from metamorphic carbon in the Tevere River are orders of magnitude larger than CO₂ drawdown fluxes from silicate weathering in these watersheds.

To estimate a total carbon budget for the Apennines, we combine our results with estimates for inorganic CO₂ emissions from gas vents and organic CO₂ exchanges². Discrete CO₂ emissions from gas vents reported on the western side of the Apennines contribute 2–12 tC km^–2 yr^–1 over an estimated area of 52,000 km² (Fig. 4)^8,36. Estimates for petrogenic organic carbon oxidation do not exist for the Apennines but are probably small in these lithologies—analogous to the small sulfide oxidation rates. Particulate organic carbon export at 200 m depth in the Tyrrhenian Sea ranges from 1.3 to 6.1 tC km^–2 yr^–1 for spring and summer and is 0.7 tC km^–2 yr^–1 in the Adriatic Sea during autumn⁴³. Estimates for dissolved organic carbon burial are lacking, but dissolved organic carbon export is probably much smaller than the particulate organic carbon export⁴⁴. The central Apennines are thus a net carbon source on the western side of the mountain range, where CO₂ emissions from metamorphic decarbonation are 2–10 times larger than organic carbon burial and 1–2 orders of magnitude larger than CO₂ drawdown from silicate weathering. On the eastern side, the inorganic CO₂ budget is dominated by silicate weathering and CO₂-releasing sulfide oxidation from carbonate weathering, although the magnitude of carbon sources is much smaller relative to the western side of the range, so they may be compensated by organic carbon burial.

Fig. 4: Overview of the regional geodynamic setting in relation to the metamorphic CO₂ contributions to spring and stream waters.

a, Coloured circles and squares illustrate samples with non-zero yearly average HCO₃ from metamorphic carbon, scaled by the concentration²¹. Where both winter and summer concentrations were available for a sample, the symbol represents an average over the two seasons. White-outlined circles and squares illustrate samples where HCO₃ from metamorphic CO₂ is zero. The purple line marks the boundary between P-wave velocity (V_p) anomalies at 52 km depth; CAW and SAW on the dashed portion of the line highlight the locations of slab windows in the Central and Southern Apennines, respectively. The orange overlay illustrates the spatial extent of measured CO₂ gas emissions, grey circles illustrate the locations and depths of seismicity deeper than 40 km and magnitude 3 or higher, and the black sawtoothed line marks the subduction front. b, Enlarged view of the results within the study area, including the locations of normal faults (black lines). Figure adapted with permission from refs. ^8,47,48, Elsevier; ref. ⁴⁹ under a Creative Commons license CC BY 4.0.

Impact of geodynamic setting on the inorganic CO₂ budget

The stark difference in both the sources of CO₂ and the magnitude of CO₂ fluxes between the Tevere (Tyrrhenian side) and Aterno-Pescara Rivers (Adriatic side) coincides with a regional east to west geodynamic and tectonic gradient defined by a westward increase in extension and heat flow and a decrease in crustal thickness^8,17,18 (Figs. 1d, 5). In contrast, climatic and lithologic differences between the two river systems are small. We propose that thin crust with high heat flow in the Tevere River drives important release of metamorphic CO₂ (Figs. 3–5). In turn, higher crustal thickness and lower heat flow in the Aterno-Pescara River inhibit substantial CO₂ release. Here only springs and river samples along or near faults provide evidence for metamorphic CO₂ release (Fig. 4), and the composition of catchment-averaged river samples of the Aterno-Pescara River can be explained without any metamorphic inputs. The geodynamic control on CO₂ release is also evident from the pattern of metamorphic CO₂ emissions measured from local gas vents³⁶ that are primarily on the Tyrrhenian side of the mountain range or are found almost exclusively along faults on the Adriatic side of the range (Fig. 4). This area coincides with the location of the slab window (CAW) (Fig. 4), whereas CO₂ emissions have not been reported in Calabria and in the northern Apennines, where a subducting slab is still intact. Slab retreat and break-off have acted as a catalyst for regional mantle convection and increased heat flow^19,20,16, which in turn facilitated melting and decarbonation of the carbonate sedimentary cover on the Adriatic plate⁸. Mantle upwelling induced by the slab dynamics is also responsible for driving long-wavelength uplift^19,16, which in turn activated the extensional structures that bring metamorphic CO₂ to the surface³⁴. Due to the apparent link between the location of CO₂ release with slab retreat and tearing, the timing of slab detachment (~2 Ma)²⁰, and normal fault activation (2.5 and 3.3 Ma), we suggest that the dominance of metamorphic CO₂ release on the Tyrrhenian side—and potentially the east–west contrast in the inorganic carbon budget—may have been present over at least 2 Ma.

Fig. 5: Schematic cross-section through the Central Apennines illustrating major patterns in CO₂ fluxes, heat flow, and crustal thickness.

The east–west patterns of CO₂ fluxes, heat flow^8,17 and Moho depth⁴⁶ across the Central Apennines. a, The location of the cross-section from A to A′ is shown in the inset. b, The intersections of the heat flow and Moho depth data with the locations of the Tevere and Aterno-Pescara catchments are illustrated with orange and blue shaded areas, respectively.

The large differences in the riverine solute budget between the two major Apennine river systems, the location of reported CO₂ gas emissions and the absence of major climatic or lithologic gradients across the study area support the notion that differences in crustal thickness and heat flow could cause order-of-magnitude variations in inorganic CO₂ cycling over length scales of a few tens of kilometres (Fig. 5). Importantly, the variations in the flux of metamorphic CO₂ release are much larger than variations in chemical weathering fluxes across the study area. Thus, in the central Apennines, the regional geodynamics and tectonics impact mountain building and the carbon cycle most significantly by modulating the release of metamorphic CO₂, not by enhancing CO₂ drawdown or release from critical-zone weathering reactions⁴⁵. Furthermore, the subduction of passive margin carbonate-rich sediments and extension-induced variations in heat flow and crustal thickness reflect orogenic processes common to other mountain ranges during the initial stages of orogenesis¹. We suggest that modelling and understanding the true impact of early-stage mountain building on the global carbon cycle should consider the broader role of geodynamics and tectonics beyond uplift and the balance of critical-zone weathering reactions.

Methods

Ion and isotope measurements

For each sample location, we collected water in high-density polyethylene bottles for cations (30 ml), anions (60 ml), alkalinity (250 ml) and δ³⁴S and δ¹⁸O(SO₄²⁻) (250 ml) analyses. We filtered water samples in the field with 0.2 μm VWR filters and acidified cation samples with two drops of ultra-pure 36% HNO₃. We also collected water in glass vials for δ¹³C and δ¹⁴C (20 ml) analyses. We measured the alkalinity of each sample within 24 hours of collection using Gran Titration with a Hach digital titrator. All samples were kept at the German Research Centre for Geosciences (GFZ) in cold storage at 4 °C before analysis.

To deconvolve the major lithologies being weathered in the Central Apennines, we measured the concentrations of major dissolved ions for each water sample. We measured major cations (Ca²⁺, K⁺, Mg²⁺, Na⁺) and dissolved silica on a Varian 720ES inductively coupled plasma optical emission spectroscope at the GFZ. To monitor machine drift, quality control samples were run for every ten measured samples, and accepted runs had a drift of <5%. We performed quality control tests using water standards SLRS-6 and USGS-T187. A set of 11 in-house standards were used to calibrate the cation measurements, and only those standards that fell within 10% of a linear fit through all standards were accepted. Similarly, we accepted only cation measurements within the range of the accepted standards. Measurement uncertainty was estimated from the maximum deviation of the calibration standards from the calibration line.

We measured major anions (F^-, Cl⁻, SO₄²⁻) at the GFZ on a Dionex ICS-1100 chromatograph. Quality control was performed using a six-point linear calibration and USGS-206 and USGS-212 standards. We quantified measurement uncertainty on the basis of the standard deviation of three repeat measurements.

To distinguish between lithologic sources of riverine sulfate, we measured δ³⁴S and δ¹⁸O(SO₄) at the Centre de Recherche Pétrographiques et Géochimiques. The δ³⁴S samples were prepared according to ref. ⁵⁰. We extracted anions from water samples using column chemistry, with cationic resin AG1X8, and subsequently dried down and diluted the samples in 5% HNO₃. We measured δ³⁴S using a Thermo Fischer Scientific multicollector inductively coupled plasma mass spectrometer Neptune Plus (IRISS platform). Values are provided in the Vienna Canyon Diablo Troilite scale, thanks to an in-house bracketing standard calibrated against the International Atomic Energy Agency (IAEA) S1 standard⁵¹. External reproducibility is based on independently purified replicates of seawater, which had average measured δ³⁴S values of 21.2 ± 0.12‰ (summer) and 21.2 ± 0.05‰ (winter), reported with 2σ errors.

We prepared δ¹⁸O(SO₄) samples by measuring 250 ml of river water and acidifying the solution with HCl 3 N to a pH of 4.2 to eliminate HCO₃ and CO₃. The initial 250 ml of water was then heated to 200 °C for 30 minutes to eliminate CO₂. The temperature was then adjusted to 70 °C, and a 5% BaCl₂ solution was added to the water in a volume proportional to the measured concentration of SO₄ in the individual water sample. The BaSO₄ was allowed to precipitate from the solution for 1 hour, and then overnight at the ambient temperature. The precipitate was filtered using a 0.2 μm Nylon filter and subsequently rinsed twice with distilled water and three times with acidified water (5 ml HCl per litre water). The precipitate was then dried at 100 °C. We measured the δ¹⁸O(SO₄) on a Thermo Fisher EAlsolink-Delta V isotope ratio mass spectrometer. Measured standards yielded δ¹⁸O(SO₄) values of 23.3 ± 0.4‰ (IAEA) and 9.3 ± 0.4‰ (NBS 127) for the winter sample set, and 23.3 ± 0.8‰ (IAEA) and 9.3 ± 0.6‰ (NBS 127) for the summer sample set (reported with 2σ errors). We note that some of the samples lack replicates from each season (labelled as ‘NA’) because there was insufficient BaSO₄ to measure δ¹⁸O(SO₄) (ref. ²¹).

To distinguish between atmospheric and rock sources of dissolved carbon, we measured DI¹³C and DIC concentrations at the Centre de Recherche Pétrographiques et Géochimiques and DI¹⁴C at the Laboratory for Ion Beam Physics at the ETH Zürich. For δ¹³C measurements, the samples and H₃PO₄ were put into glass vials and vaporized. The isotopic composition of the dissolved inorganic carbon within the remaining CO₂ gas was measured with a Thermo Fisher EAlsolink-Delta V isotope ratio mass spectrometer. The DIC concentrations were estimated relative to a pure, synthetic calcite internal standard. We assumed conservative errors of 10% on the DIC calculations due to differences in the volume of air within the sampling tubes between liquid and solid samples (estimated to be 5%). The δ¹⁴C samples were prepared by purging 6 ml aliquots of each water sample with helium, acidifying the sample with 150 μl of 85% H₃PO₄ and heating the sample to 60 °C for 2 hours. We measured δ¹⁴C from the CO₂ gas that formed from this process using an online carbonate handling system, which was connected to a mini carbon accelerator mass spectrometer (MICADAS AMS) equipped with a gas-accepting ion source.

Weathering reactions: theoretical expectations

We assume silicate and carbonate compositions equivalent to the generic endmembers normalized by Σ⁺ (refs. ^37,21) and converted to units of mol/mol.

Within this framework, we constrain endmember compositions for carbonic acid (H₂CO₃) and sulfuric acid (H₂SO₄) weathering of carbonate and silicate rock (Fig. 2 and equations (1)−(4)).

$${{\mathrm{CaSi}}}{{\mathrm{O}}}_{3}+2{{\mathrm{H}}}_{2}{\mathrm{C}}{{\mathrm{O}}}_{3}+{{\mathrm{H}}}_{2}{\mathrm{O}}\to {{{\mathrm{Ca}}}}^{2+}+{{\mathrm{H}}}_{4}{{\mathrm{Si}}}{{\mathrm{O}}}_{4}+2{{\mathrm{HC}}}{{\mathrm{O}}}_{3}^{-}$$

(1)

$${{\mathrm{CaC}}}{{\mathrm{O}}}_{3}+{{\mathrm{H}}}_{2}{\mathrm{C}}{{\mathrm{O}}}_{3}\to {{{\mathrm{Ca}}}}^{2+}+2{{\mathrm{HC}}}{{\mathrm{O}}}_{3}^{-}$$

(2)

$${{\mathrm{CaSi}}}{{\mathrm{O}}}_{3}+{{\mathrm{H}}}_{2}{\mathrm{S}}{{\mathrm{O}}}_{4}+{{\mathrm{H}}}_{2}{\mathrm{O}}\to {{{\mathrm{Ca}}}}^{2+}+{{\mathrm{H}}}_{4}{{\mathrm{Si}}}{{\mathrm{O}}}_{4}+{\mathrm{S}}{{\mathrm{O}}}_{4}^{-}$$

(3)

$${{\mathrm{CaC}}}{{\mathrm{O}}}_{3}+{{\mathrm{H}}}_{2}{\mathrm{S}}{{\mathrm{O}}}_{4}\to {{{\mathrm{Ca}}}}^{2+}+{{\mathrm{H}}}_{2}{\mathrm{O}}+{\mathrm{C}}{{\mathrm{O}}}_{2}+{\mathrm{S}}{{\mathrm{O}}}_{4}^{2-}$$

(4)

The weathering reactions in equations (1)–(4) also produce different theoretical DIC signatures⁵² that reflect modern carbon sources (for example, biogenic carbon or atmospheric carbon from meteoric water) and rock-derived, radiocarbon dead carbon sources (for example, rock and metamorphic carbon). The H₂CO₃ weathering of carbonate contributes 1 mole of modern carbon and 1 mole of rock-derived carbon to the solvent (water), so the expected fraction modern carbon (F¹⁴C) is 0.5, whereas silicate weathering by H₂CO₃ contributes only modern carbon and thus has an expected F¹⁴C signature of 1. Similarly, weathering 1 mole of carbonate minerals by H₂SO₄ contributes only rock-derived carbon (F¹⁴C = 0), whereas silicate weathering by H₂SO₄ produces no alkalinity or DIC since the reaction does not include any carbon species (equation (3)).

These theoretical expectations do not account for the dissolution of evaporites (for example, halite and gypsum). In the Tevere River, some spring and proximal river samples illustrate [Na⁺] that are higher than [Ca²⁺]. All other samples illustrate higher [Ca²⁺] than [Na⁺], even for samples derived from siliciclastic-rich turbidites. Assuming that all SO₄²⁻ and Cl⁻ are derived from evaporite and balancing the cations, virtually all of the Na⁺ would be removed from solution for halite, but 7−98% of Ca²⁺ would be removed. Thus, correcting the samples for evaporite dissolution would have the overall effect of increasing Ca/Σ⁺ and decreasing SO₄/Σ⁺.

Elemental and isotope corrections for degassing and secondary carbonate precipitation

Elemental corrections for secondary carbonate precipitation

Secondary carbonate precipitation enriches the remaining fluid with Sr²⁺ so that Sr²⁺/Ca²⁺ increases. We can express the final Sr²⁺/Ca²⁺ ratio of the fluid relative to the initial ratio of Sr²⁺ to Ca²⁺ $\left(\frac{{\left[{{{\mathrm{Sr}}}}^{2+}\right]}_{0}}{{\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{0}}\right)$, which reflects the absence of secondary precipitation:

$$\frac{[{{{\mathrm{Sr}}}}^{2+}]}{\left[{{{\mathrm{Ca}}}}^{2+}\right]}=\frac{{\left[{{{\mathrm{Sr}}}}^{2+}\right]}_{0}}{{\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{0}}{{\gamma }_{{{\mathrm{CaC}}}{{\mathrm{O}}}_{3}}}^{({{\mathrm{kd}}}-1)}$$

(5)

Here, kd is the partition coefficient for Sr²⁺, and ${\gamma }_{{{\mathrm{CaC}}}{{\mathrm{O}}}_{3}}$ is the fraction of primary calcite that remains in the fluid⁵³. The ${\gamma }_{{{\mathrm{CaC}}}{{\mathrm{O}}}_{3}}$ can range from 0 to 1, where a value of 1 reflects no loss of primary carbonate, and a value of 0 would theoretically indicate that all primary carbonate has been lost to secondary precipitation. We constrained $\frac{{\left[{{{\mathrm{Sr}}}}^{2+}\right]}_{0}}{{\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{0}}$ from bedrock ratios in generic silicate and carbonate bedrock compositions⁵⁴, which form an endmember mixing line expressed by:

$$\frac{1,000[{{{\mathrm{Sr}}}}^{2+}]}{\left[{{{\mathrm{Ca}}}}^{2+}\right]}=a+b\frac{\left[{{{\mathrm{Na}}}}^{+}\right]}{\left[{{{\mathrm{Ca}}}}^{2+}\right]}$$

(6)

where a and b are the intercept and slope of the fit, respectively. The amount of secondary carbonate precipitation is then calculated as the deviation of the solute samples from the bedrock mixing line. We can solve for $\frac{{\left[{{{\mathrm{Sr}}}}^{2+}\right]}_{0}}{{\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{0}}$ by rearranging equation (5):

$$\frac{{\left[{{{\mathrm{Sr}}}}^{2+}\right]}_{0}}{{\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{0}}=\frac{[{{{\mathrm{Sr}}}}^{2+}]}{\left[{{{\mathrm{Ca}}}}^{2+}\right]}{{\gamma }_{{{\mathrm{CaC}}}{{\mathrm{O}}}_{3}}}^{(1-{{\mathrm{kd}}})}$$

(7)

Assuming the concentration of Na⁺ does not change due to secondary carbonate precipitation, we can express the initial ratio of Sr²⁺/Ca²⁺ in terms of the Na⁺/Ca²⁺ ratio:

$$\frac{1,000{[{{{\mathrm{Sr}}}}^{2+}]}_{0}}{{[{{{\mathrm{Ca}}}}^{2+}]}_{0}}=a+b\frac{{\left[{{{\mathrm{Na}}}}^{+}\right]}_{0}}{{\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{0}}=a+b\frac{\left[{{{\mathrm{Na}}}}^{+}\right]}{\left[{{{\mathrm{Ca}}}}^{2+}\right]}{\gamma }_{{{\mathrm{CaC}}}{{\mathrm{O}}}_{3}}$$

(8)

where $\frac{{\left[{{{\mathrm{Na}}}}^{+}\right]}_{0}}{{\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{0}}=\frac{\left[{{{\mathrm{Na}}}}^{+}\right]}{\left[{{{\mathrm{Ca}}}}^{2+}\right]}$

We then combine equations (7) and (8) and solve for ${\gamma }_{{{\mathrm{CaC}}}{{\mathrm{O}}}_{3}}$ numerically:

$$\frac{1,000[{{{\mathrm{Sr}}}}^{2+}]}{[{{{\mathrm{Ca}}}}^{2+}]}{{\gamma }_{{{\mathrm{CaC}}}{{\mathrm{O}}}_{3}}}^{\left(1-{{\mathrm{kd}}}\right)}-a-b\frac{\left[{{{\mathrm{Na}}}}^{+}\right]}{\left[{{{\mathrm{Ca}}}}^{2+}\right]}{\gamma }_{{{\mathrm{CaC}}}{{\mathrm{O}}}_{3}}=0$$

(9)

We corrected for secondary precipitation with a partition coefficient of k = 0.05, which is within the acceptable range of values for k (0.02–0.20) (refs. ^55,56,57).

Isotope fractionation due to CO₂ degassing and secondary carbonate precipitation

Fractionation of bicarbonate in water happens during degassing of CO₂ and during precipitation of CaCO₃. We assess the effect of CO₂ degassing and secondary carbonate precipitation on measured DIC and Ca²⁺ concentrations and on DI¹³C isotopic signatures. Reporting ¹⁴C as fraction modern (F¹⁴C) already accounts for fractionation that occurs in nature⁵⁸, so we do not correct these values.

Degassing will preferentially result in the loss of more depleted carbon, thus enriching the remaining fluid, whereas precipitation of carbonate will result in the loss of heavier (more enriched) carbon. To correct for CO₂ degassing and secondary precipitation, we use fractionation and enrichment factors that describe how carbon isotopes are fractionated due to individual processes²¹. Following the methodology of ref. ⁵⁹, we assume (1) that CO₂ degassing and secondary precipitation are irreversible reactions within an open system¹³ and (2) that half of the enrichment is due to degassing and half is due to precipitation, so that carbon is equally distributed between the two reactions. The carbon isotopic signature is expressed as ratio R (for example, ¹³C/¹²C) where the heavier isotope is the numerator. The fractionation of R is expressed as a ratio between different states, where A refers to the final state and B refers to the initial state:

$${\alpha }_{{\mathrm{A}}-{\mathrm{B}}}=\frac{{R}_{{\mathrm{A}}}}{{R}_{{\mathrm{B}}}}$$

(10)

The enrichment factor for the fractionation of phase A and B is commonly expressed in permil (‰), and can be calculated in relation to the fractionation factor α:

$${\varepsilon }_{{\mathrm{A}}-{\mathrm{B}}}\left({{\permil}}\right)=\left({\alpha }_{{\mathrm{A}}-{\mathrm{B}}}-1\right)\times 1,000$$

(11)

When α_A–B > 1 or ε_A–B > 0, phase A becomes enriched (heavier) during fractionation, whereas the phase A will become depleted (lighter) during fractionation if α_A–B < 1 or ε_A–B < 0.

The final isotopic composition of phase B (in ‰) after fractionation $({\delta }_{{{\mathrm{B}}}_{{{\mathrm{final}}}}})$ can be related to the initial composition of phase B $({\delta }_{{{\mathrm{B}}}_{{{\mathrm{initial}}}}})$, using the approximation of ref. ⁶⁰:

$${\delta }_{{{\mathrm{B}}}_{{{\mathrm{final}}}}}={\delta }_{{{\mathrm{B}}}_{{{\mathrm{initial}}}}}+{\varepsilon }_{{\mathrm{A}}-{\mathrm{B}}}\mathrm{ln}\left(\,{f}_{{\mathrm{B}}}\right)$$

(12)

where ${f}_{{\mathrm{B}}}$ is the fraction of the material B that remains after fractionation. Once we calculate the fractionation factors due to degassing and carbonate precipitation²¹, we can then combine the fractionation factor from both reactions as follows:

$${\alpha }_{{\mathrm{A}}-{\mathrm{C}}}=\frac{{R}_{{\mathrm{A}}}}{{R}_{{\mathrm{C}}}}=\frac{{R}_{{\mathrm{A}}}}{{R}_{{\mathrm{B}}}}\times \frac{{R}_{{\mathrm{B}}}}{{R}_{{\mathrm{C}}}}={\alpha }_{{\mathrm{A}}-{\mathrm{B}}}\times {\alpha }_{{\mathrm{B}}-{\mathrm{C}}}$$

(13)

The enrichment factor for CO₂ degassing is expressed as ${\varepsilon }_{{{{\mathrm{CO}}}}_{2}({\mathrm{g}})-{{{\mathrm{HCO}}}}_{3}}$, so the isotopic signature of HCO₃ after reaction 1 $\left({\delta }_{{{{{\mathrm{HCO}}}}_{3}}_{{{\mathrm{Step}}}1}}\right)$ can be expressed as:

$${\delta }_{{{{{\mathrm{HCO}}}}_{3}}_{{{\mathrm{Step}}}1}}={\delta }_{{{{{\mathrm{HCO}}}}_{3}}_{{{\mathrm{initial}}}}}+\frac{{\varepsilon }_{{{{\mathrm{CO}}}}_{2}({\mathrm{g}})-{{{\mathrm{HCO}}}}_{3}}}{2}\mathrm{ln}\left(\,{f}_{{{{\mathrm{HCO}}}}_{3}}\right)$$

(14)

In equation (14), the enrichment factor is divided by two since we assume that half of the total enrichment occurs with reaction 1 and the other half occurs with reaction 2 (equation (15)). The enrichment factor for carbonate precipitation is expressed as ${\varepsilon }_{{{{\mathrm{CaCO}}}}_{3}-{{{\mathrm{HCO}}}}_{3}}$, so the isotopic signature of HCO₃ after reaction 2 $\left({\delta }_{{{{{\mathrm{HCO}}}}_{3}}_{{{\mathrm{Step}}}2}}\right)$ is then:

$${\delta }_{{{{{\mathrm{HCO}}}}_{3}}_{{{\mathrm{Step}}}2}}={\delta }_{{{{{\mathrm{HCO}}}}_{3}}_{{{\mathrm{Step}}}1}}+\frac{{\varepsilon }_{{{{\mathrm{CaCO}}}}_{3}-{{{\mathrm{HCO}}}}_{3}}}{2}\mathrm{ln}\left(\,{f}_{{{{\mathrm{HCO}}}}_{3}}\right)$$

(15)

We then combine equations (14) and (15) to calculate the enrichment factor that encompasses the full set of reactions:

$${\delta }_{{{{{\mathrm{HCO}}}}_{3}}_{{{\mathrm{final}}}}}={\delta }_{{{{{\mathrm{HCO}}}}_{3}}_{{{\mathrm{initial}}}}}+{\varepsilon }_{{{\mathrm{C}}}_{{{\mathrm{loss}}}}-{{{\mathrm{HCO}}}}_{3}}\mathrm{ln}\left(\,{f}_{{{{\mathrm{HCO}}}}_{3}}\right)$$

(16)

where

$${\varepsilon }_{{{\mathrm{C}}}_{{{\mathrm{loss}}}}-{{{\mathrm{HCO}}}}_{3}}=\frac{{\varepsilon }_{{{{\mathrm{CO}}}}_{2}\left({\mathrm{g}}\right)-{{{\mathrm{HCO}}}}_{3}}+{\varepsilon }_{{{{\mathrm{CaCO}}}}_{3}-{{{\mathrm{HCO}}}}_{3}}}{2}$$

(17)

We calculate ${\alpha }_{{{{\mathrm{CaCO}}}}_{3}-{{{\mathrm{HCO}}}}_{3}}$ (equation (18)) and convert it to an enrichment factor, given the relationship between fractionation and enrichment factors in equation (11).

$${\alpha }_{{{{\mathrm{CaCO}}}}_{3}-{{{\mathrm{HCO}}}}_{3}}={\alpha }_{{{{\mathrm{CaCO}}}}_{3}-{{{\mathrm{CO}}}}_{2}({\mathrm{g}})}\times {\alpha }_{{{{\mathrm{CO}}}}_{2}({\mathrm{g}})-{{{\mathrm{HCO}}}}_{3}}$$

(18)

Enrichment factors are temperature dependent, so we calculated separate enrichment factors for the winter and summer samples using the seasonal range of temperatures from cold springs in the central Apennines^21,29.

To estimate ${f}_{{\mathrm{B}}}$, we calculate the fraction of DIC lost due to CO₂ degassing associated with secondary carbonate precipitation (γ_DIC). Some CO₂ degassing controlled by diffusion may also occur in the absence of carbonate precipitation⁴¹, although we have no way to estimate the magnitude of this process. However, previous studies suggest that the effect of diffusion-controlled degassing is negligible on isotope fractionation between gaseous CO₂ (CO_2(g)) and CO₂ dissolved in water (CO_2(aq)) because the reservoir of CO_2(aq) in solution is small between pH of 6 and 9, and the isotope fractionation between CO_2(g) and CO_2(aq) is small at 25 °C (ref. ⁶¹). By contrast, degassing caused by secondary carbonate precipitation produces a large fractionation between CO_2(g) and HCO₃⁻ at ambient temperatures⁶².

Thus, we first calculate the amount of HCO₃⁻ lost due to secondary carbonate precipitation (equations (3)−(9)). For each mol Ca²⁺ lost due to secondary carbonate precipitation, we lose 2 mol HCO₃⁻ so that the concentration of HCO₃⁻ before secondary precipitation can be expressed as:

$${\left[{{{\mathrm{HCO}}}}_{3}^{-}\right]}_{{{\mathrm{Initial}}}}=2\times \left({\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{{{\mathrm{Initial}}}}-{\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{{{\mathrm{Final}}}}\right)$$

(19)

where ${\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{{{\mathrm{Final}}}}$ is the measured concentration of Ca in our water samples, and the initial concentration of Ca²⁺ before secondary carbonate precipitation $\left({\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{{{\mathrm{Initial}}}}\right)$ is:

$${\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{{{\mathrm{Initial}}}}=\frac{{\left[{{{\mathrm{Ca}}}}^{2+}\right]}_{{{\mathrm{Final}}}}}{{\gamma }_{{{\mathrm{CaC}}}{{\mathrm{O}}}_{3}}}$$

(20)

The initial DIC concentration ${\left[{{\mathrm{DIC}}}\right]}_{{{\mathrm{Initial}}}}$ can then be expressed as the sum of the measured DIC concentration ${\left[{{\mathrm{DIC}}}\right]}_{{{\mathrm{Final}}}}$ and ${\left[{{{\mathrm{HCO}}}}_{3}^{-}\right]}_{{{\mathrm{Initial}}}}$, so that the fraction of DIC lost due to secondary precipitation $\left({\gamma }_{{{\mathrm{DIC}}}}\right)$ can be expressed as:

$${\gamma }_{{{\mathrm{DIC}}}}=\frac{{\left[{{\mathrm{DIC}}}\right]}_{{{\mathrm{Final}}}}}{{\left[{{\mathrm{DIC}}}\right]}_{{{\mathrm{Initial}}}}}$$

Given the assumption that diffusion-controlled degassing should be negligible, we use ${\gamma }_{{{\mathrm{DIC}}}}$ as an approximation of ${f}_{{\mathrm{B}}}$.

MEANDIR model

Scenario parameters

Scenario parameters for the inversion with MEANDIR are given in ref. ²¹ and details about the endmember compositions in Supplementary Text 2–4. Here we normalize all endmembers to the sum of measured concentrations (in μmol l^–1) of riverine Ca²⁺, Mg²⁺, Na⁺, SO₄²⁻ and DIC (equation (21)):

$${\chi }_{{\varSigma }^{+}}=2{\chi }_{{{{\mathrm{Ca}}}}^{2+}}+2{\chi }_{{{{\mathrm{Mg}}}}^{2+}}+{\chi }_{{{{\mathrm{Na}}}}^{+}}+2{\chi }_{{{{\mathrm{SO}}}}_{4}^{2-}}+{\chi }_{{{\mathrm{DIC}}}}$$

(21)

where $\chi$ designates the number of moles. Pyrite oxidation does not source any cations, although it is a source of SO₄²⁻ and a sink of alkalinity, so we include SO₄²⁻ in the normalization and treat the pyrite oxidation endmember independently of any weathering lithology³⁷. Including DIC in the normalization also allows us to represent carbon endmembers that are decoupled from the weathering of lithologic endmembers.

Each variable is normalized by the sum of major dissolved cations given in equation (21) and is expressed in milliequivalents (mEq). To assure that the sum of variable ratios equals 1 and to maintain internal consistency for each endmember (equation (22)), we calculate the most abundant ratio through mass balance³⁷.

$$1=\frac{2{\chi }_{{{{\mathrm{Ca}}}}^{2+}}}{\chi {\varSigma }^{+}}+\frac{2{\chi }_{{{{\mathrm{Mg}}}}^{2+}}}{\chi {\varSigma }^{+}}+\frac{{\chi }_{{{{\mathrm{Na}}}}^{+}}}{\chi {\varSigma }^{+}}+\frac{2{\chi }_{{{{\mathrm{SO}}}}_{4}^{2-}}}{\chi {\varSigma }^{+}}+\frac{{\chi }_{{{\mathrm{DIC}}}}}{\chi {\varSigma }^{+}}$$

(22)

For the DIC endmember, we assume DIC is sourced exclusively from biogenic carbon, metamorphic carbon, atmospheric carbon, cyclic inputs and carbonates. We calculate the DIC contribution for cyclic inputs and carbonate through charge balance and then convert the molar contributions to units of mEq. For the biogenic carbon endmember, we select a broad range of isotopic signatures for C3 plants that are dominant in central Italy⁶³ and account for the enrichment of δ¹³C due to plant degradation. DO¹³C estimates for the Tyrrhenian side of the Apennines are not available, although the importance of C4 crops such as maize within the Tevere catchment⁶⁴ would suggest that waters may have more enriched isotopic signatures relative to those of C3 plants.

Inversion approach

We invert all 100 samples for which we have all the required elemental and isotopic measurements. To select successful runs, we employ two separate criteria. First, we select from 1 × 10⁶ simulations those with reconstructed chemical compositions that fall within prescribed misfit ranges (the ‘iterate over samples’ approach in MEANDIR). The final value and uncertainty are then calculated as the median and interquartile range of all accepted simulations. For all ion data, we allow reconstructed value within 75–125% of the observations²¹. For δ³⁴S and δ¹³C isotopes, we allow a maximum misfit of ±2‰ and a misfit smaller than or equal to 0.05 for F¹⁴C (ref. ²¹). Given these bounds, 41% of winter samples and 57% of summer samples produce successful simulations (Supplementary Text 5). Other samples have misfits that are greater than the acceptable limits (Supplementary Text 5 and Supplementary Fig. 3)²¹. Second, we follow previous approaches of inversion models^38,65 and select the best 5% of simulations to calculate the inversion result from 1 × 10⁴ simulations. This approach produces successful inversions for all samples. From all 5% of accepted simulations, we calculate minimum and maximum misfit values²¹.

In all figures we present data from the inversions that fit within the prescribed misfit bounds (those samples with successes under the iterate-over-samples approach). These results represent the most conservative treatment of the inversion because it requires successful iterations to reproduce the observations within some misfit bounds. In the supplement, we provide the MEANDIR model fractional output using the selection of the top 5% of simulations²¹ and an alternative to summary Fig. 4 (Extended Data Fig. 6) that includes the full sample set (samples with successes using the iterate-over-samples approach and the results from the iterate-over-endmembers approach for the remaining samples).

Model outputs and calculations

The fractional contribution from each endmember is expressed as the median value from all accepted simulations, which we convert to concentrations, to compare results from all sampling locations and different spatial scales. To estimate inorganic CO₂ consumption and production, we calculate the concentration of CO₂ (in μmol l^–1) that is sequestered or released from weathering. For silicate weathering, the consumed CO₂ concentration ${\left[{{{\mathrm{CO}}}}_{2}\right]}_{{{\mathrm{Sil}}}}$ is calculated by assuming that each charge-equivalent ion sequesters 0.5 mol CO₂ (refs. ^38,65), such that

$${\left[{{{\mathrm{CO}}}}_{2}\right]}_{{{\mathrm{Sil}}}}=-0.5\left(2[{{{\mathrm{Ca}}}}^{2+}]+2[{{{\mathrm{Mg}}}}^{2+}]+[{{{\mathrm{Na}}}}^{+}]\right)$$

(23)

For metamorphic CO₂ release ${\left[{{{\mathrm{CO}}}}_{2}\right]}_{{{\mathrm{Meta}}}}$, every charge equivalent of metamorphic DIC $\left({\left[{{\mathrm{DIC}}}\right]}_{{{\mathrm{Meta}}}}\right)$ acts as a source for one mol CO₂ to the atmosphere.

$${\left[{{{\mathrm{CO}}}}_{2}\right]}_{{{\mathrm{Meta}}}}={\left[{{\mathrm{DIC}}}\right]}_{{{\mathrm{Meta}}}}$$

(24)

For pyrite oxidation ${\left[{{{\mathrm{CO}}}}_{2}\right]}_{{{\mathrm{Pyr}}}}$, we consider each charge equivalent of SO₄²⁻ as a source of 0.5 mol CO₂ because of the alkalinity consumption by sulfuric acid.

$${\left[{{{\mathrm{CO}}}}_{2}\right]}_{{{\mathrm{Pyr}}}}=0.5\left(2\left[{\mathrm{S}}{{\mathrm{O}}}_{4}^{2-}\right]\right)$$

(25)

We do not include K⁺ in our unmixing model or calculations because its inclusion reduces the number of successful runs in the MEANDIR model by more than 50% without substantially affecting the estimates of weathering and carbon sources.

Where discharge measurements were available from the regional hydrologic authorities²¹, we divided these measurements by the upstream drainage area to calculate run-off and converted the CO₂ concentrations into fluxes, expressed in tons of carbon (tC km^–2 yr^–1) (ref. ²¹). Daily discharge estimates were averaged over the two summer (July–August) or winter (March–April) months during which we sampled.