Jesse R Zondervan
email: j.zondervan@ucl.ac.uk

Robert G Hilton
email: robert.hilton@earth.ox.ac.uk

Mathieu Dellinger

Fiona Clubb

Tobias Roylands

Mateja Ogrič

Rock organic carbon oxidation CO2 release offsets silicate weathering sink

Main

The tectonic activity that builds mountains can result in the uplift and exposure of organic carbon in rocks (OCpetro) alongside silicate mineral phases. The OCpetro represents carbon stored in rocks that has accumulated over millions of years, previously sequestered from the atmosphere by photosynthesis and buried in sedimentary basins [START_REF] Derry | Neogene growth of the sedimentary organic carbon reservoir[END_REF] . Indeed, sedimentary and metasedimentary lithologies presently dominate bedrock geology of Earth surface, occupying ~64% of Earth surface [START_REF] Hartmann | The new global lithological map database GLiM: A representation of rock properties at the Earth surface[END_REF] and have OC concentrations of ~0.25 to > 1.0 weight percent by mass (%), whereas igneous rocks have much lower values (~ 0% or in the case of some marine basalts < 0.1%) [START_REF] Bolton | The weathering of sedimentary organic matter as a control on atmospheric O2: II. Theoretical modeling[END_REF] . Denudation supplies OCpetro to the surface through physical plus chemical weathering [START_REF] Hilton | erosion and the carbon cycle[END_REF][START_REF] Bolton | The weathering of sedimentary organic matter as a control on atmospheric O2: II. Theoretical modeling[END_REF] , and varies with rock type, relief, tectonic uplift, climate, and vegetation [START_REF] Larsen | The contribution of mountains to global denudation[END_REF]17 . Previous work has revealed the presence of OCpetro in soils and rivers [START_REF] Galy | Recycling of graphite during Himalayan erosion: A geological stabilization of carbon in the crust[END_REF][START_REF] Blair | The persistence of memory: The fate of ancient sedimentary organic carbon in a modern sedimentary system[END_REF][START_REF] Galy | Global carbon export from the terrestrial biosphere controlled by erosion[END_REF][START_REF] Grant | Global patterns of radiocarbon depletion in subsoil linked to rock-derived organic carbon[END_REF] and quantified the erosion of unweathered OCpetro [START_REF] Copard | Storage and release of fossil organic carbon related to weathering of sedimentary rocks[END_REF] and its global flux using data from the solid load of rivers at MtC yr -1 14, [START_REF] Galy | Global carbon export from the terrestrial biosphere controlled by erosion[END_REF] . In contrast, estimated global rates of OCpetro

Rhenium as an OCpetro oxidation proxy

The development of the trace element rhenium (Re) as a proxy to trace the oxidation of OCpetro across landscapes [START_REF] Dalai | Dissolved rhenium in the Yamuna river system and the Ganga in the Himalaya: role of black shale weathering on the budgets of Re, Os, and U in rivers and CO2 in the atmosphere[END_REF][START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF] has been underpinned by (i) the link between OC accumulation in marine sediments and organic matter being a host of Re [START_REF] Selby | Re-Os geochronology of organic rich sediments: an evaluation of organic matter analysis methods[END_REF][START_REF] Morford | Rhenium geochemical cycling: Insights from continental margins[END_REF] ; (ii) the paired loss of Re and OCpetro during weathering of sedimentary rocks [START_REF] Hilton | Geological respiration of a mountain belt revealed by the trace element rhenium[END_REF][START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF][START_REF] Jaffe | Mobility of rhenium, platinum group elements and organic carbon during black shale weathering[END_REF] ; and (iii) the geochemical behaviour of Re that means it is exported as a dissolved oxyanion [START_REF] Colodner | The geochemical cycle of rhenium: a reconnaissance[END_REF] , flushed from a near-surface, oxidative weathering zone [START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF] . In addition, studies tracking the fate of carbon released from the lithosphere during rock organic carbon weathering have found it can: directly enter the atmosphere as CO2 [START_REF] Soulet | Temperature control on CO2 emissions from the weathering of sedimentary rocks[END_REF][START_REF] Roylands | Capturing the short-term variability of carbon dioxide emissions from sedimentary rock weathering in a remote mountainous catchment, New Zealand[END_REF] or first dissolve as inorganic carbon in water [START_REF] Tune | Carbon dioxide production in bedrock beneath soils substantially contributes to forest carbon cycling[END_REF] , and some can be incorporated into microbial biomass [START_REF] Petsch | Treatise on Geochemistry[END_REF] .

In this study we compile published estimates of OCpetro oxidation using the dissolved Re proxy, supplemented with new estimates derived from published dissolved Re concentrations [START_REF] Hilton | Geological respiration of a mountain belt revealed by the trace element rhenium[END_REF][START_REF] Miller | Re-assessing the surface cycling of molybdenum and rhenium[END_REF][START_REF] Dalai | Dissolved rhenium in the Yamuna river system and the Ganga in the Himalaya: role of black shale weathering on the budgets of Re, Os, and U in rivers and CO2 in the atmosphere[END_REF][START_REF] Horan | Mountain glaciation drives rapid oxidation of rock-bound organic carbon[END_REF] (see Methods). A forward mixing model is used to quantify the proportion of dissolved Re from OCpetro oxidation using ion ratios [START_REF] Horan | Carbon dioxide emissions by rock organic carbon oxidation and the net geochemical carbon budget of the Mackenzie River Basin[END_REF][START_REF] Dalai | Dissolved rhenium in the Yamuna river system and the Ganga in the Himalaya: role of black shale weathering on the budgets of Re, Os, and U in rivers and CO2 in the atmosphere[END_REF] , while constraints on organic carbon to rhenium contents of rocks being weathered ([OCpetro]/Re) come from new and published measurements (Methods, Supplementary Table S3). Our compilation includes 59 river basins, covering a range of drainage areas (50 -5,900,000 km 2 ), denudation rates and

Distribution of OCpetro availability

We spatially quantify the carbon stock and weathering flux of OCpetro at Earth's surface using a data-driven modelling approach. Our model incorporates topographic and lithological factors to estimate OCpetro stocks, denudation rates and oxidative weathering rates, and is calibrated using our Re-proxy compilation (Supplementary Table S1). Unlike silicate weathering, which quickly becomes kinetically limited with increasing mineral supply by denudation [START_REF] West | Thickness of the chemical weathering zone and implications for erosional and climatic drivers of weathering and for carbon-cycle feedbacks[END_REF] , OCpetro weathering appears to be predominately a supply-limited process [START_REF] Petsch | Treatise on Geochemistry[END_REF] . This is reflected in oxidation rates which scale with erosion up to some of the highest erosion rates found on Earth, such as Taiwan and the European Alps [START_REF] Hilton | Geological respiration of a mountain belt revealed by the trace element rhenium[END_REF][START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF] . Recent work at the rock outcrop scale has shown that temperature and hydrology can control OCpetro oxidation and CO2 release over time in locations with very high rates of denudation [START_REF] Soulet | Temperature control on CO2 emissions from the weathering of sedimentary rocks[END_REF][START_REF] Roylands | Capturing the short-term variability of carbon dioxide emissions from sedimentary rock weathering in a remote mountainous catchment, New Zealand[END_REF] . However, whilst the spatial control of denudation rates is well demonstrated on inter-catchment OCpetro oxidation rates [START_REF] Hilton | Geological respiration of a mountain belt revealed by the trace element rhenium[END_REF][START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF] our spatial catchment-scale Re-proxy compilation does not express other environmental controls (Methods). While temperature and hydrology controls likely operate, their spatial predictive power is small based on the available data. Here, oxidative weathering is modelled at a 1-km 2 grid scale, resolving at the scale of catchments constrained by the Re proxy (Supplementary Table S1).

The flux of CO2 release by OCpetro oxidation, Jox (mass × length -2 × time -1 ), can be expressed by a mass-balance of the form:

Jox = ε • ρ • [OCpetro] • χ (Eq. 1)
where ε (length × time -1 ) is the denudation rate, ρ is rock density (mass × length -3 ), [OCpetro] is the OC concentration in rock (mass × mass -1 ) and χ is the weathering intensity as the fraction of OC weathered from rock. Weathering intensity χ has been shown to vary between low values of 0.2 in highly erosive settings [START_REF] Hilton | Geological respiration of a mountain belt revealed by the trace element rhenium[END_REF] and very high values of 0.98 in slow denudation settings [START_REF] Petsch | Treatise on Geochemistry[END_REF] with most falling in a range of 0.6 -0.9 [START_REF] Hilton | Geological respiration of a mountain belt revealed by the trace element rhenium[END_REF][START_REF] Horan | Mountain glaciation drives rapid oxidation of rock-bound organic carbon[END_REF][START_REF] Horan | Carbon dioxide emissions by rock organic carbon oxidation and the net geochemical carbon budget of the Mackenzie River Basin[END_REF] . Thus, χ presents a significantly smaller variance across environments in contrast to denudation rates and [OCpetro] which vary spatially by more than four orders of magnitude.

To constrain the stock of OCpetro in the near surface we use OCpetro within the first meter of sedimentary rocks 14 , a reassessment of deep soil radiocarbon data which provides evidence for OCpetro inputs [START_REF] Grant | Global patterns of radiocarbon depletion in subsoil linked to rock-derived organic carbon[END_REF] , and is of comparable magnitude to that of global soils (2060 ± 215 Gt OC) [START_REF] Batjes | Harmonized soil property values for broad-scale modelling (WISE30sec) with estimates of global soil carbon stocks[END_REF] and marine sediments (2322 ± 75 Gt OC) [START_REF] Atwood | Global patterns in marine sediment carbon stocks[END_REF] . As opposed to soil OC stocks, the distribution of OCpetro is primarily controlled by the geological history of continents. Whilst the highest [OCpetro] is found in black shales (Extended Data Fig. 4), such rocks compose a tiny fraction of the Earth's surface [START_REF] Hartmann | The new global lithological map database GLiM: A representation of rock properties at the Earth surface[END_REF] , and instead, most OCpetro is found in fine-grained sedimentary deposits such as shales (Fig. 1b). Geospatial patterns reveal low OCpetro stocks on the African continent (Fig. 1b), owing to a low occurrence of fine-grained sedimentary rocks. In contrast, substantial portions of Eurasia, South America, and the middle of North America east of the Rocky Mountains contain shales. The overlap of OCpetro stocks and patterns of denudation driven mostly by rock uplift in mountains determines the exposure of this OC stock to oxidative weathering. We estimated denudation using a probabilistic spatial model that incorporates catchment-scale cosmogenic radionuclide (CRN) denudation rates [START_REF] Codilean | An open cosmogenic isotope and luminescence database[END_REF] , digital topography [START_REF] Amatulli | Geomorpho90m, empirical evaluation and accuracy assessment of global high-resolution geomorphometric layers[END_REF] , and lithological maps [START_REF] Hartmann | The new global lithological map database GLiM: A representation of rock properties at the Earth surface[END_REF] . The resultant modelled global denudation rate and its interquartile range is Gt yr -1 , within range of recent estimates of global denudation at Gt yr -1 16 and 15 ± 2.8 Gt yr -1 17 .

Spatial model of OCpetro oxidation

Rather than the more classical mean-field parameterization schemes previously employed to model OCpetro supply rates [START_REF] Copard | Storage and release of fossil organic carbon related to weathering of sedimentary rocks[END_REF] , we use a probabilistic approach 41 that accounts for the Across the land surface, OCpetro weathering is relatively focused (Fig. 1d), with variations in rock type and relief, which drive OCpetro content and denudation respectively, determining the magnitude of OCpetro oxidation and CO2 release. Large regions of the African continent have lower OC stocks in bedrock and have lower relief, which together limit OC weathering. In contrast, higher OCpetro oxidation rates are estimated for northern latitudes, where OC-rich rock and high-relief landscapes are more prevalent. Overall, 10% of the Earth surface with the highest OCpetro oxidation rates account for 60% of the global flux in our model. The world average rate is 0.5 tC km -2 yr -1 , hotspots (10 times world average) and hyperactive areas (all areas >5 times world average) are responsible for 32% and 44% of CO2 emissions, while representing only 1.2 % and 3% of ice-free terrestrial land area, respectively. OCpetro weathering rates in our model are more spatially concentrated than a 1-km resolution spatial model of silicate weathering [START_REF] Plank | Subducting carbon[END_REF] , where hotspots (0.51% by area) and hyperactive areas (2.9% by area) accounted for 8.6% and 19.6% of total CO2-consumption. This outcome appears reasonable because OCpetro is less common spatially than silicate minerals and react faster [START_REF] Hilton | erosion and the carbon cycle[END_REF][START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF] .

Weathering CO2 sources versus sinks

The OCpetro weathering flux and release of CO2 to the atmosphere of MtC yr -1 is similar to global terrestrial CO2 uptake by silicate weathering (94 -143 MtC yr -1 ) [START_REF] Moon | New estimates of silicate weathering rates and their uncertainties in global rivers[END_REF] . Silicate weathering involves dissolved and gaseous CO2 uptake through bicarbonate production and the release of dissolved ions, some of which then precipitate as marine carbonate rocks 4 . The resultant total transfer of carbon from the atmosphere to the lithosphere by silicate weathering is 47 -72 MtC year -1 . In addition to their opposing impacts on the transfer of carbon between the atmosphere and lithosphere, fluxes of silicate weathering vs OCpetro oxidation may have contrasting responses to climate. Silicate weathering is invoked as a negative feedback to climate warming through increased rates of silicate weathering from increased temperature and a more vigorous hydrological cycle, drawing down more CO2 [START_REF] West | Thickness of the chemical weathering zone and implications for erosional and climatic drivers of weathering and for carbon-cycle feedbacks[END_REF][START_REF] Walker | A negative feedback mechanism for the long-term stabilization of Earth's surface temperature[END_REF] . In contrast, in high denudation rate settings the CO2 release from OCpetro oxidation may increase with temperature [START_REF] Soulet | Temperature control on CO2 emissions from the weathering of sedimentary rocks[END_REF][START_REF] Roylands | Capturing the short-term variability of carbon dioxide emissions from sedimentary rock weathering in a remote mountainous catchment, New Zealand[END_REF] , while links to glacial erosion processes complicate the feedback between oxidative weathering and climate [START_REF] Horan | Mountain glaciation drives rapid oxidation of rock-bound organic carbon[END_REF] .

Silicate and OCpetro weathering processes may overlap, as sedimentary rocks contain silicate minerals as well as OC. However, the relative magnitude of these fluxes will vary spatially with climate, rock type and denudation [START_REF] West | Thickness of the chemical weathering zone and implications for erosional and climatic drivers of weathering and for carbon-cycle feedbacks[END_REF][START_REF] Walker | A negative feedback mechanism for the long-term stabilization of Earth's surface temperature[END_REF] . We assess the net balance of rock weathering within major river basins (Fig. 2), using our OCpetro oxidation model and silicate weathering estimates [START_REF] Moon | New estimates of silicate weathering rates and their uncertainties in global rivers[END_REF] .

Within uncertainties, rock weathering in about a third of the major river basins is a net source of CO2 after OCpetro oxidation is considered, even while using the values of initial atmospheric CO2 consumption of silicate weathering rather than the smaller quantity of CO2 eventually locked up in the lithosphere through carbonate precipitation of the associated released dissolved ions (Fig. 2a). The Yangtze (Changjiang) and Mekong draining the eastern flanks of the Himalayas, and the Mackenzie River draining shales west of the Rockies in Canada are major sources of CO2 from rock weathering. These high-emitting basins have in common some of the highest basin-average denudation rates and OCpetro stocks (Fig. 2b-c), which is consistent with OCpetro oxidation being driven by OCpetro stocks and denudation (Eq. 1; [START_REF] Hilton | Geological respiration of a mountain belt revealed by the trace element rhenium[END_REF][START_REF] Petsch | Treatise on Geochemistry[END_REF][START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF] ).

Hotspots of CO2 release during rock weathering appear to lie at the edges of major active mountain ranges where relatively young, marine sedimentary deposits are uplifted and supplied to oxygen through denudation. Examples include the shales of the Himalayan collision zones and east of the Rocky Mountains (Fig. 1b,1d). On the other hand, basins where rock weathering is the biggest net sink of CO2 do not necessarily lie at the extremes of low denudation and low OCpetro stocks. Whilst the tropical Congo River and volcanicsdominated Godavari River basins have low basin-average denudation rates and low OCpetro stocks, the biggest weathering sink, the Amazon River, lies in the global middle range of denudation rates and OCpetro stocks (Fig. 2b,2c). There, the kinetically limited silicate weathering reaction benefits from long sediment residence times and a warm, humid climate.

While the Andes is a hotspot for OCpetro oxidation fluxes (Figure 1d), the exceptionally large lowland drainage area of the Amazon means that OCpetro oxidation may be supply limited. In a third of river basins weathering remains carbon neutral within uncertainty such as the volcanic-rich Columbia River catchment.

To avoid large swings in atmospheric CO2 over millions of years and maintain an apparent close balance of CO2 sources and sinks [START_REF] Berner | The need for mass balance and feedback in the geochemical carbon cycle[END_REF][START_REF] Derry | Carbonate weathering, CO2 redistribution, and Neogene CCD and pCO2 evolution[END_REF] , any potential imbalances in weathering-derived carbon fluxes must be addressed by accounting for other components in the long-term carbon cycle. Solid-Earth degassing associated with volcanoes and diffuse release from metamorphism in subduction zones is responsible for 79 ± 9 MtC yr -1 released into the atmosphere (Fig. 3a; 47 ), while any additional (non-subduction) global CO2 release during orogenic metamorphism and sulfide oxidation and inorganic C uptake during seafloor weathering are more poorly constrained 3 . As our results show that the weathering of OCpetro offsets silicate weathering in the long-term carbon cycle, a large additional sink of CO2 is needed. This may be provided by burial of organic matter in ocean sediments, which could contribute as much as 170 MtC yr -1 (Figure 3b; [START_REF] Smith | High rates of organic carbon burial in fjord sediments globally[END_REF] ). In addition, as OCpetro fluxes can overtake silicate weathering during periods of more intense uplift and erosion (Fig. 2b,d; Extended Data Fig. 8), the question whether orogenic periods in Earth history are sources or sinks of atmospheric CO2 is now a reopened question [START_REF] Hilton | erosion and the carbon cycle[END_REF][START_REF] Roylands | Capturing the short-term variability of carbon dioxide emissions from sedimentary rock weathering in a remote mountainous catchment, New Zealand[END_REF][START_REF] Evans | Degassing of metamorphic carbon dioxide from the Nepal Himalaya[END_REF][START_REF] Märki | An unshakable carbon budget for the Himalaya[END_REF] . The net balance will depend on factors such as transport of terrestrial biospheric carbon to oceans ( MtC yr -1 ) and its burial [START_REF] Galy | Global carbon export from the terrestrial biosphere controlled by erosion[END_REF] . A global comparison of catchment-scale OCpetro oxidation yields and estimated terrestrial biospheric OC burial (Extended Data Figure 8) suggest the OC burial can apparently offset or even overcompensate CO2 release from OCpetro oxidation. This understanding persists when the additional marine OC burial sink in sediment is factored into global flux estimates (Fig. 3b; [START_REF] Smith | High rates of organic carbon burial in fjord sediments globally[END_REF] ). The dynamics of Earth's thermostat thus need to be revisited to account for variation in all these fluxes and consider how their relative importance may have changed as life evolved and the OC stocks of sedimentary rocks have increased [START_REF] Hilton | erosion and the carbon cycle[END_REF][START_REF] Kump | Interpreting carbon-isotope excursions: carbonates and organic matter[END_REF] . optimize the model and then extrapolate OCpetro oxidation rates (Extended Data Fig. 1).

Model simulations were implemented at 1-km grid scale (Mollweide projection, WGS84 datum) in the Python programming language. R and python code, their environments and the necessary data files to run these are all deposited in a Zenodo depository (https://doi.org/10.5281/zenodo.8144244) and additionally code is available from Github: https://github.com/jessezondervan/Global_OCpetro_Oxidation.

Methods

The workflow of the materials and methods (Extended Data Fig. 1) starts with the compilation and derivation of rhenium-derived OCpetro oxidation flux estimates (Section 1), before detailing the global spatial OCpetro oxidation model (Section 2), its denudation and OCpetro stock sub-models (Sections 2.1, 2.2) and the Monte Carlo routines used in the model approach (Section 2.4).

Section 1. Rhenium-based river catchment estimates of OCpetro oxidation From a series of dissolved rhenium measurements (typically completed by ICP-MS), the dissolved Re flux JRe (t yr -1 ) can be used to estimate OCpetro oxidation flux, JOCPetro-ox (tC yr -1 ) using:

𝐽 !"#$%&'(') = 𝐽 *$ × $ [!" !"#$% ] [*$] % - × 𝑓 . (Eqn. S1)
where fc is the fraction of Re derived from OCpetro oxidation [START_REF] Horan | Carbon dioxide emissions by rock organic carbon oxidation and the net geochemical carbon budget of the Mackenzie River Basin[END_REF] and ([OCpetro]/[Re])i is the organic carbon to rhenium concentration ratio (g g -1 ) in rocks undergoing weathering. In some of the catchments where it may be important, an additional term, not shown in Equation S1, has been applied to correct for the presence of graphite which may not undergo alteration during weathering [START_REF] Horan | Mountain glaciation drives rapid oxidation of rock-bound organic carbon[END_REF] .

Compiled published measurements

In this study we compile estimates of OCpetro oxidation using the dissolved Re proxy from published literature (Supplementary Table S1). These include: the Yamuna River, India 24 ; 10 Taiwanese Rivers 7 ; 4 rivers from the western Southern Alps 33 ; 4 rivers from the Mackenzie Basin, Canada [START_REF] Hilton | erosion and the carbon cycle[END_REF][START_REF] Horan | Carbon dioxide emissions by rock organic carbon oxidation and the net geochemical carbon budget of the Mackenzie River Basin[END_REF] ; and 6 rivers draining the Peruvian Andes 51 . Two Swiss catchments [START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF] are not included because of their very small catchment area compared to the geospatial scales over which we complete the upscaling.

For some of these case studies dissolved rhenium flux has been estimated from repeated sampling and discharge records [START_REF] Horan | Carbon dioxide emissions by rock organic carbon oxidation and the net geochemical carbon budget of the Mackenzie River Basin[END_REF] , while earlier studies all include single snapshot samples [START_REF] Hilton | Geological respiration of a mountain belt revealed by the trace element rhenium[END_REF][START_REF] Dalai | Dissolved rhenium in the Yamuna river system and the Ganga in the Himalaya: role of black shale weathering on the budgets of Re, Os, and U in rivers and CO2 in the atmosphere[END_REF] , and all include measurements of the local sedimentary rock composition. Most of these compiled studies have used dissolved ion ratios to estimate the source of dissolved Re, i.e. fc (Eqn. S1), apart from the Taiwan dataset [START_REF] Hilton | Geological respiration of a mountain belt revealed by the trace element rhenium[END_REF] . While uncertainties on the OCpetro oxidation yields appear relatively large (Supplementary Table S1), it is important to note that the measured range in yields is much larger than the uncertainties.

New estimates of OCpetro oxidation

To expand the 25 estimates of OCpetro oxidation from river catchments described previously, we build on a previous study of dissolved Re fluxes in large rivers that reports dissolved Re concentrations and fluxes for major basins around the world [START_REF] Miller | Re-assessing the surface cycling of molybdenum and rhenium[END_REF] . We use these measurements and combine them with estimates of fc and ([OCpetro]/[Re])i, discussed in the following sections, to calculate OCpetro oxidation yields with associated uncertainties using published approaches [START_REF] Horan | Carbon dioxide emissions by rock organic carbon oxidation and the net geochemical carbon budget of the Mackenzie River Basin[END_REF][START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF] In locations with significant local sources of fossil fuel combustion (e.g., coal-fired power plants or steel works), rainwater can contain concentrations of Re that approach those of river water [START_REF] Petsch | Treatise on Geochemistry[END_REF][START_REF] Ogrič | Low rates of rock organic carbon oxidation and anthropogenic cycling of rhenium in a slowly denuding landscape[END_REF] , whereas locations that have minimal impacts from local pollution sources have Re concentrations in rainwater that are below detection [START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF][START_REF] Horan | Mountain glaciation drives rapid oxidation of rock-bound organic carbon[END_REF] . In the large river dataset 9 some large rivers are noted to have markedly increased Re concentrations and fluxes, with the conclusion that this was due to anthropogenic Re inputs. In a first order catchment of the Mississippi Basin, this has been confirmed by a detailed Re mass balance [START_REF] Ogrič | Low rates of rock organic carbon oxidation and anthropogenic cycling of rhenium in a slowly denuding landscape[END_REF] . A study of Re across Indian catchments suggests that whilst Re in Himalayan catchments and the mainstem Ganges and Brahmaputra behave conservatively, peninsular lower relief catchments with denser populations and industrial activity suggest anthropogenic inputs [START_REF] Rahaman | Rhenium in Indian rivers: Sources, fluxes, and contribution to oceanic budget[END_REF] . For this study's purposes to quantify weathering reactions, we only use Himalayan rivers and the mainstem Ganges and Brahmaputra in India and we have further excluded Re data from the Danube, Mississippi, and Yangtze rivers from our analysis. Our addition of catchment Re data to the Miller dataset includes a large contribution of small upland catchments with higher average erosion rates, where the authors of these studies selected sites with minimal human disturbance (Supplementary Table S1). We further consider the role of anthropogenic Re in our model results in section 3.

Estimation of Re source and fc

To estimate the fraction of dissolved Re sourced from OCpetro, fc, for the rivers in the Re flux dataset [START_REF] Miller | Re-assessing the surface cycling of molybdenum and rhenium[END_REF] , we follow a previously used forward model mixing approach [START_REF] Horan | Carbon dioxide emissions by rock organic carbon oxidation and the net geochemical carbon budget of the Mackenzie River Basin[END_REF][START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF] :

ReOC = Retot × fc = Retot -Resulf -Resil (Eqn. S2)
Where ReOC is the rhenium concentration of OCpetro-derived Re in the dissolved load, Retot is the measured concentration, Resulf and Resil are the concentrations derived from weathering of sulfide and silicate minerals respectively. These unknowns can be quantified as:

𝑅𝑒 /012 = 𝑆𝑂 3 × $ *$ 4! & % /012 (Eqn. S3) 𝑅𝑒 /-1 = 𝑁𝑎 × $ *$ 56 % /-1 (Eqn. S4)
where the element ratios of the end members for silicate,

$ *$ 56 % /-1
, and sulfide

$ *$ 4! & % /012
are defined and with the assumption that the dissolved sulfate (SO4) and sodium (Na) respectively derive only from sulfide oxidation and silicate weathering and are conservative.

This returns an upper bound on the Resulf and Resil components (Supplementary Table S2).

Following recent work [START_REF] Horan | Carbon dioxide emissions by rock organic carbon oxidation and the net geochemical carbon budget of the Mackenzie River Basin[END_REF]

Constraints on ([OCpetro]/[Re])i

A recent compilation 54 provides measurements of [OCpetro]/[Re]i from rock samples of different ages around the world. However, most of these measurements were made on black shales, with OCpetro contents > 1% which occur on only 0.3% of the Earth surface (Fig. S5).

Riverbed material sediments from erosive catchments provide an alternative way to capture landscape-scale average rock composition, albeit with some potential for weathering to alter the primary signal. Here we compile measurements of [OCpetro]/[Re] on bed materials from rivers around the world (Supplementary Table S3; Extended Data Fig. 2) and supplement this dataset with additional samples from mudrocks of the Eastern Cape, New Zealand, and the Peruvian Andes measured using methods described in detail previously [START_REF] Hilton | Concentration-Discharge Relationships of Dissolved Rhenium in Alpine Catchments Reveal Its Use as a Tracer of Oxidative Weathering[END_REF] . We find that regions with lower OCpetro concentrations that are more typical of sedimentary rocks at the continental surface -units including fine-grained sedimentary rocks make up > 35 % of Earth surface (Extended Data Fig. 5) -have lower and more consistent ratios of OC and Re in their rocks. The samples from the Peel River in the Mackenzie River basin [START_REF] Horan | Carbon dioxide emissions by rock organic carbon oxidation and the net geochemical carbon budget of the Mackenzie River Basin[END_REF] , overlap the lower end of the published black shale values. Since this is the catchment with the highest proportion of black shales in our Re dataset, these samples allow us to capture the imprint of this important marginal lithology at the landscape-scale.

The bedrock composition in the catchments of rivers studied in the Re flux dataset 9 are not reported. However, we note the good geographic coverage and number of samples that we have from riverbed materials from erosive settings around the world. These provide constraint on the initial organic carbon to rhenium ratio in the rocks. To conservatively quantify uncertainty in the range of OCpetro oxidation rates from dissolved Re data we perform a Monte Carlo simulation in which we uniformly sample the entire range of measured [OCpetro]/[Re] values, from low values indicative of carbon-poor and/or metamorphic rocks 2.5 x 10 -8 g g -1 33 towards 1.26 x 10 -6 34 in catchments with higher OC in rocks (Supplementary Table S3; Extended Data Fig. 3).

OCpetro oxidation yields and uncertainties

Equation 1 is used for each basin in the Re flux dataset [START_REF] Miller | Re-assessing the surface cycling of molybdenum and rhenium[END_REF] . Uncertainties in fc derive from the range of values used in the sulfide and silicate end member compositions (Eqns. S3, S4). For

([OCpetro]/[Re]
) we use the range of values discussed in Section 1.2.2 (Extended Data Fig. 3).

A Monte Carlo uncertainty propagation is used on these variables, with 10,000 randomly selected combinations of input values (with uniform sampling) are used to estimate JOCpetro-ox for each basin. The median value of the Monte Carlo simulation and the interquartile range are reported (Supplementary Table S1).

Geospatial catchment boundaries

To derive the catchment outlines and areas of Re-proxy samples in our compiled dataset, we used the HYDROSHEDS flow direction grid at 3 arc-second resolution [START_REF] Lehner | New global hydrography derived from spaceborne elevation data[END_REF] , and ArcGIS Pro 56 .

For catchments in Iceland and outside the latitudinal cover of HYDROSHEDS, catchments were derived from ALOS AW3D using TauDEM functionality in OpenTopography 57 and from the HYDRO1K flow direction grid respectively [START_REF]HYDRO1k Elevation Derivative Database[END_REF] . Whilst most published sample coordinates Supplementary Table S1) give the correct location on the cited drainage systems, in a handful of cases coordinates had to be amended by up to a few km, which may reflect errors in transcribing (e.g., Kikori and Purari 9 ). Final quality control included a comparison of the extracted drainage basin areas and those published, with good agreement overall (< 2% residual). However, some drainage areas cited in the Re flux dataset 9 refer to the river mouth, rather than the river catchment upstream of the Re sample location. In these cases, we use the Re sample location and its upstream catchment. Finalised coordinates of Re samples snapped to the drainage system are given in Supplementary Table S1, together with the Re locations' upstream drainage area. Spatial files of upstream drainage boundaries and Re sample locations are available on Zenodo (Available from: https://doi.org/10.5281/zenodo.8144244).

To convert dissolved Re concentrations into Re fluxes, average annual water discharge was calculated using published numbers at gauges (Supplementary Table S1) and scaled to the upstream drainage area of Re sample locations.

In addition to spatial catchment boundaries for the Re proxy dataset, we compare our spatial model output to published estimates of silicate weathering 10 that use the GRDC dataset of Major River Basins of the World 59 . Drainage areas used by [START_REF] Moon | New estimates of silicate weathering rates and their uncertainties in global rivers[END_REF] have slight discrepancies with those found in the GRDC dataset. We account for these in our analysis of major river basin net weathering flux (Supplementary Table S4).

as the spatial derivative of elevation -decreases, resulting in an artificial flattening effect [START_REF] Larsen | The contribution of mountains to global denudation[END_REF] .

As our Monte Carlo framework is computationally intensive, using a 90-m resolution global raster input would not be feasible. However, we use a 90-m resolution slope dataset to run regression curves shown in Extended Data Fig. 6, after which we output a 90-m resolution raster dataset of estimated denudation rates using the median regression curve. By resampling the raster dataset of estimated denudation rates to 1-km resolution after conversion from slope values, we avoid the bias that can lead to an underestimation of denudation by the flattening effect. In our Monte Carlo framework, the quantile regression curves for each raster value can then be sampled to draw a representative denudation value out of the empirical distribution of denudation rates.

Model calibration

The global model is calibrated by minimising the residual with the Re-proxy based estimates of OCpetro oxidation (tC yr -1 ) from 59 globally distributed river basins (Supplementary Table S1). Model selection was performed by running a Monte Carlo simulation (10,000 runs), using the variable OCpetro stock and denudation models described above, to find the output which minimises total residuals across all 59 calibration basins simultaneously, such that the sum of all basin residuals was < 1%. These simulations were run on the University of Oxford's Advanced Research Computing (ARC) facility, taking about 24 core hours per simulation. The residuals of individual basins can be quite large for the biggest catchments (e.g., the Amazon basin), but the relative residual especially for the larger basins falls within the uncertainty of model outputs, while accurately predicting the total OCpetro oxidation flux globally (Extended Data Fig. 7). We note that overall, in basins with moderate OCpetro oxidation fluxes, the model may return conservative estimates. However, because this model has the advantage of being globally and spatially explicit, regional over-and underestimation of rock OC oxidation, especially at a local scale (< 10,000 km 2 ), trade off, while we are able to capture regional differences due to tectonics and geological setting (Fig. 1c).

Section 3. Limitations and uncertainties

There is a temporal mismatch between CRN denudation data which informs our probabilistic Results of model vs Re-predicted OCpetro oxidation fluxes help us to assess the potential for anthropogenic Re input to impact our estimates (Extended Data Fig. 7). We have considered anthropogenic Re inputs by removing three large river basins from a previous compilation [START_REF] Miller | Re-assessing the surface cycling of molybdenum and rhenium[END_REF] and by adding carefully selected river catchment sites to our Re dataset (Section 1.2). In addition, our conversion of Re fluxes to OCpetro oxidation is conservative because we uniformly sample the range of Re/OC ratios starting at the lowest measured Re/OC ratio (Section 1.2.2). This leads to error bars within our estimates that are conservatively large.

Most notably, the model outputs of OCpetro oxidation vs the Re-estimated fluxes for each basin (Extended Data Figure 7) show a tendency for the model to underpredict smaller catchments more than larger catchments. Our confidence in the weathering signal from Re in the small upland catchments is highest, and the upland, high erosion rate regions that these catchments sample contribute a dominant proportion of the global OCpetro flux in our model.

Consequently, whilst we cannot completely deconvolve the effect of anthropogenic Re in our constraints, we have confidence that the effect is unlikely to result in a significant overprediction of global OCpetro flux estimates.

The global extrapolation of OCpetro oxidation proxy data attempts to account for the dataset's underlying heterogeneities in denudation and OCpetro stocks. However, it does not consider variability in temperature or precipitation which may control weathering -as seen in small scale field measurements of OCpetro oxidation at sites of high denudation [START_REF] Soulet | Temperature control on CO2 emissions from the weathering of sedimentary rocks[END_REF][START_REF] Roylands | Capturing the short-term variability of carbon dioxide emissions from sedimentary rock weathering in a remote mountainous catchment, New Zealand[END_REF] . This is primarily due to the size of the Re-proxy catchment database, its spatial coverage and uncertainties inherent in any proxy approach. While the Re-proxy dataset is latitudinally variable (Fig. 1a) the model misfit minimization procedure shows the first order controls on flux by OCpetro stock and denudation (Extended Data Fig. 7) meaning that any climatic controls on weathering could be not resolved at the global scale. We note that any bias introduced by extrapolating the global Re-proxy data without including climatic spatial controls on weathering intensity is likely to be minimal, because the underlying dataset spans from the tropics to Arctic locations.

Previous work has suggested that OCpetro oxidation and cycling of other OC pools can take place during floodplain transport in large fluvial systems [START_REF] Bouchez | Oxidation of petrogenic organic carbon in the Amazon floodplain as a source of atmospheric CO2[END_REF][START_REF] Repasch | Fluvial organic carbon cycling regulated by sediment transit time and mineral protection[END_REF] . While the Re-proxy dataset includes large basins with extensive floodplain areas (Fig. 1a), our model-data misfit approach may attribute the downstream fluxes to any higher denudation parts of the catchment. When Finally, our model includes implicit assumptions and features of the datasets which must be acknowledged. First, the model assumes a steady state, which might not accurately describe OCpetro oxidation in regions responding to changes in uplift, deglaciation, or human activities,

which may yet to have reached steady-state conditions.

Second, the catchment-scale CRN denudation data used in our model generally derive from lithologies that are quartz-rich and coarse-grained. These typically have lower erodibilities, potentially leading to an underestimation of denudation rates of softer shales which contain the majority of OCpetro stocks.

  oxidation and CO2 release during rock weathering currently derive from carbon cycle mass balance arguments, or ballpark upscaling of global river trace element fluxes 8 , with a range of estimates from 38 MtC yr -1 21 to 100 MtC yr -1 22 . The uncertainty on OCpetro oxidation fluxes is highlighted by recent work that cites a potential overall range for CO2 release of 0 -300 MtC yr -1 23 . Consequently, to determine the role of rock weathering in the carbon cycle we require a robust, global quantification of OCpetro oxidation over Earth's surface. Here we combine a compilation of OCpetro oxidation proxy data from dissolved rhenium in well-studied catchments around the world; new probabilistic models of global OCpetro stock and denudation; and a spatially explicit OCpetro oxidation model with quantified uncertainty. This approach derives a global flux by extrapolating proxy derived OCpetro oxidation data, whilst accounting for sampling bias across variables such as denudation rate and underlying geology.

Figure 1 .

 1 Figure 1. Spatial patterns of global OCpetro stock and oxidation. (a) Locations of Re proxy samples and their upstream catchments. (b) Spatially explicit estimates of OCpetro stocks in the upper 1 m of bedrock. (c) Spatial model of rock denudation derived from 10 Be data and a global raster of topographic slope. (d) Rock organic carbon oxidation fluxes extrapolated by our calibated spatial model over the global surface.

  climate regimes (Fig. 1), excluding river basins with high Re pollution levels such as the Danube, Yangtze and Mississippi 9 (see Methods). The total OCpetro weathering flux constrained from the Re-proxy across the drainage area of river basins in the dataset is 18 MtC yr -1 (17 -23 MtC yr -1 within one standard deviation). The river basins in this study cover 18% of the Earth's continental surface, and this flux would thus scale to MtC yr -1 globally. However, OCpetro stocks are spatially heterogeneous. To obtain a robust representative total OCpetro weathering flux, in the next section, we use a spatial extrapolation model that considers patterns in OCpetro stock and denudation rates.

  uncertainties in both variables in a spatial model. In each cell, empirical probability distributions of[OCpetro] based on rock type (Extended Data Fig.4) and probability distributions of denudation based on rock type and topographic slope (Extended Data Fig.6) are sampled in 10,000 Monte Carlo simulations. We calibrated the geospatial model by minimizing the residuals between the modelled cell values of OCpetro oxidation rates (Jox) and our compilation of Re-proxy data at the river catchment scale (Methods). Thus, our approach describes the spatial patterns of oxidative weathering rate as a function of topographic slope and rock type, which leads to simulations that are consistent with an assessment of global rock nitrogen weathering patterns which are dominated by denudation of fine-grained sedimentary rocks[START_REF] Houlton | Convergent evidence for widespread rock nitrogen sources in Earth's surface environment[END_REF] .Using our spatial model, we estimate that oxidative weathering of OCpetro releases MtC yr -1 as CO2 from the land-surface environment. The flux is lower than our spatially uncorrected extrapolation of Re-proxy measurements ( MtC yr -1 ), consistent with the slight bias towards high denudation rate settings in the river basin dataset. The best estimate of the oxidative weathering flux is higher than an independent estimate of OCpetro erosion and river transport (i.e., the export of OCpetro that has not been weathered) of MtC yr -1 based on river solid load composition and flux 19 , even though the uncertainties overlap. While a direct comparison of these estimates is difficult based on their quantification from dissolved vs particulate river chemistry and flux, they suggest an average weathering intensity of OCpetro of ~60%, which is consistent with studies from large river basins 19 and intensities measured in soils 8,42 . The OCpetro oxidation model can be used to estimate the turnover time of rock organic carbon at the surface. When combined with OCpetro stocks, the model suggests that % yr -1 of the global OC stock in the first 10 cm of bedrock may be oxidized during denudation and weathering. A global OCpetro loss rate of ~0.05 % yr -1 equates to a carbon turnover time (the ratio of total OCpetro to carbon outputs by oxidation) of ~2,000 years. This is about double the value of global soils 43 , but shorter than turnover times in tundras of ~3,900 years 44 . Given the large stock of OCpetro that we report (~150 Pg C in the upper 10 cm) and its turnover time, it appears that OCpetro cannot be assumed to be inert and passive in the shallow subsurface. The input of OCpetro into soils can also impact soil residence time estimations and can lead to an underestimation of soil carbon exchange fluxes with the atmosphere 20 .

Figure 2 .

 2 Figure 2. Earth's major river basins, their carbon sinks, and sources from silicate weathering 10 and OCpetro weathering (this study), and their overall rock weathering budget based on these fluxes. (a) OCpetro vs silicate weathering fluxes and their net values. Basins that produce a net source of CO2 are shown in the shaded half of the plot, with the net magnitude of the weathering CO2 flux illustrated by the symbol color (in MtC yr -1 ). (b) Net weathering balance vs basin average denudation (red arrow: cross-over at ~ 30 mm kyr -1 ) and (c) vs basin average OCpetro stock. Error bars represent uncertainty of OCpetro oxidation model outputs based on the uncertainty of the training data (see section 1.2.3).Variable rates of uplift and erosion, climate and OCpetro stocks across Earth's surface impact OCpetro and silicate weathering rates differently, leading to regions where rock weathering is (d) a source or (e) sink of CO2.

Figure 3 .

 3 Figure 3. A shift in understanding the geological carbon cycle. (a) The inorganic geological carbon cycle relies on a global balance between solid-Earth CO2 degassing and silicate weathering. (b) The emerging understanding of the role of organic carbon in the global geological carbon cycle, supported by the high flux of OCpetro oxidation reported in this study. Hence the biological, chemical, and physical processes of biospheric organic carbon production, burial and release control long-term climate variability and stability.

  , we use a range of values for each, where $ pmol/µmol to 4 x 10 -3 pmol/µmol (23), and $ .4 x 10 -3 pmol/µmol to 2 x 10 -3 pmol/µmol. Here, we correct Na+ concentrations for atmospheric-derived Na, [Na+]*, where [Na+]* = [Na+] -[Cl-] × 0.8, assuming all Cl-derives from precipitation, which has a molar [Na+]/[Cl-] ratio of 0.8. We similarly correct for atmospheric SO4 inputs.

  denudation model, and our Re-proxy calibration data. The Re proxy based OCpetro oxidation fluxes used to calibrate our spatial extrapolation model capture fluxes from global rivers within the past decade or less. The CRN technique integrates denudation fluxes that span a millennium or more. Given that anthropogenic land-use change has doubled erosion and weathering since the early 1900s 63 , our global scale estimates of OCpetro oxidation rates therefore reflect the combined influence of natural and anthropogenic activities on global weathering rates which cannot be deconvolved in this present study.

  the model is then upscaled, in lowland floodplain areas where fluvial processing and recycling of sediment[START_REF] Repasch | Fluvial organic carbon cycling regulated by sediment transit time and mineral protection[END_REF] can allow biogeochemical reactions to continue[START_REF] Repasch | Fluvial organic carbon cycling regulated by sediment transit time and mineral protection[END_REF] , we may predict conservative OCpetro oxidation rates. At present, we lack empirical data to partition weathering between mountain and floodplain sections 3 . An alternative way to view this is that the removal of alluvial domains from contributing to denudation (since these are depositional) holds minimal control on the overall estimate (< 1%). This result comes from a comparison of model outputs under two parameterization schemes: one where denudation occurs over all ice-free lands vs one where denudation only occurs in ice-free non-alluvial landscapes. Overall, the model's largest contributor to uncertainty is in the conversion of dissolved Re fluxes to OCpetro oxidation estimates, which are extrapolated in our spatial model. This conversion depends on [OCpetro]/[Re] ratios which introduce most of the uncertainty in the resulting OCpetro oxidation rates (Section 1.2.3), and therefore in the model's global output. More constraints on the relative "grey shale" vs "black shale" contribution to catchment Re fluxes could help tighten uncertainty in [OCpetro]/[Re] ratios (see[START_REF] Charbonnier | The influence of black shale weathering on riverine barium isotopes[END_REF] for a discussion).

Extended Data Figure 1 .

 1 , M., Hilton, R. G., Torres, M. A., Burt, E. I., Baronas, J. J., Clark, K. E., Galy, V., Ccahuana Quispe, A. J., West, A. J. High rates of rock organic carbon oxidation sustained as Andean sediment transits the Amazon foreland-floodplain. In review in Proceedings of the National Academy of Sciences. Preprint at https://eartharxiv.org/repository/list/ (2023). Flow chart of data, subroutines and outcomes and the relevant sections of the Methods section. Probabilistic geospatial models of OCpetro stocks and denudation are used to extrapolate a global compilation of river catchment OCpetro oxidation rates across the Earth's surface.

  [OCpetro] from the US Geological Survey rock geochemical database, combined with global lithological maps[START_REF] Hartmann | The new global lithological map database GLiM: A representation of rock properties at the Earth surface[END_REF] and spatial chemical lithology classifications 36 . Our geospatial model simulates a large global near-

	surface OCpetro stock, with the estimate and its interquartile range at	Gt OCpetro in
	the first meter of bedrock. This estimate is consistent with a global estimate of 1100 Gt

Acknowledgments

The authors would like to acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility in carrying out this work. http://dx.doi.org/10.5281/zenodo.22558. In addition, this work is based on digital elevation products and high-performance topographic analysis services provided by the OpenTopography Facility with support from the National Science Foundation under NSF Award Numbers 1948997, 1948994 & 1948857. This study was supported by the European Research Council Starting Grant ROC-CO2 678779 (R.G.H.)

Data availability

All dissolved rhenium sample data are available in the Supplementary Materials Tables S1-S5, which in addition to geospatial data including those for Figure 1 are deposited in a Zenodo repository (https://doi.org/10.5281/10.5281/zenodo.8144244). Source data for Figure 2 and Extended Data Figures 4 -6 are also available in separate Excel and CSV files respectively (see Figure legends).

Code availability

The spatial OCpetro oxidation model contains two spatial probabilistic subroutines of (i) OCpetro stocks in surface rocks; and (ii) spatially defined denudation rates. These are combined in a Monte Carlo framework alongside the Re-proxy river catchment data to Extended Data Figure 2. Rhenium (Re) to organic carbon (OC) concentration ratio (10 -7 g g -1 ) in published black shales [START_REF] Sheen | A model for the oceanic mass balance of rhenium and implications for the extent of Proterozoic ocean anoxia[END_REF][START_REF] Crawford | Targeted Geoscience Initiative: 2018 Report of Activities[END_REF] alongside those measured in riverbed materials (Supplementary Table S3).

Peel riverbed materials capture the input of OC from black shale lithologies, which in other basins are much less common.

Extended Data Figure 3. Rhenium (Re) to organic carbon (OC) concentration ratio (10 -7 g g -1 ) of riverbed materials, organized by sample location (Supplementary Table S3). Conservatively, the Monte Carlo analysis of OCpetro oxidation rates from the dissolved rhenium proxy uniformly samples the complete measured range of Re/OC values presented here.

Extended Data

Figure 4. Organic carbon concentrations (OC in weight %) of lithological types in the USGS Rock Geochemical Database (a) and the same figure in log scale (b). Black lines show median values, boxes show the interquartile range (IQR), whiskers show IQR + 1.5 × IQR, and outliers are shown as open symbols (although still included in the analysis).

Section 2. Global spatial OCpetro oxidation model

The following section provides additional rationale and details of the modelling approaches.

In brief, they contain two spatial probabilistic subroutines of (i) OCpetro stocks in surface rocks; and (ii) spatially defined denudation rates. These are combined in a Monte Carlo framework alongside the Re-proxy river catchment data to optimize the model and then extrapolate OCpetro oxidation rates (Extended Data Fig. 1). Model simulations were implemented at 1-km grid scale (Mollweide projection, WGS84 datum) in the Python programming language [START_REF]Python Software Foundation, Python Language Reference[END_REF] .

OCpetro stocks

Rock samples from the USGS Rock Geochemical Database sorted into lithological categories (Supplementary Table S5) were mapped onto units of the highest-resolution global lithological maps currently available [START_REF] Hartmann | The new global lithological map database GLiM: A representation of rock properties at the Earth surface[END_REF] . Extended Data Fig. 4 (below) shows the OCpetro concentration of key lithologies in the USGS Rock Geochemical database. Weight percentage values from the USGS Rock Geochemical Database were converted to OCpetro stock, using rock densities (Supplementary Table S5). In our Monte Carlo framework, OCpetro stocks at each grid cell were sampled independently using the empirical distributions of rock OCpetro content derived from the USGS database (Extended Data Fig. 4) and our unit classification (Supplementary Table S5). In our lithology model, complex mapped units present in GLiM consist of a combination of carbonates, silicates and various grainsizes (Extended Data Fig. 5, Supplementary Table S5). To calculate the OCpetro reservoir among these units, we derive the fractional abundance of lithology types (Fn) from continental-scale literature estimates 36 :

Denudation model

The denudation model is parameterised using a regression approach, similar to techniques applied elsewhere [START_REF] Larsen | The contribution of mountains to global denudation[END_REF][START_REF] Houlton | Convergent evidence for widespread rock nitrogen sources in Earth's surface environment[END_REF] . We regressed a compilation of long-term catchment scale 10 Be denudation estimates 39 against mean local slope generated from the Geomorpho90m dataset [START_REF] Amatulli | Geomorpho90m, empirical evaluation and accuracy assessment of global high-resolution geomorphometric layers[END_REF] . Mean local slope was calculated using the focal statistics tool in ArcGIS Pro 56 and the Geomorpho90m slope dataset with a 5-km moving radius. Slope values were then matched to [START_REF] Moon | New estimates of silicate weathering rates and their uncertainties in global rivers[END_REF] Be denudation estimates at a single cell based on the reported longitude and latitude. A quantile regression approach [START_REF] Houlton | Convergent evidence for widespread rock nitrogen sources in Earth's surface environment[END_REF][START_REF] Koenker | quantreg: Quantile Regression, R package version 5.94[END_REF][START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF] , allows us to avoid over-and underestimations inherent in using a mean model fit to the global land surface [START_REF] Larsen | The contribution of mountains to global denudation[END_REF] (Extended Data Fig. 6). For each unique slope value in the global raster, denudation quantiles were used to construct a cumulative distribution function which could be sampled in each Monte Carlo run (c.f. [START_REF] Houlton | Convergent evidence for widespread rock nitrogen sources in Earth's surface environment[END_REF] ).

We account for differential erodibilities of sedimentary, crystalline metamorphic, and igneous rock types by running regressions between slope values and 10 Be values for each rock type (Extended Data Fig. 6). Thus, only [START_REF] Moon | New estimates of silicate weathering rates and their uncertainties in global rivers[END_REF] Be values from catchments dominated (>80%) by one rock type are used in this regression. This accounting of erodibilities is important as OC-rich shales are weaker and more erodible than OC-poor strong igneous rocks. Residuals between the CRN denudation dataset and the modelled denudation do not change when differential rock erodibility is considered. However, when combined with our OCpetro stock model, the rock erodibility-corrected OC supply rate model results in 20% higher rates. We also consider the grid-scale bias considered by previous workers [START_REF] Larsen | The contribution of mountains to global denudation[END_REF][START_REF] Houlton | Convergent evidence for widespread rock nitrogen sources in Earth's surface environment[END_REF] : as DEM resolution decreases, slope -

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Correspondence to Jesse Zondervan or Robert Hilton

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Extended Data

Extended Data Figures 1 to 8 database [START_REF] Peucker-Ehrenbrink | Land2Sea database of river drainage basin sizes, annual water discharges, and suspended sediment fluxes[END_REF] (Supplementary Table S1) to allow comparison with the previous assessment of silicate weathering vs biospheric OC burial [START_REF] Galy | Global carbon export from the terrestrial biosphere controlled by erosion[END_REF] . The exponent for YOCpetro is 0.38 ± 0.08 with r 2 = 0.43, reflecting the scatter in data owing to the spatial dependence of OCpetro oxidation on rock OC content and denudation rates (Fig. 2). Therefore, comparisons based on the global trends in this plot, without considering their spatial context (see Fig. 2 for spatially explicit comparisons), should be done with care considering the low certainty.