Rock weathering can counteract river CO₂ emissions induced by permafrost thaw

Abstract

Climate-induced permafrost thaw unlocks large stores of organic carbon that are mineralized and emitted as carbon dioxide (CO₂) from rivers to the atmosphere¹. Concurrently, warming and permafrost thaw can increase mineral weathering rates, thus affecting the release and sequestration of inorganic carbon^2–4. Yet how these biological and geological carbon cycles interact and jointly affect CO₂ dynamics (emission compared with drawdown) in permafrost rivers remains unknown⁵. Here we combine CO₂ emissions, organic and inorganic solute concentrations, dual carbon isotopes (δ¹³C–Δ¹⁴C) and geochemical modelling to infer how permafrost thaw may affect river biogeochemistry over decades to centuries across the Qinghai–Tibet Plateau. Leveraging a gradient of thermal permafrost degradation, we find that river CO₂ emissions decline, whereas solute fluxes from rock weathering increase with decreasing permafrost cover. Across this region, net CO₂ drawdown fluxes from rock weathering are about 35% of river CO₂ emissions, varying from around 15% in catchments with continuous permafrost to more than 100% in catchments with discontinuous or isolated permafrost. Thus, carbon fluxes from chemical weathering may become increasingly important with ongoing permafrost thaw, potentially even outpacing river CO₂ emissions. Our findings disentangle the interplay between biological and geological carbon fluxes that are important for the cryosphere and the global carbon cycle.

Permafrost thaw on the Qinghai–Tibet Plateau increases rock-weathering rates while reducing river CO₂ emissions, suggesting geological carbon fluxes may eventually outpace thaw-driven emissions.

Main

River networks perfuse and integrate landscapes⁶, receiving organic carbon (OC) from terrestrial primary production and dissolved inorganic carbon (DIC) $(\mathrm{D}\mathrm{I}\mathrm{C}=\sum {\mathrm{C}\mathrm{O}}_{2\left(\mathrm{a}\mathrm{q}\right)}+{{\mathrm{HCO}}_3}^{-}+{{\mathrm{CO}}_3}^{2-})$ from soil respiration and chemical rock weathering. This OC is metabolized in rivers and returned to the atmosphere as carbon dioxide (CO₂) or methane (CH₄), buried in sediments, or transported to coastal oceans. Similarly, DIC can precipitate, outgas or travel downstream^7,8. Global carbon inputs to rivers (about 3.2 petagrams of carbon (PgC) yr⁻¹), the resulting riverine carbon emissions (around 2.3 PgC yr⁻¹) and carbon export to the ocean (approximately 0.8 PgC yr⁻¹)⁸ are on par with the net terrestrial carbon sink (that is, the net primary productivity minus respiration without considering land-use changes; about 3.2 PgC yr⁻¹)⁹. Consequently, rivers forge important connections between terrestrial, marine and atmospheric carbon pools that modulate the global carbon cycle⁸. Despite major advances in understanding the role of rivers in the carbon cycle, key knowledge gaps persist regarding the interaction between biological and geological carbon sources and sinks⁵, as well as their responses to climate change.

Of primary concern is the impact of climate warming on the vast OC stocks (approximately 1,014 PgC) stored in the Northern Hemisphere permafrost soils¹⁰. Permafrost thaw is mobilizing a portion of this large, near-surface OC reservoir on Earth¹¹. The subsequent breakdown of this ancient, biolabile OC in rivers fuels in situ respiration and methanogenesis, thus amplifying emissions of aged CO₂ and CH₄, and potentially perturbing the contemporary carbon cycle^12–18. However, permafrost thaw has effects beyond mobilizing ancient OC. In particular, recent studies have demonstrated that multi-decadal increases in DIC fluxes and associated dissolved solutes in permafrost rivers could reflect intensified chemical weathering^2–4,19,20. Given that landscape-scale weathering fluxes are controlled by a combination of lithology²¹, hydrology^22–24, temperature^25,26 and exposure of reactive surfaces^27,28, climate warming and permafrost thaw could have multifaceted impacts on these fluxes^2–4. Whereas climate warming can directly increase dissolution kinetics²⁶, the associated permafrost thaw may alter weathering reactions by exposing minerals or by modulating the hydrology and promoting acidic redox conditions in sub-surface environments⁴. Importantly, weathering reactions in the critical zone affect biogeochemistry through the hydrosphere because groundwater transports weathering products—including carbon—to fluvial ecosystems.

The role of weathering reactions for the carbon cycle depends on the nature of the exposed minerals^21,29. Weathering of silicate and carbonate minerals by carbonic acid produces alkalinity and draws down CO₂ (refs. ^30,31). By contrast, weathering of sulfide minerals—such as pyrite—produces sulfuric acid and releases CO₂, either by interacting with the alkalinity pool or by dissolving carbonate minerals^32,33. In reality, biological and geological CO₂ fluxes are intertwined and co-vary across permafrost rivers. For example, acidity produced by respiration of OC could be buffered by alkalinity production from chemical weathering²⁸. These interactions may be particularly important in mountainous landscapes with widespread permafrost coverage that are strongly exposed to climate change and characterized by rapid weathering rates^34,35. Efforts to isolate the impact of permafrost thaw on chemical weathering are rare, and no studies have quantified the balance between biological and geological CO₂ sources and sinks in rivers draining permafrost landscapes subject to climate warming. These knowledge gaps introduce substantial uncertainties in understanding the contemporary and future role of permafrost landscapes and their rivers within the global carbon cycle⁸.

Here, we examine the balance of riverine CO₂ fluxes resulting from OC mineralization and chemical weathering spanning a permafrost gradient on the Qinghai–Tibet Plateau (QTP; Fig. 1a). The QTP is the largest contiguous cryosphere outside the Arctic and Antarctic³⁶, with an estimated OC storage of 50.4 Pg in its permafrost soils³⁷, partly dating back to the late Pleistocene³⁸. The permafrost on the QTP is, on average, warmer and has a higher mean active-layer thickness (about 0.21 m) compared with Arctic permafrost (about 0.10 m), with 44% of permafrost at a mean ground temperature above −0.5 °C, which makes it particularly vulnerable to climate warming³⁹. From the cold plateau in the north and west of the study area, air temperatures increase eastward and southward, and permafrost extent decreases from continuous to discontinuous, sporadic and isolated (Fig. 1a and Extended Data Fig. 1a). By substituting space for time⁴⁰, this landscape and its rivers potentially hold information about the sensitivity of biogeochemical cycles to climate warming and permafrost thaw over decadal to centennial timescales, timescales of permafrost landscape changes that are impossible to observe with long-term monitoring approaches.

Fig. 1. Environmental gradients on the QTP.

a, Map of the QTP shown in an Asia North Lambert Conformal Conic projection, showing permafrost cover and sampling locations (open dots). The green lines indicate rivers with catchment areas >1,000 km². The black outlines mark the main catchments drawn on to the border of China and to the edge of the QTP. The names of the main rivers in each catchment are shown. Numbers in sample points are the sample ID (Supplementary Table 5). b, PCA of the main environmental boundary conditions in the study area, highlighting a permafrost-climate gradient (PC1) and a lithology gradient (PC2). More than 75% of the variance in PC1 was explained by permafrost extent (30%), mean annual air temperature (33%) and mean annual precipitation (14%). The remaining variance was mainly explained by changes in normalized river steepness index (k_sn; 18%). The relationship between permafrost extent and k_sn was attributable to high permafrost extent on the flat plateau in the northern and eastern parts of the QTP. Lithology (40%), wetland extent (38%) and k_sn (11%) contributed most to the variance explained by PC2. The points are coloured by permafrost category. c–f, Environmental variables across the permafrost gradient: mean annual air temperatures (MAT; °C) (c), catchment-averaged steepness index (m^0.9) (d), mean annual precipitation (MAP; mm yr⁻¹) (e) and fraction of carbonate rock in the catchment (f_{carb rock}) (f). The points are coloured by permafrost category. Pearson’s correlation coefficients and P values are shown. The black lines are linear regressions with grey shading showing the 95% confidence interval of the regression. These are plotted only if r ≥ 0.3.

Extended Data Fig. 1. Environmental boundary conditions across the study area.

(a) Mean annual air temperature extracted from HydroATLAS. (b) Lithologic units from the Global Lithologic Map (GLiM) overlain on a hillshade⁵⁹. The legend items are: W.G. – water and glaciers; Uncons. – unconsolidated sediments; Sil. – silicate-bearing sediments; Mix. – mixed sediments; Carb. – carbonate sediments; Pyroc. – pyroclastics; V. acid – acid volcanic rocks; V. interm. – intermediate volcanic rocks; V. basic – basic volcanic rocks; P. acid – acid plutonic rocks; P. interm. – intermediate plutonic rocks; P. basic – basic plutonic rocks; Metam. – metamorphic rocks. (c) Hillshade and rivers colored by the normalized steepness index, k_sn for streams > 100 km². (d) Mean annual precipitation extracted from HydroATLAS. Black outlines in panels (a-d) mark the major catchments drawn to China’s border and to the edge of the QTP and dark-blue lines in panels (b-d) are rivers with catchment areas > 1,000 km².

A permafrost gradient on the QTP

We repeatedly sampled 50 rivers in the headwaters of the largest river systems of Asia (Yellow, Yangtze, Lancang, Nu, Derung, Yarlung Tsangpo, Marja Tsangpo and Indus Rivers; Fig. 1a) during the ice-free season between April and October over more than 3 years. The sampled headwaters cover a total area of approximately 780,000 km², span elevations from 1,650 m to 4,820 m above sea level, and drain all major lithologies of the QTP, including a variety of sedimentary, igneous and metamorphic rocks (Extended Data Fig. 1b and Supplementary Tables 1 and 2). We include basins on the cold plateau underlain by continuous permafrost and catchments draining warmer landscapes with discontinuous, sporadic or isolated permafrost cover.

Across these landscape-scale environmental gradients, we found that permafrost extent is inversely related to average annual air temperature (principal component 1, PC1; Fig. 1b,c and Extended Data Fig. 1a), consistent with thermal permafrost degradation in response to climate change⁴¹. Because permafrost extent tends to be the highest on the flat plateau in the northern and eastern parts of the study area, we also found that permafrost extent declines moderately with the catchment-averaged steepness index (k_sn), a proxy for landscape-scale erosion rates^42,43 (Fig. 1b,d and Extended Data Fig. 1c). The permafrost gradient does not substantially co-vary with factors that may affect chemical rock weathering (for example, lithology and average annual precipitation; Fig. 1b,e,f and Extended Data Fig. 1b,d). Furthermore, permafrost does not co-vary with wetland coverage, which can affect dissolved organic carbon (DOC) export to rivers⁴⁴ (Fig. 1b). Thus, our sampled catchments allow us to relate changes in permafrost extent and temperature to river biogeochemistry, mostly independently from other environmental variables that also affect weathering and carbon fluxes.

Solute and carbon sources in QTP rivers

To assess the concentrations and sources of carbon and inorganic constituents in QTP rivers, we measured CO₂ partial pressure ($p_{{\mathrm{CO}}_2}$) and emission rates, concentrations of DOC, DIC, major dissolved cations and anions, and isotopes of carbon (δ¹³C–Δ¹⁴C), sulfur (δ³⁴S) and oxygen (δ¹⁸O). We found all 50 rivers to be supersaturated in CO₂ with respect to atmospheric equilibrium, with a median saturation of 230% (interquartile range 200–270%), and $p_{{\mathrm{CO}}_2}$ of 650 (580–750) μatm and a median riverine CO₂ emission rate of 95 (81–120) mmol m⁻² day⁻¹ (Extended Data Fig. 2). These emissions are bracketed by previous observations from QTP rivers (Supplementary Table 3), but remain below the median estimate (594 mmol m⁻² day⁻¹) for global rivers⁸. Concentrations of DOC and DIC are 380 (320–440) μmol l⁻¹ and 1,800 (1,400–2,600) μmol l⁻¹ (Extended Data Fig. 2 and Supplementary Table 2), respectively, whereas total dissolved ion concentrations (4,600 (2,900–5,900) μmol l⁻¹) are dominated by Ca²⁺ (750 (580–1,000) μmol l⁻¹), Mg²⁺ (480 (230–840) μmol l⁻¹), Na⁺ (410 (250–830) μmol l⁻¹), SO₄²⁻ (430 (260–730) μmol l⁻¹) and HCO₃⁻ (2,000 (1,300–2,600) μmol l⁻¹; Extended Data Fig. 2 and Supplementary Table 2). No substantial seasonal trends in either CO₂ or dissolved chemistry were apparent over the study period (Extended Data Fig. 3), although water temperatures increased from April to August and runoff increased slightly through summer and into fall (Extended Data Fig. 4).

Extended Data Fig. 2. Distribution of chemical measurements for all 175 individual samples.

Boxplots of CO₂ emission rate (mmol m⁻² d⁻¹), and concentration (μmol L⁻¹) of dissolved constituents across all samples in the study area. Red lines and black boxes show median and interquartile range respectively. Whiskers extend to the most extreme data points within 1.5 times the interquartile range of the quartiles; values beyond are shown as black crosses. Note that the 50 distinct sampling sites were not all sampled equally often so that some sites are weighted more than others in the boxplots (Table S2).

Extended Data Fig. 3. Seasonal breakdown of chemical parameters for all 175 samples.

Boxplots of (a) CO₂ emission rate, and concentrations of (b) DOC, (c) DIC, (d) total dissolved ions (TDIs), (e) cations from silicate weathering (Cat_sil), (f) cations from carbonate weathering (Cat_carb), (g) cations from evaporite weathering (Cat_evap), and (h) sulfate from sulfide oxidation (SO₄²⁻_sulf) for samples collected in April–May, June, July, August, and September–October. Red lines and black boxes show median and interquartile range respectively. Whiskers extend to the most extreme data points within 1.5 times the interquartile range of the quartiles; values beyond are shown as black crosses. Note that seasons were not sampled equally and not all sample sites are represented equally within each time-window (Table S2).

Extended Data Fig. 4. Seasonal breakdown of climate-related parameters for all 175 samples.

Boxplots of (a) water temperature, (b) discharge, (c) runoff, and (d) permafrost extent for samples collected in April–May, June, July, August, and September–October. Red lines and black boxes show median and interquartile range respectively. Whiskers extend to the most extreme data points within 1.5 times the interquartile range of the quartiles; values beyond are shown as black crosses. Note that seasons were not sampled equally and not all sample sites are represented equally within each time-window (Table S2).

We found that the dissolution of carbonates contributed the most cations (78% (70–86%) of the total cation charge), whereas silicates and evaporites contributed a smaller fraction (6.0% (3.6–9.5%) and 6.3% (1.6–14%), respectively; Extended Data Fig. 5a and Supplementary Table 2). With one exception, samples with more than 25% and up to 78% cation contribution by evaporites occurred exclusively in eight sites of the westernmost Yellow River, Yangtze River and Lancang River, and are probably controlled by evaporitic units within the metasediments⁴⁵. Coupled isotopic compositions of δ³⁴S-SO₄²⁻ and δ¹⁸O-(SO₄²⁻–H₂O) identify a mixing trend between riverine sulfate (SO₄²⁻) derived from pyrite and evaporite sources (Extended Data Fig. 5b). We infer that sulfate from sulfide oxidation balances 23% (11–36%) of the total cation charges (Extended Data Fig. 5a).

Extended Data Fig. 5. Solute sources and unmixing.

(a) Boxplot of estimated fractional contributions of carbonates, silicates, and evaporites to the total cation charge and the ratio of sulfate to cations for all 175 samples. (b) δ³⁴S-SO₄²⁻ plotted against δ¹⁸O-(SO₄²⁻ – H₂O) for samples processed as part of our study (blue), and compiled from the literature (grey; Table S7). Expected endmember ranges of pyrite and evaporites are shown as black dashed lines. Endmember ranges of δ³⁴S are from local data (Table S11) and endmember ranges for δ¹⁸O-(SO₄²⁻ – H₂O) are from a global compilation⁶³. Samples fall between these endmembers.

Interactions of organic and inorganic carbon pools

Based on dual carbon isotopes (δ¹³C–Δ¹⁴C) and a three-endmember mixing model⁴⁶, we found that old permafrost- and rock-derived carbon substantially contributes to DOC, DIC and CO₂ pools in QTP rivers. DOC is a mix of modern (67 ± 11%) and old permafrost (21 ± 13%) as well as rock (carbonate and petrogenic OC; 12 ± 6%) carbon sources, with an average age of 2,232 ¹⁴C years (Fig. 2a,b). DIC can be modelled as a mixture of modern (49 ± 19%) and old permafrost (34 ± 19%) and rock (19 ± 8%) sources, with an average age of 3,512 ¹⁴C years (Fig. 2a,b). Riverine CO₂ falls between DOC and DIC in both its δ¹³C and Δ¹⁴C signatures and has an average age of 1,655 ¹⁴C years, consistent with a mix of modern permafrost (66 ± 11%), old permafrost (22 ± 13%) and rock (12 ± 7%) carbon sources (Fig. 2a,b).

Fig. 2. Carbon isotopes and unmixing.

a, Δ¹⁴C compared with δ¹³C for measured samples (bordered points) and literature data (unbordered points). Expected carbon isotope ranges for select endmembers are marked with black-dashed lines and boxes (Methods). The threshold of Δ¹⁴C age for the Northern Hemisphere permafrost soils is about 2,800 ¹⁴C years (ref. ⁵⁰). b, Results from a three-endmember mixing model of Δ¹⁴C data. c,d, Δ¹⁴C isotopes for paired samples collected at the same time from our study (blue) and compiled from the literature (grey) of Δ¹⁴C-CO₂ against Δ¹⁴C-DOC (c) and Δ¹⁴C-DIC against Δ¹⁴C-DOC (d). The blue datapoints are from our study, the dark grey datapoints are from the literature data of rivers within our study area, the light grey points are from the literature data on the QTP, but located outside of the studied catchments. The blue dashed line is the 1:1 line. Pearson’s correlation coefficients and P values are shown.

Importantly, we observed moderate to strong correlations between concurrently sampled Δ¹⁴C-DOC, Δ¹⁴C-DIC and Δ¹⁴C-CO₂ signatures (Fig. 2c,d) and a positive correlation between $p_{{\mathrm{CO}}_2}$ and DOC across broad spatiotemporal scales (Extended Data Fig. 6a). These patterns suggest a shared source of at least part of the organic and inorganic carbon pools or point to processes that exchange carbon between these pools. We suggest that mineralization of permafrost- and rock-derived DOC generates CO₂, thereby maintaining modest CO₂ oversaturation in QTP rivers and leading to a correspondence between Δ¹⁴C-DOC and Δ¹⁴C-CO₂ (Fig. 2c). In turn, buffering of part of this respiratory CO₂ by alkalinity from rock weathering could explain the correlation between Δ¹⁴C-DOC and Δ¹⁴C-DIC (Fig. 2d). Finally, downstream decreases in DOC and DIC ¹⁴C ages in the Yellow and Yangtze Rivers (Extended Data Fig. 6b,c) are consistent with inputs of aged carbon in the permafrost headwaters followed by mineralization and dilution by modern carbon sources during transit through non-permafrost areas⁴⁷.

Extended Data Fig. 6. Dissolved carbon dynamics.

(a) Correlation between pCO₂ with DOC. Best fit lines and coefficient of determination in black. Text is the Pearson’s correlation coefficient (‘r’) and associated p-value (‘p’). (b, c) ¹⁴C ages of DOC and DIC along the Yellow (b) and Yangtze (c) continuums. Δ¹⁴C data from our own measurements and refs. ^69,70. The distance to the coast was computed by ArcGIS for each coordinate point.

Collectively, permafrost rivers on the QTP receive substantial amounts of ancient carbon that is laterally routed from the pedosphere and lithosphere, and this carbon can be converted and released in the form of millennial-aged CO₂. Therefore, inputs of both ancient permafrost and rock carbon contribute substantially to aquatic carbon cycling and CO₂ emissions^46,48, and these old carbon contributions will probably grow as QTP permafrost further thaws.

Permafrost extent affects river biogeochemistry

Statistical analyses (principal component analysis (PCA) and multiple linear regression (MLR)) showed clear impacts of permafrost extent on river biogeochemistry (Figs. 1 and 3, Extended Data Table 1 and Supplementary Table S4). Concentrations of riverine carbon species and cations from rapidly weathering carbonates, as well as the fraction of old carbon in DIC and CO₂ pools (Fig. 3 and Extended Data Fig. 7), consistently increase from isolated to continuous permafrost areas. Conversely, silicate weathering rates decrease with permafrost extent, although this trend is apparent only in the MLR results (Extended Data Table 1). Permafrost extent explains most variance in these biogeochemical variables as inferred from MLR coefficients (Extended Data Table 1). Only CO₂ emissions and ion concentrations from evaporite and sulfide weathering seem to be insensitive to permafrost extent (Fig. 3b,g,h and Extended Data Table 1). PC1 includes effects of air temperature and erosion rates, but MLR results suggest that erosion rates (k_sn) affect only DIC, and to a lesser extent, silicate cation concentrations, whereas temperature influences ion concentrations from weathering of silicates and sulfides (Extended Data Table 1). However, contrary to expected patterns^24,26,28,34, these relationships are negative (Extended Data Table 1), which may be caused by unresolved environmental covariations. Furthermore, none of the carbon and weathering derived ion concentrations correlate with PC2—except DOC (Extended Data Fig. 8), which validates permafrost as the primary driver of biogeochemical variability across our study area. The exception may arise because DOC inputs depend on wetland extent (Extended Data Fig. 9a). In turn, lithology affects sulfide weathering (Extended Data Fig. 9b and Supplementary Table 4), probably by an association of pyrite with carbonate-bearing metasediments in the Yellow, Yangtze and Lancang catchments⁴⁵.

Fig. 3. Geochemical variables across the permafrost-climate gradient (PC1).

a–h, $p_{{\mathrm{CO}}_2}$ (a), CO₂ emission rates (b), concentrations of DOC (c), DIC (d), cations from silicate weathering (Cations_sil) (e), cations from carbonate weathering (Cations_carb) (f), cations from evaporite weathering (Cations_evap) (g) and sulfate from sulfide (SO_4 sulf) (h) plotted against PC1. Points are coloured by permafrost category (see Fig. 1a for colour scale). Geochemical values from sites with more than one sample were averaged before plotting the data for all 50 sampling sites. The error bars reflect standard deviations of these averages. The numbers in each panel show Pearson’s r and the associated P values for the relationship between the response variables and PC1. The black lines are linear regressions with grey shading showing the 95% confidence interval of the regression. These are plotted only if r ≥ 0.3. A set of six datapoints with concentrations of Na⁺, Cl⁻ and cations from evaporites of 2,300–17,000 µmol l⁻¹ are not shown and considered in the correlation and regression analyses in g. These high values probably reflect the influence of evaporitic units within the metasediments⁴⁵ in the Yellow, Yangtze and Lancang headwaters.

Extended Data Table 1.

Results of the multiple linear regression (Full results in Table S4)

Bold numbers indicate regression coefficients with absolute values > 0.3 and p-values < 0.1. Blank fields indicate a lack of correspondence.

Extended Data Fig. 7. Fractional contributions of carbon across the permafrost zones.

Results from the unmixing model for samples from different permafrost zones for riverine DOC, DIC, and CO₂. Datapoints and error bars represent mean ± SD of all unmixing results (Methods).

Extended Data Fig. 8. Geochemical variables across the lithology-wetlands gradient (PC2).

(a) pCO₂, (b) CO₂ emission rates, and concentrations of (c) DOC, (d) DIC, (e) cations from silicate weathering, (f) cations from carbonate weathering (g) cations from evaporite weathering (h) sulfate from sulfide plotted against PC2. Points are colored by permafrost category (see Fig. 1a for color scale). Geochemical values from sites with more than one sample were averaged before plotting the data for all 50 sampling sites. Error bars reflect standard deviations of these averages. Numbers in each panel show Pearson’s r and associated p-values for the relationship between the response variables and PC2. Black lines are linear regressions with grey shading showing the 95% confidence interval of the regression. These are plotted only if r ≥ 0.3. A set of six datapoints with concentrations of Na⁺, Cl⁻ and cations from evaporites of 2300–17,000 µmol L⁻¹ are not shown and considered in the correlation and regression analyses in panel (g). These high values likely reflect the influence of evaporitic units within the metasediments⁴⁵ in the Yellow, Yangtze, and Lancang headwaters.

Extended Data Fig. 9. Additional variability of geochemistry across environmental gradients.

(a) DOC versus wetland extent, (b) sulfate from sulfide plotted against fraction of carbonate rocks (c) sulfate from sulfide plotted against catchment-averaged steepness index (k_sn), (d) sulfate from sulfide plotted against k_sn sub-sampled for locations within the Yellow- Yangtze-, and Lancang watersheds (basin IDs 1–24). Consistent with previous studies on the eastern QTP^45,71,72, sulfide weathering in these catchments was erosion-rate controlled⁴⁵ (e) cations from silicate weathering plotted against k_sn sub-sampled for basin IDs 1–24, and (f) cations from carbonate weathering plotted against k_sn sub-sampled for basin IDs 1–24. Geochemical values from sites with more than one sample were averaged before plotting the data for all 50 sampling sites. Error bars reflect standard deviations of these averages. Points are colored by permafrost category (see Fig. 1a for color scale) and Pearson’s correlation coefficients (‘r’) and associated p-values (‘p’) are reported for all plots. Black lines are linear regressions with grey shading showing the 95% confidence interval of the regression. Regressions are plotted only if r ≥ 0.3.

Based on the dominant effect of permafrost shown by our statistical analyses, we propose that concurrently elevated carbonate ion and carbon concentrations in permafrost-rich catchments are caused by enhanced exposure of rocks and carbon within thawing permafrost soils^2–4 or are linked to increased hydrological connectivity and exposure of rock underneath permafrost soils. These effects may be delayed or reversed for ion concentrations from more slowly weathering silicate minerals (Fig. 3e). Collectively, our findings suggest that warming and permafrost thaw affect the dynamics of lateral transport of both organic and inorganic carbon to rivers, mineralization of carbon to CO₂ and chemical weathering in parallel across the QTP (Fig. 3 and Extended Data Table 1). We emphasize that our results do not challenge temperature, precipitation or erosion controls on weathering and carbon fluxes^23–29,34. Rather, the strong permafrost gradient across our studied catchments allowed us to isolate permafrost extent from these other controls and reveal its effects on riverine biogeochemistry.

Balance of CO₂ emissions and sequestration

To assess regional-scale impacts of QTP permafrost thaw on riverine carbon fluxes, we upscaled CO₂ emissions from individual river reaches to the entire fluvial networks (Methods). Likewise, we estimated CO₂ consumed by carbonate and silicate weathering and CO₂ produced by sulfide oxidation at the catchment scale. We present these results as carbon fluxes normalized by the catchment area upstream of each study reach. We found that CO₂ emissions from river networks increase slightly from isolated (1.2 (1.0–2.2) tC km⁻² yr⁻¹) to continuous (2.4 (1.6–3.1) tC km⁻² yr⁻¹) permafrost (Fig. 4a). Conversely, CO₂ consumption by silicate and carbonate weathering decreases with increasing permafrost extent (Fig. 4a). Relative to river CO₂ emissions, net CO₂ sequestration from weathering varied broadly from continuous (15% (8–50%)) to isolated (340% (140–530%)) permafrost (Fig. 4b) with an overall median of 78% (7–160%). With the exception of CO₂ emissions, all weathering fluxes are a product of runoff and concentration, but permafrost extent can affect weathering fluxes independently of runoff (Supplementary Text 1).

Fig. 4. CO₂ fluxes across permafrost zones.

a, Bar plot showing the median CO₂ fluxes for all river basins grouped by permafrost extent. The black lines mark the interquartile ranges. Negative fluxes refer to a CO₂ sink and positive fluxes to a CO₂ source. Numbers from sites with more than one sample were averaged before plotting the data for all 50 sampling sites. Note that the carbon fluxes do not have to balance, because a part of the carbon drawdown and release by weathering occurs on land and is then transported laterally to streams. b, The ratio of CO₂ fluxes from weathering and CO₂ emission fluxes. The red lines and black boxes show the median and interquartile range, respectively. The whiskers extend to the most extreme data points within 1.5 times the interquartile range of the quartiles; values beyond are shown as black crosses. CO₂ emission is always a carbon source and a positive number. Negative ratios imply that weathering is a CO₂ sink, and positive ratios imply that weathering is a CO₂ source. For example, a ratio of −1 means that weathering consumes as much CO₂ as is emitted by rivers. c–f, CO₂ fluxes from riverine emission (c), silicate weathering (d), carbonate weathering (e) and sulfide weathering (f) plotted against PC1. The content of the plots and text boxes follows that in Fig. 3.

These geochemical patterns across the QTP shed new light on the role of permafrost thaw for the balance between carbon sources and sinks. Our findings suggest that OC mineralization is most important in the continuous permafrost zone leading, at the present day, to elevated riverine DOC concentrations, $p_{{\mathrm{CO}}_2}$ and CO₂ emissions. Here, CO₂ sequestration fluxes from chemical weathering were small relative to river CO₂ emissions (Fig. 4b). However, with continued warming, thawing of permafrost is expected to result in a deeper active layer and eventually patchy permafrost cover⁴¹. Substituting space for time across our permafrost gradient suggests that CO₂ sinks from weathering may become increasingly important, potentially even outpacing riverine CO₂ emissions as landscapes undergo this transition over timescales of decades to centuries (Fig. 4). Where warming and permafrost thaw occur alongside elevated runoff, weathering rates could increase even further. We note that carbon fluxes from silicate, carbonate and sulfide weathering are partly offset by carbonate and sulfide precipitation in the ocean³¹ (Supplementary Text 2). However, imbalances between terrestrial weathering and marine precipitation, for example, due to warming and permafrost thaw, will persist over millennial³⁴ and million-year timescales^34,49, and are therefore important to consider within the framework of current climate-change impacts.

Next, we assessed the net carbon fluxes from the first- to eighth-order streams of the entire study area (Methods). We estimated the total riverine CO₂ emissions at 2.3 ± 0.7 TgC yr⁻¹. In turn, we obtained 1.1 ± 0.2 TgC yr⁻¹ of geogenic CO₂ production by sulfide weathering and 1.6 ± 0.3 TgC yr⁻¹ and 0.29 ± 0.07 TgC yr⁻¹ of geogenic CO₂ removal by carbonate and silicate weathering, respectively. Thus, the net CO₂ consumption by rock weathering is 0.80 ± 0.32 TgC yr⁻¹, which corresponds to 35 ± 17% of the total riverine CO₂ emissions. Note that these fluxes from the entire study area are strongly influenced by the large Lancang and Nu catchments, for which weathering is inferred to be a net carbon source. If we consider individual catchments, a median of 78% of riverine CO₂ production from respiration of OC is negated by alkalinity production from chemical weathering (Fig. 4b). These ratios could be even higher because areal CO₂ emissions are likely to be maximum estimates because of a lack of width data for the first-order streams and CO₂ emission rates from the winter (Methods).

We estimated downstream DOC and DIC export fluxes summed across the same catchments to 0.87 ± 0.13 TgC yr⁻¹ and 4.2 ± 0.7 TgC yr⁻¹, respectively. We also estimated particulate OC (POC) fluxes from the four largest catchments (about 74% of the study area) to be 0.37 ± 0.26 TgC yr⁻¹. The sum of all downstream carbon export fluxes (5.4 ± 0.7 TgC yr⁻¹) is close to twice the total carbon emissions (CO₂ (2.3 ± 0.7 TgC yr⁻¹) + CH₄ (0.68 ± 0.14 TgC yr⁻¹)¹⁸ = 3.0 ± 0.7 TgC yr⁻¹) from rivers draining these catchments. These numbers suggest that only 35% of the total fluvial carbon budget (DOC + DIC + POC + emitted CO₂ + emitted CH₄ = 8.4 ± 1.0 TgC yr⁻¹) is mineralized and emitted to the atmosphere, which is a relatively small contribution compared with the rivers across the globe (63%)⁷. Importantly, downstream DIC export—mainly driven by rock weathering—corresponds to 50% of this total riverine carbon budget in the QTP. From Δ¹⁴C mass balance (Methods), we estimated fluxes of old carbon from both permafrost and rocks in the form of DOC, DIC and CO₂ to 0.29 ± 0.11 TgC yr⁻¹, 2.1 ± 0.9 TgC yr⁻¹ and 0.8 ± 0.4 TgC yr⁻¹, respectively. Overall, our findings carry significant consequences: (1) the large old carbon loads funnelled (47%) or emitted (35%) by QTP rivers pose yet unknown impacts for downstream and atmospheric biogeochemistry; and (2) CO₂ fluxes from rock weathering can modulate the potential for CO₂ gas emission associated with warming and permafrost thaw.

Implications for the global carbon cycle

The biological component of the carbon cycle (for example, related to ecosystem metabolism)⁸ has been particularly prominent in permafrost river research, probably because of the substantial lateral OC fluxes from thawing of frozen soils, and the conventional wisdom that biological processes are more reactive to an increased supply of carbon and warming than physicochemical processes such as weathering. Findings from our dual organic–inorganic carbon approach show that weathering of minerals increasingly exposed by permafrost degradation could buffer a notable fraction of CO₂ from permafrost-derived OC mineralization, hence coupling inorganic and organic carbon cycles on human-relevant timescales. Furthermore, substituting space for time suggests that the balance between riverine CO₂ sources and sinks shifts across a gradient in permafrost extent, thereby providing a glimpse at decadal to centennial changes to carbon cycling on the QTP. At present, permafrost thaw is considered a positive carbon feedback to climate warming, with permafrost rivers acting as CO₂ sources¹⁵. In sulfide-rich permafrost areas, exposure of sulfide minerals may provide an extra CO₂ source and exacerbate the positive permafrost carbon feedback^2,4,19. However, where carbonate and silicate weathering dominate—such as over most of the QTP—a substantial portion of the additional CO₂ production from permafrost thaw could be compensated by weathering on human timescales. Therefore, stitching together biotic–organic and abiotic–inorganic carbon processes across the cryosphere in the context of climate change is essential to determine the net effect of permafrost thaw on the global carbon cycle, and ultimately, to understand its climate feedback directionality. Our study provides compelling empirical evidence that carbon cycling models should include the key mechanisms underpinning aquatic carbon sources and sinks. We propose to move beyond the canonical focus on biotic–organic carbon processes and to holistically consider the balance of all carbon transformation mechanisms to better understand the coupling of organic–inorganic carbon cycles between the hydrosphere, pedosphere and lithosphere under changing climate.

Methods

Study area and field sampling

Spanning about 30% of the entire QTP, this 780,000 km² study area is situated between the boundary of the Loess Plateau (Gansu Province, 103° E) and the border of China (Tibet Autonomous Region, 78° E), and includes the headwater of eight major river basins: the Yellow, Yangtze, Lancang–Mekong, Nu–Salween, Derung (Irrawaddy), Yarlung Tsangpo–Brahmaputra, Marja Tsangpo (Ganges) and Indus Rivers (Fig. 1a and Supplementary Table 1). This region spans gradients of climate, topography, vegetation cover, permafrost extent and lithology, with elevations between 1,600 and 8,000 m above sea level. The rivers drain the major tectonic terranes of the QTP that contain a wide range of sedimentary, igneous and metamorphic rocks^51,52 (Extended Data Fig. 1b). In the northeast of the study area, the Yellow and Yangtze Rivers drain marine carbonate and siliciclastic sediments of the eastern Kunlun–Qaidam Terrane and the Triassic deep-marine sediments of the Songpan–Ganzi flysch complex⁵¹. The Lancang, Nu and the southwestern Yangtze catchments drain mostly terrestrial siliciclastic and shallow marine carbonate rocks of the eastern Qiangtang and northern Lhasa Terrane⁵¹. In particular, the sediments of the Qiangtang Terrane contain abundant evaporites⁴⁵. By contrast, the catchments of the Yarlung Tsangpo and Indus Rivers are underlain by a series of plutonic and volcanic rocks of the southern Lhasa Terrane apart from the marine Tethyan sedimentary series of the Himalayas (Extended Data Fig. 1b). Permafrost extent across the study area varies from continuous to isolated with the most extensive permafrost extent concentrated in the Yangtze and eastern Yellow Rivers, and high-elevation areas of all other river basins⁵³. The climate is characterized by a cold and dry winter season and an ice-free season between April and October with heavy monsoon rains during the study period⁵⁴. Potential glacial influence is minimized by sampling streams at least 20 km downstream from glaciers. Flow distance and tributaries collectively reduce potential biogeochemical signatures of glacial meltwaters.

We collected 175 individual samples from 50 rivers across this area during the daytime in spring (May–June), summer (July–August) and autumn (September–October) between 2016 and 2018, and in spring ice-out (early April) in 2023. The Yellow River basin was visited eight times; the Yangtze River basin five times; and the Lancang, Nu and Yarlung River basins were all sampled on four dates, the Derung and Indus River basins twice, and the Marja River basin once. We measured, compiled, interpolated and/or calculated all variables first for each of the 175 samples (Supplementary Table 2) and then calculated mean values and their standard deviations for sites with multiple samples to obtain one estimate for each of the 50 sampling sites (Supplementary Table 5).

Topography, hydrology, lithology and climate parameters

All topographic analyses were performed on a 90-m resolution digital elevation model (DEM) from the Shuttle Radar Topography Mission (SRTM)⁵⁵ using version pre2.5 of the TopoToolbox⁵⁶. We extracted a river network and estimated, for each sample location, drainage-basin-averaged slopes, S_bsn, and normalized steepness index, k_sn, with a reference concavity of 0.45, a segment length of 1,000 m and a drainage-area threshold of 100 km². For all rivers in the network, we also extracted the stream order (with drainage-area threshold of 5 km²) and calculated the total length of rivers, $L_{{\mathrm{riv}}_i}$ with a given order, that is, upstream of each sampling point. All these analyses were performed on a DEM projected in ArcGIS-Pro using the inbuilt Asia North Lambert Conformal Conic projection. To provide an estimate of the total surface area of rivers upstream of a sampling point, A_riv, we multiplied the river length in each stream order, $L_{{\mathrm{riv}}_i}$, with an average width for rivers in that stream order, ${\overline{W}}_i$:

$$A_{\mathrm{riv}}=\sum _1^N{L}_{{\mathrm{riv}}_i}{\overline{W}}_i$$ 1

Where N is the highest stream order in each catchment. For stream orders 3–8, ${\overline{W}}_i$ and its uncertainty were based on the mean and standard deviation of 100 individual width measurements (only 30 measurements for stream order 8). Measurements from hydrologic stations at our sampling sites were combined with widths of randomly selected rivers in the study area mapped on Google Earth (Supplementary Table 6). Average width for the first- and second-order streams were estimated by extrapolating an exponential fit to rivers of orders 3–6, with an uncertainty based on the prediction band at these stream orders (Supplementary Fig. 1). We used only stream orders 3–6 for the extrapolation, because many higher-order rivers in the study area are inset into narrow bedrock gorges and break the exponential increase in stream-widths¹⁸ (Supplementary Fig. 1). Our interpolation predicted the first-order stream widths of 4.3 (1.3–13.8) m, which covers the range reported in ref. ⁵⁷ (1.9 ± 1.1 m), but is wider than the value reported more recently in ref. ⁵⁸ (0.32 ± 0.07 m), leading to a potential overestimate in CO₂ emissions.

The same DEM was analysed in TopoToolbox after projecting it with the Asia North Albers Equal Area Conic projection in ArcGIS-Pro to extract drainage areas, A_bsn, and to estimate an areal fraction of permafrost extent in the landscape upstream of each sampling point. We based the latter analysis on a published map of permafrost extent⁵³ that classifies surfaces as being underlain by continuous (≥90%), discontinuous (≥50% and <90%), sporadic (≥10% and <90%) or isolated (<10%) permafrost. Because this classification is based on ranges, we assigned values of 95%, 70%, 30% and 5%, respectively, to each permafrost class (0% for no permafrost), and then calculated the average pixel value upstream of each sampling point in TopoToolbox. Finally, we re-classified all catchment-averaged permafrost-extent values into the same permafrost categories. We generated a TIFF image from the global lithologic map⁵⁹ to extract the fraction of carbonate lithologies upstream of each sampling point in TopoToolbox. In the fraction of carbonate rocks, we included the lithologic categories ‘sc—carbonate sedimentary rocks’ and ‘sm—mixed sedimentary rocks’. We did not consider ‘mt—metamorphics’ here, but we found that including these would not make a substantial difference to our analysis. We estimated the fraction of wetlands, the mean annual air temperature and the mean annual precipitation values for the watersheds draining each of our sites by matching the coordinates of each site with the corresponding watershed in HydroATLAS⁶⁰, in which we obtained the relevant attributes.

For sampling sites within the cross-section of the hydrometric station, we obtained a measurement of discharge, Q_spl (m³ s⁻¹), and suspended sediment concentrations (Supplementary Table 2) at the time of sampling. We were also able to obtain average annual discharge, Q_annual (m³ yr⁻¹), for the most downstream sampling sites of all sampled catchments (basin IDs 9, 16, 18, 19, 22, 27, 31, 37, 45, 46, 47, 48, 49 and 50) and annual suspended sediment for the four largest outlet basins (basin IDs 7, 16, 22 and 27; 74% of the total study area). Note that suspended sediment concentrations were not available for the sampling site with ID9, but for the more upstream sampling site ID7.

Sample collection and analyses

CO₂ concentrations and fluxes

Triplicate river-water samples for $p_{{\mathrm{CO}}_2}$ were measured in situ from different locations at each site using a Qubit Dissolved CO₂ System equipped with an internal pump and a $p_{{\mathrm{CO}}_2}$ probe (S157-P, Qubit Biology). The $p_{{\mathrm{CO}}_2}$ probe was coated with a polytetrafluoroethylene membrane sleeve that is permeable to CO₂ gas, but not to water. The system was calibrated with standard CO₂ gas ranging from 0 μatm to 10,000 μatm. Recalibration of the system was done before each round of fieldwork. Water–air CO₂ emission rates were measured with $p_{{\mathrm{CO}}_2}$ collection simultaneously using four floating chambers deployed for 1 h. At each transect, chambers were held in place above a range of water depths from shallow water within 2 m of the river bank to deep water in the mid-channel. After mixing the contents in the chamber three times, 50 ml of gas was retrieved from the chambers after 0 min, 2 min, 5 min, 10 min, 30 min and 60 min of measurement and transferred to air-tight gas sampling bags for concentration determination in the laboratory by gas chromatograph equipped with a flame ionization detector (Agilent 7890B GC-FID). Characteristics and construction of the chambers followed previously tested setups that showed minimally biased results⁶¹. Local ambient air samples were also taken and used to back-calculate CO₂ concentrations in water in equilibrium with the atmosphere.

Riverine CO₂ emission rates, $F_{{\mathrm{CO}}_2}$ (mmol m⁻² day⁻¹) were derived as follows:

$$F_{{\mathrm{CO}}_2}=k\times \left(C_{\mathrm{water}}-C_{\mathrm{eq}}\right)$$ 2

where k is the gas transfer velocity (m day⁻¹), C_water is the water gas concentration (mol m⁻³) and C_eq is the gas concentration (mol m⁻³) in water in equilibrium with the local atmosphere corrected for temperature-induced changes in solubility according to Henry’s law. We assumed that $F_{{\mathrm{CO}}_2}$ is solely diffusive (that is, CO₂ ebullition is negligible). We obtained k from a linear regression of $p_{{\mathrm{CO}}_2}$ against time to eliminate possible bias due to gas accumulation in the chamber headspace. Fluxes from all chambers were averaged to yield one measurement per sample.

Physicochemical analyses

Water samples were collected simultaneously with gas samples for physicochemical analyses at each site. Water temperature, pH and dissolved oxygen were measured in situ with portable field probes (Hach HQ40d). Air temperature, air pressure and wind speed were measured in situ with a portable anemometer (Testo 480).

Water samples were filtered through 0.22 µm polyethersulfone syringe filters to measure cation and anion concentrations. We rinsed each polyethylene bottle with filtered water before filling, and acidified each bottle for cation analysis with ultrapure HNO₃. We measured major cations (K⁺, Na⁺, Mg²⁺ and Ca²⁺) and anions (Cl⁻ and SO₄²⁻) on an ion chromatograph (Dionex ICS-1100). NH₄⁺ and NO₃⁻ were determined colorimetrically with an Autoanalyzer-3 (Bran+Luebbe) following the methods in ref. ⁶². We estimated HCO₃⁻ by charge balance. Dissolved silica (Si) was analysed on a Varian 720 ICP-OES. DOC concentrations were measured on duplicate filtered water samples acidified with H₂SO₄ following ref. ¹⁸. DIC concentrations were calculated from the sum of HCO₃⁻ and $p_{{\mathrm{CO}}_2}$ concentrations. To determine the POC content of the suspended sediments, water samples were filtered in duplicates through pre-weighed combusted 0.45 µm filters. The filters were then dried at 105 °C for at least 12 h. Before POC analysis, the samples were acidified with 2 M HCl to remove inorganic carbon. No rinsing step was applied after acidification to avoid washing fine particulate material or acid-labile organic matter off the filters. The filters were subsequently dried again at 105 °C for over 5 days to ensure complete removal of residual acid and moisture. Afterwards, the filters were reweighed, and POC mass on the filters was quantified using a Vario Micro Cube elemental analyser (Elementar) with the furnace temperature set at 980 °C.

Sulfur and oxygen isotope analyses

Stable isotopic composition of sulfur, oxygen and carbon is reported in the text using delta notations:

$${\mathrm{\delta }}^{34}\mathrm{S},{\mathrm{\delta }}^{18}\mathrm{O}\mathrm{or}{\mathrm{\delta }}^{13}\mathrm{C}=\frac{R_{\mathrm{sample}}}{R_{\mathrm{standard}}}-1$$ 3

where R_sample and R_standard are ratios of heavy to light isotopes (³⁴S:³²S, ¹⁸O:¹⁶O or ¹³C:¹²C) in samples (R_sample) and in standards (R_standard) of standard mean ocean water or Vienna PeeDee Belemnite, respectively.

Stable isotopes of δ³⁴S-SO₄²⁻ and δ¹⁸O-SO₄²⁻ of dissolved SO₄²⁻ were measured following ref. ⁶³ for 34 river samples collected during the fall 2018 sampling campaign. In brief, sulfate was eluted off a Dowex resin column with 20 ml 0.8 M HCl and mixed with BaCl₂ to precipitate barite (BaSO₄). The precipitate was subsequently cleaned with 6 M HCl and rinsed three times with ultrapure water. After removing impurities with 10 ml 0.05 M DTPA, the barite was then cleaned three times with ultrapure water and dried at 70 °C. For δ³⁴S-SO₄²⁻ analysis, 400 μg of barite was combusted in excess oxygen with vanadium pentoxide in a Flash EA coupled by continuous flow and analysed by an isotope ratio mass spectrometry (Thermo Scientific 253 Plus). For δ¹⁸O-SO₄²⁻ analysis, 180 μg of barite was pyrolysed in a thermal conversion element analyser and passed through continuous He flow into an isotope ratio mass spectrometer (Thermo Scientific 253 Plus) using a ConFlo 3. We determined δ¹⁸O-H₂O using a wave scanning cavity ring-down spectrometer (Picarro L2130i) as well. Additional triplet δ³⁴S-SO₄²⁻, δ¹⁸O-SO₄²⁻ and δ¹⁸O-H₂O data for rivers within the Yellow, Yangtze, Lancang, Nu, Yarlung Tsangpo and Indus catchments were obtained from the literature (Supplementary Table 7). We had measurements from only 34 of the 50 sampling sites. For the remaining 16 sites, we substituted data from the same or closest sites reported in the literature. We then calculated the average for sites with multiple measurements to obtain a single estimate for each of the 50 sampling sites.

Carbon isotope analysis

We collected samples for δ¹³C–Δ¹⁴C analyses of DOC, DIC and CO₂ both near the river bank and in the mid-channel from the sampled rivers from 2017 to 2023 (except 2019 because of COVID restrictions). For Δ¹⁴C and δ¹³C measurements of DOC and DIC, the river-water samples were filtered using 0.45 μm polysulfone filters, then the near-bank and mid-channel samples were mixed and collected in acid-washed (10% HCl v/v, 24 h) 1 l HDPE Nalgene bottles that were rinsed three times with filtered river water before collection. Four submerged bubble traps were deployed from the near bank to the mid-channel to collect gas samples for Δ¹⁴C-CO₂ and δ¹³C-CO₂ analyses. The traps remained in place for 2–4 h before sampling. Accumulated gas was transferred into 10-l air-tight Tedlar PVF gas sampling bags to prevent contamination by contemporary atmospheric CO₂. δ¹³C was analysed on an isotope ratio mass spectrometer (Thermo Scientific 253 Plus), and Δ¹⁴C was measured at the accelerator mass spectrometry facility at Peking University, Guangzhou Institute of Geochemistry and Beta Analytic Laboratory.

We also compiled 92 concurrent δ¹³C–Δ¹⁴C measurements each for DOC and DIC within the QTP from the literature. Finally, we were able to obtain 378 total observations of fluvial DOC (n = 163), DIC (n = 147) and CO₂ (n = 68) Δ¹⁴C data, including our own measurements outlined above.

Endmembers of carbon isotopes

For Fig. 2a, we used the following δ¹³C ranges for endmember carbon sources: terrestrial OC derived from globally dominant C3 plant photosynthesis (−32‰ to −24‰)⁶⁴; autochthonous, in-stream OC production (−23‰ to −17‰)¹³; and rock sources, including kerogen (−32‰ to −17‰), carbonate rocks (−2.5‰ to 0‰) and solid Earth degassed CO₂ (−6.5‰ to 10‰ dependent on source rocks)⁶⁴.

The Stable Isotope Mixing Models in R (simmr) package was used to estimate possible contributions of three endmember sources for all Δ¹⁴C samples as detailed described in ref. ⁴⁶. Endmember sources for the QTP were further constrained by using measured Δ¹⁴C values obtained from QTP soils (Supplementary Table 8). A mass balance fitting the potential contributions of the endmember sources was solved by using a Markov Chain Monte Carlo method:

$$\mathrm{C}{14}_{\mathrm{sample}}=\mathrm{C}{14}_{\mathrm{topsoil}}+\mathrm{C}{14}_{\mathrm{deep}\mathrm{soil}}+\mathrm{C}{14}_{\mathrm{rock}}$$ 4

where C14_sample represents the ¹⁴C content of the different waterborne carbon components of each sample (in pmC), which is the sum of the mass balance among the proportional contributions of three endmember sources. To solve this mass balance, the relative contributions of the three endmember sources were assumed to sum to 1. We divided the soil column into top (<50 cm) and deep (≥50 cm) pools to where the topsoil source (C14_topsoil) is a simplified representation of the uppermost soil carbon accumulation in the active layer, reflecting the seasonally thawed, often younger soils. The deep soil source (C14_{deep soil}) represents older carbon from the deep active layer to the permafrost, including the Holocene and late Pleistocene aged sources from decaying over 5,000 years bp carbon, and decaying more than 10,000 years bp carbon, respectively. The rock source (C14_rock) represents Δ¹⁴C-dead carbon sources from kerogen and carbonates.

Unmixing major elements

For all 175 samples, we used the inverse model mixing elements and dissolved isotopes in rivers (MEANDIR)⁶⁵ to unmix contributions of solute sources to our measured riverine chemistry.

Considered solutes and endmembers

In the inversion, we considered measured concentrations of sodium [Na⁺], calcium [Ca²⁺], magnesium [Mg²⁺], chloride [Cl⁻], sulfate [SO₄²⁻] and silicate [Si], as well as the isotopic composition of sulfur in sulfate (δ³⁴S-SO₄²⁻). All elemental concentrations were normalized to the sum of the major ions [Na⁺], [Ca²⁺], [Mg²⁺] and [SO₄²⁻] (refs. ^45,65). We considered contributions from atmospheric sources and from the weathering of evaporites, sulfides, carbonates and silicates. Anthropogenic inputs were considered negligible because the area is far from major industrial activity or human settlements, and we did not consider the inputs from hot springs (Supplementary Text 3). The size of the study area and lithologic heterogeneity is large, so we used endmember compositions of silicate and carbonate weathering that reflect global averages^23,65,66 (Supplementary Text 4 and Supplementary Table 9). The range of precipitation endmembers was derived from the 5th and 95th percentiles of average precipitation compositions in each of the drainage basins (Supplementary Table 10). A range of different evaporite minerals contribute to the solute budget of the QTP rivers, which complicates the distinction between evaporite and non-evaporite solute sources⁴⁵. To address this challenge, we defined a very broad evaporite endmember that allowed for a wide range of compositions (Supplementary Table 9). Moreover, to distinguish evaporite and silicate weathering sources, we included silica in the inversion and defined a range of allowed silica concentrations for the silicate endmember using the 5th and 95th percentiles of a compilation of unmixed silicate weathering concentrations from small mountain streams for which evaporite contributions are negligible³⁵. Finally, we used published δ³⁴S compositions of sulfides and sulfur-bearing evaporites from our study area, to unmix sulfur sources (Supplementary Table 11).

MEANDIR model parameters

MEANDIR uses a Monte Carlo approach to estimate the range of fractional endmember contributions that fit the measured data. At each iteration, the model picks a set of endmember compositions randomly from user-defined endmember ranges and then fits the fractional contributions of endmembers that best fit the observed data. The final result is commonly obtained as the median of a given fraction or number of model runs with the lowest misfit between the model and the observations. Whereas this approach produces a solution to all samples, it also allows very poor fits to the data. Hence, we iterated over each sample until we had 100 solutions that fit all of the ion data within ±15% and the δ³⁴S-SO₄²⁻ data within ±2‰. We allowed a maximum of 100,000 iterations to run before the inversion was stopped. Sixteen out of the 175 samples did not have all of the major element analyses data and 10 samples did not produce the necessary 100 solutions within the defined error bounds during the inversion. Hence, only 149 samples were considered in the endmember unmixing and carbon balance. All MEANDIR input parameters are reported in the Supplementary Code.

Treatment of potassium

Inclusion of potassium [K⁺] in the inversion doubles the number of samples that cannot be well-modelled. Because [K⁺] and [Na⁺] are well-correlated (Supplementary Table 2), we made the simplifying assumption that fractional contributions to [K⁺] scale linearly with the fractional contributions to [Na⁺]. Because the concentrations of potassium are generally low, the uncertainty introduced by this approximation is small.

Areal CO₂ fluxes from weathering

From the cation charge contributed by carbonate and silicate weathering and the anion charges contributed by sulfate from sulfide oxidation, we estimated the balance of CO₂ sinks and sources from weathering in the landscapes drained by each sampled river. Any carbonate that was already precipitated in streams or soils upstream of the sampling point did not contribute to our CO₂ budget and is not considered here. We followed previous approaches^28,67 to estimate the following fluxes of CO₂, $F_{{\mathrm{CO}}_2}$, in mass of carbon per area per time (tC km⁻² yr⁻¹) with positive numbers being CO₂ production and negative numbers being CO₂ sequestration:

1. CO₂ consumed by silicate weathering, $F_{{\left(\text{C}{\text{O}}_2\right)}_{\text{sil}}}$:

   $$F_{{\left({\mathrm{CO}}_2\right)}_{\mathrm{sil}}}=-(1-f_{\mathrm{sulf}})\times M_{\mathrm{C}}\times {\left[\mathrm{Cat}\right]}_{\mathrm{sil}}^{\mathrm{eq}}\times \frac{Q_{\mathrm{w}}}{A_{\mathrm{bsn}}}$$ 5
2. CO₂ consumed by carbonate weathering, $F_{{\left(\text{C}{\text{O}}_2\right)}_{\text{carb}}}$:

   $$F_{{\left({\mathrm{CO}}_2\right)}_{\mathrm{carb}}}=-0.5(1-f_{\mathrm{sulf}})\times M_{\mathrm{C}}\times {\left[\mathrm{Cat}\right]}_{\mathrm{carb}}^{\mathrm{eq}}\times \frac{Q_{\mathrm{w}}}{A_{\mathrm{bsn}}}$$ 6

3. CO₂ produced by sulfuric acid weathering of carbonate, $F_{{\left(\text{C}{\text{O}}_2\right)}_{\text{sulf}}}$:

$$F_{{\left({\mathrm{CO}}_2\right)}_{\mathrm{sulf}}}=0.5f_{\mathrm{sulf}}\times M_{\mathrm{C}}\times {\left[\mathrm{Cat}\right]}_{\mathrm{carb}}^{\mathrm{eq}}\times \frac{Q_{\mathrm{w}}}{A_{\mathrm{bsn}}}$$ 7

where f_sulf () is the fraction of weathering by sulfuric acid, $f_{\text{sulf}}=\frac{{\left[{\mathrm{SO}}_4^{2-}\right]}_{\text{sulf}}^{\text{eq}}}{{\left[\mathrm{Cat}\right]}_{\text{sil}}^{\text{eq}}+{\left[\mathrm{Cat}\right]}_{\text{carb}}^{\text{eq}}}$, ${\left[\mathrm{Cat}\right]}_{\text{sil}}^{\text{eq}}$ and ${\left[\mathrm{Cat}\right]}_{\text{carb}}^{\text{eq}}$ (charge equivalents in mol m⁻³) are the cation charges contributed by silicate and carbonate weathering, respectively, M_c (g mol⁻¹) is the molar mass of carbon, Q_w (m³ yr⁻¹) is the annual average discharge, and A_bsn (m²) is the drainage basin area. Equations (5)–(7) assume that the sulfuric acid partitions between silicate and carbonate phases in the proportion of the fraction of cation charges contributed by each reaction. Depending on the conditions in the soil, this simplification may not apply⁶⁸. However, changing this assumption would not affect the net CO₂ balance from weathering reactions, that is, the sum of equations (5)–(7), but would instead trade off CO₂ drawdown fluxes between silicates and carbonates. We note that in the calculation of the CO₂ balance, we excluded one (out of 175) sample with f_sulf > 1, which is impossible. This estimate must have arisen because of the high evaporite load that was not correctly estimated by the inversion model. We also excluded one sample that had an anomalously high sulfate concentration compared with all other 175 samples (almost 10 times higher than the 75th percentile of all samples and twice as high as the next highest concentration), and disproportionately dominated the upscaling described in the next sections. Finally, we note that we did not have annual discharge estimates for all sampling sites (see section ‘Topography, hydrology, lithology and climate parameters’), and instead upscaled Q_w (m³ yr⁻¹) from the discharge estimate at the time of sampling, Q_spl (m³ s⁻¹), for each of the 175 samples by simply multiplying the value by the number of seconds in a year. Therefore, Q_spl for the 50 sampling sites is effectively a weighted average flux. Note that these fluxes were used only to compare relative changes across the permafrost gradient. To obtain the total fluxes from the study area, we used actual measured annual averages for the most downstream sites of the catchments (see sections ‘Topography, hydrology, lithology and climate parameters’ and ‘Total carbon fluxes from the study area’).

Areal CO₂ fluxes from river emissions

We estimated areal CO₂ emission fluxes from each of the sampled catchments (in mass of carbon per area per time) based on CO₂ emission flux rates ($F_{{\mathrm{CO}}_2}$) measured with the floating chambers as

$$F_{{\left({\mathrm{CO}}_2\right)}_{\mathrm{rem}}}=365.25\times F_{{\mathrm{CO}}_2}\times M_{{\mathrm{CO}}_2}\times \frac{A_{\mathrm{riv}}}{A_{\mathrm{bsn}}}$$ 8

where $F_{{\left({\mathrm{CO}}_2\right)}_{\mathrm{rem}}}$ (mol m⁻² day⁻¹) is the upscaled riverine emission (rem) flux.

Total carbon fluxes from the study area

We estimated the total CO₂ fluxes from weathering and river emissions as well as downstream fluxes of DOC and DIC across the study area in TgC yr⁻¹. To this end, we summed the contributions of CO₂ fluxes from the 14 most downstream sampling sites of each sampled basin. We calculated the summed weathering, DOC, and DIC fluxes based on the annual discharge estimates, Q_annual multiplied by the average concentrations in the basin, and we used the standard deviations of the concentrations to estimate the uncertainty of the summed value (Supplementary Table 5). Here, we were able to use actual measured annual discharge measurements and did not use the Q_w values upscaled from individual discharge measurements at the time of sampling. Note that we used the solute and carbon concentrations of basin 7 instead of the further downstream basin 9 because we did not have any major element chemistry for basin 9. To account for uncertainty in the stream-area calculations, we estimated the summed CO₂ emission fluxes, $F_{{\left(\text{C}{\text{O}}_2\right)}_{\text{rem}}}$, with 100,000 Monte Carlo runs. First, we randomly picked values of river widths from a normal distribution for stream orders 3–8 (Supplementary Table 5) and from a log-normal distribution for the interpolated stream orders 1–2. Multiplied by stream lengths (equation (1)), these values yield 100,000 estimates of stream areas upstream of each sampling site. We then randomly picked 100,000 $F_{{\left({\mathrm{CO}}_2\right)}_{\mathrm{rem}}}$ values from a normal distribution based on the average and standard deviation for each sample site (Supplementary Table 5) and solved equation (8) for each of the 100,000 Monte Carlo runs. The final reported value is the median and standard deviation from all 100,000 runs. We also multiplied annual suspended sediment fluxes by POC content of the largest four of the outlet basins to obtain POC fluxes. Because our measurements were limited to the ice-free season between April and October, and because our first- and second-order stream widths are higher than expected, we probably overestimate CO₂ emissions over the year.

Statistical analysis

Using R (v.4.4.2), we performed a PCA to explore the main environmental drivers and their effects on our variables of interest. The drivers considered were catchment size, average k_sn, permafrost cover, average annual precipitation, average annual air temperature, wetland cover and fraction of carbonate rocks within the catchment. These variables were scaled and centred before the PCA. We then used the two main axes of the PCA (PC1 and PC2) to explore how they were related to several variables using linear regression models. Apart from the PCA, we used an MLR model, in which each response variable was regressed against all key environmental variables (Extended Data Table 1 and Supplementary Table 4). All predictor and response variables were standardized before analysis to facilitate the comparison of effect sizes using standardized regression coefficients. We used a bidirectional stepwise variable selection procedure based on the Akaike information criterion to identify the most parsimonious set of drivers for each response variable. Model performance and the significance of individual predictors were assessed using adjusted R² and P values.

Online content

Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at 10.1038/s41586-026-10664-8.

Author contributions

L.Z., A.B., X.X. and T.J.B. conceived the study. L.Z. performed sample collection and laboratory work. A.B. and L.Z. led the data analyses with help from J.F.D., G.R.-R. and R.L. Data interpretation was led by A.B. and L.Z. with intellectual inputs from J.F.D., G.R.-R. and T.J.B. The first draft of the manuscript was written by L.Z., A.B. and T.J.B., with further editing and inputs from J.F.D., G.R.-R., R.A.S., E.H.S., J.K., D.E.B., L.H., J.D., S.P. and X.X.

Peer review

Peer review information

Nature thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

Funding

The following funding sources are acknowledged: the National Natural Science Foundation of China (T2421005, X.X.); the Second Tibetan Plateau Scientific Expedition and Research Program (2022QZKK0101, S.P. and J.D.); the National Natural Science Foundation of China (T2261129474, U25A20823 and 52039001, X.X.; 42030411, L.H.; 42401095, L.Z.; 12201031, R.L.); the ERC Starting Grant (FloW, 101164120, A.B.; ARIMETH, 101161308, G.R.-R.); the United Kingdom Research and Innovation Future Leaders Fellowship (MR/V025082/1, J.F.D.); the Swedish Research Council (2021-06667, G.R.-R.; 2020-04445, J.K.); the UW‐Madison WARF ERO STEM Award (E.H.S.); the Jack Corkery and George Corkery Jr. Endowed Professorship (D.E.B.); the National Key R&D Program of China (2024YFF0808800, L.H.).

Data availability

The data used in this study are available at the Environmental Data Initiative (10.6073/pasta/5eb76dc26b8ff0e594a4362eff2bae5c).

Code availability

The code used in this study is available at the Environmental Data Initiative (10.6073/pasta/5eb76dc26b8ff0e594a4362eff2bae5c).

Competing interests

The authors declare no competing interests.

Extended data

is available for this paper at 10.1038/s41586-026-10664-8.

Supplementary information

The online version contains supplementary material available at 10.1038/s41586-026-10664-8.