Discharge‐Modulated Soil Organic Carbon Export From Temperate Mountainous Headwater Streams

Erosion and riverine transport of organic carbon is an important component of the global carbon cycle, but the significance of this process for Earth's surface carbon budgets depends on the sources of carbon being mobilized. In this study, we aim to constrain how runoff‐driven erosion modulates the contribution of different carbon source endmembers, that is, bedrock, soil and vegetation, in three forested headwater catchments in the Swiss Prealps. The sources of organic carbon are determined using an inverse model based on bulk carbon isotope signatures and the abundances and distributions of long‐chain n‐alkane plant wax biomarkers in suspended sediments collected over a range of discharges. Despite landcover differences and contrasting bulk particulate organic carbon (POC) signatures, the increase of soil‐sourced organic carbon with runoff is similar in all three studied catchments. This apparent existence of common processes implies that export fluxes of soil organic carbon may be extrapolated to similar catchments. Overall, our analysis shows that runoff‐driven soil erosion in these alpine headwater streams is responsible for the export of at least 0.3 to 0.8 gC m−2 yr−1 as POC. Our study also shows that despite a significant variability in isotopic and molecular POC signatures at low runoff, all three catchments show a convergence of these signatures at higher discharges. Suspended sediment samples collected at above‐average runoff are hence most representative of overall endmember contributions.

The global export of POC from large fluvial catchments is primarily driven by physical erosion processes and is dominated by export from tectonically active areas Stallard, 1998). However, climate -through its modulation of physical erosion processes -also contributes to the regulation of POC export (Hilton, 2017). POC export fluxes have been observed to broadly scale with runoff (Baronas et al., 2020;Clark et al., 2013;Clark, Hilton, et al., 2017;Goñi et al., 2013;Hilton, 2017;Märki et al., 2021;Qiao et al., 2020;Qu et al., 2020;Smith et al., 2013;Takagi & Haga, 2019;Turowski et al., 2016;Wang et al., 2019). In some regions, this climatic regulation is further enhanced by extreme events such as storms that contribute disproportionally to POC export (Hilton et al., 2008;West et al., 2011). Climate and hydrology have also been suggested to impact the downstream preservation of organic matter in sedimentary basins as an invigorated hydrological cycle will promote rapid POC export, by-passing degradation processes upstream in the catchment (Lee et al., 2019;Leithold et al., 2006;Yoshida et al., 2009). Overall, these observations highlight a potential link between climate and surface carbon fluxes of global relevance. Nevertheless, most existing studies have focused on the modulation of total POC fluxes as a function of climate and river discharge, with only relatively few investigations addressing changes in the balance of biospheric versus petrogenic organic carbon export in the context of their contrasting influence on the long-term carbon cycle (Blair et al., 2010;Galy & Eglinton, 2011;Galy et al., 2015;Hilton et al., 2012Hilton et al., , 2015Leithold et al., 2006;Wang et al., 2019). To further understand short-term carbon cycle dynamics and mobilization mechanisms, improved constraints on sources of biospheric organic carbon are required, yet attempts at identifying and apportioning different components of the biospheric carbon pool in riverine sediments, in particular their response to varying runoff conditions, remain scarce. Those few studies undertaken thus far indicate that the chemical and isotopic composition of the exported carbon shifts toward signatures similar to topsoil at higher discharges (Clark et al., 2013;Goñi et al., 2013;Smith et al., 2013), implying a significant contribution of precipitation-driven erosion of plant litter and surface soil to overall organic carbon export fluxes. However, the extent to which such findings are germane to a broader range of catchments remains unclear.
In this study, we examine how variations in the runoff-driven erosion influence the contribution of different carbon source endmembers -that is, bedrock, soil and vegetation -in three forested headwater catchments in the Swiss Prealps. To complement the current understanding of POC export in forested mountain catchments, we do not only differentiate between petrogenic and biospheric carbon, but also constrain runoff-driven changes in the contributions of different endmembers, that is, bedrock, soil and vegetation, based on a combined approach using both carbon isotopic and biomarker (n-alkane) signatures. Additionally, by comparing three similar small catchments in close proximity to one another and under the same climate conditions, we evaluate how well observations on the catchment-scale can be extrapolated to predict carbon export in similar settings.

Methods
The isotopic and chemical composition of POC allows tracing the contribution of different sources. Radiocarbon activity (expressed as fraction modern F 14 C) is a powerful tool to differentiate between biospheric and petrogenic carbon sources, as the latter (fossil carbon) is devoid of 14 C. This isotopic contrast has often been used to quantify riverine export of biospheric POC (e.g., Galy & Eglinton, 2011;Leithold et al., 2006;Tao et al., 2015;Wang et al., 2019). Here, we aim to further deconvolve contributions from different components of biospheric carbon, with topsoil, deeper soil and vegetation among the potential endmembers. Hence, in addition to the bulk isotopic composition of carbon, we also focus on the relative distribution of long-chain (C 25 -C 33 ), odd-carbon-numbered n-alkane biomarker lipids, that are constituents of plant leaf epicuticular waxes (G. Eglinton & Hamilton, 1967). These and other n-alkanes occur in all potential endmembers, including bedrock, soil and vegetation (Jansen & Wiesenberg, 2017), but with distinctive distributions in terms of n-alkane chain-length (e.g., Saliot et al., 1988;Schäfer et al., 2016;Zech et al., 2010), providing a diagnostic quantitative tracer of the sources of riverine POC.
The Erlenbach, Lümpenenbach and Vogelbach catchments are located within 5 km of each other in the Alptal valley in the Swiss Prealps ( Figure 1). All three catchments have been in the focus of sustained hydrological research by the Swiss Federal Institute for Forest, Snow and Landscape (WSL) since 1967. Since 1985, discharge has been measured at 10-minute intervals at the catchment outlets. Annual precipitation in Alptal amounts to 2,300 mm. The three streams are all roughly 2 km long with an average flow velocity around 5 m s −1 (Wyss et al., 2016), so the contribution of in-stream productivity to POC export can be assumed to be negligible, especially at higher runoff. The average catchment elevation is 1300 m asl with an approximate elevation drop of 500 m for all three streams (FOEN, 2016), but they differ in area and landcover ( Figure 1).
In each catchment, the forest consists mainly of Norway Spruce (Picea abies) and European Silver Fir (Abies alba) (Schleppi et al., 1998). The dominant soil type is a low-permeability clayey gleysol resulting in a ground water table close to the surface (Hagedorn et al., 2001;Schleppi et al., 1998). The Alptal is underlain by the Wägital-Flysch formation, a turbidite sequence of interbedded mudstones and sandstones of Eocene age (Winkler et al., 1985). The bedrock in the Erlenbach catchment is dominated by fine-grained impermeable material , where creep landslides deliver material from the hillslopes into the channels (Golly et al., 2017;Schuerch et al., 2006). This phenomenon is not observed in either Lümpenenbach or Vogelbach catchments (Molnar et al., 2010) where the bedrock is composed of calcareous sandstones (Milzow et al., 2006). POC export has been previously investigated in the Erlenbach by Smith et al. (2013). Based on carbon and nitrogen concentrations as well as stable isotopes, these authors attributed an observed increase of biospheric organic carbon at high discharges to mobilization by overland flow.

Sampling
Suspended sediment samples were collected in the course of two campaigns: First, Erlenbach (gauging station: 47.04501°, 8.70911°), Lümpenenbach (47.0465°, 8.705231°) and Vogelbach (47.07578°, 8.718217°) were sampled regularly once to twice per month between June 2014 and June 2015. Second, the rivers were sampled again between April and May 2016 on rainy days in order to target a range of above average discharges. Up to 40 L of water was collected at each site and passed through pre-combusted GF/F filters (mesh size 0.7 μm) within 24hr of collection. To constrain potential endmembers that contribute carbon to the suspended sediment load, representative vegetation, topsoil, deeper soil, and bedrock samples were collected in the catchments. Bedrock and vegetation samples including the dominant tree species silver fir (Abies alba) and Norway spruce (Picea abies) as well as green alder (Alnus viridis), moss, three different grasses, common rush (Juncus effusus), horsetail (equisetum) and ground pines (lycopodium) were gathered in May 2015. 27 soil cores were collected in June 2016, as 3 groups of 9 cores each, two groups of grassland soils in the Lümpenenbach and Vogelbach catchment of 30 cm depth, one group of forest soils in the Vogelbach watershed limited to 10 cm depth as rocks in the subsurface impeded deeper sampling. Each group of cores was collected in a 3 × 3 pattern in an area of 20 × 20 m 2 . The cores were separated into "topsoil" and "deep soil" (<10 cm and >10 cm, respectively). In each case, 3 soil samples within the same group and depth interval were combined yielding in total 6 grassland top and deep soil samples, respectively, and 3 forest top soil samples. The soils and suspended sediment were analyzed for total organic carbon (TOC) content, δ 13 C, F 14 C of bulk organic carbon, and long-chain n-alkane concentrations. For vegetation and bedrock samples, only n-alkanes were measured, as stable isotopes of these endmembers are reported in Smith et al. (2013), and F 14 C values of vegetation are assumed to be equivalent to that of atmospheric carbon, while the Eocene age bedrock is considered radiocarbon dead.

Analytical Procedures
For carbon isotope analysis, approximately 10 mg of soil or 30-35 mg of filter were transferred into silver boats (8 × 8 × 15 mm, Elemental Microanalysis) and left in a desiccator for fumigation at 60°C, first with 37% hydrochloric acid to remove carbonates for four days, afterward with NaOH pellets to neutralize the acid for another four days. The decarbonated samples were then wrapped in tin boats (8 × 8 × 15 mm, Elemental Microanalysis). Total organic carbon (TOC), δ 13 C and F 14 C are determined using the on-line EA-IRMS-AMS system operated by the Biogeoscience group in the Laboratory of Ion Beam Physics at ETH Zürich (McIntyre et al., 2017).
Lipids were extracted using a microwave accelerated reaction system (CEM MARS 5). Up to 55 mg of vegetation, between 5 and 10 g of soil, or a sediment-covered GF/F filter were transferred into teflon vessels and covered with a dichloromethane (DCM): methanol (MeOH) 9:1 (v/v) solvent mixture. The extraction temperature was programmed to ramp to 100°C in 35 min and was kept at this level for another 25 min. The resulting lipid extract was then dried under nitrogen flow and redissolved in 5 mL MilliQ water with NaCl. The neutral phase was back-extracted with hexane (Hex), from which the apolar fraction containing n-alkanes was separated on a 1% deactivated silica column using Hex:DCM 9:1. Quantification of n-alkanes was performed on a GC-FID (gas chromatograph connected to a flame ionization detector, Agilent 7890A) using an external standard (Supelco Alkane standard solution C 21 -C 40 ). The relative abundances of measured n-alkanes are parametrized as (a) Carbon Preference Index (CPI), that increases with the amount of odd-carbon-numbered homologs relative to even-numbered counterparts (Equation 1), adapted from Marzi et al. (1993), with 2i and 2i+1 referring to the measured n-alkanes' even and odd carbon numbers, respectively), (b) Average Chain Length (ACL, Equation 2, adapted from Poynter and Eglinton (1990), 2i and 2i+1 analogous to CPI), the weighted average of carbon chain lengths present in the sample (further information on alkane parametrization in the Supporting Information S1).

Inverse Model
Several modeling approaches exist that are suitable to solve for the contribution of different endmembers to a mixture. For instance, the Bayesian MixSIAR framework  has been previously applied in river catchments to constrain endmember contributions (e.g., Blake et al., 2018;Brandt et al., 2016;Menges et al., 2020). In this study, the number of potential endmembers equals the number of measured parameters, and therefore a simple fully-determined system of linear equations is sufficient to delineate the contribution of different endmembers. This approach has previously been applied to riverine samples (e.g., Hemingway et al., 2020;Torres et al., 2016). As the streams are only about 2 km long and the average flow velocity is roughly 5 ms −1 (Wyss et al., 2016), transport times of suspended sediment are short and we therefore do not expect to observe transformations of the geochemical or isotopic signal of mobilized carbon during riverine transport (Scheingross et al., 2019). Working on the assumption that for each of the parameters investigated in this study (i.e., F 14 C, δ 13 C, CPI, ACL), the signal observed in the suspended sediment sample is the result of conservative mixing of the different endmembers, the suspended sediment sample can be modeled by a system of linear equations: where p i,j is the value of parameter i for endmember j, x j is the fraction of carbon sourced from endmember j in the suspended sediment sample and s i is the value of parameter i in the suspended sediment. The solution for x, the vector comprised by x j , is additionally constrained, as all of the endmember proportions x j need to be ≥0 and sum up to 1. Both s i as well as a range of possible values for p i,j are measured. Based on these results the best fit for x j is determined: For each of the potential endmembers, parameter values are picked randomly from a uniform distribution of one standard deviation around the mean parameter value determined for the respective endmember. The data is normalized using min-max feature scaling to restrict each of the parameters to values between 0 and 1. Then, the best fit for x and the root mean square error (RMSE) of the respective solution is obtained using the Python function 'scipy.optimize.nnls' (Virtanen et al., 2020). This procedure is repeated 10,000 times. The 500 solutions with the smallest RMSE are used to calculate mean, median and mode of the potential solutions for x. If all metrics differ by less than 0.05 the distribution is not skewed and the mean is used to sum up the results, otherwise the median is chosen instead.

Variations in Organic Carbon Export With Runoff
The overall export of organic carbon increases with runoff in all three catchments at a similar rate ( Figure 2). To account for the different sizes of the catchments, discharge is reported relative to catchment area as runoff (mm h −1 ). In all rivers, the exported carbon can be approximated using a power law (a * x b ) with exponents b of 0.82 ± 0.09, 0.72 ± 0.11 and 0.61 ± 0.05 for the Erlenbach, Lümpenenbach, and Vogelbach, respectively. The exponent b for the Erlenbach determined in this study is lower compared to that (1.33) calculated in Smith (2013), but the highest of the three catchments. The organic carbon content is lowest in the suspended sediment from the Erlenbach ranging between 0.2% and 3.9% with one exception of 8.3%. In the Lümpenenbach and Vogelbach, the organic carbon content of the suspended sediment lies between 2.2% and 9.5%, and between 1.3% and 13.3%, respectively.
The geochemical and isotopic parameters investigated in this study respond differently to changes in runoff (Figure 3). At low discharges, 14 C signatures exhibit large variability, with F 14 C values ranging from less than 0.10 to more than 1.05. With increasing discharge, the radiocarbon signature appears to converge toward modern values (∼1.0) in the Lümpenenbach and Vogelbach, while in the Erlenbach, F 14 C signatures stabilize at significantly lower values (older 14 C ages), ca. 0.65, at high discharge. A Levene's test (Levene, 1961) shows that the difference in variance between samples collected at average or less than average runoff (runoff ≤0.2 mm hr −1 , the mean runoff in the different catchments ranges between 0.175 mm hr −1 and 0.226 mm hr −1 , but 0.2 mm hr −1 is referred to as average runoff in all three catchments for simplicity) and samples collected at higher-than-average discharges (runoff ≥0.2) is significant for the Erlenbach and the Vogelbach (p-value <0.05). Across all discharge levels, F 14 C values in the Lümpenenenbach are less 14 C-depleted (mean F 14 C, 0.80 ± 0.18) compared to the other two catchments (F 14 C of 0.64 ± 0.22 and 0.74 ± 0.25 for the Erlenbach and Vogelbach, respectively). Stable carbon isotopic (δ 13 C) values ranging between −29.1 and −26.2 ‰, −29.5 and −26.7 ‰, and −30.5 and −24.8 ‰ in the Erlenbach, Lümpenbach and Vogelbach, respectively, do not correlate with runoff in in any of the three catchments. Similarly, CPI does not correlate with runoff, but is significantly (p ≤ 0.01) higher in the Lümpenenbach catchment (CPI, 3-8) compared to the other rivers (CPI, 1-3). The ACL values are highly variable at runoff <0.2 mm hr −1 (ACL, 27.5-29.3), while the variance decreases toward higher runoff (ACL, 28.3-29.1).
PERMDISP (Anderson, 2006), a multivariate Levene's test, where all isotopic and alkane-based parameters are considered, reveals that the difference in measurement dispersion of samples collected at low runoff compared to samples taken at above-average runoff is significant at the 0.1-level in the Lümpenenbach, and the 0.05-level in the Erlenbach and Vogelbach catchments, highlighting the role of the hydrological forcing in stabilizing POC chemical signatures.

Soil and Suspended Sediment Samples in Comparison to Potential Endmembers
The carbon isotopic signatures and n-alkane distribution of topsoil and deep soil do not significantly differ between the catchments, or between forest and grassland soil. This confirms the observation by (Smith, 2013), where the investigated metrics did not differ between Erlenbach soils and Vogelbach soils. Thus, all topsoils and deep soils, respectively, are compiled, and the soil endmember is considered the same in all catchments. The carbon content of the topsoil and deep soil samples averages at 9.25 ± 7.36% and 3.24 ± 1.58%, respectively. The bedrock in the catchments contains 0.54 ± 0.11%OC for the vegetation in the catchments, an OC content of 46.9 ± 2% is reported . Both δ 13 C and F 14 C values are similar for the soil and vegetation endmembers (Figure 4). The δ 13 C value of vegetation of −28.3 ± 1.1‰  covers the entire range of stable carbon isotope compositions of organic carbon in topsoils (−28.1 ± 0.6‰) and deep soils (−28.9 ± 0.2‰). The endmembers also overlap in F 14 C parameter space, with values of 1.02 ± 0.01, 1.03 ± 0.02 and 0.96 ± 0.07 for vegetation, topsoil and deep soil, respectively. These mean values are consistent with differences in turnover (Voort et al., 2019): that is, while the F 14 C values of vegetation are equivalent to modern atmospheric values, topsoil has a higher mean F 14 C value due to an incorporation of bomb-derived 14 C that was introduced in the 1950s. Deep soil F 14 C values are on average lower than vegetation and topsoil. Bedrock (Flysch) is assumed to be radiocarbon dead with 10% uncertainty, δ 13 C is lower than in the modern endmembers (−25.7 ± 0.4‰, Smith et al. (2013)).
While the range of F 14 C values for the suspended sediment samples is covered by the potential endmembers, the range of δ 13 C values of the endmembers does not completely encompass the δ 13 C variability observed for the suspended sediment samples, especially the Vogelbach samples (δ 13 C, −31.2 to −24.8 ‰) (Figure 4. The metrics based on n-alkanes overlap for deep soil (CPI: 4.8 ± 0.8, ACL: 29.5 ± 0.3) and top soil (CPI: 6.5 ± 1.8, ACL: 29.2 ± 0.6). In case of vegetation, the analyzed tree species (Picea abies, Abies alba) are well constrained with a CPI of 4.44 ± 1.4 and an ACL of 27.8 ± 0.3, while other vegetation samples (Alnus viridis, Lycopodium, Equisetum, Juncus effusus, grasses, moss) cover a large range of values (CPI: 9.8 ± 4.4, ACL: 28.2 ± 0.8). Further information on the n-alkane composition of the vegetation endmember is available in Supporting Information S1. The CPI of Flysch has a value of 1 ± 0.2, markedly lower compared to soil and vegetation, while the ACL of Flysch is 28.0 ± 0.1. Many of the suspended sediment samples plot within the endmember values in the CPI-ACL -parameter space, especially between flysch and soil (Figure 4b). Soils and flysch exhibit similar carbon-normalized concentrations of n-alkanes (169 ± 90 μg gOC −1 and 199 ± 41 μg gOC −1 , respectively), while n-alkane concentrations in plant tissue vary markedly among species, ranging from 66 μg gOC −1 for needles of silver fir (Abies alba) to 1227 μg gOC −1 in a grass sample.

Constraints on Endmember Contributions Using an Inverse Model
We use the F 14 C, δ 13 C, CPI and ACL of the suspended sediment to derive the proportion of organic carbon derived from flysch, soil (with topsoils and deep soils combined) and vegetation. The contribution of carbon of the dominant tree species and other vegetation is solved for separately, as the n-alkane distributions of different vegetation samples are quite variable (see Section 4.1 and in Supporting Information S1). Figure 5 shows the proportion of each endmember as a function of runoff. The results of the inverse model show that suspended sediment samples from the Erlenbach catchment contain significantly higher proportions of Flysch than the sediments from the other rivers. The Lümpenenbach samples contain the least bedrock, with suspended sediment consisting of a maximum of 20% Flysch. This is consistent with the generally higher CPI and F 14 C values for this catchment (Figures 3a and 3c). The Vogelbach sediments cluster between the samples from the Erlenbach and the Lümpenenbach.   Figure 6 shows the proportion of each endmember as a function of runoff. In Lümpenenbach and Vogelbach, the fraction of flysch-derived carbon decreases with increasing discharge toward a value of less than 20% at runoff >0.2 mm hr −1 . In the Erlenbach, the contribution of petrogenic carbon is highly variable at low runoff and converges toward 40% with increasing discharge. This difference in proportion manifests itself in the export flux of flysch: While no significant trend with increasing discharge is observable in the Lümpenenbach and Vogelbach catchments, the flysch export in the Erlenbach increases significantly, leading to the offset in F 14 C values of POC compared to the other catchments ( Figure 3). In contrast to petrogenic (flysch) carbon, the fraction of vegetation-derived organic carbon does not follow a specific trend with runoff in any catchment, though proportions of vegetation that are >50% are observed less often at runoff >0.2 mm hr −1 in all catchments.
The proportion of soil-derived organic carbon increases with runoff in all three studied catchments, and the export flux of soil can be approximated in all catchments using a power law. The best fit yields similar values for exponent b (0.57 ± 0.07, 0.60 ± 0.2 and 0.7 ± 0.08 for Erlenbach, Lümpenenbach and Vogelbach, respectively).

Capability of the Inverse Model to Delineate Organic Carbon Sources
Carbon isotopes have been frequently used to determine sources of riverine carbon (e.g., Blair et al., 2010;Hilton et al., 2008;Marwick et al., 2015;Menges et al., 2020;Nagao et al., 2005;Tao et al., 2015;Wang et al., 2019) with radiocarbon particularly well suited to differentiate between modern biospheric carbon and radiocarbon-dead petrogenic carbon. Assuming riverine carbon can be modeled as a composite of bedrock containing a fixed proportion of fossil organic carbon and a modern endmember with an invariant radiocarbon signal, radiocarbon and TOC content alone is sufficient to determine the contribution of each endmember (Blair et al., 2010; Figure 6. Export of organic carbon sourced from bedrock, vegetation and soil. The panels on the left show the proportion of suspended sediment organic carbon sourced from each endmember (a) bedrock, (b) vegetation and (c) soil as a function of runoff. In the right column, the fluxes of each endmember are displayed. The fitted curves show powerlaw relationships between the exported carbon originating from the respective source and runoff that feature a value of r 2 ≥ 0.5. The symbology is identical to the one used in Figure 2. Galy et al., 2008). If these assumptions hold true, F 14 C can then be described as a hyperbolic function of TOC with a curvature defined by the proportion of fossil carbon (Hemingway et al., 2018;Wang et al., 2019). As shown in Figure 7, a hyperbola is not found to be a suitable fit for the relation between %C and F 14 C in any of the catchments.
The lack of such a relationship implies that either more than two endmembers are needed to explain the riverine organic carbon signal or that the TOC content of the bedrock endmember varies. The inverse model used in this study is not based on these requirements: the solution of the system of linear equations is the proportion of carbon in the sample derived from the respective endmembers and is hence independent of their TOC content. The limit of endmembers that the model can solve for depends on the number of linear equations, and since four independent parameters were analyzed in this study, the model can solve for up to five endmembers.
While δ 13 C and F 14 C would be sufficient to solve for the contributions of up to 3 different endmembers, the potential sources of modern carbon, including the different types of soil and vegetation, are too similar to be resolved based on their carbon isotopic signatures alone (Figure 4). The parameters based on long-chained n-alkanes, (i.e., CPI, ACL, Equations 1 and 2), provide a further dimension to distinguish analyzed soil and vegetation samples, hence adding these metrics to the inversion model allows to constrain the contribution from different sources of biospheric organic carbon. An important consideration is whether the chosen parameters behave conservatively during transport and mixing. For example, 13 C fractionation has been observed during microbial respiration, soil development and sediment storage ([e.g., Fernandez et al., 2003;Mary et al., 1992;Scheingross et al., 2021;Schweizer et al., 1999;Werth & Kuzyakov, 2010). Furthermore, n-alkane based proxies may be affected by degradation Zech et al., 2010Zech et al., , 2012. However, as all rivers in this study are only 2 km long and devoid of significant sediment stores along their course, degradation effects occurring between the mobilization of organic carbon and sampling are considered negligible for modeling.
The parameters based on the relative abundances of different n-alkane homologs need to be weighted differently for each endmember if the concentrations of alkanes relative to TOC differ among the endmembers. As the flysch and the soil endmember are very similar in TOC-normalized n-alkane concentration 199 ± 41 μg gOC −1 and 169 ± 90 μg gOC −1 , respectively) and the vegetation endmembers are difficult to constrain as they feature a variability of alkane concentrations (averaging all vegetation samples leads to 381 ± 355 μg gOC −1 ), we assume similar n-alkane concentrations in all endmembers for simplicity, and therefore no weighting factor was applied.
As deep soil and top soil mostly overlap with respect the metrics used in this study, it is not possible to differentiate between organic carbon sourced from topsoil or deeper soil. Thus, the soil samples are combined to a single soil endmember (Figure 4). As the inverse model with 4 parameters can be solved for up to five endmembers, the dominant tree species in the catchment are considered separately from the other vegetation (further information in Supporting Information S1). Therefore, the model includes two different vegetation-derived endmembers, but their proportions are added subsequently to gain the overall contribution of vegetation-derived carbon. An additional potential endmember is POC derived from in-stream productivity, that may contribute to overall POC export especially during low flow (Clark, Shanley, et al., 2017). Given the short length of the streams Figure 7. F 14 C as a function of organic carbon content in % If the observed radiocarbon signature in the catchments was explainable by mixing of two invariable endmembers, one of them radiocarbon modern, the other one radiocarbon dead, F 14 C would be a hyperbolic function of %C (Hemingway et al., 2018). Squared symbols in the Erlenbach plot display data from Smith et al. (2013). and the average slope in the catchments, that ranges between 15% and 19% (FOEN, 2016), the residence time of water in the streams is short (Seeger & Weiler, 2014) and the potential impact of aquatic POC production hence expected to be insignificant, particularly at higher runoff. It is therefore not included in the endmember analysis.
The model requires all our parameters to be measured to solve for endmember contribution. As δ 13 C data is not available for one sample from the Erlenbach, one sample from the Lümpenenbach and four Vogelbach samples, these samples needed to be omitted from the endmember delineation.
The results of the endmember delineation show that the inverse model based on bulk carbon isotopes and n-alkane distributions is capable to distinguish between OC derived from bedrock, soil and vegetation in the studied catchments, and can potentially also be adapted for other river systems.

Endmember Contributions in the Different Catchments
The differences in geochemical composition of suspended sediment between the catchments, especially the different F 14 C values (Figure 3a) and the high CPI in the Lümpenenbach (Figure 3c), are reflected in the endmember contributions derived with the inverse model ( Figure 5). The Lümpenenbach samples contain on average 20 ± 17% bedrock-derived organic carbon compared to 46 ± 17% and 32 ± 17% in the Erlenbach and Vogelbach sample, respectively. This is in accordance with the overall higher F 14 C and CPI in the Lümpenenbach samples compared to the other two catchments.
On average, the proportion of bedrock-derived organic carbon is highest in the Erlenbach catchment. Additionally, while the relative amount of petrogenic carbon decreases with runoff in the Lümpenenbach and Vogelbach, the mobilization of bedrock-derived organic carbon in the Erlenbach is enhanced with higher runoff (Figure 6). The decreasing proportion of petrogenic carbon in the Lümpenenbach and Vogelbach is reflected in the F 14 C values measured in these catchments shifting toward a modern biospheric value of F 14 C ∼1 (Figure 3a), in contrast, the F 14 C in the Erlenbach stabilizes at values around 0.7 due to the higher proportion of bedrock-derived carbon in the suspended sediment. This additional mobilization of bedrock might be due to creep landslides that commonly occur in the Erlenbach catchment (Schuerch et al., 2006), but are not systematically observed in the two other catchments. These landslides are shallow failures of the unconsolidated glacial till that continuously deliver sediment into the channel (Golly et al., 2017;Schuerch et al., 2006). The impact of landslides in the Erlenbach catchment is also reflected in the order-of-magnitude higher overall sediment export in this catchment relative to the Lümpenenbach and Vogelbach (Figure 8). Geomorphic coupling between hillslope and channel and the resulting sediment yield thus impacts the balance of biospheric and petrogenic carbon export in forested mountainous catchments.
While no consistent trend for bedrock-and vegetation-derived organic carbon is observable between the studied catchments, the concentration of soil-derived organic carbon increases as a function of runoff with a similar rate in all studied catchments ( Figure 6). The amount of carbon mobilized from soil is hence similar in all three catchments despite differences in landcover. Applying the fitted rating functions to the discharge record for each of the Alptal streams (WSL, 2020) results in an annual erosion of soil organic carbon (SOC) of 0.7 ± 0.3 t km −2 yr −1 , 0.8 ± 0.4 t km −2 yr −1 and 0.3 ± 0.2 t km −2 yr −1 in the Erlenbach, Lümpenenbach and Vogelbach catchment, respectively. The modeled erosion of soil organic carbon in these pre-alpine catchments is an order of magnitude lower than the 9.6 t km −2 yr −1 estimated mean SOC exported by rivers from European croplands (Ciais et al., 2010). The results are therefore in accordance with the expectation that SOC erosion from the studied non-agricultural catchments are up to two orders of magnitude lower compared to croplands (Montgomery, 2007). However, as these estimations are based on extrapolations from data gathered predominantly at low to average runoff, the suspended sediment yields, and therefore also the soil-derived organic carbon export may be underestimated (See Section 4.3).
Runoff-driven mobilization of soil organic carbon has been suggested in a number of mountainous catchments (Clark et al., 2013;Goñi et al., 2013;Hilton, 2017;Hilton et al., 2008), including the Erlenbach . The results of the mixing model confirm that runoff exerts an important control on the export of soil organic carbon and, consequently, the balance of biospheric and petrogenic carbon export. The soil organic carbon export increases with runoff at a similar rate in all three studied catchments, suggesting that estimates for mobilization of soil-derived organic carbon could potentially be extrapolated to other headwater catchments in similar environmental settings. Pre-aged mineral-bound soil organic carbon may be better protected from degradation than other biospheric carbon pools and therefore sustain riverine transport to be buried on continental margins. Growing evidence suggests that soil-derived OC indeed comprises a significant fraction of organic carbon that is transferred from rivers to oceans (Holtvoeth et al., 2005;Tao et al., 2015;Vonk et al., 2010). Therefore, runoff-driven surface erosion does not only promote the mobilization of biospheric organic carbon in general, but of recalcitrant soil organic carbon, which benefits the downstream preservation of exported organic matter.

Differences in OC Yields Compared to Previous Studies
In the Erlenbach catchment, organic carbon export during high discharge events has been monitored previously by Smith et al. (2013) with a resulting estimate of annual biospheric (vegetation-and soil-derived) carbon OC export of 14.0 ± 4.4 t km −2 yr −1 . Following the mixing model, the export of biospheric (vegetation + soil) organic carbon (mgC l −1 ) in the Erlenbach can be approximated as a function of runoff (mm h −1) using a powerlaw (best fit: 1.03 ± 0.11x 0.83±0.1 , r 2 = 0.44). Applying this function to the discharge record of the Erlenbach (WSL, 2020) leads to an estimate of 1.2 ± 0.4 t km −2 yr −1 of biospheric organic carbon yield, which is a magnitude lower than that predicted by Smith et al. (2013). The POC concentration in the Erlenbach samples is 1.6 ± 1.5% in this study and therefore in accordance with the mean POC concentration of 1.45% measured by Smith et al. (2013), but the suspended sediment concentrations are consistently lower in this study ( Figure S4 in Supporting Information S1) leading to the differences in organic carbon yields. In the context of long-term surveillance data of the Erlenbach (Eawag, 2021),that shows a high variability in suspended sediment concentration with discharge, the suspended sediment concentrations measured in both studies are plausible ( Figure S4 in Supporting Information S1). The differences could be caused by different sampling strategies: While Smith et al. (2013) filtered 100 ml water during storm events in July 2010, the suspended sediment samples analyzed in this study were collected between June 2014 and May 2016 by filtering 10-40 l of water during rainfall, so only a single sample per event could be obtained. The different sample volumes and strategies could lead to inconsistencies between the different data sets. Additionally, it is possible that suspended sediment fluxes are not constant and change over time. Longterm surveillance data suggests that in the year 2010, when sampling for the study by Smith et al. (2013) took place, suspended sediment export was significantly higher (p < 0.05) compared to that of the overall surveillance period (2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019). Furthermore, more than half of the annual suspended sediment export occurs during events at runoff values >2 mm hr −1 . While Smith et al. (2013) cover these high-discharge events extensively, they are not well represented in this study's data set, therefore an extrapolation of suspended sediment export based on this data might be biased. Indeed, the discrepancy between the data suggests that our estimate is comparatively conservative and rather constrains a lower boundary of suspended sediment export, and consequently organic carbon yields, from forested mountainous headwater catchments.
While the correlations between runoff and soil-derived organic carbon export may not lead to accurate estimations of export fluxes due to the extrapolation into discharge regimes that are not represented in the present data set, they show, that the hydrological forcing of the composition of organic carbon due to hillslope erosion is already observable at average runoff (∼0.2 mm hr −1 ) during rainfall.

Changes in Organic Matter Characteristics With Runoff
In all three headwater catchments, the variance of the geochemical signatures of POC decreases significantly with increasing discharge. As the isotopic and alkane-based parameters measured in the samples result from mixing of different endmembers, the observed convergence of parameter values implies that while at low discharges the contribution from the different sources varies considerably, carbon contributions from the respective sources at higher discharges are more uniform. The predominant sources at higher discharges vary between the studied catchments: In the Lümpenenbach and Vogelbach catchments, the results of the mixing model imply that only the export of carbon sourced from radiocarbon modern endmembers increases with discharge ( Figure 6), leading to the observed stabilization at near modern F 14 C values. In contrast, export of flysch-derived carbon increases along with soil-sourced carbon in the Erlenbach, and hence F 14 C values converge at intermediate values (0.55-0.65), reflecting a mixture of petrogenic and modern carbon.
Increasing uniformity in the chemical or isotopic composition of riverine POC at high discharges has been observed previously in some mountainous catchments, with the sample composition converging toward carbon predominantly sourced from bedrock in the Waipaoa river (Gomez et al., 2003) or soil in the Jiolong river (Qiao et al., 2020). Takagi and Haga (2019) show a distinct convergence of C/N in suspended sediment samples with discharge in a Japanese headwater catchment. In contrast, almost no reduction in geochemical variability has been observed in the Santa Clara, Umpqua and Eel rivers (Goñi et al., 2013;Hatten et al., 2012), while in the Min Jiang river (Wang et al., 2019), the variance in δ 13 C values decreases significantly only at one of the six sampling locations (Heishui station). Currently, however, studies that focus on changes of the composition of POC with discharge and encompass a sample density that is sufficiently high to constrain differences in variance remain too sparse to constrain those conditions that drive convergence of POC composition, and to determine the isotopic or chemical compositions upon which POC will converge with increasing discharge. Putatively, the convergence occurs due to the availability of carbon from different sources at low compared to high discharges (Clark, Shanley, et al., 2017). At low discharges, a river may mostly mobilize carbon available within or in close proximity to the channel. In case of the studied mountainous rivers, several sources of carbon with distinct isotopic and geochemical composition are available at or close to the channel including the incised bedrock, soil of different depths and vegetation. During high-discharge events, carbon eroded from the hillslopes by runoff seems to dominate the exported POC, therefore the composition of POC may converge toward the carbon available for runoff-driven surface erosion in the respective catchment. Further studies targeting this question would improve our understanding of the processes that drive the balance between biospheric and petrogenic organic carbon export, as well as our ability to predict and refine riverine organic carbon export fluxes from small mountainous catchments.
The observed decrease in chemical and isotopic variability within suspended sediment POC with increasing discharge implies that suspended samples should ideally be collected at above-average discharges in order to best approximate the overall carbon export. Additionally, high discharge events contribute disproportionally to the overall carbon flux, thus the endmember contributions observed during these conditions have higher relevance for the overall carbon export. In contrast, samples collected during low flow conditions may not be representative given that the contribution of different carbon sources may shift with increasing discharge, and that intrinsic sample-to-sample variability is likely to be higher.

Conclusions
We applied an inverse model using bulk carbon isotopes and n-alkane metrics (i.e., CPI and ACL) to suspended sediment samples from three pre-alpine headwater catchments to assess the fractional contribution of putative sources of organic carbon, namely bedrock, soil, and vegetation. The results of the model reveal an increase of soil-sourced organic carbon with discharge due to runoff-driven erosion across all three studied catchments. This indicates that the export fluxes of soil organic carbon can potentially be extrapolated to other temperate mountain catchments despite contrasting bulk POC signatures. Differences in the exported carbon signal among the three studied catchments manifest themselves most strongly in radiocarbon signatures, with significantly lower F 14 C values at high runoff in the Erlenbach compared to the other two catchments. This offset is due to an enhanced export of petrogenic carbon at high discharge that is only observed in the Erlenbach catchment, and likely reflects landslides that mobilized bedrock-sourced sediment. Notably, all three catchments show a convergence in chemical and isotopic compositions at higher discharges. Suspended sediment samples collected at above-average discharges are thus better suited to constrain carbon export since they not only account for most of the total export flux but also offer less stochastic variability that may confound geochemical signatures if only few samples can be collected.