Natural and human-induced erosion supplies high amounts of soil organic carbon (OC) to terrestrial drainage networks. Yet OC fluxes in rivers were considered in global budgets only recently. Modern estimates of annual carbon burial in inland river sediments of 0.6 Gt C, or 22% of C transferred from terrestrial ecosystems to river channels, consider only lakes and reservoirs and disregard any long-term carbon burial in hillslope or floodplain sediments. Here we present the first assessment of sediment-bound OC storage in Central Europe from a synthesis of ~1500 Holocene hillslope and floodplain sedimentary archives. We show that sediment storage increases with drainage-basin size due to more extensive floodplains in larger river basins. However, hillslopes retain hitherto unrecognized high amounts of eroded soils at the scale of large river basins such that average agricultural erosion rates during the Holocene would have been at least twice as high as reported previously. This anthropogenic hillslope sediment storage exceeds floodplain storage in drainage basins <105 km2, challenging the notion that floodplains are the dominant sedimentary sinks. In terms of carbon burial, OC concentrations in floodplains exceed those on hillslopes, and net OC accumulation rates in floodplains (0.7 ± 0.2 g C m−2a−1) surpass those on hillslopes (0.4 ± 0.1 g C m−2a−1) over the last 7500 years. We conclude that carbon burial in floodplains and on hillslopes in Central Europe exceeds terrestrial carbon storage in lakes and reservoirs by at least 2 orders of magnitude and should thus be considered in continental carbon budgets.
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 Anthropogenic soil erosion mobilizes organic-rich topsoils at an estimated 35 Gt a−1 [Quinton et al., 2010], causing land degradation, reduced soil fertility, sediment pollution, and undermining of agricultural livelihoods in many parts of the world. The erosion and redeposition of soil organic carbon (OC) attached to fine sediments is also an important but insufficiently understood component of the global carbon cycle [Aufdenkampe et al., 2011; Stallard, 1998; Van Oost et al., 2007]. Against this backdrop, sediment flux is a key metric for gauging the severity of soil degradation, siltation of reservoirs and river deltas, and the cycling of nutrients, contaminants, and other biogeochemical constituents from local to global scales [Syvitski et al., 2005; Vörösmarty et al., 2003; Walling, 2006]. Sediment-associated OC fluxes have been insufficiently considered in the global carbon cycle, and hence, large uncertainty remains regarding the contribution of human-induced soil erosion. This uncertainty is exemplified by the diverging views of whether soil erosion is a source or sink of atmospheric CO2, owing to the competition of mineralization of organic-rich topsoils caused by the breakdown of soil aggregates [Lal, 2005; Victoria et al., 2012], and the burial and stabilization of eroded carbon in depositional environments [Stallard, 1998; Van Oost et al., 2012; Van Oost et al., 2007], respectively.
 Despite elevated soil erosion rates during the last several thousand years [Hoffmann et al., 2009b; Verstraeten et al., 2009], distinct mismatches between reported on-site loss of topsoil and sediment delivery downstream arise from the storage of sediment along hydrological pathways [Phillips, 2003; Wilkinson and McElroy, 2007] (Figure 1). The rate of sediment delivered to a basin mouth normalized by its upstream area is known as specific sediment yield and thought to decline downstream because of increasing floodplain aggradation in larger valley fills and decreasing erosion rates on less steep hillslopes. The fraction of sediment leaving a given basin with respect to upstream erosion defines the sediment delivery ratio, which similarly decays with increasing basin size [Church et al., 1999; Hassan et al., 2008; Walling, 1983]. The simplistic assumption that larger river systems with commensurately larger floodplains provide more accommodation space to store sediment [Walling, 1983] and buffer more strongly the fluvial response to environmental changes [Dearing and Jones, 2003] has impeded the study of sediment-related carbon storage on largely unchannelized hillslopes and its impact on riverine OC fluxes.
 We argue that quantifying sediment storage is essential to gauging the effects of related carbon storage on atmospheric CO2 consumption. Data on sediment and carbon storage on hillslopes and floodplains are scarce and mostly inferred from net differences between modelled hillslope erosion and sediment yields estimated at basin outlets. Studies that attempted quantifying hillslope and floodplain sediment storage have focused on small drainage basins <1000 km2 [e.g., Houben, 2008; Notebaert et al., 2011; Rommens et al., 2006], affording only limited transferability to larger basins [Hoffmann et al., 2007]. This shortcoming raises two pertinent research questions: How does sediment storage on hillslopes and on floodplains change with basin size? How relevant is such storage to extrapolating sediment-bound carbon storage to the continental scale?
2 Large-Scale Sediment Storage
2.1 Human Impact in Central Europe
 Agricultural soil erosion in Central Europe began during the Neolithic as early as 7500 years ago [Houben, 2008; Notebaert et al., 2009] and was mostly focused on loess-covered areas (Figure 1) that yielded readily to primitive plows, provided the most fertile conditions for the first continuous settlements, and concomitant increases in population density. Agricultural expansion into the less productive Central European uplands commenced as late as the Iron Age (800–0 BC), and declined during phases of decreased population density, such as following the Roman and Medieval Periods (350–700 AD and 1500–1700 AD, respectively) [Zimmermann et al., 2009]. From this soil resource-driven pattern of stepwise agricultural expansion and intermittent decline, we expect specific trends in soil erosion, sediment and carbon storage in loess and upland areas to be recorded in the Holocene sedimentary archives.
2.2 Estimation of Scaling Relationship
 In order to detect and quantify these hypothesized differences, we compiled published data of sediment storage on Central European regions that were affected by human-induced soil erosion during the last 7500 years (Table S1). This unprecedented inventory contains both hillslope (n = 41) and floodplain (n = 36) storage of fine sediments (<2 mm) ranging in basins sizes from 6 × 10−3 km2 to 28 × 103 km2. Sediment storage in Central Europe is generally inferred from a large number of auger holes and boreholes evenly spaced on hillslopes and floodplains to estimate the thickness of sediments associated with human-induced soil erosion. In the case of hillslope storage, sediment volumes for larger areas are extrapolated based on relationships of sediment thickness and topographic parameters. Floodplain storage is generally quantified by multiplying the extent of floodplains along selected channel reaches with representative thicknesses of overbank fines [Notebaert et al., 2011; Rommens et al., 2006]. In both cases, hillslope and floodplain storage is related to fine sediments resulting from agricultural soil erosion. Even though the history of deposition of hillslope and overbank fines is modified by Holocene climate changes, the majority (~85%) of total storage volumes relates to human impacts after the onset of Neolithic agriculture some 7500 years ago [Hoffmann et al., 2007; Verstraeten et al., 2009].
 We approximate the scaling relationship of fine sediment storage S (109 kg = Mt) with basin area A (km2) by a simple power law:
where b is the scaling exponent and a (Mt) the storage related to an arbitrarily chosen reference area Aref. Here we used reference areas of 103 km2, representing roughly the mean basin size of all considered hillslope and floodplain storage estimates (Figure 2). The prediction of sediment storage using equation (1) and the derived scaling exponent b are independent of the chosen Aref. Regression coefficients a and b were determined using (i) linear least square regression of log-transformed data (log-LR) and (ii) nonlinear least squares estimates (NL) using untransformed data. Errors of the regression coefficients are given by the standard deviation, based on bootstrap estimates of n = 2000 resampled subsets. Predictions (Figure 3) and root-mean-square errors (RMSE; Table 1) of the regression models were calculated using a jackknife, i.e., a leave-one-out validation. Linear and nonlinear regression were compared using Akaike's Information Criterion (AIC) [Xiao et al., 2011]. We tested for significant overestimations of large values, which is frequently observed using log-LN regression. Since RMSE and AIC for the log-LR was much smaller than for NL (Table 1), and predictions are in better agreement with measured values using log-LR (Figure 3), all coefficients stated refer to log-LR.
Table 1. Summary of Regression Results of Sediment Scalinga
aa and b are coefficient and exponent in equation (1), respectively. RMSE = root mean square error, AIC = Akaike's Information Criterion. Units of a and RMSE are given in megaton (Mt). Uncertainties are standard deviations of a and b, derived from 2000 bootstrap runs. In case 2a, power-law regression was applied to all hillslope data irrespective of their loess cover. Case 2b is calculated based on weighted means of a and b for loess hillslopes (representing 19.8% of Central Europe, case 3) and of upland hillslopes (e.g., 80.2% of Central Europe, case 4).
Log-Transformed Linear Regression
Hillslope (weighted mean)
Hillslope (weighted mean)
 All bootstrapped scaling exponents are normally distributed. Thus, significant increases of sediment storage (e.g., b being significantly higher than unity) and differences between the scaling exponents on hillslopes and in floodplains were tested based on a t test at the 95% confidence level.
 In the absence of large-scale estimates of human-induced hillslope sediment storage, we use equation (1) to calculate hillslope sediment storage for the nonalpine part of the Rhine basin (125,000 km2). We observe no obvious scale break at catchment scales beyond the largest known hillslope budgets [e.g., which are 750 to 1500 km2 according to Notebaert et al., 2009; Seidel and Mäckel, 2007] and our study area upstream of the Rhine delta. This assumption is supported by the statistical analysis of the available sediment storage data (Figure 2 and Table 1).
 The studied loess basins are generally larger than the nonloess basins resulting in a biased estimate of b when log-LR is applied to the entire hillslope dataset. We used weighted means of a and b for loess and upland basins. The weighting for a and b was obtained from the relative loess coverage Rloess = 19.8% in Central Europe: aHS = Rloess × aloess + (1 − Rloess) × anonloess, where aHS, aloess, and anonloess are the scaling coefficients of hillslopes, loess hillslopes, and uplands, respectively. The loess coverage was taken from Haase et al. .
2.3 Results and Discussion
 The impacts of preferential and continuous farming since the Neolithic in loess areas are captured by a hillslope storage coefficient aloess = 611 ± 235 Mt that is twice as high as in upland areas (aupland = 303 ± 201 Mt; Figure 2a). The scaling exponents remain statistically indistinguishable with nearly linear increases of sediment storage per basin area (b = 1.06 ± 0.6 and 1.09 ± 0.9, respectively). These results are consistent with the notion that sustained human occupancy and soil erosion in loess areas has led to larger amounts of eroded soils stored on hillslopes than in areas with less fertile substrates.
 In contrast to the scaling of hillslope storage, which shows only a slight increase for drainage basin areas between 10−2 and 103 km2, we find that floodplain storage grows significantly with basin size (b = 1.23 ± 0.06, Figure 2b). This supports the observation of declining specific sediment yields in drainage basins affected by human-induced soil erosion [Church et al., 1999; Walling, 1983]. Although the importance of hillslope sediment storage in sediment budgets has been established for smaller river basins [Notebaert et al., 2009; Verstraeten et al., 2009], our analysis shows the first direct comparison of hillslope and floodplain storage at the scale of larger river basins (>103 km2). Given the estimated scaling coefficients, even for basins up to 105 km2 hillslopes store as much sediment as floodplains (Figure 2b) and thus retain a surprisingly large amount of sediment.
 This substantial sink of soil sediment has largely been neglected in sediment budgets of large drainage basins [Wilkinson and McElroy, 2007], thus promoting underestimates of long-term soil erosion rates. Our scaling relation for hillslope storage indicates a total of 67 ± 39 Gt for the nonalpine part of the Rhine basin, compared to 59 ± 13 Gt of floodplain and delta storage [Hoffmann et al., 2007]. This total sediment storage of 126 ± 41 Gt necessitates a minimum average Holocene soil erosion rate of 1.2 ± 0.32 t ha−1 a−1. This is twice the rate of 0.55 ± 0.16 t ha−1 a−1 that was previously inferred from floodplain and delta storage only [Hoffmann et al., 2007]. This updated erosion rate approaches the contemporary average of 2.7 t ha−1 a−1 for Germany [Auerswald et al., 2009]. Given that modern soil erosion rates are generally an order of magnitude higher than Holocene rates [Hoffmann et al., 2009b; Verstraeten et al., 2009], the similarity between modern and millennial (storage-derived) soil erosion rates suggests that hillslopes form a major and hitherto unrecognized millennial-scale sedimentary sink for human-induced soil erosion in Central Europe. This important finding challenges the conventional view that floodplains are the dominant sediment sinks in such large basins [Wilkinson and McElroy, 2007].
3 Large-Scale Organic Carbon Storage
3.1 Estimation of Organic Carbon Storage
 To address the implications of sediment storage on long-term OC storage, we compiled published measurements of OC concentrations from Holocene hillslope (n = 366), overbank (n = 756), and channel-fill (n = 370) deposits (Figure 4). These data were compiled to estimate carbon storage in the Rhine basin using mean OC concentrations of 0.8 ± 0.1%, 1.1 ± 0.1%, and 7.6 ± 1.4% for hillslopes, overbank, and channel-fill deposits, respectively (Figure 4). Using published transects through a number of floodplains in the Rhine basin, Hoffmann et al. [2009a] estimated a relative abundance of 85 ± 10% and 15 ± 10% for overbank and channel-fill deposits, respectively, resulting in an average weighted concentration of post-Neolithic floodplain deposits of 2.1 ± 0.8%. The uncertainty of the weighted average is given by the standard deviations of the measured OC concentrations and relative abundances of floodplain deposits, which are propagated using Gaussian error calculation). Detailed comparison of OC concentrations in floodplains and on hillslopes covers several orders of basin magnitudes with insignificant differences for varying basin size. Mean OC weight concentration (OCMC) for hillslope (0.8 ± 0.1%) and floodplain deposits (2.1 ± 0.8%) were multiplied with stored sediment masses (Figure 2c) to calculate post-Neolithic OC stocks on hillslopes and floodplains. Multiplication of sediment masses with the same OCMC independently on basins size does not alter the scaling exponent b in equation (1) but changes a coefficients of sediment storage as aOC = aSED × OCMC. Net OC stocks were divided by 7500 years, i.e., the approximate time that agricultural land use commenced in Central Europe, to calculate averaged burial rates (Table 2). Floodplains had formed well before 7500 years, representing approximately 15% of the Holocene total [Hoffmann et al., 2009a; Verstraeten et al., 2009]. Thus, we considered only 85% of the floodplain sediment masses to be post-Neolithic.
Table 2. Extrapolation of Sediment and Organic Carbon Storage on Hillslopes (HS) and in Floodplains (FP) in the Nonalpine Part of the Rhine Basin (Basin Size = 125,000 km2)a
aHillslope storage is based on case 2b (weighted mean) in Table S1. Errors are derived from standard deviations of the bootstrap analysis and propagated using the Gaussian error propagation.
bValues of carbon burial in lakes are taken from Kastowski et al. . We used carbon accumulation rates (tC a−1) for lakes smaller and larger than 5 km2 given for region 8 in their Table 5 and the corresponding lake area as given in their Table 2. Based on these numbers, we calculated specific accumulation rates (tC m−2a−1) for lakes smaller and larger than 5 km2 and multiplied these rates with lake areas in the Rhine basin derived from the Global Lakes and Wetland Database (GLWD) [Lehner and Döll, 2004].
cC-deposition rates represent post-Neolithic rates. Therefore, we calculated that 85% of the Holocene floodplain sediments are deposited after the Neolithic. All hillslope sediments are treated as post-Neolithic.
 Observed basin-averaged OC stocks of hillslope and floodplain deposits range between 0.36 and 10.1 kg C m−2 (Figure 2c). Part of the buried OC is produced in situ and is not derived from deposition of OC eroded on hillslopes. This holds for the channel-fill deposits but to some extent also for the overbank floodplain deposits [cf. Hoffmann et al., 2009a; Van Oost et al., 2012]. However, OC concentrations versus depth (Figure 4) show that OC concentrations remain at values comparable to the topsoil OC down to 2.5, 4, and even 5.5 m in the case of hillslope, overbank, and channel-fill deposits, respectively. Thus, hillslope and floodplain deposits retain significant amounts of OC below the topsoil (e.g., below ~1m), which is typically not considered in continental soil carbon budgets. A more detailed accounting of the different sources of OC on hillslopes and floodplains is needed to better understand the role of anthropogenic enhanced erosion and deposition on terrestrial carbon budgets [Hoffmann et al., 2013] but is outside the scope of this study.
 Regardless of basin size, hillslope and floodplain OC storage are statistically indistinguishable in terms of scaling coefficients (i.e., hillslope OC aHS,OC = 2.9 ± 1.4 Mt C; floodplain OC aFP; OC = 3.9 ± 1.6 Mt C) but significantly different in terms of the scaling exponent. We find that OC concentrations vary strongly between different regions obscuring any relationships between OC concentration and drainage basin size. Thus, we multiplied sediment storage with average OC concentration at all scales, obtaining scaling exponents of 1.08 ± 0.07 for hillslopes and 1.23 ± 0.03 for floodplain OC storage. Given their prominent role in storing sediment, hillslopes are also an important—though previously neglected—component in the Central European carbon budget. Storage of OC in eroded soil deposits on hillslopes is particularly pronounced in small- to medium-sized basins, i.e. <103 km2. This is 2 orders of magnitude below the basin size at which hillslope sediment storage balances that of floodplains (~105 km2), reflecting larger and more long-lived OC storage in floodplains as opposed to hillslopes [Van Oost et al., 2012]. In basins >103 km2 OC storage in floodplains dominates as a millennial-scale sink dating back to as early as the Neolithic.
 In summary, we present the first systematic scaling relationship between sediment and OC storage on hillslopes and floodplains in Central European drainage basins covering nearly 6 orders of magnitudes (10−2 to 105 km2). Despite some scatter, these empirical relationships are indispensable tools for quantitatively refining regional- to continental-scale estimates of sediment and OC storage, including the OC sink associated with soil erosion over the last ~7500 years. Mean OC stocks of 3.1 ± 1.0 and 5.0 ± 1.3 kg C m−2 for hillslope and floodplain storage, respectively, result in long-term, post-Neolithic OC accumulation rates of 0.44 ± 0.14 and 0.61 ± 0.16 g C m−2 a−1. These rates are an order of magnitude below the fluxes in the terrestrial carbon budgets of Europe during the last decades [Luyssaert et al., 2010]. Carbon gains in forests and grasslands in Germany and Belgium were 78.1 and 28.5 g C m−2 a−1 during the 1990s and counteracting combined carbon losses in croplands and peats of −34.7 and −18.2 g C m−2 a−1 [Janssens et al., 2005]. Yet carbon gains related to increasing biomass due to forest management are sustained only for several decades. In contrast, the cumulative effects of storage and stabilization of carbon in sedimentary sinks on hillslopes and floodplains integrate over millennia, thus imposing a strong legacy of past human impact through agricultural erosion on current carbon storage in sediment stores [Van Oost et al., 2012]. Specific OC burial on hillslopes and floodplains (1.05 ± 0.30 g C m−2 a−1) amounts to only ~13% of specific OC burial of 8.6 g C m−2 a−1 in Central European lakes and reservoirs [Kastowski et al., 2011], indicating a higher efficiency of OC storage in lakes and reservoirs. Yet the inferred post-Neolithic carbon burial on hillslopes and in floodplains (0.23 ± 0.11 Mt C a−1) is ~170 times larger than total lake storage within our study area (Table 2). Strong erosion-induced OC storage and the limited area occupied by lakes in Central Europe certainly provide an upper limit to this ratio but indicate that significant larger areas of floodplains and hillslope deposits compensate for their lower efficiency of OC storage compared to lakes and reservoirs.
 Long-term storage of organic-rich sediment on hillslopes and floodplains substantially contribute to the carbon budget in Central Europe and may have considerable effects on the global scale. Current global estimates of continental carbon burial in lakes and reservoirs are of the order of 0.6 Gt C a−1 [Aufdenkampe et al., 2011; Battin et al., 2009]. Given the low lake density in the Rhine basin and the Holocene history of human settlement in Central Europe, the relative importance of hillslopes and floodplains versus lakes and reservoirs (given here by a ratio of 1:170) does certainly not provide a representative global average and we caution against oversimplifying this ratio. But given the widespread human-induced land cover change [Kaplan et al., 2011] and subsequent erosion during the Holocene, global estimates of continental carbon burial may increase substantially if considering long-term OC sequestration in both floodplains and hillslopes. Adjusting these previous estimates of continental carbon burial accordingly has direct consequences for net carbon balances of the terrestrial biosphere because of the need to balance the global carbon budget, CO2 outgassing, and carbon burial and export to the oceans. However, continental-scale estimates of post-settlement sediment and carbon storage focus generally on floodplains only [e.g., Hoffmann et al., 2009a; Wilkinson and McElroy, 2007]. Future research on extrapolating sediment-related carbon budgets beyond Central Europe and more accurate accounting of the carbon sources and the effects of accelerated human-induced soil erosion are needed [Hoffmann et al., 2013]. We anticipate that similar scaling relations of carbon storage in other parts of the world will further elucidate the global impact of agricultural soil erosion and varying long-lived land use histories.
 We provide the first systematic comparison of post-Neolithic sediment and carbon storage on hillslopes and floodplains at the scale of larger river basins in Central Europe. We show that hillslope sediment storage exceeds floodplain storage even for basins up to 105 km2. Our scaling relation for hillslope storage indicates a total of 67 ± 39 Gt for the nonalpine part of the Rhine basin, compared to 59 ± 13 Gt of floodplain and delta storage. This total sediment storage of 126 ± 41 Gt necessitates a minimum average Holocene soil erosion rate of 1.2 ± 0.32 t ha−1 a−1. In terms of carbon burial, OC concentrations in floodplains exceed those on hillslopes, and net OC accumulation rates in floodplains (0.7 ± 0.2 g C m−2a−1) surpass those on hillslopes (0.4 ± 0.1 g C m−2a−1) over the last 7500 years. Total OC storage in floodplains dominates as a millennial-scale sink for soil sediments in basins >103 km2. OC burial in floodplains and on hillslopes in Central Europe is a comparatively slow but continuous and widespread process and exceeds terrestrial carbon storage in lakes and reservoirs by at least 2 orders of magnitude during the Holocene and is thus important for refining continental carbon budgets. Much work lies ahead to quantify OC burial in floodplains and on hillslopes in other parts of the Earth's surface under varying climate and land use histories.
 TH, GV, and BN acknowledge the LUCIFS-network (www.lucifs.uni-bonn.de) for workshops and discussions on sediment-associated carbon fluxes. Funding was provided for MS through the DFG-SFB 806 and for OK by the Potsdam Research Cluster for Georisk Analysis, Environmental Change and Sustainability (PROGRESS). Statistics were computed using the R software environment (www.r-project.org).