SUPPLEMENTARY INFORMATION

Transcription

1 In the format provided by the authors and unedited. SUPPLEMENTARY INFORMATION DOI: /NCLIMATE3263 Human-induced erosion has offset one-third of carbon emissions from land cover change Zhengang Wang 1*, Thomas Hoffmann 2,3, Johan Six 4, Jed O. Kaplan 5, Gerard Govers 6, Sebastian Doetterl 7,8, and Kristof Van Oost 1 1 Georges Lemaître Center for Earth and Climate Research (TECLIM), Earth and Life Institute, Université catholique de Louvain, 1348 Louvain-la-Neuve, Belgium 2 Department of Geography, University of Bonn, Meckenheimer Allee 166, Bonn, Germany 3 German Federal Institute of Hydrology, Am Mainzer Tor 1, Koblenz, Germany 4 Department of Environmental Systems Science, Swiss Federal Institute of Technology, ETH Zurich, 8092 Zurich, Switzerland 5 Institute of Earth Surface Dynamics, University of Lausanne, Geopolis, 1015 Lausanne, Switzerland 6 Department of Earth and Environmental Sciences, K.U. Leuven, 3001 Heverlee, Belgium 7 Institute of Geography, Augsburg University, Alter Postweg 118, Augsburg, Germany 8 ISOFYS-Isotope Bioscience Laboratory, Ghent University, Coupure Links 653, 9000 Gent, Belgium * zhengang.wang@uclouvain.be NATURE CLIMATE CHANGE Macmillan Publishers Limited, part of Springer Nature. All rights reserved.

2 Supplementary material S1: overview of the methods 1. Overview The approach used in this study is schematically represented in Fig. S1. In our model, the land surface is represented by 1000 virtual catchments, which are composed of five geomorphic classes (stable, eroding, colluvial, and alluvial cropland and alluvial non-cropland). Our approach consists of four main parts. First, we reconstructed the temporal and spatial evolution of global cropland expansion for the period 6000BC-2015AD. Second, we derived mean soil organic carbon (SOC) profiles for the five geomorphic classes within four climate zones (tropical, dry, temperate, and continental climate zones, see also section 2) from available soil profile databases that are representative for global cropland. Third, we estimated the cumulative amount of redistributed and exported sediment and associated SOC by agricultural soil erosion during the Holocene in each virtual catchment using a parsimonious erosion model. In response to this agricultural erosion or deposition, changes in SOC depth profile as a result of lateral redistribution were then calculated for each geomorphic class. Finally, the SOC stock variation, relative to stable sites, in each geomorphic unit was then combined with the lateral SOC fluxes to infer erosion-induced soil-atmosphere C exchange. A Monte Carlo approach was used to quantify the uncertainties associated with model input parameters. 2. Anthropogenic land cover change (ALCC) We analyzed the ALCC scenarios at the scale of the four major climate zones considered in our study. The four major climate zones are based on the Köppen climatic classification system, i.e. climate zone A (tropical climate), climate zone B (dry climate), climate zone C (temperate climate) and climate zone D (continental climate). Climate zone E (polar and alpine climate) was omitted due to its negligible contribution to global cropland. Each climate zone has 250 virtual equal-area catchments covering in total an area equal to twice that of the current (2015) cropland area in each climate zone. These catchments are considered to be the smallest units for land use; i.e., land use change cannot occur in a fraction of a catchment only. The number of virtual catchments under cropland in each climate zone at any particular time was calculated as the cropland area divided by the virtual catchment area. The number of cropland catchments will change with time to reflect changes in cropland area within the relevant climate zone. This approach allows us to account for the fact that areas that have a similar land use at a certain moment in time may have a completely different land use history, which will be reflected in SOC storage within the catchment (see below). An exploratory analysis showed that simulation results were not affected when the area was further divided into more than 250 catchments. Given that land cover change is the main driver of our model, we used two frequently used but different ALCC scenarios, i.e. HYDE 1,2 and KK10 3 as the basis for our study. However, these two ALCC scenarios strongly differ in their estimates of per capita land use at low population densities, whereby the conversion of non-cropland to cropland occurs at a much higher rate during the early phases for the KK10 scenario. This results in substantial differences in our simulations of cumulative agricultural soil erosion and associated fluxes of SOC between these two base scenarios. The cumulative sediment flux mobilized in a catchment due to agricultural erosion is related to its land use history as it integrates changes in cropland area and average erosion rate over time. Thus, we can gain insights as to what extent a land use scenario is realistic by comparing observed and 2

3 modelled cumulative sediment fluxes. We used a modified version of the erosion model developed by Van Oost, et al. 4 (see supplementary material S3 section 2) to 13 real catchments for which empirical observations on anthropogenic sediment accumulation during the Holocene are available (Table S1). We confronted observed cumulative sediment fluxes with our model simulations of sediment generation to evaluate and constrain the ALCC scenarios. Note that because subsoil erosion (i.e. from gullying and landsliding) constitutes a significant part of the total sediment generation in the Yellow River catchment 5, the observed total cumulative anthropogenic sediment was divided into topsoil and subsoil sediments. This is needed because our model only considered sediment generation in the upper layer of the soil profile. The correction factor, whereby topsoil erosion represents about half of the total erosion, was based on published data 5. We ran our model using the HYDE and KK10 scenarios for the 13 catchments and we obtained estimates of anthropogenic sediments that were consistent with the observations (i.e. in the correct order of magnitude). However, our analysis also clearly showed that the HYDE scenario underestimates the cumulative agricultural fluxes while the KK10 scenario overestimates the cumulative agricultural fluxes (Fig. 2). Based on this observation, we considered the HYDE and KK10 scenarios to represent the low and high end members of ALCC in our simulations and constructed combined scenarios. We introduced a weight factor to determine the temporal evolution of cropland area in a given Monte Carlo scenario based on the HYDE and KK10 land use scenarios: = +1 (1) where A(t) (m 2 ) is the cropland area at time t (yr), A H (t) (m 2 ) and A K (t) (m 2 ) are the cropland area at time t (yr) in the HYDE and KK10 land use scenarios, respectively, and W K is a weight factor that ranges between 0 and 1. The probability distribution of W k was estimated using generalized likelihood uncertainty estimation (GLUE) 6 by confronting the simulated cumulative anthropogenic erosion with observations in 13 catchments covering a large variety of agricultural trajectories and environmental conditions (Table S1). The root mean square (RMS) of the residuals of a simulation scenario was assessed using the following equation: = (2) where RMS(i) is the root mean square of the residuals of scenario i, Sim k(i) (kg) and Obs k (kg) are the simulated and observed anthropogenic sediments in scenarios i of the catchment k, respectively, and n is the number of catchments. The reciprocal of the RMS of the residuals was used as the likelihood of this scenario. The derived likelihood of each scenario was then used to quantify the probability distributions of model output at the catchment or global scales using the methodology described by Beven and Binley 6. In order to validate our simulation of the cumulative erosion at the catchment scale, we used a jackknife resampling technology, i.e., we selected 12 catchments and estimated the weights of the parameter sets with the observed cumulative erosion using GLUE, and predicted the cumulative anthropogenic erosion of the remaining one catchment. In all cases an intermediate ALCC scenario, 3

4 combining HYDE and KK10 estimates, better predicted sediment fluxes than either HYDE or KK10, with a relative error of prediction of ca. 25% (Fig. 2). In a final series of simulations, we therefore used all 13 catchments to constrain the ALCC weighting factor (W K ), using the same probalistic approach as described above. The median value of W K we obtained was 0.43 with an interquantile range of 0.30 to The relative error between the simulation and observation is 25% (range 11%-82%) (Fig. S2). This distribution was used in consecutive simulations of sediment and C fluxes at the global scale. 3. Primary emission by ALCC The C emission resulting from ALCC is determined from the ALCC scenarios and the C cycling models that relate land use change with C emission. In our study, we derived a temporal series of C emission by combining the estimations by Kaplan, et al. 3 and Stocker, et al. 7. Kaplan, et al. 3 used HYDE and KK10 land use scenarios and the Lund-Potsdam-Jena Dynamical Global Vegetation Model (LPJ- DGVM) 8. Stocker, et al. 7 used HYDE and H2 land use scenarios and the Bern Carbon Cycle-Climate (BernCC) model 9.The H2 land use scenario is roughly in line with KK10 land use scenario. In total, 4 major C emission series were obtained by combining the two land use scenarios and the two C cycling models in these two studies. For the land use scenarios, we used our constrained weight factors of the two land use scenarios (HYDE and KK10). Given that no assessment on the two C cycling models exists, we used equal weight factors for the two models. Thus, we derived the temporal series of C emission by ALCC as follows:!"=0.5 &!" '()*+ +1!",(-()* &!" / !",( (3) where Ep(t) (kg) is the cumulative primary emission due to ALCC at time t (yr). HYDE, H2 and KK10 represent land use scenarios and DGVM and BernCC represent C cycling models. 4. Soil profiles We used soil profile data from six sources: (i) the Global World Soil Profile database developed by ISRIC 10, (ii) the Africa Soil Profiles Database (AfSP) complied by ISRIC ( (iii) the Brazil soil database compiled by Cooper, et al. 11, (iv) soil profile data from the US provided by the US National Cooperative Soil Survey (NCSS) Soil Characterization Database ( (v) soil profile data from Europe and US compiled by Van Oost, et al. 4, and (vi) soil profile data from the Rhine catchment compiled by Hoffmann, et al. 12 (Fig. S3). From this information, we selected those profiles for which the geomorphic position could be inferred (see below). These soil profiles were categorized into five geomorphic classes and four climate zones. The five geomorphic classes considered were stable, eroding, colluvial and alluvial cropland sites and alluvial non-cropland site. Stable sites refer to locations with negligible erosion or deposition. Eroding sites refer to locations on steep land where erosion occurs. Colluvial sites refer to the footslope or valley bottoms where eroded sediments are deposited. Alluvial sites refer to the floodplain where overbank deposition occurs. Due to the fact that the land use of the floodplain that stores the mobilized soils by agricultural erosion can be either cropland or non-cropland, the alluvial sites were further divided into cropland and non-cropland. 4

5 Climate information was extracted using the geographical coordinate attribute of the soil profile databases. For soil profiles from the databases i-iv, the land use information is either explicitly described in the database or derived from the description of soil layers. Soil profiles which had an Ap layer (i.e. plowed topsoil layer) were considered to be cropland. Alluvial soil profiles were identified by selecting Fluvisols or where the parent material was described as an alluvial deposit. From the remaining soil profiles, profiles located on slope gradients above 10% were regarded as eroding soil profiles. Information on slope gradient was available in databases i, ii and iii, while for the database iv, the slope of the soil profile was derived from high-resolution (10 m) spatial data (Gridded Soil Survey Geographic (gssurgo) Database from United States Department of Agriculture, From the remaining soil profiles, colluvial soil profiles were identified using information on landform and position (depression, low-gradient foot slope or valley floor) or parent material (colluvial deposits). The soil profiles that were not classified using the above criteria were then regarded as soil profiles at stable locations (i.e. profiles with negligible erosion or deposition). Database v only contains stable, eroding and colluvial profiles, and they are classified based on 137 Cs inventories. The amount of 137 Cs from a flat site that has been undisturbed by erosion or deposition was regarded as the local reference 137 Cs inventory. The 137 Cs inventories from other sites were compared with the local reference 137 Cs inventories and, hence, sites of higher inventories were regarded as depositional sites while sites of lower inventories were regarded as eroding sites. In order to remove the influence of extreme values, profiles with SOC contents in the top layer (0-20 cm) within the highest and lowest 5% of the data were excluded from the analysis. The procedure described above resulted in 6580 profiles with SOC observations and provides a globally representative sample of SOC profiles across climatic and geomorphic gradients (Fig. S3). Given that soil texture and depth are important factors controlling SOC content 13-15, the average SOC profiles for each combination of geomorphic position-climate were then estimated using a non-linear regression model: 45= : ; < += (4) where C(z) is the C content (%) at depth z (m), Clay(z) is the clay content (%) at depth z (m), z is soil depth (m), and α, β and = are regression coefficients. The parameter values derived from regression analysis are presented in Table S2. These parameter values were used in the model implementation. In order to increase confidence in the prediction capability of our C profile model, we used only 70% of the observations for calibration while the remaining 30% were used for evaluation. We used a cross-validation technique, where we partitioned the data randomly in 200 different ways, to assess the robustness of our model: this shows that the interquantile ranges for model performance measures (coefficient of determination (R 2 ) and root mean squared deviation (RMSD)) are very small for both calibration (R 2 = 0.27±0.01, RMSE = 0.61±0.01) and validation (R 2 = 0.26±0.01, RMSE = 0.61±0.01). This shows that the values obtained from validation mirror those obtained during calibration, and together with the very narrow interquantile ranges, this suggests that the predictive model performed well and is also robust. In order to ensure a robust estimation, we focus on the representation of the average condition for each climate-geomorphic class (using a limited set of predictors which can be estimated accurately at 5

6 the global scale) rather than predicting the single observations precisely. The coefficients of the nonlinear regression model are significant for all the climate-geomorphic classes. A model-data comparison shows that our simulated SOC profiles agree well with the median SOC profiles of each climate-geomorphic class (Fig. S4, R 2 =0.83). Furthermore, tests (sum of square reduction test, p<0.05) show that the coefficients of the corresponding models are significantly different from those of the stable site within the same climate zone (Fig. 3), which confirms that the classification is valid and that the model can well represent the average conditions of the SOC profiles. We also evaluated whether the moment of land use conversion has an impact on SOC storage. We used the optimal land use scenario derived from erosion simulations (see section 2) to estimate the time at which land use conversion occurred. The average age of the cropland in each grid was calculated based on the temporal series of land use maps for this scenario. Using this map-derived cropland age as a proxy of the age of the SOC profile located in the corresponding grids, we further divided the SOC profiles of each climate-geomorphology group into young and old classes whereby the average cropland age (200 years) was used as the limit between young and old cropland. The difference of the SOC profiles of different classes was tested using the sum of square reduction test (Table S3). This comparison revealed that there was no significant variation of SOC stock over time. 5. Modelling erosion-induced soil-atmosphere exchange Here we describe the approach used to simulate the erosion-induced soil-atmosphere exchange. A detailed description with the corresponding equations can be found in supplementary material S3. The model represents the land surface by a series of virtual catchments: in each catchment the geomorphic cascade (Fig. 1) is simulated, whereby the sediment from eroding areas is either deposited in colluvial/alluvial settings or exported to the aquatic environment. The fraction of each catchment that is occupied by each geomorphic class is allowed to vary between simulations within reasonable bounds (see Eq. 5). The average present-day erosion rate of each climate zone was derived from Van Oost, et al. 4. In the model, agricultural erosion occurs when land is used as cropland, and ceases when the cropland is converted to non-cropland. The model assumes that the erosion rate (per unit area of cropland) is temporarily variable: the steepest, most erodible and hence least favorable soils will only be used as cropland when no other land is available 16. We accounted for this temporal variation of the erosion rate (per unit area of cropland) by linearly linking the erosion rate with the cropland area (see Eq. 8). Erosion rates (per unit area of cropland) in the past are lower than present-day rates when the past cropland area is smaller than the current cropland area. The mobilized sediments are either deposited in colluvial/alluvial settings or transported to the aquatic system. These transfer rates, that also control the amount of deposition in colluvial and alluvial depositional setting, are characterized in the model by sediment delivery ratios of hillslopes and the river system (see Eqs ). Water erosion and depositional processes have been reported to be selective with respect to SOC, resulting in C enrichment or depletion in sediments compared to the source soils 17,18. Thus, the mobilization and redistribution of the associated SOC among different geomorphic units by erosion, deposition and export was obtained by introducing C enrichment ratios for the various sediments (see Eqs , 20-22). 6

7 We used previously published methods to estimate erosion-induced C uptake or release from soils 19,20. In short, changes in SOC stock, relative to a non-eroding cropland profile, reflect the combined effect of lateral C fluxes (i.e. lateral C input or loss) on the one hand, and erosion-induced soil-atmosphere C exchange on the other hand. The erosion-induced soil-atmosphere C exchange could then be inferred from our model simulations because changes in SOC stock were derived from the soil profile database and lateral C fluxes (see Eqs ) were explicitly represented: the erosioninduced soil-c exchanged is therefore equal to the difference between the lateral C flux and the change in SOC storage. This method is a black box approach because it does not explicitly consider the underlying C cycling processes but it does allow for estimating the net erosion-induced soilatmosphere C exchange. 6. Model implementation Evidently, our parameter value estimations for the different model components are uncertain. Therefore, we explored an entire range of possible model parameter sets by modeling agricultural erosion and the resulting C uptake or release as a series of Monte Carlo scenarios. The model represents erosion-induced land-atmosphere C exchanges as a function of 18 model parameters which are described in detail in supplementary materials S3. In each Monte Carlo scenario, the values of the 18 parameters (i.e. C scaler, E scaler1, E scaler2, W K, F 1, F 2, R 1, R 2, CER 1, CER 2, SDR 1, SDR 2,TE, F k, F 3, CBE s, CBE k and CBE o ) were randomly selected assuming a uniform distribution within a realistic range (Table S4). In order to quantify the uncertainties of the model output associated with the input parameters, the Fourier Amplitude Sensitivity Test (FAST) 21,22 was applied using the MATLAB package developed by Cannavó 23. This method is based on ANOVA decomposition, which quantifies the relative contribution of only a given parameter to the total variance of the model output. 7

8 Supplementary material S2: Model evaluation Comparison with earlier estimates of anthropogenic erosion, C mobilization, sediment delivery and erosion-induced C fluxes support our results. Our simulation resulted in a global cumulative agricultural sediment flux of 31000±9000 Pg for the period of agriculture. This is larger, but in the same order of magnitude, than the earlier assessment that humans have displaced approximately Pg of sediments through cropland erosion over the history of civilization 24. Nevertheless, we argue that our approach provides a more robust estimate of cumulative agricultural erosion because our estimates were not simply extrapolated from a single population estimate (as was done in Wilkinson and McElroy 24 ) but were calculated using a spatially explicit approach in which field observations and two contrasting ALCC scenarios were used to constrain and evaluate the model. Our study estimated that present-day erosion on global cropland results in a sediment export of 2.0±0.4 Pg yr -1 to the ocean. This export rate is in line with the estimation that humans have increased global sediment transport by rivers through soil erosion by 2.3±0.6 Pg yr -1, based on a riverby-river analysis 25. Our model simulations predicted that current-day soil erosion on cropland results in a global SOC mobilization of 0.44±0.06 Pg yr -1 (Fig. 4c), which compares well to published estimates of , and Pg yr -1 using spatially explicit approaches where high-resolution patterns of erosion rate and SOC content were considered. Finally, our model estimates that soil erosion results in a net C flux of 0.10±0.024 Pg yr -1 from the atmosphere to the cropland, which agrees well with the estimation of 0.12 (range 0.06 to 0.27) Pg yr -1 from the atmosphere to the soil using 137 Cs and C inventories measurements from a large-scale survey 4. 8

9 Supplementary material S3: detailed model description 1. Representation of the catchment structure The fractional area occupied by each geomorphic class describes the geomorphic structure of a catchment. The fraction of the catchment area that is stable (i.e. non-sloping landforms where no erosion or deposition occurs) is represented by the model parameter F 1. Two other model parameters, R 1 and R 2, represent the ratio of eroding areas, on the one hand, and colluvial and alluvial areas of cropland, on the other hand. The eroding cropland area of a catchment is then given by: 1 = 1 = 1 > A B (5) where A e (m 2 ) is the area of eroding sites of the catchment, A (m 2 ) is the area of the catchment, F 1 is the fraction of stable area in the catchment, R 1 is the ratio of eroding area to colluvial deposition area, and R 2 is the ratio of eroding area to alluvial deposition area. The area of the catchment that is covered by colluvial (A c, m 2 ) and alluvial (A a, m 2 ) soils is then given by A c =A e /R 1 and A a =A e /R 2. Because the land use of the alluvial deposition sites of the catchments can be both cropland and non-cropland, we used the parameter F 2 to represent the fraction of alluvial soils that were used as cropland. Together, these four parameters describe the geomorphic/land use layout of a catchment. 2. Sediment fluxes The present-day average erosion rate was obtained using the soil erosion rate of cropland estimated by Van Oost, et al. 4, who obtained spatially distributed soil erosion rates for cropland at a resolution of 5 arc-minutes based on the key controlling factors (i.e. topography, climate and soils) of soil erosion. In order to account for the uncertainty associated with the estimation of erosion rate, we introduced a scaling factor that varies with Monte Carlo scenarios:! CDE1F =! CDE12! DG12DH1 (6) where E scaled is the scaled erosion rate (m yr -1 ), E scaler1 is the parameter to scale the erosion rate, and E average (m yr -1 ) is the average erosion rate of a given climate zone. Agricultural erosion occurs when land is used as cropland, and ceases when cropland is re-converted to non-cropland (the latter can occur when cropland area decreases over time). Given the fact that flatter areas have larger likelihood to be converted as cropland first, the average slope of the cropland increases with the increasing cropland area 16. The temporal variation of erosion rate (per unit area of cropland) was represented by linking erosion rate to cropland area. We used the present-day erosion rate as a baseline. Hence, we represent the erosion rate (per unit area of cropland) at the start of agriculture as a fraction of the present-day erosion rate (per unit area of cropland):! ' =! CDE12/! (7) 9

10 where E 0 (m yr -1 ) is the soil erosion rate at the beginning of agriculture, E (m yr -1 ) is the present-day erosion rate, and E scaler2 is a factor to scale the erosion rate. Note that the erosion rate here was the average erosion rate of the whole cropland catchment rather than that of the eroding area. As erosion is controlled by climate 4, we used different erosion rates for the four climate zones (see Table S5). The erosion rate (per unit area of cropland) of a given period was then linearly related to the cropland area:!= - I J I (8) where E(t) (m yr -1 ) is the average erosion rate in period t, A 0 (m 2 ) is the cropland area at the beginning stage of agriculture, A(t) (m 2 ) is the cropland area of period t. The effect of cropland area on the temporal variation of erosion rate (per unit area of cropland) was explored within the Monte Carlo scenarios of this study (Fig. S5). It shows that the erosion rate (per unit area of cropland) at the beginning of agriculture can be 40% lower than that of present day. The amount of soil that is cumulatively eroded for a given catchment can then be calculated as follows: 1,L = L! N 1 O (9) where S e,t (kg) is the cumulatively eroded sediments until period t, B e (kg m -3 ) is the bulk density of the eroding area for a given climate zone and T(t) (yr) is the length of period t. We derived the bulk density of each geomorphic-climate group from the compiled soil profile data in this study (Table S6). By introducing two parameters, SDR 1 and SDR 2, that control the delivery of sediments to other geomorphic units, we estimated sediment accumulation in colluvial and alluvial zones. The cumulative amount of sediment deposited in colluvial/alluvial settings for a given catchment was estimated as: C,L = 1,L 1 P (10) D,L = 1,L P 1 P / (11) where S c,t (kg) and S a,t (kg) are the cumulative amount of sediment deposited in colluvial and alluvial settings for a given catchment at time t, respectively. SDR 1 is the ratio of eroded sediments that are yielded to those reaching the river system, and SDR 2 is sediment delivery ratio of sediments entering the river system to those reaching the ocean. Based on a review of sediment delivery ratios derived from case studies (Table S7), the ranges of SDR 1 and SDR 2 in our simulation were set to be The effect of SDR 1 and SDR 2 on the erosion-induced C exchange between the atmosphere and the land-river-ocean system was explored within the Monte Carlo scenarios of this study (Fig. S6). It shows that the uncertainty regarding SDR 1 can cause a variation of ca. 20 Pg C of the C exchange between the atmosphere and the land-river-ocean system, while the C exchange is not significantly sensitive to the variation of SDR 2. The cumulative amount of sediments exported from the catchment equals: 1Q,L = 1,L P P / (12) 10

11 where S ex,t (kg) is the cumulative amount of sediment exported from a given catchment at time t (yr). The sediments trapped in reservoirs for a given catchment can be calculated as:,l = L! N 1 O P P / O! (13) where S s,t (kg) is the cumulative amount of sediment deposited in the reservoirs for a given catchment at time t (yr). TE(t) is the trap efficiency of the reservoirs of period t (yr). The current-day trap efficiency (TE) of the reservoirs of low elevations (<3000m) was estimated to range from The temporal variation of the trap efficiency of reservoirs of each climate zone was derived from the temporal variation of the reservoir capacity 28. The sediments trapped in the lakes for a given catchment were calculated as:,l = 1,L > (14) where S k,t (kg) is cumulative amount of sediments trapped in the lakes at time t (yr). F k is the fraction of mobilized sediments trapped in the lakes. F k is estimated to range between at the global scale 29. The cumulative amount of sediments that reach the ocean (S o,t, kg) can then be calculated as: R,L = 1Q,L,L,L (15) 3. Erosion-induced lateral C fluxes Soil erosion occurs at the surface layer of the soil profile and we used the SOC concentration of the upper 1 cm of the profile, as derived from available soil profile database (see above), to estimate the SOC content of eroded soil. The cumulatively eroded SOC at time t for a given cropland catchment was then obtained using the following equation: 4 1,L = 1,L 4S 1_LRU 4! (16) where C e,t (kg) is the cumulatively eroded C for a given catchment until time t (yr), and CP e_top (%) is the C content of top layer of the profile of the eroding area. CER 1 is the C enrichment ratio of eroded sediments, i.e. the ratio of the C content in the eroded sediment to that of the source soil. The cumulative deposited SOC in the colluvium (C c,t ) and alluvium (C a,t ) for a given catchment at time t (yr) can be calculated using the following equations: 4 C,L = 1,L 4S 1_LRU 4! P 4! / (17) 4 D,L = 1,L 4S 1_LRU P 1 P / 4! / (18) where C c,t (kg) and C a,t (kg) are the cumulative deposited SOC in the colluvium and alluvium for a given catchment at time t (yr), respectively. CER 2 is the C enrichment ratio of the exported sediments to the river, i.e. the C content of the sediments entering the river to that of the source soil. Based on a review of C enrichment ratios in case studies 17,18,30, the ranges of CER 1 and CER 2 were set to and 1-2, respectively. 11

12 In order to account for the uncertainty associated with the SOC profile estimates, we introduced a scaling parameter C scaler that varies between Monte Carlo scenarios: 4 CDE1F 5=4 CDE12 45 (19) where 4 CDE1F 5 (%) is the scaled SOC content at depth z (m),,and C(z) (%) is the C content at depth z (m) for soil profiles from a combination of geomorphic unit and climate zone. C scaler was allowed to vary for various scenarios within the range (Table S4). This range reflects the 95% prediction interval. The resulting range of simulated SOC profiles for various climate-geomorphology groups using this SOC scaling factor is presented in Fig. 3. The cumulative SOC flux after colluvial and alluvial deposition that enters the river system (C ex,t, kg) at time t (yr) can then be calculated as: 4 1Q,L = 1,L 4S 1_LRU P P / 4! / (20) Similarly, the C initially deposited in the reservoirs (C s,t, kg) and lakes (C k,t, kg) can be calculated as: 4,L =,L 4S 1_LRU 4! / (21) 4,L =,L 4S 1_LRU 4! / (22) The cumulative SOC flux after deposition in the reservoirs and lakes in the river system (C r,t, kg) at time t (yr) can then be calculated as: 4 2,L =4 1Q,L 4,L 4,L (23) 4. Estimation of erosion-induced soil-atmosphere C exchange 4.1 Concept The method for the assessment of erosion-induced C exchange (ΔVC) is based on Quine and Van Oost 19 and Van Oost, et al. 20. In this method, the net effect of soil erosion on soil-atmosphere C exchange was derived from a black box model, which inferred erosion-induced C exchange directly through the SOC stock variation and lateral SOC fluxes without considering the underlying C cycling processes explicitly. The net change in C stock (ΔC z0 ) down to a soil profile of z0 m depth undergoing erosion or deposition was described by the following mass-balance (Fig. S7): 4 <' =4 F1U 4 12R +4 W + X4 (24) where C dep (kg) and C ero (kg) are the laterally derived C gains (positive values) or C losses (negative values), as a result of deposition and erosion, respectively; C sub (kg) is the amount of subsoil C from below z0 m depth that is incorporated into (in the case of erosion, positive value), or is exported from (in the case of deposition, negative value) the upper z0 m of the soil profile under consideration. X4 (kg) is then the residual amount of C that is needed to balance the C budget. The residual was then attributed to the difference between C decomposition and sequestration processes induced by erosion/deposition. Therefore, the erosion-induced C exchange at time t (yr) was estimated as: 12

13 X4 L = 4 <' 4 W,L 4 EDL,L (25) where C lat,t (kg) is the net cumulative lateral SOC fluxes at time t (yr), which equals C e,t (kg) in the case of erosion, and C c,t (kg) or C a,t (kg) in the case of colluvial and alluvial deposition, respectively. ΔC z0 (kg) was derived from the difference between a stable C profile and an erosion/depositional profile (both were derived from our C depth model). 4.2 Estimation of ΔC z0 C sub The C stock changes (i.e. ΔC z0 C sub ) were estimated separately for eroding (ΔC e,t ), colluvial (ΔC c,t ) and alluvial (ΔC a,t ) profiles. ΔC e,t was then calculated as: ZI[\ ],^ _] <' 4 1,L =Y 4S 1 5 N 1 1 Y _` 4S 5 N 1 (26) <' where 4 1,L (kg) is the cumulative C stock change of the eroding area at time t (yr), CP s (z) (%) and CP e (z) (%) are the value of C content at the SOC profile of stable and eroding sites at depth z (m) respectively, D e,t (m) is the cumulative erosion depth at time t (yr), and B s (kg m -3 ) is the soil bulk density of the stable area of a given climate zone. <' A similar approach was used to estimate 4 C,L and 4 D,L : <'?( a,^ <' ZI _a _` 4 C,L =Y 4S C 5 N C C Y 4S 5 N C (27) <'?( b,^ <' <' ZI _b _` 4 D,L =Y 4S D 5 N D D Y 4S 5 N D (28) where 4 C,L (kg) and 4 D,L (kg) are the cumulative C stock variation of the colluvial and alluvial deposition area at time t (yr), respectively, CP c (z) (%) and CP a (z) (%) are the value of C content at the SOC profile of colluvial and alluvial deposition sites at depth z (m) respectively, D c,t (m) and D a,t (m) are the depth of colluvial and alluvial deposits at time t (yr), respectively, and B c (kg m -3 ) and B a (kg m - 3 ) are the soil bulk density of colluvial and alluvial deposition area of a given climate zone, respectively. The soil profile model was discretized with an increment of 1 cm in the model. The reference depth z0 was set to be 1 m as most differences between SOC profiles are observed within the first upper meter of the soil profile. The sum of the cumulative C stock variation of eroding, colluvial and alluvial sites at time t (yr) results in the net C stock variation in the catchment at time t (yr) in response to soil erosion and deposition, i.e. <' 4 E,L = 4 1,L + 4 C,L + 4 D,L (29) where 4 E, (kg) is the cumulative C stock variation of the whole catchment at time t (yr). 4.3 Estimation of C exchange For a given geomorphic unit, the net SOC stock variation is the outcome of the erosion-induced vertical C fluxes between the land and the atmosphere and the net lateral fluxes through this geomorphic unit. Therefore, the erosion-induced vertical C fluxes were estimated using the following equations: 13

14 X4 1,L = 4 1,L +4 1,L (30) X4 C,L = 4 C,L 4 C,L (31) X4 D,L = 4 D,L 4 D,L (32) where X4 1,L (kg), X4 C,L (kg), X4 D,L (kg) are the cumulative erosion-induced vertical C flux from the atmosphere to the land at the eroding, colluvial deposition and alluvial deposition areas at time t (yr), respectively. The total erosion-induced vertical flux of the whole catchment was summed up: X4 E,L = X4 1,L + X4 C,L + X4 D,L = 4 E,L +4 1Q,L (33) where X4 E,L (kg) is the cumulative erosion-induced vertical C flux of the whole catchment from the atmosphere to the land at time t (yr). In order to present the C budget for the coupled land-river-ocean system, we also included a net loss term in the aquatic system before the sediment and C reach the global ocean. The SOC buried in the reservoirs is not totally preserved but partly mineralized. The SOC preserved in the reservoirs can be calculated as: 4,L =4,L 4N! (34) where 4,L (kg) is the cumulative preserved SOC in the reservoirs at time t (yr). CBE s is the C burial efficiency in the reservoirs. CBE s is set to be The erosion-induced reservoir-atmosphere C exchange was calculated as: X4,L =4,L 1 4N! (35) where X4,L (kg) is the erosion-induced cumulative reservoir-atmosphere C exchange at time t (yr). The SOC buried in the lakes is not totally preserved but partly mineralized. The SOC preserved in the lake can be calculated as: 4,L =4,L 4N! (36) where 4,L (kg) is the cumulative preserved SOC in the lakes at time t (yr). CBE k is the C burial efficiency in the lakes. CBE k is set to be The erosion-induced lake-atmosphere C exchange was calculated as: X4,L =4,L 1 4N! (37) where X4,L (kg) is the erosion-induced cumulative lake-atmosphere C exchange at time t (yr). Particulate organic carbon (POC) in the river is also partly mineralized in the fluvial system during its transport to the ocean 33,34. We used a simple loss term to represent this process using the following equation: 14

15 4 R,L =4 2,L 1 > c (38) where C o,t (kg) is the cumulatively exported SOC to the ocean at time t (yr) and F 3 is the fraction of SOC that is mineralized during transport in the river system. It was found that CO 2 produced by aquatic metabolism contributes ca. 28% of CO 2 evasion from streams and rivers 35. Global CO 2 evasion from streams and rivers are estimated to range from 0.65 to 1.8 Pg C per year 34,36. This means that Pg C yr -1 was mineralized in the global streams and rivers. Given that the total lateral input of non-recalcitrant C into inland water was estimated at 2.5 Pg C yr -1, we constrain F 3 to range between 0.07 and 0.2. The erosion-induced river-atmosphere C exchange was calculated as: X4 2,L =4 2,L > c (39) where X4 2,L (kg) is the erosion-induced cumulative river-atmosphere C exchange at time t (yr). The SOC exported to the ocean is not totally preserved but partly mineralized. The terrestrial POC preserved in the ocean can be calculated as: 4 R,L =4 R,L 4N! R (40) where 4 R,L (kg) is the cumulative preserved SOC in the ocean at time t (yr). CBE o is the C burial efficiency in the ocean. The range of CBE o was set to be The erosion-induced ocean-atmosphere C exchange was calculated as: X4 R,L =4 R,L 1 4N! R (41) where X4 R,L (kg) is the erosion-induced cumulative ocean-atmosphere C exchange at time t (yr). The integrated effect of erosion on the land-river-ocean system can then be quantified as: X4 E2R,L = X4 E,L + X4,L + X4 2,L + X4 R,L (42) where X4 E2R,L (kg) is the cumulative erosion-induced C exchange between the atmosphere and the land-river ocean system at time t (yr). The mineralized POC in the aquatic systems can also be released to the atmosphere in the form of CH 4. The greenhouse efficiency was reported to be 3.67 and 24 for CO 2 and CH 4, respectively. Therefore, we denoted the whole greenhouse gas effect of the aquatic POC mineralization with CO 2 equivalents: X4:d De,L =& X4 2,L + X4,L + X4,L + X4 R,L. g1 > 3h + /h c.ij > 3hk (43) Where X4:d De,L (kg) is the GHG effect of aquatic POC mineralization in terms of CO 2 -C, and F CH4 is the fraction of C that is released in the form of CH 4 in the total mineralized POC. F CH4 was estimated to be ca. 1% from case studies from various environments

16 Supplementary material S4: supplementary discussion 1. C turnover at eroding sites It has been suggested that eroding landscapes can be either C sinks or sources, but it has proven difficult to identify precisely the underlying mechanisms. Two competing processes, the decomposition of old soil C and the sequestration and stabilization of fresh C inputs 43, take place simultaneously. Generally, the turnover rate of deep SOC is slower than that of comparable topsoil SOC sources Exposure of deep SOC by erosion of surface soil and associated changes in microclimatic conditions are likely to increase the rate of deep SOC decomposition. For example, when erosion exposes subsoil layers they come into contact with fresh labile C sources from plant growth on the eroding hillslope. Addition of 'labile' C to a soil C pool can stimulate the decomposition of soil C that was previously decomposing more slowly 48. This addition may occur when fresh SOC from topsoil horizons is mixed with formerly deep SOC, providing readily available energy sources for decomposers, which speeds up the decomposition rate of older, previously stable C. New soil organic matter formation from vegetation inputs may replace some or all of the eroded SOC 49. Observations covering a broad range of environmental conditions have shown that a substantial part of the eroded SOC in agricultural soils can be replaced by new photosynthates It has been suggested that only partialreplacement of eroded SOC occurs during several decades that follow an erosion-induced perturbation (e.g. conversion from grassland to cropland) while sustained erosional forcing permits the establishment of a new equilibrium in which full replacement of eroded SOC occurs 53. If the eroded SOC is replaced, even when only partial, a net sink for atmospheric CO 2 is created at the scale of the eroding hillslopes. Finally, continued erosion may drive the deterioration in soil quality and overall ecosystem health and this may then prevent the replacement of the eroded SOC and may turn the eroding hillslopes into a net source rather than a sink. Although we estimated a cumulative SOC mobilization of 783±243 Pg from the eroding area for the considered agricultural period, a comparison of SOC profiles between stable and eroding areas indicates that SOC stocks in the eroding upland only decreased by 59±19 Pg. We interpret this as the replacement of eroded SOC by atmospheric photosyntates 49, which dominate potential increases in C turnover through priming. Although our data contains cases where erosion-induced ecosystem degradation resulted in substantial SOC stock decline, at the global scale, in most cases the erosional SOC loss can be compensated over long timescales. This is consistent with both empirical and model-based observations and is likely related to the fact that only a small fraction of NPP, typically less than 10%, is removed by erosion, even at higher erosion rates 53, C turnover during transport A large part of the controversy on the role of soil erosion in the C cycle relates to what happens during transport of eroded SOC and after deposition. Studies to date have highlighted two main processes taking place during transport: (i) increased mineralization of C due to the breakdown of aggregates, and (ii) C enrichment in sediments relative to source soils due to selective transport and deposition of C. Easily mineralizable C encapsulated within aggregates represents a large proportion of deposited Ci.e. 55 and can easily be released to the atmosphere upon breakdown of the aggregates However, results on increased mineralization after breakdown of aggregates differ 16

17 greatly, with between 0% and 100% increases relative to C fluxes at the reference source soil. In addition, the increase in CO 2 flux appears to be short-lived and limited to the days following the rainfall events 59,60. When observed over longer periods, CO 2 release from eroded soil eventually reaches a point where there is no observed difference compared to non-eroded controls 61,62. Our profile data does not allow us to identify these mechanisms during transport. However, given the observation that recently deposited SOC, i.e. the SOC that is found in the upper layers of the depositional profiles (Fig. 3), is not strongly depleted in SOC, we conclude that increased mineralization during and after transport is not the main pathway of eroded SOC. 3. Turnover and preservation of C at depositional sites On average, only 10-30% of the eroded topsoil material is subsequently transported into lakes and oceans via major river systems 63,64. This implies that most sediment is deposited at footslopes, as well as in colluvial valley bottoms and alluvial floodplains 29. In depositional areas, SOC undergoes a fundamentally different dynamic than it was subjected to at its source. In eroding/depositional landscapes, several studies have shown that, when C burial takes place, SOC stocks below 30 cm (i.e. below plow layers and the zone of intense mixing by mammals) can account for more than 80% of a soil profile s total SOC stock in the upper 2 m of soil 55, Transported and deposited SOC can be protected from decomposition if efficiently buried in slow turn-over environments, leading to large C sinks in colluvial and alluvial sediments Over timescales of decades to centuries, erosion and subsequent deposition can then result in large deposits of C rich soil material of varying quality. However, the amount of C buried over time will depend largely on the rate of burial, the time since burial, the nature and amount of mobilized C, and the environmental conditions that the buried C is exposed to after deposition. The capacity of this process to constrain SOC mineralization may be reduced over time and as a function of environmental factors and sedimentation rates 20,67. For example, the protection of C within aggregates or by organo-mineral association might be weakened if aggregates lose stability and mineral weathering alters the chemical reactivity of minerals to C. Hence, changes in C stocks with depth at depositional sites can shed light on the underlying mechanisms for the persistence and turnover rates of buried C 72,73. Deeper soil layers have generally lower C concentrations and more stable SOC pools than comparable topsoils 46,74. While well aerated colluvial and alluvial soils often show strong depth gradients of C concentrations, with lower C concentrations in the deepest, hence oldest, layers, water-saturated, and hence oxygen limited, alluvial soils can store C for centuries with no measurable changes 12,20. Therefore, if burial is fast and conditions at depositional sites are favorable for C conservation, sediment deposition at foothills, valleys and floodplains can result in the burial of C enriched in labile compounds 75. If decomposition during sediment transport, deposition and burial has led to significant degradation of more easily decomposable C fractions, depositional sites can accumulate smaller but highly stable C stocks with long residence times 67,70,76. In our study we calculated that 357±136 Pg and 243±84 Pg of mobilized SOC were deposited in colluvial and alluvial soils, respectively. However, the SOC stock in colluvial and alluvial soils only increased ca. 58±17 and 30±10 Pg, respectively, relative to areas not affected by soil erosion or deposition. This results in C burial efficiencies of 15% to 19% for the colluvial and alluvial stocks These global estimates are on the same order of magnitude, but lower than previously reported 17

18 burial efficiencies for colluvial and alluvial stores, which range between 20-30% 12,20,70 and % 12,20,76, respectively. Finally, C cycling on agricultural land is not only affected by physical soil redistribution. Soil redistribution results in spatial variability of soil properties such as soil mineral composition and aggregation, which further affects C cycling 55,73. Furthermore, studies have shown that patterns of crop yield show a close similarity to soil redistribution patterns 77,78 and higher C input from plant can be expected in sites of soil deposition. Moisture and temperature regimes may vary between eroding and depositional sites 60,79, thereby affecting SOC dynamics in the soil. SOC content was found to be positively correlated with precipitation and negatively correlated with temperature 15, which is consistent with our observation that the SOC stocks in tropical, temperate and continental soils are significantly higher than that of the dry climate zone (sum of square reduction test, p<0.05, Fig. 3). Environmental conditions such as high temperature and moisture in the tropical climate zones favor the mineralization of buried SOC in the colluvial and alluvial stores, and thus C burial efficiency in the tropical climate zone is low in contrast to temperate and continental climate zones with moderate burial efficiency and the dry climate zone with high burial efficiency (Table S8). 18

19 Table S1. Observed and simulated cumulative catchment-scale anthropogenic sediment flux. No. Reference Catchment Region Koppen climate zone 1 Enters, et al Dearing, et al. 81 Frickenhauser See Lake catchment Havgardssjon Lake catchment 3 Beach 82 Indian Creek catchment 4 Anselmetti, Salpeten Lake et al. 83 catchment 5 Houben 84 Rockenberg catchment 6 Beach 82 Hay Creek catchment 7 Beach 82 Beaver Creek catchment 8 van Hooff Gultland and catchment Jungerius 85 9 Trimble 86 Coon Creek catchment 10 O'Hara, et Patzcuaro Lake al. 87 catchment 11 Van Oost, et Dijle al. 20 catchment 12 Hoffmann, Rhine River et al. 12 catchment 13 Saito, et al. Yellow River 88 ; Shi, et al. catchment 89 Area (km 2 ) Period Germany Temperate AD 600- AD 2000 Sweden Temperate BC- AD2000 USA Continental 17 AD1851- AD1988 Guatemala Tropical BC- AD2000 Germany Temperate BC- AD2000 USA Continental 125 AD1851- AD1988 USA Continental 144 AD1851- AD1988 Luxembourg Temperate BC- AD1984 USA Continental 360 AD1853- AD1975 Mexico Temperate BC- AD2000 Belgium Temperate BC- AD2000 Central Temperate BC- Europe AD2000 China Temperate, AD1- Continental AD2000 Observed sediments (g) a Simulated sediments (g) HYDE KK10 This study (7.89±1.56) 10 9 (3.77±1.12) (1.06±0.51) (1.49±0.27) (2.99±1.14) (2.27±0.60) (1.07±0.11) (4.33±0.44) (7.13±1.33) (2.29±0.23) (1.06±0.20) (4.14±1.86) (1.70±0.41) (2.52±0.25) (1.05±0.40) (3.33±0.33) (2.40±0.24) (2.89±0.70) (7.89±0.79) (6.21±0.63) (7.04±0.75) (1.12±0.11) (6.43±1.49) (2.64±0.72) (1.08±0.11) (5.79±0.58) (8.21±1.21) (4.11±0.96) (4.58±0.86) (2.25±0.78) (3.87±0.53) (2.48±0.43) (7.78±3.70) (3.03±0.51) (3.61±0.45) (1.42±0.53) (8.94±1.95) (5.29±0.53) (2.57±0.76)

20 a Data for the Yellow River catchment and the Rhine catchment are derived from the total amount of sediments deposited in colluvial and alluvial settings. Data for the remaining sites are derived from estimates of total soil loss by agricultural erosion. 20

21 Table S2. Parameters for the SOC profile model (Eq. 4) as a function of the geomorphic position and climate. The parameters were derived from an analysis of a global soil profile database. The clay content reflects the average value per climate zone. Clay (%) Tropical Dry Tempera 29.4 te 9 Contine 27.0 ntal 0 Global cropland non-cropland stable Eroding colluvial alluvial alluvial α β = α β = α β = α β = α β =

22 Table S3. Comparison between young and old SOC profiles of various climate-geomorphology group of cropland. The comparison was performed using the sum of square reduction test (p<0.05). Stable Eroding Colluvial Alluvial Tropical < > Dry - - < Temperate - - Continental > Global < < indicates that the SOC profiles of old fields are significantly lower than that of the young fields. > indicates that the SOC profiles of old fields are significantly higher than that of the young fields. indicates that the SOC profiles of the old and young fields are not significantly different. indicates that the split of the SOC profiles results in the fact that one class does not have enough profiles for the test. 22

23 Table S4. Ranges of model parameters used in the simulations. Parameter range C scaler E scaler1 E scaler2 W K F 1 R 1 R 2 F 2 CER 1 CER 2 SDR 1 SDR 2 TE F k F 3 CBE s CBE k CBE o [0.8, [0.8, [0.1, [0, [0.2, [5, [20, [0.1, [1, [1,2] [0.3, [0.3, [0.12, [0.03, [0.07, [0.5, [0.4, [0.22, 1.2] 1.2] 0.9] 1] 0.4] 10] 40] 0.9] 1.5] 0.5] 0.5] 0.2] 0.05] 0.2] 0.65] 0.6] 0.3] 23

24 Table S5. Average present-day cropland erosion rates for the four climate zones 4. E (Mg ha -1 yr -1 ) Tropical Dry Temperate Continental

25 Table S6. Bulk density (kg m -3 ) of soils of various geomorphic-climate groups. These results were derived from the database i, ii and iii (see supplementary material S1 section 4), where the bulk density data are available. n indicates the number of soil samples. Cropland Non-cropland Stable Eroding Colluvial Alluvial Alluvial Tropical 1378±233 (n=513) 1399±287 (n=76) 1490±221 (n=271) 1546±274 (n=438) 1387±261 (n=193) Dry 1621±243 (n=169) 1708±320 (n=29) 1576±159 (n=139) 1651±192 (n=232) 1534±242 (n=201) Temperate 1409±277 (n=507) 1428±208 (n=50) 1579±217 (n=118) 1509±220 (n=256) 1475±359 (n=131) Continental 1178±447 (n=16) 1624±275 (n=13) 1455±64 (n=6) 1411±237 (n=53) 1393±262 (n=33) 25

26 Table S7. Overview of sediment delivery ratios derived from case studies 90. Source Catchment Catchment Region Period (yr) SDR 1 (%) 1 SDR 2 (%) 2 SDR 1 SDR 2 (%) 3 area (km 2 ) Notebaert, et al. 91 Dijle 758 Belgium Trimble 92 Coon Creek 360 USA Verstraeten and Prosser 93 Murrumbidgee Australia Rommens, et al. 94 Nethen 52 Belgium Rommens, et al. 95 Nodebais 1.03 Belgium Lewis and Lepele 96 Nebraska 0.92 USA Millennia 47 van Hooff and Jungerius 85 Tonnbaach 1.5 Luxembourg van Hooff and Jungerius 85 Reckenerbaach 2.1 Luxembourg van Hooff and Jungerius 85 Schrondweilerbaach 2.3 Luxembourg van Hooff and Jungerius 85 Wellerbaach 2.5 Luxembourg van Hooff and Jungerius 85 Deifebaach 2.8 Luxembourg van Hooff and Jungerius 85 Keiwelsb./Mosergr. 3.4 Luxembourg van Hooff and Jungerius 85 Kieselbaach 3.4 Luxembourg van Hooff and Jungerius 85 Metschbaach 3.8 Luxembourg van Hooff and Jungerius 85 Buttebaach 4.6 Luxembourg van Hooff and Jungerius 85 Laangbach 5.1 Luxembourg van Hooff and Jungerius 85 Giel-Schlecken 6.9 Luxembourg Wolf and Faust 97 Delle 2 (Schwochau) 0.2 Germany Wolf and Faust 97 Delle 1 (Zehren) 0.3 Germany Wolf and Faust 97 Delle 3 (S-basin) 0.3 Germany Wolf and Faust 97 Delle 3 (Löbschütz) 1.5 Germany Fuchs, et al. 98 Aufsess 95.5 Germany Houben 84 Rockenberg 10.2 Germany Beach 82 Indian Creek 17 USA Beach 82 Hay Creek 125 USA Beach 82 Beaver Creek 144 USA Phillips 99 Tar 1119 USA Phillips 99 Neuse 1997 USA Phillips 99 Deep 3748 USA

27 Phillips 99 Haw 4217 USA Wasson, et al. 100 Jerrabomberra Creek 136 Australia SDR 1 indicates sediment delivery ratios on the hillslope. 2 SDR 2 indicates sediment delivery ratios in the channel. 3 SDR 1 SDR 2 indicates the ratio of yielded sediments to mobilized sediments. 27

28 Table S8. C burial efficiency of buried SOC in the colluvial and alluvial stores in various climate zones. Tropical Dry Temperate Continental Colluvium 0.12± ± ± ±0.07 Alluvium 0.13± ± ± ±

29 Figures Fig. S1. Schematic representation of the model framework. a, b, c and d indicate the tropical, dry, temperate and continental climate zones, respectively. 29

30 Fig. S2. Simulated anthropogenic sediment flux using the parameters constrained with the observed data of all 13 catchments. The error bars show the interquartile range (25% to 75%) of the distribution (obtained from Monte Carlo scenarios) associated with each simulation. The numbers in circles denote the identification of the catchment, which is shown in Table S1. 30

31 Fig. S3. Locations of soil profiles used in this study. 31

32 Fig. S4. Observed versus predicted C concentration. The observed values indicate the median value of the C contents in the corresponding depth layers (0-20 cm, cm, cm, cm and cm), while the errors indicate the range of the percentiles from 47.5% to 52.5%. The simulated values indicate the predicted C contents at the depths of 10 cm, 30 cm, 50 cm, 70 cm and 90 cm, while the errors indicate the ranges of the 95% confidence interval of the prediction at the corresponding depths. 32

33 Fig. S5. The effect of cropland area on the erosion rate (per unit area of cropland). Erosion rate ratio denotes the ratio of erosion rate at a given time to the current-day erosion rate and is calculated using Eq. 8. Cropland ratio denotes the ratio of cropland area at a given time to the cropland area of current day. The error bars show the interquartile range (25% to 75%) of the distribution (obtained from Monte Carlo scenarios) associated with each simulation. 33

34 Fig. S6. The effect of sediment delivery ratios on the erosion-induced C uptake. (a) SDR 1 is the ratio of eroded sediments that are yielded to the river system, and (b) SDR 2 is the ratio of sediments delivered to the ocean with respect to those entering the river system. The error bars show the interquartile range (25% to 75%) of the distribution (obtained from Monte Carlo scenarios) associated with each simulation. 34

35 Fig. S7. Schematic representation of various C fluxes that change the C stock of a soil profile of z0 m depth. ΔC z0 indicates the net change in C stock down to a soil profile of z0 m depth; C dep and C ero are the laterally derived C gains (positive values) or C losses (negative values), as a result of deposition and erosion, respectively; C sub is the amount of subsoil C from below z0 m depth that is incorporated into (in the case of erosion, positive value), or is exported from (in the case of deposition, negative value) the upper z0 m of the soil profile under consideration. X4 is then the residual amount of C that is needed to balance the C budget. 35

36 Fig. S8. The matrix of relative variance of model outputs caused by model parameters, as indicated by the FAST (Fourier Amplitude Sensitivity Test) coefficients for two different periods: (a) pre-industrial (6000BC-1850AD), and (b), industrial ( AD). The model parameters are described in detail in the supplementary material S3. For visualization purposes we aggregated model parameters into groups representing mobilization of SOC (M), land use scenarios (L), geomorphic structure of the catchment (S), connectivity of the catchment (C) and the fate of the C exported to aquatic systems (A). For the model responses, C denotes the lateral C fluxes, C C stock variation and VC the net landatmosphere exchange. Subscripts reflect the geomorphic positions (e: eroding uplands; c: colluvium; a: alluvium; s: reservoir, k: lake, r: river; l: land; l-r: land+river; l-r-o: land+river+ocean). 36