The model framework was based on coupling the process-based biogeochemistry model CENTURY to the RUSLE2015 erosion model. This model integration has been presented in previous studies, and a summary flowchart is given as fig. S1. We summarized the model setup and main assumptions as follows.

1) The CENTURY model was ran at a resolution of 1 km2 for the agricultural soil of the EU, using the soil erosion from RUSLE2015 model as input for CENTURY. Starting from 1900, the erosion process was implemented, keeping the climate, soil, and topographic factors (R, K, and LS, respectively) constant. While we considered K and LS factors quite invariable on a centennial scale, the C factor associated with the crop type was dynamically varied with crop rotations and land use changes. The simulated land use was based on the CORINE Land Cover 1990, 2000, and 2006, supplemented with Eurostat (Statistical Office of the European Communities)/FAO (Food and Agriculture Organization of the United Nations) statistics to build up crop rotations and implement consistent agronomic inputs (fertilization, irrigation, etc.). Before 1990, we assumed the same land use but with different agricultural techniques characterized by lower productivity crops, lower rates of mineral N, and different rotation schemes.

2) Originally, we assumed that each 1-km2 grid cell is composed of an eroding area and a depositional area, the latter retaining a proportion of eroded C. The partition was based on the study of Van Oost et al. (11), who found that 53 to 95% of eroded SOC were retained in the catchment and redeposited in a limited area (14 to 35%) within the same catchment. Taking the central values, we assumed that 25% of our grid cells were depositional areas, which received 70% of eroded soil. The remaining 30% was accounted for as leaving the grid cell as potential sediments and C discharged to riverine systems. These assumptions on sediment distributions, necessary to work at continental scale, were further tested using a delivery/sedimentary model in regional simulations, as detailed in section S3. After the intercomparison between the original and the sedimentary model–driven configuration, we set a new sediment delivery ratio of 0.11, as most of the sediments were predicted to be retained in land under the delivery/sedimentary model runs.

3) The replacement of eroded soil in the fixed profile comes by “recruitment” from the subsoil layers (SSLs), characterized by a SOC composition defined quantitatively and qualitatively as a partition among the three CENTURY SOC pools (active, slow, and passive). These pools are functionally defined on the basis of mean residence time, as opposed to measured fractions, and thus cannot be constrained by measurements applicable at the EU scale. The most rational approach was to adopt the calibration of Harden et al. (7), which implicitly related the subsoil composition to the topsoil composition; accordingly, the subsoil SOC pools at time t = 0 (that is, 1900) were assumed to be composed as a fraction of the top soil pools, as followsEmbedded Image

The lower horizon pools were decremented at each time step using the following relationships for each of the three SOC pools (i)Embedded Imagewhere t is the time and FLOST is the fraction of topsoil lost to erosion [for the sake of clarity, SSLi(t − 1) × FLOST(t) is the C moving up from subsoil annually].

Although CENTURY does not explicitly simulate depositional processes, they can be mimicked while ensuring conservation of mass (soil and C) within the system boundaries. First, we calculated the amount of soil transported from the eroding to the depositional fraction of each grid cell. Second, we simulated the burial effect of the deposition event as a “negative” erosion event, which moves a SOC fraction below the fixed soil profile (C burial flux), proportional to the amount of soil deposited on the surface. Last, the associated amount of deposited C was controlled by setting the incoming SOC pool in the model. This procedure required an iterative process, running the model year by year, first in the eroding area and then in the depositional area of each pixel. A check of the C balance closure was done at the end of simulations.

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