The CENTURY model was parameterized to simulate the soil C and N turnover in a fixed profile of 0 to 30 cm. When the model incorporates soil erosion (22), an upward C flux from a subsoil pool follows the erosion event (as described in point 3 of the “Model framework and configuration” section). Moreover, the C balance accounts for C displacement components, some of them representing C moving outside the land domain (such as C to rivers, lakes, and ocean). For the purpose of the study, we set our boundary conditions to the land and, despite estimating a lump term accounting for C delivered to the riverine system, we did not calculate its decomposition (to CO2) related to the turnover outside the land.

For the eroding area, the C balance isEmbedded Image(3)where ΔSOC is the SOC stock change in the fixed profile, CI is the C input through the remaining net primary productivity (NPP; after C exportation by harvest but including roots and manure), CH is the heterotrophic respiration, CS is the incoming SOC from a deeper layer, CE is the lateral C flux by sediment transport, and DOC is the C exported as dissolved organic C.

For the depositional area, the balance isEmbedded Image(4)where CD is the C deposited coming from eroding areas and CB is the C that is moved out (that is, buried) of the simulated profile as a consequence of soil deposition.

However, the net changes in SOC storage do not directly equate to the net CO2 exchange from soil to the atmosphere due to the combination of vertical C fluxes (CI − CH) of eroding and depositional areas and the mineralized fraction of SOC upon displacement. Therefore, the net soil C flux (as CO2) in the grid cell is given byEmbedded Image(5)where [CI − CH] is the net vertical C flux, CTm represents the fraction of eroded SOC mineralized during the transport, and CBm is the fraction of buried C that is mineralized in depositional area. Because the uncertainty in simulating C turnover in deeper layers increases with depth (due to cumulative sediment deposition), the cumulative CB fluxes, over the period 2016–2100, were assumed to be preserved from decomposition with two contrasting burial efficiency rates over a 100-year horizon (0.95 and 0.2). The corresponding CO2 flux to the atmosphere was then calculated as CB × (1 − burial efficiency).

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