The model was run with the current climate up to 2015 and with the same HadGEM2-ES_rcp45 scenario for the 2016–2100 time frame for consistency. Monthly precipitation and maximum and minimum air temperature were downloaded from the World Climate Research Programme–Coordinated Regional Downscaling Experiment (WCR-CORDEX) portal (https://esgf-node.ipsl.upmc.fr/search/cordex-ipsl/). The present land use and agricultural management remained the same to isolate the climate effect on both productivity/turnover and erosion C feedbacks.

In the accelerated erosion (AE) scenario, we linearly interpolated the soil erosion rates since 2016, considering the two soil erosion projections at 2050 and 2070. The name “accelerated erosion” refers to the average effect of rainfall erosivity change on increasing soil erosion. Higher and lower rainfall erosivity patterns are present at the EU level, as depicted in fig. S8. In the current erosion (CE) scenario, we kept the actual soil erosion rates.

Given the fact that there is limited consensus on C preservation/decomposition upon its displacement, we ran the model with two configurations, enhancing (e model setup) and minimizing (r model setup) the erosion as an induced C sink (or source). In particular, in the e configuration, the enrichment factor (that is, the C concentration in eroded sediments with respect to the bulk soils) was set to 2, the C mineralization during sediment transport to 2% yearly, and the burial efficiency (that is, the amount of C preserved when moved downward into the soil profile) to 95%. In the r configuration, the three parameters were set to 1, 10, and 20%, respectively.

According to previous sensitivity analyses, a higher enrichment factor promotes a higher dynamic replacement of C (inducing a C sink in eroding position), while lower mineralization and higher burial efficiency preserve the displaced C. Considering the ranges of parameters from different studies, our configuration should reflect the outer boundary of the erosion effect in inducing a sink/source of C.

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