Table 4.

LOSS driver and its representation in (data = GPASOIL-v0) and (data = GPASOIL-v1).

Driver name	LOSS (P losses through soil erosion)
Description of its effect on the soil P	Losses of P due to water erosion and runoff processes
Corresponding variables in our approach	Losses of P for each soil P pool ($f{P}_{loss}^{m\to out}$ with m in {i-lab, o-lab, o-sta, i-prim, i-sec, x-occ}).
Dataset ref used in (data = GPASOIL-v0)	Losses were computed using the soil P content simulated in GPASOIL-v0, the sediment gross fluxes resulting from erosion provided by van Oost et al.74 and the weight of top 0–0.3 m soil computed from bulk density of the same horizon provided by Soilgrids database (ISRIC – World Soil Information, 2016)
Issues related to the use of this dataset in GPASOIL-v0	We did not consider temporal change in the sediment gross fluxes resulting from erosion (but we considered historical changes in agricultural land area, see LUCC)). Also, gross (and not net) erosion rates were considered. Finally, we considered that the erosion rates concerns exclusively the top soil layer (top 0–0.3 m).
Representation in (data = GPASOIL-v1)	The same approach as used in (data = GPASOIL-v0) was used. Sediment gross fluxes resulting from erosion with a cropland/grassland distinction were computed following the approach described in Borrelli et al.54 Losses through erosion of P in soil solution (Pi-solu) was set to 0. We made the same assumptions as done in GPASOIL-v0: no temporal change in the gross rate of erosion, focus on gross (instead of net) erosion rate, effect of erosion exclusively on the top layer considered in our study. See Eqs. 57, 58.
Characteristics of the spatially explicit dataset used in (data = GPASOIL-v1)	Dataset were provided by Pasquale Borrelli, pers.comm, (2020) and corresponded to the use of the approach described in Borrelli et al.54 here applied to the land-use dataset described in LUCC for year 2000 to simulate the gross soil losses (in (kg of soil) yr−1 ha−1) through erosion with a cropland/grassland distinction at 250mx250m resolution. Bulk density and volumetric fraction of coarse fragment were provided by Soilgrids 2.021 at half-degree resolution.