Table 7.

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

Driver name	SPRO (soil properties)
Description of its effect on the soil P	Soil properties involved in the computation of the soil P dynamics
Corresponding variables in our approach	Variables considered within the SPRO drivers vary between GPASOIL-v0 and GPASOIL-v1: - in (model = GPASOIL-v0), SPRO encompasses parameters involved in the Langmuir equation used to describe the equilibrium between Pi-lab and Pi-sec (so-called KS and Smax parameters) - in (model = GPASOIL-v1), SPRO encompasses soil properties involved in parameterizations for soil P dynamics: soil texture (sand, clay, silt percentages: ss, sc, si respectively, in %), soil water pH (pH, no unit), C is soil carbon concentration (in gC.(kg of soil)−1)
Dataset ref used in (data = GPASOIL-v0)	A coupled of values for (KS, Smax) was used for each soil order. These values were provided by Wang et al.15. The global distribution of soil orders was similar to the one used in Yang et al.4.
Issues related to the use of this dataset in GPASOIL-v0	Soil orders are likely a poor predictor of soil P buffering capacity in (model = GPASOIL-v0). Other properties (texture, pH, carbon) were not used in (data = GPASOIL-v0).
Representation in (data = GPASOIL-v1)	KS, Smax are not used any more in (model = GPASOIL-v1). Soil texture, soil water pH, and soil carbon concentration for top 0.3 m were get from Soilgrids 2.021. We assumed that that soil properties at half-degree resolution could be applied to the cropland/grassland (soils) fraction. Soil properties were involved in equations described in Table 10.
Characteristics of the spatially explicit dataset used in (data = GPASOIL-v1)	Soil texture, soil water pH, and soil carbon concentration for top 0.3 m were computed by averaging values for 0–0.05, 0.05–0.15 and 0.15–0.30 m soil layers provided by Soilgrids 2.021. The Soilgrids procedure allows to download the data at the resolution needed here (half degree spatial resolution).