Table 10 Original parametrizations provided by Wang et al.¹⁸ and modified parametrizations used in this study after i) exclusion of oxalate concentrations from explanatory variablex and ii) setting k parameters as constant in time.

From: A global dataset on phosphorus in agricultural soils

Parameters	Name in Wang et al.¹⁸	unit		Equation	r²
\({P}_{c,\infty }\)	\({C}_{\infty }\)	mgP L⁻¹	¹⁸	\({P}_{c,\infty }=1{0}^{\left[-1.7425+1.7782\left(1-exp\left(-1.6653{C}_{X}\right)\right)\right]}\)	0.54
\({P}_{c,\infty }\)	\({C}_{\infty }\)	mgP L⁻¹	This study	\({P}_{c,\infty }=0.1\)
b	b	dimensionless	¹⁸	\(b=exp\left(0.532-0.13{O}_{x}-37.49{f}_{i-sol}+0.81{f}_{i-lab}+0.003{s}_{s}\right)\)	0.43
b	b	dimensionless	This study	\(b=exp\left(-0.628-36.702{f}_{i-sol}+1.102{f}_{i-lab}+0.0024{s}_{s}\right)\)	0.23
\({k}^{i-lab\to i-sol}\)	k_WL	day⁻¹	¹⁸	\({k}^{i-lab\to i-sol}=-4.82+209{f}_{i-sol}+14.64{f}_{x-occ}+9.26{f}_{i-sec}-0.008C-0.0003{P}_{i-tot{\rm{\backslash prim}}}-0.018{s}_{{\rm{i}}}\)	0.28
\({k}^{i-lab\to i-sol}\)	k_WL	day⁻¹	This study	Same as¹⁸ but use of \({P}_{i-tot{\rm{\backslash prim}},\infty }\) instead of \({P}_{i-tot{\rm{\backslash prim}}}\)
\({k}^{i-sol\to i-sec}\)	k_SW	mgP (kg soil)⁻¹ day⁻¹ (mg P/L)^−b	¹⁸	\({k}^{i-sol\to i-sec}=exp\left(0.002+4.0{f}_{i-sec}+0.0008{P}_{o-tot}+0.012C+0.108{T}_{a}-0.0002{P}_{i-tot{\rm{\backslash prim}}}\right)\)	0.64
\({k}^{i-sol\to i-sec}\)	k_SW	mgP (kg soil)⁻¹ day⁻¹ (mg P/L)^−b	This study	Same as¹⁸ but use of \({P}_{o-tot,\infty }\) and \({P}_{i-tot{\rm{\backslash prim}},\infty }\) instead of P_o-tot and \({P}_{i-tot{\rm{\backslash prim}}}\), respectively
\({k}^{i-sec\to x-occ}\)	k_OS	day⁻¹	¹⁸	\({k}^{i-sec\to x-occ}=1.6{e}^{-5}+0.0001{f}_{x-occ}-0.0001{f}_{i-sec}+1.3{e}^{-5}pH-9.0{e}^{-6}Ox-4.48{e}^{-7}{s}_{c}+1.1{e}^{-7}C\)	0.90
\({k}^{i-sec\to x-occ}\)	k_OS	day⁻¹	This study	\({k}^{i-sec\to x-occ}=3.68{e}^{-5}+9.60{e}^{-5}{f}_{x-occ}-1.47{e}^{-4}{f}_{i-sec}+1.22{e}^{-5}pH-4.07{e}^{-7}{s}_{c}+5.16{e}^{-8}C\)	0.90

All parameterizations are built from a stepwise multivariate linear regression against the database used in Wang et al.¹⁸. r² provided in the last column characterize either the original parametrizations (and thus they are equal to values given in Table 2 of Wang et al.¹⁸) or parametrizations after excluding oxalate from explanatory variables (this study). The parameters k were kept constant in time through i) the use of a constant-in-time value for f_m for any soil pool m and, ii) the use of \({P}_{o-tot,\infty }\) and \({P}_{i-tot\mathrm{\backslash prim},\infty }\) in the parametrizations instead of \({P}_{o-tot}\) and \({P}_{i-tot\mathrm{\backslash prim}}\), respectively.
Note: C is soil carbon concentration in gC (kg of soil)⁻¹, O_x is oxalate metal oxide (Al and Fe) concentration in mmol(kg of soil)⁻¹, C_x is the ratio of total soil C and oxalate metal oxide concentrations in g/mmol (C_x = 0.001 C/O_x), s_s, s_c and s_i are sand, clay and silt percentages, respectively, T_a is the mean annual near-surface air temperature in °C, pH is soil pH measured in water (no unit), P_o-tot is the total soil organic P in mgP (kg of soil)⁻¹ and \({P}_{i-tot\mathrm{\backslash prim}}\) is the total inorganic P minus primary P in in mgP (kg of soil)⁻¹, f_m denotes the ratio (no unit) at steady-state of pool m and \({P}_{i-tot\mathrm{\backslash prim},\infty }\). Subscript ∞ denotes pools at the steady-state.

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Table 10 Original parametrizations provided by Wang et al.¹⁸ and modified parametrizations used in this study after i) exclusion of oxalate concentrations from explanatory variablex and ii) setting k parameters as constant in time.

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