. 2024 Jan 2;11:17. doi: 10.1038/s41597-023-02751-6

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.

Parameters	Name in Wang et al.¹⁸	unit		Equation	r²
$P_{c, \infty}$	$C_{\infty}$	mgP L⁻¹	¹⁸	$P_{c, \infty} = 1 0^{[- 1.7425 + 1.7782 (1 - e x p (- 1.6653 C_{X}))]}$	0.54
$P_{c, \infty}$	$C_{\infty}$	mgP L⁻¹	This study	$P_{c, \infty} = 0.1$
b	b	dimensionless	¹⁸	$b = e x p (0.532 - 0.13 O_{x} - 37.49 f_{i - s o l} + 0.81 f_{i - l a b} + 0.003 s_{s})$	0.43
b	b	dimensionless	This study	$b = e x p (- 0.628 - 36.702 f_{i - s o l} + 1.102 f_{i - l a b} + 0.0024 s_{s})$	0.23
$k^{i - l a b \to i - s o l}$	k_WL	day⁻¹	¹⁸	$k^{i - l a b \to i - s o l} = - 4.82 + 209 f_{i - s o l} + 14.64 f_{x - o c c} + 9.26 f_{i - s e c} - 0.008 C - 0.0003 P_{i - t o t \prim} - 0.018 s_{i}$	0.28
$k^{i - l a b \to i - s o l}$	k_WL	day⁻¹	This study	Same as¹⁸ but use of $P_{i - t o t \prim, \infty}$ instead of $P_{i - t o t \prim}$
$k^{i - s o l \to i - s e c}$	k_SW	mgP (kg soil)⁻¹ day⁻¹ (mg P/L)^−b	¹⁸	$k^{i - s o l \to i - s e c} = e x p (0.002 + 4.0 f_{i - s e c} + 0.0008 P_{o - t o t} + 0.012 C + 0.108 T_{a} - 0.0002 P_{i - t o t \prim})$	0.64
$k^{i - s o l \to i - s e c}$	k_SW	mgP (kg soil)⁻¹ day⁻¹ (mg P/L)^−b	This study	Same as¹⁸ but use of $P_{o - t o t, \infty}$ and $P_{i - t o t \prim, \infty}$ instead of P_o-tot and $P_{i - t o t \prim}$ , respectively
$k^{i - s e c \to x - o c c}$	k_OS	day⁻¹	¹⁸	$k^{i - s e c \to x - o c c} = 1.6 e^{- 5} + 0.0001 f_{x - o c c} - 0.0001 f_{i - s e c} + 1.3 e^{- 5} p H - 9.0 e^{- 6} O x - 4.48 e^{- 7} s_{c} + 1.1 e^{- 7} C$	0.90
$k^{i - s e c \to x - o c c}$	k_OS	day⁻¹	This study	$k^{i - s e c \to x - o c c} = 3.68 e^{- 5} + 9.60 e^{- 5} f_{x - o c c} - 1.47 e^{- 4} f_{i - s e c} + 1.22 e^{- 5} p H - 4.07 e^{- 7} s_{c} + 5.16 e^{- 8} C$	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 $P_{o - t o t, \infty}$ and $P_{i - t o t \prim, \infty}$ in the parametrizations instead of $P_{o - t o t}$ and $P_{i - t o t \prim}$ , 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 $P_{i - t o t \prim}$ 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 $P_{i - t o t \prim, \infty}$ . Subscript ∞ denotes pools at the steady-state.