Fig. 4

Half-degree grid-cell distribution of each flux parameter involved in (model = GPASOIL-v1). Each panel corresponds to one parameter. In each panel, the red bar gives the min - max range of values for this parameter provided by Wang et al.¹⁸ (mainly from Fig. S2 of Wang et al.¹⁸), the magenta bar corresponds to the values required to make the output flux from a pool smaller than the size of this pool, the blue bar corresponds to the grid-cell distribution of this parameter in the current study and green bars correspond to the distribution of variables used to compute this parameter in the current study. The values required to make the output flux from a pool smaller than the size of this pool are given in magenta. For instance, the gross flux from P_i-sec to P_i-sol (called \(f{P}_{desorp}^{i-sec\to i-sol}\)) is computed with Eq. 4: \(f{P}_{desorp}^{i-sec\to i-sol}={k}^{i-sec\to i-sol}.{P}_{i-sec}\). The inequality \(f{P}_{desorp}^{i-sec\to i-sol} < {P}_{i-sec}\) at daily time-step is equivalent to \({k}^{i-sec\to i-sol} < 1\) (with \({k}^{i-sec\to i-sol}\) in day⁻¹) and thus we compared the distribution of \({k}^{i-sec\to i-sol}\) to 1 in the panel (d). Similarly, the gross flux from P_i-sol to P_i-sec (called \(f{P}_{sorp}^{i-sol\to i-sec}\)) is computed as follows: \(f{P}_{sorp}^{i-sol\to i-sec}={k}^{i-sol\to i-sec}.{\left({P}_{i-sol}/{W}_{{\rm{abs}}}\right)}^{b}\). Thus, the inequality \(f{P}_{sorp}^{i-sol\to i-sec} < {P}_{i-sol}\) at daily time-step is equivalent to \({k}^{i-sol\to i-sec} < \overline{{W}_{{\rm{abs}}}}{\left({P}_{C,\infty }\right)}^{1-b}\) with \({k}^{i-sol\to i-sec}\) expressed in mgP (kg soil)⁻¹ day⁻¹ (mg P/L)^−b. Thus, we compared the distribution of \({k}^{i-sol\to i-sec}\) to \(\overline{{W}_{{\rm{abs}}}}{\left({P}_{C,\infty }\right)}^{1-b}\) in the panel (c) Green bars correspond to the distribution of variables used to compute each parameter. For instance, panel (a) focuses on \({k}^{i-lab\to i-sol}\). The equation to compute this parameter is: \({k}^{i-lab\to i-sol}=-4.82+209{f}_{i-sol}+14.64{f}_{x-occ}+9.26{f}_{i-sec}-\) \(0.008C-0.0003{P}_{i-tot{\rm{\backslash prim}},\infty }-0.018{s}_{{\rm{i}}}\), (cf. Table 10), thus the blue bar corresponds to the distribution of \({k}^{i-lab\to i-sol}\) and green bars corresponds to the distribution of −4.82 (1^st green bar), \(+209{f}_{i-sol}\) (2^nd green bar), \(+14.64{f}_{x-occ}\) (3^rd green bar), etc. This shows the contribution of each variable to the value of the parameter. The parameter b is without unit, \({k}^{i-sec\to x-occ}\), \({k}^{x-occ\to i-sec}\), \({k}^{i-lab\to i-sol}\) and \({k}^{i-sec\to i-sol}\) are in day⁻¹, \({k}^{i-sol\to i-sec}\) and \({k}^{i-sol\to i-lab}\) are in mgP (kg soil)⁻¹ day⁻¹ (mg P/L)^−b. \({k}^{x-occ\to i-sec}\), \({k}^{i-sol\to i-sec}\) and \({k}^{i-sec\to i-sol}\) are log transform to express them as a sum of another variables.