Table 1 Determinations of parameter values in the application of fm

Parameters Descriptions Value estimated by soil properties Value recommended if not available sources and notes
a SOC–microorganism collocation factor Can be estimated by clay content (cc) $$a = \left\{ {\begin{array}{*{20}{l}} {0,c_{\rm c} \le 0.016} \hfill \\ {2.8c_{\rm c} - 0.046,0.016 < c_{\rm c} \le 0.37} \hfill \\ {1,c_{\rm c} > 0.37} \hfill \end{array}} \right.$$ Fig. 6
b O2 supply restriction factor Depend on O2 supply 0 ≤ b ≤ 1.7 0.75 Supplementary Data 1
θ op Optimum water content Can be calculated implicitly by soil properties $$\nu _{DO}\frac{{\theta _{{\rm op}}}}{{K_\theta + \theta _{{\rm op}}}}\alpha m_{{\rm SOC}}\phi ^{a\left( {m_{\rm s} - n_{\rm s}} \right)}\theta _{{\rm op}}^{an_{\rm s}} = k_{{\rm GO}}\phi ^{m_{\rm g} - n_{\rm g}}\left( {\phi - \theta _{{\rm op}}} \right)^bD_{{\rm GO,0}}$$ 0.65ϕ 4, 18
ϕ Soil porosity Can be estimated by soil bulk density (ρb) and mineral density (ρs) $$\phi = 1 - \frac{{\rho _b}}{{\rho _s}}$$ 67
n s Saturation exponent Depend on soil structure and texture 2 45
K θ Moisture constant Depend on organo-mineral associations 0.1 24