[9] Decomposition of organic matter in soil was simulated with a first‐order kinetics equation [Huang et al., 1998] as: where COM is the daily amount of carbohydrate degraded from organic matter amendments (g m−2 d−1). The impact of soil texture and soil temperature on decomposition was quantified by the soil index (SI) and the temperature index (TI), respectively. OMN and OMS represent nonstructural and structural components of incorporated organic matter (g m−2, dry matter), respectively. Constants k1 and k2 represent the first‐order potential decay rate for OMN and OMS with the values of 2.7 × 10−2 and 2 × 10−3 d−1, respectively [Huang et al., 1998]. The constant 0.65 is a reduction factor of field flooding on decomposition [Huang et al., 2002].

[10] The amount of carbohydrates derived from rice plants was simulated by the following equation [Huang et al., 1998]: where CR represents carbohydrate (g m−2 d−1) derived from rice plants and W is rice aboveground biomass (g m−2) on a given day. VI is a variety index identifying relative difference in methane production among rice varieties. Rice aboveground biomass was computed by a logistic growth equation [Huang et al., 1998] as: where W0 and Wmax represent rice above ground biomass at transplanting and at harvesting, respectively. Time variable t (d) is scaled in days after transplanting. The GY is rice grain yield (g m−2). The constant r is an intrinsic growth rate for above ground biomass.

[11] The effect of soil texture on CH4 production was expressed by a dimensionless soil index (SI) that is linked with soil sand content (SAND) as equation (6) [Huang et al., 1998]. The TI was introduced to quantify the influence of soil temperature on CH4 production as equation (7) [Huang et al., 1998].

[13] The effect of soil redox potential (Eh) on methane production was described by equation (8). where FEh is a reduction factor of soil redox potential, 0 < FEh ≤ 1.0 [Huang et al., 1998].

[14] The net reaction of anaerobic carbohydrate fermentation with methanogenesis was assumed to be an overall reaction of C6H12O6 ⇒ 3CH4 + 3CO2. From this reaction, a conversion factor on a mole weight basis of C6H12O6 to CH4 is approximately 0.27 (3[CH4]/[C6H12O6] = 0.27). Rate of methane production, P (g m−2 d−1), is then determined by the availability of methanogenic substrates and the influence of environmental factors by the equation:

[15] The fraction of produced methane emitted via rice plants, Fp, was simulated by [Huang et al., 1998]: where W and Wmax has the same definition as in equation (3).

[16] The CH4 emission via plants (Ep) was then computed as: