A method for estimating coefficients of soil organic matter dynamics based on long-term experiments

The one-compartment C model Ct=C0e−k2t+k1A/k2(1−e−k2t)Ct=C0e−k2t+k1A/k2(1−e−k2t) is being long used to simulate soil organic C (SOC) stocks. Ct is the SOC stock at the time t; C0, the initial SOC stock; k2, the annual rate of SOC loss (mainly mineralization and erosion); k1, the annual rate to which the added C is incorporated into SOC; and A  , the annual C addition. The component C0e−k2tC0e−k2t expresses the decay of C0 and, for a time t, corresponds to the remains of C0 (C0 remains). The component k1A/k2(1−e−k2t)k1A/k2(1−e−k2t) refers, at time t, to the stock of SOC derived from C crops (Ccrop). We herein propose a simple method to estimate k1 and k2 coefficients for tillage systems conducted in long-term experiments under several cropping systems with a wide range of annual C additions (A) and SOC stocks. We estimated k1 and k2 for conventional tillage (CT) and no-till (NT), which has been conducted under three cropping systems (oat/maize −O/M, vetch/maize −V/M and oat + vetch/maize + cowpea −OV/MC) and two N-urea rates (0 kg N ha−1 −0 N and 180 kg N ha−1 −180 N) in a long-term experiment established in a subtropical Acrisol with C0 = 32.55 Mg C ha−1 in the 0–17.5 cm layer. A linear equation (Ct = a + bA) between the SOC stocks measured at the 13th year (0–17.5 cm) and the mean annual C additions was fitted for CT and NT. This equation is equivalent to the equation of the model Ct=C0e−k2t+k1A/k2(1−e−k2t)Ct=C0e−k2t+k1A/k2(1−e−k2t), so that a=C0e−k2ta=C0e−k2t and bA=k1A/k2(1−e−k2t)bA=k1A/k2(1−e−k2t). Such equivalences thus allow the calculation of k1 and k2. NT soil had a lower rate of C loss (k2 = 0.019 year−1) than CT soil (k2 = 0.040 year−1), while k1 was not affected by tillage (0.148 year−1 under CT and 0.146 year−1 under NT). Despite that only three treatments had lack of fit (LOFIT) value lower than the critical 5% F value, all treatments showed root mean square error (RMSE) lower than RMSE 95% indicating that simulated values fall within 95% confidence interval of the measurements. The estimated SOC stocks at steady state (Ce) in the 0–17.5 cm layer ranged from 15.65 Mg ha−1 in CT O/M 0 N to 60.17 Mg ha−1 in NT OV/MC 180 N. The SOC half-life (t1/2 = ln 2/k2) was 36 years in NT and 17 years in CT, reflecting the slower C turnover in NT. The effects of NT on the SOC stocks relates to the maintenance of the initial C stocks (higher C0 remais), while increments in Ccrop are imparted mainly by crop additions.