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

The one-compartment C model C-t = C(0)e(-k2t) + k(1)A/k(2) (1 - e(-k2t)) is being long used to simulate soil organic C (SOC) stocks. C, is the SOC stock at the time t; Co, the initial SOC stock; k(2), the annual rate of SOC loss (mainly mineralization and erosion); k(1), the annual rate to which the added C is incorporated into SOC; and A, the annual C addition. The component C(0)e(-kt) expresses the decay of Co and, for a time t, corresponds to the remains of Co (Co main,). The component k(1)A/k(2) (I - ek2l) refers, at time t, to the stock of SOC derived from C crops (C,,,p). We herein propose a simple method to estimate k(1) and k(2) 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 k(1) and k(2) 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 Co = 32.55 Mg C hat in the 0-17.5 cm layer. A linear equation (C, = 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 C, = Coe(-k2t) + k(1)A/k(2) (1 - e(-k2t)), so that a = C(0)e(-k2t) and bA = k(1)A/k(2)(1 - e(-12t)). Such equivalences thus allow the calculation of k(1) and k(2). NT soil had a lower rate of C loss (k(2) = 0.019 year(-1)) than CT soil (k(2) = 0.040 year(-1)), while k, 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 (C,) 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 (t(1/2) = 1n 2/k(2)) 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 C-0 (remais)), while increments in C-crop are imparted mainly by crop additions. (c) 2006 Elsevier B.V. All rights reserved.