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

Abstract

The one-compartment C model C t = C 0 e − k 2 t + k 1 A / k 2 ( 1 − e − k 2 t ) is being long used to simulate soil organic C (SOC) stocks. C t is the SOC stock at the time t; C 0, 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 − k 2 t expresses the decay of C 0 and, for a time t, corresponds to the remains of C 0 ( C 0 remains ). The component k 1 A / k 2 ( 1 − e − k 2 t ) refers, at time t, to the stock of SOC derived from C crops ( C crop). 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 C 0 = 32.55 Mg C ha −1 in the 0–17.5 cm layer. A linear equation ( C t = 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 t = C 0 e − k 2 t + k 1 A / k 2 ( 1 − e − k 2 t ) , so that a = C 0 e − k 2 t and b A = k 1 A / k 2 ( 1 − e − k 2 t ) . 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 1 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 e) 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 = ln 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.