The nature of depth distribution of soil organic carbon (SOC) was examined in 85 soils across New South Wales with the working hypothesis that the depth distribution of SOC is controlled by processes that vary with depth in the profile. Mathematical functions were fitted to 85 profiles of SOC with SOC values at depth intervals typically of 0–5, 5–10, 10–20, 20–30, 30–40, 40–50, 50–60, 60–70, 70–80, 80–90 and 90–100 cm. The functions fitted included exponential functions of the form SOC = A exp (Bz); SOC = A + B exp (Cz) as well as two phase exponential functions of the form SOC = A + B exp (Cz) + D exp (Ez). Other functions fitted included functions where the depth was a power exponent or an inverse term in a function. The universally best-fitting function was the exponential function SOC = A + B exp (Cz). When fitted, the most successful function was the two-phase exponential, but in several cases this function could not be fitted because of the large number of terms in the function. Semi-log plots of log values of the SOC against soil depth were also fitted to detect changes in the mathematical relationships between SOC and soil depth. These were hypothesized to represent changes in dominant soil processes at various depths. The success of the exponential function with an added constant, the two-phase exponential functions, and the demonstration of different phases within the semi-log plots confirmed our hypothesis that different processes were operating at different depths to control the depth distributions of SOC, there being a surface component, and deeper soil component. Several SOC profiles demonstrated specific features that are potentially important for the management of SOC profiles in soils. Woodland and to lesser extent pasture soils had a definite near surface zone within the SOC profile, indicating the addition of surface materials and high rates of fine root turnover. This zone was much less evident under cropping.
Integration method of non-elementary exponential functions using iterated Fubinni integrals
