Estimating vital statistics and age distributions of measurable soil organic carbon fractions based on their pathway of formation and radiocarbon content

Radiocarbon measurements have been used in combination with “bomb 14C” models to estimate turnover of soil organic carbon fractions. However, the bomb 14C models assume that all SOC fractions are formed directly from external inputs of carbon, which is not always valid because some SOC fractions may receive carbon from other SOC fractions. Due to the continuous inputs of organic carbon, we argue that the most appropriate way to describe the age of SOC is by an age distribution. We developed age distributed models of SOC fractions and derived analytical solutions to them. The models all assume that SOC fraction decay can be described by first-order kinetics, but differ in their assumptions about the pathway of SOC fraction formation. The solutions can be used to estimate age distributions at steady state of different SOC fractions based on their radiocarbon content. These age distributions can be used to calculate the mean age, mean residence time, and other vital statistics of each measurable SOC fraction. Furthermore, if a sequential scheme is used to isolate the SOC fractions, an estimated age distribution of the total SOC can be obtained by adding the contributions of each soil fraction. The age distributions can be very helpful in interpretations of soil organic carbon dynamics in different soils.