Probability Distributions of Radiocarbon in Open Linear Compartmental Systems at Steady-State

Radiocarbon (C-14) is commonly used as a tracer of the carbon cycle to determine how fast carbon moves between different reservoirs such as plants, soils, rivers, or oceans. However such studies mostly emphasize the mean value (as Delta C-14) of an unknown probability distribution. We introduce a novel algorithm to compute Delta C-14 distributions from knowledge of the age distribution of carbon in linear compartmental systems at steady-state. Our results demonstrate that the shape of the distributions might differ according to the speed of cycling of ecosystem compartments and their connectivity within the system, and might contain multiple peaks and long tails. The distributions are also sensitive to the variations of Delta C-14 in the atmosphere over time, as influenced by the counteracting anthropogenic effects of fossil-fuel emissions (C-14-free) and nuclear weapons testing (excess C-14). Lastly, we discuss insights that such distributions can offer for sampling and design of experiments aiming to capture the precise variance of Delta C-14 values present in the multi-compartmental ecosystems.

Automated summary

This article introduces a new algorithm to compute Delta C-14 distributions in linear compartmental systems at steady-state. The results demonstrate that the shape of the distributions may vary depending on the cycling speed and connectivity of ecosystem compartments, and may contain multiple peaks and long tails. The distributions are also sensitive to the variations of Delta C-14 in the atmosphere over time, affected by anthropogenic influences.