δ¹³C Simple model in: Atmosphere, Biosphere, & upper Ocean

Abstract

Carbon is a vital component of the Earth’s system and climate change dynamics. Quantifying the carbon cycle is essential to understanding the fate of anthropogenic emissions. The isotope δ¹³C serves as a tracer for carbon sources and sinks. This study presents a box model that simulates δ¹³C concentrations in the atmosphere, biosphere, and ocean from 1850 to 2022. The model utilizes over thirty-four datasets to achieve a comprehensive understanding of the carbon cycle and close the carbon budget. A novel method was developed to accurately calculate atmospheric carbon stocks, accounting for the impact of changing CO₂ concentrations on the isotopic budget. By tuning the model with available atmospheric and ocean surface measurements, we achieved a root mean square error (RMSE) of 0.04‰. Annual average global photosynthesis fractionation was calculated based on rising CO₂ levels. Key findings include a continuous decline in forest cover (contradicting the global greening hypothesis), an estimated annual atmosphere-biosphere carbon exchange of approximately 120 PgC/year, and a consistent 9.43‰ δ¹³C difference between the atmosphere and ocean surface, indicating a flux of 110 PgC/year between these reservoirs. The results suggest enhanced ocean surface-atmosphere mixing or increased ocean stratification in recent decades. Our δ¹³C-based calculation of the ocean carbon sink reveals a 17 PgC overestimation in the Global Carbon Project (GCP) estimate. This, combined with the GCP budget imbalance, suggests a 30 PgC gap potentially due to unmodeled sinks such as the biological pump. We also introduce the concept of "carbon mummification," where carbon becomes inert due to pollution, contamination, anoxia, or stable compound formation. This process could help explain the observed imbalance in the carbon budget.