Modeling the evolution of pulse-like perturbations in atmospheric carbon and carbon isotopes: the role of weathering–sedimentation imbalances

Abstract. Measurements of carbon isotope variations in climate archives and isotope-enabled climate modeling advance the understanding of the carbon cycle. Perturbations in atmospheric CO₂ and in its isotopic ratios (δ¹³C, Δ¹⁴C) are removed by different processes acting on different timescales. We investigate these differences on timescales of up to 100？000？years in pulse-release experiments with the Bern3D-LPX Earth system model of intermediate complexity and by analytical solutions from a box model. On timescales from years to many centuries, the atmospheric perturbations in CO₂ and δ¹³CO₂ are reduced by air–sea gas exchange, physical transport from the surface to the deep ocean, and by the land biosphere. Isotopic perturbations are initially removed much faster from the atmosphere than perturbations in CO₂ as explained by aquatic carbonate chemistry. On multimillennial timescales, the CO₂ perturbation is removed by carbonate compensation and silicate rock weathering. In contrast, the δ¹³C perturbation is removed by the relentless flux of organic and calcium carbonate particles buried in sediments. The associated removal rate is significantly modified by spatial δ¹³C gradients within the ocean, influencing the isotopic perturbation of the burial flux. Space-time variations in ocean δ¹³C perturbations are captured by principal components and empirical orthogonal functions. Analytical impulse response functions for atmospheric CO₂ and δ¹³CO₂ are provided.

Results suggest that changes in terrestrial carbon storage were not the sole cause for the abrupt, centennial-scale CO₂ and δ¹³CO₂ variations recorded in ice during Heinrich stadials HS1 and HS4, though model and data uncertainties prevent a firm conclusion. The δ¹³C offset between the