Fig. 2: Comparison of proxy and simulated vertical δ¹³C gradients of dissolved inorganic carbon in the upper ocean during the three hyperthermals.

Proxy data are from marine carbonate δ¹³C of three depth-dependent depositional settings (Supplementary Data 1) during the three hyperthermals: Permian−Triassic, early Toarcian and Palaeocene−Eocene Thermal Maximum. The average of simulated δ¹³C of dissolved inorganic carbon (δ¹³C_DIC) is calculated from low to middle latitudes (48.6° S to 48.6° N), where most sections are located (Supplementary Fig. 1). Both proxy and modelled δ¹³C_DIC values are adjusted as an offset from the average δ¹³C_DIC in surface water (Methods). Error bars represent the one standard deviation. a–c Proxy (grey) and simulated δ¹³C_DIC depth profiles at pre-carbon isotope excursion (CIE) phases with low temperatures for “microbial metabolism” (red), “eutrophication” (blue) and “circulation change” (green) scenarios. d–f The proxy and simulated δ¹³C_DIC depth profiles at peak CIE phases with global warming for “microbial metabolism”, “eutrophication” and “circulation change” scenarios. g–i Vertical δ¹³C_DIC gradients (mean ± 1 s.d.) are calculated from the δ¹³C difference between surface water (~40 m) and mid-water (~130 m), expressed as the δ¹³C_DIC change per 100 m of water depth (‰/hm).