The boron isotope ratio of seawater (δ11Bsw) is a parameter which must be known to reconstruct palaeo pH and CO2 from boron isotope measurements of marine carbonates. Beyond a few million years ago, δ11Bsw is likely to have been different to modern. Palaeo δ11Bsw can be estimated by simultaneously constraining the vertical gradients in foraminiferal δ11B (∆δ11B) and pH (∆pH). A number of subtly different techniques have been used to estimate ∆pH in the past, all broadly based on assumptions about vertical gradients in oxygen, and/or carbon, or other carbonate system constraints. In this work we pull together existing data estimates alongside limitations on the rate of change of δ11Bsw from modelling, and combine these into an overarching statistical framework called a Gaussian Process. The Gaussian Process technique allows us to bring together data and constraints on the rate of change in δ11Bsw to generate random plausible evolutions of δ11Bsw. We reconstruct δ11Bsw, and by extension palaeo pH, across the last 65Myr using this novel methodology. Reconstructed δ11Bsw is compared to other seawater isotope ratios, namely 87/86Sr, 187/188Os, and δ7Li, which we also reconstruct with Gaussian Processes. Our method provides a template for incorporation of future δ11Bsw constraints, and a mechanism for propagation of uncertainty in δ11Bsw into future studies.

Reconstructing atmospheric CO2 concentration in the Late Miocene is crucial for understanding the relationship between greenhouse gas concentrations and climate change in a warmer-than-modern world. Both δ11B-based and alkenone-ep-based CO2 estimates feature uncertainties due to poorly constrained past seawater chemistry, and algal physiological processes, respectively. Additionally, both proxies estimate CO2[aq], so they require reliable surface ocean temperatures to calculate solubility and atmospheric CO2. To evaluate proxy coherence, in this study we generate new records of alkenone ep and δ11B, from the western Tropical Atlantic ODP Site 926 during the Late Miocene. We provide surface ocean temperature estimates from coccolith clumped isotope thermometry, alkenone undersaturation ratios, and planktonic foraminiferal Mg/Ca ratios. The warm temperatures estimated from our new clumped isotope records, together with alkenone temperatures >29°C, confirm warm tropics, and provide constraints on the assumptions of seawater Mg/Ca and dissolution corrections for foraminiferal Mg/Ca SST estimates. The new alkenone ep CO2 estimates at 926 yield generally similar CO2 as the new and published δ11B-based CO2 records for the site, and are similar to published alkenone ep CO2 records from the South Atlantic ODP Site 1088. However, over the 7.3 to 7.8 Ma interval, the CO2 values from ep are lower than other records. We evaluate which proxy indicators can best predict variations in algal physiology which may bias the ep-based CO2 reconstructions in this interval at Site 926.