Deep time foraminifera Mg/Ca paleothermometry: Nonlinear correction for secular change in seawater Mg/Ca

The Mg/Ca ratio of foraminifera tests is increasingly being utilized as a paleotemperature proxy. Deep time (pre‐Pleistocene) Mg/Ca paleothermometry is complicated by the fact that the Mg/Ca ratio of seawater (Mg/Casw) has undergone considerable secular variation over the Cenozoic. Previous studies have corrected for this by assuming an invariant Mg distribution coefficient (DMg) with Mg/Casw. More recent laboratory culturing has shown that this is not the case, demonstrating that a power relationship best describes the variation in test Mg/Ca (Mg/Catest) with Mg/Casw. Therefore, previous corrections are likely to have led to inaccurate temperature reconstructions. Here, we show how the systematics of such a correction should be applied and demonstrate why this provides good evidence that the Mg/Ca ratio of Paleogene seawater was lower than previously implied by foraminiferal constraints, in agreement with the majority of the proxy Mg/Casw evidence. We also demonstrate how it is indirectly possible to constrain the value of H, the power component of a Mg/Catest–Mg/Casw calibration, potentially enabling the appropriate correction of results derived from species where this relationship has not been calibrated. However, this technique should not be treated as a substitute for culturing. The previous erroneous assumptions regarding both (1) the relationship between Mg/Catest and Mg/Caswand (2) the Mg/Ca ratio of seawater at a given time in the past may counteract each other to differing extents. As a result, previous absolute pre‐Pleistocene paleotemperature estimates derived from Mg/Ca ratios in foraminifera should be treated with caution, although relative temperature changes over short (