A nonlinear multi-proxy model based on manifold learning to reconstruct water temperature from high resolution trace element profiles in biogenic carbonates

Abstract. A long standing problem in paleoceanography concerns the reconstruction of water temperature from δ18O carbonate. It is problematic in the case of freshwater influenced environments because the δ18O isotopic composition of the ambient water (related to salinity) needs to be known. In this paper we argue for the use of a nonlinear multi-proxy method called Weight Determination by Manifold Regularization (WDMR) to develop a temperature reconstruction model that is less sensitive to salinity variations. The motivation for using this type of model is twofold: firstly, observed nonlinear relations between specific proxies and water temperature motivate the use of nonlinear models. Secondly, the use of multi-proxy models enables salinity related variations of a given temperature proxy to be explained by salinity-related information carried by a separate proxy. Our findings confirm that Mg/Ca is a powerful paleothermometer and highlight that reconstruction performance based on this proxy is improved significantly by combining its information with the information for other trace elements in multi-proxy models. Although the models presented here are black-box models that do not use any prior knowledge about the proxies, the comparison of model reconstruction performances based on different proxy combinations do yield useful information about proxy characteristics. Using Mg/Ca, Sr/Ca, Ba/Ca and Pb/Ca the WDMR model enables a temperature reconstruction with a root mean squared error of ± 2.19 °C for a salinity range between 15 and 32.