Geoscientific Model Development Discussions www.geosci-model-dev-discuss.net 1991-9611 1991-962X 3 3 2010 10.5194/gmdd-3-1105-2010 http://www.geosci-model-dev-discuss.net/3/1105/2010/ http://www.geosci-model-dev-discuss.net/3/1105/2010/gmdd-3-1105-2010.html http://www.geosci-model-dev-discuss.net/3/1105/2010/gmdd-3-1105-2010.pdf 1105 1138 2010-07-22 A nonlinear multi-proxy model based on manifold learning to reconstruct water temperature from high resolution trace element profiles in biogenic carbonates M. Bauwens msbauwen@vub.ac.be H. Ohlsson K. Barbé V. Beelaerts F. Dehairs J. Schoukens Earth System Sciences & Department of Analytical and Environmental Chemistry, Vrije Universiteit Brussel, Elsene, Belgium Department of Fundamental Electricity and Instrumentation, Vrije Universiteit Brussel, Elsene, Belgium Division of Automatic Control, Department of Electrical Engineering, Linköping University, Linköping, Sweden A long standing problem in paleoceanography concerns the reconstruction of water temperature from δ¹⁸O carbonate, which for freshwater influenced environments is hindered because the isotopic composition of the ambient water (related to salinity) affects the reconstructed temperature. In this paper we argue for the use of a nonlinear multi-proxy method called Weight Determination by Manifold Regularization 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 of other trace elements in multi-proxy models. Using Mg/Ca, Sr/Ca, Ba/Ca and Pb/Ca the WDMR model enabled a temperature reconstruction with a root mean squared error of ±2.19 °C for a salinity range between 15 and 32. Aubert, A., Lazareth, C. 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