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. In the modern oceans, the relative abundances of glycerol dialkyl glyceroltetraether (GDGT) compounds produced by marine archaeal communities show asignificant dependence on the local sea surface temperature at the site ofdeposition. When preserved in ancient marine sediments, the measuredabundances of these fossil lipid biomarkers thus have the potential toprovide a geological record of long-term variability in planetary surfacetemperatures. Several empirical calibrations have been made between observedGDGT relative abundances in late Holocene core-top sediments and modernupper ocean temperatures. These calibrations form the basis of the widelyused TEX86 palaeothermometer. There are, however, two outstandingproblems with this approach: first the appropriate assignment of uncertaintyto estimates of ancient sea surface temperatures based on the relationshipof the ancient GDGT assemblage to the modern calibration dataset, andsecond, the problem of making temperature estimates beyond the range of themodern empirical calibrations (&gt; 30 ∘C). Here weapply modern machine learning tools, including Gaussian process emulatorsand forward modelling, to develop a new mathematical approach we callOPTiMAL (Optimised Palaeothermometry fromTetraethers via MAchine Learning) to improvetemperature estimation and the representation of uncertainty based on therelationship between ancient GDGT assemblage data and the structure of themodern calibration dataset. We reduce the root mean square uncertainty ontemperature predictions (validated using the modern dataset) from∼ ±6 ∘C using TEX86-basedestimators to ±3.6 ∘C using Gaussian processestimators for temperatures below 30 ∘C. We also provide anew quantitative measure of the distance between an ancient GDGT assemblageand the nearest neighbour within the modern calibration dataset, as a testfor significant non-analogue behaviour.

OPTiMAL: a new machine learning approach for GDGT-based palaeothermometry