Palaeoclimate reconstructions of periods with warm climates and high atmospheric CO concentrations are crucial for developing better projections of future climate change. Deep-ocean and high-latitude palaeotemperature proxies demonstrate that the Eocene epoch (56 to 34 million years ago) encompasses the warmest interval of the past 66 million years, followed by cooling towards the eventual establishment of ice caps on Antarctica. Eocene polar warmth is well established, so the main obstacle in quantifying the evolution of key climate parameters, such as global average temperature change and its polar amplification, is the lack of continuous high-quality tropical temperature reconstructions. Here we present a continuous Eocene equatorial sea surface temperature record, based on biomarker palaeothermometry applied on Atlantic Ocean sediments. We combine this record with the sparse existing data to construct a 26-million-year multi-proxy, multi-site stack of Eocene tropical climate evolution. We find that tropical and deep-ocean temperatures changed in parallel, under the influence of both long-term climate trends and short-lived events. This is consistent with the hypothesis that greenhouse gas forcing, rather than changes in ocean circulation, was the main driver of Eocene climate. Moreover, we observe a strong linear relationship between tropical and deep-ocean temperatures, which implies a constant polar amplification factor throughout the generally ice-free Eocene. Quantitative comparison with fully coupled climate model simulations indicates that global average temperatures were about 29, 26, 23 and 19 degrees Celsius in the early, early middle, late middle and late Eocene, respectively, compared to the preindustrial temperature of 14.4 degrees Celsius. Finally, combining proxy- and model-based temperature estimates with available CO reconstructions yields estimates of an Eocene Earth system sensitivity of 0.9 to 2.3 kelvin per watt per square metre at 68 per cent probability, consistent with the high end of previous estimates.

The exclusive use of carbonate reference materials is a robust method for the standardization of clumped isotope measurements • Measurements using different acid temperatures, designs of preparation lines, and mass spectrometers are statistically indistinguishable • We propose new consensus values for a set of 7 carbonate reference materials and updated guidelines to report clumped isotope measurements

Clumped isotopes provide a theory‐based proxy to reconstruct formation temperatures of carbonates. With the introduction of the empirical transfer function (ETF) and several carbonate standards, interlaboratory comparison has become achievable. Due to the rare occurrence of the multiply substituted isotopologues, the analytical precision of these measurements is very low. In order to improve precision, we investigate the optimal strategy for the conversion into the absolute reference frame using a simulation approach. We find that changing the relative proportions of the standards to include more standards that are closer to the unknown target Δ47 value can greatly improve attainable precision. The inclusion of a hypothetical 4 °C standard results in only modest improvements in final temperature estimates for Earth surface temperature (0 and 40 °C) samples, indicating that the set of ETH‐1–3 standards is suitable for most applications. Full interpolation between two subsequent hypothetical standards, with Δ47 values of CO2 equilibrated at 1000 and 25 °C, results in modest improvements for samples with extreme Δ47 values. With a more optimal distribution of standards it is possible to measure more sample replicates before the uncertainty derived from the ETF becomes limiting. We provide suggestions for the optimal distribution of standards for all target sample Δ47 values and the R code to perform these simulations based on different laboratory settings. These optimizations can also be applied for ETFs using heated and equilibrated gases. We demonstrate numerically how optimizing the distribution and relative abundance of standards can increase measurement precision.

Abstract. Cenozoic stable carbon (δ13C) and oxygen (δ18O) isotope ratios of deep-sea foraminiferal calcite co-vary with the 405 kyr eccentricity cycle, suggesting a link between orbital forcing, the climate system, and the carbon cycle. Variations in δ18O are partly forced by ice-volume changes that have mostly occurred since the Oligocene. The cyclic δ13C–δ18O co-variation is found in both ice-free and glaciated climate states, however. Consequently, there should be a mechanism that forces the δ13C cycles independently of ice dynamics. In search of this mechanism, we simulate the response of several key components of the carbon cycle to orbital forcing in the Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir model (LOSCAR). We force the model by changing the burial of organic carbon in the ocean with various astronomical solutions and noise and study the response of the main carbon cycle tracers. Consistent with previous work, the simulations reveal that low-frequency oscillations in the forcing are preferentially amplified relative to higher frequencies. However, while oceanic δ13C mainly varies with a 405 kyr period in the model, the dynamics of dissolved inorganic carbon in the oceans and of atmospheric CO2 are dominated by the 2.4 Myr cycle of eccentricity. This implies that the total ocean and atmosphere carbon inventory is strongly influenced by carbon cycle variability that exceeds the timescale of the 405 kyr period (such as silicate weathering). To test the applicability of the model results, we assemble a long (∼22 Myr) δ13C and δ18O composite record spanning the Eocene to Miocene (34–12 Ma) and perform spectral analysis to assess the presence of the 2.4 Myr cycle. We find that, while the 2.4 Myr cycle appears to be overshadowed by long-term changes in the composite record, it is present as an amplitude modulator of the 405 and 100 kyr eccentricity cycles.

Wang et al., 2004), carbonate clumped isotope analysis has developed into a valuable tool for paleothermometry in the geosciences. Clumped isotope analysis is based on the thermodynamic principle that molecules with multiple heavy isotopes (so-called "multiply-substituted isotopologues") have lower vibrational energies than molecules containing lighter isotopes (Urey, 1947). Consequently, the increase in system entropy at higher temperatures causes a decrease in the occurrence of multiply-substituted isotopologues, and "clumping" of heavy isotopes within the same molecule is favored in low-energy systems (Eiler, 2007). In carbonates, this principle causes heavy carbonate ions (e.g., 13 C 18 O 16 O 2 ; mass 63 or 12 C 18 O 2 16 O; mass 64) to become more abundant with decreasing calcification temperatures (Ghosh et al., 2006). The distribution of these isotopologues is proportional in the CO 2 gas after reaction of carbonates with acid (e.g., 13 C 18 O 16 O; mass 47 and 12 C 18 O 2 , mass 48 respectively) and is measured with reference to the distribution of isotopologues in a fully scrambled heated CO 2 gas with the same isotopic composition:

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Seasonal variability in sea surface temperatures plays a fundamental role in climate dynamics and species distribution. Seasonal bias can also severely compromise the accuracy of mean annual temperature reconstructions. It is therefore essential to better understand seasonal variability in climates of the past. Many reconstructions of climate in deep time neglect this issue and rely on controversial assumptions, such as estimates of sea water oxygen isotope composition. Here we present absolute seasonal temperature reconstructions based on clumped isotope measurements in bivalve shells which, critically, do not rely on these assumptions. We reconstruct highly precise monthly sea surface temperatures at around 50 °N latitude from individual oyster and rudist shells of the Campanian greenhouse period about 78 million years ago, when the seasonal range at 50 °N comprised 15 to 27 °C. In agreement with fully coupled climate model simulations, we find that greenhouse climates outside the tropics were warmer and more seasonal than previously thought. We conclude that seasonal bias and assumptions about seawater composition can distort temperature reconstructions and our understanding of past greenhouse climates.

Abstract. Cenozoic stable carbon (δ 18O composite record spanning the Eocene to Miocene (34 to 12 Ma) and perform spectral analysis to assess the presence of the 2.4 Myr cycle. We find that, while the 2.4 Myr cycle appears to be overshadowed by long-term changes in the composite record, it is is present as 15 an amplitude modulator of the 405 and 100 kyr eccentricity cycles.