Foraminiferal tests are a common component of many marine sediments. The oxygen isotope ratio (δ18O) of test calcite is frequently used to reconstruct aspects of their life environment. The δ18O depends mainly on the isotope ratio of the water it is precipitated from, the temperature of calcification, and, to a lesser extent, the carbonate ion concentration. Foraminifera and other organisms can potentially preserve their original isotope ratio for many millions of years, although diagenetic processes can alter the ratios. Work on oxygen isotope ratios of foraminifera was instrumental in the discovery of the orbital theory of the ice ages and continues to be widely used in the study of rapid climate change. Compilations of deep sea benthic foraminifer oxygen isotopes have revealed the long history of global climate change over the past 100 million years. Planktonic foraminifer oxygen isotopes are used to investigate the history of past sea surface temperatures, revealing the extent of past ‘greenhouse’ warming and global sea surface temperatures.

Oxygen isotope paleotemperature studies of the Mesozoic and Paleozoic are based mainly on conodonts, belemnite guards, and brachiopod shells—material resistant to diagenesis and generally precipitated in oxygen isotope equilibrium with ambient water. The greatest obstacle to accurate oxygen isotope paleothermometry in deep time is uncertainty in the oxygen isotopic composition of the ambient seawater. The second greatest obstacle is fossil diagenesis. Useful application of the oxygen isotope method to brachiopod shells requires extreme care in sample screening and analyses, and is best done with scanning-electron microscopy, and petrographic and cathodoluminescence microscopy, and trace-element analysis. Correct interpretation of oxygen isotope data is greatly aided by thorough understanding of the paleolatitude, paleoecology, and depositional environment of the samples. The oxygen isotope record for the Triassic, based on brachiopod shells, is too sparse to show any distinct isotopic features. Jurassic and Early Cretaceous δ18O records, based on belemnites, show a Toarcian (Jurassic) decline (warming), a Callovian-Oxfordian acme, and an Early Cretaceous increase (cooling) to a Valanginian-Hauterivian maximum, followed by a decline (warming) to a middle Barremian minimum. Deep-time applications to oxygen isotope thermometry provide evidence for cooling and glaciation in the Ordovician, Carboniferous, and Permian. The δ18O values from Silurian and Devonian brachiopod shells and conodonts average lower than those of the remaining Phanerozoic because of the absence of continental glaciers and possibly higher temperatures (~37°?), although slightly lower (≤2%o) seawater δ18O cannot be ruled out. The hypothesis of high temperatures in the early Paleozoic implies a relatively constant hydrospheric δ18O, which is supported by clumped isotope paleotemperatures. However, more research is needed to develop methods for evaluating clumped isotope reordering in fossils. Ongoing and future research in oxygen isotope and clumped isotope thermometry hold the promise of resolving deep-time temperatures, seawater δ18O, and salinity with heretofore unavailable accuracy (±2°, ±0.4%o, and ±2 psu), providing the environmental setting for the evolution of metazoan life on Earth.

Oxygen isotopic analysis of the phosphate in bioapatite has become a standard paleoclimatological tool with results documented in a rapidly expanding literature. Phosphate-based measurements are particularly important for samples where carbonates preservation is suspect (as is the case for many Paleozoic sites). Important analytical and observational advances that have fueled the expansion of phosphate-based studies include: 1) Oxygen isotopic ratios of biogenic apatite can be measured on small enough samples (≥ ~300 μg), quickly enough, cheaply enough, and accurately enough to permit meaningful high resolution paleoclimatic studies of trends through time, along spatial transects, and/or among taxa, 2) biogenic apatite is precipitated in approximate equilibrium with ambient waters and thus records the interplay of temperature and the isotopic composition of the water in which a sample grew, 3) tooth enamel and conodont crown material are quite resistant to diagenetic alteration and are preferred targets for both paleotemperature and paleoecological studies, 4) Paleozoic conodont δ18O records seem to provide robust paleotemperature information on time scales ranging from thousands of years to 100's of millions of years, and generation of increasingly refined paleotemperature records from this diagenetically resistant phase is likely to continue to be a useful field of study, 5) paleoenvironmental variations in δ18O values of seawater have been documented (e.g., differences between glacial and interglacial oceans), but whether and by how much the δ18O value of the hydrosphere may have increased since the Cambrian remains unresolved, and 6) differences in δ18O values among conodont taxa are increasingly well documented and, coupled with the potential to study growth series using ion microprobe techniques, are providing novel perspectives on and important tests of conodont paleoecology.

The underlying basis for Mg/Ca paleothermometry is that the amount of magnesium in calcite precipitated from seawater is dependent on temperature. Here we review the state of the art of the Mg/Ca seawater paleotemperature proxy, summarized by the following: 1) Calcite, whether formed abiotically or biologically as foraminifera and ostracode shells, incorporates variable amounts of magnesium into the crystal structure. 2) Uptake of Mg varies positively with temperature. 3) The relationship between temperature and the amount of Mg in calcite has been quantified by experiments on synthetic calcite growth and by culture, core top, and sediment trap experiments using living organisms. 4) The most careful calibrations of the Mg/Ca paleothermometer have been done for planktic foraminifera, then benthic foraminifera; there are species-specific variations in the amount of Mg incorporated into foraminifera shells. 5) The Mg/Ca ratio of calcite from planktic foraminifera in deep-sea cores has been widely used to interpret sea surface temperatures. 6) Measurement of both Mg/Ca and δ18O in planktic foraminifera have been used to calculate δ18O in seawater, and after correction for global ice volume, salinity could be inferred. 7) Mg/Ca from benthic foraminifera have been used to reconstruct deep-sea temperatures and cooling of ~12° over the last 50 million years. 8) One problem with the Mg/Ca seawater temperature proxy is partial dissolution of foraminifer shells, which lowers the Mg/Ca, and leads to an underestimation of ocean temperature. Benthic foraminifers appear to be more resistant to partial dissolution. 9) Past changes in the Mg/Ca ratio of seawater are an important factor in determining the amount of Mg in fossil skeletal calcite, and thus add another variable to the Mg/Ca temperature proxy. All Mg/Ca paleotemperature studies on fossil calcite older than Pleistocene should take into account the Mg/Ca of the seawater from which it precipitated.

Clumped isotopes geochemistry measures the thermodynamic preference of two heavy, rare, isotopes to bind with each other. This preference is temperature dependent, and is more pronounced at low temperatures. Carbonate clumped isotope values are independent of the carbonate δ13C and δ18O, making them independent of the carbon or oxygen composition of the solution from which the carbonate precipitated. At equilibrium, it is therefore a direct proxy for the temperature in which the carbonate mineral formed. In most cases, carbonate clumped isotopes record the temperature of carbonate formation, irrespective of the mineral form (calcite, aragonite, or bioapatite) or the organism making it. The carbonate formation temperatures obtained from carbonate clumped isotope analysis can be used in conjunction with the δ18O of the same carbonate, to constrain the oxygen isotope composition of the water from which the carbonate has precipitated. There are, however, cases of deviation from thermodynamic equilibrium, where both clumped and oxygen isotopes are offset from the expected values. Such carbonates must be characterized and calibrated separately. For deep-time applications, special care must be paid to the preservation of the original signal, in particular with respect to diagenetic alteration associated with atomic scale diffusion that may be undetectable by common tests for diagenesis.

Microbial communities adjust the chemical structure of their cell membranes in response to environmental temperature. This enables the development of lipid-based paleothermometers such as the glycerol dialkyl glycerol tetraether (GDGT) proxies described here. Surface-sediment calibrations establish a strong empirical relationship between the relative distribution of GDGTs and temperature. GDGT proxies can be used in marine, lacustrine, and paleosol sequences as long as the organic material is not thermally mature. Thus far, GDGT proxies have been applied to sediments dating back to the middle Jurassic. Many of the key uncertainties of these proxies are related to our emerging understanding of archaeal (and for the branched GDGTs, bacterial) ecology.

Seasonal temperature variation at any location is most strongly regulated by the annual cycle of solar insolation, which is controlled by latitude and orbital parameters; other factors are continentality, albedo feedbacks, stratification and advection, and water depth. Seasonal minima, maxima, and range vary with change in mean annual temperature (MAT) across latitudes; seasonal variation in ocean-water temperature is highest in the mid-latitudes. Seasonal temperature range at depth is likely to be less than that at the sea surface. The chemistry of accretionary biogenic carbonate can preserve a record of seasonal temperature variation experienced by an organism over some portion of its ontogeny. Sampling early parts of ontogenies will yield a more complete temperature record because growth is faster (so temporal resolution is higher) and more likely to be continuous throughout the year. Biases due to preferential season of growth can be recognized by characteristic patterns of isotope data when plotted versus distance along the ontogenetic trajectory. Multiple years are needed to reliably characterize seasonal temperature range and inter-annual variability for a stratigraphic horizon in a given region; single-shell studies are less useful in this regard unless they contain very long records. Data from multiple time intervals or regions using the same taxon, sampled the same way, and from the same facies can establish meaningful trends in average temperature and seasonal range. Deep-time studies exploring seasonal temperature extremes and ranges can be coupled with proxies for mean annual temperature to offer a more complete understanding of changing climate conditions through time.

Carbon isotopes in Neogene-age fossil teeth and paleosol carbonates are commonly interpreted in the context of past distributions of C3 and C4 vegetation. These two plant types have very different distributions in relation to climate and ecology, and provide a robust basis for reconstructing terrestrial paleoclimates and paleoenvironments during the Neogene. Carbon isotopes in pre-Neogene fossil teeth are usually interpreted in the context of changes in the δ13C value of atmospheric CO2, and variable climate-dependent carbon-isotope discrimination in C3 plants. Carbon isotopes in pre-Neogene soil carbonates can be used to estimate past levels of atmospheric CO2. Oxygen isotopes in fossil teeth and paleosol carbonates primarily are influenced by the oxygen isotopic compositions of ancient rainfall and surface waters. The oxygen isotopic composition of rainfall is has a complex, but tractable, relationship with climate, and variably relates to temperature, elevation, precipitation amount, and other factors. Mammal species that rely on moisture in dietary plant tissues to satisfy their water requirements (rather than surface drinking water) may have oxygen isotopic compositions that track aridity. Thus, oxygen isotopes of fossil mammals can place broad constraints on paleoaridity. Carbonate clumped isotope thermometry allows for reconstruction of soil temperatures at the time of pedogenic carbonate mineralization. The method is unique because it is the only thermodynamically based isotopic paleothermometer that does not require assumptions about the isotopic composition of the fluid in which the archive mineral formed. Soil temperature reflects a complex interplay of air temperature, solar radiative heating, latent heat effects, soil thermal diffusivity, and seasonal variations of these parameters. Because plants and most animals live in and/or near the soil, soil temperature is an important aspect of terrestrial (paleo)climate.

Leaf physiognomy (size and shape) in fossils is commonly used to reconstruct terrestrial paleoclimate. Physiognomic leaf-climate methods are underpinned mostly by the covariation between toothed margins and mean annual temperature (MAT) and between leaf size and mean annual precipitation. Digital leaf physiognomy, a multivariate method based largely on variables that are functionally linked to climate and that can be measured by computer algorithm, minimizes many of the deficiencies present in other approaches. Nevertheless, the relationships between MAT and many physiognomic variables, especially tooth-related variables, are confounded by leaf thickness, leaf habit (deciduous vs. evergreen), and phylogenetic history. Until these factors are properly accounted for, a minimum error in MAT of ±4 ° for digital leaf physiognomy and ±5 ° for other methods should be assumed.

This article discusses past greenhouse climates with an emphasis on recent progress in the comparison of models and data in the Eocene. These past climates—about 10° warmer than modern—provide valuable lessons in the climate dynamics of a world with higher-than-modern greenhouse-gas concentrations, reduced temperature gradients, and a lack of polar ice. Some key points that emerge from this analysis are: 1) Past greenhouse climates are characterized by warmer-than-modern global mean temperatures and winter season warmth, as well as strong polar amplification of warming that generates weak meridional temperature gradients. 2) A trade-off exists between heat transport in a warmer world and a world with smaller temperature gradients; a range exists in which a warmer world with weak temperature gradients can transport as much heat as a cooler world with stronger gradients. 3) These features can be reproduced in models if global mean and tropical temperatures are allowed to increase significantly over modern values. 4) Local radiative-convective feedbacks play an important role, perhaps dominating over transport, or acting in conjunction with transport to maintain relatively warm, weak temperature gradient climates. 5) Past greenhouse climates appear to have many of the modern modes of variability from orbital to interannual. 6) Modeling efforts are most useful when done independently of proxy data; model output can then be compared with proxies to evaluate potential weaknesses in the model. 7) Model-data mismatch might be due to incorrect boundary or initial conditions or resolution, or to missing or incomplete representation of relevant physics. 8) Refinements and new developments in proxies for temperature and other variables offer much potential for discriminating among the next generation of modeled scenarios, thereby allowing a better understanding of the conditions under which greenhouse climates exist.