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Paleoclimatology (also spelled palaeoclimatology) is the study of Earth's climate before the instrumental record began in the mid-19th century. It draws on Earth system science, geology, and climatology to reconstruct how climate has varied and what has caused those variations. Direct measurements cover less than two centuries of Earth's 4.54-billion-year history, so paleoclimatologists rely on natural archives that preserve physical, chemical, isotopic, or biological signals of past conditions. These signals, known as climate proxies, are used to reconstruct past temperature, precipitation, atmospheric circulation, ocean currents, ice volume, and the composition of the atmosphere.

By reconstructing climates ranging from the glacial–interglacial cycles of the Quaternary to the greenhouse and icehouse states of the deep past, paleoclimatology defines the natural range of climate variability and helps constrain climate sensitivity, the response of global temperature to changes in radiative forcing, particularly from carbon dioxide. Past climates also provide independent tests for general circulation models and Earth system models. Paleoclimate records indicate that the present rate of human-caused warming is faster than any known natural change of the past 66 million years.

A climate proxy is a preserved material whose measurable properties responded systematically to environmental conditions when it formed. Modern paleoclimatology often describes the link between climate and a proxy measurement with a proxy system model, a framework developed by Michael Evans and colleagues. In this framework, a climate variable _X_(t), such as sea surface temperature or rainfall, is transformed into a laboratory measurement Y by three processes:

1. Sensor: the biological or chemical process that responds to the environment and records the signal. Examples include the temperature-dependent growth of a foraminiferal shell, the response of tree growth to moisture, and isotopic fractionation in condensing snow. Biological sensors often respond non-linearly, may record only part of the year, and can be affected by species-specific physiological ("vital") effects.
2. Archive: the processes that preserve and alter the signal after it forms. Examples include mixing of the upper 5 to 10 cm of seafloor sediment by burrowing animals (bioturbation), which smooths short-term signals; diffusion in the firn of ice sheets; and dissolution of carbonate shells below the lysocline.
3. Observation: sampling resolution, measurement error, and uncertainty in the age model.

To convert a proxy record _Y_(z), measured at depth z, into an estimate of past climate _X̂_(t), researchers use empirical transfer functions, calibrated by regression against overlapping instrumental records. Alternatively, they invert proxy system models within a statistical framework. In paleoclimate data assimilation, used for example in the Last Millennium Reanalysis, proxy networks are combined with climate model simulations using an ensemble Kalman filter.

Building a timeline requires converting depth in an archive (z) into age (t). The main methods are:

• Counting annual layers: archives with annual layers can be dated to the exact year. Examples include tree rings (dendrochronology); seasonal layers of dust, chemistry, and electrical conductivity in ice cores; annual density bands in corals and mollusc shells (sclerochronology); and annually layered lake or marine sediments (varves).
• Radiometric dating: based on radioactive decay, _N_(t) = N₀ e^−_λt_, where λ = ln 2/_t__1/2 is the decay constant.
• Radiocarbon dating (half-life 5,730 ± 40 years; useful back to about 50,000 years). Carbon-14 produced in the upper atmosphere is incorporated into living organisms and dissolved carbon; after death or isolation it decays to nitrogen-14. Because atmospheric ¹⁴C has varied with changes in Earth's magnetic field, solar activity, and the carbon cycle, radiocarbon ages must be converted to calendar ages (cal yr BP, before 1950) using the IntCal radiocarbon calibration curves. Marine samples must also be corrected for the marine reservoir age, typically about 400 years but over 1,000 years in some regions.
• Uranium–thorium dating (half-life of ²³⁰Th 75,584 years; useful to about 600,000 years). Uranium dissolves readily in natural waters, whereas thorium is insoluble. Cave speleothems and corals therefore incorporate uranium but almost no thorium when they form. Measuring the gradual ingrowth of ²³⁰Th by mass spectrometry gives ages with uncertainties of about 0.1 to 1%.
• Potassium–argon and argon–argon dating (half-life of ⁴⁰K 1.248 billion years) and uranium–lead dating are used to date volcanic ash layers within older sedimentary sequences.
• Stratigraphic markers: records from different archives can be aligned using events recorded simultaneously around the world. These include volcanic ash layers identified by their chemistry (tephrochronology), reversals and excursions of Earth's magnetic field (magnetostratigraphy), such as the Brunhes–Matuyama reversal (about 773,000 years ago) and the Laschamp event (about 41,000 years ago), and the associated peaks in cosmogenic beryllium-10 in ice cores and marine sediments.
• Orbital tuning (astrochronology): for marine sediment cores spanning millions of years, cycles in properties such as benthic δ¹⁸O, carbonate content, or magnetic susceptibility are matched to calculated variations in Earth's orbit (Milankovitch cycles), using solutions computed by Jacques Laskar and others.

Main paleoclimate archives

Deep ice cores from the Greenland ice sheet (such as GISP2, GRIP, NGRIP, and NEEM, which reach back about 120,000 to 130,000 years at depths of about 3 km) and the Antarctic ice sheet (such as Vostok, Dome Fuji, WAIS Divide, and EPICA Dome C, which reaches back 800,000 years) provide the most direct records of late Quaternary climate and atmospheric composition. The Beyond EPICA project has recovered ice about 1.2 million years old, and discontinuous ice several million years old has been found in blue-ice areas such as the Allan Hills.

Water contains stable isotopes of hydrogen (¹H, 99.9885%; deuterium, ²H or D, 0.0115%) and oxygen (¹⁶O, 99.757%; ¹⁷O, 0.038%; ¹⁸O, 0.205%). Most water molecules are H₂¹⁶O (mass 18), with small amounts of the heavier forms HD¹⁶O (mass 19) and H₂¹⁸O (mass 20). Isotopic composition is expressed in delta notation, in parts per thousand (‰), relative to Vienna Standard Mean Ocean Water (VSMOW), for which ¹⁸O/¹⁶O = 2.0052 × 10⁻³:

Heavier water molecules have lower zero-point energy and lower vapour pressure than light ones. At equilibrium, the liquid or solid phase is therefore enriched in heavy isotopes relative to the vapour, by a fractionation factor α = R_condensate/_R__vapour > 1. For ¹⁸O, α ≈ 1.0098 for liquid and vapour at 20 °C and ≈ 1.0152 for ice and vapour at 0 °C; α increases as temperature falls.

Water vapour evaporated from subtropical oceans (with δ¹⁸O of about −10 to −13‰) cools as it moves poleward and rises over ice sheets, producing precipitation along the way. Each precipitation event removes heavy isotopes preferentially, so the remaining vapour becomes progressively more depleted. This process, Rayleigh distillation, is described by:

where f is the fraction of the original vapour remaining. The isotopic composition of snow is then approximately:

Because the amount of moisture air can hold depends strongly on temperature (Clausius–Clapeyron relation), colder conditions remove more moisture before air reaches the ice sheet (smaller f) and also increase α. Snow that falls during cold glacial periods, or in winter, is therefore strongly depleted, with δ¹⁸O as low as about −50 to −58‰ in central East Antarctica. Snow that falls during warm interglacials, or in summer, is less depleted. Willi Dansgaard showed in 1964 that, across polar regions, δ¹⁸O varies approximately linearly with mean annual surface air temperature T (°C):

Relationships derived from changes over time at a single site are often weaker, with slopes of about 0.3 to 0.8‰ per °C, depending on seasonality and the strength of near-surface temperature inversions.

Measuring both isotopes allows calculation of the deuterium excess:

The factor 8 is the slope of the global meteoric water line defined by Harmon Craig. During equilibrium condensation, δD and δ¹⁸O change in a ratio close to 8, so d is relatively insensitive to condensation temperature. Instead, it is set mainly by non-equilibrium (kinetic) fractionation during evaporation, when the two heavy isotopologues diffuse through air at slightly different rates. Ice-core deuterium excess therefore records the sea surface temperature and relative humidity of the distant moisture source. Measurements of ¹⁷O-excess provide additional information on source humidity.

Surface snow, with a density of about 300 to 350 kg/m³, is gradually compacted into firn as it is buried, forming a porous layer about 50 to 120 m thick. In the upper firn, the pore spaces remain connected to the atmosphere, so air can mix and diffuse downward. When the firn reaches a density of about 815 to 830 kg/m³, at the close-off depth, the pores are sealed into isolated bubbles containing about 10% air by volume. Below depths of about 700 to 1,200 m, high pressure converts the bubbles into solid air clathrate hydrates, so deep ice appears clear until it relaxes at the surface.

These bubbles are direct samples of past air. Gas is extracted by crushing, grating, or melting the ice under vacuum and is analysed by gas chromatography, laser spectroscopy, and isotope-ratio mass spectrometry. Over the past 800,000 years, ice-core records show that:

• carbon dioxide varied between about 180 to 190 ppm at glacial maxima and about 250 to 300 ppm during interglacials (lower values in interglacials before about 430,000 years ago);
• methane varied between about 350 and 700 to 800 ppb;
• nitrous oxide varied between about 200 and 280 ppb.

Because air continues to exchange with the atmosphere until close-off, the air in a bubble is younger than the surrounding ice at the same depth. This difference, the gas-age/ice-age difference (Δage), is:

Its size depends on temperature and snowfall rate, as described by firn densification models such as the Herron–Langway model:

• At relatively warm sites with high snowfall, such as WAIS Divide or central Greenland during interglacials (accumulation of about 20 cm of ice per year), the firn compacts quickly and Δage is only tens to a few hundred years.
• At very cold, dry sites in the East Antarctic interior, such as Vostok or Dome C during glacial periods (temperatures of about −55 to −65 °C and accumulation of 1 to 2 cm per year), burial to the close-off depth takes thousands of years, and Δage reaches about 2,500 to 6,000 years.

The isotopic composition of nitrogen and argon in trapped air helps to reduce this uncertainty. Because the isotopic composition of atmospheric nitrogen and argon is essentially constant on these timescales, changes in δ¹⁵N and δ⁴⁰Ar in bubbles reflect two physical processes in the firn:

1. Gravitational settling: heavier isotopes become slightly enriched with depth in the still air of the firn, according to the barometric relation δ_grav ≈ Δ_m_ g z_diff/(RT), where Δ_m_ is the mass difference, z_diff is the thickness of the diffusive firn column, R is the gas constant, and T is temperature. This provides a measure of past firn thickness.
2. Thermal diffusion: during abrupt warming, such as a Dansgaard–Oeschger event in Greenland, the surface warms before the deeper firn. Heavier isotopes migrate toward the colder base of the firn, producing an additional signal:

δ¹⁵N_total = δ¹⁵N_grav + Ω_T Δ_T_ where Ω_T is the thermal diffusion sensitivity and Δ_T_ is the temperature difference across the firn.

Because this signal is recorded in the trapped air itself, at the same depth as the methane and CO₂ measurements, it allows the timing of abrupt warming to be compared directly with greenhouse-gas changes, largely avoiding Δage uncertainties. It also allows the size of abrupt warming events to be estimated.

Dendroclimatology reconstructs past climate from the annual growth rings of long-lived trees, including conifers such as Great Basin bristlecone pine (Pinus longaeva), larch, and Fitzroya, and broadleaf trees such as oak. Where growth stops each year, because of winter cold or a dry season, the vascular cambium produces a distinct layer of wood (xylem) each growing season:

• Earlywood forms in spring and has large, thin-walled cells that conduct water efficiently.
• Latewood forms in late summer and has smaller, thick-walled, heavily lignified cells that provide strength. The sharp boundary between latewood and the next year's earlywood marks each annual ring.

Using the principle of cross-dating established by Andrew Ellicott Douglass, the patterns of wide and narrow rings are matched between living trees, dead wood, wood preserved in bogs and lakes, and historical timbers. This allows missing or false rings to be identified and produces chronologies dated to the exact year. Absolutely dated chronologies, such as the Hohenheim oak and pine chronology in Europe, extend back more than 12,000 years, and their dating has been confirmed using Miyake events.

To separate climate signals from other influences, Edward Cook's linear aggregate model represents ring width in year t as:

where _C_(t) is the climate signal, δD₁ and δD₂ represent disturbances within the forest stand (such as competition) and from outside it (such as fire, insects, or windthrow), _E_(t) is random error, and _A_(t) is the age-related growth trend. Because a tree adds wood around an ever-larger circumference, ring width tends to decline with age regardless of climate. Removing this trend without also removing genuine long-term climate trends (the "segment length curse") requires methods such as regional curve standardization, which aligns many trees by age rather than fitting a curve to each tree individually.

Following Harold Fritts's principle of limiting factors, trees are sampled where a single climate factor most strongly limits growth. Four main measurements are used:

1. Ring width at dry forest margins: trees at warm, dry lower forest borders are limited by moisture, so ring width reflects soil moisture and drought indices such as the Palmer drought severity index. Networks of such records have been used to build drought atlases for North America, Europe and the Mediterranean ("Old World"), and monsoon Asia, which map droughts over the past two millennia.
2. Maximum latewood density at cold tree lines: trees near the cold northern or alpine tree line are limited by summer warmth. Ring width tends to carry over from one year to the next because of stored reserves, but maximum latewood density, measured by X-ray densitometry or by the reflection of blue light ("blue intensity"), responds more directly to late-summer temperature. It also records sharp cooling after large volcanic eruptions.
3. Carbon isotopes: according to Graham Farquhar's model, photosynthetic discrimination against ¹³C is Δ¹³C = a + (b − a)(c_i/_c__a), where a = 4.4‰ (diffusion through stomata), b ≈ 27‰ (fixation by RuBisCO), and c_i/_c__a is the ratio of CO₂ inside the leaf to that in the air. Tree-ring δ¹³C therefore records changes in stomatal behaviour and intrinsic water-use efficiency (the ratio of photosynthesis A_n to stomatal conductance g_s).
4. Oxygen isotopes: cellulose δ¹⁸O reflects the isotopic composition of soil water (and thus precipitation), modified by evaporative enrichment of leaf water. This enrichment is greater in dry air and is partly diluted when about 40% of the oxygen exchanges with stem water during cellulose formation. Isotope ratios in tree rings generally show much weaker age trends than ring width and can help identify annual cycles in tropical trees that lack clear rings.

For low- and mid-latitude land regions, records extending far beyond the range of tree rings come from cave deposits and plant fossils:

• Speleothems: rainwater passing through soil, where respiration raises CO₂ concentrations to thousands of ppm, becomes acidic and dissolves limestone (CaCO₃ + H₂CO₃ → Ca²⁺ + 2HCO₃⁻). When the water drips into a cave with lower CO₂, CO₂ escapes and calcite or aragonite is deposited in layers. Because speleothems such as stalagmites can be dated precisely back to about 600,000 years by uranium–thorium dating, records from caves such as Hulu, Sanbao, and Dongge in China provide a well-dated record of monsoon variability on orbital (about 23,000-year precession) and millennial timescales. The interpretation of Chinese speleothem δ¹⁸O as local rainfall amount is debated; it may also reflect changes in moisture source and atmospheric circulation. Speleothem δ¹³C and trace-element ratios (Mg/Ca and Sr/Ca) record soil activity, vegetation changes, and drought.
• Fossil leaves: for periods beyond the range of ice cores, fossil leaves provide two widely used proxies:
• Stomatal index: F. Ian Woodward showed in 1987 that plants produce fewer stomata when CO₂ is higher. The stomatal index, SI = [_S_/(S + E)] × 100%, where S is the number of stomata and E the number of other epidermal cells, is therefore inversely related to atmospheric CO₂. Applied to fossil leaves of species with living relatives such as Ginkgo and Metasequoia, or combined with gas-exchange models, it is used to reconstruct past CO₂.
• Leaf margin analysis: in floras of woody flowering plants, the proportion of species with smooth (untoothed) leaf margins increases with mean annual temperature. Leaf margin analysis and the related multivariate method CLAMP are used to estimate land temperatures in the Late Cretaceous and Cenozoic. It has been hypothesized that teeth enhance early-season sap flow and photosynthesis in cool climates.

Continuous ice-core records extend back only about a million years. Climate over the Cenozoic and Mesozoic eras (back to about 180 million years, the age of the oldest surviving oceanic crust) is therefore reconstructed mainly from marine sediment cores recovered by scientific ocean drilling, including the International Ocean Discovery Program and its predecessors, supplemented on land by lake sediment cores. Open-ocean sediments typically accumulate at 1 to 5 cm per 1,000 years, but rates of 10 to 100 cm per 1,000 years in sediment drifts allow centennial-scale changes to be resolved.

Much of Cenozoic paleoceanography is based on the chemistry of the calcite shells of foraminifera, single-celled organisms. Planktonic species such as Globigerinoides ruber and Trilobatus sacculifer live in the upper 200 m and record surface conditions. Benthic species such as Cibicidoides wuellerstorfi and Uvigerina peregrina live on or in the seafloor and record deep-water conditions.

In 1947, Harold Urey showed that when calcium carbonate forms in equilibrium with water, it is enriched in ¹⁸O relative to the water, and that this enrichment decreases as temperature rises, by about 0.21 to 0.23‰ per °C. Samuel Epstein and colleagues developed this into an empirical paleotemperature equation in 1953, later revised by Harmon Craig. It relates calcification temperature T (°C) to the δ¹⁸O of the shell (δ¹⁸O_c, on the VPDB scale) and of the seawater (δ¹⁸O_w, converted from VSMOW by subtracting 0.27‰):

The method was applied to deep-sea cores by Cesare Emiliani in 1955. In 1967, Nicholas Shackleton showed, using benthic foraminifera from the deep ocean, where temperature cannot fall much below freezing, that foraminiferal δ¹⁸O depends on two factors:

1. Water temperature: cooling by 1 °C increases δ¹⁸O_c by about 0.22‰.
2. Global ice volume: snow that builds ice sheets is strongly depleted in ¹⁸O (δ¹⁸O of about −30 to −45‰). When large ice sheets such as the Laurentide and Fennoscandian ice sheets grow, they remove isotopically light water from the ocean, leaving seawater enriched in ¹⁸O. At the Last Glacial Maximum (about 21,000 years ago), about 50 million km³ of ice lowered sea level by about 120 to 130 m and raised the δ¹⁸O of the whole ocean by about 1.0‰, roughly 0.008‰ per metre of sea-level fall. Surface waters are also affected locally by evaporation and precipitation.

Deep waters were also about 2 to 3 °C colder at the Last Glacial Maximum, adding about 0.5 to 0.7‰. The total difference in benthic δ¹⁸O between glacial and interglacial conditions is therefore about 1.5 to 1.8‰. Stacks of records from many cores, notably the LR04 stack of Lisiecki and Raymo (covering the past 5.3 million years) and the CENOGRID compilation (covering the whole 66-million-year Cenozoic), define the marine isotope stages (MIS). Odd-numbered stages are warm periods with low δ¹⁸O, such as MIS 1 (the Holocene), MIS 5e (the last interglacial, about 125,000 years ago), and MIS 11 (about 400,000 years ago). Even-numbered stages are cold periods with high δ¹⁸O, such as MIS 2, which includes the Last Glacial Maximum.

The carbon isotope ratio (δ¹³C) of benthic foraminifera records that of deep-water dissolved inorganic carbon. Phytoplankton preferentially take up ¹²C (organic matter has δ¹³C of about −22‰), leaving surface waters enriched in ¹³C (about +2‰). Newly formed North Atlantic Deep Water therefore has relatively high δ¹³C (about +1‰). Water that has spent longer in the deep ocean accumulates ¹²C from decomposing organic matter and has lower values: about +0.3 to +0.5‰ in Antarctic bottom water and around 0‰ or slightly below in the deep North Pacific. Benthic δ¹³C, together with cadmium/calcium ratios, neodymium isotopes (ε_Nd), and protactinium/thorium (²³¹Pa/²³⁰Th) ratios, is used to reconstruct past changes in the Atlantic meridional overturning circulation (AMOC).

Because foraminiferal δ¹⁸O depends on both temperature and seawater δ¹⁸O, it is combined with other proxies that depend mainly on temperature:

Major marine temperature and carbon-system proxies

Combining marine, ice-core, and terrestrial records shows how the Earth system responds both to astronomical forcing and to feedbacks within the climate system.

Variations in Earth's orbit and axial tilt, caused mainly by the gravitational influence of Jupiter, Venus, Saturn, and the Moon, were proposed as a cause of ice ages by Joseph Adhémar and James Croll in the 19th century and were placed on a quantitative basis by the Serbian scientist Milutin Milanković between 1920 and 1941. These Milankovitch cycles consist of three components:

• Eccentricity (periods of about 100,000 and 405,000 years): the departure of Earth's orbit from a circle, ranging from nearly 0 to about 0.058 (currently 0.0167). Eccentricity is the only orbital parameter that changes the total sunlight Earth receives over a year, which varies as (1 − e²)^−1/2. This changes global annual mean insolation by at most about 0.2% (about 0.5 W/m²), too little to drive ice ages directly, but eccentricity controls the strength of the precession cycle.
• Obliquity (period of about 41,000 years): the tilt of Earth's axis, which varies between about 22.1° and 24.5° (currently 23.44° and decreasing). Greater tilt strengthens the seasons in both hemispheres and increases annual mean sunlight at high latitudes. Lower tilt gives cooler high-latitude summers, allowing winter snow to survive and ice sheets to grow.
• Precession (periods of about 19,000 and 23,000 years): the slow change in the orientation of Earth's axis and the rotation of its orbit, which together determine the season in which Earth is closest to the Sun (perihelion). Precession has opposite effects in the two hemispheres, and its effect disappears when the orbit is circular. Combined with high eccentricity, it can change summer insolation at 65°N by about 100 W/m² (about 20%) between its extremes.

In 1976, James Hays, John Imbrie, and Nicholas Shackleton published the spectral analysis "Variations in the Earth's Orbit: Pacemaker of the Ice Ages", which showed that variations in global ice volume recorded in deep-sea cores contain the 100,000-, 41,000-, and 23,000/19,000-year orbital periods. The results were consistent with Milankovitch's proposal that summer insolation at high northern latitudes controls ice-sheet growth. Because the orbital changes mainly redistribute sunlight by season and latitude, they act as a pacemaker that triggers strong feedbacks within the climate system. These include the ice–albedo feedback, ice-sheet elevation feedbacks, changes in dust, and changes in atmospheric CO₂ of about 90 to 100 ppm between glacial and interglacial periods, much of it attributed to changes in the Southern Ocean.

Benthic δ¹⁸O records also reveal the Mid-Pleistocene Transition, between about 1.25 and 0.7 million years ago, which occurred without any change in orbital forcing. Before it, glacial cycles followed the 41,000-year obliquity cycle and had moderate amplitude. Afterward, they became larger, strongly asymmetric cycles of about 100,000 years, with slow ice growth over 80,000 to 90,000 years followed by rapid deglaciations (terminations) lasting about 10,000 years. One leading hypothesis is that erosion of soft sediment beneath the North American ice sheets exposed hard bedrock, allowing ice sheets to grow thicker before collapsing. Long-term decline in atmospheric CO₂ has also been proposed.

Greenland ice cores and North Atlantic sediments show that the last glacial period was punctuated by repeated abrupt climate changes:

• Dansgaard–Oeschger events: about 25 events occurred between 115,000 and 12,000 years ago. In each, Greenland changed abruptly from a cold stadial to a milder interstadial state, warming by about 5 to 16 °C within a few decades. These warmings were accompanied by increased snowfall, reduced dust, and a rise in atmospheric methane of about 50 to 200 ppb, as tropical wetlands expanded with a northward shift of the Intertropical Convergence Zone. Each event was followed by gradual cooling over centuries.
• Heinrich events: during some of the coldest stadials, roughly every 7,000 to 10,000 years, parts of the Laurentide Ice Sheet collapsed through Hudson Strait, releasing large numbers of icebergs into the North Atlantic. As they melted, the icebergs deposited distinctive layers of ice-rafted debris rich in carbonate rock. Proposed causes include internal oscillations of the ice sheet ("binge–purge" cycles) and warming of subsurface ocean water.
• The bipolar seesaw: these events, and the Younger Dryas cold interval (12,900 to 11,700 years ago), are thought to involve changes in the Atlantic meridional overturning circulation. Freshwater from melting ice is thought to have weakened the formation of North Atlantic Deep Water, allowing sea ice to spread south across the North Atlantic. Because the AMOC normally carries heat northward across the equator, weakening it causes heat to accumulate in the Southern Hemisphere. Ice cores synchronized using methane records confirm this pattern, described by Wallace Broecker and formalized as the thermal bipolar seesaw by Thomas Stocker and Sigfus Johnsen. While Greenland is cold, Antarctica gradually warms; when the AMOC strengthens and Greenland warms abruptly, Antarctica begins to cool.

Over the Cenozoic, Earth passed through four broad climate states: a "Warmhouse" in the Paleocene and the middle to late Eocene, a "Hothouse" around the early Eocene (about 56 to 47 million years ago), a "Coolhouse" from the Oligocene to the Pliocene, and an "Icehouse" from about 3.3 million years ago, with large ice sheets in both hemispheres. Warm intervals provide analogues for high-CO₂ climates and help constrain long-term climate sensitivity:

• Paleocene–Eocene Thermal Maximum (PETM, about 56 million years ago): the most prominent rapid warming event of the Cenozoic. Over an onset of a few thousand years, a large release of carbon, probably linked to volcanism in the North Atlantic Igneous Province and the heating of organic-rich sediments, produced a negative carbon isotope excursion of about 3 to 5‰ (larger in some land records). Estimates of the amount of carbon released range from about 3,000 to more than 10,000 PgC. Global temperatures rose by about 5 to 6 °C above an already warm, ice-free climate, with Arctic sea surface temperatures reaching about 23 °C. Ocean acidification raised the carbonate compensation depth by more than 2 km, dissolving seafloor carbonate and causing a major extinction of benthic foraminifera. Recovery, largely through silicate weathering, took about 120,000 to 200,000 years. Even so, the rate of carbon release during the PETM (probably less than about 1.5 PgC/yr) was roughly ten times slower than present fossil-fuel emissions (about 10 PgC/yr).
• Mid-Pliocene Warm Period (about 3.3 to 3.0 million years ago): the most recent time when atmospheric CO₂ was similar to today (about 350 to 450 ppm, from boron isotopes and alkenone carbon isotopes) and continents were in nearly their present positions. Global temperature was about 2.5 to 4 °C above pre-industrial levels, forests grew in the Canadian High Arctic, and reduced ice sheets in Greenland and Antarctica kept sea level roughly 10 to 25 m higher than today.
• Equilibrium climate sensitivity and Earth system sensitivity: by combining estimates of past radiative forcing with reconstructed global temperature changes for the Last Glacial Maximum, the Pliocene, and the Eocene (an approach set out by the PALAEOSENS project), paleoclimatology distinguishes two measures of the response to a doubling of CO₂ (a forcing of about 3.9 W/m²):

1. Equilibrium climate sensitivity (ECS; likely about 2.5 to 4 °C, best estimate about 3 °C) includes fast feedbacks, such as water vapour, lapse rate, clouds, snow, and sea ice, but treats ice sheets and vegetation as fixed. Paleoclimate evidence makes values below about 1.5 °C extremely unlikely.
2. Earth system sensitivity (ESS) also includes slow feedbacks acting over centuries to millennia, such as changes in ice sheets, vegetation, and natural greenhouse gases. It is considerably larger, with estimates of about 4 to 6 °C or more, and describes the long-term warming that would follow a sustained increase in CO₂.

• Geologic temperature record
• Ice age
• Paleoclimate modelling
• Historical climatology
• Temperature record of the last 2,000 years