Earth’s Climate History from 4.5 Billion Years to One Minute

ABSTRACT

Earth’s climate history is important for understanding the dynamics and feedbacks of the climate system. However, atmospheric sciences generally focus on shorter timescales, while geological sciences focus on longer timescales, but a unified picture is desired. This paper reviews the observations of Earth’s climate history from 4.5 billion years to one minute with emphasis on temperature, sea level, and atmospheric carbon dioxide. Earth’s climate history shows dominant climate modes such as the supercontinent cycles, interglacial cycles, millennial cycles, multi-decadal oscillation, interannual oscillation, seasonal cycle and diurnal cycle. The amplitudes of the dominant climate variability generally decrease from the billion-year timescales to interannual timescales, then significantly increase at subannual to diurnal timescales.

RéSUMé

[Traduit par la redaction] L’histoire du climat de la Terre est importante pour comprendre la dynamique et les rétroactions du système climatique. Cependant, les sciences atmosphériques mettent généralement l’accent sur des échelles de temps plus courtes, tandis que les sciences géologiques se concentrent sur des échelles de temps plus longues, mais une image unifiée est souhaitée. Le présent article passe en revue les observations de l’histoire du climat de la Terre, de 4,5 milliards d’années à une minute, en mettant l’accent sur la température, le niveau de la mer et le dioxyde de carbone atmosphérique. L’histoire du climat de la Terre montre des modes climatiques dominants tels que les cycles des supercontinents, les cycles interglaciaires, les cycles millénaires, les oscillations multidécennales, les oscillations interannuelles, les cycles saisonniers et les cycles diurnes. Les amplitudes de la variabilité climatique dominante diminuent généralement de l’échelle de temps des milliards d'années à l’échelle de temps interannuelle, puis augmentent de manière significative à l’échelle de temps subannuelle et diurne.

KEYWORDS:

• Earth’s clime history
• palaeotemperature
• sea level change
• carbon dioxide

1 Introduction

The planet Earth, our beautiful hometown, was born 4.54 billion years ago together with the birth of the Sun and the whole solar system (Holmes, 1946, 1956; Patterson, 1956), which was long after the big bang of the universe 13.8 billion years ago (Planck Collaboration, 2016). The Earth has gone through four eons: Hadean, Archean, Proterozoic and Phanerozoic (Schmitz & Ogg, 2012; Fig. 1A). Evidence from detrital zircons suggest that the Earth’s crust and oceans formed by 4.3 billion years ago (Ackerson et al., 2018; Mojzsis et al., 2001; Piani et al., 2020; Ushikubo et al., 2008; Valley et al., 2002, 2014; Watson & Harrison, 2005; Wilde et al., 2001), and there have been five major supercontinent cycles with the assembly and breakup of supercontinents Kenorland, Nuna/Columbia, Rodinia, Gondwana/Pannotia, and Pangea (Hawkesworth et al., 2016; Fig. 1B). Microfossils and other evidence indicate that the earliest life on Earth appeared 3.77–4.5 billion years ago (Betts et al., 2018; Dodd et al., 2017; Knoll & Nowak, 2017; Fig. 1C).

Fig. 1 (A) The geological timescale (adapted from image by Jonathan R. Hendricks. Image in the public domain). (B) History of Earth’s crust and plate tectonics (from Hawkesworth et al., 2016). (C) Evolution of life (from Knoll & Nowak, 2017).

In a sphere shape, the Earth has a well-defined four-layer structure, including the atmosphere, hydrosphere, mantle and core (Fig. 2). Earth’s climate refers to the state of its outer layers. The global climate system is generally defined to have five components: the atmosphere, ocean, land, sea ice and biogeochemical cycles. The basic structure of the global climate system includes the zonal-mean Hadley circulation, Ferrel circulation and polar circulation, tropical Walker circulation, stratospheric Brewer-Dobson circulation, upper ocean upwelling and gyres, deep ocean thermohaline circulation, ice sheet volume change and sea ice change, and greenhouse gas changes. The global climate system is modulated by external radiative forcing, external gravitational forcing, plate tectonics, and various internal feedbacks such as circulation-convection feedback (Byers & Braham, 1948; Lin et al., 2006, 2015; Zipser, 1977), ocean-atmosphere feedback (Bjerknes, 1969; Lin, 2007; Wallace, 1992), land-atmosphere feedback (Brooks, 1928; Dirmeyer et al., 2012; Koster et al., 2004), ice-atmosphere feedback (Imbrie & Imbrie, 1980; Saltzman et al., 1984), as well as radiative feedbacks by clouds, aerosols and carbon cycle (Bony & Dufresne, 2005; Friedlingstein et al., 2014; Lin et al., 2014; Soden & Vecchi, 2011; Webb et al., 2006). These external forcings and internal feedbacks generate a wide spectrum of significant and complex climate variability such as the supercontinent cycle (Nance et al., 1986, 2014; Worsley et al., 1982), Phanerozoic cycles (Shaviv & Veizer, 2003; Veizer et al., 2000), interglacial cycles (Hays et al., 1976; Past Interglacials Working Group of PAGES, 2016; Raymo, 1997), millennial Heinrich/Dansgaard–Oeschger/Bond events (Bond et al., 2001; Dansgaard et al., 1993; Heinrich, 1988), Atlantic Multi-decadal Oscillation (Enfield et al., 2001; Schlesinger & Ramankutty, 1994), Pacific Decadal Oscillation/Interdecadal Pacific Oscillation (Zhang et al., 1997), El Nino-Southern Oscillation (Bjerknes, 1969), seasonal monsoons, intraseasonal Madden-Julian Oscillation (Madden & Julian, 1971), convectively coupled equatorial waves (Wheeler & Kiladis, 1999) and diurnal variation, as well as disastrous extremes such as droughts, floods, heat waves, tropical cyclones, winter blizzards, thunderstorms and tornadoes (Fig. 2).

Fig. 2 (Upper) The Earth system with external forcings and internal climate feedbacks. (Lower) Dominant variability and disastrous extremes of Earth’s climate system.

Traditionally, geological sciences often focus on thousands to billion years before the present (e.g. Gradstein et al., 2004; Holmes, 1947, 1960; Schmitz & Ogg, 2012), while atmospheric sciences generally focus on the recent centuries (e.g. IPCC, 1990, 1995, 2001, 2007, 2013; U.S. Committee for the Global Atmospheric Research Program, 1975), but a unified picture of the Earth’s climate history is desired. Kutzbach and Bryson (1974) first presented a variance spectrum of temperature fluctuations on time scales from 1 to 10,000 years from a combination of botanical, chemical, historical and instrumental records from locations in the North Atlantic sector. Mitchell (1976) presented a variance spectrum of climatic variability that spans all time scales from about one hour (10⁻⁴ years) to the age of the Earth (Fig. 3). However, observations were quite limited at that time, with the interglacial cycles just discovered in that year (Hays et al., 1976). Mitchell stated that “it is to be emphasized that the spectrum portrayed there is little more than an educated guess as to many details shown, especially those for periods longer than l0⁵ years. The most that I would wish to claim for the veracity of Fig. 1 is (1) that spectral peaks appear to belong everywhere that they are shown in Fig. 1, whether or not they are shown correctly as to relative shape, magnitude, and width; (2) that the spectrum between periods of 10 and l0⁵ years is consistent with the general picture of Quaternary climatic history published in Fig. A.2 of U.S. Committee for GARP (1975); and (3) that the spectrum for periods shorter than 10 years is consistent with instrumental observations of atmospheric variability in the twentieth century (see, e.g. Griffith et al., 1956)”. Later studies on the spectra of different timescales often focused on the shape of the background continuum (Ditlevsen et al., 2020; Franzke et al., 2020; Huybers & Curry, 2006; Lovejoy, 2015; Nilsen et al., 2016; Paillard, 2001; Pelletier, 1997; Shao & Ditlevsen, 2016; von der Heydt et al., 2021; Williams et al., 2017; Wunsch, 2003).

Fig. 3 Estimated relative variance of climate over all periods of variation (from Mitchell, 1976).

This paper reviews the observations of Earth’s climate history from 4.5 billion years to one minute with emphasis on surface temperature, sea level, and atmospheric carbon dioxide. These variables are the common topics of palaeoclimate research at different timescales and have the largest number of observational datasets. Among them, surface temperature has the largest number of observations across all timescales, followed by sea level, and atmospheric carbon dioxide. Other important variables, such as precipitation and wind circulation, are more difficult to derive from palaeoclimate proxies and do not have complete coverage for different timescales. Therefore, in this paper, we will focus on surface temperature, sea level, and atmospheric carbon dioxide. Section 2 will review the palaeoclimate proxies. Section 3 will review Earth’s surface temperature history. Section 4 will review Earth’s sea-level history. Section 5 will review Earth’s CO₂ history. For each variable, we will zoom in from Precambrian starting 4.54 billion years (Ga) ago to the current Phanerozoic eon staring 541 million years (Ma) ago and the Cenozoic era staring 66 Ma ago, to the current Quaternary period starting 2.6 Ma ago and the last glacial cycle starting 110 thousand years (ka) ago, to the current Holocene epoch starting 11.8 ka ago and the past two millennia, to the past 140 years with modern instrument records available, and to sub-annual to diurnal variations. Summary and discussions will be given in Section 6.

2 Palaeoclimate proxies

Fig. 4 summarizes the methods for observing Earth’s climate and weather. Palaeoclimatology began in the seventeenth century but started to flourish in the twentieth century after radioisotopic dating and stable isotope analysis were developed. Robert Hooke (1635–1703) is sometimes regarded as the first scientist in palaeoclimatology (Schwartzbach, 1963). Hooke observed giant turtles and oversized ammonites in the Portlandian (uppermost Jurassic) of Dorset in England and concluded that they indicated a once warmer climate. Stenonis (1669) set up the basic principles for stratigraphy, and Smith (1815, 1816) applied them to large-scale settings. Rutherford (1905) pioneered radioisotopic dating, and modern techniques of mass spectrometry were devised by Dempster (1918) and Aston (1919). Various palaeoclimate proxies were adopted in early- to mid-twentieth century, such as tree rings (Shvedov, 1892; Douglass, 1909; Kapteyn, 1914), ocean sediments (Kullenberg, 1947; Pfleger, 1948; Arrhenius et al., 1951; Emiliani, 1955), speleothems (Orr, 1952, 1953; Broecker et al., 1960), and ice cores (Coachman et al., 1958; Scholander et al., 1962; Langway et al., 1965; Dansgaard et al., 1969). The time periods covered by each type of proxies are shown in Fig. 4. In the past 100 years, numerous samples have been collected and analyzed, and the results have been compiled into data archives, such as the Precambrian and Phanerozoic GEOROC database and Veizer database (GEOROC, 2020; Shields & Veizer, 2002; Veizer & Prokoph, 2015; Fig. 5A), and the Quaternary, Holocene and Common Era datasets in the NOAA NCEI Palaeoclimatology data archive. The amount of data increases from Quaternary (Lisiecki & Stern, 2016; Shakun et al., 2015; Fig. 5B), to Holocene (Kaufman et al., 2020; Fig. 5C), to Common Era (PAGES 2k Consortium, 2017; Fig. 5D). After a large amount of data had accumulated, palaeoclimate field reconstructions were developed (Fritts, 1965; Stockton & Meko, 1975; Cook & Jacoby, 1977). The recent PAGES 2K consortium is the largest international effort in the history of palaeoclimatology to reconstruct the climate history of the common era (Anchukaitis & McKay, 2014; PAGES 2k Consortium, 2017), which has led to the latest continent-scale temperature reconstructions (PAGES 2k Consortium, 2013) and the first generation of palaeoclimate reanalysis (Hakim et al., 2016; Steiger et al., 2018).

Fig. 4 Observations of Earth’s climate and weather.

Fig. 5 Temperature records for (A) Precambrian and Phanerozoic (single, used in this study), (B) Quaternary (continuous, used in this study), (C) Holocene (from Kaufman et al., 2020), (D) Common Era (from PAGES 2k Consortium, 2017), (E) Modern land surface stations (number of years with measurements. Triangles are ARM stations. Adapted from Lawrimore et al., 2011), and (F) Modern SST (number of observations between 1880 and 1889, from Woodruff et al., 2011). (G) Modern tidal gauge stations (from Dangendorf et al., 2019). (H) Modern CO₂ stations with flask (red) and continuous (blue) measurements (from Ciais et al., 2014).

Table 1 lists the major palaeoclimate temperature datasets. There are many methods for temperature reconstruction, such as d¹⁸O, d³⁰Si, dH, TEX-86, Alkenone, Mg/Ca and Sr/Ca. SST is often derived using Alkenone and Mg/Ca methods. The alkenone-derived palaeotemperature estimates are based on the conversion of the abundance ratios of long-chain unsaturated alkenones with two to three double bonds into SST (Muller et al., 1998). The alkenone SST proxy accuracy and precision has been internationally calibrated and standardized amongst 24 laboratories worldwide (Rosell-Mele et al., 2001). The Mg/Ca ratio measured on surface-dwelling planktonic foraminifera is a well-established SST proxy that has been internationally calibrated by 25 laboratories (Greaves et al., 2008; Rosenthal et al., 2004). Temperature over land is often estimated using stable isotopic proxies. The d¹⁸O measurements provide excellent palaeotemperature records (Dansgaard, 1964; Rozanski et al., 1992, 1993; Urey, 1947), and are converted to temperature through regional empirical scales for ocean sediments (Bemis & Spero, 1998; Duplessy et al., 2002; Epstein et al., 1953; Shackleton, 1974), Greenland ice cores (Alley, 2000; Cuffey et al., 1995; Dahl-Jensen et al., 1998; Johnsen et al., 1995; Kindler et al., 2014), Antarctica ice cores (Graf et al., 2002), tropical ice cores (Thompson et al., 2000; Yao et al., 1996; Yu et al., 2021), tropical and mid-latitude speleothem cores (Dorale et al., 1998; Lachniet, 2009; Mangini et al., 2005), and lake sediments (Leng & Marshall, 2004; Stansell et al., 2017; von Grafenstein et al., 1999). dH is often used for the Antarctica ice cores (Jouzel et al., 2007), and d³⁰Si is often used for deriving Precambrian temperature.

Table 1. Palaeoclimate temperature datasets used in this study.

Region (abbrevition)	Project/site	Material	Method	Reference
Global (GLB)	Precambrian	Cherts	d30Si	Robert and Chaussidon (2006) Andre et al. (2006) van den Boorn et al. (2007) Steinhoefel et al. (2009) Abraham et al. (2011) Heck et al. (2011) Chakrabarti et al. (2012) Ding et al. (2017)
	Precambrian	Cherts	d18O	Tartese et al. (2017) Robert and Chaussidon (2006)
	Precambrian	Marine carbonate	d18O	Veizer and Prokoph (2015) Shields and Veizer (2002) Veizer et al. (1999)
	Precambrian	Resurrected proteins	Biological	Gaucher et al. (2008)
	Precambrian	Biological species	Biological	Schwartzman (2015)
	Phanerozoic	Marine carbonate	d18O	Verard and Veizer (2019)
	Phanerozoic	Marine carbonate	d18O	Song et al. (2019)
	Phanerozoic	Ocean sediment	d18O	Westerhold et al. (2020)
	Cenozoic	Ocean sediment	d18O	Mudelsee et al. (2014)
	Cenozoic	Ocean sediment	d18O	Cramer et al. (2009)
	Cenozoic	Ocean sediment	d18O	Huang et al. (2007)
	Cenozoic	Ocean sediment	d18O	Zachos et al. (2001)
	Quaternary	Ocean sediment	Model	Stap et al. (2016)
	Quaternary	Ocean sediment	Alkenone Mg/Ca	Shakun et al. (2015)
	Quaternary	Ocean sediment	d18O	Waelbroeck et al. (2002)
	Holocene	Multiple	Multiple	Kaufman et al. (2020)
	Holocene	Multiple	Multiple	Marcott et al. (2013)
	Common Era	Multiple	Multiple	PAGES 2k Consortium (2013)
	Common Era	Coral	Multiple	Tierney et al. (2015)
Northern Hemisphere (NH)	Quaternary	Ocean sediment	Model	de Boer et al. (2014)
	Common Era	Tree Ring		Guillet et al. (2017)
	Common Era	Tree Ring		Wilson et al. (2016)
	Common Era	Tree Ring		Schneider et al. (2015)
	Common Era	Multiple	Multiple	Ljungqvist (2010)
	Common Era	Multiple	Multiple	Mann et al. (2009)
	Common Era	Multiple	Multiple	Moberg et al. (2005)
	Common Era	Tree ring	Multiple	Esper et al. (2002)
	Common Era	Multiple	Multiple	Briffa (2000)
Continental Mean	Europe	Tree Ring		Luterbacher et al. (2016)
	Asia	Tree Ring		Cook et al. (2013)
	North America	Tree Ring		Trouet et al. (2013)
	South America	Multiple
	Australia	Multiple		Gergis et al. (2016)
	Arctic Antarctica	Multiple Multiple		Werner et al. (2018)
Antarctica (ANT)	EPICA Dome C	Ice core	dH	EPICA Community Members (2010)
	Vostok	Ice core	dH	EPICA Community Members (2010)
	EDML	Ice core	d18O	EPICA Community Members (2010)
	TALDICE	Ice core	d18O	Stenni et al. (2011)
	WAIS	Ice core	d18O	Steig et al. (2013)
Arctic (ARC)	NGRIP	Ice core	d18O	NGRIP Community Members (2004)
	GISP2	Ice core	d18O	Alley (2000)
	GRIP	Ice core	d18O	Vinther et al. (2010)
Africa (AFR)	Lake Malawi	Lake sediment	TEX86	Johnson et al. (2016)
	Kilimanjaro	Ice core	d18O	Thompson et al. (2002)
	Cold Air Cave	Speleothem	d18O	Holmgren et al. (1999)
	Lake Bosumtwi	Lake sediment	d18O	Shanahan et al. (2009)
	Dante Cave	Speleothem	d18O	Voarintsoa et al. (2016)
Asia (ASIA)	Sanbao Cave	Speleothem	d18O	Cheng et al. (2016)
	Borneo	Speleothem	d18O	Carolin et al. (2013)
	Borneo	Speleothem	d18O	Meckler et al. (2012)
	Soreq Cave	Speleothem	d18O	Grant et al. (2012)
	Soreq Cave	Speleothem	d18O	Bar-Matthews et al. (2003)
	Guliya	Ice core	d18O	Thompson et al. (1997)
	Dongge Cave	Speleothem	d18O	Yuan et al. (2004)
	Kesang Cave	Speleothem	d18O	Cheng et al. (2016)
	Tonnelnaya cave	Speleothem	d18O	Cheng et al. (2016)
Australia (AUS)	Cave KNI-51	Speleothem	d18O	Denniston et al. (2017)
	Mt. Arthur	Speleothem	d18O	Hellstrom et al. (1998)
	New Zealand	Speleothem	d18O	Williams et al. (2010)
Europe (EUR)	Cueva de Asiul	Speleothem	d18O	Smith et al. (2016)
	Spannagel Cave	Speleothem	d18O	Fohlmeister et al. (2013)
	Ammersee	Lake sediment	d18O	von Grafenstein et al. (1999)
	Lake Nuudsaku	Lake sediment	d18O	Stansell et al. (2017)
North America (NAM)	Devils Hole	Speleothem	d18O	Landwehr et al. (2011)
	Devils Hole	Speleothem	d18O	Moseley et al. (2016)
	Leviathan	Speleothem	d18O	Lachniet et al. (2017)
	Pink Cave	Speleothem	d18O	Asmerom et al. (2007)
	Buckeye Creek Cave	Speleothem	d18O	Cheng et al. (2019)
	Lac Aurelie	Lake sediment	d18O	Bajolle et al. (2018)
	Alaska lakes	Lake sediment	Midge	Clegg et al. (2011)
	North America	Pollen	Pollen	Viau et al. (2006)
South America (SAM)	Botuverá Cave	Speleothem	d18O	Cruz et al. (2005)
	Santiago Cave	Speleothem	d18O	Mosblech et al. (2012)
	Huascarán	Ice core	d18O	Thompson et al. (1995)
	Sajama	Ice core	d18O	Thompson et al. (1998)
	Laguna Pumacocha	Lake sediment	d18O	Bird et al. (2011)
	Cascayunga Cave	Speleothem	d18O	Wang et al. (2017)
Indian Ocean (IND)	ODP722	Ocean sediment	Alkenone	Herbert et al. (2010)
	SO189	Ocean sediment	Mg/Ca	Mohtadi et al. (2014)
Tropical Western Pacific (TWP)	ODP806B	Ocean sediment	Mg/Ca	Medina-Elizalde and Lea (2005)
	ODP1145	Ocean sediment	Mg/Ca	Oppo and Sun (2005)
	MD81	Ocean sediment	Mg/Ca	Stott et al. (2004)
	Borneo	Speleothem	d18O	Carolin et al. (2016)
Tropical eAstern Pacific (TEP)	ODP846	Ocean sediment	Alkenone	Herbert et al. (2010)
	TR163-22	Ocean sediment	Mg/Ca	Lea et al. (2006)
	ME0005A-24JC	Ocean sediment	Alkenone	Dubois et al. (2014)
	ME0005A-24JC	Ocean sediment	Alkenone	Kienast et al. (2006)
	RC11-238	Ocean sediment	Alkenone	Koutavas and Sachs (2008)
	KN176-2	Ocean sediment	Alkenone	Pahnke et al. (2007)
Northwestern Pacific (NWP)	MD882	Ocean sediment	Alkenone	Martínez-Garcia et al. (2010)
	MD01-2421	Ocean sediment	Alkenone	Yamamoto et al. (2005)
	MD01-2421	Ocean sediment	d18O	Oba and Murayama (2004)
	MD01-2412	Ocean sediment	Alkenone	Harada et al. (2006)
	IDOP U1429	Ocean sediment	Mg/Ca	Clemens et al. (2018)
Southwestern Pacific (SWP)	MD97-2120	Ocean sediment	Mg/Ca	Pahnke et al. (2003)
Northeastern Pacific (NEP)	ODP1020	Ocean sediment	Alkenone	Herbert et al. (2001)
	ODP1012	Ocean sediment	Alkenone	Herbert et al. (2001)
	ODP1019	Ocean sediment	Alkenone	Barron et al. (2003)
Southeastern Pacific (SEP)	ODP1233	Ocean sediment	Alkenone	Kaiser et al. (2005)
North Atlantic (NAO)	ODP982	Ocean sediment	Alkenone	Lawrence et al. (2009)
	MD01-2443	Ocean sediment	Alkenone	Martrat et al. (2007)
	SU8118 and MD952042	Ocean sediment	Alkenone	Bard (2002)
	MD952042	Ocean sediment	d18O	Shackleton et al. (2000)
	MD99-2275	Ocean sediment	Alkenone	Sicre et al. (2008)
TROPICAL Atlantic (TAO)	ODP662	Ocean sediment	Alkenone	Herbert et al. (2010)
	MD03-2707	Ocean sediment	Mg/Ca	Weldeab et al. (2007)
	GeoB3129/3911	Ocean sediment	Mg/Ca	Weldeab et al. (2006)
	M35003-4	Ocean sediment	Alkenone	Ruehlemann et al. (1999)
	ODP658C	Ocean sediment	Alkenone	Zhao et al. (1995)
South Atlantic (SAO)	ODP1090	Ocean sediment	Alkenone	Martínez-Garcia et al. (2010)
	MD02-2594	Ocean sediment	Mg/Ca	Dyez et al. (2014)

Table 2 lists the major palaeoclimate sea level and CO₂ datasets. Sea level can be estimated from shoreline markers, reefs and atolls, oxygen isotopes, Sr isotopes, borehole drilling, sequence stratigraphy, and palaeogeographic maps. CO₂ concentrations can be retrieved using ice cores, stomata, marine carbon isotopes, palaeosols, phytoplankton, liverworts, boron-d¹¹B, boron-B/Ca, nahcolite, calcified cyanobacteria, aeronomical evidence, and data-driven biogeochemical models. Table 3 lists the modern instrument datasets for surface temperature, sea level and CO₂. The global maps of stations are shown for land surface temperature observations (Fig. 5E, Lawrimore et al., 2011), sea surface temperature observations (Fig. 5F, Woodruff et al., 2011), tidal gauge stations (Fig. 5G, Dangendorf et al., 2019), and surface CO₂ stations (Fig. 5H, Ciais et al., 2014).

Table 2. Palaeoclimate sea level and CO₂ datasets used in this study.

Variable	Material/method	Reference
Sea Level	Precambrian d87Sr/86Sr Phanerozoic Sea Level Datasets Quaternary Sea Level Datasets Holocene Sea Level Datasets	Shields and Veizer (2002) Veizer et al. (1999) GEOROC Miller et al. (2020) Verard et al. (2015) Miller (2005) Hallam (1989) Exxon (1988) Haq et al. (1987) Spratt and Lisiecki (2016) Shakun et al. (2015) de Boer et al. (2014) Grant et al. (2014) Bintanja et al. (2005) Lea et al. (2002) Waelbroeck et al. (2002) Grant et al. (2012) Arz et al. (2007) Siddall et al. (2003) Lambeck et al. (2014) Angulo et al. (1997) Kopp et al. (2016) Kemp et al. (2018)
CO2	Precambrian CO2 Datasets Phanerzoic CO2 Datasets Quaternary and Holocene CO2 Datasets	Sheldon (2006) Mitchell and Sheldon (2010) Sheldon and Tabor (2009) Kaufman and Xiao (2003) Rye et al. (1995) Hessler et al. (2004) Kah and Riding (2007) Lichtenegger et al. (2010) Schrag et al. (2013) Royer (2014) Berner (2006) Petit et al. (1999) Beerling and Royer (2011) Zhang et al. (2013) Foster et al. (2017) Bereiter et al. (2015) Bauska et al. (2021) Ahn and Brook (2008) Kawamura et al. (2003) Barnola et al. (1987) Lisiecki (2010) Bereiter et al. (2012) Smith et al. (1997) McElwain et al. (2002) Kouwenberg (2004) Ahn et al. (2012) Indermuhle et al. (1999) Oyabu et al. (2020) Meinshausen et al. (2017)

Table 3. Modern instrument datasets used in this study.

Variables	Datasets	Time Period	Reference
Land-Ocean Surface Temperature	National Aeronautics and Space Administration (NASA) Goddard Institute for Space Studies (GISS) Hadley Center/Climatic Research Unit (HadCRUT) National Oceanic and Atmospheric Administration (NOAA) National Center for Environmental Information (NCEI)	1880–2016 1880–2016 1880–2016	Hansen et al. (2010) Morice et al. (2012) Vose et al. (2012)
Sea Surface Temperature	International Comprehensive Ocean Atmosphere Data Set (ICOADS) Extended Reconstructed Sea Surface Temperature (ERSST) Version 4 Hadley Centre Sea Surface Temperature (HadSST3) Hadley Centre Sea Ice and Sea Surface Temperature (HadISST1) Centennial In Situ Observation-Based Estimates (COBE2)	1880–2016 1880–2016 1880–2016 1880–2016 1880–2016	Freeman et al. (2017) Huang et al. (2015) Kennedy et al. (2011) Rayner et al. (2003) Hirahara et al. (2014)
Surface Air Temperature	Global Historical Climatology Network (GHCN) Climatic Research Unit Surface Air Temperature High Resolution (CRUTS) University of Delaware Surface Air Temperature (UDEL) Atmospheric Radiation Measurement (ARM) Stations One-Minute Data	1880–2016 1901–2014 1900–2014 2016–2017	Lawrimore et al. (2011) Harris et al. (2014) Willmott and Robeson (1995) Stokes and Schwartz (1994)
CO2	All surface stations Mauna Loa AIRS/Aqua satellite Aircraft measurements Chemical methods	1965–2016 1959–2016 2003–2016 2004–2016 1812–1963	https://airs.jpl.nasa.gov/data/carbon_dioxide Beck (2007)
Global Sea Level from Tidal Gauge Stations	Permanent Service for Mean Sea Level (PSMSL) dataset for 2200 tidal stations around the world Global Extreme Sea Level Analysis (GESLA) dataset Global sea level reconstructions	1806–Now 1806–Now 1900–2018 1900–2015 1900–2010 1808–2009 1880–2013 1900–2007	Holgate et al. (2013) link Woodworth et al. (2017) Frederikse et al. (2020) Dangendorf et al. (2019) Hay et al. (2015) Jevrejeva et al. (2014) Church and White (2011) Ray and Douglas (2011)
Global Sea Level from Satellite Measurements	NASA AVISO University of Colorado	1993–2016 1993–2016 1993–2016	https://podaac-ftp.jpl.nasa.gov/dataset/MERGED_TP_J1_OSTM_OST_GMSL_ASCII_V4 https://www.aviso.altimetry.fr/en/data/products/ocean-indicators-products/mean-sea-level.html http://sealevel.colorado.edu

Dating plays a key role in palaeoclimate studies. Some of the proxies, such as tree rings, ice cores, coral reefs and speleothems, have natural annual layers, allowing accurate dating using annual layers counting up to 40 ka. Several time scales have been developed for Greenland and Antarctica ice cores, such as the Greenland Ice Core Chronology 2005 (GICC05) (Andersen et al., 2006; Rasmussen et al., 2006, 2008; Svensson et al., 2006, 2008; Vinther et al., 2006), the NEEM ice core chronology (Rasmussen et al., 2013), the INTIMATE event stratigraphy (Rasmussen et al., 2014), the Antarctic ice core chronology (AICC2012) (Bazin et al., 2013; Veres et al., 2013), the WAIS Divide deep ice core WD2014 chronology (Buizert et al., 2015; Sigl et al., 2016), and the South Pole ice core SP19 chronology (Winski et al., 2019). Bipolar synchronization has been realized (Lemieux-Dudon et al., 2010; Veres et al., 2013). However, manual layer counting is a tedious and sometimes subjective method. The GICC05 chronology was developed over several years and involved the efforts of many researchers: counting, comparing, and recounting the annual layers recorded in multiple data records from several Greenland ice cores. Automated counting approaches are being developed (Wheatley et al., 2012; Winstrup et al., 2012). For the speleothems, most of the cores were radiometrically dated and a global speleothem isotope database with multiple age-depth models is being developed (Comas-Bru et al., 2020). Ocean sediment cores are difficult to date precisely (see review by Lisiecki & Stern, 2016). Radiocarbon offers relatively good age control for the last 40 ka but is costly and can still have calendar age uncertainties of more than 1000 years due to calibration and reservoir age uncertainty. Beyond 40 ka, sediment cores are generally dated by correlating a palaeoclimate proxy to either a better-dated climate archive (e.g. ice cores or speleothems) or to changes in Earth’s orbital configuration (i.e. “orbital tuning”). These dating methods assume that the ocean sediment records are in phase with the target archive or orbital configuration, but in reality, there may exist a physical time lag. Raymo (1997) demonstrated an absolute “constant sedimentation rate” timescale using radiometric age constraints. Significant advances have been made in developing the global ocean sediment timescales (Imbrie et al., 1984; Lisiecki & Raymo, 2005; Lisiecki & Stern, 2016; Shackleton & Opdyke, 1973).

3 Earth’s surface temperature history

Earth’s temperature history at billion-year timescales has been examined by many studies using zircon and quartz in earliest rocks (Ackerson et al., 2018; Valley et al., 2002; Watson & Harrison, 2005), oxygen isotope from cherts and phosphates (Blake et al., 2010; Hren et al., 2009; Karhu & Epstein, 1986; Knauth, 2005; Knauth & Epstein, 1976; Knauth & Lowe, 1978, 2003), marine carbonate isotope (Prokoph et al., 2008; Shields & Veizer, 2002), silicon isotopes in cherts (Abraham et al., 2011; Andre et al., 2006; Chakrabarti et al., 2012; Ding et al., 2017; Heck et al., 2011; Marin-Carbonne et al., 2012; Robert & Chaussidon, 2006; Steinhoefel et al., 2009; van den Boorn et al., 2007), resurrected proteins (Gaucher et al., 2008), and upper-temperature limits for growth of living organisms (Schwartzman, 2015). For the Hadean eon (4.5–4.0 billion years ago), Watson and Harrison (2005) discovered using ancient zircons from Western Australia's Jack Hills that Earth’s surface temperature has cooled down to about 700°C, while Ackerson et al. (2018) found that quartz crystals in Tuolumne samples record crystallization temperatures of 474–561°C. For the Archean, Proterozoic and Phanerozoic eons, Knauth and Epstein (1976) made the first estimate of temperature using oxygen isotope from cherts and suggested that the average climatic temperatures reached about 70°C at 3 Ga, decreased to about 52°C at 1.3 Ga, decreased from about 34°C to 20°C through the Palaeozoic, increased to 35–40°C in the Triassic, and then decreased through the Mesozoic to Tertiary values of about 17°C (Fig. 6A). Robert and Chaussidon (2006) analyzed silicon isotopes in cherts and suggested that seawater temperature changes from about 70°C at 3.5 Ga to about 20°C at 0.8 Ga, but with much larger variability than that derived from oxygen isotopes (Fig. 6B). Gaucher et al. (2008) used resurrected proteins to infer Precambrian temperature and suggested that temperature cooled down from about 72°C at 3.6 Ga to 39°C at 0.8 Ga. Hren et al. (2009) did a combined analysis of oxygen and hydrogen isotopes in cherts and suggested that the Archean temperature at 3.42 Ga. was below 40°C. This low Archean temperature scenario was supported by Blake et al. (2010), who examined oxygen isotopes in phosphate and found a sea water temperature between 26°C and 35°C in 3.2–3.5 Ga, which is close to today’s temperature.

Fig. 6 (A) Precambrian temperature derived from oxygen isotope and silicon isotope in cherts (from Tartèse et al., 2017). (B) Phanerozoic temperature derived from marine oxygen isotope (from Veizer & Prokoph, 2015). (C) Quaternary SST from the individual (cyan) and stacked (blue) records (from Shakun et al., 2015). (D) Late Quaternary temperature from Greenland and Antarctica ice cores (from EPICA Community Members, 2006). (E) Common Era northern hemisphere mean surface temperature (from IPCC, 2013). (F) Modern global mean surface temperature anomalies (from IPCC, 2013).

The Phanerozoic temperature history has been studied using oxygen isotopes in carbonates and phosphates (Cramer et al., 2009; Grossman, 2012; Mills et al., 2019; Prokoph et al., 2008; Royer et al., 2004; Scotese et al., 2021; Shaviv et al., 2014; Shaviv & Veizer, 2003, 2004; Veizer et al., 1999, 2000; Veizer & Prokoph, 2015). Veizer and Prokoph (2015) found that the sea water temperature was about 30°C above today’s value at 480 Ma, which shows a general cooling trend since then but with significant variability (Fig. 6C). Oscillations with an amplitude of about 5–10°C were reported. Veizer et al. (2000) found a prominent ∼140 Ma oscillation, which was connected to the oscillation of galactic cosmic ray flux (Shaviv & Veizer, 2003). Shaviv et al. (2014) reported a significant 32 Ma oscillation with a secondary 175 Ma frequency modulation, which is consistent with parameters postulated for the vertical motion of the solar system across the galactic plane, modulated by the radial epicyclic motion.

The Cenozoic temperature history has been analyzed using ocean sediments (Cramer et al., 2009; Friedrich et al., 2012; Lear et al., 2000; Miller et al., 1987; Miller et al., 2020; Mudelsee et al., 2014; Shackleton & Kennett, 1975; Westerhold et al., 2020; Zachos et al., 2001), and continental sediments (Mosbrugger et al., 2005). All proxies consistently show a long-term cooling of 10–20°C in deep ocean and over the continents throughout the Cenozoic. On top of the strong cooling trend, Zachos et al. (2001) found rhythmic or periodic cycles driven by orbital processes with 10⁴- to 10⁶-year cyclicity and rare rapid aberrant shifts and extreme climate transients with durations of 10³–10⁵ years. Westerhold et al. (2020) identified four climate states-Hothouse, Warmhouse, Coolhouse, Icehouse-on the basis of their distinctive response to astronomical forcing depending on greenhouse gas concentrations and polar ice sheet volume.

The Quaternary temperature history has been examined by many studies using ocean sediments (Emiliani, 1955; Hays et al., 1976; Imbrie et al., 1973; Imbrie et al., 1984; Lisiecki & Raymo, 2005; Martinson et al., 1987; Raymo, 1997; Shackleton et al., 1990; Shackleton & Opdyke, 1973; Shakun et al., 2015; Waelbroeck et al., 2002; Zachos et al., 2001), ice cores (Petit et al., 1999; Alley, 2000; EPICA Community Members, 2004, 2006; NGRIP Members, 2004; Vinther et al., 2010; Jouzel, 2013), lake sediments (Camuera et al., 2019; Tzdakis et al., 1997), and speleothem (Carolin et al., 2013; Cheng et al., 2016; Johnson et al., 2016; Lachniet et al., 2017; Landwehr et al., 2011). The interglacial cycles were first discovered in ocean sediment cores (Emiliani, 1955; Imbrie et al., 1973). Shackleton and Opdyke (1973) proposed the formalization of Marine Isotope Stages (MIS) 1–22, using the d18O in foraminifera in core V28–238 from the Eastern Equatorial Pacific, a practice which has been gradually extended over the entire Pleistocene, Pliocene and beyond in later timescales such as Imbrie et al. (1984) and Lisiecki and Raymo (2005). Hays et al. (1976) proposed that the interglacial cycles are linked to the Milankovitch cycles – the eccentricity (100,000 year), obliquity (41,000 year) and precession (23,000 year) cycles of Earth’s orbit (Milankovitch, 1941). Raymo (1997) confirmed the relationship using an untuned constant sedimentation rate timescale. Ice cores from Antarctica and Greenland show similar cycles (EPICA Community Members, 2004, 2006; Petit et al., 1999). By data compilations, Past Interglacials Working Group of PAGES (2016) showed that despite spatial heterogeneity, MIS 5e (last interglacial) and 11c (∼400 ka ago) were globally strong (warm), while MIS 13a (∼500 ka ago) was cool at many locations. A step-change in the strength of interglacials at 450 ka is apparent only in the Antarctic and deep ocean temperature. The range of temperature variation is about 3°C for the global ocean mean but could be as large as 14°C at individual ocean locations and 20°C in Greenland (Alley, 2000; Shakun et al., 2015; Fig. 6C). The dominant oscillation period is about 100,000 years in the recent 1 Ma but 41,000 years before (Lisiecki, 2010). The interglacial cycles over land are often different from those in oceans and polar regions. Using pollen records from Europe, Tzdakis et al. (1997) showed that the terrestrial cycles have stronger high-frequency variability. Using speleothem records from China, Cheng et al. (2016) found strong precession cycles rather than eccentricity cycles in the past 640,000 years.

The temperature history of the last glacial cycle has been studied using ice cores (Dansgaard et al., 1971; EPICA Community Members, 2006; Jouzel et al., 2007; NGRIP Members, 2004; Thompson et al., 1997), speleothem (Carolin et al., 2013; Cheng et al., 2019; Cruz et al., 2005; Lachniet et al., 2017; Mosblech et al., 2012; Wang et al., 2001), lake sediments (van der Hammen et al., 1971; Woillard, 1978), and ocean sediments (Bard, 2002; Cacho et al., 1999; Dyez et al., 2014; Harada et al., 2006; Hodell et al., 2010; Kaiser et al., 2005; Lea et al., 2000; Lisiecki & Stern, 2016; Martrat et al., 2007; Mohtadi et al., 2014; Sancetta et al., 1973; Schulz et al., 1998; Shackleton et al., 2000; Vautravers & Shackleton, 2006; Voelker et al., 2006; Voelker & de Abreu, 2011). Millennial-scale oscillations have been discovered, such as the Heinrich events (Heinrich, 1988), the Dansgaard–Oeschger (D–O) events (Dansgaard et al., 1993) and the Antarctica Isotope Maximum (AIM) events (EPICA Community Members, 2006; Fig. 6D). The Heinrich events have an oscillation period of 6000–10,000 years, while the DO and AIM events have an oscillation period of 1000–2000 years. Greenland has the strongest temperature anomalies of ∼10°C associated with the Heinrich and DO events. Antarctica has clear but weaker anomalies of ∼2–4°C. There is an SST anomaly of ∼5°C in North Atlantic (Bard, 2002; Shackleton et al., 2000), ∼2°C in the South Atlantic (Dyez et al., 2014), ∼1°C in the Indian Ocean (Mohtadi et al., 2014; Schulz et al., 1998), ∼5°C in Northwest Pacific (Harada et al., 2006), and ∼2°C in Southeast Pacific (Kaiser et al., 2005). Lisiecki and Stern (2016) compiled stacked records for each ocean basin and the global oceans. Over land, there are temperature anomalies of 2–6°C in Asia (Carolin et al., 2013; Cheng et al., 2016; Wang et al., 2001), South America (Cruz et al., 2005; Mosblech et al., 2012) and North America (Cheng et al., 2019; Lachniet et al., 2017).

The Holocene temperature history has been studied using lake sediments (Bajolle et al., 2018; Davis et al., 2003; Viau et al., 2006), ice cores (Thompson et al., 2000; Thompson et al., 1995; Thompson et al., 1998; Thompson et al., 2002), speleothem (Affolter et al., 2019; Asmerom et al., 2007; Fohlmeister et al., 2013; Holmgren et al., 1999; Persoiu et al., 2017; Smith et al., 2016; Stansell et al., 2017; Wang et al., 2005; Williams et al., 2010), ocean sediments (Goslin et al., 2018; Hald et al., 2007; Kim et al., 2004; Staubwasser et al., 2003), northern hemisphere reconstructions (Marsicek et al., 2018; Pei et al., 2017) and global reconstructions (Kaufman et al., 2020; Marcott et al., 2013). Many records show two distinct events: a 4.2 ka event which is most strongly recorded in proxy climate records from mid- and low latitudes, and an 8.2 ka event which is a short-lived near-global episode (Walker et al., 2019). Bond et al. (1999, 2001) discovered a millennial-scale oscillation with a period of ∼1500 years.

The Common Era temperature history has been examined by numerous studies with reconstructions of the northern hemisphere mean temperature (Briffa, 2000; Esper et al., 2002; Guillet et al., 2017; Jones et al., 1998; Mann et al., 1999, 2009; Moberg et al., 2005; Ljungqvist, 2010; Schneider et al., 2015; Wilson et al., 2016; Fig. 6E), continental mean temperature (Cook et al., 2013; Gergis et al., 2016; Luterbacher et al., 2016; PAGES 2k Consortium, 2013; Trouet et al., 2013; Werner et al., 2018), ocean basin mean temperature (Tierney et al., 2015) and local temperature (see Table 1). The Common Era temperature displays significant Medieval and Roman warm periods and Little Ice Age cold period, as well as strong multi-decadal oscillations (Fig. 6E).

Modern instrument measurements were available for the past 170 years since 1850. The global mean surface temperature has been constructed, which shows global warming of ∼1°C from 1910 to 2010 (Hansen & Lebedeff, 1987; Hansen et al., 2010; Jones et al., 1986; Morice et al., 2012; Vose et al., 2012; Fig. 6F). The global mean temperature is also affected by the AMO (DelSole et al., 2011; Tung & Zhou, 2013; Wu et al., 2011), IPO (England et al., 2014; Meehl et al., 2013, 2014), and ENSO (Fyfe et al., 2016; Trenberth, 2015).

Fig. 7 summarizes Earth’s temperature history from 4.5 billion years to one minute. Precambrian temperature oscillates with the supercontinent cycle – the alternate aggregation and breakup of supercontinent (Fig. 7A), Phanerozoic temperature shows a 100–200 million year cycle (Fig. 7B), while the Quaternary temperature is dominated by the 100,000 year interglacial cycle (Fig. 7C). The late Quaternary temperature of the last glacial cycle displays millennium-scale cycles such as the Heinrich events and D–O events (Fig. 7D), while Holocene temperature shows centennial- to millennial-scale cycles (Fig. 7E). Common Era temperature is dominated by multi-decadal oscillations (Fig. 7F). For the modern instrument period (Fig. 7G), the magnitude of global warming is about 1°C century⁻¹. There are also global mean temperature signals associated with AMO and ENSO. The oscillation amplitudes decrease from billion-year time scales to centennial timescales but strongly increase at seasonal and diurnal timescales. Fig. 7H illustrates the one-minute surface temperature measurements at different latitude belts, which include seasonal cycle, diurnal cycle, and other high-frequency phenomena such as the MJO, tropical waves, mesoscale convective systems, and thunderstorms. The oscillation amplitudes range from 10–20°C over tropical and mid-latitude oceans to 40–50°C over mid-latitude and high-latitude continents. The global map of seasonal temperature ranges displays a 10°C range over tropical continents and a 20–60°C range over extratropical continents (data not shown). The diurnal temperature range is more uniform (8–16°C) around the globe except for Greenland, which has a 20+°C day-night temperature difference (not shown).

Fig. 7 Earth’s surface temperature history for (A) Precambrian, (B) Phanerozoic, (C) Quaternary, (D) late Quaternary, (E) Holocene, (F) Common Era, (G) 1880–2019, and (H) 2015 (one-minute data from the ARM stations in Fig. 5E).

Overall, Fig. 7 demonstrates three key points. First, Earth’s temperature history shows significant oscillations at all timescales. Secondly, the oscillation amplitudes decrease from 40°C to 60°C at billion-year timescale to about 1°C at interannual timescales, then strongly increase at seasonal and diurnal timescales. Oscillation amplitudes at seasonal and diurnal timescales are similar to those at billion-year timescales. Thirdly, fewer datasets and larger uncertainties exist for observations at longer timescales such as Precambrian and Phanerozoic.

4 Earth’s sea-level history

Sea level is affected by plate tectonics (sea area, dynamic topography, ridge volume, sea floor volcanism, icesheet-induced isostatic depression), ocean sediment thickness, and climate (ice volume, ocean thermal expansion, ground water) (Miller et al., 2005; Conrad, 2013; Fig. 8A, B). The Precambrian sea-level history has been studied using sequence stratigraphy (Eriksson, 1999; Eriksson et al., 1999, 2005; Krapez, 1993) and 87Sr/86Sr (Halverson et al., 2007). Krapez (1993) assessed the stratigraphic succession of the 3580–2770 m.y. old granite-greenstone terrain of the Pilbara Block by the first- and second-order sequence-stratigraphic techniques and identified two sea-level cycles associated with the Supercontinent Cycles. Halverson et al. (2007) compiled the 87Sr/86Sr records from 0 to 0.9 Ga. In this study, we extended the 87Sr/86Sr records to 0–3.5 Ga using the Veizer Precambrian and Phanerozoic databases (Shields & Veizer, 2002; Veizer et al., 1999) and the GEOROC database.

Fig. 8 (A) Physical processes contributing to sea level variation from 1 yr to 100 Ma. SF, sea floor. Cont, continent (from Miller et al., 2005). (B) Physical processes contributing to Phanerozoic sea level variation (from Conrad, 2013). (C) Phanerozoic sea-level history (from Verard et al., 2015). (D) Quaternary sea-level history (from Shakun et al., 2015). (E) Late Quaternary sea-level history based on oxygen isotope (line) and coral terraces (black circles) (from Chappell et al., 1996). (F) Modern sea level history (from IPCC, 2013).

The Phanerozoic sea-level history has been examined using palaeogeographic maps (Egyed, 1956; Hallam, 1971; Hallam, 1984, 1989; Hays & Pitman, 1973; Pitman, 1978), seismic stratigraphy (Haq et al., 1987; Haq & Schutter, 2008; Posamentier & Vail, 1988; Vail et al., 1977), borehole drilling (Kominz et al., 1998; Miller et al., 1998; Miller et al., 2005; Watts & Steekler, 1979), and 87Sr/86Sr record (Francois & Walker, 1992; Montafiez et al., 1996; Verard et al., 2015). Using early palaeogeographic data, Egyed (1956) estimated that global sea level was 70 m higher than today at 350 Ma. With updated palaeogeographic maps, Hallam (1984, 1989) constructed a detailed sea-level curve for Phanerozoic. Vail et al. (1977) first developed the method of seismic stratigraphy, which uses the seismic data to derive depositional sequence, local relative sea-level change and global sea-level cycles. This led to the Exxon sea-level curve (Haq et al., 1987; Posamentier & Vail, 1988) and the Haq and Schutter (2008) curve. Watts and Steekler (1979) developed the backstripping method using borehole data, which is an inverse technique that can be used to quantitatively extract sea-level change amplitudes from the stratigraphic record. It accounts for the effects of sediment compaction, loading (the response of crust to overlying sediment mass), and water-depth variations on basin subsidence. Miller et al. (2005) derived a sea-level curve based on backstripping stratigraphy data. The 87Sr/86Sr record reflects weathering of the Earth and has been shown to be a good proxy for global sea level (Francois & Walker, 1992; Montafiez et al., 1996). Verard et al. (2015) derived a sea-level curve using 87Sr/86Sr records with consideration of the tectonics effects. The latest Phanerozoic sea-level curves are shown in Fig. 8C. The various methods produce similar “double hump” pattern, although the magnitudes of the peaks differ.

The Cenozoic sea-level history has been analyzed using higher resolution borehole and ocean sediment datasets (e.g. Kominz et al., 1998; Miller et al., 2020; Zachos et al., 1999). The Cenozoic sea-level records the evolution from an ice-free Early Eocene to Quaternary bipolar ice sheets. Miller et al. (2020) found that peak warmth, elevated global sea level, high CO₂, and ice-free “Hothouse” conditions (56–48 Ma) were followed by “Cool Greenhouse” (48–34 Ma) ice sheets (10–30 m changes). Continental-scale ice sheets (“Icehouse”) began ∼34 Ma (>50 m changes), permanent East Antarctic ice sheets at 12.8 Ma, and bipolar glaciation at 2.5 Ma. The largest global sea-level fall (27–20 ka; ∼130 m) was followed by a >40 mm yr⁻¹ rise (19–10 ka), a slowing (10–2 ka), and a stillstand until ∼1900 CE, when rates began to rise. High long-term CO₂ caused warm climates and high sea levels, with sea-level variability dominated by periodic Milankovitch cycles.

The Quaternary sea-level history has been studied using direct dating of shoreline markers and reefs (Emery & Garrison, 1967; Hails, 1965; Shepard, 1964; Shepard & Suess, 1956; Vries & Barendsen, 1954) and oxygen isotopes in ocean sediments (Emiliani, 1955; Shackleton, 1967). The two approaches can be combined together to yield accurate and high-resolution sea-level records (Chappell & Shackleton, 1986; Fairbanks, 1989). Sea level curves have been constructed for the Quaternary (de Boer et al., 2014; Bintanja et al., 2005; Grant et al., 2014; Lea et al., 2002; Shakun et al., 2015; Spratt & Lisiecki, 2016; Waelbroeck et al., 2002; Fig. 8D) and the last glacial cycle (Bard et al., 1990; Chappell et al., 1996; Grant et al., 2012; Lambeck & Chappell, 2001; Lisiecki & Stern, 2016; Siddall et al., 2003; Siddall et al., 2008; Siddall et al., 2010; Fig. 8E). The Quaternary sea-level shows a >100 m oscillation, which is mainly controlled by ice volume change associated with the interglacial cycles (Fig. 8D). Within the last glacial cycle, global sea level is affected by the Heinrich events and D–O events, and shows a 20–30 m oscillation (Fig. 8E).

The Holocene sea level history has been examined by numerous studies using radio-isotopic dating of shoreline markers and/or reef terraces in Greenland (Bennike et al., 2011; Long et al., 2003; Sparrenbom et al., 2006), Atlantic coast of U.S. (Engelhart & Horton, 2012), Atlantic coast of Europe (Garcia-Artola et al., 2018), Pacific coast of North America (Shugar et al., 2014); Pacific coast of central North America (Engelhart et al., 2015), U.S. Gulf Coast (Tornqvist et al., 2004), east coast of China (Song et al., 2013), east coast of India (Banjeree, 2000), Southeast Asia (Mann et al., 2019), Brazilian coast (Angulo & Lessa, 1997; Angulo, 2005), Australian coast (Lewis et al., 2013), Pacific islands (Rashid et al., 2014), south coast of Africa (Garrett et al., 2020), Chilean coast (Cooper et al., 2018), and Antarctica coast (Watcham et al., 2011). There was a decrease in sea level in Holocene around the world except for the North Atlantic Ocean where there was a sea-level rise (Fig. 9). Several reconstructions of global sea level have been developed (Kopp et al., 2016; Lambeck et al., 2014). The Lambeck et al. (2014) reconstruction uses mainly observations from the Pacific and Indian oceans and shows a decrease in global sea level, while the Kopp et al. (2016) reconstruction uses mainly observations from the Atlantic Ocean and shows an increase in global sea level. Regional curves have also been generated, for example, for the North Atlantic (Kemp et al., 2018) and South Atlantic (Angulo & Lessa, 1997; Angulo et al., 2005). Currently, global map of sea level is being developed for Holocene and Common Era (Horton et al., 2018; Khan et al., 2015, 2019).

Fig. 9 Holocene sea-level history in different regions from (1) Sparrenbom et al. (2006); (2) Engelhart and Horton (2012), (3) Garcia-Artola et al. (2018); (4) Shugar et al. (2014); (5) Tornqvist et al. (2004); (6) Song et al. (2013); (7) Banjeree (2000); (8) Mann et al. (2019), (9) Angulo et al., 2006; (10) Lewis et al. (2013); (11) Rashid et al. (2014); (12) Garrett et al. (2020); (13) Cooper et al. (2018); (14) Watcham et al. (2011). World map courtesy of NOAA.

Modern measurements of ocean tides and global sea level began in the mid-seventeenth century using float tide gauges (Matthaus, 1972). The first generation of self-recording tide gauges was developed in the 1830s by Palmer, Mitchell, Bunt and others (Palmer, 1831; Matthaus, 1972). Since then, many tidal gauge stations have been set up around the world. The Permanent Service for Mean Sea Level of the UK National Oceanography Center was established in 1933 and has been collecting global sea level measurements till now (Holgate et al., 2013). Now the longest continuous tide record and global sea-level reconstruction go back to 1700 (van Veen, 1945). Starting from 1991, satellite measurements of sea surface height has been available from TOPEX/Poseidon, Jason-1, Jason-2, ERS-1, ERS-2, Envisat and other platforms (Ablain et al., 2015; GSFC, 2017; Nerem et al., 2018). Global tidal models have been developed and calibrated by the observations (e.g. Egbert & Erofeeva, 2002). Reconstructions of global sea level have been developed for 1807-now from the gauge records with the help of recent satellite measurements and tidal models (e.g. Jevrejeva et al., 2006; Jevrejeva et al. 2014; Jevrejeva et al. 2008; Merrifield et al., 2009; Church & White, 2011; Ray & Douglas, 2011; Dangendorf et al., 2019).

In summary, the global sea level also demonstrates significant oscillations at different timescales (Fig. 10). Precambrian sea level oscillates dramatically with supercontinent cycles with an amplitude of 100–200 m (Fig. 10A), while Phanerozoic sea level also shows a 100–200 m oscillation (Fig. 10B). Quaternary sea level displays the well-known 100-m oscillation associated with global interglacial cycle (Fig. 10C), and sea level in the last glacial cycle shows 10–50 m oscillation associated with the millennium-scale Heinrich and D–O events (Fig. 10D). The amplitudes decrease substantially to about 1 m for Holocene sea level (Fig. 10E) and 0.1 m for Common Era sea level (Fig. 10F). The modern global sea level displays a trend of ∼0.2 m century⁻¹ (Fig. 10G). There is a tendency for positive trend in low latitudes but negative trend in high latitudes (not shown). Sea level also shows decadal and interannual oscillations with amplitudes smaller than 0.5 m. The oscillation amplitudes of sea-level increase strongly at subseasonal and diurnal timescales, driven by the well-known lunar and solar tidal force. Fig. 10H illustrates the hourly measurements from coastal and island tidal gauge stations at different latitudes. Sea level rises and falls by 1–10 m everyday throughout the year, which is contributed by all constituents of tidal force as well as surface winds. The largest tidal constituent – the semi-diurnal lunar M2 tide, has a >0.4 m oscillation around most coastal regions (Egbert et al., 2002).

Fig. 10 Earth’s sea-level history for (A) Precambrian, (B) Phanerozoic, (C) Quaternary, (D) late Quaternary, (E) Holocene, (F) Common Era, (G) 1880–2019, and (H) 2017 (hourly data from tidal gauge stations).

5 Earth’s atmospheric CO₂ history

Precambrian CO₂ history has been studied using various proxies such as palaeosols, calcified cyanobacteria and aeronomical evidence (Rye et al., 1995; Kaufman & Xiao, 2003; Hessler et al., 2004; Sheldon, 2006; Kah & Riding, 2007; Sheldon & Tabor, 2009; Mitchell & Sheldon, 2010; Lichtenegger et al., 2010; Driese et al., 2011; Schrag et al., 2013; Kanzaki & Murakami, 2015; Catling & Zahnle, 2020; Fig. 11A). Rye et al. (1995) analysed palaeosols from 2.75Ga and found that CO₂ concentration must be less than 10^−1.4 atm, which is about 100 times the present-day atmospheric level (PAL). Hessler et al. (2004) studied palaeosols from 3.2 Ga and found a lower limit of CO₂ concentration being several times higher than present-day values. Sheldon (2006) used a different model and found consistently high pCO2 from 2.5 to 1.8 Ga ago and a substantial drop in atmospheric pCO2 at some time between 1.8 and 1.1 Ga ago. Kah and Riding (2007) used calcified cyanobacteria between 1 and 2.5 Ga and derived CO₂ concentration that is about 10 times today’s value. Lichtenegger et al. (2010) showed aeronomical evidence of a CO₂ amount in the early nitrogen-rich terrestrial atmosphere 3.8 Ga ago of at least two orders of magnitude higher than the present-time level. Kanzaki and Murakami (2015) derived from palaeosols CO₂ concentration to be 85–510 PAL at 2.77 Ga, 78–2500 PAL at 2.75 Ga, 160–490 PAL at 2.46 Ga, 30–190 PAL at 2.15 Ga, 20–620 PAL at 2.08 Ga and 23–210 PAL at 1.85 Ga.

Fig. 11 (A) Precambrian CO₂ history from a model (black line, yellow shading indicates its 95% confidence level) and various observations (from Catling & Zahnle, 2020). (B) Phanerozoic CO₂ history from proxies (from Royer, 2014). (C) Quaternary CO₂ history from Antarctic ice core composite and temperature from EPICA (from Luthi et al., 2008). (D) Late Quaternary CO₂ history from Byrd Station, Antarctica together with other climate variables (from Ahn & Brook, 2008). (E) Common era CO₂ history from ice core measurements in Greenland (symbols) and Antarctica (line) (from Barnola et al., 1995). (F) Common era CO₂ history from ice core measurements in NEEM, Dome Fuji, Law Dome, WDC, EDML and South Pole (from Oyabu et al., 2020). (G) Common era CO₂ history from stomata (dots) and ice core (black line) (from Finsinger & Wagner-Cremer, 2009). (H) Historical CO₂ concentrations used by IPCC AR6 (from Meinshausen et al., 2017).

The Phanerozoic CO₂ history has been examined by numerous studies using stomata (e.g. Konrad et al., 2020; McElwain & Steinthorsdottir, 2017; van der Burgh et al., 1993), phytoplankton (e.g. Pagani et al., 1999), liverworts (Fletcher et al., 2008), palaeosols (e.g. Suchecki et al., 1988), boron-d¹¹B (Pearson et al., 2009), boron-B/Ca (Tripati et al., 2009), nahcolite (Lowenstein & Demicco, 2006), and data-driven biogeochemical models (Berner, 1991, 1994, 2006; Berner & Kothavala, 2001; Godderis et al., 2014; Rothman, 2002; Shaviv & Veizer, 2003). An increase in the atmospheric carbon dioxide (CO2) concentration results in a decrease in the number of leaf stomata, and van der Burgh et al. (1993) found a nearly perfect linear correlation between them. Pagani et al. (1999) showed a good correlation between pCO₂ and ϵ_p values based on carbon isotope analyses of diunsaturated alkenones and planktonic foraminifera. Fletcher et al. (2008) estimated ancient atmospheric CO2 concentrations on the basis of δ13C measurements on liverwort gametophyte compression fossils, which spanned 150 Ma and were sampled from 12 localities on 5 continents. Lowenstein and Demicco (2006) estimated pCO₂ from coprecipitation of nahcolite (NaHCO₃) and halite (NaCl) from surface waters in contact with the atmosphere and found a value of 1125 ppm between 49 and 56 Ma. As reviewed by Royer (2014; Fig. 11B), there is a broad agreement among methods. The Phanerozoic CO₂ history is characterized by a “double hump” pattern with elevated CO₂ around 180 and 400 Ma, both of which are above 1000 ppm. The Cenozoic CO₂ history has also been examined using higher resolution data (e.g. Beerling & Royer, 2011; Pagani et al., 2011; Pearson & Palmer, 2000; Rugenstein & Chamberlain, 2018; Steinthorsdottir et al., 2016; Zhang et al., 2013). Zhang et al. (2013) found consistent results among alkenone data, boron isotope, pH data and stomatal index records. CO₂ levels were highest during a period of global warmth associated with the Middle Miocene Climatic Optimum (17–14 Ma), followed by a decline in CO₂ during the Middle Miocene Climate Transition (approx. 14 Ma).

The Quaternary CO₂ history has been studied using ice cores (Barnola et al., 1987; Bereiter et al., 2015; Delmas et al., 1980; Kawamura et al., 2003; Luthi et al., 2008; Neftel et al., 1982; Petit et al., 1999; Fig. 11C) and marine carbon isotopes (Lisiecki, 2010). CO₂ concentration shows an ∼100 ppm oscillation associated with the interglacial cycles and is in phase with the temperature oscillation. High-resolution ice core data were used to study the millennial-scale variability of CO₂ (Ahn & Brook, 2008; Bereiter et al., 2012; Bauska et al., 2021; Indermuhle et al., 2000). Ahn and Brook (2008) found that CO₂ concentration has an ∼20 ppm variation associated with the Heinrich events and is positively correlated with Antarctic temperature, implying a strong connection to Southern Ocean processes (Fig. 11D). Bereiter et al. (2012) found that during Marine Isotope Stage (MIS) 5, the peak of millennial CO₂ variations lags the onset of Dansgaard/Oeschger warmings by ∼250y. During MIS 3, this lag increases significantly to ∼870y. Bauska et al. (2021) found that on the millennial scale, CO₂ tracks Antarctic climate variability, but peak CO₂ levels lag peak Antarctic temperature by more than 500 years. Centennial-scale CO₂ increases of up to 10 ppm occurred within some Heinrich stadials, and increases of ∼5 ppm occurred at the abrupt warming of most D–O events.

The Common Era CO₂ history has been examined using ice cores (Ahn et al., 2012; Anklin et al., 1995, 1997; Barnola et al., 1983; Barnola et al., 1995; Etheridge et al., 1996; Friedli et al., 1986; Indermuhle et al., 1999; MacFarling Meure et al., 2006; Neftel et al., 1985; Oeschger et al., 1988; Oyabu et al., 2020; Siegenthaler et al., 1988; Siegenthaler et al., 2005; Siegenthaler & Sarmiento, 1993; Smith et al., 1997; Sowers et al., 1997; Stauffer et al., 1984) and stomata (Finsinger & Wagner-Cremer, 2009; Kouwenberg, 2004; Kouwenberg et al., 2005McElwain et al., 2002; Rundgren & Beerling, 1999; Rundgren & Bjorck, 2003; Rundgren et al., 2005; Wagner et al., 2002; Wagner et al., 1999; Wagner et al., 2004). The early Antarctica ice cores show a simple monotonic increase of CO₂ concentration with little variability (Friedli et al., 1986; Neftel et al., 1985; Siegenthaler et al., 1988; Siegenthaler & Sarmiento, 1993), which has been used in the IPCC reports till today (Meinshausen et al., 2017; Fig. 11H). Newer Antarctica ice cores show significant variability at multi-decadal to centennial timescales (Ahn et al., 2012; Etheridge et al., 1996; MacFarling Meure et al., 2006; Siegenthaler et al., 2005). Frank et al. (2010) conducted an ensemble reconstruction of CO₂ concentration based on the new Antarctica ice cores and found that the variability is more consistent with the temperature variability. The Greenland ice cores consistently show higher CO₂ concentrations by 10–40 ppm than the Antarctica ice cores, as well as stronger variability (Anklin et al., 1995, 1997; Barnola et al., 1995; Oeschger et al., 1988; Oyabu et al., 2020; Smith et al., 1997; Sowers et al., 1997; Stauffer et al., 1984; Fig. 11E, F). The results were shown to be highly robust by validations in multiple labs using different instruments and using both dry extraction and wet extraction. Delmas (1993) proposed that the bipolar difference is caused by higher concentration of impurities in Greenland ice, which could produce CO₂ by chemical reactions. However, the latest satellite and surface measurements show that there indeed exists significant bipolar difference of >10 ppm in CO₂ concentrations (e.g. Pagano et al., 2014; Jiang et al., 2016; Fig. 12C, E), which is largest during the northern summer when Greenland gets the largest amount of snowfall (Castellani et al., 2015). CO₂ concentrations reconstructed from stomata show even larger scatters (e.g. Finsinger & Wagner-Cremer, 2009; Kouwenberg, 2004; Fig. 11G). Similar scatters have been observed in continuous tower measurements (Bakwin et al., 1998; Miles et al., 2012; Andrews et al., 2014; Fig. 13H), and satellite maps show significant spatial variability for monthly, seasonal and annual means (Fig. 12D–H).

Fig. 12 (A) Annual mean CO₂ concentrations measured at Montsouris, France, 1877–1910 (from Stanhill, 1982). (B) Monthly mean CO₂ concentrations measured at two stations in Scandinavia, 1955–1959 (from Bischof, 1960). (C) Zonal-mean CO₂ concentration measured by NOAA ESRL (from Jiang et al., 2016). (D) Seasonal mean CO₂ concentration for JAS 2008 measured by IASI (from Crevoisier et al., 2009). (E) Climatological monthly mean CO₂ concentration for May measured by AIRS (from Pagano et al., 2014). (F) Monthly mean CO₂ concentration for May 2015 measured by OCO-2 (from Eldering et al., 2017) (G) Monthly mean CO₂ concentration for May 2010 measured by GOSAT (from Crisp et al., 2012). (H) Annual mean CO₂ concentration for 2009 measured by SCIAMACHY (from Schneising et al., 2011).

Fig. 13 Earth’s CO₂ history for (A) Precambrian, (B) Phanerozoic, (C) Quaternary, (D) late Quaternary, (E) Holocene, (F) Common Era, (G) 1880–2019, and (H) 2010 (continuous 5-minute data from towers).

The modern instrument measurements of atmospheric CO₂ began in the early nineteenth century. The existence of CO₂ in Earth’s atmosphere was discovered by Joseph Black in 1752–1754 (Black, 1807; see review by Letts & Blake, 1902). Thenard (1813) devised the first method for measuring the atmospheric CO₂ concentration, while Pettenkofer (1858) designed a more accurate method. Numerous measurements have been conducted in the 140 years between 1812 and 1958 (e.g. Bischof, 1960; Brown & Escombe, 1905; Fonselius & Koroleff, 1955; Stanhill, 1982; see reviews by Letts & Blake, 1902 and Beck, 2007). For example, Stanhill (1982) presented a 33-year (1877–1910) time series of CO₂ concentrations measured at the Montsouris Observatory in France (Fig. 12A). Kreutz (1941) reported more than 64,000 measurements at the meteorological station in Giessen, Germany, between 1939 and 1941. Bischof (1960) presented 5 years (1955–1959) of continuous measurements from 19 stations in Scandinavia (Fig. 12B). Beck (2007) compiled data measured in rural areas from 180 papers and presented a 140-year (1812–1961) time series of CO₂ concentration. More works are needed to analyse and compile these historical CO₂ measurements, which may extend the current modern instrument time series back to the early nineteenth century. It would be interesting to conduct a side-by-side comparison of the old instruments and new instruments using the same air samples, and analyse the historical station locations together with nearby weather station data. Keeling (1958) invented a new technique for the measurement of atmospheric CO₂ using cryogenic condensation of air samples followed by NDIR spectroscopic analysis against a reference gas with manometric calibration. This technique was adopted for CO₂ determination throughout the world, including in the NOAA Global Greenhouse Gas Reference Network (e.g. Peters et al., 2007; Tans et al., 1989; Yuan et al., 2019). Measurements are also conducted on very high towers (Andrews et al., 2014; Bakwin et al., 1998; Miles et al., 2012) and aircrafts (Gerbig et al., 2003; Sweeney et al., 2015). A compilation of global in situ measurements since 1957 has been released by the Cooperative Global Atmospheric Data Integration Project (2017). In the past 60 years, the annual mean CO₂ concentration at Mauna Loa increased from 316 ppm in 1959 to 414 ppm in 2020. The year-to-year increasing rate is affected by ENSO (Bacastow, 1976; Bacastow et al., 1980; Betts et al., 2018; Jones et al., 2001; Keeling et al., 1995; Luo et al., 2018; Piao et al., 2020). Jones et al. (2001) showed that the CO₂ difference between El Nino and La Nina is about 0.5–2 ppm. Using a global terrestrial biosphere model, Betts et al. (2018) successfully predicted the record CO₂ rise associated with the 2015/2016 El Nino, which is mainly due to the weakening of tropical land carbon sink. For the annual cycle, Keeling et al. (1976) reported a range of 6 ppm at Mauna Loa, Yuan et al. (2019) reported a range of 10 ppm at Mount Zugspitze, Germany, while the global marine surface average shows a range of 4 ppm. The range of annual cycle is much stronger in the northern hemisphere than in the southern hemisphere (Jiang et al., 2016; Fig. 12C). Using tower measurements across the United States, Bakwin et al. (1998) found that the range of annual cycle increases with a height from 10 ppm at the surface to ∼30 ppm above 100 m height. For the diurnal cycle, Yuan et al. (2019) reported a range of 1 ppm at Mauna Loa and 1–2 ppm at Mount Zugspitze, Germany. Bakwin et al. (1998) found that the range of diurnal cycle in the central U.S. decreases significantly with height in summer from >40 ppm at 10 m to <5 ppm above 400 m.

Satellite measurements of atmospheric CO₂ have been conducted using different sensors such as the High-Resolution Infrared Radiation Sounder (HIRS) onboard the NOAA polar orbiting satellites (Chedin et al., 2003), the Infrared Atmospheric Sounding Interferometer (IASI) onboard the European MetOp satellite (Crevoisier et al., 2009; Fig. 12D), the Atmospheric Infrared Sounder (AIRS) instrument onboard NASA’s AQUA satellite (Crevoisier et al., 2004; Chahine et al., 2008; Pagano et al., 2014; Fig. 12E), the Orbiting Carbon Observatory-2 (OCO-2) (Eldering et al., 2017a, 2017b; Fig. 12F), the Greenhouse Gases Observing Satellite (GOSAT) (Crisp et al., 2012; Hammerling et al., 2012; Yokota et al., 2009; Fig. 12G), and the SCanning Imaging Absoprtion spectroMeter for Atmospheric CHartographY (SCIAMACHY) instrument onboard the ENVISAT satellite (Buchwitz et al., 2005; Schneising et al., 2011; Fig. 12H). All satellite maps show strong spatial variability of CO₂ concentration. In the tropics, the seasonal mean CO₂ concentration demonstrates a 10-ppm difference between different locations (Fig. 12D). Over the globe, the climatological monthly mean CO₂ concentration shows a 10-ppm difference between the Arctic and the southern oceans (Fig. 12C, E). High-resolution monthly satellite maps over the continents show larger spatial variability (Fig. 12F, G). The annual mean map still shows a strong spatial variability with ∼10-ppm differences among different regions (Fig. 12H). The strong spatial variability may explain the difference between Antarctic ice core data and Greenland ice core data, the difference between Antarctic ice core and other proxies such as the stomata, and the difference between the chemistry measurements in 1812–1958 and later measurements (Fig. 11E–H, Fig. 12A–B).

CO₂ concentration demonstrates the most dramatic variability among the different components of Earth’s climate system (Fig. 13). Precambrian CO₂ concentration reaches 17,000 ppm around 2 billion years BP, which is 50 times today’s value (Fig. 13A). Phanerozoic CO₂ concentration oscillates by 4000–10,000 ppm (Fig. 13B). The oscillation amplitude decreases significantly to 60–100 ppm for Quaternary interglacial cycles (Fig. 13C) and 10–20 ppm for Heinrich and D–O events in the last glacial cycle (Fig. 13D). For Holocene and Common Era, the Greenland ice cores report higher CO₂ concentrations than the Antarctica ice cores, while the stomata reconstructions show larger variabilities than the ice core reconstructions (Fig. 13E–F). For the modern measurement period, the chemistry measurements before 1958 show larger variabilities than later measurements (Fig. 13G). Similar to temperature and sea level, CO₂ oscillation amplitudes increase substantially at seasonal and diurnal timescales. Fig. 13H illustrates the continuous 5-minute CO₂ measurements from towers at different latitudes, which are generally considered the most accurate measurements of CO₂ concentration. CO₂ concentrations oscillate by about 200 ppm at a high-latitude inland station, 150 ppm at a high-latitude station near the coast, and 30–50 ppm at a subtropical station. These are contributed by the seasonal cycle, diurnal cycle, as well as other high-frequency variability.

6 Summary and discussions

This paper synthesized the first global unified picture of Earth’s climate history from the longest timescale to the current climate, which provides an observational benchmark for understanding and modelling Earth’s climate system and global climate change. Earth’s climate history shows dominant climate modes such as the supercontinent cycles, interglacial cycles, millennial cycles, multi-decadal oscillation, interannual oscillation, seasonal cycle and diurnal cycle. The amplitudes of the dominant climate variability generally decrease from the billion-year timescales to interannual timescales, then significantly increase at the seasonal to diurnal timescales (Fig. 14). For oscillations at each timescale, comparing the phase of temperature (Fig. 7), sea level (Fig. 10) and CO₂ (Fig. 13) can reveal important physical relationships and possible underlying mechanisms.

Fig. 14 Summary of the amplitudes of dominant climate variability. The amplitudes of oscillations are estimated using standard deviation multiplied by 2, while that of global warming is simply the increase from 1880 to 2020.

The Earth’s climate history is modulated by external forcings and internal feedbacks (Fig. 2). The external forcings change with time and can drive trends and oscillations. For example, theories suggest that solar luminosity was weak in Precambrian and had been increasing since then (Feulner, 2012). The solar forcing at 4 Ga was ∼75% of today’s value. On top of this multi-billion-year trend, there is rich variability generated by changes in Earth’s orbit and the planetary system, such as the Milankovitch cycles dominating the Quaternary climate. The internal feedbacks also change with time. For example, the ocean-atmosphere feedback is dominated by upper ocean processes for the interannual ENSO (Bjerknes, 1969) but by deep ocean thermohaline circulation for the multi-decadal AMO and millennial Heinrich/D–O/Bond events (Lynch-Stieglitz, 2017; Zhang et al., 2019), deep ocean halothermal circulation for the Phanerozoic climate (Hay, 2008; Horne, 1999), and entire ocean mixing for the Precambrian climate events (Ashkenazy et al., 2013; Hoffman et al., 2017). The interplay of the external forcings and internal feedbacks led to the observed Earth’s climate history.

The physical processes connecting Earth’s surface temperature, sea level and CO₂ are complicated and vary at different timescales, which are under active research. A highly simplified framework assumes that variations of CO₂ controls variations of Earth’s surface temperature, while other physical processes provide feedbacks to either enhance or reduce the resultant temperature change. Following this framework, an equilibrium climate sensitivity is often defined as the steady-state global surface temperature increase for a doubling of CO₂ (IPCC, 2007; IPCC, 2013; IPCC, 2021; Sherwood et al., 2020), which has been accessed using observational datasets from modern instrument period (e.g. Gregory et al., 2002; Lewis & Curry, 2015, 2018; Skeie et al., 2014), the Common Era (Hegerl et al., 2006; Rind et al., 2004), the last glacial cycle (e.g. Annan & Hargreaves, 2013; Schmittner et al., 2011), the late Quaternary (e.g. Köhler et al., 2015, 2017; Royer, 2016; Snyder, 2019), the Cenozoic (e.g. Hansen et al., 2013; Inglis et al., 2020; PALAEOSENS, 2012; Rae et al., 2021; Zhu et al., 2020) and the Phanerozoic (e.g. Farnsworth et al., 2019). The estimated equilibrium climate sensitivity varies significantly at different timescales. This is likely because the highly simplified framework of CO₂ controlling temperature may not be valid when other physical processes unrelated to CO₂, such as solar forcing and plate tectonics, are playing a key or leading role in changing Earth’s temperature. Similarly, sea level is affected not only by temperature but also by plate tectonics (sea area, dynamic topography, ridge volume, sea floor volcanism, icesheet-induced isostatic depression) and ocean sediment thickness, which dominate sea-level change at timescales longer than one million years (Fig. 8A, B).

There are numerous unanswered questions about Earth’s climate history. For the Precambrian climate, there are three key unanswered questions. The first one is a long-lasting question of how the Earth kept a warm temperature when the solar forcing was ∼70% of today’s value, which is termed the “faint young sun problem” (Feulner, 2012; Hu & Tian, 2015). All temperature reconstructions show anomalies of 20–60°C warmer than today’s temperature (Fig. 7A), which is difficult to explain using the observed CO₂ concentrations (Fig. 13A). The second question is the “snowball Earth” hypothesis (Hoffman et al., 2017; Kirschvink, 1992), which is based on the observations of widespread low-latitude glaciation in both Palaeoproterozoic era (Evans et al., 1997) and Neoproterozoic era (Hoffman et al., 1998). However, none of the temperature reconstructions show a temperature anomaly significantly colder than today’s temperature (Fig. 7A). Higher-resolution datasets are needed to resolve any possible short-term events. The third question is how climate changes are associated with the supercontinent cycles. Theories suggest that the assembly of the supercontinent tends to cause a decrease in sea level, a decrease in CO₂ concentration, and a cooling of Earth’s surface temperature. The latest temperature (Fig. 7A) and sea level (Fig. 10A) curves appear to support the theories, while the number of CO₂ observations is not enough to resolve any changes associated with the supercontinent cycles (Fig. 13A). More efforts are needed to collect new datasets and develop new methods and new proxies.

For the Phanerozoic climate, an interesting question is why temperature (Fig. 7B) does not show a double-hump curve similar to sea level (Fig. 10B) and CO₂ (Fig. 13B)? The temperature curves, on the other hand, are dominated by higher-frequency oscillations. Theories suggest that the higher-frequency oscillations are mainly driven by external solar forcing rather than the greenhouse effect or ice-sheet dynamics.

For the interglacial cycles, the ocean temperature (Fig. 7C), sea level (Fig. 10C) and CO₂ (Fig. 13C) are all dominated by the 100-ka eccentricity cycle, while the continental temperature is often dominated by the 41-ka obliquity cycle. There are three key unanswered questions. First, why is ocean temperature dominated by the 100-ka eccentricity cycle when the solar insolation is dominated by the 41-ka obliquity cycle and 23-ka precession cycle? This is the long-lasting “100,000-yr problem” (Lisiecki, 2010). Secondly, why did the dominant oscillation period change from 100- to 41-ka before 1 Ma? Thirdly, most of the Quaternary datasets are orbitally tuned, making it difficult to examine the phase relationship among different regions or among temperature, sea level and CO₂. How can we develop accurate un-tuned Quaternary datasets?

The climate of the last glacial cycle is dominated by millennial-scale variability, especially the Heinrich events and D–O events. These events generate strong surface temperature signals around the world (Fig. 7D), as well as significant sea-level signals (Fig. 10D) and CO₂ signals (Fig. 13D). It is well established that the Heinrich events and D–O events are closely connected to the Atlantic Meridional Overturning Circulation (AMOC). However, observations show that the fresh water input lags the abrupt climate transitions, and model experiments of AMOC changes show overly weak global responses compared to observations. There are two key unanswered questions. First, what drive the AMOC transitions associated with the Heinrich and D–O events? Secondly, what drive the observed strong global signals associated with the Heinrich and D–O events?

The Holocene and Common Era are the time periods with the largest number of observational data (Fig. 5C–D). Palaeoclimate field reconstructions and palaeoclimate reanalysis have been developed using these datasets. There are three key questions. The first important question is how to combine datasets with different dating methods since annual layer counting has high accuracy, but radiometric dating has large uncertainty at these timescales. The standard deviation of radiometric ages could be 40–150 years. Synchronization of nearby records, such as what the GICC2005 chronology did for the Greenland ice cores (Andersen et al., 2006; Rasmussen et al., 2006; Svensson et al., 2006; Vinther et al., 2006), would significantly improve the dating. The second question is whether the Bond events are global events and whether the little ice age is part of the Bond cycles. The third question is whether the ongoing global warming is unprecedented in the Common Era or the Holocene. Fig. 15 shows the regional mean surface temperature in the past 2000 years for (A) Arctic (Werner et al., 2018), (C) Europe (Lutebacher et al., 2016), (E) Asia (Cook et al., 2013), (G) Northern Hemisphere (Guillet et al., 2017), and (I) Northern Hemisphere (Schneider et al., 2015). Linear trends are shown for 100-year periods ending at 100AD, 200AD, … , 1900AD and the last year of data (blue lines). The corresponding 100-year running trends (warming rates) are shown in (B) (D) (F) (H) and (J), respectively, which is defined as a linear trend of temperature for the 100-year period ending at the year of interest. Both the temperature records and the warming rates show significant oscillations. Warming rates before the industrial revolution are sometimes comparable to or even higher than the maximum warming rate in the industrial era. Therefore, in terms of the warming rate, the ongoing warmings of Arctic, Europe, Asia and Northern Hemisphere are not unprecedented in the past 2000 years. Larger uncertainties are associated with the reconstruction of global mean surface temperature.

Fig. 15 Regional mean surface temperature in the past 2000 years for (A) Arctic (Werner et al., 2018), (C) Europe (Lutebacher et al., 2016), (E) Asia (Cook et al., 2013), (G) Northern Hemisphere (Guillet et al., 2017), and (I) Northern Hemisphere (Schneider et al., 2015). Linear trends are shown for 100-year periods ending at 100AD, 200AD, … , 1900AD and last year of data (blue lines). The corresponding 100-year running trends (warming rates) are shown in (B) (D) (F) (H) and (J), respectively. Colour stars denote the linear trends that are above the 95% confidence level.

We are witnessing rapid advances in palaeoclimatology and expect to see the following progress in the near future:

1. New dating methods, especially un-tuned dating for interglacial cycles.

2. Synchronization and inter-calibration of nearby records.

3. Intercomparison of different proxies, especially for CO₂.

4. High-resolution reconstructions of Holocene climate.

5. Palaeoclimate reanalysis for Holocene, the last glacial cycle and Quaternary.

6. Collection of more datasets for Precambrian and Phanerozoic climate.

In the next 50 years, we might be able to finish the data collection and analysis for palaeoclimatology, develop Earth system models for all timescales, and achieve a comprehensive understanding of Earth’s climate history. The Earth’s four layers – atmosphere, hydrosphere, mantle and core – are all rotating and convecting fluids. Geophysical fluid dynamics was founded by Laplace, who published the famous Laplace equations of tidal dynamics in the late eighteenth century (Laplace, 1775, 1798). These are basically linearized forms of the primitive equations and have been used to this day in studying atmospheric and ocean tides. The Navier–Stokes equations were determined in the nineteenth century (Navier, 1822; Stokes, 1842). The complete primitive equations were published by Poincare (1901) and V. Bjerknes (1904), which were applied later to theoretical atmospheric models (e.g. J. Bjerknes, 1937; Rossby, 1939), ocean models (e.g. Ekman, 1905; Sverdrup, 1947), mantle models (e.g. Pekeris, 1935; Runcorn, 1962) and core geodynamo models (e.g. Herzenberg, 1958; Larmor, 1919). Using computers, numerical models have been developed for all four layers based on primitive equations. It would be possible to combine the models for the four layers to form a model of the whole Earth system, which will be able to simulate Earth’s climate variability from 4.5 billion years to one minute.

Acknowledgements

Part of this work was done by TQ when working in the Department of Geography, The Ohio State University. We thank Paul Knauth for sharing the Precambrian chert dataset and discussions on temperature estimates, Christian Verard for sharing the Phanerozoic sea level datasets, and Phil Woodsworth for his comments on an earlier version of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was supported by NSF Grant AGS-1347132.