Air density 2.7 billion years ago limited to less than twice modern levels by fossil raindrop imprints


According to the ‘Faint Young Sun’ paradox, during the late Archaean eon a Sun approximately 20% dimmer warmed the early Earth such that it had liquid water and a clement climate1. Explanations for this phenomenon have invoked a denser atmosphere that provided warmth by nitrogen pressure broadening1 or enhanced greenhouse gas concentrations2. Such solutions are allowed by geochemical studies and numerical investigations that place approximate concentration limits on Archaean atmospheric gases, including methane, carbon dioxide and oxygen2,3,4,5,6,7. But no field data constraining ground-level air density and barometric pressure have been reported, leaving the plausibility of these various hypotheses in doubt. Here we show that raindrop imprints in tuffs of the Ventersdorp Supergroup, South Africa, constrain surface air density 2.7 billion years ago to less than twice modern levels. We interpret the raindrop fossils using experiments in which water droplets of known size fall at terminal velocity into fresh and weathered volcanic ash, thus defining a relationship between imprint size and raindrop impact momentum. Fragmentation following raindrop flattening limits raindrop size to a maximum value independent of air density, whereas raindrop terminal velocity varies as the inverse of the square root of air density. If the Archaean raindrops reached the modern maximum measured size, air density must have been less than 2.3 kg m−3, compared to today’s 1.2 kg m−3, but because such drops rarely occur, air density was more probably below 1.3 kg m−3. The upper estimate for air density renders the pressure broadening explanation1 possible, but it is improbable under the likely lower estimates. Our results also disallow the extreme CO2 levels required for hot Archaean climates8.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: The 2.7-billion-year-old Ventersdorp Supergroup raindrop imprints lithified in tuff at Omdraaivlei, South Africa.
Figure 2: Experimental relationship between raindrop area and dimensionless momentum.
Figure 3: Theoretical predictions of the variation of air density with terminal velocity and dimensionless momentum at the surface.
Figure 4: Atmospheric density given the maximum raindrop diameter that created the largest imprints at Omdraaivlei, South Africa.


  1. 1

    Goldblatt, C. et al. Nitrogen-enhanced greenhouse warming on early Earth. Nature Geosci. 2, 891–896 (2009)

  2. 2

    Kasting, J. Theoretical constraints on oxygen and carbon dioxide concentrations in the Precambrian atmosphere. Precambr. Res. 34, 205–229 (1987)

  3. 3

    Ohmoto, H., Watanabe, Y. & Kumazawa, K. Evidence from massive siderite beds for a CO2-rich atmosphere before 1.8 billion years ago. Nature 429, 395–399 (2004)

  4. 4

    Claire, M., Catling, D. & Zahnle, K. Biogeochemical modelling of the rise in atmospheric oxygen. Geobiology 4, 239–269 (2006)

  5. 5

    Domagal-Goldman, S., Kasting, J., Johnston, D. & Farquhar, J. Organic haze, glaciations and multiple sulfur isotopes in the Mid-Archean Era. Earth Planet. Sci. Lett. 269, 29–40 (2008)

  6. 6

    Haqq-Misra, J., Domagal-Goldman, S., Kasting, P. & Kasting, J. A revised, hazy methane greenhouse for the Archean Earth. Astrobiology 8, 1127–1137 (2008)

  7. 7

    Driese, S. G. et al. Neoarchean paleoweathering of tonalite and metabasalt: implications for reconstructions of 2.69 Ga early terrestrial ecosystems and paleoatmospheric chemistry. Precambr. Res. 189, 1–17 (2011)

  8. 8

    Kasting, J. & Howard, M. Atmospheric composition and climate on the early Earth. Phil. Trans. R. Soc. B 361, 1733–1742 (2006)

  9. 9

    Bekker, A. et al. Dating the rise of atmospheric oxygen. Nature 427, 117–120 (2004)

  10. 10

    Holland, H. D. The oxygenation of the atmosphere and oceans. Phil. Trans. R. Soc. B 361, 903–915 (2006)

  11. 11

    Farquhar, J., Bao, H. & Thiemens, M. Atmospheric influence of Earth’s earliest sulfur cycle. Science 289, 756–758 (2000)

  12. 12

    Garvin, J. et al. Isotopic evidence for an aerobic nitrogen cycle in the latest Archean. Science 323, 1045–1048 (2009)

  13. 13

    Knauth, L. & Lowe, D. High Archean climatic temperature inferred from oxygen isotope geochemistry of cherts in the 3.5 Ga Swaziland Supergroup, South Africa. Geol. Soc. Am. Bull. 115, 566–580 (2003)

  14. 14

    Lyell, C. On fossil rain-marks of the Recent, Triassic, and Carboniferous periods. Q. J. R. Geol. Soc. 7, 238–247 (1851)

  15. 15

    Spilhaus, A. Raindrop size, shape and falling speed. J. Atmos. Sci. 5, 108–110 (1948)

  16. 16

    Magono, C. On the shape of water drops falling in stagnant air. J. Meteorol. 11, 77–79 (1954)

  17. 17

    Matthews, J. & Mason, B. Electrification produced by the rupture of large water drops in an electric field. Q. J. R. Meteorol. Soc. 90, 275–286 (1964)

  18. 18

    Lorenz, R. The life, death and afterlife of a raindrop on Titan. Planet. Space Sci. 41, 647–655 (1993)

  19. 19

    Pruppacher, H. R. & Klett, J. D. Microphysics of Clouds and Precipitation (Kluwer Academic, 1997)

  20. 20

    Willis, P. & Tattelman, P. Drop-size distribution associated with intense rainfall. J. Appl. Meteorol. 28, 3–15 (1989)

  21. 21

    Dodd, K. On the disintegration of water drops in an air stream. J. Fluid Mech. 9, 175–182 (1960)

  22. 22

    Beard, K. V. Velocity and shape of cloud and precipitation drops aloft. J. Atmos. Sci. 33, 851–864 (1976)

  23. 23

    Clift, R., Grace, J. R. & Weber, M. E. Bubbles, Drops and Particles Ch. 7 (Academic, 1978)

  24. 24

    Foote, G. B. & du Toit, P. S. Terminal velocity of raindrops aloft. J. Appl. Meteorol. 8, 249–253 (1969)

  25. 25

    van der Westhuizen, W., Grobler, N., Loock, J. & Tordiffe, E. Raindrop imprints in the Late Archaean-Early Proterozoic Ventersdorp Supergroup, South Africa. Sedim. Geol. 61, 303–309 (1989)

  26. 26

    Reineck, H. & Singh, I. S. Depositional Sedimentary Environments 61 (Springer, 1980)

  27. 27

    Huang, C., Bradford, J. M. & Cushman, J. H. A numerical study of raindrop impact phenomena: the elastic deformation case. Soil Sci. Soc. Am. J. 47, 855–861 (1983)

  28. 28

    Easton, R. Stratigraphy of Kilauea Volcano. In Volcanism in Hawaii (eds Decker, R., Wright, T. & Stauffer, P. ) 243–260 (US Government Printing Office, US Geol. Surv. Prof. Pap. 1350, 1987)

  29. 29

    Zachos, J., Dickens, G. & Zeeber, R. An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics. Nature 451, 279–283 (2008)

  30. 30

    Hren, M., Tice, M. & Chamberlain, C. Oxygen and hydrogen isotope evidence for a temperate climate 3.42 billion years ago. Nature 462, 205–208 (2009)

  31. 31

    Knauth, L. Temperature and salinity history of the Precambrian ocean: implications for the course of microbial evolution. Palaeogeogr. Palaeoclimatol. Palaeoecol. 219, 53–69 (2005)

Download references


This work was supported by NASA Exobiology/Astrobiology grant NNX08AP56G. We thank W. Van der Westhuizen of the University of the Free State in South Africa, and E. and D. Jackson of Omdraaivlei for their assistance when sampling in the field. We also thank E. Stüeken, A. Chen and K. Huntington at the University of Washington for laboratory assistance, and the staff at Metron Corporation for data acquisition. XRF measurements were performed by the Washington State University Geoanalytical Laboratory. Funding and field logistics for the Iceland fieldwork was supported by the Coordination Action for Research Activities on life in Extreme Environments (CAREX), a project supported by the European Commission Seventh Framework Programme. Funding and field logistics for the Hawaiian fieldwork was supported by the University of Washington Department of Earth and Space Sciences, and its Geoclub. D.C.C. was also supported by NASA Exobiology/Astrobiology grant NNX10AQ90G.

Author information

D.C.C. conceived the research project and established maximum-raindrop-size terminal velocity dependence on air density, R.B. led the field work in South Africa, collected the latex peels and analysed the grain sizes of the Ventersdorp tuff, J.P.H. found additional geographic and stratigraphic occurrences of raindrop imprints while performing field work and helping collect latex peels, P.M.P. collected experimental data and measured the Eyjafjallajökull and Pahala ash grain sizes, and S.M.S. developed the method of dimensionless momentum, collected the volcanic ash from Hawaii and Iceland, analysed the data, and led the experimental work. S.M.S., R.B. and D.C.C. discussed results and prepared the manuscript.

Correspondence to Sanjoy M. Som.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary References, Supplementary Figures 1-5 and Supplementary Tables 1-4. (PDF 3169 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Som, S., Catling, D., Harnmeijer, J. et al. Air density 2.7 billion years ago limited to less than twice modern levels by fossil raindrop imprints. Nature 484, 359–362 (2012).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.