arXiv:1105.5425v2 [astro-ph.EP] 30 May 2011 os ffc n leowr h aeas same the were albedo and green- Earth’s the effect the from If house energy today. does the it of that Sun 83% to 76% ceived greenhouse stronger a needed. [1]; is effect al. et Rosing by nie ihtelwlvlo CO of level low rec- the be with A onciled cannot paradox. climate the Archean resolving of temperate by two short of falls factor albedos a surface and cloud reduc- ing assumptions, plausible with strongest even that, the show We sur- reflective. and less resolved clouds face Earth’s be early can the paradox making as by the known that al. et is claim Rosing [1] this paradox’. at Sun today; young generally ‘faint as the was warm climate as least the but young, etl,Wsigo 89,UA cgold- USA. 351580, 98195, [email protected] Box Washington Washington, Laboratory,Seattle, of Planetary University Virtual and ment 94035, California MS Field, USA. Center, Moffett Research Ames 245-3, NASA sion, .H le .J jru,Ntr 464, Nature Bjerrum, J. C. & Sleep H. N. rsn rm .T oig .K Bird, K. D. Rosing, T. M. from: Arising uigteAcenen h at re- Earth the eon, Archean the During h u a ane hnteErhwas Earth the when fainter was Sun The 2 1 re omncto Arising Communication Brief pc cec n srbooyDivi- Astrobiology and Science Space rsn drs:AtooyDepart- Astronomy address: Present 4–4 (2010). 744–747 a n on u aao remains paradox Sun young Faint oi Goldblatt Colin 2 suggested 1 , 2 n ei .Zahnle J. Kevin and 1 fmr hn5 Wm 50 than more effect— of greenhouse the the increasing or reducing pos- albedo a forcing—from requires radiative paradox’ itive Sun young ‘faint w r nagailpro o) With Earth the now). reaching by period energy given of glacial amount a the in today are than (we warmer the typically that rare was indicates Archean are evidence sediments geological How-and glacial Archean Equator. ago, the ever, years reaching billion glaciers one with until contin- freeze in been deep have ual would Earth the now, iedfii nteAcenwudhv been have would (1 Archean the in deficit tive n euto ohg luswudcuea cause would Methods). cooling. clouds the high to in reduction described Any (our is paradox’ model Sun cloud young ‘faint forc- the a resolve Wm gives 25 This of entirely. ing clouds low remov- by ing found be would decreasing reflectivity abso- by cloud warming the on Therefore bound upper lute clouds. high dom- effect in greenhouse in inates the dominates and colder Reflection clouds, are low they surface. if the effect than greenhouse add the also they to but sunlight reflect they fects: 38Wm 1368 n h rsn-a oa constant solar present-day the ing oige l 1 utf less-reflective justify [1] al. et Rosing ef- radiative competing two have Clouds − 0 . 79) 2 F < F n albedo and = 2 afo hti eddto needed is what of half , 0Wm 50 1 4 (1 − 2 . 1 2 α α eouino the of Resolution . 3 Wm 239 = ) 0 = . ) h radia- the 3), 2 S (us- = clouds with the incorrect statements that Increasing the CO2 mixing ratio to 1000 most cloud condensation nuclei (CCN) are parts per million by volume (p.p.m.v.; the from biogenic dimethyl sulphide (DMS), upper bound according to Rosing et al. [1]) and that DMS is solely produced by eu- gives a forcing of 6 Wm2. Rosing et al. karyotes. DMS is also produced micro- [1] rely on 1000 p.p.m.v. CH4 for much bially [2]. Products of DMS contribute of their warming, ignoring relevant atmo- only 3% of Northern Hemisphere CCN and spheric chemistry. As the partial pressure 10% of Southern Hemisphere CCN today of CH4 (pCH4 ) approaches that of CO2 [3]. Other biological [4] and non-biological (pCO2 ), hydrocarbon haze forms in the sources, especially sea salt, provide CCN. If stratosphere, the cooling effect of which CCN production were to depend only on eu- outweighs the greenhouse effect of CO2 and karyotic DMS emissions1, we would expect CH4 [10,11]. Numerical models [12] predict to see significant cooling when eukaryotes haze production when pCH4 / pCO2 50.1 evolved, but no such cooling is evident. and haze production has been seen in labo- Nevertheless, we can assume no biologi- ratory experiments13 where pCH4/pCO2 = cal CCN supply and quantify the resulting 0.3. With 1000 p.p.m.v. CO2, the max- forcing. Over the modern ocean the effec- imum CH4 concentration that can give tive radius re of cloud drops rarely exceeds warming is 300 p.p.m.v., which would con- 15 µm [5] even in remote and unproductive tribute 7 Wm2 of additional forcing. regions (the re of 17 µm to 30 µm used by Changes to clouds could in theory con- Rosing et al. [1] is too high). For an upper siderably reduce the amount of greenhouse bound, we increase low cloud droplet size by gases required, because gaseous absorption 50% from our standard case, from 11 µm to depends on the logarithm of gas abundance. 16.5 µm. With no change in cloud thick- But even with the highly unlikely assump- ness, the forcing is 7 Wm2. Clouds with tion of no biological CCN supply, cloud larger drops may rain out faster. Param- changes can provide only one-quarter to eterizations of enhanced rain-out vary from one-half of the required radiative forcing. 1 proportional to (re,0/re) to proportional to Any changes to clouds would require strong 5 (re,0/re) .37 [6,7]; the corresponding extra justification, which Rosing et al. [1] do not forcing would be 4–15 Wm2 (remote sensing provide. A strong greenhouse effect is re- data for marine stratus suggest that the low quired in the Archean. The alternative is an end of this range is more appropriate [8]). extremely cold climate with continual mid- The sum is 11 Wm2 to 22 Wm2, with the to low-latitude glaciation, for which there is low end being most likely. no evidence The authoritative estimate of the global Methods We calculate the radiative energy budget [9] gives global mean and forcing (change in net flux at the ocean albedos of 0.125 and 0.090 respec- tropopause) on a single global annual mean tively. The largest realistic surface dark- atmospheric profile, with three layers of ening is from the present mean to an all- clouds that overlap randomly [14]. The ra- ocean world, which gives a radiative forcing diative fluxes on eight sub-columns corre- of 5 Wm2. sponding to each cloud combination are cal-

2 culated with the RRTM model [15]. For 9. Trenberth, K. E., Fasullo, J. T. & Kiehl, our standard case, cloud water paths are J. T. Earth’s global energy budget. Bull. Am. 2 [Whigh,Wmid,Wlow] = [20, 25, 40]gm , frac- Meteorol. Soc. 90, 311–323 (2009). tions are [fhigh,fmid,flow] = [0.25, 0.25, 0.40] 10. McKay, C. P., Lorenz, R. D. & Lunine, and the surface albedo is 0.125. Standard J. I. Analytic solutions for the anti-greenhouse effect: Titan and the early Earth. Icarus 91, lowand mid-level clouds are liquid with re = 11 µm and high clouds are ice with gener- 93–100 (1991). 11. Haqq-Misra, J. D., Domagal- alized effective size of D = 75 µm. For ge Goldman,S.D., Kasting,P. & Kasting, J.F. radiative forcings described in the text, the A revised,hazy methane greenhouse for the low cloud water path is varied but all other Archean Earth. Astrobiology 8, 1127–1137 parameters are unchanged. (2008). 12. Domagal-Goldman, S. D., Kasting, J. 1. Rosing, M. T., Bird, D. K., Sleep,N.H. & F., Johnston, D. T. & Farquhar, J. Organic Bjerrum, C. J. No climate paradox under the haze, glaciations and multiple sulfur isotopes faint early Sun. Nature 464, 744–747 (2010). in the Mid-Archean Era. Earth Planet. Sci. 2. Lin, Y. S., Heuer, V. B., Ferdelman, T. G. Lett. 269, 29–40 (2008). & Hinrichs, K.-U. Microbial conversion of inor- 13. Trainer, M. G. et al. Organic haze on ganic carbon to dimethyl sulfide in anoxic lake Titan and the early Earth. Proc. Natl Acad. sediment (Plussee, Germany). Biogeosciences Sci. USA 103, 18035–18042 (2006). 7, 2433–2444 (2010). 14. Goldblatt, C. & Zahnle, K. J. Clouds 3. Woodhouse, M. T. et al. Low sensitiv- and the faint young Sun paradox. Clim. Past ity of cloud condensation nuclei to changes in 7, 203–220 (2011). the sea-air flux of dimethyl-sulphide. Atmos. 15. Clough, S. A. et al. Atmospheric radia- Chem. Phys. 10, 7545–7559 (2010). tive transfermodeling: a summary of the AER 4. Leck, C. & Bigg, E. K. Source and J. Quant. Spectrosc. Radiat. Transf. evolution of the marine aerosol–a new per- codes. spective. Geophys. Res. Lett. 32, L19803, 91, 233–244 (2005). doi:10.1029/2005GL023651 (2005). Author Contributions: C.G. and 5. Breon, F. Tanre, D. & Generoso, S. Aerosol effect on cloud droplet size, monitored K.J.Z. discussed the article to which this from satellite. Science 295, 834–838 (2002). note responds. C.G. performed all model 6. Kump, L. R. & Pollard, D. Amplifica- runs and quantitative analysis. C.G. and tion of Cretaceous warmth by biological cloud K.J.Z. both contributed qualitative analysis feedbacks. Science 320, 195 (2008). and both contributed to writing the paper. 7. Penner, J. E. et al. Model intercompari- Competing financial interests: de- son of indirect aerosol effects. Atmos. Chem. clared none. Phys. 6, 3391–3405 (2006). doi:10.1038/nature09961 8. Kaufman, Y. J., Koren, I.,Remer, L. A., Rosenfeld, D. & Rudich, Y. The effect of smoke, dust, and pollution aerosol on shallow cloud development over the Atlantic Ocean. Proc. Natl Acad. Sci. USA 102, 11207–11212 (2005).

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