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Home , Arctic sea ice decline

The future of ice sheets and : Between reversible retreat and unstoppable loss

Dirk Notz1

Max Planck Institute for Meteorology, 20146 Hamburg, Germany

Edited by Hans Joachim Schellnhuber, Environmental Change Institute, Oxford, United Kingdom, and approved September 22, 2009 (received for review March 3, 2009) We discuss the existence of cryospheric “tipping points” in the briefly review the possible existence of the so-called “small ice-cap Earth’s climate system. Such critical thresholds have been sug- instability” before moving on to discuss the stability of the three gested to exist for the disappearance of sea ice and the elements of the Earth’s that are probably the most retreat of ice sheets: Once these ice masses have shrunk below crucial for the future evolution of the Earth’s climate: sea ice, the an anticipated critical extent, the ice– feedback might lead ice sheet, and the West Antarctic ice sheet (WAIS). to the irreversible and unstoppable loss of the remaining ice. We The paper closes with a short discussion. here give an overview of our current understanding of such thresh- old behavior. By using conceptual arguments, we review the recent The Ice–Albedo Feedback findings that such a tipping point probably does not exist for the The assumed existence of a tipping point during the loss of the loss of Arctic summer sea ice. Hence, in a cooler climate, sea ice Earth’s ice masses is often motivated by the destabilizing ice– could recover rapidly from the loss it has experienced in recent albedo feedback: If a certain ice cover is decreasing in size, the years. In addition, we discuss why this recent rapid retreat of Arc- albedo (i.e., reflectivity) of the formerly ice-covered region usually tic summer sea ice might largely be a consequence of a slow shift decreases. Hence, more sunlight can be absorbed, the additional in ice-thickness distribution, which will lead to strongly increased heating of which gives rise to further shrinkage of the ice cover year-to-year variability of the Arctic summer sea-ice extent. This until all ice is gone. variability will render seasonal forecasts of the Arctic summer sea- As simple as this feedback loop seems to be, it does not neces- ice extent increasingly difficult. We also discuss why, in contrast to sarily lead to an instability during the loss of ice, as described by Arctic summer sea ice, a tipping point is more likely to exist for the the so-called feedback factor. To explain this concept to a reader loss of the and the West Antarctic ice sheet. who is unfamiliar with it, it is instructive to use a very simple zero- dimensional energy-balance model that shows how a very simple Greenland | West Antarctic | | tipping point | Arctic negative (i.e. stabilizing) feedback, namely the increase of outgo- ing longwave radiation, can prevent the accelerating loss of a polar arely any other component of the Earth’s climate system has ice cover. B received as much public attention with respect to the possible Such a simple energy-balance model is often given by the bal- existence of so-called “tipping points” as the ice masses covering ance of incoming shortwave radiation and outgoing longwave the polar oceans, Greenland, and the Antarctic. This attention is radiation (e.g., 5); i.e., probably due to a number of reasons, including (i) the ease with dT 4 which the ice–albedo feedback and its possible consequence of c = (1 − α(T))FSw − εσT . [1] a tipping point can be explained; (ii) the rapid decrease of Arc- dt tic summer sea-ice extent in 2007; and (iii) the consequences for Here, c is heat capacity, T is temperature, t is time, FSw is the the global sea level if indeed the Greenland ice sheet and/or the mean incoming shortwave radiation at the ground, α is albedo, ε Antarctic ice sheet were to melt rapidly. is the effective emissivity, describing the partial opaqueness of the Although these points may well have led to a tipping point atmosphere to outgoing longwave radiation, and σ is the Stefan– in the public perception of the future melting of the Earth’s ice Boltzmann constant. In a warmer climate, the albedo of the Earth masses, there still exists a significant lack of scientific understand- is likely to decrease because of the smaller extent of snow and ice. ing of the cryospheric “tipping elements”. In this contribution, we Following ref. 6, we approximate this temperature dependence of review some of the recent scientific progress regarding the future the albedo as linear and set evolution of the Earth’s cryosphere and discuss conceptually the α(T) = α − βT. possible existence of cryospheric tipping points. Following ref. 1, 0 these tipping points are here defined to exist if the ice does not To examine the stability of the temperature to small changes recover from a certain ice loss caused by climatic warming even ΔT, we substitute T with T + ΔT in Eq. 1 and linearize to obtain if the climatic forcing were to return to the colder conditions that + Δ d(T T) 4 3 existed before the onset of that specific ice loss. This definition is c = (1 − α0 + βT + βΔT)FSw − εσT − 4εσT ΔT. more restrictive than the one recently formulated in ref. 2: For a dt tipping point to exist according to our definition, the response of a [2] climatic element must show significant hysteresis. We believe that Subtracting Eq. 1 from Eq. 2 leads to this definition is in accordance with the early parlance of tipping d(ΔT) points in the sociological literature (3, 4) and with most of the pre- c = (βF − 4εσT 3)ΔT. [3] vious analysis of nonlinear cryospheric behavior that is reviewed dt Sw in this contribution. Note also that we here do not discuss a tipping of the external atmospheric and oceanic forcing that could lead to the irreversible loss of sea ice or ice sheets. We instead focus on Author contributions: D.N. designed research, performed research, analyzed data, and tipping points that are inherent to the cryosphere. wrote the paper. In the following, we first outline in a simple energy-balance The author declares no conflict of interest. model why the existence of the ice–albedo feedback does not This article is a PNAS Direct Submission. necessarily lead to instability of the Earth’s ice masses. We then 1E-mail: [email protected].

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For (see cover discussion). ice the radi- the of longwave stabilizing outgoing thus size the ation, the increases well decreases also only might but not region pole ice-covered warming the any at because cover stable ice be an mechanism, feedback albedo too-low e.6 and 6) ref. nusal edakwudb salse.Introducing established. be would 5.67 feedback than larger unstable is an change side temperature right-hand small the any on zero, expression bracketed the If Notz oe htetnsfo h ot oea es sfrsuhas south far as ice least polar at a Pole to North latter the the from 78 and for- extents ocean the that ice-free with type”, cover an glacial to a polar and referring oceanic type mer of mild a types polar possible, two in are “only cover Meteorological climate that ice concluded Royal finite-sized He a the (10). of at regions stability discussed the London Brooks P. in Society E. C. 1924, In Instability Ice-Cap Small The will which section. following instability, the ice-cap in small reviewed so-called be the often of decades, a few context not last the has the in climate or in warmer attention a whether theoretical in much of stable received be question indeed will The cover triggered ice feedback. finite-sized instability ice–albedo obvious very the suffi- apparently by be of the might increase remove climate, the to warmer here cient a in feedback, radiation stabilizing longwave any outgoing that eluci- fact model the longwave energy-balance outoing dates important simple in this change more the Nevertheless, be than radiation. might ice sea exchange Arctic heat stabilizing for lateral example, in for suggests, changes study that His (7). Winton as by neglected, recently been discussed have factors num- relevant a other because and least feedbacks not of estimate masses, ber quantitative ice Earth’s reliable the a of give instability to the of used be not should 9). and (1, not studies in modeling discussed more-complex as in reason found nonlinear. also different is strongly a Ice, be for Sea could but cover result, smaller ice similar energy- smaller a A a simple with to this climate transition unstable warmer the in become future well stable might a were it in climate, cover today’s ice for model an balance if even of Hence, value space, the into hence emission longwave and of efficiency the Eq. concentration, in gas stability the determining eoesalradsalrutli disappears. it self-induced until this smaller and decrease, hence would smaller to cover become ice were The more. cover and more ice diminish would this albedo. cooling high of its self-induced to extent owing the the cause on would If cover rapidly based of ice disappear is large cap a argument and that ice His cooling unstable an climate. be where warming would land, a size on in certain ice a for than held less also argument his that omncto) h tblt rtro eue o oa’ climate to today’s for reduces criterion stability personal the Voigt, communication), (A. model circulation general ocean–atmosphere w motn ocuin a edanfo Eq. from drawn be can conclusions important Two h eodipratcnlso eae oterl of role the to relates conclusion important second The ◦ oeta h ipeeeg-aac oe rsne eecan- here presented model energy-balance simple the that Note β< .Atog i icsinfcse nsaie eremarked he ice, sea on focussed discussion his Although N. 2 · , 10 0.0154K T β −8 = orsodn oa nufiin tegho h ice– the of strength insufficient an to corresponding , β Wm 5 serf ) h rcee xrsini Eq. in expression bracketed the 7), ref. (see K 255 = −1 0.0145K −2 ie rvosetmtsof estimates previous Given . K −4 h ml c-a Instability). Ice-Cap Small The svr ieyt eraei h future. the in decrease to likely very is ε, −1 β< n enAci ausof values Arctic mean and ≈ serf ) h oa c oe were cover ice polar the 8), ref. (see 0.022K .,a siae rmacoupled a from estimated as 0.7, ihicesn greenhouse- increasing With 4. ΔT −1 ε ol rwrpdy and rapidly, grow would nsc climate, a such In ε: β = 0.009K F is,for First, 4. Sw −1 = Arctic σ (see ε 173 [4] in = 3 et,alcletdi h aIS aae 1,1) o consis- the For to similarly 19). modified were (18, data these dataset studies, HadISST earlier with the tency in ship collected of all combination measure- satellite a ments, and from flights, derived reconnaissance until were aerial 1953 data observations, from The extent 1). sea-ice (Fig. Arctic 2008 minimum of series time the sea-ice Arctic of such perspective really the long-term 2007 for the summer exist evolution? in was does But event point ice. unusual sea tipping an summer a Arctic increased that of given claim loss has decrease the This to (17). momentum 1950s early the during as hwtecag netn rmoeya otenext. the to bottom year the one at from bars extent the in and extent, change sea-ice the minimum show the shows line blue The 1. Fig. c xeto rtcsaiedcesdb oeta . million 1.6 than more by decreased ice sea one minimum km Arctic just the recent of of 2007, the course September extent to the until ice contrast In 2006 in ice. September be sea from to summer year, Arctic appear of first sum- retreat of at loss rapid might the ice for exists sea instability mer no probably that finding The Ice Sea ice Arctic sea of free 9). virtually 7, is (1, that year ice-covered entire Ocean seasonally the Arctic a throughout an from to transition instability Ocean the an Arctic whereas for ice, exist sea instability well summer such Arctic might no of that loss probable the number indeed for a is exists it Recently, that instability. they found ice-cap that studies small expected of the was show it not transport, might real- heat more North of employ by representations usually models detail istic complex in more explained that Given was (16). instability the removes regions 15). 14, edge the (e.g., at cover transition ice albedo nonlinear the smooth a of a for or the disappears transport of instability heat interior its diffusive the the by example, from exemplified For diffusion as cover. heat cover, ice of ice strength the the of and effect albedo parameteri- cooling the the on of crucially zation the depends Therefore, instability Brooks. the by for described threshold initially an that by and to caused similar 11–14, is effect instability (refs. the models, instability these similar In therein). a references showing models with models, such has energy-balance main- of many exists times to indeed early enough instability the large since this debated is Whether been that (9). claims one climate principle own is its cover in tain ice which stable instability, only the ice-cap that small the as known oeaieti usin ti ntutv ofis ipylo at look simply first to instructive is it question, this examine To h atta olna ettasotit n u ftepolar the of out and into transport heat nonlinear a that fact The now is what describe to first the probably is account Brooks’ 2 edn oasme e-c xetta a nyhl slarge as half only was that extent sea-ice summer a to leading , vlto fmnmmAci e-c xetfo 93utl2008. until 1953 from extent sea-ice Arctic minimum of Evolution PNAS eebr8 2009 8, December o.106 vol. o 49 no. 20591

SUSTAINABILITY ENVIRONMENTAL SPECIAL FEATURE SCIENCE SCIENCES procedure described by Meier et al. (20): All data since 1997 were replaced by the updated dataset given by the National Snow and Ice Data Center sea-ice index (http://nsidc.org/data/seaice_index/, ref. 21), and the HadISST data predating 1997 were adjusted by a positive offset of 0.25·106 km2. This adjustment results in a some- what larger recent decrease in ice extent than was described by the original HadISST dataset. The blue line in Fig. 1 shows the resulting minimum sea-ice extent, and the bars at the bottom show the year-to-year changes. Whereas the extreme minimum of summer 2007 clearly stands out, the year-to-year change from 2006 to 2007 is only somewhat larger than previous extreme changes: From 2006 until 2007, the mini- mum sea-ice extent decreased by 1.63 · 106 km2. Previous record reductions were observed from 1978 to 1979, then amounting to a decrease in ice extent of 1.39·106 km2, and from 1967 to 1968, then with a decrease in ice extent of 1.38 · 106 km2. The rapid recent retreat that was experienced in summer 2007 is hence, per se, not necessarily an indication that a tipping point exists for Arctic summer sea ice. The observed loss of ice extent in summer 2007 can instead read- ily be explained by a smooth and gradual change in ice-thickness distribution, with no need to employ the concept of a tipping point. In the Arctic, sea-ice thickness varies greatly on all hori- zontal length scales from a few meters to the width of the basin. While the large-scale differences in ice thickness come about from differences in atmospheric and oceanic forc- Fig. 2. Comparison of the impact of a certain amount of summer melt on the ice-covered area for two different ice-thickness distributions. The black ing, the small-scale differences are usually a result of local sea-ice line shows which percentage of a certain area is covered by ice that is thicker dynamics. This variety of ice thicknesses can be visualized by their than the ice thickness indicated along the x axis at the beginning of the melt histogram, which then forms the ice-thickness distribution (22). season (cumulative ice-thickness distribution). A shows a possible cumulative In such ice-thickness distribution, there is usually a typical, modal thickness distribution of thick ice and B shows that of thinner ice. The colored ice thickness that covers a comparably large area (see sample lines indicate the shift of the ice-thickness distribution for a uniform melting distributions in the insets of Fig. 2). during summers of 0.5 m (cold summer, blue), 0.75 m (normal summer, green) Integrating an ice-thickness distribution results in the so-called and 1.0 m (warm summer, red), respectively. Note the much stronger variabil- cumulative ice-thickness distribution, which is shown in the main ity of the remaining ice-covered area in the case with thinner ice. The Inset frames of Fig. 2 for an area covered with thick ice (Fig. 2A is shows roughly the noncumulative ice-thickness distribution for each case. Here, the y axis indicates normalized area that is covered by the ice thickness exemplary for Arctic sea ice until the early 1990s) and for an area shown along the x axis. covered with thinner ice (Fig. 2B is representative of much of today’s Arctic sea ice). In each case, the black line indicates which percentage of the area is covered by ice that is thicker than the ice has sometimes been described as an increase in “open-water effi- thickness that is given along the x axis. cacy” (e.g., 26, 27). Because of the nonlinear ice-thickness dis- The black line is assumed to show the cumulative ice-thickness tribution, a gradual thinning of the ice cover can initially lead distribution for a certain area at the onset of summer melting, to an acceleration, and, at some point, a very rapid loss of ice- and the three colored lines represent different amounts of thin- covered area during summer. Once the modal ice thickness is less than a typical summer melt rate, the additional ice retreat ning during summer. For simplicity, we make the assumption that will again proceed at a slower rate. This conceptual image might all ice in this area experiences roughly the same thinning, which help to rationalize the possibly rather sudden future reduction implies that the ice-thickness distribution preserves its shape dur- in summer sea-ice extent, followed by a slower retreat of the ing summer and is simply shifted to the left. The area that becomes remaining ice that has been found in a number of recent modeling ice-free during a particular summer is given by the area initially studies (26–28). covered by ice thinner than the assumed total thinning during A second conclusion that can be drawn from considering the that summer. Because most ice for the thick-ice case in the top shift in the ice-thickness distribution is the fact that with a thinner frame is much thicker than 1 m, only a small fraction of the area sea-ice cover, the size of the area that becomes ice-free during becomes ice-free during summer, whether the summer is relatively summer depends much more on the actual weather during a par- cool with, say, just 0.5 m thinning or relatively warm with 1.0 m ticular summer than is the case for thicker ice. Therefore, with the of thinning. Hence, with thick overall ice cover, the year-to-year ongoing thinning of the ice cover (23, 25), we are likely to experi- variability of ice extent during summer is relatively small. ence both large negative and large positive year-to-year changes Now consider Fig. 2B, which shows the impact of a much thin- in Arctic summer sea-ice extent. This variability directly implies a ner ice-thickness distribution: Because here most of the ice has much-reduced predictability of sea-ice extent a season ahead than a thickness of around 1 m, the area that becomes ice-free during does thicker ice. The increased variability will continue until most summer crucially depends on the amount of total melting: In the of the ice cover is thinner than the typical summer melting rate, example shown here, 90% of the area remains ice covered for a at which point most of the ice will disappear during summer, with total melt of 0.5 m during a relatively cool summer, whereas only only small year-to-year changes. The decreased predictability that 50% of the area remains ice covered for1moftotal thinning goes along with such an increase in variability was also found in a during a warmer summer. recent more complex modeling study (27). From this qualitative description, we can draw two conclusions, The transition to a state with a much-reduced summer sea-ice which might prove crucial in the assessment of recent years’ melt- cover will probably show periods of strongly increased rates of ice ing events: First, with a thinner ice-thickness distribution, the same loss, as has been discussed above. Nevertheless, a number of recent amount of heat input leads to a much larger ice-free area, as has studies find that the transition to a seasonally ice-free Arctic is been noted by several previous studies (23–27). This relationship probably reversible in a climate that is cool once again. (1, 7, 9, 28).

20592 www.pnas.org / cgi / doi / 10.1073 / pnas.0902356106 Notz Downloaded by guest on September 25, 2021 Downloaded by guest on September 25, 2021 itr hsso oe eyefiinl nuae h xsigice existing the insulates efficiently very the cover of most snow throughout ice This this on winter. of cover lead- snow 1, amounts thicker much November a significant before to ice ing here, preexisting shown the on example accumulate fast, snow the very grows in initially First, ice second, twofold: thin the and are thickness ice increase low this the its of for 4c, because reasons figure sea- The his become has ice-free. In to Arctic sonally (33): the similar once 1966 is increases finding from thickness ice This Budyko maximum growth. by its results was of early which onset the ice, the preexisting at the thicker winter, than cm during 85 thickness grow to ice less larger surprisingly, to months a two Maybe assumed reaches has graph). is it though (blue water even m 1 ice, open 1.75 this November from about on forms of growing that thickness start ice ice The maximum graph). the follow- a the (red at reaches During cm it September. 85 early winter, about in that ing of season ice the melting thickness the the of ice of here, an end end shown has the example summer after the one In months survived the 3). to some (Fig. exposed water season forms, open melting that in ice of forcing, evolution same the and summer tain snow. of impact even the becomes considers that also ice effect one the if winter—an stronger summer, during during rapidly thinning recover below strong can well very remain after temperatures air even winter freezing, feedback as has This long as 32). as 31, feedback, (e.g., that stabilizing studies implies of a number to a by rise discussed gives been growth thick faster than faster This substantially ice- grows (30), ice. ice 1889 the thin in that growth to known been ice has related on it works feedback early Stefan’s stabilizing Since a rate: sea growth by of retreat compensated the during is instability feedback, ice, an trigger ice–albedo could the itself that by find an which transition to authors finally the and These cover of Arctic. (29), ice seasonal space ice-free a Thorndike phase to cover by the ice permanent examine described a from to setup them the allows on which largely model based simplified a setup use (1) Wettlaufer and Eisenman example, For top on snow-cover isolating thinner the former. the of of because Note ice thickness ice. preexisting maximum preexisting larger the the a than reaches of ice season forming 1, melting newly November the the on nevertheless, of that, start end to forcing. the prescribed oceanic after was or months ice 67) atmospheric two sea the ref. first-year to (see the ice of model the formation zero-layer from Ice feedback a For clima- no by is (66). Arctic simulated there Untersteiner by was and and given growth Maykut ice are by the snowfall, summarized simplicity, of as values amount mean the boundary tological and oceanic and fluxes, and sensible atmospheric heat radiation, incoming The represented latent the is including areas. ice simulation, red this the for and of conditions top blue on shaded snow The the (red). by ice preexisting of and (blue) 3. Fig. Notz opr,freape h vlto fieta uvvdacer- a survived that ice of evolution the example, for Compare, ceai oprsno h c-hcns vlto ffis-erice first-year of evolution ice-thickness the of comparison Schematic nryblnemdl hsi qiaett nicesdvlefor value simple increased an the to β In equivalent cover. is until sea-ice this to winter spring model, energy-balance disappearing enough from rapidly feedback up a ice–albedo heated to lead the be increasing all will ice-free possibly water long becomes autumn, open area for the certain ice-covered round, a remains Once year summer. Arctic the the of of periods cover sea-ice most widespread winter, This a during 9). with of Today, strength 7, the feedback: in (1, change ice–albedo point the the by tipping rationalized part a in of is point existence tipping the find studies recent summer Arctic ice. the for sea of allow response probably corresponding will immediate warming rather global a to reverse taken even is or that down measure slow any that implies feedback 2007. summer summer stabilizing in This in observed extent again minimum the increase after to 2009 and extent 2008 sea-ice Arctic the for possible as thickness same the ice. preexisting almost with single of one area ice just the of with end covered the at season, is, growth. growth area its ice-free formerly down the slowing effect, significantly In atmosphere, cold the from h osbeeitneo ipn on o h iapaac of disappearance the for point assess tipping to a importance greater of of existence likely possible most the IPCC is it last summer, the the vives for used models the the to 40). of contrast (39, in most report (38), by decades slight simulated three a last reports trend study the recent over A trend therein). upward (refs. references ice 1970s and sea late 37 the Antarctic until and of century 36 twentieth retreat the a of middle for the ref- evidence since data, and debated whaling 35 some on is (ref. based there extent records suggest proxy sea-ice studies Including Antarctic of therein). total number erences in a eventu- decades, trends to few large ice last no sea the For of it. underside melt the transport ally to can due heat eddies is of ocean ice Ocean, amounts Southern this winter significant the of during in loss that there The fact formed the summer. to is following the rather that survive is ice not situation sea does the the Antarctic, of the Most In different: ice. expected sea and Arctic observed the of on changes exclusively focussed have we far, So Ice Sea ice-free Antarctic an to transition that the given in case (26). the nonlinearity Arctic especially show is models This definition. many al. to tempera- according et the behavior Lenton tipping in show the change well might the small ice in relatively sea forcing, ice a ture sea by of triggered disappearance are complete future possible Arctic the of state and retreat different ice observed qualitatively the sea a that Given into perturbations.” “switched small be by can tipping it shows if element al. climate behavior et a definition, Lenton their of to definition According broader (2). the to according behavior ping (IPCC) Change Climate on model (34). Panel in report presented Intergovernmental were spread last that the ice the by sea in of reflected evolution also future the is for that projections ice sea complexity. of future model the evolution regarding of uncertainty significant range a of still large is number there a However, a employed in that confirmed given been studies arguments all recent the have Although they amounts winter. conceptual, are significant during here form if still only ice last exists sea cooler the reversibility of become during this to were experienced (iv) climate ice and the if again; sea reversible be of to loss likely is the years (iii) future; significantly increase the to in likely year- is the extent (ii) sea-ice unlikely; in seems variability to-year here point used tipping definition a the ice to sea according summer Arctic of (i) disappearance why the to as during studies complex more from results recent some section nEq. in o h oso itrsaiei uhwre lmt,some climate, warmer much a in ice sea winter of loss the For was it why part in explains that feedback stabilizing this is It ie httdyarayls hn1%o naci e c sur- ice sea Antarctic of 15% than less already today that Given tip- show well might ice sea summer Arctic of loss the that Note this in rationalized have we arguments, conceptual using By 4. PNAS eebr8 2009 8, December o.106 vol. o 49 no. 20593

SUSTAINABILITY ENVIRONMENTAL SPECIAL FEATURE SCIENCE SCIENCES Antarctic winter sea ice. Such a disappearance would have a pro- Fourth, there is no paleoclimatic evidence for any tipping-point found impact on Southern Ocean circulation (e.g., 41). In light of behavior of Arctic sea ice during the past several million years, the so-called Weddell in the 1970s, and taking the struc- during which the Arctic ocean has probably been permanently ture of the Southern Ocean into account, there has been some ice-covered (48). In contrast, there is widespread consensus on speculation about the possibility of a sudden, sustained disappear- the existence of paleoclimatic evidence for ice-sheet instability ance of sea ice over a large area triggered by so-called thermobaric during that time (49, 50), with at least two sudden events during convection that would bring warm water to the surface and prevent the last deglaciation that led to a sea-level rise of 20 m in a few winter ice formation (42). However, more-sophisticated modeling centuries (51, 52). Notwithstanding the potential for future insta- studies are needed to assess the likelihood of such an event taking bility of the Earth’s ice sheets, it should be noted that a sea-level place, not least under a global-warming scenario. Currently, our rise even remotely this large seems impossible in the foreseeable understanding of the Southern Ocean is too limited to assess real- future (53), not least because those meltwater pulses contributed istically the likelihood of a sudden, irreversible decrease in sea-ice the equivalent of between 1.5 and 3 Greenland ice sheets each (51). extent occurring over the next several decades. Fifth, there is some evidence from general circulation models that the removal of the Greenland ice sheet would be irreversible, Greenland and WAIS even if climate were to return to preindustrial conditions (54), which increases the likelihood of a tipping point to exist. This Most early studies that dealt with instabilities of the Earth’s cryo- finding, however, is disputed by others (55), indicating the as-of- sphere did not distinguish between ice on land and ice in the sea. yet very large uncertainty in the modeling of ice-sheet behavior in Given that chances are high that there is no tipping point accord- a warmer climate (56). ing to our definition for the loss of summer sea ice in the Arctic, the Sixth, there is also some indication for the existence of a tipping question therefore naturally arises whether the same might hold point for the loss of the WAIS in a warming climate. The change of for the large ice sheets covering Greenland and the West Antarc- the scientific consensus with time whether this ice sheet is stable tic. To answer this question, it is instructive to discuss briefly, with is an example for the existence of what has been referred to as no claim to be complete, some of the main differences between “negative learning” (57): soon after the early works of Mercer in the loss of sea ice and the loss of ice sheets, mostly to show why the late 1960s, culminating in his famous 1978 publication (58), the nonexistence of a tipping point for the former has no conse- it was widely agreed that the WAIS was indeed unstable. During quences for the existence of a tipping point for the latter. These global warming, floating ice shelves would disintegrate rapidly, differences can be summarized as follows. giving way to an accelerating loss of the vast ice sheets covering First, as discussed above, the growth rate of sea ice depends cru- the western Antarctic. This paradigm lost some momentum during cially on its thickness, with thin ice growing much faster than thick the 1980s and early 1990s when some modeling studies suggested ice. This faster growth allows both for a relatively strong resilience that the ice sheet might be stable even if the floating ice shelves against a sudden acceleration of sea-ice volume loss and for a quick were lost. More-recent satellite observations and laser altimetry recovery of summer sea ice when the climate becomes cold once have in turn again suggested that the WAIS might indeed be unsta- again. For ice sheets, there are also a number of stabilizing feed- ble, contributing significantly to sea-level rise in the coming two backs. The growth of ice sheets depends almost exclusively on the centuries (for details see reviews in refs. 59 and 60). A recent accumulation of snow on its surface, and because warmer air can analysis of the stability of ice-sheet grounding lines has also given transport more moisture, the amount of snow-fall usually increases renewed evidence that the WAIS might indeed be unstable (61) if in a warmer climate and with decreasing surface elevation. Model global warming exceeds a certain threshold. Recent modeling and studies have also found some stabilizing feedback relating to air- paleoproxy studies also suggest that small changes in the forcing circulation changes at the ice-sheet margin (43). Although these can lead to “brief but dramatic” retreats of the WAIS (62, 63). two effects combined provide some negative feedback to keep ice It seems, hence, at the moment well possible that a tipping point sheets stable over a certain range of climatic conditions, their mag- exists for a possible collapse of the WAIS. nitude is probably not comparable with the very strong stabilizing Note that there are a great number of additional processes that feedback that is exhibited by the large increase of the growth rate render the behavior of ice sheets inherently different from that for thin sea ice. of sea ice. Nevertheless, this brief overview already indicates the Second, a smaller sea-ice extent basically enhances the original possible existence of a tipping point for the loss of the Earth’s ice warming only because of the ice–albedo feedback mechanism. Ice sheets. In this context, it should be noted that the local warming sheets, however, will additionally have their surface temperature ◦ needed to slowly melt the Greenland ice sheet is estimated by increase by 0.6–1 C per 100-m loss of their vertical extent. This ◦ some authors to be as low as 2.7 C warming above preindustrial increase is due to the adiabatic lapse rate that makes the surface temperatures (64, 65). This amount of local warming is likely to temperature increase by a certain amount with reduced height. ◦ be reached for a global warming of less than 2 C (39). Third, as far as dynamics are concerned, a thinner sea-ice cover is more prone to the ice floes being squeezed together to even- Conclusion and Summary tually pile up on top of one another. This tendency provides for two different mechanisms which both can increase ice thickness. In this contribution, we have examined the existence of so-called First, the piled-up ice floes constitute thicker ice. Second, ice piling tipping points during the loss of sea ice and during the melting up produces more open water (22) (where during summer more of the Greenland and WAIS. We have discussed why sea ice solar radiation can be absorbed but where in winter more new sea and ice sheets show greatly different behavior, with different ice can be formed) than if that area had remained ice-covered. consequences for the existence of a tipping point. A thinning of sea ice can hence lead to changes in its dynamics For Arctic sea ice, we have explained why the recently observed that can slow down this thinning—another stabilizing feedback. rapid decrease in ice extent might just be a consequence of a Such feedback does not exist to the same extent for the loss of ice smooth and slow shift in ice-thickness distribution. We have also sheets where, usually, changes in ice dynamics will lead to faster explained how the ice cover is stabilized in more-complex studies ice loss in a warmer climate. Although the details of the impact because of the strong increase of ice-growth rate with shrinking of global warming on ice-sheet dynamics remain unclear, in part ice thickness. These more-complex studies conclude that there is because of a lack of understanding of the induced changes in basal probably no tipping point (according to the definition used here) friction and the seaward margin of the ice sheet (44), it seems likely for the loss of Arctic summer sea ice. Hence, sea ice is probably that the observed acceleration of many of the Greenlandic outlet capable of recovering rapidly once the climate turns cold again, glaciers is due to a combination of several effects linked to such and any measures taken to slow down climate warming can imme- warming (45–47). diately slow down future sea-ice loss. If no measures are taken to

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Fellowship Planck this Research three Junior Max by improve a through suggestions significantly funded of was and to work version comments This helped previous for that a thankful reviewers very on anonymous am comments I and and manuscript. 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