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Sea will rise ‘to levels of last Ice Age’

Filed under: — stefan @ 26 January 2009 - (Italian) (Chinese (simplified))

cogee beachThe British tabloid Daily Mirror recently headlined that “Sea will rise ‘to levels of last Ice Age’”. No doubt many of our readers will appreciate just how scary this prospect is: sea level during the last Ice Age was up to 120 meters lower than today. Our favourite swimming beaches – be it Coogee in Sydney or the Darß on the German Baltic coast – would then all be high and dry, and ports like Rotterdam or Tokyo would be far from the sea. Imagine it.

But looking beyond the silly headline (another routine case of careless science reporting), what was the real story behind it? The Mirror article (like many others) was referring to a new paper by Grinsted, Moore and Jevrejeva published in Climate Dynamics (see paper and media materials). The authors conclude there that by 2100, global sea level could rise between 0.7 and 1.1 meters for the B1 emission scenario, or 1.1 to 1.6 meters for the A1FI scenario.

The method by which they derive these estimates is based on a semi-empirical formula connecting global sea level to global temperature, fitted to observed data. It assumes that after a change in global temperature, sea level will exponentially approach a new equilibrium level with a time scale τ. This extends the semi-empirical method I proposed in Science in 2007. I assumed that past data will tell us the initial rate of rise (and this initial rate is useful for projections if the time scale τ is long compared to the time horizon one is interested in). The new paper tries to obtain both the time scale τ and the final equilibrium sea level change by fitting to past data.

Therefore, my approach is a special case of Grinsted’s more general model, as you can see by inserting their Eq. (1) into (2): namely the special case for long response times (τ >> 100 years or so). Hence it is reassuring and a nice confirmation that they get the same result as me for their “Historical” case (where they get τ=1200 years) as well as their τ=infinite calculations, despite using a different sea level data set (going back to 1850, where I used the Church&White 2006 data that start in 1880) and a more elaborate statistical analysis.

However, I find their determination of τ is on rather shaky ground since the data sets used are too short to determine such a long time scale with any confidence. That their statistics suggest otherwise cannot be right – you can tell by the fact that they get contradictory results for different data sets (e.g., 1200 +/- 500 years for the “Historical” case and 210 +/- 70 years for the “Moberg” case). Both can’t be correct, so the narrow uncertainty ranges are likely an underestimate of the uncertainty.

The problem gets even more apparent when looking at the equilibrium sea level resulting from their data fit. From paleoclimatic data (see Figure) we expect that per degree of temperature change, the final equilibrium sea level change is somewhere between 10 and 30 meters (as I argue in my Science paper – this was my basis for assuming τ must be very long). Grinsted et al. find from their data fit that this is only 1.3 +/- 0.4 meters (for the Moberg case, which they call the most likely) – see Figure. This means that getting the sea level lowering of ~120 meters that is well-established for the Last Glacial Maximum would have required a global cooling of about 90 ºC according to their model. And for the future, the model would predict that melting all ice in Greenland and Antarctica (resulting in 65 meters of sea level rise) would require about 50 ºC of global warming. This lack of realism matters, since it is directly linked to the short τ: the observed sea level rise of the past century or so can either be fitted by a short τ and a small equilibrium rise, or by a long τ and a large equlibrium rise (per degree). I consider the latter case the realistic one.

Global mean temperature and sea level (relative to today’s) at different times in Earth’s history, together with the projection for the year 2100 (which is not an equilibrium change!). The red line shows the “most likely” equilibrium response according to Grinsted et al. [Modified after Archer (2006) and WBGU 2006; see p. 33 there for references and discussion.]

Grinsted et al. did apply some paleoclimatic data constraints, but they are based on a misunderstanding of these data. They assume (their constraint 3) that the last interglacial was globally 3-5 ºC warmer than present – however the reference cited in support (the IPCC paleoclimate chapter, of which I am a co-author) explains that these are Arctic summer temperatures. This Arctic summer warming is due to orbital changes which cause cooling elsewhere on the planet, resulting in global mean changes that are very small (see e.g. Kubatzki et al. 2000). Grinsted et al make the same mistake for glacial climate (their constraint 4), where they assume glacial maximum temperatures were globally 17 ºC below present – the reference cited states already in the abstract that this only applies to the latitude band 40-80ºN. Glacial cooling was highly non-uniform, with global mean cooling estimated as 4-7ºC (see Schneider et al. 2006, “How cold was the Last Glacial Maximum?”) These misguided paleo-constraints lead Grinsted et al. to limit equilibrium sea level rise to a fraction of what the data points show in the Figure above, and this rules out a good data fit for long time scales τ.

For these reasons I am unconvinced by the short τ found (or assumed) by Grinsted et al. which is the key difference to my earlier study, and I would still maintain that assuming the equilibration time to be very long is a more robust assumption. Note that (unlike Grinsted et al.) this does not assume that the approach to equilibrium is exponential with a single time scale, which in itself is doubtful given the different processes involved. It only assumes that the initial rate of rise scales with temperature and is relevant on time scales of interest. On the positive side, Grinsted et al. have shown that the data fit and projected sea level rise for the case of large τ is robust with respect to the chosen statistical method and data set.

Refinements of the semi-empirical approach are welcome – I had hoped that my paper would stimulate further work in this direction. While empirical approaches will not give us definitive answers about future sea level since the past can never be a perfect analogue of the future, these analyses can still be useful to give us a better feeling for how the sea level responded in the past and what that might imply for what lies ahead. But one thing is certain: I’m not too worried that sea level might drop to glacial levels during this century.

68 Responses to “Sea will rise ‘to levels of last Ice Age’”

  1. 51
    Florifulgurator says:

    Well, sure my guess was not supported by models and observations (except for the estimate of current Greenland melt rate). I didn’t even need a pencil to do the math (programmers know powers of 2 by heart).

    Looks the SLR thing is the most alarmo-thrillo aspect of AGW, making even Gavin’s hair stand on end. So it can’t be (and we can’t say) meters by 2100 because 1m would already be catastrophic? Come on, every skeptical thinker knows 1m is no problem. 1cm/y bah!

    (Sorry for ranting. Feel free to delete this post.)

    Now something positive:
    It is delicious to see the experts discuss their research here. Even if most readers don’t understand or know the details, providing the opportunity to watch this is a great service to public education. The Internets university, my dream. Keep up the great work.

  2. 52
    Sekerob says:

    Florifulgurator #51

    Come on, every skeptical thinker knows 1m is no problem

    Is this your qualified “skeptical opinion? I think you’ve been reading too much Monckton, Spencer, Wotts, McIntyre, Hays, Booker and their auto-nodders. 1 meter global average is not evenly spread. Rivers will be backing up. Many tens of billions have to be spend to heighten levies, many low lying islands will incur high tide flooding, beaches will wash away large scale. What I do know is that the local coastal town at 1 meter will run under even without any tide.

    Oh and do skeptical thinkers all “think”? Reflect a moment about a country like Bangladesh that’s poor as it is and low lying.

  3. 53
    Deep Climate says:

    #52 To be fair to Flori, he’s not a “skeptic” if he finds Hannsen’s “horror” credible. But that’s another problem with the unrealistic projections – compared to those, 1 m “sounds” OK, and the skeptics can more easily get away with saying: “You see? There’s no catastrophe coming after all!”

    To Sekerob’s list we could add that higher SLR *plus* more high-intensity storms (with surges) in the North Atlantic will be a real problem even for “developed” low lying coastal areas.

  4. 54

    If there’s an award for the stupidest headline to trigger an interesting discussion, this must be it. Well done on moving fast from pointing out the obvious flaw in the headline to quality discussion of the science.

  5. 55
    Nigel Williams says:

    Although useful for short term planning I suggest that our focus on the amount of SLR expected by 2100 is somewhat misplaced. As a civilisation we have to start preparing for the final equilibrium state, not just a level at some arbitrary intermediate stage.

    We cannot afford to heighten coastal defences again and again, or relocate critical infrastructure such as airports, coastal refineries, cities and food production areas repeatedly as we are chased up the hill by the SLR. We are running out of our primary source of cheap energy, and many minerals are also approaching peak known reserves so our ability to rebuild is peaking right when we need it most. We need a safe target to aim for once and for all.

    In relation to the equilibrium conditions for SLR, if we take BAU for the next 50 years or so we are very likely to get CO2 well past 400ppm. That will have the well-discussed immediate warming effects plus the lag as the oceans catch up – the ‘warming in the pipeline’.

    We have to accept that in the short term the rate of SLR is fairly difficult to predict due to the plethora of variables involved such as ice sheet instability dynamics and a healthy raft of currently not-well-understood phenomena. So while This High by This Year is useful, it is perhaps more helpful to know how high it will get in the end. Then we can make our own judgement about how far up and how often we move.

    What then in your view are the likely equilibrium sea levels for say 400ppm (virtually certain) and 450ppm (quite likely if we keep on using coal)?

  6. 56

    @Deep Climate (50): I did not quote a number because there is a real chance that my model breaks down when extrapolated too far (all the way to equilibrium). However, since you insist: I get somewhere between 1-5 m/°C (with the lower estimates being from the model-experiment i designate to be most likely.) I do not consider Rahmstorfs estimates of 10-30 m/°C to be realistic. I emphasize “consider” because I want to make it clear that this is only an opinion. I consider 10 m/°C to be the maximum plausible. (This is roughly what I get when fitting the observed rise using the deglaciation response time of 2500 years).

    @Florifulgurator (51): Our models (Rahmstorfs and my own) are only applicable if the system dynamics do are not radically different in the projection and calibration periods (given their empirical nature). E.g. we know from the last deglaciation (~10 kyrs ago) that the decay of ice sheets can be have some short periods of sudden rapid decay. Meltwaterpulse 1A had a rise rate of ~4m/century for 500yrs. Our semi-empirical models would not be able to capture such non-linearities. We need better physical ice sheet models before we have a good chance at foreseeing that. Until we know better, I feel we have to consider it a real risk, that we may face a similarly rapid sea level rise. So, there should be a huge incentive to act swiftly. (Despair is not constructive.)

  7. 57

    Sekerob — note, also, that sea level rise doesn’t have to be very great to make a city uninhabitable. All it has to do is be enough to back up sewers and seep into aquifers. 1 meter sea level rise could be enough to lose the US and other countries several coastal cities.

  8. 58
    Aaron Lewis says:

    Hank re: 34
    This has been a known issue since before the IPCC was formed, and yet land-based ice was left out of the GCM. I bring up ice fracture processes, and I get comments as if I am delusional – and yet those fracture processes are clearly visible as ice calves off the face of glaciers. Years later, I still do not see good models of ice sheet physics. Every bright college grad that does not go into investment banking, should be writing ice sheet models. This is the big question of our time.

    Such geology as addressed in these papers tells us the total amount of sea level rise we can expect, but not how fast to expect that rise in sea level. Previous sea level rises were forced very slowly and gently by geological processes, and still we have evidence of “punctuated equilibrium”. That is, evidence of ice sheet or glacier events that result in rapid rise of sea level.

    What would Feynman think? He would think about ice cubes dropped into a glass of tea. Drop an ice cube in to a glass of cold tea and put it in the refrigerator – and you have the case of gentle geological forcing, and it takes a long time for the ice to melt. Drop the ice cube in a glass of cold tea, then set the glass in a microwave set on high and the ice cube will melt much faster. Thus, the time to melt depends on the forcing. Drop the cube into the glass of cold tea and shake it in a cocktail shaker and it will melt rapidly; showing that forcing can come in different forms. Finally, drop the ice cube into a large glass of rum and shake it. That was the Feynman way to melt ice. In Feynman’s world, ice could melt very fast. Ice could melt so fast it fractured and shattered.

    Yes, these are two interesting papers, that tell us very little about the potential rate of sea level rise and thus the potential risk that we can expect as a result of AGW. This failure to answer the great question of our age is the fault of congress and its purse strings, politically appointed policy makers at the EPA and other science agencies, mid-level managers at the science agencies that prepare budget requests, and individual proposal writers. It is my fault because my letters to congress my letters to congress were not persuasive. There is a model on my laptop, but Gavin says the numbers it provides are, “not helpful.”

    We need “helpful risk management” numbers, not “best”, not even “good”, but “helpful”.

  9. 59
    Ray Ladbury says:

    Aaron Lewis, so where are the good models of ice sheet physics? There are a lot of unknown unknowns in that physics. The IPCC was chartered to determine the credibility of the threat, not to develop engineering models We’ve got a lot of science projects we need to do before we can start doing engineering.

  10. 60

    Ray, speaking of engineering projects, this sounds rather like the old saying to the effect that you can only railroad when it is *time* to railroad; the necessary pieces have to be in place first. A fair simile?

    And if so, can I invite you to speculate about what some of those “pieces” might be?

  11. 61
    Ray Ladbury says:

    Kevin, This is really a problem in risk mitigation. The risk posed by a threat is the probability of the threat times the cost if the threat is realized. The problem we have is that there are some threats we cannot rule out that have extremely high cost–e.g. the end of civilization, mass extinction, the Yankees winning the World Series and so on. Even if these events are very low probability, they could wind up dominating the risk calculus as we now understand it. So, one thing we need is better models.
    In the mean time, there are two things we can do–start planning for the threats like sea-level rise, which are a virtual certainty, and do whatever we can to decrease CO2 going into the atmosphere so that we can buy time for science and technology to work. We need to look at this globally–a solar plant in India that keeps them from building a coal-fired power plant accomplishes just as much as a solar plant here.
    I suspect that the institutions we will need to survive this threat may not even exist yet. I suspect that there will be on one solution, but many. I sort of look on it as our species’ midterm exam. We’d better start cramming.

  12. 62
    Florifulgurator says:

    (ugh. perhaps triple post, perhaps not posted. interface no feedback.)

    @Sekerob (52) – My “skeptical thinker” was not meant serious, but rather as a dark sarcastic oxymoron, alluding to “skeptical environmentalists” and writers such as you named. I’m well aware that 1m is catastrophic enough. Alas, it’s just one detail of the outlooks, 2100 being even far in the future (nobody cares about grandgrandchildren). Misery will not come by the waters – it will be Homo S “Sapiens” making things worse and do the shedding of blood – a global Darfur style suigenocide? — Hell, you need to be scientificly cold blooded to face the prospects, otherwise you risk a broken heart. That’s perhaps why so many “skeptics” exert more brain power at avoidance of facing things than it would take to confront the outlooks.
    It is time to drown the “skeptics” in sarcasm and ridicule…

    @Aslak (56) – Thanks for the hint at Meltwater Pulse 1A. So my systems dynamics evaluation intuition wasn’t that bad? Except for Greenland is perhaps not a good candidate for rapid melting: Sqeezing giganto tons of ice thru the outlets takes it’s time, as well as melting kilometers of ice from top down. But then, perhaps the ice cap could get porous (moulins and all that)? Or, is there a way for ocean water to intrude inlands (some is below sea level) and eat up the ice from below? …
    I can imagine that modelling ice dynamics is even harder than doing clouds.

  13. 63
    ike solem says:

    RE#56: The model you are using is a single-component feedback model, right? It doesn’t even attempt to separate the thermal expansion component from the land-bound ice melt estimate, does it?

    None of these models address the issues of changes in ocean circulation, either, or what the effects of a decrease in vertical ocean mixing would be. Thus, any claims based on personal opinions are pretty much worthless, as in “X meters per degree C”. In reality, the rate of sea level rise will depend on complex interacting factors, not on a simple one-component feedback process. The simplifications just don’t work.

    This has all been dealt with before, in the Douglass and Knox attempt to use a similar one-component model and the Pinatubo explosion to get an estimate of a low climate sensitivity – the approach you are using is essentially identical, right? Likewise, you come up with a low sea level response sensitivity.

    The problem is the same – not taking into account the response time of the oceans. The Douglass-Knox model might work – if the ocean was only a few hundred meters deep.

    In contrast, the recent results (Solomon et al PNAS) that show long-term climate responses do take the ocean into account, and the results are in several news articles:,0,2633118.story

    The complete article is available here:

    The problem with estimates like yours and those of Douglass and Knox, other than being gross over-simplifications of complex processes, are that they allow people to claim that the effects of adding massive amounts of CO2 to the atmosphere are reversible over short (decadal) time periods – and that’s simply wrong. Here is the relevant quote from Solomon et. al on this:

    We have shown that this assumption is incorrect for carbon dioxide emissions, because of the longevity of the atmospheric CO2 perturbation and ocean warming. Irreversible climate changes due to carbon dioxide emissions have already taken place, and future carbon dioxide emissions would imply further irreversible effects on the planet, with attendant long legacies for choices made by contemporary society. Discount rates used in some estimates of economic trade-offs assume that more efficient climate mitigation can occur in a future richer world, but neglect the irreversibility shown here.

    Similarly, understanding of irreversibility reveals limitations in trading of greenhouse gases on the basis of 100-year estimated climate changes (global warming potentials, GWPs), because this metric neglects carbon dioxide’s unique long-term effects.

    The warming ocean waters in the Artic and Southern Ocean are not going away, are they?

    Not only that, paleoclimate data indicates we are heading for conditions similar to some 3 million years ago, when sea levels were some 35 meters higher than today. The only real question appears to be how fast we’ll get there – and there’s no reason to believe that the last glacial deglaciation is all that great a model for the present ice melt.

    Take a look at the sea level projections:

  14. 64
    Harmen says:

    Another safe bet…

    Glacier retreat the coming decade vs. glacial growth the coming decade..


  15. 65

    I did not read every word above, but I suspect that consideration of risk has not been featured yet in this discussion. A totally rational mind would say, let’s dramatically change the way we live so that we can reduce the risks of 11C global temperature rise (like the Permian rise) and massive ocean level rise. If the risk of billions being forced from homes, or starving, or fighting wars due to climate change as well as peak oil/gas and other resource problems, if that risk is only 20%, shouldn’t we act to be slightly uncomfortable for the next 100 years but greatly reduce the risks? Science seems to put the risk of the above at more than 90% (IPCC). But our behaviors as a human society in response to this warning are FAR from rational.

    I think we need to remember how irrational and uninformed (a two-pronged problem) most people are, and then figure out what to do. A daunting but perhaps solvable challenge.

  16. 66
    Uli says:

    @Aslak Grinsted,
    I have read your paper but I don’t understand the choose of temperatures in section “4. A priori constraints”.
    For the temperatures feeding in the model you use global mean HadCRUT3v and different northern hemisphere temperature reconstructions. But for the constraints in section 4 you use polar land temperatures 3-5°C for the LIG and -17 °C for the LGM, which must be the northern land temperatures in the vicinity of ice sheets I guess (antarctic would be -10°C). But the global mean temperature changes relative to preindustrial level are about 1°C for the LIG (this means very roughly equal to the temperatures in the start of 21st century) and -4 to -7 °C for the LGM. Although it has advantages to use temperatures near the ice sheets and ice caps, using local land temperatures in the past for the constraints, but using global (or NH) land+ocean data for the forcast seems unordinary. What the reason for that?

  17. 67
    Tom Fiddaman says:

    I took a look at this in some detail (replicating the models & data) and can basically confirm this critique. It’s hard to discriminate among time constants (except ruling out short ones), but the IPCC-too-low result is robust. Details here:

  18. 68
    barry says:

    Stephen Goddard is positing that the current rise in sea levels is a more sedate continuation of a much faster rise out of the last ice age.

    While I’m sure it’s a poorly investigated piece, it does raise an interesting question. If global temperatures are climbing faster than ever in human history, why do we not expect a faster sea level rise than that which occured in the last deglaciation?

    Worth a post?

    [Response: There was a lot more ice to melt then. – gavin]