What is not new
Ultimately sea levels will rise several feet, given the present levels of CO2 in the atmosphere. We already knew this by examining paleo data, and finding periods in the past with similar surface temperatures and/or similar atmospheric CO2 levels as today.
I put a graphic from a paper by Gavin Foster and Eelco Rohling at the top of the post. It does a good job of summarizing the paleo data.
If we keep pumping CO2 into the atmosphere at current, or even somewhat reduced, levels for a few more decades, the ultimate increase in sea levels will be significant. Find the 400–500 ppm CO2 range on the map and notice that the average sea level rise in times past, indicated by the horizontal orange-reddish line, is 14 meters.
Let me rephrase that to make it clear. We have already caused something like 14 meters of sea level rise. Like the horrifically sad words uttered by a movie or TV character who has received a fatal wound and turns to the killer, uttering “You’ve killed me” (then they die), we’ve done this. It is just going to take some time to play out. But it will play out.
A conservative estimate is that likely sea levels will rise 8 meters or more, quite possibly considerably more. But generally, people who talk about sea level tend to suggest that this will take centuries. Part of the reason for that is that it takes a long(ish) time for the added CO2 to heat up the surface, then it takes a while for that heat to melt the ice sheets. However, there is no firm reason to put a time frame on this melting.
A new paper that is making a great deal of news, and that is still in peer review, suggests that the time frame may be shorter than man have suggested. We may see several meters of sea level rise during the lifetime of most people living today.
What is not known
We don’t really how long this will take. Looking at the paleo record, we are lucky to get two data points showing different ancient sea levels that are less than a thousand years apart. There are a few moments during the end of the last glaciation where we have data points several centuries apart during which sea levels went up several meters. We don’t have a good estimate for the maximum rate at which polar ice caps and other ice can melt.
The current situation is, notably, very different from those periods of rapid sea level rise. The amount of CO2 in the atmosphere is approximately double the Pleistocene average, and the rate at which CO2 levels and temperatures have gone up has not been seen in tens of millions of years. Whatever rate of sea level rise over the last several tens of thousands of years must be regarded as a minimum, perhaps a very low minimum.
What is new
The new paper argues for more sea level rise, ultimately, than many others have suggested, but it is still within the range of what we had already guessed from the paleo record. Most current research on the rate of glacial melting show relatively slow levels compared to what the new paper suggests. In particular, the new paper suggests that this is wrong, and that we may see three meters of sea level rise over the next fifty years.
The paper is very complex and covers a lot of ground that I will not attempt to address here. The tl;dr is that the researchers model the current melting of ice, and finds that the rate is accelerating over time. This means that current rates are a gross underestimate of the rate of sea level rise.
Here are two interviews with Michael Mann on the new work.
See also this by Joe Romm. Climate Crocks has Hansen, lead author, on CNN, here. See also this explainer by the paper’s first author.
Mann talks about some of the effects of sea level rise, including global effects. We are already seeing food prices being affected now and then by climate catastrophes. Consider the fact that much of the rice grown in southeast Asia is grown on land that will be inundated by this sea level rise. This applies to the US as well. This combined with increased drought in places that are not flooding, and social unrest such as occurred in Syria when crops fail – causing further agriculture in those areas to simply stop happening – will cause a major food crisis in the near future. Our children and grandchildren will be hungry, at war, living in a post-civilization world. That is the world those who deny climate science and stand in the way of taking action are causing.
Here is the abstract of the paper:
There is evidence of ice melt, sea level rise to +5–9 meters, and extreme storms in the prior interglacial period that was less than 1°C warmer than today. Human-made climate forcing is stronger and more rapid than paleo forcings, but much can be learned by combining insights from paleoclimate, climate modeling, and on-going observations. We argue that ice sheets in contact with the ocean are vulnerable to non-linear disintegration in response to ocean warming, and we posit that ice sheet mass loss can be approximated by a doubling time up to sea level rise of at least several meters. Doubling times of 10, 20 or 40 years yield sea level rise of several meters in 50, 100 or 200 years. Paleoclimate data reveal that subsurface ocean warming causes ice shelf melt and ice sheet discharge. Our climate model exposes amplifying feedbacks in the Southern Ocean that slow Antarctic bottom water formation and increase ocean temperature near ice shelf grounding lines, while cooling the surface ocean and increasing sea ice cover and water column stability. Ocean surface cooling, in the North Atlantic as well as the Southern Ocean, increases tropospheric horizontal temperature gradients, eddy kinetic energy and baroclinicity, which drive more powerful storms. We focus attention on the Southern Ocean’s role in affecting atmospheric CO2 amount, which in turn is a tight control knob on global climate. The millennial (500–2000 year) time scale of deep ocean ventilation affects the time scale for natural CO2 change, thus the time scale for paleo global climate, ice sheet and sea level changes. This millennial carbon cycle time scale should not be misinterpreted as the ice sheet time scale for response to a rapid human-made climate forcing. Recent ice sheet melt rates have a doubling time near the lower end of the 10–40 year range. We conclude that 2°C global warming above the preindustrial level, which would spur more ice shelf melt, is highly dangerous. Earth’s energy imbalance, which must be eliminated to stabilize climate, provides a crucial metric.
And here is a key graphic:
The reference for the paper: Ice Melt, Sea Level Rise and Superstorms: Evidence from Paleoclimate Data, Climate Modeling, and Modern Observations that 2°C Global Warming is Highly Dangerous, by James Hansen, Makiko Sato, Paul Hearty, Reto Ruedy, Maxwell Kelley, Valerie Masson-Delmotte, Gary Russell, George Tselioudis, Junji Cao, Eric Rignot, Isabella Velicogna, Evgeniya Kandiano, Karina von Schuckmann, Pushker Kharecha, Allegra N. Legrande, Michael Bauer, Kwak-Wai Lo.
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There is no way to avoid the +2c global average warming that some scientists called “safe:” it’s already “locked in.” Perhaps humanity will avoid +4c with hard work, or avoid +3c with Draconian measures started immediately.
A physicist group that meets in Los Alamos, New Mexico, thinks we can avoid +2c if there is an immediate world-wide implementation of ocean fertilization, performed in small amounts but also performed everywhere and at the same time. This would be very “hard” on the world’s oceans, but it is also the best known short-term (50 years and less) solution.
It would also need to be done in secret.
Chemtrails. That’s the ticket.
Greg,
Hansen et al don’t model ice melt, I think; they assume exponential melt increase and see what happens with ocean and surface temperatures. Their suspicion is that this could happen in the coming decades/centuries and they give arguments why this may be plausible, or even likely.
Desertphile:
There is no way to avoid 2C warming but there is a way to avoid 2C warming? Which is it?
Doubling time for ice mass loss from Greenland and Antarctica in the last couple of decades is around 5 or 6 years. Hansen et al think that Greenland cannot sustain this acceleration for very many years, but Antarctica probably can. Palaeoclimate data shows that sea level rise can hit nearly half a metre per decade with a much smaller planetary energy imbalance than we’re causing now, and that the the total rise is around 20m per degree C of warming. Not good…
Lennart, predicting a future trajectory with a curve is modeling. You may be thinking of the more restricted term simulation modeling.
Hansen also has an explanatory piece here: http://www.huffingtonpost.com/dr-james-hansen/multi-meter-sea-level-rise-is-an-issue-for-todays-public_b_7875828.html
I would argue that it’s entirely irrelevant how long it will take.
The only thing that matters is the world that we leave to future generations. If we wouldn’t want for ourselves a 2-4+ °C warmer world with sea level 6-60+ metres higher and with all the attendant loss of biodiversity and ecosystem function, why should we visit it on our grandchildren or on our decendants 1000-10,000+ years hence?
It’s a peculiar (a)morality that alters with distance into the future. All that matters is what we are entraining at plateau, and what we work to avoid. And to date it’s been a small fraction of bugger-all.
On the other hand, if a 14m sea level rise is already locked in and inevitable, then the further it is in the future, the more time we have to adapt to it. At a meter per century, it’s one of the more important factors affecting the future construction of human cities. At a meter per decade, it’s a looming humanitarian crisis. (The numbers are just examples, but faster is always going to be worse.)
Greg,
You write: “the researchers model the current melting of ice, and finds that the rate is accelerating over time.”
I think they assume the acceleration, in three scenario’s 5-10-20 yrs doubling, and see what happens to ocean and atmosphere.
So the doubling times are not predictions but what-if scenario’s. If current doubling times of around 10 yrs are extrapolated, then we would get multi-meter SLR.
And yes, they do think a doubling time of 10-20 yrs seems more likely than a linearly accelerating ice melt.
I’m a bit leery of arguments about near-future sea level rise (SLR) based on maximum rates of SLR from the post-last glacial maximum (LGM) deglaciation. At the end of the LGM there were extremely large ice sheets positioned at relatively low latitudes, especially in eastern North America. In that configuration, there’s a virtually unlimited supply of potential meltwater.
But that ice mostly isn’t available now for rapid SLR. It’s already in the oceans. Greenland is the obvious exception, but the Greenland ice sheet is a lot smaller than the Laurentide ice sheet was at the end of the LGM, and doesn’t extend nearly as far south.
What matters is not just the rate of temperature rise, but the spatial extent of ice available to melt, particularly ice that extends into lower latitudes.
Ned, that is correct, I imagine ice melting would have been very fast if things got warm in those regions where ice sheets were very far south in the NH. On the other hand, in paleo contexts, there where large areas of the Antarctic ice sheet, which were not very far north (obviously) totally melted.
However, it is not correct to say that the position and extent of the ice sheets matter and temperature (absolute or rate of rise) does not. That simply ignores the major forcing component. As far as maximum melt, there isn’t any question about that because we’ve seen it happen before during the current era (wrt continental position). The ice that is there now has melted in the past to a greater degree than now under roughly similar conditions of CO2 and temperature as today. In other words, as I stated above, we are currently in a situation where sea levels should be higher by several meters than the actually are, and we in fact see a negative mass balance. So the paleo and the empirical observations match.
As far a rate, your point is relevant (in part, as I noted) but it does not tell us the rate. On the other hand, Hansen et al argue for an increased rate. In order to be legitimately leery you have to address the specific arguments made by Hansen. In other words, while I appreciate your incredulity, as an actual argument it doesn’t cut it!
Bernard: “I would argue that it’s entirely irrelevant how long it will take.”
I have more or less been arguing that all along as well. Not that it is entirely irrelevant (it is relevant because the rate of sea level rise controls the nature of the adaptation). Rather, people seem to argue, or at least imply, that since it is in the far future (whenever that is) it does not matter. But a major change in the geography of the planet matters a great deal whether it is happening in 200 years, 100 years, or 50 years!
You wrote above… “We have already caused something like 14 meters of sea level rise.” By “we” I assume you are talking about mankind. When exactly did mankind cause 14 meters in sea level rise? Sea levels have not risen 14 meters in centuries. They have barely risen a foot in the last century. What exactly are you talking about?
Dave: Let me rephrase that to make it clear. We have already caused something like 14 meters of sea level rise. Like the horrifically sad words uttered by a movie or TV character who has received a fatal wound and turns to the killer, uttering “You’ve killed me” (then they die), we’ve done this. It is just going to take some time to play out. But it will play out.
In my opinion science does not understand the effect of CO2 levels on global temperatures. The models have failed terribly. Global temperatures are not rising as predicted. The Arctic and Antarctic are not melting as predicted. Sea levels are not rising as predicted. You may be proven right, I may be proven wrong, but the science is not settled and the future is not certain.
OK, I know I’m bad tempered, and I’m working on it. Really I am. But seriously:
“In my opinion science does not…”?
So is this nuance-free, thought-stopping assertion of an opinion based on your expertise as a climate scientist, or is it something that you’ve formed in your hindquarters after five minutes of admiring some barroom blowhard?
“…the future is not certain.”
Yeah, like there’s no such thing as risk assessment which means there’s no such thing as risky behavior, so yippee, let’s not waste time thinking about it!
Platitudes rule, dude!
Obstreperous… It is so like the alarmists to use personal invectives against anyone who raises doubt about apocalyptic predictions and pronouncements that are based on an unproven hypothesis. The scientific method has been turned on its head in climate science. You don’t have to be a scientist to understand that. Take your blinders off and realize the issue is a lot more complex than you apparently believe it is.
No. I’m pointing out to you that your comments are evidence-free talking points and platitudes. Anybody who reads them can verify it for themselves. For some peculiar reason you don’t seem to think that’s important, but you deflect anyway.
I suggest that you take your blinders off and realize that the issue is a lot more complex than you think it is.
GL: “However, it is not correct to say that the position and extent of the ice sheets matter and temperature (absolute or rate of rise) does not.”
Of course that would be wrong, and sorry if I was unclear. Sea level would presumably rise the fastest when both factors are amenable — temperatures are rising fast, and there are large ice sheets extending down into midlatitude regions.
GL: “The ice that is there now has melted in the past to a greater degree than now under roughly similar conditions of CO2 and temperature as today. In other words, as I stated above, we are currently in a situation where sea levels should be higher by several meters than the actually are, and we in fact see a negative mass balance. So the paleo and the empirical observations match.”
Yes, I agree completely, I was only commenting on the rate. .
GL: “In order to be legitimately leery you have to address the specific arguments made by Hansen. In other words, while I appreciate your incredulity, as an actual argument it doesn’t cut it!”
Yes, and I’ll say right now that I’ve only yet made it part way through the Hansen et al manuscript. I’m not claiming or attempting to rebut that.
But I was just expressing some reservations about your own post, in the “What is not known” section above. In the first paragraph of that section, you refer to the meltwater pulses during post-LGM deglaciation. I guess I’ve gotten a bit jaded with people implying that near-future SLR could be much much higher because it was that high when the Laurentide ice sheet was collapsing. It seems to me that it would be helpful, when mentioning those post-LGM rates of SLR, to note that the ice sheet that furnished most of that rapid rate of increase no longer exists. In the next paragraph, you do talk about differences between the post-LGM vs 21st century conditions … but only about the difference in CO2, not in the amount and extent of ice that’s available to melt.
Not trying to be unfairly or excessively critical, and I obviously agree on all the main points — there is still a lot of ice out there and much of it will melt over the next few centuries as the planet warms due to anthropogenic greenhouse gases.
Dave, pretty much everything you said there is way wrong. You are entitled to your own opinion but you are not entitled to your own facts.
Ned: “Yes, and I’ll say right now that I’ve only yet made it part way through the Hansen et al manuscript”
That is an admirable feat. This is a hella dense paper.
Anyway, yes, in this simple overview of the situation I’ve not touched on the important details you mention. Indeed, there may have been really rapid melting when the LGM gave way to the Holocene. The earliest events are utterly obscure to us now, but if a similar level of melt occurred right now there are places in this world where people would go to bet at night a good distance from the sea and wake up in the morning with wet feet! (Look at a map of the on and offshore topography of southern Australia, for example!)
To melt rapidly seems to depend on large volumes of ice moving into contact with the sea, whereby heat imported from further afield can be utilized to melt the ice. So the issue of rapid SLR, isn’t just really the area of ice versus air temperature, its much more about how exposed the ice is to sea water temperatures. We just don’t know how this is going to play out. We do know that there are deep channels leading deep inland from the coast in Greenland, and West and even East Antarctica, so there is at least the potential for significant volumes of what we formerly thought of as safely landbased ice to come into contact with warm water. But most of these discoveries are very new, and we just don’t know how the dynamics will play out.
I see no reason why the time evolution should be exponential. Exponential is what you get with a system that is linearly unstable. The current system isn’t like that, its driven (by climate change) , and the form the response will take have to be worked out by models which incorporate the relevant physics. Fitting a couple of decades worth of melt data to an exponential really doesn’t tell us much.
dave andrews:
dave, Kuhn showed that, subject to basic rules of evidence and analysis, it’s up to the scientists doing the work to choose their methods, and to their peers to decide if those methods are valid. If you were a scientist, or at least had practical training equivalent to the graduate level, you’d understand that. I have little doubt you’re capable of understanding it, but you’d need to put the time in. Your simplistic notion of “the” scientific method makes it clear you haven’t, and hanging out on AGW-denier blogs doesn’t meet the requirement. Sorry, but there’s no way to sugar-coat it: you are a victim of the Dunning-Kruger effect.
Be of good courage and give Holland a call Greg , to ask for advice on how best to emulate its efforts at home and abroad– the Norfolk Broads in particular.
What 17th century Dutchmen with shovels can accomplish , 21st century technologies– and economies — can amplify .
Now back to saving Venice;. Again.
Omega: “, its much more about how exposed the ice is to sea water temperatures. We just don’t know how this is going to play out. ”
That is important, and Hansen et al do address that.
Thanks for the post Greg- I’m a non scientist who has watched the climate issue for a couple decades now. Sure seems to be a pattern of cautious predictions followed by newer feedback loop info that each time calls for the world to come to grips with this sooner rather than later. I might humbly suggest that these feedback loops require massive data [and interpretation] to get an accurate prediction. From subglacial lakes in Greenland to circumpolar deep water effects in the Antarctic to permafrost carbon releases due to wildfire- it looks to me that they are always an accelerant but very difficult to quantify re their overall contributions. Someone made the point that climate change is an ‘experiment ‘ with way too little chance of a good outcome. And way too complex to demand year by year accuracy [what would be the result , say, if El Nino develops a lifespan of years instead of months?] Kudos to Hansen et al for attempting to add lights and siren to the alert. I’ll plant another tree today.
Curtis, yes, I think that is in fact the pattern!
@ Ned W #13
I think this may be to misunderstand what is suggested.
The Hansen et al. paper and others examine MSL highstands in the late Eemian, which are thought to be the consequence of partial or fairly complete collapse of the WAIS. This is expected to occur as a consequence of upwelling warm water eroding the ice shelves currently blocking the free flow of the major drainage glaciers into the sea. Once these impediments break up, glacier flow rate increases sharply and the unstoppable, gravity-driven drainage of the ice sheet begins in earnest. Since the WAIS is a marine ice sheet on a retrograde grounding slope, it is likely to be inherently unstable if seawater begins to penetrate further and further beneath the ice. Combine this potential instability with increased glacial drainage and an accelerating break-up of the ice sheet becomes inevitable.
BBD +1
Wow, I filled my Climate Denier Bingo card! Thanks, Dave Andrews!
“Global temperatures are not rising as predicted.”
A little bit slower than predicted.
“The Arctic and Antarctic are not melting as predicted.”
Both are melting faster than predicted. That indeed is quite worrisome.
“Sea levels are not rising as predicted.”
Also faster than predicted. Quite worrisome indeed. Slightly lower temperature trend, but ice melt and sea levels are at the high end of the predictions.
Somehow Dave Andrews seems to think this means it is all too uncertain…
Greg,
You write a nice post, but I still think your wording as I quoted above is not accurate. I think Scott Johnson in Ars Technica got it right: http://arstechnica.com/science/2015/07/no-scientists-arent-predicting-10ft-higher-sea-level-by-2050/ He says: “sea level rise was an input controlled by the researchers, not a prediction from the model (or some other analysis)”. So Hansen et al don’t “find sea level accelerating over time”, they assumed it, with 5-10-20 yrs doubling times.
I’d like to see Jim HAnsen and his co-authors put aside framing long enough to quantify the change in ocean volume integrals arising from isostasic chages in both past and current natural, and future anthropocene post-glacial rebound.
Come on, Russell-cheeky-with-the-framing 😉
You see regional sea level change from isostatic rebound, not global.
Come on , BBD- as has been remarked of politics, in human terms , all sea level is local, and the magnitude of the impacts depends on the hifference between global rise and local changes in whether the ground is going up or down relative to the solid geoid.
Since local changes in isostasy can and do run to millimeters a year , you have to deal with this mere fact of geophysics- which cuts both ways: : just as deglaciated regions are still rebounding , great river deltas are still sinking as the weight of accumulating sediments deforms the crust beneathe them: they are going under independent of anthropocene climate change jast as the shores of Hudson’s Bay and the Baltic are rebounding faster than the global rate of seal level rise.
Russell
Eeemian MSL highstand was >6m above our late Holocene idyll.
Is anyone (other than you) suggesting that isostatic rebound during the Eemian contributed significantly to this? Because I can’t find any studies that support this view.
This begs the question: where’s the isostatic rebound contribution today? Was the ice sheet extent and consequent crustal loading so much greater during the Wolstonian than the Devensian glaciation? We should be told.
Alternatively, when it’s about 1C hotter than it is now, the GrIS, WAIS and sectors of the EAIS lose enough mass to increase MSL by >6m.
The focus on sea level rise from ice sheet melt and arguments about how soon it could happen, what the maximum rate of rise could be, whether it will be a true exponential, etc., is interesting, but it seems to miss a large part of the Hansen et al. paper. As I understood the paper, increased cold, freshwater from melting ice sheets can affect the north Atlantic deep water production and the Antarctic deep water production and can result in increased stratification. This has consequences for latitudinal temperature differentials, baroclinicity, etc., tending to produce stronger and more frequent superstorms. It seems to me that a sea level rise of a bit less than half a meter in 50 years combined with more frequent stronger superstorms would be sufficiently unpleasant.
The problems with the model used in Hansen et al. (frequently stressed in that paper) should also be taken into account. For example, the problem with the mixing rate clearly suggests that the deeper warm water eating away at the bottoms of Antarctic ice shelves will in fact be warmer and saltier than in their model, meaning more rapid melting from beneath.
Bill, I actually didn’t address those aspects of the paper because those are the areas where I think there will be the most discussion in the near term about methods and results. My sense is that Hansen et al are essentially correct but that there will be some reconsideration, and the results may change somewhat. But you are correct, this is important, and the implications are profound.
BBD, do you know if there are any studies done on the relative effects of isostatic rebound on sea level in other regions? Or the effect of ocean depth (gravitational) change on marine regions? (My brother did his doctorate on isostatic rebound in the Arctic – I’ll ask him as well, but he’s moved on to other things in the meantime.)
“Is anyone (other than you) suggesting that isostatic rebound during the Eemian contributed significantly to this? Because I can’t find any studies that support this view.
”
When I learned about Eemian high strand lines it was commonly assumed that these were due to continental buoyancy (which is not exactly the same as isostatic rebound). I don’t know what the textbooks were saying but the people with whom I was working who were studying high strand lines in North and South Africa were thinking this.
I suspect this was a widely held assumption that had to do with our general inability as humans to grasp vertical changes in land or sea other than simple mountain building, especially the sea.
Maybe this goes back to when we first evolved as tiny microbes in the sea ( 🙂 ), but historically people looking at major patterns in geology have gravitated towards the sea level simply never changing and all the other stuff that happens is the land going up and down. Darwin and his contemporaries (and Darwin was one of the first scientists to study this issue) made a lot of mistakes in figuring out the past because of their assumption that land could go up and down easily while the sea never moved.
In Africa it made sense because Africa does seem to be a somewhat “buoyant” continent. All the edges are up. This, though, probably has more to do with the position of Africa in one or more earlier super-continents (and subsequent rifting) than any actual innate buoyancy.
“… their assumption that land could go up and down easily while the sea never moved. their assumption that land could go up and down easily while the sea never moved.”
Greg, in my experience, this is not just an assumption, but literally true. I lived for many years where the land bounced up and as much as 30 feet with a period of about 12 hours. See http://tidesandcurrents.noaa.gov/noaatidepredictions/NOAATidesFacade.jsp?Stationid=9455920 for a graph of currently land-bouncing there.
Have you been to the Bay of Fundy?
No. I have heard and read about the Bay of Fundy, of course. But on such a crucial question as whether the sea is rising (lowering) or the land is moving up and down, I was careful to restrict my testimony to a case with which I had extensive personal experience. No hearsay evidence.
Regarding consequences of stratification mentioned in #40 above, the comment by Timothy Chase on Tamino’s blog post is relevant: https://tamino.wordpress.com/2015/07/28/hansen-et-al/#comment-89860
Dave Andrews, it’s been a few years since I’ve seen you around the traps spruiking scientifically-unsupported statements and scientifically incorrect about science. As others have observed above, those few years haven’t seen you garner anything remotely resembling an understanding of science: you’ve simply accumulated more of your Dunningly-Krugered denialism.
You see, the world’s best and brightest scientists disagree with you. Contrary to you staement that “the science is not settled” the experts have no doubt that it is. Take Nathan Bindoff for example, a well-known and highly competent lead author for many of the assessment reports. He says at 1:05:00-1:05:30 here:
Who should I believe – a noted expert in the discipline, or an uncredentialled nobody on the internet who is partial to logical fallacy and ideological denialism?
…scientifically-unsupported and scientifically incorrect statements about science…
It isn’t that Hansen et al. are predicting exponential sea level rise at ~5 years/doubling out to 2100, it is that they are using an exponential melt model for the first 1m of sea level rise as an input for the model. Figure 8 clips the melt volume to 1 (or 5) meters and uses that to get bounds on the fluxes over the next 40-100 years.
Clipping the melt volume at 1 meter worth of SLR, and using exponential curves to back-load the melt on the end of the melting period seem like reasonably conservative flux models.
With the flux cutoff at 1m of SLR, Hansen’s model is not melting more ice than can be melted in the next 100 years, but it is well within that Rahmstorff limit.