Could you elaborate on the reasons for the discrepancy between semi-empirical and process-based projections of SLR?
There seems to be this peculiar situation where adherents of both approaches don’t think anything of the competing approach. E.g. from glaciologists I sometimes hear that there is no evidence for mechanically enhanced melt of ice sheets (which would be needed to arrive at higher estimates than their current process-based projections). One could say that absence of evidence is no evidence of absence of course, but that’s rather unsatisfying.
What reasons could there be for process-based methods underestimating the (speed of) response of SLR to temperature? And what potential reasons could there be for semi-empirical methods overestimating the same? (This is not to imply that the truth would necessarily be in the middle; just trying to understand the differences between the different methods)
[Response: Bart, I can’t fully answer this, but note that the expert elicitation cited specifically asked glaciologists, and if they are right this would close much of the gap between process models and semi-empirical models. -Stefan]
Station i in [0, n] gets weight factor (n over i)/2^n. So in this case, with n=6 and where A corresponds to i=0 and G to i=6, we get:
B: 6/64 = 3/32
D: 20/64 = 5/16
F: 6/64 = 3/32
Doesn’t seem like a balanced average to me…
[Response: Here is one solution, but is it right? What do other readers think? -Stefan]
Here I compare Rahmstorf (2007) sea-level rise and global temperatures with Vukcevic 2009 negative magnetic field change due to the convection in the underlying mantle associated with the Post-glacial Laurentide uplift http://www.vukcevic.talktalk.net/SeaLevel.htm
Well I am confused. Half an hour? I must have missed something.
Assuming there is no linear/area weighting & there being no other ambiguity that I know of with the averaging of just two numbers, the seven stations get the following weighting in the final all-encompassing virtual station. A&G 4, BC&D 2, E&F 1. It would appear not to be an averaging method that immediately recommends itself.
[Response: You mean it took you just five minutes? In any case, you got what I got, too. Although to get a total of 1 you then have to divide the numbers by 16. Thanks for participating! -Stefan]
I would find a weight for each station by integrating a decreasing function of distance over the ocean area.
For example, take all available satellite data and find the correlation between sea level at a point in the ocean and level measured at a station of interest. To find the station weight add this up over the whole ocean.
However, I have no detailed knowledge of how sea level works, so this may suffer from a fatal flaw…
Ah, I see what I did in my first comment. It appears I interpreted the virtual station method as first replacing A-G with virtual stations AB, BC, …, FG, and then replacing those with virtual stations ABC, BCD, …, EFG, and repeat until you get a single virtual station ABCDEFG. In this interpretation, you get the answer I gave above.
Doing it the way you meant it (i.e. first merging B and C into BC, then E and F into EF, then A and BC into ABC, etc) I get the same answers as you:
A, G: 1/4
B, C, D: 1/8
E, F: 1/16
Either way, it’s a peculiar method for doing averages.
Jan W.: read the instructions. Step one is to combine the closest stations together – that would be the stations that are 1000 units apart, eg, E&F and B&C. Because step one turns E&F and B&C into one virtual station each, E&F _have_ to have the same weight, as do B&C.
“The implication of our closure of the budget is that a relationship between global climate change and the rate of global-mean sea-level rise is weak or absent in the past.”
Scientists have an obligation to not provide global warming deniers opportunities like the above quote to misinterpret the meaning of a paper. Without compromising the integrity of their research, scientists must be aware that climate science is under attack by commercial and ideological forces that are not interested in the truth. Clear communication is essential and whether the scientific community likes it or not, the ambiguous and sometimes convoluted academic language of journals will be scoured by those with an ax to grind and every phrase that can be misunderstood will be misunderstood.
Thanks for the great post. I can’t tackle the quiz right now, but I wondered if Stefan would mind commenting on this video by Prof. Alley? Particularly the last ten minutes or so where he suggests that a relatively sudden sea level rise of about three meters can not be ruled out.
The video has attracted some interested comments from other posters here on the open thread, so I thought it would be valuable for all of us to hear another expert’s evaluation of it while we are discussing slr. Thanks ahead of time for any insight you can throw on this troubling/horrifying possibility.
[Response: I'm a huge fan and friend of Richard's, but I do not think this is plausible at all, if by "sudden" it is meant within 100 years or less. Even if all the glaciers in Greenland start flowing at 5 times their current rate, and do so for the next 100 years, we still perhaps 2 m of sea level rise. That would be catastrophic, but it's probably impossible, and definitely at the upper end of possibilities. Having said all that, >3 is probably inevitable over the next several hundred years if we continue to burn fossil fuels at the current rate.--eric]
[Response: Like Eric, I'm a fan of Richard and consider myself a friend - I have not had time to look at this video, so can't comment specifically. Also, I am by no means an expert on the stability of the WAIS which appears to be the theme of his lecture. -Stefan]
Wouldn’t it be interesting to start map water distribution with SLR, to get a map with Hotspots? I think this would help with policy making, since SLR along the U.S. Atlantic Coast is increasing about three to four times more than the global average. And ofc to include the potential for abrupt SLR, which would mean +2 meters.
I agree with 12 Larry Saltzman. Intentional misunderstanding deserves a new word. I call it “disunderstanding” to indicate intention. Disunderstanding is also used by provokers. Provokers are people who intend to get people angry.
I have for a long time been puzzled by the scepticism many experts have for the semi-empirical model approach to project future sea level rise. This scepticism has prevailed until this day, despite that by now many papers have been published based on the method in good scientific journals, and despite that, to my knowledge, no fatal criticism to the semi-empirial methodology have yet been published in a scientific journal. The paper that you discuss in this post is perhaps the best attempt to discredit the semi-empirical method, but the arguments used in the paper seem flawed, as you show in this post. I think this kind of methodological discussions are very important and I hope that you will also publish a reply in the journal.
Another point that I would like to hear your thoughts on is the relevance of potentially greater than linear rate of sea-level rise contribution from the great ice-sheets. As I understand it, the semi-empirical models presume linear responses. Given that there is a risk of supra-linear responses (e.g. as indicated by the views of some of the glaciologists who participated in the study by Bamber & Aspinall), this would imply that the semi-empirical models represent LOWER BOUNDS, rather than the upper bounds that they often are used as.
Furthermore, this would mean that while semi-empirical methods are only able to make accurate hindcasts and forecasts when the response can be approximated by a linear function, the model would break down when the non-linear responses become dominant. Is this correct understood?
[Response: Correct, I already discussed this in my original 2007 Science paper. And semi-empirical models have been criticised for potentially underestimating non-linear ice-sheet responses, like what Richard Alley talks about in his lecture. I think there are some arguments why these models might underestimate and some why they might overestimate future sea-level rise, but ultimately we do not know. -Stefan]
If we are averaging the sea level rise based on area and expect a dependence on latitude, then each station will be weighted according to the area it represents in its latitude band. Therefore, given the triangular shape of the ocean, the weights will be proportional to the distance from the pole. So the area weight for A = 1/49, B= 3/49, C=5/49 etc up to G=13/49.
Brian @ 6:44pm If the inter-tidal gauge distances were not integers, wouldn’t the most isolated gauge always get a weight of 1/2 ?
Integers or not, only if it stays isolated to the very end. As other gauges are merged, the positions change and distances change. You can end up with groupings that are farther apart (more isolated) than any individual station was, so the original isolated station will get merged with a group before the final groups get merged.
FYI, the merge order I get from the example is:
A B C D E F G (original individual stations)
A BC D EF G (doesn’t matter if you do BC and EF together, or as discreet steps in this case)
ABC DEF G (again, same result if two steps)
Before the second last merge, the two distances are 3003 (ABC to DEF) and 2252.5 (DEF to G), so distances are much more variable between groups than they ever were between individual gauges.
Eric (moderator response at #13) – I’m assuming you haven’t watched Dr Alley’s lecture because your comment is a mischaracterization of it. The Greenland ice sheet is not the concern, the West Antarctic ice sheet is. I’m sure you’re familiar with the topography, and the buttressing effect which slows the flow of the glaciers into the ocean.
Now many “warmist” commenters tend to get a bit carried away with possible future rates of sea level rise, and that may be what you responded to, but the fact that global sea level rose rapidly during the last interglacial highstand, when only the Greenland and Antarctic ice sheets existed (i.e. no gigantic Laurentide or Fennoscandian ice sheets) suggests that scientists cannot get too complacent about this. Especially when we’ve warmed the planet so rapidly, and process-based modelling of ice sheet behaviour is presently out-of-kilter with observations.
As Dr Hansen notes, comparison between rates of paleo-sea level rise driven by a much slower warming, and present rapid global warming, may not be valid. I, of course, hope he is wrong, but…….
[Response: You are right I haven't watched Richard's lecture (I will do so), but I stand by what I said, including Antarctica. >3 m is less than 100 years is virtually unpossible (h/t Walt Kelly). Saying "we can't rule it out" is accurate, but misleading. I am sure Richard agrees. --eric]
Alley wasn’t talking about Greenland, but most specifically about Thwaites glacier, West Antarctica. His position seems to be we can’t rule out upto 3m in less than a century once Thwaites would start draining, all the way to the Trans-Antarctic Mountains.
The question is how soon that process could start. Alley says we don’t really know, but it could maybe just as well be wihtin decades as after centuries or millennia.
Comment by Lennart van der Linde — 10 Jan 2013 @ 4:11 AM
Deepest thanks, eric, for addressing my request for an evaluation of Alley’s video. Alley actually seems to agree with you (between minutes 18 and 21) that Greenland is probably not going to be able to flow into the sea in a shorter time period than centuries or millennia because of it’s ‘gnarly’ bedrock.
From that point in the video, though, he moves on to a discussion of parts of West Antarctica that he claims do show characteristics that would allow for a relatively rapid rise, and he has models of exactly how that could happen. This is the section of concern and the process I was interested in a second opinion on, not the Greenland issue (which, though ultimately worrying, does not seem, as you said, to be likely to achieve the rates of flow to pose an extreme short-term risk on its own).
So, sorry to be a pest, but I would still like to hear you or someone’s response to the claims made especially in the last ten minutes or so of the video (and it sounds as if I am not alone in this request here).
Thanks ahead of time, and for all you folks do.
[Response: I'll watch it and get back to this thread to comment. It is very unlikely Richard and I disagree about this, based on numerous conversations I have had with him; it's more a matter of whether we tend to emphasize the likelihoods or the unlikelihoods.--eric]
Thanks, Stefan, for your response at both 13 and for the related response at 19. It is interesting that there are reasons to think that models may underestimate and that they may overestimate. Uncertainty indeed.
(Unfortunately, unlike what many denialists seem to think, uncertainty is not necessarily our friend. It makes it harder to plan. I still think that if Alley is setting forth even a rather remote possibility, it is something worth worrying about and starting to plan for–and especially to stop pushing the system toward! By the way, if you don’t want to watch the whole of the Alley video, the gist is really in the last ten minutes or so.)
Eric, wili needs help understanding what Alley is saying in that video.
Starting around 34:15 (the last 10 minutes as Wili says), Alley is using slides from Christianson et al. 2011. There he talks about loss of the ice shelf on the end of the Thwaites, and about the deep basin behind that ice front, and that _if_ the calving front retreats to that deep hole we could get an ‘insane’ amount of ice breaking off. He says you don’t sleep right next to El Capitan because even a little rock falling off a face that tall is a lot, and points out the ice is enormously thick over that deep basin but it’ll be easily melted _if_ the calving front retreats to that area.
Then he talks about what the ice is actually doing, and how a little bump of sediment out at the calving front blocks warm sea water from getting in under the ice — but if the front retreats behind that little bump, suddenly water can get far back under the ice.
Then he cites Christianson and assorted PSICERS, in review — perhaps you have access to the paper? at 36:49 in the video.
There’s the rub. He says the calving front is almost off that bump — and once it passes that point, a very long span of ice will be floating and subject to tidal and storm flexing.
He mentioned earlier that you can see the ice 80km up the glacier changing its speed with the tidal cycle, so it’s expected to be very sensitive to loss of that obstruction at the calving front.
I do think it’d be good if several of the scientists could get together a review _of_ the videos out there. Above I mentioned that I’d been asking about stuff that seemed to be fringe speculation six or seven years ago at William Connolley’s blog about how fast erosion happens under the ice — stuff like the first ever observation of creation of a drumlin under the ice, and how astonished people were at the speed of change below a glacier.
That stuff and the stuff about groundwater surging up from sediments under a glacier as it lifts, increasing the flow rate — is still pretty new.
There’s probably a blind-men-and-elephant problem with ice cap science just because there’s so much information flooding out that nobody has time to go deeply into other people’s research, but at this rate of change I think the risk is that the assumptions underlying one person’s work are apt to be changed by the news from someone else’s work.
Eric, see the video at minute 37:00-38:00 for Alley’s description of the “big jump”
At about 40:00 he states the uncertainties — the ice might survive this entire interglacial; we have some paleo evidence it has gone away in previous interglacials.
And there is where he says we can think of one disaster scenario that gives three meters “and rather than talking about centuries to millenia you start talking about centuries to decades. And would I pound on the table about any of that? No! We do not have the physics of a mile high cliff in anybody’s calving model ….”
Thanks, Hank. As usual, you are much more articulate, precise and thorough than my blundering self. I rib you sometimes, but you really are a rare treasure here (especially when you manage to resist the temptation to feed trolls ‘-).)
I hadn’t heard of that (potential? observed?) effect of “groundwater surging up from sediments under a glacier as it lifts” before. Is that in the Stoat discussion that you linked to earlier, or do you have another linky to point me to?
(I know, I know, I should get off my lazy @$$ and find it myself, but perhaps you can spare me the endless two minutes of the hard labor of google-scholar-ing ‘-).)
I vote something like eadler2′s latitude-band method (@22): Apply a smoothing kernel over the stations’ measurements, defining their positions by latitude, then project the resulting smoothed estimator over latitude-bands across the ocean width.
“A kernel smoother is a statistical technique for estimating a real valued function f(X)…by using its noisy observations, when no parametric model for this function is known. The estimated function is smooth, and the level of smoothness is set by a single parameter.” (Wikipedia, “kernel smoother”)
This is (1) mathematically mechanistic, (2) much better than the virtual station method, and (3) actually sensible.
The averaging exercise takes on real importance when we remember that wind and thermohaline currents can affect local sea level by significant fractions of a meter. Global warming is changing atmospheric circulation patterns and and we are seeing thermal anomalies in sea surface temperatures. Thus, some local sea levels are likely to change much more than the global average, no matter how it is calculated. How we do the average makes a huge difference in the global average number. And, the global average number may not reflect the extent and impact of local sea level rise.
Ice melts from the bottom up. (Most of the heat required to melt big ice is collected by oceans somewhere else.) Glaciers move downhill from cold to warm, so they still have cold cores. And, glaciers sit on rock. When the bottom of a glacier melts, the upper parts of the glacier still sit on rock. When the bottom of an ice sheet melts, the top of the ice sheet falls into the melt zone. The fallen ice then melts (drop a 10 ton block of ice a few kilometers and see how fast it melts), and the process repeats. As the buttresses fail, ice from the bottom of the central ice massif is forced horizontally outward by the pressure of the ice above it. High speed hydraulic flows are generated. Such flows can pass through the narrowest fjords with the greatest of ease.
I am sure the folks here will tell me to go read the literature just as they did when I first brought up moulins way back in 2003.
[Response: Correct, I already discussed this in my original 2007 Science paper. And semi-empirical models have been criticised for potentially underestimating non-linear ice-sheet responses, like what Richard Alley talks about in his lecture. I think there are some arguments why these models might underestimate and some why they might overestimate future sea-level rise, but ultimately we do not know. -Stefan]
We’re on track to reach 450 ppm CO2 in about 30 years, and that won’t be the max. What was sea level the last time CO2 was 450?
Comment by Pete Dunkelberg — 10 Jan 2013 @ 3:20 PM
26 wili says, ” Alley actually seems to agree with you (between minutes 18 and 21) that Greenland is probably not going to be able to flow into the sea in a shorter time period than centuries or millennia because of it’s ‘gnarly’ bedrock”
Google Greenland bedrock map. You’ll see that the middle of Greenland, as currently squished by ice, is a huge inland sea mostly to the north, and some minor seas scraggling off to the south and west. At the end of those southern seas is a great canyon that not only cuts 100+km through the mountains to the sea, but cuts deep below sea level. At the ocean it’s -500?ft, but get back 30-40km and it dives to -1400?ft. Visualize the Grand Canyon at sea level directly draining the interior of Greenland. Maybe you’ll live long enough to see it…
Getting through the mountains, carving up the south, and then marching northwards towards ever-colder climes… conquering the Greenland ice sheet isn’t a “decades” type of project. “Centuries to millennia” opens the door to a whole new order of magnitude in the debate.
estimates 4.5e19J into GRIS in 2011 from albedo increase. Is the rest coming from ocean or rain or air ? Pfeffer (2008) says 300Km^2 gate area for GRIS. So if we were to melt all the 1.5mm for 2012 in place, we need around 1-10 KW/m^2 thru those gates to make up the rest of the heat from the ocean into the ice. Don’t think so, I think the rest is ice exporting itself to the ocean to melt at leisure.
WAIS and APIS ? 1/2 mm from there lately. No albedo change or rain. Heat gotto go into ice thru the ocean or ice has to export itself. The latter is more likely. Mile high, hundred mile wide, 2mile deep calving front, anyone ?
Model mass flux thru (possibly fractal) phase change boundaries is messy, but we need to deal with the mess, or else we will deal with other, bigger messes.
A number I like to keep in mind is a mole of Joules. 6m SLR, all of GRIS or all of WAIS. Also about 100 yr of current radiative imbalance. The ocean has a few tenths of a mole of Joules to throw around, but will cool perceptibly if it does, as Hansen states.
All numbers subject to error, love to see corrections.
Eric Steig “>3 m is less than 100 years is virtually unpossible (h/t Walt Kelly)”
Maybe. But sea level rise during the last interglacial highstand may have reached rates of 0.6 – 2.5 metres per century (Rohling et al ) above present-day. Only the Greenland and Antarctic ice sheets remained then. If correct, this infers that collapse of the West Antarctic ice sheet may indeed be very possible in the future. The topography and other issues discussed by Richard Alley, provide a physically-based starting point for how this geologically-rapid jump in sea level rise may have occurred.
Rather than proclaiming something is unpossible, it would indeed be very handy to see some modelling of the physics of ice sheet behaviour that gives some confidence that the current “mainstream” view is correct.
The West Antarctic ice sheet may, or may not, respond dramatically during this century. But whenever it does it’s possible that sea level rise is going to be faster than is presently anticipated.
And one last thing, I do agree with Dr Hansen that direct comparison between slow paleo-planetary warming, and rapid present-day warming, is a flawed approach insofar as the ice sheet response is concerned. Yet to be convinced of anything approaching 5 metres this century though – not sure I understand the rationale behind that.
[Response: This isn't an argument about the science, but about what is responsible reporting of the science. We had a little argument about this here at RC a few years ago, and it's telling that the argument was not about whether 5 m was likely, but whether anyone had claimed it was likely! My view comes from published modeling work e.g. by David Pollard, Penn State and Ian Joughin at University of Washington. Pollard's results with their state-of-the-art ice sheet model shows that if you crank up the heat to the ice shelves in Antarctica by a huge amount (factor of four, as I recall), you might get West Antarctica to contribute 50cm/century. Jougin's model focusses on Pine Island / Thwaites glacier and he get even slower rates. There simply isn't a known way to evacuate that much ice, notwithstanding Richard Alley's point that we don't have a good model of the physics of calving yet. Another point is that the rapid rise at the end of the glaciation occurred when the Antarctic ice sheet was expanded to the edge of the continental shelf. That was a lot of ice at the edge of very deep water. Evacuating ice across shelf -- as would have to happen today -- is much harder; the icebergs would get stuck. Finally, Tad Pfeffer has done the relevant calculation here) including the possible contributions from Antarctica, and finds there is no way to get more than 2 m in the next century. See our friendly discussion with Pfeffer about this, here. A key sentence from that paper's abstract: We find that a total sea-level rise of about 2 meters by 2100 could occur under physically possible glaciological conditions but only if all variables are quickly accelerated to extremely high limits.
The bottom line is that until we discover something new that suggests otherwise, the current state of knowledge is that a rise in sea level above 2 m in the next century is extremely hard get, and should not be discussed seriously as a possibility. The likely value of 1 m or more from Stefan and others' work is serious enough! --eric]
Eric – You appear to be arguing a strawman, and you links are strawmen too. I’m not sold on the idea that rates of sea level above 2 metres are likely to occur this century. Other commenters may have done so, so you’re probably lumping me in with them. What I’m pointing out is that the West Antarctic may collapse as some future point and bring with it much higher rates of SLR – hence my earlier comment that the West Antarctic ice sheet may, or may not, respond this century.
“Another point is that the rapid rise at the end of the glaciation occurred when the Antarctic ice sheet was expanded to the edge of the continental shelf. That was a lot of ice at the edge of very deep water.”
Do you have references for that? Save me some time digging through the peer-reviewed literature. I wasn’t aware we had such accurate assessments of the state of the ice sheets at the last interglacial highstand.
[Response: I agree it is a bit of a stawman, but I was responding to points other raised, suggesting 3 m of "sudden" sea level rise was plausible. Yes, the modeling is not mature. No, in my assessment, no amount of maturing is going to change my point. Regarding the continental shelf, I'm not talking about the last integlacial, but the last glacial. No reference I can think of that makes my specific inference, but the glacial limit (at the shelf edge) is well known, many many references going back to Scott and Amundsen. Start with the name "Denton" and you'll find a bunch of stuff. --eric
Eric, thanks for a clear and candid assessment in your answer to post #41. This is a very helpful and useful discussion to me.
Did you see this from Stefan’s new post here:
“A factor-two revision and a newly discovered first-order mechanism are both not exactly signs of a mature stage of modelling having been reached. I know enough about modelling the Greenland and Antarctic ice sheets and mountain glaciers to be certain that a lot of work remains to be done before these models can be called mature.”
Do you agree with this assessment of the state of the modeling? If so, how certain can we be of your 2 meter limit? When you use a phrase like “the current state of our knowledge” do you think you should add “which is not very mature”?
Thanks again for clear responses and for all you very important work.
[Response: Read the Pfefffer paper in detail regarding the 2 m limit. That's the best answer to your question. Of course, *anything* can happen in science, but some things are more likely than others. This point changing is not likely. But I agree with you and Stefan that the state of the modeling is not mature; I'm very supportive of additional work in this area. But I think it is exceedlingly unlikely that the basic picture will change; significant contributions of Greenland and Antarctica to sea level rise are certain, but their rates being dramatically larger than the upper estimates (which are already very liberal) given e.g. in Pfeffer et al. are simply not supported by any analysis I'm aware of. --eric]
“Since the global warming signal increases over time while the amplitude of natural climate variability does not (much)“
Can someone point me to a good resource about natural climate variability increasing (not much)? I had always just assumed things had not changed enough for natural variability to have changed (pretty ignorant on this point).
Very nice review but I am disappointed that you didn’t address Goelzer et al. 2012. Educators like me who are not experts are lost as to why Goelzer’s millennial scale projections seem to suggest a much smaller sealevel rise by 2100 than provided by most other recent papers. Local sealevel rise skeptics in North Carolina (remember House Bill 819?) are all over this.
Skeptics are pointing to Figure 3 in Goelzer et al. 2012 to argue that the LOVECLIM model suggest a maximum sealevel rise of ~50cm (~20 inches) by 2100 which puts us closer to the low AR4 estimates again. Why is their model projection so low? What am I missing here? Any clarification would be much appreciated.
Millennial total sea-level commitments projected with the Earth system model of intermediate complexity LOVECLIM
H Goelzer et al 2012 Environ. Res. Lett. 7 045401
chris, thanks for the link to the new paper by Foster & Rohling.
Some bad news: +2C of global warming (400-450 ppm CO2) will eventually lead to between 9-31 meter of sea level rise, in equilibrium.
Some good news: Not much additional response in SLR until 650 ppm. “sea level stays more or less constant for CO2 changes between 400 and 650 parts per million and it is only for CO2 levels above 650 parts per million that the researchers again saw a strong sea level response for a given CO2 change.”
This indicates the relative stability of the East Antarctic Ice Sheet. However, I don’t think we should take this as an excuse for burning fossil fuels up to 650 ppm, as the additional forcing will probably cause a faster rate of sea level rise.
Alex, I’d also be interested in an expert consideration of Goelzer et al. From my brief perusal of their paper, the rather slow and relatively limited sea level response relates to a very low climate sensitivity in their preferred model (climate sensitivity of 1.6 oC). That’s very, very much on the low side of the range broadly accepted as conforming to observational, paleo and modelling evidence, and seems particularly low as the time scale of their analysis (extending to the year 3000) would seem to require a consideration of some of the longer term feedbacks inherent in the earth system sensitivity. On the other hand their model has a high polar amplification….
But I might well be mssing something, and I should probably read their paper more thoroughly. Better ‘though would be to have an expert viewpoint on Goelzer’s choice of model/parameterization…
The averaging question looks like one common in geostatistics; not my field but that of a few who I frequent. I suspect there may be good, defendable approaches that are significantly more sophisticated than the one described. In orebody and oilfield evaluation, many millions of dollars can depend on rigorous probabilistic answers to questions of highly under-sampled averaging. I think Robert Rohde at Berkerly has recently been applying some of these techniques to climate science.
[Response: Robert Rohde is using kriging, and I agree this could be helpful here. But I think the best answer would come from a spatial pattern/data assimilation approach that used information from the spatial variations seen by the satellites to estimate the correlations between the far field and the gauge data. - gavin] [... which is what Church&White (2006) have done. - stefan]
Krige, of course, was a South African mining engineer*. Geostats appears to have moved on a bit to techniques based more in statistical simulation. As I understand it, you attempt to replicate the spatial field in a probabilistic model arranged to reproduce all the knowns: the point samples (with errors), the “geology” (inferred spatial patterns / discontinuities), and the variograms / correlations for each domain. Then you just monte carlo-up an answer.
You’re suggesting get that “geology” from the satellite record patterns, also the variograms / correlations. Makes sense. A bit of a look how some in another field have done it might be helpful.
(* I think he’s still with us, though I doubt practicing.)
Milankovitch cycles are on the order of multiples of 10k years (variations in the planet’s orbit, precession, etc.).
Very occasionally there is a big enough change in sunspot activity to put the planetary climate in a different regime.
You can find a summary of the scale of solar variability vs. greenhouse warming here. The critical thing is greenhouse warming is the bigger effect, but it increases in steps that are smaller in the short term than natural variability, so it does not overwhelm natural variability unless you look at a sufficiently long period.
Thanks for your thoughtful and useful response, eric. It certainly would seem reasonable and prudent, given the best science, to start looking at starting to move away from the lowest meter above sea level.
And of course, time does not stop at the end of the century. The Foster and Rohling paper are talking about an eventual rise of 9 to 31 meters. That means most of the major cities along the eastern sea board will be totally or largely under water. Not tomorrow, perhaps, but something we now have to consider for long term plans.
It takes a very long time to make changes necessary to accommodate the evacuation of cities holding collectively tens of millions of people (billions, worldwide, iirc). We should at least start to be sending the right signals, and to avoid major infrastructure investments that will be likely or certainly threatened by high sea levels and by the increasingly intense surges and storms that are coming in the next few decades, at least. I see little hint, though, of this type of talk among policy makers at this point yet.
The ice sheet models are being run in conjunction with the general circulation models that notoriously missed the Arctic Sea Ice Melt Event. While this has been blamed on various factors, I think these models understate transport of latent heat into the Arctic.
I expect the ice sheet models run in conjunction with the community circulation models to understate ice sheet melt and collapse to the same extent that Arctic Sea Ice Melt was understated, and for the same problems with the same models.
“The kinematic constraint may have relevance to the Greenland ice sheet, although the assumptions of Pfeffer at al. (2008) are questionable even for Greenland. They assume that ice streams this century will disgorge ice no faster than the fastest rate observed in recent decades.
That assumption is dubious, given the huge climate change that will occur under BAU scenarios, which have a positive (warming) climate forcing that is increasing at a rate dwarfing any known natural forcing. BAU scenarios lead to CO2 levels higher than any since 32 My ago, when Antarctica glaciated. By mid-century most of Greenland would be experiencing summer melting in a longer melt season. Also some Greenland ice stream outlets are in valleys with bedrock below sea level. As the terminus of an ice stream retreats inland, glacier sidewalls can collapse, creating a wider pathway for disgorging ice.
The main flaw with the kinematic constraint concept is the geology of Antarctica, where large portions of the ice sheet are buttressed by ice shelves that are unlikely to survive BAU climate scenarios. West Antarctica’s Pine Island Glacier (PIG) illustrates nonlinear processes already coming into play. The floating ice shelf at PIG’s terminus has been thinning in the past two decades as the ocean around Antarctica warms (Shepherd et al., 2004; Jenkins et al., 2010).
Thus the grounding line of the glacier has moved inland by 30 km into deeper water, allowing potentially unstable ice sheet retreat. PIG’s rate of mass loss has accelerated almost continuously for the past decade (Wingham et al., 2009) and may account for about half of the mass loss of the West Antarctic ice sheet, which is of the order of 100 km3 per year (Sasgen et al., 2010).
PIG and neighboring glaciers in the Amundsen Sea sector of West Antarctica, which are also accelerating, contain enough ice to contribute 1-2 m to sea level. Most of the West Antarctic ice sheet, with at least 5 m of sea level, and about a third of the East Antarctic ice sheet, with another 15-20 m of sea level, are grounded below sea level. This more vulnerable ice may have been the source of the 25 ± 10 m sea level rise of the Pliocene (Dowsett et al., 1990,
1994). If human-made global warming reaches Pliocene levels this century, as expected under BAU scenarios, these greater volumes of ice will surely begin to contribute to sea level change.
Indeed, satellite gravity and radar interferometry data reveal that the Totten Glacier of East Antarctica, which fronts a large ice mass grounded below sea level, is already beginning to lose mass (Rignot et al., 2008).
The eventual sea level rise due to expected global warming under BAU GHG scenarios is several tens of meters, as discussed at the beginning of this section. From the present discussion it seems that there is sufficient readily available ice to cause multi-meter sea level rise this century, if dynamic discharge of ice increases exponentially.”
How certain can we be that Hansen & Sato are wrong and that the ice sheets are not as vulnerable as they fear or suspect?
Comment by Lennart van der Linde — 15 Jan 2013 @ 2:10 AM
Just to clarify, I am sure you meant that the shift could explain the huge downward fluctuations in 2007 and 2012, not the general nonlinear decline of sea ice that accounts for over 50% reduction in volume over 40 years. Right?
#58, 60–Well, since the Morison et al says: “Here we use observations to show that during a time of record reductions in ice extent from 2005 to 2008…” one would be assuming & extrapolating even WRT 2012, let alone the long-term trend.
And actually, I don’t see anything in either link that supports Dan’s contention. For example, the lead in the NASA link says:
“A new NASA and University of Washington study allays concerns that melting Arctic sea ice could be increasing the amount of freshwater in the Arctic enough to have an impact on the global “ocean conveyor belt” that redistributes heat around our planet.”
Anything in there suggesting the paper is about attributing ice loss? Sounds like it’s about attributing Arctic freshening, rather.
The closest thing to Dan’s interpretation appears to be:
“Knowing the pathways of freshwater is important to understanding global climate because freshwater protects sea ice by helping create a strongly stratified cold layer between the ice and warmer, saltier water below that comes into the Arctic from the Atlantic Ocean,” said Morison. “The reduction in freshwater entering the Eurasian Basin resulting from the Arctic Oscillation change could contribute to sea ice declines in that part of the Arctic.”
But note that that is a “could” statement, not a “does” statement, and that its scope is regional–”that part of the Arctic”–not pan-Arctic.
If the idea is to represent the SLR of the entire ocean area from samples just along the edge (and I think this is correct), then perhaps a better weighting scheme is:
1. Determine the center of the ocean area of interest. Call this point C.
2. Determine the distances D from each gauge to point C.
3. Weight each gauge by the factor W=1/D²
4. Run a standard weighted average using these weights.
Comment by Keith Pickering — 17 Jan 2013 @ 1:35 PM
Comment by David B. Benson — 17 Jan 2013 @ 7:58 PM
Actually kriging is just a special case of least-squares collocation, a variant of the least squares method especially suitable for time series and spatial fields developed by geodesists like Helmut Moritz and Torben Krarup, primarily for use in modelling the gravity field.
Geodesists would have things to give to climatology in the field of statistical methodology. Gauss was a land surveyor / geodesist ;-)
Also Church and White’s method is well known in the geodesy / adjustment theory literature, as a ‘hybrid-norm optimization method’ combining observational and a priori data (and I’m pretty sure its formal equivalence to LSC could be shown). It is well described in Kaplan et al. 2000.
Stefan, just curious: you say that your 2007 paper in Science was “with over 300 citations to date it turned out to be the second-most-cited of the ~10,000 sea-level papers that were published since 2007″.
Which paper is the most cited sea level paper in that period? Pfeffer et al 2008?
So Krige just reinvented an existing technique in geodesy? I don’t know that it matters; popularising techniques across disciplines seems to be something important in itself. Another example is the Cooley–Tukey fast fourier transform, one of the more technologically important algorithms of our time. Turns out that one is also down to Herr Gauss (and geodesy?), well over a century before.
On the formal equivalence suggestion — maybe, but it somehow feels unlikely. (How would multiple mean replacement equate with something involving squares of differences…) But then I admit to being surprised, long ago, to discover that Thiessan polygons and the Voronoi triangulation are equivalent. (If you use a conventional triangulation-based contouring algorithm to compute a spatial average, the answer should be identical to what you’d get with the Thiessan construction.)
BTW, John Church has been in the media a bit here lately. His humble but firm, “I’m sorry, but the quote is wrong” nicely deflated Mr Murdoch’s putative journal of record (The Australian newspaper).
I searched the Web of science for “sea level” OR “sea-level” from 2007 and onwards and the winner in terms of number of citations was this paper: http://www.pnas.org/content/105/6/1786.full (Hint: Stefan Rahmstorf is also a co-author)
excerpt follows (press release, references to journals at the original —-
“… the first high-resolution topographic map of one of the last uncharted regions of Earth, the Aurora Subglacial Basin, an immense ice-buried lowland in East Antarctica larger than Texas….
“We chose to focus on the Aurora Subglacial Basin because it may represent the weak underbelly of the East Antarctic Ice Sheet, the largest remaining body of ice and potential source of sea-level rise on Earth,” said Donald Blankenship, principal investigator for the ICECAP project ….
Because the basin lies kilometers below sea level, seawater could penetrate beneath the ice, causing portions of the ice sheet to collapse ….
… the East Antarctic Ice Sheet grew and shrank widely and frequently, from about 34 to 14 million years ago, causing sea level to fluctuate by 200 feet. Since then, it has been comparatively stable, causing sea-level fluctuations of less that 50 feet. The new map reveals vast channels cut through mountain ranges by ancient glaciers that mark the edge of the ice sheet at different times in the past, sometimes hundreds of kilometers from its current edge.
“We’re seeing what the ice sheet looked like at a time when Earth was much warmer than today,” said Young. “Back then it was very dynamic, with significant surface melting. Recently, the ice sheet has been better behaved.”
However, recent lowering of major glaciers near the edge detected by satellites has raised concerns about this sector of Antarctica.
Young said past configurations of the ice sheet give a sense of how it might look in the future, although he doesn’t foresee it shrinking as dramatically in the next 100 years.
————end excerpt ——–
Oh, well, then, 100 years …. waitaminit, last I heard it was a thousand …
Thanks for the reference to the Aurora Basin. I have been watching Totten, Moscow University (which drain the Aurora region) and Amery further west for a while, and I suspect the EAIS is not as deep in slumber as is assumed. See e.g.Pritchard et al. (Nature 2012, v484 pp 502 et seq., doi:10.1038/nature10968) documenting dynamic thinning of EAIS shelves, driven by CDW.
Seem that everywhere we look we see big holes under the ice upstream of the grounding lines. I wonder if all thos glaciers are perched on pinning points downstream of the giant pits.
Uh, oh. This is the kind of thing I was speculating about over at Stoat years ago, back when the notion of rapid change under the ice was just beginning to be mentioned as a possibility, back when drumlins were first noticed forming fast.
A meltwater origin for Antarctic shelf bedforms with special attention to megalineations
“The geomorphology of troughs crossing the Antarctic shelf is described and interpreted in terms of ice-stream hydrology. The scale of tunnel channels on the inner shelf and the absence of sediment at their mouths are taken to infer catastrophic drainage. Drumlins on the inner and outer shelves with pronounced crescentic and hairpin scours are also interpreted as products of catastrophic flow. Gullies and channels on the continental slope and turbidites on the rise and abyssal plain point to abundant meltwater discharge across the shelf.
“Attempts to explain this morphology and sedimentology in terms of release or discharge of meltwater by pressure melting, strain heating, Darcian flow, or advection in deforming till are shown to be unrealistic. We suggest that meltwater flow across the middle and outer shelves might have been in broad, turbulent floods, which raises the possibility that megascale glacial lineations (MSGL) on the shelf might originate by erosion in turbulent flow. This possibility is explored by use of analogs for MSGL from flood and eolian landscapes and marine environments. An extended discussion reflects on objections that stand in the way of the flood hypothesis.”
Just one thing, I know that acronyms sort of proofs ones deeper understanding of ones subject, ahem, but I prefer to see how the writer thinks without needing my ‘lexicon of current acronyms’ :)
It can become a little tiresome for someone interested to look up all acronym’s used by you guys/gals. When I use such I also make the effort to put the acronym used into words, at least once (inside a parenthesis normally. It simplifies the understanding, and allows you to catch the flow of ideas better.)