Excuse me? Seriously? The SLR since roughly 1870 is clearly published in a number of places and amounts to roughly 9 inches. Quite aside from the infinity of statistical fallacies one can generate by fitting linear trends to timeseries data: http://wmbriggs.com/blog/?p=51..., or if you prefer a longer and much more detailed statistical (Bayesian) explication of the problems: http://wmbriggs.com/blog/?p=51..., and the fact that those problems are multiplied enormously when you seek to fit a nonlinear trend to the data, to argue that this timeseries reveals "acceleration", presumably correlated with increased CO_2 near the end, in spite of the fact that its greatest visible period of "acceleration" is in the early 20th century when CO_2 levels were nearly irrelevant to any observed climate change in everybody's models is not terribly sensible.
Then we could analyze the other fallacies in this sort of graph used as an argument for 5 meter SLR by 2100. For example, the current rate of SLR is around maybe 3 cm/decade -- a bit over an inch a decade. In the 8.5 decades left in the century, we might be looking at anywhere from 8 inches to a foot of SLR based on the data as we have it now, foolishly extrapolating a linear trend indefinitely into the future for a highly nonlinear chaotic system that is perfectly capable of things like glacial transitions (either way) or century-scale droughts without any help at all from humans. However, this still doesn't do the problem justice, because of the differential probable error bars visible even in the figure you present, and the fact that the measurement methodology changes near the end, and the fact that to properly account for SLR either way one really has to take gravity and surface deformation into account in multiple ways. In particular, the crust is continuing the process of isostatic rebound resulting from the melting of an ice layer several kilometers thick on the polar regions "only" 12,000 or so years ago. The continents continue to drift. The sea bottom continues to remodel as this occurs. Much of this produces changes that we are only barely able to measure, in some places some of the time, now (mostly with satellites and e.g. GRACE, but there is a bit of chicken and egg problem there as well). There is the fact that an isostatic ocean produces LOCALIZED SLR where warm water floats on cooler water and can produce this sort of SLR in mid-ocean far from any tidal gauges. Tidal gauges in coastal areas are largely locked to local surface temperatures of the water. The satellite record includes this -- the tide gauge record does not, and since 70% of the Earth's surface is ocean, and nearly all of this ocean is "far" from continental boundaries and the comparatively tiny number of measurement stations that go back into the distant past with isostatic changes that are impossible to measure retroactively or correct for in the present, the probable error in global SLR visible in these curves is IMO at least almost certainly significantly underestimated, and that is before one gets to the factor of roughly 10 that Briggs asserts one is likely to underestimate true error by when fitting a linear trend to a timeseries.
So what the data might justify is this. The "rate" (linear trend) of SLR over the last 145 years is something like 2 plus or minus 2 mm/year -- it could be anywhere from basically 0 to as much as 4 mm/year, and this might well still underestimate the probable error. The "current rate" (measured with much better precision, but beware picking endpoints!) is perhaps order of 3 mm/year, plus or minus what, a mm/year? At least? Well within the long term average, and clearly visible as being (probably) equaled or exceeded in the past in periods with little possible correlation/causality linkage with CO_2, even in so short a record.
There isn't any conceivable argument that can be made on the basis of either statistics or physics for the extrapolation of this already poorly known linear trend, augmented by an even more poorly known nonlinear trend, e.g. a quadratic term into the future. Statistically it is pure nonsense. Physically one has to make a complex, teetering tower of assumptions about how air temperatures will change, in what spatiotemporal pattern they will change, and how those changes will melt the kilometer-thick layers of ice on top of Greenland and Antarctica, where the surface temperature of either one almost never does so much as reach the melting point of ice from below. That "teetering tower" are all Bayesian priors to the assertion of any sort of probable SLR rate in the future, and every single time somebody like James Hansen has gone public with his wild statements of Manhattan "probably" being underwater by now or SLR "probably" being 5 meters by 2100, they have been or are being actively falsified by the mere progress of time, which in statistics means you have to go back and re-assess the posterior probabilities and essentially falsify or weaken the probable truth of your assumptions.
The simple fact of the matter is that we have no idea what SLR will be by 2100. The models that predict rapid, radical rise are the same models that are failing to predict the current stagnation in global warming, which is real enough that it is the continuous focus of climate papers at this point and rated its own "box" in chapter 9 of AR5. As Bayesian priors they are not so good, even before you add in all of the other assumptions needed to melt a few million cubic kilometers of ice that currently never reaches the melting point and spends most of the year well below it.
What we do know is that there is little reason to fear catastrophic damage from any rate of SLR observed with human instruments in the last 150 years. Or, really, a rate twice that size. This is actually the approximate limit of sober papers on the issue in climate science -- a few might still claim 30 inches (less than 1 meter) by 2100 but every additional year with a rate closer to 10 inches by 2100 when extrapolated reduces the probability that the higher end claims are going to be correct.
On a similar basis, Bayesian reanalysis of climate models is reducing their median predictions of total climate sensitivity. That "median prediction" is another statistical travesty, but since I'll probably get hammered as a denier as it is from pointing all of this out, we might as well leave that for another time. I'll only say that I hammer "stupid skeptics" just as hard when they fit a quadratic trend to (say) some post-2000 interval of global average surface temperatures and use it to argue that the planet is definitely cooling and the ice age cometh. My own assertion is simple: When we look at the simplest nonlinear systems -- things far, far simpler than the earth -- we observe a richness and complexity of phenomena that is utterly inexplicable in the simple, linearized models that dominate climate science discussions. We also learn things about how reliable even qualitative conclusions are when we attempt to integrate nonlinear fluid dynamic systems numerically at spatiotemporal scales much, much larger than the Kolmogorov scale of the dynamics.
What we learn there should make us consider the climate problem to be unsolved. Period. It would be absolutely amazing -- a miracle of sorts -- if climate models worked! Yes, they produce something that looks like "weather" (all the way back to Lorenz's original much simpler computational models). But that weather is chaotic, and chaotic systems self-organize when one changes their driving. Entire patterns of turbulence appear and disappear (in sufficiently complex systems) even when one doesn't change any of the driving forces, and things like thermal efficiency and mean temperature abruptly and discontinuously change along with them. Perhaps one cannot prove that the Earth is a self-organizing system along the lines of Prigogene's suggestion, one that will nonlinearly oppose any change in its average state by reorganizing its dissipative mechanisms, but it is certainly an heuristically plausible possibility.
In other words, physics itself should make us very, very wary of any sort of linearization or extrapolation of observed linear trends in what is almost certainly the most difficult problem in nonlinear, chaotic dynamics humans have ever attempted to solve with resources that on the surface of things are utterly inadequate do perform the computations at a scale that has any substantial chance of getting the right answers.
But there isn't any fame, fortune or warm fuzzy I'm saving the world feelings to be had from stating "I don't know, and we are unlikely to be able to do any sort of computation that can be relied on to predict, the future of the climate with or without increasing CO_2." All we know is that claims of that sort of knowledge by the supposedly most knowledgeable have failed, time and again, and that the best computations of the uncomputable to date have failed to show much predictive skill on that front as well. Why is this even surprising? In other area of science of equal complexity would anyone take the slightest notice. But then, in no other area of science (except, perhaps, medicine where again fame, fortune., and warm fuzzies are often on the line) does anyone make such sweeping assertions with so flimsy a foundation.
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