Latest Sea Level Rise Projections

The situation on global sea-level rise due to climate change seems to be slowly becoming clearer.  At the time of the fourth IPCC assessment report (AR4 in 2007) there was a big controversy over the numbers cited there.  The problem was that those numbers ignored ice-dynamics (the fact that the big ice-sheets on Greenland and Antarctica might start to break up at the edges and slide rapidly into the ocean, rather than just slowly erode in place).  It had become clear in the 2000s that ice sheets were much more dynamic than had been previously assumed and in particular, water was pouring down channels (moulins) in the ice to the base and lubricating their movement in the summer - glaciers were accelerating unexpectedly.  This process was not well understood quantitatively, but appeared likely to be the most important mechanism by which ice sheets broke up (and in turn, a major contributor to sea level rise).

What the IPCC elected to do was present numbers that explicitly excluded the ice dynamics contribution, which struck me as a poor decision at the time.  In a summary publication of that kind, intended for the public and policymakers, it seems to me that if you can't quantify the most important effect, it would be better to admit ignorance and not to present numbers at all, rather than present numbers for the second and third order effects that you believe you can quantify, but which are bound to be badly wrong as a summary of the overall situation.

In the interim, satisfactory ice dynamics models based on the fundamental physics are still not available, and more empirical methods are coming to the fore.  The latest paper on this is Vermeer and Rahmstorf in Proceedings of the National Academy of Science (there is also an interesting account of the genesis of this work at RealClimate).  The paper is pretty impressive, at least to this non-specialist.  It's an easy read - a hazy memory of your undergraduate calculus course will get you through if you are otherwise quantitatively literate - and the results, for what is a very simple model, are intriguing.

The basic idea is to model the rise in sea level as being governed by two terms.  The first term says that there is a contribution to the rate of rise in sea level that is proportional to the difference between the current global temperature, and some reference temperature T₀. The idea is that the sea level is eventually - in millenia - going to be a lot higher, but the rate at which it starts to go towards that higher value is proportional to how much above pre-industrial temperatures we are. The second term basically assumes that there is a contribution to sea level itself that is directly proportional to temperature (that some aspects of the ocean expand immediately in response to temperature expansion). There is a substantial plot twist in the paper around this term, but I will let you go read it if you are curious.

In any case, they take this simple three parameter model, and use a fit to global temperature and sea level from 1880-2000 to estimate the parameters.  I have added the emphasis on 2000 as the end date of their fit - we will come back to that point later.

As you can see in this figure taken from their paper, the model provides a beautiful fit to the data:

Here the thin wavy red line is the annual sea level data, the thicker red line is a smoothed version of it, and the dark blue line is the result of their model.  So the point is that the thick red line and the dark blue line are almost exactly on top of one another - a very simple model is clearly capturing a great deal of what is going on.

In any multi-parameter model, there is always the danger of overfitting - if you throw enough parameters into the model, you will get it to fit the data, but it will be fitting the noise as much as the real signal, and the symptom of this will be that when you try to use it to predict outside the interval on which you fit, it will fall apart and predict something crazy. To assess this, they show in the pale blue and the pale green lines what happens when you fit to the first half of the data only, and the second half only.  As you can see, the resulting predictions would not have been perfect - they are off by maybe 10% of the total change in the interval, but they are much better than useless - you would have been in the ballpark of what actually happened (giving one some hope that predictions going forward into the 21st century might also get you into the ballpark).

Those predictions are as follows:

For the range of climate models used in the IPCC AR4, and for multiple different emissions models, they show the prediction range associated with that model (the different colored bands).  The interesting thing that emerges here is that it sort of doesn't matter much what we do as a society - the model predicts about the same amount of sea level rise regardless.  (A1FI and A2 are both high emissions scenarios, but B1 is a mitigation scenario in which the world transitions away from fossil fuels over the course of the twenty first century:

The reason is that sea-level is kind of a doubly integrated quantity.  The temperature change itself integrates over carbon emissions, and the sea level integrates over the temperature change.  So that means there are huge lags between what you do, and when the full effect shows up (it's not that different emissions levels won't make a huge difference to sea level in the long term - they will, just that the full effect of the difference will take hundreds of years to show up).

So this model says to expect, ballpark, 1-2m of sea level rise over the course of the twenty-first century.  This is likely to be very painful regionally, but hardly catastrophic globally.

For example, I found this site flood.firetree.net which estimates what areas would potentially be flooded under various amounts of sea level rise.  Here's the effect of one meter of sea level rise on the area I currently live in Northern California:

As you can see, we lose a bunch of farmland in the Sacramento river delta, and various low lying regions around the San Francisco Bay, but the main cities are for the most part going to still be above water.  Decisions are going to have to be made about what is to be protected by levees, and what is to be abandoned to the sea.  But it's not like the ability of Silicon Valley to design technology products is seriously threatened by this, nor the ability of financial firms to operate in the financial district of San Francisco.

Still, anyone that owns real estate in those newly blue areas might want to think about selling it before the broader public realizes the situation...

Two meters is about the same situation, but a bit more so:

To give a broader feeling, here's one meter in the Thames estuary in the UK:

And here's two meters in Tokyo:

Tokyo is definitely not pretty - they are going to have to build a lot of levees, and Japan is earthquake prone.

So, in terms of the four factor model I discussed the other day, this is a stressor: there's no way this alone would cause a collapse of global civilization by itself, but it is certainly going to be another substantial ongoing stressor.

There is one important caveat discussed in the paper:

In addition, highly nonlinear responses of ice flow may become increasingly important during the 21st century. These are likely to make our linear approach an underestimate. Therefore, we have to entertain the possibility that sea level could rise faster still than suggested by the simple projection based on Eq 2.

To get a feeling for this, here are the best recent estimates I'm aware of for the surface mass balance of the Greenland ice sheet, (from van den Broeke et al in Science last November).

The blue curve shows the change in the mass of the ice sheet, and the orange curve is runoff due to melting.  Although it's perhaps too soon to say for sure how much of this to attribute to natural variability, the orange curve certainly raises the possibility of a pretty non-linear response in which some threshold has been crossed and now the situation is accelerating rapidly.  Note that this has largely occurred since 2000, and thus wouldn't be taken account of in Vermeer and Rahmstorf's model fit (which was only to data through 2000, but in any case, it's going to take significantly longer before there's enough data to really tell what that means).

Update: sea level rise around the US in the last fifty years, from Global Climate Change Impacts in the United States: