31 January 2013

Sea level's climate time scale

My 'reality-based decision making' post prompted a comment asking for my thoughts about sea level rise, which is more than sufficient excuse to turn to that.  An additional excuse is that it provides a chance to look at how to decide climate time scales for something other than temperatures.  For global mean temperature trends, I found that you need 20-30 years to determine a climate trend.  We'll see that it is 40-60 years, 60 for preference, for sea level.

My starting point for data was the University of Colorado sea level group.  They provide satellite data back to late 1992.  High quality data, but only for a short period of time.  If global sea level's time scales are like global mean temperature's, then it's only just gotten long enough to provide a climate number.  Fortunately they list links to other sea level groups, including the Permanent Service for Mean Sea Level.  They have three global reconstructions available.  I'll take this one -- published in the scientific literature as: Recent global sea level acceleration started over 200 years ago?", Jevrejeva, S., J. C. Moore, A. Grinsted, and P. L. Woodworth (2008), Geophys. Res. Lett., 35, L08715, doi:10.1029/2008GL033611 -- on the grounds that it covers the longest time period and has the most recent literature publication date.  It will be a good project for a reader to see if the conclusions here change, and how, if you use one of the others instead.

My starting point with any data is, plot it and start to get a sense of what we're looking at.  This includes not to draw lines between data points, as the lines can mislead me as to what's going on.  Try it some time.  The lines typically make the data look much smoother than they do if you leave them off.  That's not always a help, as it can push you to thinking that you have a significant relationship that you don't.  Anyhow, the first plot of the 300 years of data is:

Two things seem obvious from this figure.  First, the data before about 1880 have a lot more scatter than the more recent data.  Second, the change in sea level is markedly more rapid in the more recent half than the first half.  Read the paper for the discussion of the change in rise, how confident you can be that it's truly different and not just a matter of noisy data, and so forth.

For our purposes, I'll start with 1880, same as the NCDC global temperature record, and look from there for the climate time scale on sea level.  The straightforward plot of the data is now:
This is markedly better-behaved.  Looking.  But it also puts me in mind of an old post of mine on climate normals using cumulative sums, where Tamino observed at his blog that there are distinct problems with using cumulative sums.  I didn't/don't think that his concerns truly applied to my application then, and you can follow that up in some update articles I wrote later (links in updates at the end of the article.)  But here ... I'm more concerned about those issues.

Sea level is the cumulative sum of changes in sea level.  When you get to calculus, you'll find the term is sea level is the integral of sea level change, or, equally, sea level change is the first derivative of sea level itself.  Physically, we're not so much concerned with sea level itself, at least in the sense of how many meters from the top of the ocean to the center of the earth.  We're more concerned with the change -- if sea level gets to be higher than it used to be, it can drown ports, amplify flooding from storm surge, and so forth.  As we eyeball the data above, we see that there's a strong general trend towards higher sea level.  On the other hand, if we look very closely, we see that there are some large changes year to year above and below the main body of the trend.

Since, again, eyeballs can be fooled, let's do the more direct thing and compute how much sea level changed from one year to the next and plot that:
Whew!  This is some serious scatter!  The average is 1.9 mm/year over the 123 years (1880-2002) of the record.  But in any given year, the rate can easily be 5 times that -- either as a rise or a fall.  (The standard deviation is 9.2 mm/year.)  This suggests (an exercise left to the reader*) a time scale of about 60 years for looking at sea level's climate.

I'll return, though, to my simple approach of looking for a time period around which the estimates of trend don't change much as you change the length of the period.  Below are figures for trends ending in 2002, starting from the noted year (working with the whole time series now, not just the recent segment), and for trends ending in 1940 (from 1700-1939) or starting from 1940 (ending in the noted year).

It's no challenge to see that within 20 years of the year we reference, the trends are wildly variable and sensitive to just how long a time period you take.  So anything less than 20 years needs some much more sophisticated analysis methods than I'm using on this blog.  (You'll see some examples of what more sophisticated means when you hit the scientific literature.)  To get some more or less consistent trend estimates, you need 40-60 years of global sea level data.  60 for preference, according pretty well, even though it didn't have to, with the estimate above from mean vs. standard deviation.

In some of my fooling around with the data, there was some eyeball suggestion of a 60-ish year cycle in sea level change.  That encouraged me to look to the scientific literature for whether a 60-ish year cycle has been noticed as a possibility already.  The answer is yes, and it appears to be even more complex than this simple analysis would suggest.  See Is there a 60 year oscillation in global mean sea level?, also at the University of Colorado sea level group's page.

If there's a strong possibility of 60 year cycle in the data, then you definitely want to average over the 60 years.  My simple fooling around with it suggested that the magnitude of the cycle is about 20 mm, with recent years having been at the bottom of the cycle. That would suggest that using only simple analysis of the data for recent years would be leading to sizeable underestimates of sea level rates of change. As the scientific literature is already suggesting the rate of sea level rise has been increasing, that's not comforting news.

So, where are we? Well, on one hand, it suggests that trying to understand sea level change only by looking at data is a much more difficult matter than looking at global mean surface air temperatures is. Not least, that you need 60ish years of data to establish a 'climate' in sea level, while temperature can be done in 20-30 years. On the second hand, the large variability in year to year sea level change says that there are very large sources and sinks for water that can operate for a year or two (or several).  "What are they exactly?" On another hand, it says that there must be something interesting to learn about the climate system -- "Why is sea level change so variable as compared to surface air temperature?

Therefore ... more posts will be coming on sea level.  I was quite surprised by the year to year variability in sea level.

* 'exercise for the reader' is notorious textbook-speak for "this can be done, but it'll take a lot of time and be more involved than I feel like doing here".  If you know your college intro. to statistics material, the math I'm referring to is obvious.  If you don't, it'll take a fair amount of time to explain it.


Tom said...

Hi Robert,

Thanks for this post. I find it helpful and informative.

The only real question I have at the moment is why you think looking at 60 years is enough for analysis with 'simpler' equations.

As someone who does brute force simple math for a lot of my work, I'd be whining for 180 years.

Robert Grumbine said...

If you're the Tom who posted at the 'reality based decision making', I'm puzzled. That Tom was treating as significant wiggles in the sea level history that were only 5 years.

The approach I'm taking to finding climate time scales is that the averaging period has to be long enough that making it a bit longer or shorter doesn't change your answer substantially. That clearly isn't true for 20-30 years, where you can still see some wild variations as you make the period a little longer or shorter. At about 60 years, if you make it 5-10 years longer or shorter, you still get about the same rates of sea level rise. That makes it adequate.

Part of what it is adequate for is to prevent us from making the mistake of looking at just a few years of data, as that Tom did, and interpret it as making statements about climate. Sea level has a lot of variability, including, perhaps, a 60 year period of variation. Looking at early 2000s vs. late 2000s is looking at that free variability -- not climate and climate change.

Given 60 years to establish a climate for sea level rise, 180 years of data is certainly desirable. I'd really like 6000 years, myself. With 100x the averaging period for a climate on sea level rise, we should get a better perspective on prior climates (in rates of sea level rise) and be able to check better questions of whether there's a 60 year period (or other multidecadal values, maybe some century long periods).

As someone who does brute force simple math, I'll invite you to follow up and look at how different things look if you apply the post's methods to the Church data (one of the other data sets at the PMSL site). Or to try fitting polynomials to the sea level data here, first through, say, 6th order polynomials. I found the amazing, to me, result that the 2nd through 6th orders all gave nearly identical curves. First time I've encountered that on real data. Such behavior does mean that sea level rise has certainly accelerated over the past 300 years.

Tom said...

Hi Robert,

I'm the same Tom. My previous remarks regarding short term changes were in response to others who used the short term for assertions. I felt constrained to use the same time frame and it carried over into other, separate statements.

I'm well aware of the advantages of using as much data as is available and am a champion of it.


Robert Grumbine said...

Better to respond to me, or the article, or other commenters here. Confusion reigns when your comments are to people and statements not present.

At any rate, do carry out that exercise of running different order polynomials through the data. You'll see that it demands a second order -- i.e., accelerating rise -- curve to make a decent fit. And you can see that the acceleration is required even before the satellite era (late 1992 for sea level).

Tom said...

Hi Robert

The steric contribution to sea level rise--does it have upper bounds?

Because it seems to me that fitting a polynomial to the data is something I would want to do later in the process, after understanding the physical processes involved a bit better.

If ocean heating will cause sea level rises to accelerate from 2mm/year to say 5mm/yr, I will approach this issue in one manner. If 20mm/year, in another.

If all of our concerns are about melting caps in Greenland and Antarctica, I think the approach would necessarily be different.

In any event, using shared assumptions would surely avoid later contention, right?

Robert Grumbine said...

(n.b. Steric sea level rise is for sea level rise that comes from changing the ocean's temperature and/or salinity)

Let's take the broader question -- are any of the sources for sea level rise limited?

Main sources are:
* Warming the ocean
* Melting glaciers
* Melting Greenland and Antarctica.

Glaciers represent a few 10's of cm. So they're definitely limited. Any estimate of sea level increase higher than, say, 40 cm above present requires other sources of sea level rise.

Greenland represents about 7 m of sea level rise (about 23 feet). So it's limited, but so large that if that were what prevented the level from rising even higher, we'd still be in trouble.

Antarctica is somewhere around 60 m. We really don't want that to be what limits sea level from being even higher. It's about 200 feet.

Warming the ocean .... When water gets warmer, it expands. This occurs up to its boiling point. So, no, no limit. (At least not one that makes sense to be concerned about here -- we'd be seriously affected long before global mean temperatures had gone from current ca. 15 C to 100 C.)

But thinking about limits to sea level change from warming points to a different issue about sea level rise. That is, so far most of the sea level rise from warming has been a matter of warming the uppermost ocean, call it the top 100 meters. The ocean's average depth is 3730 meters. If (a big question, for reasons I'll take up in a post of its own) the rest of the ocean gets a warming as large as the top 100 meters, we'd be looking at an increase another 36 times what we've already seen from ocean warming. Roughly 10 cm in the 20th century, so 3.6 meters when it equilibrates.

The next question being how fast any of this could happen. Antarctica certainly can't all melt in 100 years, insofar as we're ever certain in science. Nor could that ocean temperature equilibration finish in 100 years.

Anyhow, if I remember correctly, current scientific literature has the range for year 2100 as 0.8 to 1.8 meters increase from 2000. Warming the ocean alone can do that, as could melting part of only Greenland or Antarctica. In looking at sea level change, then, anything below 200 feet is not limited by the potential sources of sea level rise.

Tom said...

Thanks, Robert. So, no upper bounds on steric rise.

I have difficulty in thinking about SLR in part because the argument so often seems to be about the tail wagging the dog. I keep thinking we should be talking about the ocean's effects on the atmosphere but the conversation seems so often to be the other way around.

Robert Grumbine said...

You hit on a peeve of mine, or, rather, a very important and common misconception about science, scientists, and how science is done. Namely, referring to 'the conversation' or 'the argument' as something other than you and me (plus so-far-lurkers, which we haven't had so far) discussing the science. That makes sense if all scientists are in full agreement with each other on absolutely every point, so that comments by one are the same (necessarily) as what another does/should/must think. But if you're discussing science with me, you get _my_ biases, strengths, interests, and weaknesses. These are different from any other scientist's, so the discussion is necessarily different.

Since I think of myself more of an oceanographer than meteorologist, if you're talking with me (for any value of 'you', not unique to Tom), you'll get a more oceanographic than meteorological bias in the discussion. Take up the same point with Jim Hansen, you'll get different biases, as his scientific origins are more to astrophysics than mine (though I do have some biases that way), and then more to meteorology than mine. To a fairly large degree these 'biases' are a matter of what the person is interested in than of errors. We're all interested in different things to different degrees.

Anyhow, in talking about climate with any scientist, they'll respond most strongly on areas they're most interested in. Meteorologists are generally not very interested in sea level rise, Jim Hansen being an exception in fact -- being perhaps more so than most oceanographers and glaciologists. Oceanographers being much more than meteorologists interested in sea level. (It's 'our' ocean after all.) So if you talk to one of 'us', you'll get different responses from one of 'them'. The element of 'peeve' enters when someone (anyone) assumes that because some other person says something, that the rest of us (whoever it is of 'us' that they perceive to be of the 'same' group) must necessarily agree in all details. We don't, never have, never will (within science), happen. In a discussion with me (or anybody else in science) you'll get my thoughts (or theirs). These will _not_ (ever, in entirety) be in entire agreement with what you hear from somebody else one on one.

One reality, which contributes to your perceptions, is that more of the people who are most public in the climate change 'debate' (see debate vs. discussion for the importance of those terms) are meteorologists, or at least atmospherically biased, than are oceanographers and ocean-biased. Oceanographers, and meteorologists, and glaciologists, and ... don't think, or prioritize, or ... as each other. So now, consider that the conversations you've had with other people are really not very useful clues as to what you can have with me (or any unnamed other scientist). If you talk to meteorologists, then the atmosphere is most important and interesting. If you talk to oceanographers, then the oceans are most important and interesting. If it's glaciologists, it's ice that's most important and interesting. And so forth. If we (scientists in any one field) thought some other field were the most important or interesting, we'd be working in that other field instead. It's a bias, but an incredibly easy one to predict and to accurately compensate for.

So, again, if you're here, carry on the conversation with me and the people who comment here. It will certainly be different than if you were talking with someone else in some other place.

Tom said...

That's actually the soundest piece of advice I've read regarding climate conversations in quite some time, and seems appropriate to far more than this specific post. You might consider elevating it to post level.

Let me consider the implications of what you have written throughout this post a bit more.

My immediate (and hence usually wrong) reaction is this:

If climate sensitivity is 3C or below then, absent contribution from dynamic changes in ice caps in Greenland and/or Antarctica, steric rise of between 18 and 59 cm (as per AR4) is what we should expect this century.

There is a lot of back and forth about potential contributions to SLR from Greenland and/or Antarctica. The jury is still out.

If there is a 60 year cycle we have not identified the components that cause it nor the magnitude of their individual contributions to this cycle.

Even if SLR is currently at a low level, varying between 2mm/yr and 5mm/yr, this is no cause for complacency with regards to the issue.


Robert Grumbine said...

Not sure what you are referring to with 'that' in your first sentence, but glad you found something of merit.

What science papers are leading you to think that 'the jury is still out' in any meaningful sense (i.e., that Greenland and Antarctica are capable of contributing tens of cm in the next century, each)? As always, there are questions about which will contribute more, and exactly how much.

If there's a 60 year cycle, its magnitude is about 2 cm, as I mentioned in the article. Certainly we want to understand where it comes from (if it's real). But as it is a cycle, it doesn't change the long term -- climate -- sea level.

It'll be some days-weeks before I return to sea level. In the mean time, Jason Box, who does some of the original research on, especially, Greenland has recently posted:
Icy Contenders Weigh In, which has a lot of good material.

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