Sea unLevel

Sea level is by no means “level.” Not only are there small changes in the geoid (the gravitational equipotential surface), the sea itself does not conform to the geoid because of winds and currents, tides and storms. These geographical variations are in addition to the constant fluctuations caused by the exchange of water between land, oceans, ice, and atmosphere, and of course the changes wrought by global warming.

NOAA’s Laboratory for Satellite Altimetry has sea level time series derived from satellite data, not just for the globe, but for a number of different regions around the globe. Let’s take a look.

First we’ll note that the sea level data from NOAA does not include the isostatic adjustment applied by the University of Colorado Sea Level Research Group (and most other groups for that matter), so the absolute values, and the trends, of their data sets are not the same. We’ll ignore that issue, because we’re mainly interested in exploring how sea level changes have varied from place to place . We’ll use the data based on TOPEX, Jason-1, and Jason-2 satellite missions, since the other satellites don’t really add much additional information and some of their data is problematic (especially from the Envisat mission). We’ll also use the data with the seasonal signal removed (although there’s interesting information in the seasonal signal itself, including its variations from place to place).

First let’s look at the global average sea level:

Its linear rate of increase is 2.8 mm/yr, and if we add the 0.3 mm/yr isostatic adjustment it’s the same as the rate of 3.1 mm/yr estimated by the Univ. of Colorado group. In spite of the never-ending ups and downs, the rate of sea level rise has been reasonably constant while satellites have been watching. If we subtract the trend line (estimated by linear regression) we can see the residuals:

This makes it clear that superimposed on the dominant trend are both fast ups-and-downs, and slower (but still not very long-lasting) movements.

Part of the “very fast” fluctuation is a periodic variation with period about 59.09 days, as revealed by Fourier analysis of the residuals from the smooth of the residuals from the linear trend (click the graph for a clearer view):

The period for two lunar months is 59.06 days, so I suspect that this cyclic variation in sea level is somehow related to the orbit of the moon — but I don’t really know. In any case, we can get a clearer picture of the cycle by “folding” the data with period 59.09 days to reveal its pattern:

The cycle isn’t constant because its amplitude has changed (the graph shows semi-amplitude, which is just half the full amplitude):

Now let’s look at some regional time series. The largest regions reported are the Pacific, Atlantic, and Indian oceans:

Numbers in parentheses in the title are linear trend rates. Note that the Pacific is rising more slowly than the global rate, the Atlantic slightly so, and the Indian Ocean much faster than the global rate. Note also that the rapid rise of global sea level since about 2011 is mainly a Pacific ocean phenomenon, slightly present in the Atlantic, and for the most part absent from the Indian ocean data.

Another large region is the “Southern Ocean,” which, like the Indian ocean, is rising faster than the global average rate:

It also shows an extreme spike at the final data point, which is far enough from the trend line that I wonder whether or not it’s an “outlier.”

Most of the other regions are much smaller, so they tend to show much greater variation than the large ocean basins. The Mediterranean, for instance, varies between -100 and +200 mm even though it shows a smaller trend rate than the globe:

There are also large variations in trend rate between regions. Slowest is the Bering Sea, rising at a mere 0.26 mm/yr:

Fastest is the Indonesian region, which has undergone some extreme fluctuations but with an overall trend rate of a whopping 7.38 mm/yr:

To look for common patterns, I subjected the time series to Principal Component Analysis (PCA). Some of the regions overlap (the Pacific includes the North Pacific, for example) but I just did a straight PCA anyway, this is only an exploratory analysis. The regional time series are not recorded at the same times, so I interpolated them onto a regular time grid using a Gaussian smooth with short time scale (to capture most of the faster fluctuations).

The first PC accounts for 42% of the variation, far more than any other PC (the second only accounts for 10%). Its time series pattern is this:

Note that there are no “units” for the y-axis, this is simply the time series vector normalized (so that the sum of squares is equal to 1). It shows the most common pattern, a steady rise with a rapid up-tick at the very end.

The “co-vector” to the time series pattern tells us how each regional time series correlates with this pattern (although again, there are no units, this is a normalized vector so its numerical values don’t give the actual correlation):

Note that all regions correlate with the main pattern except the Bering Sea, which shows slight (but not statistically significant) anticorrelation. It seems the Bering Sea is the “odd man out,” not participating in the pattern shared by other regions.

Of some interest is the 3rd PC, with this time series pattern:

Many of its large ups and downs correspond to el Nino and la Nina events. Hence it’s no surprise that one of the areas correlating most strongly with this pattern is the Nino 3.4 region:

It is, however, a bit of a surprise that the strongest correlation is with the Bering Sea. Perhaps, in part, that’s because the Bering Sea shows so little overall trend that its non-trend fluctuations (like its response to the el Nino southern oscillation) can dominate its total variation. Perhaps I’ll do a PCA on the de-trended regional time series to find out.

The bottom line is that different regions have shown markedly different sea level changes, both in terms of the fluctuations and in terms of their trend. Globally, sea level is rising rapidly, but generally faster in the Indian Ocean and especially the Indonesian region, as well (to a lesser degree) over the Southern Ocean. In any case, sea level is not really “level,” nor will it remain so over the coming decades.

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14 responses to “Sea unLevel

  1. All the usual caveats…you can’t blame Climate Change for any one specific weather event, drought, flood, blah, blah, blah…. BUT as you’ve noted in the past…come hell or high water, expect both. It certainly looks like the mix present for Sandy does include some elements that can definitely be linked to Climate Change…the warmer waters off the east coast, the persistent blocking patterns. As Jeff Masters has noted at his blog in past……it is getting to the point where it is hard to avoid the increasingly obvious…..this is not your daddy’s climate. See Jeff’s current blog for an update!

  2. In hindsight, I think the moon-orbit-cycle makes a lot sense based on: something like 30% of the Earth’s surface is land, and at times when the moon’s pull is centered on a large land mass, it won’t be raising the water surface as much as at other times, when it is centered on a large water mass.

    Interesting post, as usual.

  3. Arjan van Beelen

    Dear Tamino, are the regional results influenced by the gravitational effects of ice melt? E.g. if Greenland melts, most of the sea level rise will be near Antarctica and the least in regions close to the Arctic.

  4. David B. Benson


  5. Could the 59.09 day period be a fresult of observation/tidal time of day aliasing?

    [Response: I doubt it. For one thing, the frequency isn't right. For another thing, the time sampling isn't even and there is sufficient irregularity that the aliases would be muted, with more distant aliases showing reduced spectral power. But the spectrum out to 500 cycles/day shows that the 59.09-day period is the stronger than all its aliases.]

  6. A substantial part of the 59-day cycle is due to the rotation of the orbital plane of these satellites. The orbital plane does a full rotation around the Earth every 120 days. The half period is 60 days. This is an area of active investigation st the moment. It COULD be due to something as simple as the difference in solar effects on the satellite when it is in full sun all the time and when it is in partial eclipse.

    The TOPEX/Poseidon orbit was designed to minimize tidal aliasing, but there is still some. One of the results of this is another frequency around 60 days.

  7. It would seem possible that the behaviour of the Bering Sea is due to the presence of floating sea ice for large portions of the year. Whilst in other areas, greater Oceanic Heat Content would lead to greater water temperature, which would increase Sea level by thermal expansion of seawater, in the Bering Sea more incoming heat would produce, first, less sea ice and, then, only after all of the sea ice has melted, an increase in the temp of the water.

    (Please accept my apologies for that appalling last sentence. The number of clauses is almost certainly highly correlated with the ignorance of the writer.)

  8. From when are the last data from?

  9. “Globally, sea level is rising rapidly, but generally faster in the Indian Ocean and especially the Indonesian region,”, as might be expected because it sort of locks the warmed up water in and only periodically surges to the atlantic (at cape of good hope) and deeply enough (at ~50S, but not sure of this) to connect with the antarctic circumpolar current. the Pakistanian/SE Asia extreme monsoons are of no surprise, as they are the third way to lose the heat accumulating in the Indian ocean by the action of normal global conveyor belt of oceanic waters. Might I add that once the monsoon has dropped to the Himalayas the residual heat is the likely reason for the Russian/Siberian heatwaves in recent years (well in case of the Siberian heatwave we must remember everything is relative, and that Siberian warming may well have also other reasons) . Thanks for the post. The ENSO connections to other weather phenomena are so numerous that one might program them as integral parts of some kind of model (appropriately randomized of course.)

    Temporarily de-webbed, so nothing new on the blog.

  10. Yes, sea level varies:

    “Globally, sea level is rising rapidly”

    Rapid is a subjective term. The satellite trend around 3 mm/year is larger than the longer term and expectedly noisy tide gauge trend of around 2 mm/year, but the variation probably doesn’t make them significantly different:

    [Response: The "longer term ... tide gauge trend" is about 1.5 mm/yr, and it is significantly different from the satellite-data trend.]

  11. In the CSIRO( ), AVISO ( ) and U. of Colorado data the spike in sea level rise of mid-to-late 2012 is not evident.

    But in the NOAA data it appears that sea level rise has returned with fury.

    From what date are the last sea level data from NOAA, and when will the other datasets be updated?

  12. > when will the datasets be updated?

    CSIRO’s website refers to
    ” … delays getting the most recent data into the PSMSL archive, which is where we get this data from. This is simply due to the the time it takes the various national archives to compile and submit the data….

    … Website … Last modified 23/02/12

    You can find the links to the sources at CSIRO.

    AVISO and UColo probably have the information on their websites also