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<h3>Changes in sea level since the last glaciation </h3>
<p>22,000 years ago, the Earth was in a glacial period, and since glaciers are made of water, sea level was more than 130 meters lower than today. Since that time, the glaciers have been melting. It takes thousands of years for all the ice to melt, and we still have a lot of ice in Greenland and Antarctica, which could conceivably melt and add water to the oceans. </p>
<p>It is worth noting that <em>floating</em> ice does not affect sea level when it melts--floating objects displace water equal to their weight, so when they melt, that water is no longer displaced, but the same weight of water is added to the reservoir. (You can verify this in your kitchen.) Technically, since floating ice does not incorporate salt, it displaces <em>salt water</em> equal to its weight, so there is a small error in this argument, but it is not significant. </p>
<p>The melting was slow at first, but over the last 14,000 years, sea level has risen 130 meters, as shown in the following graph:</p>
<p> </p>
<p><img src="interests/Climate/Post-Glacial_Sea_Level.png" width="526" height="359"> </p>
<p> </p>
<p>A more detailed explanation of the graph can be found <a href="http://en.wikipedia.org/wiki/File:Post-Glacial_Sea_Level.png">here</a>. Although it is interesting and not trivial how these numbers are reached, it doesn't seem to be at all controversial. Everyone agrees that this is what happened to sea level since the last glacial maximum. Note that North America was populated, apparently over a land bridge from Asia, ten to fifteen thousand years ago, when the lower sea level allowed for the existence of that land bridge.</p>
<p>The most recent 9000 years is shown in the following graph, in which the vertical scale allows for more detail: </p>
<p><img src="Holocene_Sea_Level.png" width="512" height="364"></p>
<p>A more detailed explanation of this graph can be found <a href="http://en.wikipedia.org/wiki/File:Holocene_Sea_Level.png">here</a>. </p>
<p>It looks like the graph is leveling off, doesn't it? So what's going to happen next? In the past there have been many cycles of glaciation, separated by "interglacials" such as the present one. So it seems likely that there will be another glacial period, and sea levels will decrease. I can't find any evidence of disagreement about the future thousands of years ahead: another glacial period is coming. Big glaciers will cover northern lands as they did before. Humans will need technology and ingenuity if civilization is to survive. But that will take thousands of years, and for us it is a point of interest what the maximum will be before the sea level decreases again. </p>
<p>An obvious question is, what happened in previous interglacials? The Wikipedia article on Sea Level Rise states, without any references, </p>
<p> "During the previous interglacial about 120,000 years ago, sea level was for a short time about 6 m higher than today, as evidenced by wave-cut notches along cliffs in the Bahamas. There are also Pleistocene coral reefs left stranded about 3 metres above today's sea level along the southwestern coastline of West Caicos <a href="http://en.wikipedia.org/wiki/West_Caicos"></a> Island in the West Indies. These once-submerged reefs and nearby paleo-beach deposits are silent testimony that sea level spent enough time at that higher level to allow the reefs to grow (exactly where this extra sea water came from�Antarctica or Greenland�has not yet been determined). Similar evidence of geologically recent sea level positions is abundant around the world." </p>
<p>That conclusion is supported in the <a href="http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_Ch06.pdf">Report of the Working Group on Paleoclimatology</a> of the IPCC, page 458, section 6.4.3.3, where we find "Direct sea level measurements based upon coastal sedimentary deposits and tropical coral sequences (e.g., in tectonically stable settings) have clearly established that eustatic sea level was higher than present during this last interglacial by approximately 4 to 6 m." That section goes on to discuss ice core data, which seems to lead to the conclusion that the ice in Canada and sourthern Greenland melted completely, but some remained in northern Greenland, and that since this isn't enough to account for the sea level rise, some Antarctic ice must have melted too.</p>
<p>Hence: either <li>the interglacial period will last a bit longer, and we'll have more time to prepare for the coming glacial, but meantime, sea level could rise a few meters, or </li>
<li>the sea level will not rise much more, and the next glacial period will come sooner.</li>
<p>This is the longer-term context in which we should consider the much-debated question of what sea rise to expect by 2100. </p>
<p>If the ice on Greenland, or the ice on Antarctica, were to melt overnight, there would be a several-meters rise in sea level, flooding coastal areas and causing quite a bit of trouble for humans. These dramatic scenarios have stimulated both public and scientific interest in the question of how likely such a melt-off might be. Facts relevant to that question will be discussed on other pages (devoted to Arctic ice and Antarctic ice). Here we note only that at the present rate of melting, it would take many thousands of years; hence dramatic scenarios involve unforeseen accelerations of the meltoff due to unknown processes. That raises the question, whether in past interglacials, there was anything dramatic about the rate of change of sea level as the maximum sea level was approached. I did not find any discussion about that; it seems to be difficult enough to establish the minimum extent of glaciation.</p>
<h3>Sea level rise at the present time </h3>
<p>One could hope that we could just measure the sea level and see how it is changing. But we are talking about a change on the order of 2 mm per year. Obviously you can't just go down to the local pier and measure that; it will be swamped, for example, in the daily tides. Besides, there are a lot of factors influencing sea level over short time scales: not only daily tides, but lunar tide cycles, and cycles of length 14 months and 18.2 years with astronomical origins. See the <a href="http://en.wikipedia.org/wiki/Current_sea_level_rise">Wikipedia article</a> on sea level rise for more details. </p>
<p>Since land masses also change in elevation, even if we averaged many high-tide readings at the same location, we would still be measuring only the sea level relative to that land mass. A better method is to use satellites to measure the sea level relative to the Earth's center of mass. This is also a complicated business; but here is what NASA says is the result: 3.1 mm per year at present: </p>
<p><img src="interests/Climate/800px-The_Rising_Sea_Level.jpg" width="800" height="522"> </p>
<p> </p>
<p>You can read what NASA has to say about these satellite measurements at <a href="http://earthobservatory.nasa.gov/IOTD/view.php?id=6638">this NASA page</a> and by following links from there. Curiously, this 3.1 mm/yr number is higher than the numbers (more like 2.1 mm/yr) derived from land measurements, but obviously both methods don't have pinpoint accuracy. For example, the satellite uses radar to measure its height above the ocean, but its own position may not be known exactly due to orbital decay, so it is constantly recalibrated using measurements of its distance from land stations whose height above mean sea level is presumed known by surveying.</p>
<p>At 3 mm/year, by 2100 the sea level would rise 30 cm. That is in the mid-range of the IPCC's six scenarios in their 2007 Assessment Report; the six scenarios range from 19 to 58 mm by 2100.</p>
<h3>Sea level in the 20th century</h3>
<p>The facts about sea level rise in the recent past may be relevant, if one is trying to prove or refute that human activities have influenced sea rise. The last part of the Holocene graph above looks constant, on that vertical scale. So are we now experiencing a faster rise in sea level than in the recent centuries? Here we are on tricky ground.</p>
<p>The British National Environment Reseach Council runs the Proudman Oceanographic Laboratory. Their <a href="http://www.pol.ac.uk/psmsl/longrecords/longrecords.html">web page</a> is a good source of information about land-based sea level measurements. The sources of sea level data are explained <a href="http://www.pol.ac.uk/psmsl/pub/ancill_rep.htm">here</a>. </p>
<p>A typical one is the Kronstadt gauge in Finland. A history of this gauge and its data can be found in a <a href="http://www.pol.ac.uk/psmsl/longrecords/ReportsFGI_2000_1.pdf">report</a> published by the Finland Geodetic Society. </p>
<p>Here's what the data looks like. Each data point is a yearly averages of measurements. There was a catastrophic flood in 1824, and after that, the gauge probably wasn't replaced at exactly the same height as before. Also at other time the gauge may have been disturbed, according to the report. </p>
<p><img src="interests/Climate/Kronstadt1.jpg" width="691" height="335"> </p>
<p>To understand how noisy this data is, look at the monthly (instead of yearly) averages:</p>
<p><img src="interests/Climate/Kronstadt2.jpg" width="715" height="587"> </p>
<p>You will note, though, that this data doesn't seem to show sea level rising. Why not? Well, there are reasons, which very will illustrate the difficulties of measuring sea level. I quote from the cited report: </p>
<li>change of the departments responsible for observations at the Kronstadt gauge has occurred and observation regulations have been changed;</p>
</li>
<li>the amount of technogenous load of Siniy Most, on the pier of which the gauge zero point is fixed, has increased considerably;</li>
<li> the amount of piezometric depression has increased sharply up to regional scales (radius about 50-100 km, amplitude ~60 m), with the centre in St. Petersburg, this depression was formed in the course of intensive exploitation of the Gdov aquifer underground waters;</p>
<li> the level regime has changed as a result of the construction of the Leningrad dam (the complex of flood defence facilities); etc.</p>
</li>
<p>Now that you see what the raw data is like, let's consider the peer-reviewed paper <em> </em><a href="http://www.pol.ac.uk/psmsl/author_archive/church_white/GRL_Church_White_2006_024826.pdf">An Acceleration in Global Sea Level Rise</a>. This paper uses satellite data (which only began in 1993) to "reconstruct" past sea level rise data. I did not understand how this was done, but here is the result:</p>
<p><img src="interests/Climate/1870-1995SeaLevel.jpg" width="930" height="256"> </p>
<p>The authors then fit a quadratic curve to the sea-level data, which would correspond to fitting this graph by a line. That line would obviously slope upward a bit. They are happy that this confirms a computer model prediction of an "acceleration", while previous measurements had not shown an acceleration. Near the end they say "The quadratic implies that the rate of rise was zero in about 1820 when GMSL [global mean sea level] was about 200 mm below present day values. This level is consistent with estimates from bench marks carved in rock in Tasmania in 1840 [Hunter et al., 2003] and the height of ancient Roman fish tanks[Lambeck et al., 2004], which implies virtually no long-term average change in GMSL from the first century AD to1800 AD." Well, that same quadratic would obviously imply that sea level was decreasing before 1820, which is patently false. If you fit a quadratic to data that goes from 1870 to 1995, you can't expect it to say anything about times before 1870. Both the first and last paragraphs of this paper emphasize the "confirmation" of the computer model. But to say that a graph as wiggly as that one confirms an acceleration requires very fancy statistics, to say the least. </p>
<p>We already mentioned an unexplained discrepancy between sea level rise numbers based on terrestrial measurements, and the satellite-based numbers. Note that the numbers in the above graph for the satellite era are the satellite-based numbers (3.1 mm), whereas the earlier numbers must be based on terrestrial measurements, somehow "reconstructed". I suspect that the unexplained discrepancy has crept into that graph. Since this graph is not based directly on measurements, I don't count it as a "fact".</p>
<h3>Causes of changes in sea level</h3>
<p>There are two factors changing sea level: </p>
<li>Thermal expansion of the oceans</li>
<li>Net melting of Greenland and Antarctic ice</li>
<p>Over geological time periods, changes in the size and shape of ocean basins can also affect sea level, but nobody expects such changes by 2100.
Note the phrase <em>net melting</em>: enough snow falls on the Greenland ice pack to lower sea level 8 mm/yr, but also, the ice melts constantly, so these effects almost balance out, and it will be difficult to establish which one is greater, since both are an order of magnitude greater than the difference. These issues are properly considered as issues of ice, rather than issues of sea level. </p>
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