Saturday, December 01, 2012

Sea level rise is the most reliable way to see global temperature trends

Tonight, I skipped another (3-hour) catastrophic movie on TV, Flood (2007). Some skeptics are writing lots of e-mails about a silly study that says that the sea level rise proves man-made global warming – without a glimpse of evidence supporting the attribution. It apparently has some impact in the U.S.

I am already way too bored by this junk. People who keep on writing this stuff are inferior inkspillers and one of the goals of my writing about the climate in recent years has been to convince sensible people that they should pay no attention to these liars and idiots. So it would be hypocritical – and a sort of masochism at the same time – if I were reading much of the alarmist garbage that is being published.

Via NOAA. Battery, NY is named after artillery batteries that use to stand there to protect the settlers from David Cameron's predecessors. If you think the trend is only this straight in New York, try Boston, San Francisco, Seattle, and London.

But concerning sea level rise, I want to say one thing. It is a great benchmark to estimate the rate of something that could be called the global mean temperature – a better method than the manual averaging of weather stations or satellites. The main reason why I say such a thing is that unlike the graphs of the global mean temperature reconstructed from weather stations or satellites, the graphs of the sea level rise are unbelievably straight. And you don't need to measure the sea level at lots of places in the whole world. One place, e.g. Southwest of Manhattan – see the graph above – is enough.

Compare the sea level graph with some typical graph of global mean temperatures over a similar period:

I think you must agree that the sea-level graph may be classified as a straight line with some nearly white noise added while the global mean temperature graph is much further from such a description: the global mean temperature graphs resemble random walks whose "trends" are changing all the time. Well, I am sure that you may demonstrate the visually obvious point quantitatively, too.

The Battery, NY sea level graph is constructed so that the average seasonal cycle – a rather simply calculable function of time that only depends on astronomy – is subtracted. What is left is a remarkably straight line despite the fact that the difference between the (two) maxima and (two) minima of sea level on a given day in Battery, NY is almost 2 meters and we need to isolate millimeters every year. It's so straight that NOAA has calculated the rate of the sea level rise as\[

\ddfrac{h}{t} = (27.7\pm 0.9) \frac{\rm cm}{\rm century}.

\] The relative error is just 3%. Quite amazing: the error of the known temperature increase in the last 100 years exceeds 10%. When you see how straight the graph is and how the rate hasn't visibly changed in the last 100 years, you must also agree that it's very hard to imagine that the sea level rise in the next 100 years will be too far from these 27.7 centimeters. Every sensible person knows that 27.7 centimeters per century is negligible for practical purposes. It makes no sense to be afraid of a sea level that 27.7 centimeters higher in 2112 than it is today.

You should also be able to see – just visually – that the average acceleration of the sea level rise is almost exactly zero. It's so close to zero that the error of the acceleration coefficient would be comparable to the acceleration itself. So it makes no sense to try to extract the acceleration from the time series: there's none. That's why I found a long text by Stefan Rahmstorf redundant and useless. It's a futile task to try to extract the acceleration from this graph simply because there's no significant acceleration in the graph. Otherwise his main claim is totally illogical. He tells you that you shouldn't try to estimate acceleration by fitting a quadratic. However, the average acceleration over the period is pretty much by definition the quadratic coefficient in the best-fit quadratic (times two, to celebrate Mr Brook Taylor). So the precise procedure he wants to ban is surely valid. The actual correct claim is that you shouldn't try to calculate the acceleration at all because within the error margin, it's zero (equivalently, the error margin is as large as the acceleration itself) and because the additional non-linearities that seem non-quadratic imply that it's not a good approximation to talk about a constant acceleration at all! But as long as you want to talk about a universal, constant acceleration, it is nothing else than the quadratic coefficient from the best-fit quadratic (times two), despite Rahmstorf's silly discouragement.

I think that the sea nicely averages the heat at many places of the globe. Well, let's admit that the sea level graph is smoother also because the oceans have a significant "inertia" – well, I mean heat capacity. But it doesn't matter. The inertia is just doing something like 5-year or 10-year running averages of an underlying trend that could be more bumpy. But it's still true that the sea level in Battery, NY shows nothing like the global cooling between the 1940s and the 1970s. The sea level was rising rather uniformly (linearly) throughout the last 120 years or so, independently of CO2 production, aerosol emissions, and other things. The linear shape of the graph is a strong piece of evidence that the sea level rise isn't (mostly) caused by the bumpy (and exponentially increasing: the CO2 emissions increase e times every 57 years) human activity.

Despite the widespread hype about melting, most of the trend above is actually caused by thermal expansion of the ocean. (Melting accounts for 20% or so.)

On the graph above, you see that the density of water is actually minimized at approximately 4 °C (Howard W. is telling me that the salty seawater has the minimum elsewhere, actually at –2 °C). Water expands if you cool it or warm it from this particular temperature. At reasonable "room temperatures" (or the ocean temperature in a large majority of the globe), the coefficient of thermal expansion is something like 0.025% per Celsius degree. So if the ocean temperature increased by 0.5 °C in a century (probably a bit less than that because the oceans were warming less quickly than the land), you may see that the "height of water" should have increased by something like 0.01% in the last century.

Because we know that the actual rise was about 30 centimeters, we may estimate the relevant part of the ocean that was heating up and expanding. 30 centimeters is 0.01% of how much? Well, we get 3 kilometers. It's surely a thicker layer of the ocean surface than what is usually considered as the "circulating part of the ocean" capable of storing heat. But there are different effective descriptions at different time scales. If you consider longer time scales, like 20 years instead of 5 years, deeper layers of the world ocean become relevant.

It's remotely conceivable that the melting of glaciers and ice sheets in the Greenland or Antarctica could become more important in the future and the trend may start to change quite suddenly. But the impressive constancy of the sea level trend in Battery, NY – and any place that measures it as well as the Newyorkers do (there aren't too many places like that) – is a strong indication that such a melting contribution (and, independently of that, the human contribution) hasn't started to be important yet. Could we please postpone all the climate worries to the moment when the sea level rise trend (measured at least from a decade of data) increases at least to 50 centimeters per century? The data available so far indicate that we haven't changed an iota about the natural trends yet and the continuing expansion of the New York City is a strong hint that 27.7 centimeters per century is just fine from all points of view.

Bonus fun: Prof Chimp

Do you believe that this video via Peter F. is legit?

ALL IS IN ORDER from Science News on Vimeo.

He's better than you and me, isn't he? The official caption says: After touching the white circle to start a round, Ayumu breezily reconstructs the order of briefly flashed numbers. Credit: T. Matsuzawa, Primate Research Institute


  1. Hi Lubos,

    I understand why you detest pro Anthropogenic Global Warming people, but I don't really support your ultimate stance. I understand that many of the "scientists" involved in producing the results for AGW are pretty low quality - and I mean that in a very simple way - they were mostly the guys/gals you knew at school who weren't that good at maths, physics, chess, computers etc - most stuff that makes the best scientific brains.

    But maybe these individual idiots have finally discovered something actually worthwhile, such a large quantity has enabled a little bit of quality to emerge.

    Yes, it's annoying that the same anti-science idiots who have been shouting their dumb mouths off for decades might finally have found something worth shouting about, but if man-made influences are changing our climate in bad ways it's a big deal, no?

    I mean, my own city, London was afflicted by a terrible smog less a century ago simply because of coal burning fires - it was not a natural occurence.

    However, I wish these idiots would also support a small fraction of the trillions of dollars for fundamental physics research - this, in the end, will probably enable clean energy beyiond our dreams today.

    The idiots rather hope we can return to the middle ages, with windmills and such, and for that, I hate them too

  2. And you don't need to measure the sea level at lots of places in the whole world. One place, e.g. Southwest of Manhattan – see the graph above – is enough.

    I have read elsewhere (sorry, can't remember where) that at present, most of the "sea level" rise in major coastal cities worldwide is actually subsidence of land due to extraction of water from the groundwater table. So one would need to filter out this confounding influence, as well as any changes from earthquakes or continental drift.

  3. In some cities, like Seattle where I live, the ground is squishy enough to sink under heavy buildings. There's an "underground Seattle tour" popular with tourists, through abandoned passages that used to be at ground level.

  4. SteveBrooklineMADec 2, 2012, 12:27:00 AM

    I don't know Lubos, the sea level problem seems pretty serious to me. The NY Times last weekend had an artist's rendering of the how things will look in a few years:

    Plus they have this app that shows the effect on various cities:

    I don't think we can continue to deny these threats.

  5. I lack the skills to adequately critique all this jazz. I think the efforts to address the problem are misguided. I am a supporter of geo-engineering if only because I think it is inevitable we will have to find ways to manage the weather and undertake massive geo-engineering products to transform the landscape. Taking the GHG as a given, I believe we have absolutely no chance of reducing GHG output, it will take too long and require such a fundamental transformation of our economies that it won't happen. So spend the money on geo-engineering.

    My inspiration comes from a trivial source. Masters of Orion 2 the game, where soil enrichment, terraforming, weather control, and gaia transformation are mandatory technologies in the game. Also, a set of papers by the Royal Society in 2007(?) which argued that geo-engineering is the only practical and realistic solution.

    BTW part of the sea level rise is now believed to be due to all the ground water we have sourced and has now found its way to the oceans. I have trouble with that because it suggests we have sourced huge amounts of ground water.

  6. And in that NYT essay, third comment from the top is by the daughter of a veritable Nobel prize winner. Whom I knew well back in the day, she was one of my ex-girlfriend's best friends. A sweet lady and a gifted artist. Now she's a fixture on Andy Revkin's Dot Earth. I'm told she had an offer to move to England for a year on a stipend but declined out of concern that the Gulf Stream might collapse, leaving her stranded on an ice-packed frozen island. You could hop on the T and say hello for me. I think they still have "open studio day" once a year.

  7. The article you cite pictures the Statue of Liberty submerged. With a pedestal to torch height of 92.99 meters and a sea rise of 27.7 cm per century, the statue will indeed be submerged.

    In 33,570 years. Provided we wait to start the countdown until the island on which the statue is built is submerged up to the base.

    Or did I do the math wrong?

  8. I live in Manhattan, so I find this interesting.

    The lower reaches of the Hudson are an example of a fjord, an inlet with steep sides carved by a glacier. Hence most of Manhattan is built on solid bedrock strata known as Manhattan Schist. This is how the
    skyscrapers can be solidly anchored. In fact there is a gap in the Manhattan skyline between midtown and downtown because the schist layer bows downward below a looser layer of glacial fill between Washington Square and Chambers Street.

    Hence, there is little problem with land subsidence here. Furthermore, the freshwater feeding the Hudson is reliable, so the estuary just southwest of lower Manhattan has a stable water input and is geologically solid. This means sea level is predictable, once you adjust for tides and air
    pressure . The low pressure bulge of seawater during the Sandy hurricane coincided with a high tide with sun and moon aligned.

    The reliable water source, deep harbor and geographic location at a concavity on the land mass (and hence a focus of land routes from the Southern and Middle Atlantic states to New England) account for the city's growth.

    Of course, socialist economics can destroy any city no matter how favorably situated.

  9. Dear Robertson, you did the arithnetics right assuming the linear growth.

    But the growth simply can't continue linearly. Even if all the ice in the Greenland (7 m) and Antarctica melts, one gets at most 30 meters.

    Because 0.5 deg C gave something like 20 cm from thermal expansion, 1 deg C gives 40 cm and 80 degrees gives 32 meters.

    Above 100 deg Celsius, water evaporates, so the statue won't be submerged in a liquid, anyway. 32+30 is still less than 93 meters so the statue simply can't be submerged with the water available on Earth.

    The potential for the opposite motion, dropping sea levels, is much greater because the continental ice sheets may grow in an almost unlimited way. The oceans were 100 meters lower just 15,000 years ago or so. And they will again be this lower in something like 60,000 years.

  10. Cool, interesting ways how to find a chain leading to Phil Anderson. She must be great but not going to a Western country because of the fear of catastrophes resulting from the imminent stop of the Gulf Stream is a condition that would probably require a psychiatrist.

    I am sometimes doubting even about myself when I rejected tons of offers to go to China or Canada because of the need to run to embassies to get the visas but I suspect it's still more healthy a justification than a stopped Gulf Stream.

    The Gulf Stream is ultimately driven by West-East asymmetries of the winds, and to stop that, you would need to stop the spinning of the Earth around its axis – a change that would affect days and nights in the U.S., too.

  11. Yes, it's annoying that the same anti-science idiots who have been shouting their dumb mouths off for decades might finally have found something worth shouting about, but if man-made influences are changing our climate in bad ways it's a big deal, no?

    If we're occupied by extraterrestrial aliens tomorrow, it's also a big deal. What's somewhat important here is that none of these two fears is justifiable by the evidence, isn't it?

  12. Hi Lubos, Interesting post. You suggest that the New York measurement of relative sea level change is as good or better than measurements made elsewhere. Which is likely true. However one also has to bear in mind that most points on the earth's land surface are either sinking or rising irrespective of what's happening to the water. Rates are generally low, of the order of +/-1mm/year, and large regions will be close to zero, but the possibility of such background local subsidence or uplift, particularly at and near latitudes which were covered by ice at the last glacial maximum, has to be taken into account if one wants to use a single site to represent global sea level change.
    I don't think that's in dispute.
    More speculatively, I wouldn't be surprised if New York is still in fact quite a good choice.

  13. Right, plausible, but whatever the tectonic contributions are, their rate seems to be constant, too.

    I've added links to graphs of sea level in Boston and San Francisco. The same thing. The tectonic local issues may decide whether the trend is 28 or 32 cm in a century but they don't change the overall story about the constancy.

  14. I also live in Seattle and have taken the underground tour. The abandoned passages are there because the original street levels were close to high tide so the city raised the street level one floor and the passages are the old sidewalks with the old store fronts. The buildings didn't sink, they were just built on low ground. I think that the ground around here is still rebounding from the last ice age.

  15. Thanks, Lubos, for the additional links. Actually I agree with you: if many widely separated sea level measurement stations show only a linear increase, this is evidence that there is no global acceleration in sea level rise.
    The 3 tidal stations near London which are in your link are all subject to the regional isostatic (tectonic) post-glacial subsidence of (I think) about 1mm/year.That figure has to be subtracted from the tide-gauge figures (each about 2mm/year) to obtain a figure for the component of local relative sea level rise attributable to thermal expansion of the oceans, melting ice etc.

    Fig 2 in your Seattle link, which is taken from IPCC 2007 WG1 Fig 5.13 (p.410) seems to show an acceleration in sea level rise. The diagram is a spaghetti graph with time series ensembles of different origins bundled together. The thin black line is based on satellite data and shows “…deviations from the average of the red (sic!) curve for the period 1993 to 2001...” The blue line shows “…tide gauge measurements since 1950…”, while the red line shows “…reconstructed sea level fields since 1870 (updated from Church and White, 2006)…”. I find this way of presenting data better calculated to mislead than to inform.

  16. Hmmm. So now the earth was heating up between the 40's and 70's? This is a radical statement...

    I find this post very interesting, though I'm not sure you have the right explanation. Recent work has (supposedly) put limits of sea level rise due to polar ice melting at 11 mm/ 20 years. (See So, what mechanism, related to global warming, would essentially suck water out of land and lakes, eventually depositing it in the oceans??

    Here's an alternative idea, which I'm confident you will reject. :-) Dr. LaViolette has developed a theory, called subquantum kinetics, that predicts continual creation, that occurs preferentially where massive bodies have already developed. Continual creation should (using intuitive arguments; I've calculated nothing) raise the bottom of oceans further than land which is farther from earth's center. The sea bottom has less weight to push up against, than the earth's crust under land at a shoreline, at the same radial distance from the center of the earth, as the ocean bottom.

    The earth's rotational period is 17 milliseconds longer than a century ago, so something is slowing it up. I have no idea about whether or not tidal forces can account for this, completely.

    Subquantum kinetics has a number of experimental confirmations.(See Some physicist has said that LaViolette deserves "2 Nobel prizes", for his discovery (via subquantum mechanics) of the mass-luminosity relationship extending to planets.

  17. " And you don't need to measure the sea level at lots of places in the whole world. One place, ... is enough."

    See 'Isostatic Glacial Adjustement'

    'Vertical velocities show present-day uplift (∼10 mm/yr) near Hudson Bay, the site of thickest ice at the last glacial maximum.'

    'large parts of New Orleans are subsiding more than 10 mm/year, and so they see a much higher rate of sea level rise that has nothing to do with climate change.'

  18. Dear Metamars, the sea level measures a different kind of "global mean temperature", one that only counts the heat in the ocean but also counts it with the appropriate weight - the volume of water that is involved - and that may be differently affected by the phase transitions, and so on.

    So there's not a necessary "contradiction" between the fact that the sea level was going up uniformly even between the 1940s and 1970s while the "global mean temperature" from weather stations was not. The latter is being constantly revised, so while people used to talk about significant cooling between the 1940s and 1970s, they try to erase it today. It may be fudging of the data or not. I have mixed feelings about it.

    But whatever is the answer, the measurement of the sea level at any place I mentioned - New York, Boston, San Francisco, London, Seattle - seems much less controversial and there's no room for correction. And the answer seems much more natural - linear growth. It surely says something about the temperature or heat of the oceans and "some kind" of the global mean temperature, too. Because there's no room for controversies and revisions, it seems like a less controversial measure to me. One knows that 30 cm sea level rise corresponds to 0.6 deg C of global mean temperature or so - we roughly know the scaling - but the sea level actually knows much more accurate information about the acceleration (more precisely, the lack of it so far).

    I have doubts that sucking of water from land and lakes is a significant contributor to changes of the sea level.

    Is continual creation meant to contradict mass conservation laws? Thanks but in that case, i will leave it to others haha.

  19. It wouldn't be so unfortunate if the world's governments realised the best approach is trillions for fundamental physics research, the biggest scientific project in history - to understand microscopic reality.

    This would almost surely lead to brilliant energy generation ideas.

    But no, the governments favour schemes that a 5 five old can understand - sea, sun and wind - probably because that's the level of understanding of most of the politicians involved.

  20. The Manhattan Schist is solid but even it can move up or down (or tilt) in response to flows within the earth’s mantle and I think it does. Several months ago I looked into the various studies (right down to the raw data) of sea level changes and their causative phenomena. I concluded that the rise rate is 1.7 +/- 0.4 mm/year. Land levels generally move up and down roughly +/- 1 mm/year everywhere but the local rate can be much greater. Tidal gauge data, therefore, need careful analysis but it is the most reliable measurement method. Melting land ice contributes 1/3 to the rise rate while thermal expansion accounts for the remaining 2/3. I am pretty sure that the Manhattan Schist (at least on the southern end of your island) is subsiding at about 1 mm/year. The nearest tidal gauge to my home is on the shore of San Pablo Bay and it shows a steady rise rate of 1.8 mm/year.

    I am in agreement with Lubos on the acceleration question. There is zero evidence for acceleration and anything more than a slight acceleration is implausible. In the year 2100 our seas will be 5-7 inches deeper than they are now and there is nothing we can do about it. It is unlikely that a total and immediate cessation of all fuel burning would have a measureable effect on sea levels in 2100 unless a much more precise measurement method is developed.

  21. It wasn’t called smog a century ago. Herb Caen, a San Francisco Chronicle columnist coined the term about fifty years ago. He was disparaging LA, which was extremely “smoggy" at the time.

  22. Here is a longer video from youtube:

    Why bother about making breakthroughs in any field of science (except perhaps botany) when you can so easily make people keep you supplied with apples and bananas?! ;-)

  23. I'm a bit foggy on how the ocean temperature makes for a more accurate world average temperature. Particularly with regard to the execution of a conversion between the two. I'm well sold that the oceans control the world's climate.

    It's just the execution of it that I need, because I want to apply it to the situation on Titan. See because there has only been one spot on Titan that had it's temperature taken directly, in the equatorial "warm" region. That's why Wikipedia says Titans global average temperature is 93.7 K .

    But it seems to me a shoddy practice to take a thermometer reading for 2 minutes at the equator of a moon then claim that it is "The Temperature" of the entire globe.

  24. Dear papertiger, the approximate relationship between sea level and the average temperature defined otherwise obviously depends on the context (e.g. amount of water and its typical circulation), so the conversion seen on Earth - 1 deg C adds something like 60 cm to sea level - can't be used on Titan...

    However, I don't believe your story about Titan's temperature being measured by one spot or even by a "thermometer".

  25. I guess I'll lay my cards on the table.

    Remember back when it was announced that Titan has an ozone hole (and please allow me the use of this term in it's generic form as a shorthand description of an atmospheric feature of planets, which is used only on Earth as a convenient scapegoat by ecoterrorists, socialists, and doomsday prophets, in order to ease their way to complete energy regulation)?

    The main report was about seasonal rain storms developing.

    During that time I became interested in a comparison between Titan and Hyperion, a small football shaped moon of Saturn with almost the same albedo and temperature as Titan, but without any atmosphere.

    In the reports about Titan they included language to the effect that Titan would be much much colder without methane in it's atmosphere. It's just the "powerful greenhouse effect" that keeps Titan so balmy and warm.

    At that time Wikipedia listed Titan's average temp as between 92-94 K with a link back to a "bulk characteristics of the outer planets" NASA page as the reference.

    And I watched in real time as the Wiki changed Titan's temperature to 93.7 K liked back to an obscure Harvard Abstract talking about atmospheric methane relative humidity on Titan. There's nothing in the part they'll allow me to read about temperature or thermometers, but I happen to know from online converters that minus -291 Fahrenheit (reported temp from the Huygens landing site) equals 93.7 degrees K.

    If they didn't revise it the way I suggest it happened, does it really matter. The result is still they took the temperature in Hawaii and decided the Earth's average temperature is 27 °C.

  26. But I degress, I guess what I was hoping for was a formula that would allow a determination of the average global temperature, from just one data point, based on the angle and deflection of the sunshine, and knowing the average temperature and location on the globe of a data point like Hawaii.

    It hadn't ocurred to me that the volume of the water was what let you do the calculation.

  27. Pat Michaels writes in his blog, "The continuous record of water level at Battery Park shows a pretty
    steady rise of about 17 inches since 1856. About half of this was caused
    by the fact that the land is sinking (as shown in 2009 by S.E.
    Englehart in Geology)."

  28. Hi, I'm very interested what's your opinion on this model:

  29. The paper provides absolutely no information about the origin of the warming. It just says that the sea level is linearly approaching some higher ultimate predetermined equilibrium. While it is able to produce the straight line for some complicated temperature input, it produces the straight line for any other input, too, so one can't make any conclusions out of it whatsoever.

    The claim that they explain 98% of the variance is just a reference to the simple linear profile of the sea level. One may explain this feature by their (very simple) model but by many other models, too.

    And of course, nothing in the paper can resolve the natural vs man-made question.

  30. Hi Lubos, what do you think about this lecture ?
    Thank in advance.

  31. Dear Ondro, I've spent 10 minutes now with that, getting pieces, clicking at 30 places of the talk as well. Sorry, I don't have time to dedicate 100 minutes to that.

    Looks somewhat similar to some of my talks about the basics of atmospheric physics and climatology and related issues, so it's fair etc. Of course I realize that he's still closer to the other side of the aisle but I still find it natural that people should agree about some basic science.

  32. Just to make sure I understand you, let me rephrase. Lubos gives a rise of sea level at the Battery, southwest of Manhattan of 27.7 cm per century.. You are saying that the land here is subsiding at 1 mm per year, or 10 cm per century.

    So, we get your actual sea level rise of 17 cm per century (or 1.7 mm/year)..And this agrees with the sea level rise you compute elsewhere.

    Instead of your 6.7 inches (17 cm) per century, the New York Times app cited by SteveBrooklineMA gives a sea level rise of 5 feet (152.4cm) as "probable level in 100 to 300 years", 12 feet (365.8 cm) as "probable level in 2300 if nations make only modest pollution cuts" and 25 feet (762 cm) as the "potential level in coming centuries based on historical climate data."

    Their numbers and phraseology are laughable. Why do they quantify 25 feet if it occurs in the unquantifiable "coming centuries"? And their talk of "modest pollution cuts" assumes that carbon dioxide, essential to plant life, is a pollutant.

  33. Yes, Robert, they are laughable but so are the other dire claims of the AGW crowd. I like the sea level studies because they constitute the most direct falsification of this nonsense.

    We may double the pre-industrial CO2 concentration before it peaks (or we may not) to the benefit of us all. If, on the other hand, the pre-indusrtial level were cut in half we would all starve to death. Some pollutant.

  34. Hi Lubos: Very enlightening post. On a related topic I have often thought about the use of a single number, average global temperature anomaly (surface temps), as a meaningful metric. My opinion is that a more meaningful approach would be the global distribution of anomalies, i.e. a matrix. For example a warming of the poles is more important than warming of the Sahara desert. What is your opinon?

  35. I'm not sure I fully understand the portion about CO2 emissions. If CO2 output is rising exponentially, and sea levels are rising linearly, what exactly makes you conclude that there is no connection, rather than a logarithmic one? I assume it's a simple matter of using some underlying model, or avoiding curve-fitting, but I'm curious as to how it applies in this particular case. Purely from what's written I don't quite see why I can discount the possibility of a logarithmic relationship, with smaller variances in CO2 production damped by the high heat capacity of oceans. Would the damping effect not be sufficient enough to account for the "noise" in CO2 production rates?

  36. Dear Jack, I mostly agree. Well, it depends on the question. There are questions for which the equatorial warming/cooling is more important and the primary cause of other things.

  37. Dear numbers314,

    the reason why your alternative explanation is impossible is that what is rising exponentially are *emissions* or, almost equivalently, the excess CO2 above the natural 280 ppm level, but what the warming depends upon logarithmically is the whole CO2 concentration, and not just C-280.

    So the CO2's contribution to the temperature is

    A * ln (280 + B*exp(T))

    and you may check that because of the 280 extra term, this is far from a linear function, especially in the past when the emissions are relatively low. It only converges to the linear in the future. But because the CO2 excess or CO2 emissions were 10 times lower a century ago, the formula above predicts almost 10 times lower rate of sea level rise from CO2 for the years such as 1900 - almost a horizontal profile - but the rate has been constantly even from those times.

    The problem of the CO2 explanation isn't really the "CO2 noise" which is negligible. The problem is that the rise of CO2 was negligible 100 years ago relatively to the present, and even ln(C) was many many times more slowly, but the sea level rose by the same rate.

    All the best

  38. Glaringly obvious in retrospect. Thank you for your time.

  39. In Mahattan as someone else above noted the basement rock is crystalline, so subsidence due to development is not an issue. However, there are almost certainly ongoing isostatic changes related to the melting of the Laurentide Ice Sheet whose lower edge covered Manhattan with about a mile of ice. Since the bulk of the LIS was north and west of Manhattan, it would not be astonishing at all if the outer edges of the depression sank as the middle - up in Canada - rebounded.

  40. Great piece, though I did want to mention (not that it changes your analysis, all you're looking at is a straight versus an allegedly not straight pair of graphs) that you can't just choose one spot to measure sea level because sea level is based not just on how fast the sea is rising or falling but also how fast the land at the point where you're measuring is rising or falling. The crust of the Earth is not quite as constant as some might have you believe. But I suspect you know that.

  41. May I also point out it's difficult if not impossible to trust the data on "global temperatures" provided by those who've proven to be incapable of accurately providing same? That's where I was going with that "allegedly not straight" phrase in my other comment.

  42. The past few years I have noticed the Gulf Stream is carrying warmer water northward (as an aside, I am not surprised the Arctic ice is melting more than before), so, Lubos, if I understand you correctly, the thermal expansion of the ocean at the NY Battery accounts for 2/3's of the sea level rise there. Is that correct? thank you.

  43. Sounds plausible, I don't know the exact percentage. A third could be due to the tectonics and a fifth could be due to melting, so maybe only 1/2 in NY is due to expansion.

    Did you actually measure the sea temperature or is it some impression only? ;-)

  44. No. I am only, as they say, an educated layman who stumbled across a website last year that showed a graph of the Gulf Stream showing it warmer than "normal". If I recall correctly, it also mentioned that the water flowing north past Japan through the Bering Strait was warmer.

    The site may have had something to do with a positive NAO of the recent decades, but unfortunately, I didn't maintain notes back then, so hopefully, my memory serves me correctly.

  45. In any case, everyone in London knew that the dark pall over the city were a result of all the coal burning done in the city. No one argued that it was natural.

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    studio, or have a CD requiring radio-ready mastering, we can
    provide the services you need. Phone: 248-291-4029. See Featured
    Listing above.

    recording studio southwest
    somerset recording