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Sea level rise due to floating ice?

Posted on 28 September 2011 by MartinS

It is widely believed that melting of floating sea ice does not contribute to sea level rise. Is this really true?

Let us think of a simple experiment we are all familiar with: imagine an ice cube floating in a glass of water. What happens to the water level in the glass when the ice cube melts? Right, nothing happens. The ice cube displaces its own weight in the underlying water and the water level remains constant when the ice melts, because the melting process replaces the water which has already been displaced by the ice. This effect is known as Archimedes’ principle.

Now let us consider a slightly different experiment. It’s again water with some ice in it, but now the water is salty (like the real ocean). The blue color has no effect on the experiment, but it shows the ice cube in the water more clearly.


It took quite a time to melt all ice but finally it was done and the result is clear: The water level is higher!


Doesn’t that contradict Archimedes’ principle?

According to Noerdlinger and Brower (2007) it doesn’t because the principle refers to weight and not volume.  The salt in sea water raises its density from about 1000 kg/m3 for salt free water to 1026 kg/m3 for normal sea water. The ice however is nearly salt free because of a process called “brine rejection” (the salt from sea water doesn’t enter the crystal structure of ice).

When the ice melts then this is a kind of freshening of the ocean and the overall salinity is lowered. The lower salinity, the lower density  and the larger volume.

The melting of sea ice therefore doesn’t increase the mass but it increases the volume and therefore causes the water level to rise. After Noerdlinger’s and Brower’s calculations the volume of the meltwater is about 2.6% larger than the displaced sea water.

But what is the actual relevance of this effect? Does is contribute significantly to sea level rise? Before answering this questions we should deal with an objection raised by Jenkins and Holland (2007). They are arguing that a huge amount of energy is required to melt the ice. They find that the energy comes from the ocean, as the albedo (reflectivity) of ice is very high, it doesn’t absorb much solar energy. Hence the ocean will cool a bit, causing the density of the briny water to increase (It should be noted that fresh water exhibits the peculiar behavior that its density increases as the temperature falls almost all the way to freezing; but just before freezing, the density is reduced. Briny water does not exhibit that reversal). The cooling  therefore offsets the density decrease at least partially in the words of Jenkins and Holland.

As they put it, Noerdlinger’s and Bower’s result is a good first approximation in cold waters where most floating ice is found. The density of cold water is mainly determined by its salinity while for warmer water temperature is also an important factor. Therefore in warmer water the cooling effect matters.

Back to the question, if this effect contributes to sea level rise in a relevant way. Shepherd et al 2010 examine this. They combine satellite observations for an assessment of the loss of floating ice. According to this 743 km3/yr floating ice was lost in average between 1994 and 2004. They further conclude that 1.6% of current sea level rise (about 3.1 mm per year) is caused by loss of sea ice. This is not very much compared to other sources. However the authors assert that this effect should be considered for future assessments of global sea level rise.

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Comments 1 to 23:

  1. So Shepherd et al calculate (49 ± 8 μm yr−1) rise in mean sea level due to melting sea ice decreasing the salinity of the ocean and thereby reducing the specific density of the oceans.

    As long as we are looking at miniscule adjustments to sea level projections, has anybody ever looked at the slight decrease in sea level caused by salts being emptied into the oceans by rivers?

    The adjustment of 1/20th of a millimeter per year for sea ice melt is small, even compared to the approximate 0.3mm/year rise caused by the mining of water from ground aquifers or the approximate 0.4mm/yr reduction in rise caused by reservoir impoundment. (Ref: Church et al 2010, Revisiting the Earth's sea-level and energy budgets from 1961 to 2008)
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  2. CharlieA...

    You're right. This is a small effect...and the future impacts are limited by the amount of sea ice available for melting. I think it's just kind of a neat wrinkle to an old truism that says something about chemisrty/physics of the ocean. I'd think the more important effects of salinity changes from sea icea melting are related to the the local bouyancy effects of melting sea ice on currents and associated heat transfer.

    To get changes in salinity related to the hydrologic cycle you need to either increase the salinity of the incoming water (by increasing weathering) or alter the balance between river inflow and evaporation from the ocean. There is some evidence for increasing alkalinity (HCO3- and Ca++) of some major rivers (e.g. the mississippi). I'm guessing that does not affect salinity too much because of the dominance of NaCl as a solute. Haven't done the calcs though.

    As Rob painting has pointed out, there are some net movements of water between the ocean and land on multiyear timescales that could influence salinity a little. That must imply evaporative concentration of salts in the ocean. My guess is that accounts for only a small proportion of the recent sea-level rise anomaly though, but it would be interesting to know.
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  3. Heh one of the few things I remember from school was one of my teachers telling the class that global warming was a load of bollocks because melting ice couldn't raise sea level because it just displaced it's own mass in water. I don't know why that stuck in my mind, I think I speak for the rest of the class that I was rather indifferent to the content of his claim at the time, but I think I remembered it simply for the sudden way he delivered such a passionate claim in a lesson that had nothing to do with melting ice let alone global warming.

    Looking back on it I've always regarded his mistake was threefold: not taking into account melting ice on land, not taking into account thermal expansion of sea water and not taking into account that global warming is more than sea level rise. Now from reading this article I can add a fourth mistake.
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  4. Wingding your teacher had a serious case of Dunning-Kruger.
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  5. If Arctic sea ice melts, it reduces ocean salinity. How does this affect ocean penetration by warmer currents such as the Gulf Stream?
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  6. agnostic, the volume of the ocean is 1.3billion cubic km. The maximum volume of Arctic sea ice 20-30 years ago was just over 30thousand cubic km. This year's minimum sea ice is a mere 4.3 thousand cubic km where the 'long-term average' minimum was ~13 thousand. In terms of affecting ocean wide salinity the figure to worry about is the minimum - or not.

    Seeing as we've already lost more of the old minimum, 9,000, than now remains at minimum, 4,300, any salinity impact should be showing up.

    My best guess would be that any further impact on oceans would be local and transient, as well as being totally swamped by other heating impacts.
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  7. Within this closed system (Jar) the salinity of the water in the Jar would increase as the ice formed due to the salt leaching out of the ice. When the Ice melts it lowers the salinity of the water back to where it was in the first place. Bringing us back to square one. One needs an ever decreasing sea ice volume as in the real world for the example to work. With very little sea ice left in the Northern Hemisphere its addition to the rise in sea level is ever diminishing to 0.
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  8. I've been posting the following comment -- or variations thereon -- on several sites over the last week. I've not received much in the way of criticism (it seems to silence most people in denial). I'd be grateful for any constructive comments; and, in the light of MartinS' post, whether I should add any anything further.

    There's a point that those who just look at the rate of melting ice and say, "sea level rise is very slow, so why are we worrying?", fail to recognise.

    It requires a lot of energy to change the state of ice to water. That change, with no rise in temperature between the point at which water is solid, and then water is liquid, uses 80 times more energy than it does to raise the temperature of water between, say, two degrees and three degrees, or three degrees and four. Thus, currently, melting ice provides huge attenuation to the warming we experience. To melt, ice literally sucks heat out of the sea and thence the atmosphere and the land; delaying the worst effects of our actions. This is high school physics -- clearly way beyond the level of C.Booker, J. Delingpole and Co. Check it up. [Link provided to basic physics site].

    As a consequence, as the ice disappears, the massive amount of energy currently being used to melt ice becomes suddenly available to warm the ocean and the atmosphere -- warming which will then be at a rate 80 times faster than we're experiencing today. So the rate of melt accelerates the less ice remains. That's why extrapolating sea level rise from the current rate of melt is likely to produce a false sense of security.

    This is why scientists are so concerned. They understand this. Polar ice is the shock absorber on the suspension; the buffers on the carriages; the pendulum on the clock. And it's also the canary in the coal mine.

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    [DB] For all the reasons you mention, I refer to the Arctic Ocean sea ice cap as the Northern Hemisphere's refrigeration system.  That ice cap is being lost at record rates; once it is gone the thermostat will get ratcheted up.

    As for the rates of oceanic warming sans ice...that picture is complicated by issues with turbidity, mixing layers and changing currents all now relatively constrained by the ice cap.  We'll all be taking that journey together, so we'll see.

  9. >>>warming which will then be at a rate 80 times faster than we're experiencing today.

    I do not think that is necessarily true, as the ocean is not a perfectly thermally mixed medium, and also because not all of the heat that is transferred to the Arctic goes only toward melting sea ice.

    It would be very surprising and unrealistic if Arctic temperatures warmed at such a fast rate, we're talking about 0.3-0.4˚C/dec (at a minimum now) to 2-3˚C/year or more? I don't think so.
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  10. I should perhaps add that it was the Times' '15% Greenland ice loss' mistake that lead to my originally posting the comment. So I wasn't just referring to sea ice when I made the comment and I wasn't making -- what I thought at the time to be -- the very elementary mistake that melting sea ice raises sea level.

    Thanks for the comments so far and I look forward to any additions.
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  11. While this experiment works for multi-year sea ice, it will not for recently frozen sea water. It takes time (several years) for trapped brine to drain throught the ice. After several years (decades) of increasing sea ice, much of the brine has drained into the ocean, leaving a largely ice-free sheet of ice. As this has melted in recent years, it has contirbuted to sea level rise. The freshly frozen sea ice has a rather large concentration of brine. Roughly 75% of the sea ice melts and re-freezes each year. The melting of this ice will not inflence sea levels. Only melting of multi-year ice will have an effect.
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    Moderator Response: [Dikran Marsupial] Please supply a verifiable reference to support that argument. As I understand it, the salts are never incorporated into the ice as the ice accumulates molecule by molecule on the underside/edges of the ice sheet, excluding the salts as it goes (as they don't fit well into the crystal structure).
  12. Dikran,

    see the following explanation.
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    Moderator Response: [Dikran Marsupial] Cheers, much appreciated! Link activated.

    Having read the link, I suspect the overall salinity of the ice (with the brine inclusions) is still much lower than the sea water. What proportion of the ice sheet is made up of brine inclusions? I suspect it is fairly low. AFAICS there is nothing there to suggest that this is substantially alters the argument presented in this article, even for newly formed ice, unless there is some quantitative information available.
  13. is the sea level supposed to be static?
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    Moderator Response: [Dikran Marsupial] No. If you have a point to make, please do so directly, rather than asking rhetorical questions.

    Welcome to Skeptical Science! There is an immense amount of reference material discussed here and it can be a bit difficult at first to find an answer to your questions. That's why we recommend that Newcomers, Start Here and then learn The Big Picture.

    I also recommend watching this video on why CO2 is the biggest climate control knob in Earth's history.

    Further general questions can usually be be answered by first using the Search function in the upper left of every Skeptical Science page to see if there is already a post on it (odds are, there is). If you still have questions, use the Search function located in the upper left of every page here at Skeptical Science and post your question on the most pertinent thread.

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  14. Jonathan,

    Did you mean to say, "...leaving a largely salt-free sheet of ice", instead of "ice-free"?
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  15. Yes Martin,

    ice-free ice does not form often.


    I do not know if anyone has any quantative data on the salinity of the ice.

    As opposed to the experiment where the ice constitutes abot half the volume, over 99.9% of the water in the Arctic Ocean is present in the liquid state. The melting ice probably does not change the density by any measureable amount.
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  16. When sea ice forms it is a mixture of ice crystals and salt water. As the ice crystals link together and expand they squeeze the brine into pockets. The brine pockets end up being squeezed out along the bottom of the ice.

    Newly formed ice contains about 33% brine in pockets. The lateral pressures in the ice structure tend to squeeze these brine pockets into vertical structures. The ice continues to reject brine until the ice melts or until it contains insignificant quantities of brine.
    The initial brine rejection is the major driver of haline circulation, but further brine rejection is significant as the ice ages, e.g. in the Beaufort Gyre.

    These free resources may help readers to understand the processes of brine pocket formation and brine rejection:

    JPL poster

    Brine rejection... Vrbka and Jungwirth

    Arctic Sea Ice Microstructure
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  17. This is a two-parter.

    1 -- I recently thought about this sort of experiment and made the same mistake (of not realizing we were in a sense talking about two different liquids), so I see this as a timely article.

    One way to help see the effect more clearly is to assume the liquid bath is some super dense liquid. Approximately, that liquid is like a solid when you put the ice on top because almost no liquid is displaced, as only a tiny volume of it is needed to match the weight of the ice. The ice cube would basically just sit there almost entirely above the surface line. Once the ice melts, of course, almost all of that water will go to raise the level of liquid on the beaker, with the increase almost matching the entire volume of the ice.

    2 -- OK, with the on-topic material out of the way, I want to ask, has the Forster/Gregory 2006 paper discussed in this article or the article itself been analyzed on this site? The article is a critique of the IPCC and the peer review process.

    In that critique, the author (apparently someone practiced with statistical analysis) makes a fair (if subjective) point from a mathematical analysis point of view but appears to ignore the context of the data.

    To mention one side point that hints at the author's mentality, he attacks other climate studies that use models and data instead of just data. However, I think it makes lots of sense in many cases to prefer conclusions that take into account the result of models that have been proven to some degree over simply flying blindly with a limited data set. This is particularly important when the data set is of a rather short time period on the climate scale, deviates from historical averages, and so could not really make honest conclusions too far out into the future.

    The specific link I gave is to one of a few comments I made that gives my (amateur) interpretation. In short, it seems to me that the IPCC may have done the right thing if they were going to use the FG06 results. A normal distribution assumed around average slope values calculated from temp/flux global data points going back only a few decades (ie, the FG06 results for Y) can easily point in many directions and even potentially towards strong climate cooling, just as would be the case (to use an analogy) if we focus on a short-term Dow Jones Industrial hill (local maxima) near the top of that hill. The right thing to do to make future predictions using slopes based off a curve biased by short-term behavior is to place those average slope values in context. For example, we could rely on models based on physics and shown to have fair predictability over longer time spans. To continue with the stock market analogy, we'd want to use models and analysis that recognize that the DJI has always been headed upwards over the longer trend decades due to factors such as inflation of the currency upon which it is measured. Predicting long term off a local effect is bad.

    To conclude, that critique appears to be rather new and appears intended to make the IPCC look bad (dishonest or at least somewhat flawed). The author (Nic Lewis) assumes the results of FG06, the Y value, should be centered inside a normal PDF. I think that is wrong because the data is biased; thus, whatever the IPCC did to "skew" the S value PDF shown in the IPCC report, it was in effect adding context missing from the FG06 Y results.
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  18. Jose,

    If the IPCC did in in fact skew the results of FG06, then they should have reported such when using their results. Looing at the figure in the AR4 report, the curve is definitely skewed, while the original report argues for a Gaussian distribution. If they believed the data was biased, then the data should have been omitted instead of altered in the graph (that would be my choice, I would never alter anyone else's data).
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  19. There may be gravitational effects due to the mass of the sea ice.
    When the ice is formed then the local sea level will be higher in the arctic when the ice melts then this may cause a relative lowering of SL there and a corresponding further increase further away at distance.
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  20. Jonathon, I agree omitting that data is better than hiding some manipulation of it. If you can't explain it properly, then you should not try to sneak it in. However, as the criticism points out, there were sufficient clues and the citing to allow someone with experience to realize exactly what was done. It's a fail of sorts, but it doesn't appear dishonest. A few of the issues I wanted to raise were in questioning the perspective taken in that article that a normal distribution was acceptable (I don't believe it was) and that what the IPCC did, if explained sufficiently, was less than average and perhaps showed unwarranted bias (again I would disagree).
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  21. Jose,

    We are getting off topic, and the moderator is likely to step in and discontinue this discussion. Scientifically, a normal distribution is considered most probably unless a constraint is placed on one end (such as counts cannot be negative or exceed 100% of the population). Reading the report, I can see no reason why a normal distribution would not be acceptable. The article does indicate that the IPCC showed bias (actually the article was not that polite) in displaying a non-Gaussian distribution. A better reference would be something like based on- or derived from- the data...

    In your super dense liquid scenario, if we assume that the ice covers the entire surface area of the liquid, then the melting of the ice would raise the liquid level to same height as the liquid + solid starting height.
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  22. Jonathon, Jose, my understanding is that Forster was involved in the decisions of the IPCC, and that he disagrees with the interpretation in the cited article. In fact he states:

    "Firstly, Thanks for the interest in our paper and much useful discussion.

    I think the blog analysis is roughly correct, but I disagree completely with its interpretation. I disagree strongly that the IPCC authors were at fault for changing the priors and I disagree strongly that the uniform feedback prior is the best choice. Thirdly I disagree on the significance of all of this. I’ll deal with each in turn

    1) I was fully aware about the use of our data and the choice of priors by the ipcc. However, my paper was published so I didn’t need to approve of it’s use by IPCC, as it was is the public domain. In fact to keep the chapter as objective as possible I did not get involved in the assessment of my own paper and was happy to let my expert colleagues decide on it’s merit or otherwise.
    I also believe that the work put into assessing our paper by the IPCC authors is in fact a great testament of their professionalism. Rather than take our published numbers at face value, they looked very carefully at our paper and took the deliberative step, using their statistical and climate expertise, to modify our results to a uniform prior in sensitivity. They plainly state this in the report and are not trying to hide this. They also did this for sound science reasons based on the current literature at the time and acknowledge the problem of choosing the right prior in the chapter.

    Like Nic, I personally really like Non-GCM ways of estimating sensitivity, but I quite understand why IPCC didnt give it any more weight than any other study. The major problems with FG06 are the short time period of observations, regression errors and satellite data errors. This was again a perfectly sound example of expert assessment.

    2) Nic keeps mentioning OLS regression as the physics- based correct method, and that using this means that one should choose a uniform prior in feedback. If you read FG06 we infact spend a lot of time worrying about the choice of regression model. In the end we went for OLS, but this choice is not clearcut in complex systems where everything is interacting and isolating cause and effect becomes hard. All this means is that, as Annan Points out in his climatic change paper, the choice of prior isn’t an easy call and is very subjective. There is no one right answer for the best prior choice.

    3)My third point is that in the meantime, just as Fred Moolten points out above, the science moves on. The work by James Annan shows clearly the effects of different prior choices and that there is not one “correct” answer. Gregory and Forster 2008 and other papers show how high sensitivities don’t really make any difference to current climate change rate, as high sensitivities slow down the system response. Finally, we have repeated FG06 with updated observations from ERBE and CERES in Murphy et al. (2010), JGR D17107 and got a median climate sensitivity estimate much higher, around 3. 0 C. Note that the murphy paper quotes a feedback value of 1.25 watts per square metre per K. We deliberately did not invert for sensitivity as we are unclear how representative these values are for the longer term climate response."

    Clearly there is no issue here.

    What is an issue it your desire to pursue off topic comments in violation of the comments policy. Where I a moderator I would have simply deleted Jose's original comment in total. If you are so discourteous as to deliberately flout comments policy rules, you are owed zero extra effort by the moderators to ensure that your on topic comments stand. Is it really too much to ask that you seek out an appropriate thread for the discussion rather than try and divert discussion where it is not relevant? As it stands, I think it is certainly appropriate for the moderator to even now snip your original post and all responses (including this one).
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  23. That seems a curious position. If a comment is so off-topic, what possible incentive is there for anyone to pursue it? Am I being too naive here?
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