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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 51 to 69 out of 69:

  1. Just to add, Wikipedia has a nice brief explanation about how liquid volumes should be measured to take the meniscus into account.  Note in particular observations should be made with the top of the liquid at eye level to avoid parallax errors.  Compare this with MatrinS's experiment and with thorconstr's.  I knew this already because I did chemistry at school.  It is alright not to know this, but it is not alright to repeatedly ignore this sort of knowledge when problems with experiments are pointed out to you by those who do.

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  2. Thankyou Dikran, for reminding me of thorcontr's empty challenge about blowing up the images to show the lips of the glass:

    H-res version here.

    Close examination on the left of the glass shows the water level not up to the lip in either photo, ie, either with ice present (upper image) of melted (lower image).  If, however, you look to the right hand side (under the yellow arrows), in the upper image the inside of the lip is clearly visible.  In constrast, in the lower image the lip is obscured from vision by the meniscus.  Clearly the meniscus must have risen higher than the lip to obscure it from vision, and hence has shown an increase in level.  Indeed, the difference in camera angles tends to obscure this fact.

    Clearly the surface of the glass slopes downward from left to right, resulting in the meniscus being above the lip on the right, but below it on the left.  Also, if you look closely, this is obscured in the first image by the surface of an ice cube partially concealing the lip on the left, giving an apparent slope in the other direction to casual observation.

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  3. Tom@47,

    the ice in fresh water ill have only 0.042 m^3 above the surface, but 0.044[0.054] m^3 above the surface if floating in fresh [salt] water[...] 0.002 m^2 more volume than it displaced in sea water

    You made a slight arithmetic mistake, corrected above. Consequenttly, the difference in displaced water is: 0.458 - 0.446 = 0.012m^2 (rather than your incorrect 0.002 m^2 result). So, after that correction we conclude that the perceived increase of volume of seawater (dV) in your setup increased by 0.8% (0.012m^3 out of 1.446m^3).

    So, in Thor's setup, where the proportion of ice is much less, say some 50ml in 250ml (he didn't give me the number because he wants to discuss his rhetorics rather than science), I estimate dV would be some 3-4 times smaller (per my quess of his proportions), therefore dV in his experiment was some 0.3%, which translates to dh of 0.3mm over 10cm high glass. Or even less: some 0.2mm, because his glass has signifficantly higher crosss section where dh is measured.

    In conclusion, such small dh (0.2mm) is undistinguishable by eye and within the menisk shape uncertainty, as pointed earlier by DM. Therefore, Thor's experiment cannot be used to confirm this simple science herein. We know, that Thor set it up not for confirming science but for his baseless rhetorics.

    On the other hand, an original experiment as setup by MartinS confirms the science: I estimate his dh should be about 1mm (because the ice chunk proportion looks as big as Toms') which looks about right on his picture.

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  4. chriskoz @53, thanks for picking up, and correcting the errors.

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  5. Could it be that thorconstr's ultimate goal was to provke regular SkS commenters in order to "proove" that SkS is ideologically biased? If so, the ice-in-glass-of-water "experiment" was just a ruse.

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  6. This whole discussion is perfect example of what seems to go on with climate change denial, on a larger level. 

    One side is trying to point out how the science works. The other side starts with a presumption of fact, rejects known physics, does incorrect experiments/analysis, claims those doing the science are politically motivated when the results conflict with their expected outcomes, and in the end storms off unable to process the fact that they are wrong on the science.

    It's hard to be the person proven wrong. It takes a strong person to look at evidence and admit an error. All too often I see people double down on their error and run away rather than facing hard facts, as thorconstr has done.

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    Moderator Response:

    [Dikran Marsupial] Please can we restrict the discussion to the science.

  7. After giving this some thought, I thought I would try a little different experiment.  I made 1L of 5% salt solution (naturally there was a change in volume when adding the salt and I wasn't going for an exact salt concentration).  Assuming the mass of ice to be equal to its mass of water I  poured 1L of the salt solution into a 2L graduated cylinder, using a 1L graduated cylinder and using the same, rinsed graduated cylinder, I added 1L of fresh water to the 2L cylinder.  Temps were the same so no thermal difference and the volume was 2L, no change.  What is wrong with my thinking?

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  8. ECLife @57 : At a quick glance, I would say that your "discrepancy" arises from the cases being different.

    You have added 1 L of fresh water onto the top of the heavy saline (and done so slowly and carefully, I presume, to allow the fresh to "float" above the saline ~ not that this is necessary: yet it does look a "prettier" experiment done that way . . . and even prettier if you add a touch of blue dye to the saline first). But the essential point is that the fresh was not displacing the saline.

    OTOH, for the earlier experiment, the (fresh) ice was displacing the heavy saline : so (according to Archimedes) it was actually displacing a smaller volume [of saline] than its own (freshwater-equivalent) volume.

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  9. Thanks for pointing out my quick assumption.  I repeated the experiment with a balloon floating in 5% and 15% salt solutions and because it wasn't frozen, less dense, the balloon almost appeared neutrally buoyant in the 5% but more so in the 15% but the mass would be the same, displacing it's mass.  When I popped the balloon, the change in the 5% was not really noticeable but was in the 15% solution.  

    Conversely, I would say that as sea ice is formed, the ocean will get more briney and levels would drop.  It helps to think it through and realize our level is due to the floating and subsequent melting of ice, not the addition of 2 liquids.

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  10. I'm following this but I have to say it appears as though the lab experiments have been conducted in error. Glaciel ice does not solely precipitate from beneath, when ocean levels reach tempuratures below 28.8f - the tempurature at which water with a salinity content of 35ppt will freeze. Most glacial ice precipitates from above, and is compacted by its own weight, coupled with occasional rainfall and warmer air tempuratures. With all this is mind, it is time to do the "melt test".
    If you fill a 5 gallon bucket with snow and melt it, you will get approximately 10%wbv. If you fill the same bucket with glaciel ice, melting results in 30%wbv, on average. Glacial ice, or compacted snow, can be as much as 70%wbv if it is trapped in a valley on a hard surface, with no exit, and low air tempuratures. Glacial ice which flows, melts underneath, or forms above water seldom reaches 50%wbv. On average, 35%wbv.
    Understanding these factors, realize that clear ice cubes are clear because they are more than 90%wbv, while glacial ice or snowpack is not clear becuase its composition includes more oxygen than water due to its crystaline structure. To conduct an accurate lab test, scrape the snowy sides of your freezer and compact it into an ice tray. Drop your snowballs into a glass of 35ppt NaCl (salt) and record the level. Melt the snowballs, and record the level. Be surprised. The displacement of glacial ice, which floats 90% below surface and 10% above surface, is a definite factor. With warmer ocean tempuratures due to sea ice dissipation, evaporation increases resulting in heavier precipitation.


    ppt: parts per thousand, or 35grams of salt per 1000grams of water

    wbv: water-by-volume, or 1gallon of water per 10gallons of snow

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  11. Spaded Ace @60, the argument is not whether the melting of glacial ice will, or will not, raise sea level; but whether the melting of sea ice, ie, the ice that forms on the surface of the sea at low temperatures, will (or will not) raise sea levels.

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  12. Can anyone tell me how much is trapped in sea ice and there released when sea ice melts? There must be billions of tons of trapped air in floating sea ice I would assume, but I'm no expert. I don't have to be an expert to know what happens to the water level in my bath tub when I push a cup into in upside down.

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    Moderator Response:

    [JH] How much what? Please clarify.

  13. What about ice that is trapped below sea level as in this:

    since that ice is not bobbing above the surface, doesn't its melting actually create more space, and hence actually lower sea level?  if not, why not?

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    Moderator Response:

    [JH] Fill a glass with ice cubes and water. Let it melt and see what happens. (Hint: When a given volume of ice melts, it turns into an equivalent amount of water.)

  14. Ewinsberg @63 ,for grounded ice, as the bottom ice melts, the upper ice sags downwards.

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  15. @eclectic  cool. thanks.   Someone should tell that to the people that drew the diagram in that guardian piece.

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  16. Oh my god. You can't say in absolute sentence that the sea level arises everywhere on earth because of melting ice! Once and for all: it depends where on earth you are.

    A second thing is that ice will attract to water. So at the east coast of America there the sea level will decrease, because of the melting ice. Why? Because of the mass of ice will be significantly less because of the melting ice. so it attract less water!


    Happy science

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  17. Savantking,

    Please provide a reference for your claim that US sea level will not increase from ice sheet melt.

    Antarctic melt causes increased sea level rise in the US:

    antarctic melt

    This NASA article on sea level rise describes Greenland ice melt raising US sea level.  It appears that the US rise will be about average for the world.  Northern Europe will get a little less from Greenland, perhaps that is what you meant. 

    Both areas will get more than average from the Antarctic.  I do not think that any area where people live except Greenland itself will see sea level decrease although Iceland might. 

    Certainly the claim that the US will luck out is deliberately false.  I suggest you screen your sources better.  Denier sites spread false information.

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  18. I realized that the figure I copied does not make much sense without the caption.  Here it is:

    Fig. 1. Sea-level change in response to the collapse of the
    WAIS computed by using (A) a standard sea-level theory (5),
    which assumes a nonrotating Earth, no marine-based ice, and
    shorelines that remain fixed to the present-day geometry with
    time, as well as (B) a prediction based on a theory (6) that
    overcomes these limitations. Both predictions are normalized by
    the EEV associated with the ice collapse. In (B), the total volume
    of the WAIS is used in the calculation, whereas in (A) only an
    amount of ice with a volume that matches the EEV is removed
    (because the latter cannot take into account the inundation of
    marine-based sectors). (C) The difference between predictions
    generated by using the two sea-level theories [(B) minus (A)].

    B is the part of the figure that relates to this discussion. source

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  19. Why aren't we talking about the amount of fresh water rain falling into the oceans on a yearly basis? Wouldn't this reduce salinity and raise ocean levels also?

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    Moderator Response:

    [DB] In the same fashion that breathing in is offset by breathing out, rainfall is offset by evaporation over climate-related timescales.

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