Arguments
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.
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)
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.
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.
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.
Thanks.
[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.
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.
Thanks for the comments so far and I look forward to any additions.
see the following explanation.
http://nsidc.org/seaice/characteristics/brine_salinity.html
I also recommend watching this video on why CO2 is the biggest climate control knob in Earth's history.
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Did you mean to say, "...leaving a largely salt-free sheet of ice", instead of "ice-free"?
ice-free ice does not form often.
Dikran
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.
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
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 http://judithcurry.com/2011/07/05/the-ipccs-alteration-of-forster-gregorys-model-independent-climate-sensitivity-results/#comment-115656 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.
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).
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.
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.
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).