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Thermal expansion and sea-level rise: why satellite altimetry is not directly useful for coastal sea-level predictions

Below are highlights from a conversation I had in 2013 with Profs. Robert Brown of Duke and John Hubisz of NCSU, both physicists, about the differing effects of thermal expansion on sea-level as measured by satellite altimetry (over the open ocean) and sea-level at the coasts.

The bottom line is that to the extent that sea-level measured by satellite altimetry includes a thermosteric component, due to warming of the upper layer of the ocean, it becomes less useful for coastal planning. 

This is (most of) my email to Prof. Brown:

Dear Dr. Brown,

This is a blog comment on sea-level rise which I posted to Tom Moriarty's blog:

This blog post also serves as a draft of a planned letter to FEMA (and probably other recipients) about the use of sea-level projections for coastal planning purposes, and especially in the context of the U.S. Biggert-Waters Flood Insurance Reform Act of 2012, and contemplated revisions to it.

Point #4 of my blog comment is the interesting one, on which I'd like your feedback. (My comment begins, "4. But, most importantly, comparing coastal sea-levels, measured by tide stations, to open-ocean sea-levels, measured by satellites, is fundamentally a comparison between two very different quantities, like comparing apples to oranges.")

The Biggert-Waters Flood Insurance Reform Act contains provisions requiring that projections of future accelerated sea-level rise be used when planning for future coastal flooding, and it is nearly certain that they will try to use the "39 inches by 2100" projection which the most extreme Climate Campaigners are pushing (which, as you know, is 5x to 10x the rise suggested by the historical sea-level record from most coastal tide-gauges). 

There are, of course, multiple severe problems with such a projection, the most obvious being that, despite all the greenhouse gas emissions and supposed global warming, thus far there has been no detectable acceleration in globally averaged rates of coastal sea-level rise in at least eighty years.

But that's not the focus of my letter. The focus is a more fundamental problem with using such a projection for coastal planning, a problem which hardly anyone writing these "assessment reports" and laws seems to understand. The problem is that only about half of the predicted sea-level rise is to be from additional water in the ocean.

The other half is supposed to be caused by thermal expansion of the warming oceans. But, although thermal expansion affects sea-level in the open ocean measured by satellite altimetry, it cannot significantly affect coastal sea-levels, so it should not be used in projections for coastal planning.

Explaining that concept is challenging, but it's what I tried to do in my blog comment.

Please read my blog comment, and tell me whether I made any mistakes, and how it could be improved, and whether you would be willing to include your name with mine (and perhaps some others) on a published letter making that point.

Thank you!

Warmest regards,


We were talking about this blog comment of mine, which begins, "Tom, you should not expect...

4. But, most importantly, comparing coastal sea-levels, measured by tide stations, to open-ocean sea-levels, measured by satellites, is fundamentally a comparison between two very different quantities, like comparing apples to oranges.
Satellite measurements of sea level include thermal expansion. In fact, the IPCC estimates that thermal expansion accounts for about half of current & projected sea-level rise. But thermal expansion has almost no effect on coastal sea-levels and tide gauges measurements.
That might surprise you, but it should not surprise a physicist.
To understand how density changes in the upper ocean affect sea-level, remember Archimedes’ Principle, or consider the case of floating ice. The reason that an iceberg sticks up out of the ocean is that it has lower density than the water in which it floats. The amount of water that it displaces depends only on its mass, not on its density or shape.
Imagine an iceberg wrapped in a plastic bag. If it melts, its density increases, and the the exposed part that rises above the water sinks, but the volume of the iceberg below the surface does not change at all. If the iceberg in the plastic bag refreezes, it will rise up and protrude above the surface, but its displacement — the volume of seawater that it displaces — still will not change.
Because the amount of seawater that it displaces is unaffected by changes in its density, when it freezes/expands or thaws/contracts, it causes no lateral water flows. Only the localized elevation of its upper surface changes. It does not affect sea-level elsewhere.
Note that it is only the density of the floating object which matters, not whether it is solid, liquid, or slush. Displacement is measured in units of mass, and it isn't affected by changes in density or solidity or shape.
The reason for that is that gravity balances mass, not volume. The same thing happens with density changes in liquid water. The upper layer of the ocean floats like an iceberg on top of the very cold water in the ocean depths, and there’s little mixing between them. When water in the upper layer of the ocean warms and expands, it rises up in place, like a very stubby iceberg. Gravity balances mass, not volume, so the thermal expansion causes no lateral water flows.
The exception to that rule is for water at the bottom of the ocean. If it expands, it has an effect similar to raising the ocean floor, which does cause lateral flows. But, in reality, that doesn't happen at all in the deep ocean, where temperatures are extremely stable.
Almost all thermal expansion takes place in the upper layer of the ocean. Only a small portion of the ocean is shallow enough for warming to reach the water at the bottom and cause thermal expansion there. That means only a small portion of the ocean’s thermal expansion can cause lateral water flows and affect sea-level at the shorelines.
Without substantial lateral flows of water, there can be no significant effect on the coasts. Of course, temperature changes do affect the density of water at the shore, but that doesn't cause the shoreline to advance or retreat. When water warms it gets deeper where it warms, by a (small) percentage of its depth. ... Were that not the case, beaches would be wider and the shoreline would be further out to sea in the winter (when the water is cold) than in the summer (when the water is warm).
In summary, it is a mistake to compare satellite-measured deep-ocean sea-level rise to tide gauge-measured coastal sea-level rise. Even if the satellite data were trustworthy (which it isn't), and even if we had perfectly accurate numbers for PGR/GIA corrections (which we don’t), and even if we also had accurate corrections for local subsidence (due to factors like groundwater extraction, oil & gas extraction, etc.), and even if we had comprehensive tide-gauge coverage of all the world’s coasts, it would still be a mistake to compare coastal sea-levels and deep-ocean sea-levels, because they are different quantities. Comparing them is like comparing apples to oranges.

By way of background, note that NASA reports that the deep deep oceans have not warmed at all:
NASA study finds Earth’s ocean abyss has not warmed | October 6, 2014 

I sent the same question to my friend, Physics Prof. Emeritus John Hubisz, of NCSU.  His reply was terse:

On Thu, Jul 4, 2013 at 9:49 AM, hubisz  wrote:
Very good #4 response.


Prof. Brown agreed with me, too, but his reply was much more detailed:

On Mon, Jul 1, 2013 at 10:26 AM, Robert G. Brown wrote:
Your physics here is impeccible.  I pummel my intro physics students
with a series of example problems on this very point (see the series of
problem in the Introductory Physics Review Guide on my website below,
click "Class" first and then you can access my intro physics textbooks
and review problem collections, the latter a work in eternal progress).
If you melt an ice cube in a class of water, the level of the water does
not change.

The ocean is (approximately) isostatic -- certainly there is little
reason to think that it is on average anything but isostatic -- and we
HAVE no baseline for the depth of the middle ocean.  It is damn
difficult to measure ocean level even at the shore -- and I say this
watching the tide come up outside my window.  The tide varies constantly
with the moon, the sun, the wind, the local air pressure, and more.
Differentiating a long run increase at all is pretty difficult.  But I
certainly trust the tide gauge record more than anything else because it
is a single, reasonably consistent collection of measurements mostly
made long before any thumbs were applied to scales to support "AGW",
catastrophic or otherwise.

The point you do not make as solidly as you might is that the failure of
tide gauge data to "accelerate" suggests that there has been no
acceleration of the rate of land-based ice melt, the only source of
actual additional real volume of the ocean.  I have asserted for some
time that the ocean itself is the best global thermometer we've got,
because precisely as you note, coastal levels represent an UPPER BOUND
on the expansion warming of coastal waters.  All of them.  This in turn
is a boundary condition on the entire ocean.  If there is land ice melt
going into the oceans, this actually DECREASES one's expectation of
coastal warming as then the increase in SL at the coasts has to be split
between land ice melt and thermal expansion, which strictly reduces the
contribution from thermal expansion.  Land ice melt is the only "real"
increase in oceanic volume, and the only thing likely to significantly
impact coastal SLR in the long run, because the ocean is isostatic and
cooling in one hemisphere where it is warming in another so that even
local thermal expansion in one place is balanced by small changes in
prevailing currents to maintain isostasis.

The fundamental problem is that the actual rate of EITHER tide gauge
data OR satellite data projects out to around a foot of SLR by 2100,
utterly ignorable, just as the 9+ inches we have had since 1870 was not
even noticed by the people living on the sea.  I have asked my
neighbors, who have lived on the ocean where I'm staying in Beaufort for
over 40 years (since their back yards were built up from a sandspit
island with a small sea wall), if they have observed any increase in SL.
In principle, they should have had around 3-4 inches over 40 years, but
they cannot see it -- their docks are still out of water on the highest
of spring tides, their yards are still underwater on a storm surge from
a hurricane (which happens here as it has happened here before over all
40 years, every four or five years), it is still impossible to launch a
boat from the ramp in my backyard at anything but high tide.  The
barnacles on the piers of their docks and the sea wall itself tell the
same story -- the line where they survive has not visibly increased over
the entire multi-decade lifetime of dock pilings or the sea wall.

Personally, I think Hansen's assertion of 5 meter SLR by 2100 to be
criminal, the equivalent of yelling fire in a movie theater because you
think that the theater MIGHT catch on fire in 90 years because you think
that the movie theater's projector MIGHT overheat by then.  I think
taking steps now as if there will be even 1 meter of SLR by 2100 is
silly.  Right now, the sensible rate to use as a projection of the
future is one inch per decade.  Even Trenberth, hardly a skeptic,
acknowledges as much -- SLR even according to the probably inflated
satellite record is a whopping 30-35 cm/century.

If this rate really does change, it isn't going to do so overnight.
There will be DECADES to react.  Spending money as if we know what SLR
is going to do 80 years from now when it isn't doing it now is just
plain dumb.

Robert G. Brown              
Duke University Dept. of Physics, Box 90305
Durham, N.C. 27708-0305
Phone: 1-919-660-2567  Fax: 919-660-2525