Will polar ice melt more quickly than previously thought?

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Hugh Easton

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Apr 14, 1995, 3:00:00 AM4/14/95
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Recent events in Antarctica indicate that the polar ice caps may be more
susceptible to melting than previously supposed. The Larsen ice shelf now
appears to be in the process of breaking up: a huge iceberg has broken off
it, but more importantly a large part of the ice shelf has disintegrated
altogether, leaving open water between James Ross island and the Antarctic
peninsula for the first time since Antarctic exploration began. Also there
have been reports of a 40-mile long crack opening up in the Larsen ice
shelf, apparently after the iceberg broke off.

Temperatures in the Antarctic peninsula (where these events and the earlier
breakup of the Wordie ice shelf took place) have risen by 2.5 C over the
last 40 years. Although some melting of polar ice has been anticipated as
a consequence of global warming, the speed and scale of recent events in
Antarctica appear to have taken the scientific community completely by
surprise.

Ice is not a very good conductor of heat: the thermal conductivity at
273.15 K (0 C) is 2.26 W/(m.K), but it improves slightly at lower
temperatures - at 260 K it is 2.35, and at 240 K it is 2.50 W/(m.K) [from
table 33 "Thermophysical properties of saturated water substance", Handbook
of heat transfer fundamentals 2nd ed., McGraw-Hill 1985]. Putting a
physical perspective to these figures, this is the amount of heat in watts
per square metre that would travel through a 1m thick sheet of ice with a
temperature difference of 1 C between the top and bottom.

Now apply these figures to an Antarctic ice shelf, such as the Larsen ice
shelf. A typical thickness of ice for these is about 200m, and we have
heard that 2.5 C of warming has taken place. Assuming that it has
penetrated the top 100m of ice already, how long would it take to warm the
remainder?

The 100m of ice which has not yet warmed has a mass of about 10e8
g/m^2, to warm this by 2.5 C requires a heat input of 2.5 x 10e8 J/m^2
(assuming a thermal capacity for ice of 1 J/(g.K) - the actual figure
may well be higher, in which case the heat input required will
increase correspondingly).

The heat flux through 100m of ice is (2.5W/(m.K) / 100m) x 2.5K
temperature difference, or 6.25 x 10e-2 W/m^2. This will take 4 x 10e9
seconds to provide the 2.5 x 10e8 J/m^2 required, or a little over a
century.

Before the ice shelf actually broke up, substantial melting would have to
take place. The latent heat of fusion for the water-ice transition is over
300 J/g. With the heat flux just calculated, it would take over three
thousand years for the bottom half of the ice shelf to melt. No wonder
glaciologists are not too concerned about the prospect of the polar icecaps
melting in the near future!

So why is the Larsen ice shelf breaking up? I think it is because of a
physical property of ice that has hitherto been overlooked - transparency.
Water is extremely opaque to infrared radiation of any wavelength, but the
same is not necessarily true of ice. The molecules in water can vibrate or
rotate freely, while those in ice are bound into a rigid crystal lattice
and so cannot move. The various different vibrational and rotational modes
of the water molecule occur at the right frequencies to make it a good
absorber of infrared; when they are suppressed, infrared absorbtion no
longer occurs.

Imagine for a moment that ice is completely transparent to infrared. We saw
earlier how, using regular heat conduction, it would take a century or more
for heat to get through a 100m thickness of ice. Using the same example
given earlier but including the effects of infrared transmission:

for a 2.5K temperature difference at 260K the net heat transmission
is s.T2^4 - s.T1^4 = 269.2 - 259.1 or about 10 W/m^2
(where s is the Boltzmann constant, 5.67 x 10e-8 W/(m^2.T^4), T1 is
260K, T2 is 262.5K).

This is nearly 200 times more than the heat flux calculated earlier.
Instead of taking 3000 years to melt, the ice shelf is gone in little more
than a decade.

With the limited time and resources at my disposal, I have so far been
unable to find any research which conclusively proves or disproves whether
ice is sufficiently transparent in the relevant parts of the infrared
spectrum (from about 4um to 120um) for infrared heat transmission to work.
However, I have found some supporting evidence in the book "Radiative Heat
Transfer" (Michael F. Modest, McGraw-Hill 1993 ISBN 0-07-042675-9). In
chapter 11, "Radiative properties of semitransparent media", there is a
graph (Fig 11-4, p442) "Spectral absorbtion coefficient of clear water (at
room temperature) and clear ice (at -10 C)". It shows that the absorbtion
spectra of water and ice are almost identical for ultraviolet, visible and
near infrared. However, for infrared wavelengths beyond 10um the spectral
properties of water and ice abruptly diverge - the ice becomes
significantly more transparent than water, so that for a wavelength of 20
um (this is end of the range the graph covers) ice is over 10 times more
transparent than water. Unfortunately, this does not indicate what happens
at longer wavelengths, or when the temperature is lowered or the pressure
increased.

It is also possible that other mechanisms than infrared heat transmission
could give rise to anomalously high rates of long-range heat transfer
through ice - for instance phonons, individual quanta of sound energy, can
probably travel quite long distances through ice and could perhaps
transport significant quantities of heat - they do in liquid helium.

Given the evidence that "bulk" ice such as ice shelves and glaciers appears
to be melting at a faster rate than simple theory would suggest, and given
the catastrophic consequences if the polar ice caps should melt, I think
that the possibility that unconventional modes of long-range heat
conduction operate in ice deserves thorough investigation. The experiments
necessary to conclusively settle this issue one way or the other should not
be that difficult or expensive to conduct. Is anyone reading this message
prepared to carry them out?

--
Hugh Easton <Hu...@daflight.demon.co.uk>

Simen Gaure

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Apr 19, 1995, 3:00:00 AM4/19/95
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It is also possible that other mechanisms than infrared heat transmission
could give rise to anomalously high rates of long-range heat transfer
through ice - for instance phonons, individual quanta of sound energy, can
probably travel quite long distances through ice and could perhaps
transport significant quantities of heat - they do in liquid helium.

Is there any evidence that the ice has actually melted?
It has broken up, yes, but is that due to large scale melting?
It might also be the case that there's now more ice in
Antarctica (e.g. due to increased precipitation).
I'd guess (although I haven't made any computations) that
even a minor increase in ice thickness (say 1 metre) will
result in a lot of ice floating outwards towards the sea.

--
Simen Gaure, Department of Mathematics, University of Oslo

Ivan D. Reid

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Apr 21, 1995, 3:00:00 AM4/21/95
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In article <Simen.Gaure-19...@ma-mac17.uio.no>,
Simen...@math.uio.no (Simen Gaure) writes...

> It is also possible that other mechanisms than infrared heat transmission
> could give rise to anomalously high rates of long-range heat transfer
> through ice - for instance phonons, individual quanta of sound energy, can
> probably travel quite long distances through ice and could perhaps
> transport significant quantities of heat - they do in liquid helium.

>Is there any evidence that the ice has actually melted?


>It has broken up, yes, but is that due to large scale melting?
>It might also be the case that there's now more ice in
>Antarctica (e.g. due to increased precipitation).
>I'd guess (although I haven't made any computations) that
>even a minor increase in ice thickness (say 1 metre) will
>result in a lot of ice floating outwards towards the sea.

A good point. One must remember that the ice-sheets are dynamic,
even though they move at glacial speed. (Sorry, pun intended...) One case
I have personal knowledge of was at Mawson in 1980. The seismo reckoned
from his traces that there'd been an ice-fall several km along the coast, so
he and I went to look for it. The fall was, from memory, about 200 m across
and a similar distance long. It appeared that it had been projecting out as
an ice sheet into the sea and via a combination of undercutting and flow had
reached the point where its weight was no longer supported by the sea. It
cracked across, and fell down into the sea, hitting the rock bottom and
sliding out maybe 50 m. The destruction was tremendous, an outer region
several hundred metres across where seawater had been thrown out across the
sea-ice, then a few hundred metres of cracked ice, then a hundred metres or
so where the sea-ice (1 m thick) was cracked into small chunks and tumbled
together in confusion. An impressive amount of energy had been liberated!
Oh, the height of the ice-wall left behind was of the order of 20 m above sea
level. (All figures are from memory, so I may be a bit out here and there).

Ivan Reid, Paul Scherrer Institute, CH. iv...@psi.ch

Ben Sharvy

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Apr 21, 1995, 3:00:00 AM4/21/95
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>In article <Simen.Gaure-19...@ma-mac17.uio.no>,
> Simen...@math.uio.no (Simen Gaure) writes...

>>Is there any evidence that the ice has actually melted?


>>It has broken up, yes, but is that due to large scale melting?
>>It might also be the case that there's now more ice in
>>Antarctica (e.g. due to increased precipitation).
>>I'd guess (although I haven't made any computations) that
>>even a minor increase in ice thickness (say 1 metre) will
>>result in a lot of ice floating outwards towards the sea.

Global sea-levels are rising about 1.2 mm per year. Also, glaciers and
ice masses are retreating. 2+2=4.

--
Live Globally, Die Locally. Witches Heal. So Do Blowjobs. Liberate the
Weirdos and You Liberate the Squares.

Simen Gaure

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Apr 22, 1995, 3:00:00 AM4/22/95
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In article <3n9iin$n...@efn.org>, bsh...@efn.org (Ben Sharvy) wrote:

In <21APR199...@erich.triumf.ca> iv...@erich.triumf.ca (Ivan D.
Reid) writes:

>In article <Simen.Gaure-19...@ma-mac17.uio.no>,
> Simen...@math.uio.no (Simen Gaure) writes...

>>Is there any evidence that the ice has actually melted?
>>It has broken up, yes, but is that due to large scale melting?
>>It might also be the case that there's now more ice in
>>Antarctica (e.g. due to increased precipitation).
>>I'd guess (although I haven't made any computations) that
>>even a minor increase in ice thickness (say 1 metre) will
>>result in a lot of ice floating outwards towards the sea.

Global sea-levels are rising about 1.2 mm per year. Also, glaciers and
ice masses are retreating. 2+2=4.

Glaciers in Norway are advancing, rapidly. To the extent that
nearby houses are threatened. So are glaciers in
New Zealand. Rising sea level isn't evidence for large scale
melting of Antarctic ice, it may also be due to expansion
(due to global warming). 2+2=5.

My point was simply that one should have some evidence that ice
in Antarctica is actually melting, not just assume that it is.
After all, it's well below freezing most of the time in Antarctica,
ice simply doesn't melt then. (Under normal pressure).

Len Evens

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Apr 22, 1995, 3:00:00 AM4/22/95
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In article <3n9iin$n...@efn.org>, Ben Sharvy <bsh...@efn.org> wrote:
>In <21APR199...@erich.triumf.ca> iv...@erich.triumf.ca (Ivan D. Reid) writes:
>
>>In article <Simen.Gaure-19...@ma-mac17.uio.no>,
>> Simen...@math.uio.no (Simen Gaure) writes...
>
>>>Is there any evidence that the ice has actually melted?
>>>It has broken up, yes, but is that due to large scale melting?
>>>It might also be the case that there's now more ice in
>>>Antarctica (e.g. due to increased precipitation).
>>>I'd guess (although I haven't made any computations) that
>>>even a minor increase in ice thickness (say 1 metre) will
>>>result in a lot of ice floating outwards towards the sea.
>
>Global sea-levels are rising about 1.2 mm per year. Also, glaciers and
>ice masses are retreating. 2+2=4.
>

It is a bit more complicated than that. Warming produces sea level
rise just by thermal expansion. See my recent previous posting.


Leonard Evens l...@math.nwu.edu 708-491-5537
Dept. of Mathematics, Northwestern Univ., Evanston, IL 60208

Len Evens

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Apr 22, 1995, 3:00:00 AM4/22/95
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In article <Simen.Gaure-22...@ma-mac17.uio.no>,
Simen Gaure <Simen...@math.uio.no> wrote:

>In article <3n9iin$n...@efn.org>, bsh...@efn.org (Ben Sharvy) wrote:
>
> In <21APR199...@erich.triumf.ca> iv...@erich.triumf.ca (Ivan D.
>Reid) writes:
>
> >In article <Simen.Gaure-19...@ma-mac17.uio.no>,
> > Simen...@math.uio.no (Simen Gaure) writes...
>
> >>Is there any evidence that the ice has actually melted?
> >>It has broken up, yes, but is that due to large scale melting?
> >>It might also be the case that there's now more ice in
> >>Antarctica (e.g. due to increased precipitation).
> >>I'd guess (although I haven't made any computations) that
> >>even a minor increase in ice thickness (say 1 metre) will
> >>result in a lot of ice floating outwards towards the sea.
>
> Global sea-levels are rising about 1.2 mm per year. Also, glaciers and
> ice masses are retreating. 2+2=4.
>
>Glaciers in Norway are advancing, rapidly. To the extent that
>nearby houses are threatened. So are glaciers in
>New Zealand. Rising sea level isn't evidence for large scale
>melting of Antarctic ice, it may also be due to expansion
>(due to global warming). 2+2=5.
>
>My point was simply that one should have some evidence that ice
>in Antarctica is actually melting, not just assume that it is.
>After all, it's well below freezing most of the time in Antarctica,
>ice simply doesn't melt then. (Under normal pressure).
>
>--
>Simen Gaure, Department of Mathematics, University of Oslo


This is basically correct. In fact, warming, through increased
precipitation could result in an increase in the Antarctic ice sheet.
The (1990) IPC Report in fact concludes that changes in the Antarctic
ice sheet in the past century have probably resulted in a drop in
sea level, but this conclusion is far from certain.

With respect to mountain glaciers, however, anecdotal evidence from
Norway or New Zealand doesn't tell us anything. Again, if I
understand the IPCC Report, it is generally believed that overall
mountain glaciers have been retreating in the past 100 years.

In any case, as Simon Gaure points out, all this ignores thermal
expansion which is probably the major factor in sea level rise.

Ben Smith

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Apr 22, 1995, 3:00:00 AM4/22/95
to

This looks like too much fun to pass up!!!!!


Not that I am right, but please ponder on a few ideas...

First, As others have pointed out themal expansioin of an incredibly
large body of water (oceans) can have an effective rise of a whopping 1
mm /year, at that rate I better move away from the coastline. Have you
considered the effects of erosion? Or the fact that the plates
(tectonics) float on the mantle! Well this could mean that any
particular point is just a reference, and that reference is subject to
sinking and rising. Many geologist beleive that the land under the great
ice sheets that now are uncovered will rise just like an added weight on
a floating boat. Okay, well this causes a problem when someone puts a
stick in the ground and records sea rise over time, ranted the continent
is not going to rise a few feet per year byt this mechanism, but the
mechanism must be considered.

Next, global warming is an odd term. Lets say the globe warms. The
tropical zones on earth will increase (one theory) the semi arid regions
will decrease and the frigid areas will grow. The earth is a big dynamic
system, constantly shifting energy from here to there. The last ice age,
for example is beleived to have been composed of large tropical and artic
regions, with very little semi arid regions. How can this happen, well
the increase in heat, evaporates more water that moves to the equator and
the poles via trade winds. Then the evaporated water precipitates as
rain or snow and ice, depending on the region, vegetation grows or
glaciers grow. A glacier can exist anywhere the rate of deposition of
snow/ice excedes the melting of snow/ice.

Also, something else puzzles me, I heard some talk on the tube that the
sun dishes out enough energy to power (something, wasn;t paying enough
attention). Well, that sunlight, a few hundred years ago, was used to as
fuel for things to grow. Now it is used to heat things up (skysrapers,
highways, parking lots, etc). How would this change the scenario of
global warming and the dreaded green house gases! Anyway this was just
for fun,

the world is a little too complicated for 2+2 = 4!!!!!


Ben Smith smi...@weiss.che.utexas.edu

(The above statments may not be my employer's!)

Hugh Easton

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Apr 23, 1995, 3:00:00 AM4/23/95
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In article <Simen.Gaure-22...@ma-mac17.uio.no>
Simen...@math.uio.no "Simen Gaure" writes:

>
> In article <3n9iin$n...@efn.org>, bsh...@efn.org (Ben Sharvy) wrote:
>
> In <21APR199...@erich.triumf.ca> iv...@erich.triumf.ca (Ivan D.
> Reid) writes:
>
> >In article <Simen.Gaure-19...@ma-mac17.uio.no>,
> > Simen...@math.uio.no (Simen Gaure) writes...
>
> >>Is there any evidence that the ice has actually melted?
> >>It has broken up, yes, but is that due to large scale melting?
> >>It might also be the case that there's now more ice in
> >>Antarctica (e.g. due to increased precipitation).
> >>I'd guess (although I haven't made any computations) that
> >>even a minor increase in ice thickness (say 1 metre) will
> >>result in a lot of ice floating outwards towards the sea.
>
> Global sea-levels are rising about 1.2 mm per year. Also, glaciers and
> ice masses are retreating. 2+2=4.
>
> Glaciers in Norway are advancing, rapidly. To the extent that
> nearby houses are threatened. So are glaciers in
> New Zealand.

Bruce Hamilton mentioned this some weeks back in another thread on
sci.environment. From the responses to his posting it emerged that this
is actually an indication that the glacier is melting - it results from
increased lubrication from meltwater underneath the glacier, and loss of
mechanical strength in the ice making up the glacier.

> Rising sea level isn't evidence for large scale
> melting of Antarctic ice, it may also be due to expansion
> (due to global warming). 2+2=5.
>

While we're on the subject, that rate of 1.2 mm/yr for sea level rise
that Ivan Reid mentioned is substantially less than the observed rate
over the last two years. Quoting from NASA press release 94-202:

The insights from TOPEX/Poseidon add to data collected from
tide gauges over the last century which suggest that average sea level
has been rising at a rate of about .04 to .08 inches (1 to 2
millimeters) per year, roughly equivalent to the rate expected from
global warming, Nerem said. "The data (from Dec. 1992 to Sept. 1994)
show a rise in average sea level of about .12 inches (3 millimeters)
per year, which is in reasonable agreement with the tide gauge
results," Nerem explained. However, tide gauge measurements can
be affected by the movement of land masses and are too sparsely
distributed to provide global coverage.

The tidal gauge data shows a 1-2mm/yr sea level rise over the last century,
and the sea level rise over the last two years was 3mm/yr. Seems to
indicate that the rate of sea level rise has increased substantially in
the last few years, which is what you would expect if polar ice was now
beginning to melt.

> My point was simply that one should have some evidence that ice
> in Antarctica is actually melting, not just assume that it is.
> After all, it's well below freezing most of the time in Antarctica,
> ice simply doesn't melt then. (Under normal pressure).
>

It does start to lose its strength well below freezing point though. Also,
the ice near the bottom of a glacier or an ice sheet is under considerable
pressure, which lowers its freezing point.

> --
> Simen Gaure, Department of Mathematics, University of Oslo
>

--
Hugh Easton <Hu...@daflight.demon.co.uk>

Ivan D. Reid

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Apr 23, 1995, 3:00:00 AM4/23/95
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In article <798635...@daflight.demon.co.uk>,
hu...@daflight.demon.co.uk writes...

>> In article <3n9iin$n...@efn.org>, bsh...@efn.org (Ben Sharvy) wrote:
>> In <21APR199...@erich.triumf.ca> iv...@erich.triumf.ca (Ivan D.
>> Reid) writes:
>> Global sea-levels are rising about 1.2 mm per year. Also, glaciers and
>> ice masses are retreating. 2+2=4.

>While we're on the subject, that rate of 1.2 mm/yr for sea level rise


>that Ivan Reid mentioned is substantially less than the observed rate
>over the last two years.

I'd just like to point out that it was bsh...@efn.org (Ben Sharvy)
who wrote that -- although he included an attribution to me, he completely
snipped all of my posting to reply to the post I had quoted. I wouldn't
want anyone to get the idea I'm an expert on global climate!

Simen Gaure

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Apr 23, 1995, 3:00:00 AM4/23/95
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In article <3nb95k$k...@news.acns.nwu.edu>, l...@schur.math.nwu.edu (Len

Evens) wrote:

With respect to mountain glaciers, however, anecdotal evidence from
Norway or New Zealand doesn't tell us anything. Again, if I
understand the IPCC Report, it is generally believed that overall
mountain glaciers have been retreating in the past 100 years.

Certainly, local evidence tells very little about the global
situation, I posted that in response to the general claim that
"glaciers are retreating". (And it's certainly not "anecdotal").

My main concern is that there's some evidence of
a global warming going on, we then need precise information
to create and adjust our models, we don't need statements
generalized from John Doe's personal experience with his freezer
during the power fallout of '67.

When people make statements like "a consequence of global warming
is that glaciers retreat", then, the sheep farmer watching
his nearby glacier demolishing the stone fence his great grandfather
built, will conclude that there's certainly not any global warming
going on. This becomes critical when politicians jump to the
same conclusion. (They're not always very eager to listen to
proper scientists, sadly enough.)

Simen Gaure

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Apr 23, 1995, 3:00:00 AM4/23/95
to
In article <798635...@daflight.demon.co.uk>, hu...@daflight.demon.co.uk wrote:

Bruce Hamilton mentioned this some weeks back in another thread on
sci.environment. From the responses to his posting it emerged that this
is actually an indication that the glacier is melting - it results from
increased lubrication from meltwater underneath the glacier, and loss of
mechanical strength in the ice making up the glacier.

Now, wait a second. Now both retreat and advance of a glacier have
become evidence for melting. This doesn't immediately add up.

However, we may make it add up.
The facts are that there have been massive snowfalls during
the last decade. This has caused two things:

1 The glaciers have become heavier, causing an increase in the pressure.
This again causes two phenomena.

1a Some ice at the bottom melts, causing increased lubrication.
1b The ice, even if it doesn't melt, moves downwards due to
its "liquid" nature.

2 The new snow on top of the glacier hasn't turned into hard ice yet;
hence it's more likely to melt. This may also cause
increased lubrication.

In this way it's correct to say that there's melting going on, but
the glacier still has grown larger. However, the statement
"the glacier melts" is quite misleading.
Of course, the increased snowfall may very well be evidence for
global warming, but I don't think one should insist that the
"glacier melts" just to convince laymen that global warming
is taking place.


[...]


> My point was simply that one should have some evidence that ice
> in Antarctica is actually melting, not just assume that it is.
> After all, it's well below freezing most of the time in Antarctica,
> ice simply doesn't melt then. (Under normal pressure).
>

It does start to lose its strength well below freezing point though. Also,
the ice near the bottom of a glacier or an ice sheet is under considerable
pressure, which lowers its freezing point.

It does, but at that depth (assuming now land-ice) there's no
way any climate change can have reached yet. However, the pressure
may very well have increased due to increased precipitation.
(Anyway, there seems to be a complete lack of facts about the
precipitation in Antarctica in this group; so it's hard to speculate
any further.)

Len Evens

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Apr 23, 1995, 3:00:00 AM4/23/95
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In article <Simen.Gaure-23...@ma-mac17.uio.no>,
>--
>Simen Gaure, Department of Mathematics, University of Oslo


I don't disagree with anything you say. Let me say again what I
meant to say. According the the IPCC Report (1990) and Supplement
(1992), the prepoderant evidence indicates that, _on_the_average_,
mountain glaciers have been retreating. Indeed, this is taken as
one argument that some global warming has taken place in the
last century. Of course, that doesn't mean that your favorite sheep
farmer's glacier is retreating.

The latest IPCC report (1994) has just appeared, and I have ordered
my copy. I llok forward to what they say now two years later on this
and other matters.

Len Evens

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Apr 23, 1995, 3:00:00 AM4/23/95
to
In article <798635...@daflight.demon.co.uk>,

Hugh Easton <hu...@daflight.demon.co.uk> wrote:
>
>While we're on the subject, that rate of 1.2 mm/yr for sea level rise
>that Ivan Reid mentioned is substantially less than the observed rate
>over the last two years. Quoting from NASA press release 94-202:
>
> The insights from TOPEX/Poseidon add to data collected from
> tide gauges over the last century which suggest that average sea level
> has been rising at a rate of about .04 to .08 inches (1 to 2
> millimeters) per year, roughly equivalent to the rate expected from
> global warming, Nerem said. "The data (from Dec. 1992 to Sept. 1994)
> show a rise in average sea level of about .12 inches (3 millimeters)
> per year, which is in reasonable agreement with the tide gauge
> results," Nerem explained. However, tide gauge measurements can
> be affected by the movement of land masses and are too sparsely
> distributed to provide global coverage.
>
>The tidal gauge data shows a 1-2mm/yr sea level rise over the last century,
>and the sea level rise over the last two years was 3mm/yr. Seems to
>indicate that the rate of sea level rise has increased substantially in
>the last few years, which is what you would expect if polar ice was now
>beginning to melt.
>

My memory of the satellite data was that it showed an increase of about
2 mm/year, but I could have got that wrong. In any case, one should
be a bit careful about drawing conclusions from just two or three
years of data. More to the point, since greenhouse gas concentrations
have been growing exponentially, it would not be inconsistent to have
a 1-2mm/year increase over the past 100 years and a 2-3 mm/year increase
at present. You don't have to assume the Greenland and Antarctic
ice caps are melting. (The melting of the north polar ice cap should
not lead to sea level rise, as has been pointed out several times in
this thread.)

Steinn Sigurdsson

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Apr 23, 1995, 3:00:00 AM4/23/95
to

In article <Simen.Gaure-22...@ma-mac17.uio.no>
Simen...@math.uio.no "Simen Gaure" writes:


> In article <3n9iin$n...@efn.org>, bsh...@efn.org (Ben Sharvy) wrote:

> Global sea-levels are rising about 1.2 mm per year. Also, glaciers and
> ice masses are retreating. 2+2=4.

> Glaciers in Norway are advancing, rapidly. To the extent that
> nearby houses are threatened. So are glaciers in
> New Zealand.

Bruce Hamilton mentioned this some weeks back in another thread on


sci.environment. From the responses to his posting it emerged that this
is actually an indication that the glacier is melting - it results from
increased lubrication from meltwater underneath the glacier, and loss of
mechanical strength in the ice making up the glacier.

It really is quite wonderful. Clearly if glaciers retreat,
then the glaciers are melting and on average the region
is warmer. Now, if glaciers are advancing, this also evidence
they are melting! What one wonders, do glaciers do when they
are growing?

For what it is worth, certain classes of glaciers, "skridjoklar",
can advance when melting, for the reason noted above, they can
also advance when growing. In general, "icecap" glaciers shrink
when melting and grow when cooling. What counts is the
volume of ice, and that has increased in recent years in some
regions.

Dennis Schulze

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Apr 24, 1995, 3:00:00 AM4/24/95
to
l...@schur.math.nwu.edu (Len Evens) writes:

>My memory of the satellite data was that it showed an increase of about
>2 mm/year, but I could have got that wrong.

I am just curious... how satellites which orbit the Earth in 800-36000 km
height can measure a length of a few millimeters. Are these global data?
Have been taken into account that the wind force may press the water mass
to one edge of the ocean and that this effect can result in a change of
a magnitude (sorry, but that's what I learned at university, any corrections
are welcome) higher than the mentioned 2 mm!?

One should be careful to draw quick conclusions from these data.

Regards,

Dennis
--
Dennis Schulze Free University of Berlin
Fax/Voice: (+49 30) 793 49 51 Department of Meteorology
Email: den...@bibo.met.fu-berlin.de
http://www.met.fu-berlin.de/~dennis/ #include <standard.disclaimer>

Bruce Hamilton

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Apr 24, 1995, 3:00:00 AM4/24/95
to

>In article <...> Simen...@math.uio.no "Simen Gaure" writes:


>> In article <...>, bsh...@efn.org (Ben Sharvy) wrote:
>> <> iv...@erich.triumf.ca (Ivan D. Reid) writes:

>> >In article <Simen.Gaure-19...@ma-mac17.uio.no>,
>> > Simen...@math.uio.no (Simen Gaure) writes...
>> >>Is there any evidence that the ice has actually melted?
>> >>It has broken up, yes, but is that due to large scale melting?
>> >>It might also be the case that there's now more ice in
>> >>Antarctica (e.g. due to increased precipitation).

....


> Global sea-levels are rising about 1.2 mm per year. Also, glaciers and
>> ice masses are retreating. 2+2=4.
>> Glaciers in Norway are advancing, rapidly. To the extent that
>> nearby houses are threatened. So are glaciers in
>> New Zealand.

>Bruce Hamilton mentioned this some weeks back in another thread on
>sci.environment. From the responses to his posting it emerged that this
>is actually an indication that the glacier is melting - it results from
>increased lubrication from meltwater underneath the glacier, and loss of
>mechanical strength in the ice making up the glacier.

As I noted at the time, this is silly. Anything "glaciers"
do is claimed by some to indicate global warming.

Some proponents of global warming want to claim the retreat of
glaciers _is_ evidence of global warming - without bothering to
qualify which glaciers or why. Now some others, or perhaps
even the same proponents :-), also want to claim the advance of
glaciers is also evidence of global warning, once again without
qualification.

It would seem that there are many factors at work in a large
glacier, including water lubrication, pressure and snow burden,
and perhaps there are several types of glacier. The responses
to my post ( that I saw ) postulated possible mechanisms for
the advance, they were not verified, definitive explanations.

There are 360 glaciers in the NZ Southern Alps, and two of the
largest are advancing, I don't know about the others.
I haven't been looking at any literature or reports, but it would seem
to me that the use of "glacier advance or retreat" as "evidence" of
anything to do with global warming is extremely suspect.
The claims need to be qualified.

[ rest deleted - sea level increase due to thermal expansion,
mantle land mass movement, Antartic water sliding into ocean,
more water from combustion of fossil CO2, or increased human
peeing, is being debated by others more qualified than I. ]

Bruce Hamilton

John Hellstrom

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Apr 24, 1995, 3:00:00 AM4/24/95
to
The Glaciers on NZ's west coast are advancing due to very heavy snowfall
in recent winters, not colder temperatures. The increased precipitation
is said to be caused by the extended El Nino phase of the Southern
Oscillation during the 1990's (how or if El Nino is related to global
warming is anyone's guess).

The glaciers, BTW, are extremely impressive at the moment, moving up to
1m/day, pushing boulders, trees etc before them (even at 1m/day, they are
several years from regaining their positions of late last century).

John Hellstrom.

Robert Grumbine

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Apr 24, 1995, 3:00:00 AM4/24/95
to
In article <3ng0dt$p...@fu-berlin.de>,

Dennis Schulze <den...@hamrun.met.fu-berlin.de> wrote:
>l...@schur.math.nwu.edu (Len Evens) writes:
>
>>My memory of the satellite data was that it showed an increase of about
>>2 mm/year, but I could have got that wrong.
>
>I am just curious... how satellites which orbit the Earth in 800-36000 km
>height can measure a length of a few millimeters. Are these global data?
>Have been taken into account that the wind force may press the water mass
>to one edge of the ocean and that this effect can result in a change of
>a magnitude (sorry, but that's what I learned at university, any corrections
>are welcome) higher than the mentioned 2 mm!?
>
>One should be careful to draw quick conclusions from these data.
>
Careful, yes, but it isn't impossible. The conclusion was that the
sea level had risen globally at a rate of about 3 mm per year for the
two years. It was noted that this is consistent with global warming
scenarios, but that many other things also cause such changes (including
having a couple ordinary warm years).

The satellite orbits near the low end of the range given. More like
700 km, I think. It is a radar based satellite, measuring return time
for an emitted pulse. Features which get measured include:
Waves
Tides
Ocean Current Systems
Sea Level
The gravity field of the earth

All of these give characteristic signatures to the returns. The
tides, for instance, have a well-known structure and extremely accurately
known periods. Ocean current systems have predictable length scales and
strengths. The gravity field has different length scales and is nearly
constant. Sea level (_global_) shows up as a uniform increase in elevation
at global scale. It is because of the differences in space and time
scales that the various signals can be disentangled.

Keep in mind, too, that in estimating global sea level, the measurement
is one of combining thousands of observations (the footprint of the beam,
I think, is about 50 km) to estimate the mean (on a daily basis). Then
you further reduce those daily measurements to a handful of long term
averages.

This is not to say that the problem is easy, or that it has necessarily
been solved in the best possible way. Just an outline of some things
which are considered. What I've seen of the Topex/Poseidon work has
been very good, so I'm inclined to accept their figure as accurate (to
the limit they gave, I think it was +- 1 mm/yr).

Followups directed to sci.geo.meteorology. I apologize to the spectroscopy
readers, but this should be the last note you see.

--
Bob Grumbine rm...@access.digex.net
Sagredo (Galileo Galilei) "You present these recondite matters with too much
evidence and ease; this great facility makes them less appreciated than they
would be had they been presented in a more abstruse manner." Two New Sciences

Richard I Cullather

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Apr 24, 1995, 3:00:00 AM4/24/95
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In article <3ng952$a...@charm.magnus.acs.ohio-state.edu>,
Richard I Cullather <rcul...@magnus.acs.ohio-state.edu> wrote:
>As I understand this,
>

I defer to Dr. Grumbine.

~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~
Richard Cullather
Polar Meteorology Group
Byrd Polar Research Center

Richard I Cullather

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Apr 24, 1995, 3:00:00 AM4/24/95
to
In article <3ng0dt$p...@fu-berlin.de>,
Dennis Schulze <den...@hamrun.met.fu-berlin.de> wrote:
>l...@schur.math.nwu.edu (Len Evens) writes:
>
>>My memory of the satellite data was that it showed an increase of about
>>2 mm/year, but I could have got that wrong.
>
>I am just curious... how satellites which orbit the Earth in 800-36000 km
>height can measure a length of a few millimeters. Are these global data?
>Have been taken into account that the wind force may press the water mass
>to one edge of the ocean and that this effect can result in a change of
>a magnitude (sorry, but that's what I learned at university, any corrections
>are welcome) higher than the mentioned 2 mm!?
>

As I understand this, the accuracy of an individual point measurement _can_
be made to within a few centimeters, which is achieved by knowing
the satellite's orbit to a high degree of accuracy using laser ranging.
The measurements are absolute with respect to the Earth's geocenter, so
the corrections you refer to are not necessary.
The interannual change in the global sea level is inferred at a higher
resolution "...given the observed variations and the known error sources."
The TOPEX-POSEIDON figure of three mm/yr over the first two years of
observations was widely quoted from R.S. Nerem (GSFC) at the AGU fall meeting.
The figure does not appear in the abstract, however. Would anyone know of
any interannual global sea level change value published from TOPEX data,
this study or otherwise?

For what it's worth, V. Gornitz has an excellent review of estimates based on
tide gauge data (in Climate and Sea Level Change, RA Warrick et al.,
Eds, 1993), most of which are in the 1 to 2 mm/yr range.


~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~~~~ ~~
Richard Cullather

Polar Meteorology Group
Byrd Polar Research Center

Grant W. Petty

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Apr 24, 1995, 3:00:00 AM4/24/95
to
In article <3nekre$r...@news.acns.nwu.edu>,

Len Evens <l...@schur.math.nwu.edu> wrote:
>
>My memory of the satellite data was that it showed an increase of about
>2 mm/year, but I could have got that wrong. In any case, one should
>be a bit careful about drawing conclusions from just two or three
>years of data. More to the point, since greenhouse gas concentrations

While I agree completely on the need to be cautious about looking for
trends in short time series, it seems to me that, unlike (say) direct
measurements of atmospheric temperature, an observation of sea level
rise must already represent an integrated (i.e., smoothed) response to
something happening over a much longer time period.

In short, I (a non-specialist on this topic) would personally tend to
view the observed sea level rise over 2-3 years as stronger evidence
for a disturbing long-term trend than anything in the available record
of observed global tropospheric temperature, despite the much greater
length of the latter.

Has anyone yet been able to determine whether the observed sea level
rise is associated with (1) a large temperature increase in the
near-surface layers of the ocean or (2) a smaller increase over a much
greater depth?


- Grant

--
Grant W. Petty gpe...@rain.atms.purdue.edu
Asst. Prof. of Atmospheric Science
Dept. of Earth & Atmospheric Sciences (317) 494-2544
Purdue University, West Lafayette IN 47907-1397 FAX:(317) 496-1210

Robert Grumbine

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Apr 24, 1995, 3:00:00 AM4/24/95
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In article <3nglkt$3...@mozo.cc.purdue.edu>,

Grant W. Petty <gpe...@rain.atms.purdue.edu> wrote:
>In article <3nekre$r...@news.acns.nwu.edu>,
>Len Evens <l...@schur.math.nwu.edu> wrote:
>>
>>My memory of the satellite data was that it showed an increase of about
>>2 mm/year, but I could have got that wrong. In any case, one should
>>be a bit careful about drawing conclusions from just two or three
>>years of data. More to the point, since greenhouse gas concentrations
>
[deletia]

>In short, I (a non-specialist on this topic) would personally tend to
>view the observed sea level rise over 2-3 years as stronger evidence
>for a disturbing long-term trend than anything in the available record
>of observed global tropospheric temperature, despite the much greater
>length of the latter.

I'd agree that the ocean is a better integrator than the atmosphere.
But, seat of the pants, I don't think it is enough better to justify
preferring a 2-3 year ocean record to a 100 year atmospheric record.
Certainly better than 2-3 years of atmospheric information.

>Has anyone yet been able to determine whether the observed sea level
>rise is associated with (1) a large temperature increase in the
>near-surface layers of the ocean or (2) a smaller increase over a much
>greater depth?

Based on a talk by Ted Fujita on El Nino, which included a video of
Topex/Poseidon sea level data as well as SST, my impression is that
much of the signal is surface/upper ocean derived. Further, potentially
a significant portion of the 3? mm/year signal is due to the presence
of an El Nino, rather than (necessarily) a global climate signal.
This latter effect was mentioned in the NASA press release that I
base the 3? mm/year estimate on.

I was just down to the reading room looking for something else, and
ran across the December, 1994 issue of J. Geophysical Research. This
is a special issue on the Topex/Poseidon mission. Several hundred
pages on how the thing works and all the wondrous information which
can be derived from it. Global sea level change, unfortunately, was
not one of the papers (to casual glance).

Aside to Rich Cullather: No need for deference. Aside from the
laser versus radar issue, everything you said squares with my understanding.
And I could have been wrong on the radar.

Followups to sci.geo.meteorology.

Jan Schloerer

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Apr 24, 1995, 3:00:00 AM4/24/95
to
What a wonderful ice & sea level mess. Let me try to enhance it ;-)

I won't reply to individual articles, there are too many, they do not
arrive well ordered, and so on. Apologies for any repetitions.
Some inappropriate groups removed, followup set to sci.environment.

Regarding glaciers, the most recent major piece of work I happened
to come across suggests that, on global average, glaciers have indeed
retreated during the past hundred years. The observed glacier retreat
is consistent with (although no proof for) a surface warming trend of
0.66 degrees C per century. This may not be the last word. There are
uncertainties, factors other than air temperature affect the mass
balance of glaciers. Anyway, about a year ago this was the most
plausible explanation Oerlemans could think of.

Johannes Oerlemans, Quantifying global warming from the retreat
of glaciers. Science 264 (8 April 1994), 243-245.
Discussion: Science 265 (23 Sept 1994), 1790-1791


Last I heard, it was unclear whether the Antarctic and Greenland ice
sheets are presently gaining or losing mass. I can dig out some 1992/3
references in case anyone is interested. I do not know, whether the
state of affairs resp. knowledge has changed since. Anyone ?

Assessing and predicting sea level change may be even more difficult
than thought previously. A presumably minor quirk is that humans may
literally put some water into the oceans by extracting it from aquifers
and other water reservoirs. Sahagian et al. estimated that this may
currently account for a sea level rise of about 0.5 mm per year. A long
discussion ensued, which to my amateurish eye showed that this quantity
is difficult to estimate and open to revision.

Dork L. Sahagian, Frank W. Schwartz & David K. Jacobs,
Direct anthropogenic contributions to sea level rise in the
twentieth century. Nature 367 (6 Jan 1994), 54-57.
Discussion: Nature 369 (1994), 615-616. Nature 370 (1994), 258.
Nature 371 (1994), 481.

Perhaps more important, the dominant role of air temperature and preci-
pitation for the mass balance of the major ice sheets has been called
into question. So far, it was often assumed that precipitation over
Greenland and Antarctica depends mainly on temperature. Warm air can
deliver more moisture than cool air, so warming should increase preci-
pitation and the mass of the ice sheets. This in turn should tend to
slow down sea level rise.

In the GISP2 Greenland ice core, Kapsner et al. compared temperature
and accumulation (which is closely correlated with precipitation) over
the past 18,000 years. Their data suggest that temperature probably was
not the dominant control for precipitation. They think that changes in
atmospheric circulation, specifically of the dominant storm track, look
like a better candidate. The results are broadly consistent with
previous shorter records from Greenland. Precipitation over Antarctica
may also strongly be influenced by changes of storm patterns.

How storm patterns and tracks may change under a changing climate, and
how this may influence the mass balance of the ice sheets, does not yet
seem very clear. Anyway, estimates are likely to get more difficult.

W.R.Kapsner, R.B.Alley, C.A.Shuman, S.Anandakrishnan & P.M.Grootes,
Dominant influence of atmospheric circulation
on snow accumulation in Greenland over the past 18,000 years.
Nature 373 (5 Jan 1995), 52-54
David Bromwich, Ice sheets and sea level, ibid. 18-19


Finally, the recent IPCC Report "Climate Change 1994" (Cambridge Univ.
Press 1995) addresses greenhouse gases, aerosols, radiative forcing
and related topics. It doesn't say anything about sea level change.
According to a preliminary outline of the contents, this will be treated
in the forthcoming Second IPCC Assessment, scheduled for late 1995.


Jan Schloerer schl...@rzmain.rz.uni-ulm.de
Uni Ulm Klinische Dokumentation D-89070 Ulm Germany

David P Norwood

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Apr 25, 1995, 3:00:00 AM4/25/95
to
Ben Sharvy (bsh...@efn.org) wrote:

: >In article <Simen.Gaure-19...@ma-mac17.uio.no>,
: > Simen...@math.uio.no (Simen Gaure) writes...

: >>Is there any evidence that the ice has actually melted?
: >>It has broken up, yes, but is that due to large scale melting?
: >>It might also be the case that there's now more ice in
: >>Antarctica (e.g. due to increased precipitation).

: >>I'd guess (although I haven't made any computations) that


: >>even a minor increase in ice thickness (say 1 metre) will
: >>result in a lot of ice floating outwards towards the sea.

: Global sea-levels are rising about 1.2 mm per year. Also, glaciers and

: ice masses are retreating. 2+2=4.

Is this because there's more water or because the water is warmer (on
average)?

dave


: --

David P Norwood

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Apr 25, 1995, 3:00:00 AM4/25/95
to
Len Evens (l...@schur.math.nwu.edu) wrote:
: >

: >Global sea-levels are rising about 1.2 mm per year. Also, glaciers and
: >ice masses are retreating. 2+2=4.
: >

: It is a bit more complicated than that. Warming produces sea level


: rise just by thermal expansion. See my recent previous posting.

Oops. I suffer from premature posting. Sorry.

dave

: Leonard Evens l...@math.nwu.edu 708-491-5537

Hugh Easton

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Apr 25, 1995, 3:00:00 AM4/25/95
to
In article <Simen.Gaure-23...@ma-mac17.uio.no>
Simen...@math.uio.no "Simen Gaure" writes:

> > My point was simply that one should have some evidence that ice
> > in Antarctica is actually melting, not just assume that it is.
> > After all, it's well below freezing most of the time in Antarctica,
> > ice simply doesn't melt then. (Under normal pressure).
> >
>
> It does start to lose its strength well below freezing point though. Also,
> the ice near the bottom of a glacier or an ice sheet is under considerable
> pressure, which lowers its freezing point.
>
> It does, but at that depth (assuming now land-ice) there's no
> way any climate change can have reached yet.

That assumption is wrong if an unconventional mode of long range heat
conduction (such as infrared heat transmission) does operate in ice. Did
you not see my posting that started this thread, which included physical
data and calculations clearly demonstrating this?

> However, the pressure
> may very well have increased due to increased precipitation.

How much precipitation are you talking about? My understanding is that,
although there is a lot of snow blowing around, the actual rate of
precipitation in Antarctica is very low - a few centimetres a year.
Even if the rate of precipitation doubled (and if it did I am sure
someone would notice) it would take centuries to increase the pressure
significantly.

> (Anyway, there seems to be a complete lack of facts about the
> precipitation in Antarctica in this group; so it's hard to speculate
> any further.)
>

> --
> Simen Gaure, Department of Mathematics, University of Oslo
>

--
Hugh Easton <Hu...@daflight.demon.co.uk>

Simen Gaure

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Apr 25, 1995, 3:00:00 AM4/25/95
to
In article <798770...@daflight.demon.co.uk>, hu...@daflight.demon.co.uk wrote:

How much precipitation are you talking about? My understanding is that,
although there is a lot of snow blowing around, the actual rate of
precipitation in Antarctica is very low - a few centimetres a year.
Even if the rate of precipitation doubled (and if it did I am sure
someone would notice) it would take centuries to increase the pressure
significantly.

I read your comments about infrared heat transmission, it may be
well worth looking at; however, to explain the current breakup
it may be wise to look at more conventional explanations first.
As I understand it, there's no evidence that the structure of the ice
has changed dramatically, I suppose your theory could be checked
by analyzing some samples.

Actually, I don't have the foggiest idea how much precipitation
there is in Antarctica each year, it just struck me as a plausible
reason for increased thickness and hence disintegration of
the ice at the rim. Btw, not only precipitation in the form
of snow should be taken into account, but also steam freezing
on the ground (perhaps not much due to extremely low humidity).
I'd guess on average some 4-5 cm each year (my guess is based
on which depth an expedition expected to find Amundsen's tent).

Note also for instance that "El Niño" has changed not long ago, this
may indicate local climate changes and hence change in precipitation.

Now, the regular cause for calving along the rim is that the ice
is pushed outwards by its own weight, in an almost stable system
this will be the major reason. (This happens all the time, even
if there's no "melting" going on).
If then the precipitation increases (even by a tiny amount)
it seems evident that the disintegration at the rim will increase,
probably some or many years after (depending on properties
of the ice) the increase in precipitation.

What one needs to check this, is some knowledge of the ice structure,
some knowledge of the level of precipitation and one or more
differential equations. (And probably a computer.)

It could even be as simple as looking at figures for outwards
ice transport, if they exist. (After all, there are some
research stations down there, they must have done something.)

Hugh Easton

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Apr 25, 1995, 3:00:00 AM4/25/95
to
In article <Simen.Gaure-25...@ma-mac17.uio.no>
Simen...@math.uio.no "Simen Gaure" writes:

>
> I read your comments about infrared heat transmission, it may be
> well worth looking at; however, to explain the current breakup
> it may be wise to look at more conventional explanations first.

What is the conventional explanation for the recent events in Antarctica?
Using the values for thermal conductivity I quoted earlier from the
Handbook of heat transfer fundamentals (2nd ed.), McGraw-Hill 1985, there
just hasn't been enough time for the small amount of warming detected so
far to have a significant effect.

> As I understand it, there's no evidence that the structure of the ice
> has changed dramatically,

Melting and disintegration are fairly dramatic structural changes.

For the benefit of those who don't know what we are discussing, allow me
to quote from the BAS press release which was issued shortly after
January's events:

<p>The disintegration of an ice shelf and the calving of a new giant
iceberg have dramatically changed the outline of Antarctica.
Satellite images relayed to Cambridge from the British Antarctic
Survey's (BAS) Rothera Research Station confirm that recent
warming of the Antarctic Peninsula is having a major impact on
the ice sheet covering this climatically sensitive region..
<p>The ice shelf which formerly occupied Prince Gustav Channel and
connected James Ross Island to the Antarctic Peninsula has
disintegrated. For the first time in recorded history, James
Ross Island is circumnavigable. The new iceberg calved from the
Larsen Ice Shelf and measures 78 km x 37 km, (roughly the size of
Oxfordshire), and is around 200 m thick. .
<p>Alerted by glaciologists 9000 miles away in Cambridge, scientists
on board a BAS Dash 7 aircraft confirmed both the disintegration
and calving, and reported a dense plume of ice fragments
extending several hundred kilometres into the sea..
<p>Speaking from Antarctica, chief geologist Dr Mike Thomson said,
"Looking out of the aircraft window I was utterly amazed to see
the dramatic and very recent changes to the Larsen Ice Shelf. In
25 years of Antarctic field work I have never seen anything like
it.".
<p>These observations come hard on the heels of the disintegration
of Wordie Ice Shelf on the west coast of the Antarctic Peninsula,
also discovered by BAS scientists. There is now little doubt
that the retreat of these ice shelves is, in the short-term,
irreversible. The retreat is a result of a warming of the
regional climate by 2.5.C since the 1940's..

From this account it appears that the scientists who study Antarctica
were taken completely by surprise. What if a similar sudden disintegration
takes place in the near future, this time affecting the comparatively
unstable West Antarctic ice sheet? From what I have read, this would
result in a six metre (about 20 ft) rise in sea levels worldwide, enough to
flood many coastal cities and completely submerge some island nations. Even
if there was several years advance warning, very little could be done to
prevent disaster: at the moment CO2 levels are increasing at an exponential
rate, and the trend is expected to continue for the forseeable future.

Suppose that clear signs of serious instability in the West Antarctic ice
sheet begin to appear in, for instance, 20 years time. By then CO2 levels
will be substantially higher than they are now (the doubling time for
the excess above preindustrial levels is about 30 years). In order to
prevent the ice sheet from collapsing, three events have to take place.
Firstly, CO2 emissions would have to be drastically reduced - the IPCC
estimate that emissions would have to be cut by 60 percent just to
stabilise CO2 levels, bringing CO2 levels back down again would require
even greater cutbacks. These alone would presumably require several years
to implement.

Once the necessary cutbacks were made it would still take some time for
CO2 levels to fall. Since the rate at which the biosphere is absorbing
CO2 is under half the rate at which we are emitting it, the fall in CO2
levels would take longer than the initial rise did ie several decades
just to bring CO2 levels back to what they are now. In fact the ice sheet
would not become stable until the accumulated heat from the whole manmade
greenhouse era was lost. CO2 levels would have to fall to the preindustrial
level before this cooling process could even begin.

In short, by the time any signs of an impending large-scale breakup of
the polar icecaps become apparent, it will be far too late to prevent it.
That is why any gap in our understanding of the physical properties of
ice that could allow heat transfer to occur more quickly than expected
needs to be investigated now.

>
> I suppose your theory could be checked
> by analyzing some samples.
>

Admittedly it lies completely outside my own particular area of expertise,
but I think it would probably be quite straightforward to perform the
experiments necessary to test whether any unusual modes of heat
conduction operate in ice. Temperatures can fall below -80 C, and ice sheets
can reach a thickness of 2km in Antarctica (this would correspond to a
pressure of around 200 atm at the bottom). A reasonable range of conditions
to test would be temperatures down to about 200K at atmospheric pressure. If
that shows a 'positive' result, the experiment will need to be repeated at
a range of higher pressures so that the effects on the rate of warming of
polar ice can be accurately modelled.

As far as I know the only major contaminant of Antarctic ice is air bubbles,
so the water used to make the ice for the experiments should be very pure
(ie not tap water). Actually measuring the infrared absorbtion spectrum from
4um to 120um is probably a trivial exercise with the kind of equipment
available today.

For the sake of completeness it might also be worth checking that no other
unusual modes of heat conduction operate. This can best be done by
measuring the rate of heat conduction through a small thickness of ice
(eg 1cm) and a much larger distance (eg 1m), and see whether there is
any discrepancy between the heat conduction rates across the two
different thicknesses of ice.

>
> --
> Simen Gaure, Department of Mathematics, University of Oslo
>

--
Hugh Easton <Hu...@daflight.demon.co.uk>

William Connolley

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Apr 25, 1995, 3:00:00 AM4/25/95
to
In article 798770...@daflight.demon.co.uk, Hu...@daflight.demon.co.uk (Hugh Easton) writes:

> In article Simen...@math.uio.no "Simen Gaure" writes:
> How much precipitation are you talking about? My understanding is that,
> although there is a lot of snow blowing around, the actual rate of
> precipitation in Antarctica is very low - a few centimetres a year.
> Even if the rate of precipitation doubled (and if it did I am sure
> someone would notice) it would take centuries to increase the pressure
> significantly.
>
> > (Anyway, there seems to be a complete lack of facts about the
> > precipitation in Antarctica in this group; so it's hard to speculate
> > any further.)

Let me attempt in inject a few facts (as far as they are known) about
precipitation in and around Antarctica.

The average annual ppn on the Antarctic continent is 154 mm/year, with an uncertainty
of about 30 mm/y. The ppn is, howevber, very unevenly distributed. The interior is
high and cold - consequently little moisture-bearing air gets in. A large fraction
of area (perhaps 35%) has ppn less than 50 mm/year. However, around the edges of the
continent ppn is much higher, particularly around the Peninsula where the Larsen ice
shelf is. There, ppn may exceed 1 m/year in places.

References for this:
Weather and Climate of the Antarctic, W. Schwerdtfeger, Elsevier.
- A general all-round good book about Antarctic met.
Surface balance in drainage systems of Antarctica, Giovinetto and Bentley,
Antarctic journal of the US, v 20, p6-13, 1985.
- Just the ppn.

William Connolley.

http://www.nbs.ac.uk/public/icd/wmc
http://www.nbs.ac.uk/public/icd/bas_publ.html - pictures of iceshelf disintegration


Markus Kellerhals

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Apr 26, 1995, 3:00:00 AM4/26/95
to
In article <798854...@daflight.demon.co.uk>, Hu...@daflight.demon.co.uk (Hugh Easton) writes:
> In article <Simen.Gaure-25...@ma-mac17.uio.no>
> Simen...@math.uio.no "Simen Gaure" writes:
>
> >
> > I read your comments about infrared heat transmission, it may be
> > well worth looking at; however, to explain the current breakup
> > it may be wise to look at more conventional explanations first.
>
> What is the conventional explanation for the recent events in Antarctica?
> Using the values for thermal conductivity I quoted earlier from the
> Handbook of heat transfer fundamentals (2nd ed.), McGraw-Hill 1985, there
> just hasn't been enough time for the small amount of warming detected so
> far to have a significant effect.
>

................cut - discussion of recent events in Antarctica ...........

--
I doubt very much that infrared radiation is transmitted any great
distance through ice. In "Boundary Layer Climates" (T.R. Oke, 1993) the longwave
emmisivity of ice is tabulated as 0.92 - 0.97 in other words ice is almost
a perfect blackbody with respect to IR radiation. That range of .92 - .97 leaves
3 to 8% to be either transmitted or reflected. The portion that is transmitted
is then subject to exponential extinction with depth.

Anecdotal evidence against significant IR transmission is provided by the
fact that arctic glaciers are typically observed to be frozen to their bed year
round and that their basal temperatures show little if any seasonality. The
surface I.R. budget on the other hand is very strongly seasonal.

To determine how the heat is being conducted (by non radiative
mechanisms) through the ice one could observe the propagation of the annual and
diurnal temperature wave through the ice. The idealized temperature profile is
a sinusoid decreasing in amplitude exponentially with depth. By observing the
magnitude and phase lag of the variousannual waves one can determine the thermal
diffusivity* of the medium in question.Or alternatively if one knows the
properties of the medium well the profile can be used to infer the recent
paleoclimate of the area.

In studies of this sort done in the Canadian Arctic the maximum depth to
which the temperature waves have been observed is about 100 m, below that the
annual waves are indistinguishable from noise. These studies were done on
permafrost not ice, but I am almost sure similar temperature profiles have been
done in ice.

If you calculate the depth to which the effects of a step change in
temperature occurring 20 years ago (for the sake of arguement) have propagated I'm
sure that you will find it is nowhere near the thickness of the Antarctic Ice
Sheet. (If you want to do the calculations the relevant equation is Eq. 9-11 on
page 136 of "Physical Climatology" (W.D. SELLERS,1965).)


------------------------------------------------------------
Markus Kellerhals (mke...@geog.ubc.ca)
Department of Geography,
University of British Columbia, B.C.

Hugh Easton

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Apr 26, 1995, 3:00:00 AM4/26/95
to
In article <3nkdl4$c...@nntp.ucs.ubc.ca>
mke...@geog.ubc.ca "Markus Kellerhals" writes:

> I doubt very much that infrared radiation is transmitted any great
> distance through ice. In "Boundary Layer Climates" (T.R. Oke, 1993) the
> longwave emmisivity of ice is tabulated as 0.92 - 0.97 in other words ice
> is almost a perfect blackbody with respect to IR radiation. That range
> of .92 - .97 leaves 3 to 8% to be either transmitted or reflected. The
> portion that is transmitted is then subject to exponential extinction
> with depth.

It is difficult to know where to start with this argument, other than to
say that it is completely wrong and displays a profound ignorance of basic
radiative physics. You are saying that ice cannot trannsmit infrared
radiation because the polar icecaps are very close to being a perfect
"blackbody" to longwave infrared, with an emissivity of .92 - .97
(corresponding to an albedo of 3 to 8 percent). The oceans have a very low
albedo to incoming sunlight of about 2 to 3 percent (hence their dark blue
colour when seen from space), which, applying your reasoning, means that
seawater cannot transmit very much light. On the other hand, a concrete
block painted a light colour might have an albedo of over 50 percent, so
according to your argument this would be much more transparent to light
than seawater!

> Anecdotal evidence against significant IR transmission is provided by
> the fact that arctic glaciers are typically observed to be frozen to
> their bed year round and that their basal temperatures show little if any
> seasonality. The surface I.R. budget on the other hand is very strongly
> seasonal.

There certainly is a large seasonal variation in the amount of sunlight in
polar regions, but a large bulk of ice such as a glacier has got a
tremendous amount of thermal inertia which will tend to smooth out
seasonality (whether significant IR transmission takes place or not).

> To determine how the heat is being conducted (by non radiative
> mechanisms) through the ice one could observe the propagation of the
> annual and diurnal temperature wave through the ice. The idealized
> temperature profile is a sinusoid decreasing in amplitude exponentially
> with depth. By observing the magnitude and phase lag of the
> variousannual waves one can determine the thermal diffusivity* of the
> medium in question.Or alternatively if one knows the properties of the
> medium well the profile can be used to infer the recent paleoclimate of
> the area.

Fair enough, but I think it would be a lot easier to settle the issue by
means of a simple laboratory experiment as outlined in my previous post.

> In studies of this sort done in the Canadian Arctic the maximum depth
> to which the temperature waves have been observed is about 100 m, below
> that the annual waves are indistinguishable from noise. These studies
> were done on permafrost not ice, but I am almost sure similar temperature
> profiles have been done in ice.

I read something a year or two back about this. Didn't they find evidence
of a strong warming trend since the beginning of this century?

> If you calculate the depth to which the effects of a step change in
> temperature occurring 20 years ago (for the sake of arguement) have
> propagated I'm sure that you will find it is nowhere near the thickness
> of the Antarctic Ice Sheet. (If you want to do the calculations the
> relevant equation is Eq. 9-11 on page 136 of "Physical Climatology" (W.D.
> SELLERS,1965).)

Unfortunately I will not have an opportunity to chase up that reference
until next week at the earliest, but I'm sure that the equation would show
that any temperature rise would take centuries to propagate through a large
thickness of ice such as the Wordie or Larsen ice shelves. Since you have
the equation handy, how about plugging in some figures? A 2.5 C rise in
temperature beginning in the 1940's could be approximated as your step
change in temperature occurring 20 years ago, and the ice thickness is
about 200m. How deep should the temperature increase have penetrated so
far?

>
> ------------------------------------------------------------
> Markus Kellerhals (mke...@geog.ubc.ca)
> Department of Geography,
> University of British Columbia, B.C.
>

--
Hugh Easton <Hu...@daflight.demon.co.uk>

Robert Grumbine

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Apr 27, 1995, 3:00:00 AM4/27/95
to
In article <3nn1dh$a...@rs10.tcs.tulane.edu>,
David P Norwood <d...@mailhost.tcs.tulane.edu> wrote:
>Hugh Easton (Hu...@daflight.demon.co.uk) wrote:
>: From this account it appears that the scientists who study Antarctica

>: were taken completely by surprise. What if a similar sudden disintegration
>: takes place in the near future, this time affecting the comparatively
>: unstable West Antarctic ice sheet? From what I have read, this would
>: result in a six metre (about 20 ft) rise in sea levels worldwide, enough to
>: flood many coastal cities and completely submerge some island nations. Even
>: if there was several years advance warning, very little could be done to
>: prevent disaster: at the moment CO2 levels are increasing at an exponential
>: rate, and the trend is expected to continue for the forseeable future.
>
>
>Twenty feet !? I am thoroughly ignorant on this whole issue, but I've
>never heard any estimate this high. Can others please respond?
>
>(He said, posting nervously from New Orleans, Louisiana [although he is
>on the fifth floor])
>
As usual, Hugh is not providing the whole story. The part he did
provide is mostly correct (which is unusual) -- if the West Antarctic
ice sheet were to collapse, the sea level rise associated with that
event would be on the order of 5-6 meters. This would indeed flood
many coastal cities (including where I am) and island nations.

The rest of the story, though, is that that collapse, even if it
were to occur, would be on a time scale of, at minimum, decades --
not 'several years', several decades. More likely is a couple centuries.
It is not clear whether warming effects would stabilize the sheet
(through increased precipitation) or destabilize the sheet (through
ocean melting of the ice shelves).

Note regarding the recent large ice berg which calved from the Larsen
Ice Shelf: Christina Hulbe (hope I got your name spelled correctly)
posted to sci.geo.oceanography a while ago that now that the berg has
calved, the Larsen Ice shelf is about the same size it was in 1960.

Regarding Hugh's comments on the IR transmissivity of ice: A case of
irrelevant physics.
First, the absorption depth of IR in water is such that most energy
is absorbed in the first 1 mm. For IR transfer to have much effect on
an ice shelf, the distance needs to be comparable to the ice shelf
thickness -- 200-1000 meters, or 5-6 orders of magnitude greater. Hugh's
researches lead to an at most 1 order of magnitude difference. Greatly
insufficient, even if one takes his work as correct.
Second, it make little difference what the transmissivity of
monocrystalline ice is. a) ice shelves are not monocrystalline b) ice
shelves are covered with snow. Snow, and polycrystalline ice, have much
higher absorptivities (lower transmissivities) than monocrystalline ice.
Third, ice shelves do not calve due to heat conduction, they calve due
to brittle fatigue of the ice and related mechanical processes. One
related mechanical process is a thermal stress caused by having the top
of the ice shelf much colder than the bottom (the bottom being at the
freezing point due to the presence of the ocean). Hugh's conduction (if
there were such a thing) would _reduce_ this stress by equalizing the
temperatures through the ice sheet.

Yet another geography note for Hugh: The Larsen Ice shelf _is_ part
of the West Antarctic ice sheet.

From the preceeding notes in the thread, I've been convinced that it
is time to bring out the sea level faq again. First time will be the
old version which should still be obtainable from rtfm.mit.edu, in the
sci.answers directory. It probably won't be until August that I can
get it revised to include the recent work on the Greenland ice sheet
mass balance, and on the anthropogenic impoundment of water and draining
of aquifers, among other things which are overdue for inclusion.

Markus Kellerhals

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Apr 27, 1995, 3:00:00 AM4/27/95
to
From mkeller Thu Apr 27 10:42:58 1995
Newsgroups: sci.environment,sci.geo.meteorology,sci.physics,sci.techniques.spectroscopy
From: mke...@geog.ubc.ca (Markus Kellerhals)
Subject: Re: Will polar ice melt more quickly than previously thought?
Path: geog.ubc.ca!mkeller
Distribution:
Followup-To:
References: <Simen.Gaure-25...@ma-mac17.uio.no> <798854...@daflight.demon.co.uk> <3nkdl4$c...@nntp.ucs.ubc.ca> <798935...@daflight.demon.co.uk>
Organization: Geography Department, University of B.C., Canada
Keywords:

> In article <798935...@daflight.demon.co.uk>, Hu...@daflight.demon.co.uk (Hugh Easton) writes:

> In article <3nkdl4$c...@nntp.ucs.ubc.ca>
> mke...@geog.ubc.ca "Markus Kellerhals" writes:
>
> > I doubt very much that infrared radiation is transmitted any great

> > distance through ice. In "Boundary Layer Climates" (T.R. Oke, 1987) the


> > longwave emmisivity of ice is tabulated as 0.92 - 0.97 in other words ice
> > is almost a perfect blackbody with respect to IR radiation. That range
> > of .92 - .97 leaves 3 to 8% to be either transmitted or reflected. The
> > portion that is transmitted is then subject to exponential extinction
> > with depth.
>
> It is difficult to know where to start with this argument, other than to
> say that it is completely wrong and displays a profound ignorance of basic

I am glad you find my statements profound!!

> radiative physics. You are saying that ice cannot trannsmit infrared
> radiation because the polar icecaps are very close to being a perfect
> "blackbody" to longwave infrared, with an emissivity of .92 - .97
> (corresponding to an albedo of 3 to 8 percent). The oceans have a very low
> albedo to incoming sunlight of about 2 to 3 percent (hence their dark blue
> colour when seen from space), which, applying your reasoning, means that
> seawater cannot transmit very much light. On the other hand, a concrete
> block painted a light colour might have an albedo of over 50 percent, so
> according to your argument this would be much more transparent to light
> than seawater!

I'm afraid that you misunderstood my line of arguement here. I am **not** saying
that since ice has a high long wave emmisivity that therefore no infrared
radiation is transmitted ice. My statement was that a high infrared
emmissivity/absorptivity means that of the total incident less IR less is
available for transmission.

You are correct however in suggesting that the bulk absorptivity of a semi
transparent medium reflects absorption at many levels within the medium, not just
at the surface. For visible light in water the absorption of course occurs over
a column of up to several hundred metres. For IR radiation in water "total"
absorption occurs in a matter of centimetres. I was postulating (but not proving)
that the same is true of ice.

I don't think we should really argue about this further in the absence of
facts. The IR transmissivity of ice is undoubtedly tabulated. Also experiments
have been done measuring radiative profiles within ice and snowpacks. I don't
have anny references offhand but they wouldn't be too hard to find. (In "the
Physics of Glaciers" (Paterson,1969) the author implies but does not actually
state, on page 48 that longwave (IR) is completely absorbed very near the surface
of a glacier.


> > Anecdotal evidence against significant IR transmission is provided by
> > the fact that arctic glaciers are typically observed to be frozen to
> > their bed year round and that their basal temperatures show little if any
> > seasonality. The surface I.R. budget on the other hand is very strongly
> > seasonal.
>
> There certainly is a large seasonal variation in the amount of sunlight in
> polar regions, but a large bulk of ice such as a glacier has got a
> tremendous amount of thermal inertia which will tend to smooth out
> seasonality (whether significant IR transmission takes place or not).

The thermal inertia of the ice is more or less irrelevant to the question of IR
transmission. If IR radiation is indeed transmitted through the ice as Hugh
proposes then it must be absorbed at the base of the ice (assuming that its not
reflected from the rock and retransmitted back up through the ice. The degree of
heating in this limited region would be more or less independent of the large
bulk of ice above. The thermal inertia of the ice is *very* relevant if you are
talking heat transfer by conduction.

> > ------------------------------------------------------------
> > Markus Kellerhals (mke...@geog.ubc.ca)

> --
> Hugh Easton <Hu...@daflight.demon.co.uk>


------------------------------------------------------------
Markus Kellerhals (mke...@geog.ubc.ca)
Department of Geography, Tel: (604) 822-2663
University of British Columbia, B.C. Fax: (604) 822-6150


David P Norwood

unread,
Apr 27, 1995, 3:00:00 AM4/27/95
to
Hugh Easton (Hu...@daflight.demon.co.uk) wrote:
: From this account it appears that the scientists who study Antarctica

: were taken completely by surprise. What if a similar sudden disintegration
: takes place in the near future, this time affecting the comparatively
: unstable West Antarctic ice sheet? From what I have read, this would
: result in a six metre (about 20 ft) rise in sea levels worldwide, enough to
: flood many coastal cities and completely submerge some island nations. Even
: if there was several years advance warning, very little could be done to
: prevent disaster: at the moment CO2 levels are increasing at an exponential
: rate, and the trend is expected to continue for the forseeable future.

Twenty feet !? I am thoroughly ignorant on this whole issue, but I've
never heard any estimate this high. Can others please respond?

(He said, posting nervously from New Orleans, Louisiana [although he is
on the fifth floor])

dave

Hugh Easton

unread,
Apr 28, 1995, 3:00:00 AM4/28/95
to
In article <3no404$f...@access5.digex.net>
rm...@access5.digex.net "Robert Grumbine" writes:

> As usual, Hugh is not providing the whole story. The part he did
> provide is mostly correct (which is unusual) -- if the West Antarctic
> ice sheet were to collapse, the sea level rise associated with that
> event would be on the order of 5-6 meters. This would indeed flood
> many coastal cities (including where I am) and island nations.
>
> The rest of the story, though, is that that collapse, even if it
> were to occur, would be on a time scale of, at minimum, decades --
> not 'several years', several decades. More likely is a couple centuries.

How about backing up that statement with some supporting evidence?

> It is not clear whether warming effects would stabilize the sheet
> (through increased precipitation) or destabilize the sheet (through
> ocean melting of the ice shelves).
>

The Antarctic ice sheets are the result of many thousands of years of
accumulated snow, indeed ice that originally fell as snow around 250,000
years ago has been recovered at the Vostok site in East Antarctica. You
would have to greatly increase the rate of precipitation for a very
long period of time (several centuries or more) before you produced a
significant effect.

About 14,000 years ago the last ice age ended abruptly when CO2 levels
jumped from just under 200ppm to around 280ppm, where they have remained
up until the last century. At the same time the vast ice sheets which
covered much of North America and Europe melted. The transition took
place incredibly quickly - there is some evidence to suggest that it
may have been as little as 50 years - and when it was over two thirds of
the world's ice had melted, raising sea levels by around 100m.

Over the last 150 years CO2 levels have increased by a further 80ppm to
360ppm. Are we about to experience another 2/3 reduction in the volume
of ice to match?

> Note regarding the recent large ice berg which calved from the Larsen
> Ice Shelf: Christina Hulbe (hope I got your name spelled correctly)
> posted to sci.geo.oceanography a while ago that now that the berg has
> calved, the Larsen Ice shelf is about the same size it was in 1960.

Not around James Ross Island it isn't. And what about the Wordie ice shelf?
In the early stages of the breakup of the Antarctic ice cap, you would
expect to see accelerated flow of the ice sheets covering the continent.
This would tend at least initially to replace the ice lost from more
frequent calving of giant icebergs from the ice shelves.

>
> Regarding Hugh's comments on the IR transmissivity of ice: A case of
> irrelevant physics.
> First, the absorption depth of IR in water is such that most energy
> is absorbed in the first 1 mm. For IR transfer to have much effect on
> an ice shelf, the distance needs to be comparable to the ice shelf
> thickness -- 200-1000 meters, or 5-6 orders of magnitude greater. Hugh's
> researches lead to an at most 1 order of magnitude difference. Greatly
> insufficient, even if one takes his work as correct.

The graph I mentioned which shows that ice is significantly more
transparent than water to infrared was (if I remember correctly, I no
longer have the refernce to hand) lifted from a paper published in the
early 70's - presumably no one has investigated the infrared spectral
properties of ice further since then. Unfortunately it only covered
wavelengths down to 20um, and was conducted at a single temperature,
-10 C. It showed that for wavelengths shorter than 10um (ie ultraviolet,
visible light and short-wavelength infrared) the spectral properties of
water and ice were almost identical. Beyond 10um, they diverge. The water
remains very opaque, while the ice becomes more transparent so that at
20 um (where the graph ends) the ice is over 10 times more transparent
than the water.

This immediately suggests that the transparency of ice compared to water
will increase further at longer wavelengths. In fact at very long
wavelengths ice is known to be extremely transparent while water absorbs
strongly. It is actually possible to boil water inside a block of ice
in a microwave oven (see Scientific American, April 1994, p96).

It also highly likely that colder temperatures will increase the
magnitude of the effect (temperatures in Antarctica can fall below
-80 C), and there is a possibility that increasing the pressure could
also enhance the effect (in ice the pressure increases with depth by 10
atmospheres every 110 metres).

> Second, it make little difference what the transmissivity of
> monocrystalline ice is. a) ice shelves are not monocrystalline b) ice
> shelves are covered with snow. Snow, and polycrystalline ice, have much
> higher absorptivities (lower transmissivities) than monocrystalline ice.

Snow reflects and scatters light much more effectively than solid ice,
because of the fact that it is made up of many tiny crystals separated
by pockets of air. That is why fresh snow is a brilliant white colour -
it can have an albedo as high as 85 percent (ie it reflects 85 percent of
the light striking it). However, the efficiency of scattering depends
strongly on wavelength - as long as the wavelength is smaller than the
size of the ice crystals, as with light, efficient scattering occurs.
However, long-wavelength infrared, as the name implies, has a much longer
wavelength than visible light and so is much less susceptible to
scattering. In fact, as Markus Kellerhaus pointed out earlier on, polar
ice has an albedo of only 3 to 8 percent to longwave infrared, suggesting
that the crystal size must be too small to have much effect.

> Third, ice shelves do not calve due to heat conduction, they calve due
> to brittle fatigue of the ice and related mechanical processes. One
> related mechanical process is a thermal stress caused by having the top
> of the ice shelf much colder than the bottom (the bottom being at the
> freezing point due to the presence of the ocean). Hugh's conduction (if
> there were such a thing) would _reduce_ this stress by equalizing the
> temperatures through the ice sheet.
>

It might well mean that thermal stress contributes somewhat less to the
calving of ice floes than previously anticipated, but I fail to see the
relevance to this discussion.

> Yet another geography note for Hugh: The Larsen Ice shelf _is_ part
> of the West Antarctic ice sheet.
>
> From the preceeding notes in the thread, I've been convinced that it
> is time to bring out the sea level faq again. First time will be the
> old version which should still be obtainable from rtfm.mit.edu, in the
> sci.answers directory. It probably won't be until August that I can
> get it revised to include the recent work on the Greenland ice sheet
> mass balance, and on the anthropogenic impoundment of water and draining
> of aquifers, among other things which are overdue for inclusion.
>
> --
> Bob Grumbine rm...@access.digex.net
> Sagredo (Galileo Galilei) "You present these recondite matters with too much
> evidence and ease; this great facility makes them less appreciated than they
> would be had they been presented in a more abstruse manner." Two New Sciences
>

--
Hugh Easton <Hu...@daflight.demon.co.uk>

Grant W. Petty

unread,
Apr 28, 1995, 3:00:00 AM4/28/95
to
In article <3nol9f$v...@nntp.ucs.ubc.ca>,
Markus Kellerhals <mke...@geog.ubc.ca> wrote:

> I don't think we should really argue about this further in the
> absence of facts. The IR transmissivity of ice is undoubtedly
> tabulated. Also experiments have been done measuring radiative
> profiles within ice and snowpacks. I don't have anny references
> offhand but they wouldn't be too hard to find. (In "the Physics of
> Glaciers" (Paterson,1969) the author implies but does not actually
> state, on page 48 that longwave (IR) is completely absorbed very near
> the surface of a glacier.
>

Here are the facts:

Thermal radiative transfer at terrestrial temperatures occurs
primarily at wavelengths between 3 and 100 micrometers. Within this
range, the imaginary part M_im of the complex index of refraction is
between about 10^{-3} and nearly unity, according to Warren (1984;
"Optical constants of ice from the ultraviolet to the microwave",
Applied Optics).

Since K_abs = 4*pi*M_im / wavelength , even the low end of the above
range for M_im implies infrared absorption on the order of 1 unit of
optical thickness (i.e., one e-folding depth) per millimeter through
the ice. Even without doing any further calculations, it's pretty
clear that IR transfer will be negligible compared with ordinary
thermal conduction.

Hugh Easton's hypothesis of significant long-distance propagation of
thermal energy via infrared radiation through polar ice thus seems to
have been dealt a mortal blow...

Grant W. Petty

unread,
Apr 28, 1995, 3:00:00 AM4/28/95
to
In article <799028...@daflight.demon.co.uk>,
Hugh Easton <hu...@daflight.demon.co.uk> wrote:

>This immediately suggests that the transparency of ice compared to water
>will increase further at longer wavelengths. In fact at very long
>wavelengths ice is known to be extremely transparent while water absorbs
>strongly. It is actually possible to boil water inside a block of ice
>in a microwave oven (see Scientific American, April 1994, p96).
>

See my previous post, giving actual absorption figures for ice at
thermal infrared wavelengths. To recap, these appear to rule out any
significant infrared transport of thermal energy in ice, relative to
ordinary conduction.

>It also highly likely that colder temperatures will increase the
>magnitude of the effect (temperatures in Antarctica can fall below
>-80 C), and there is a possibility that increasing the pressure could
>also enhance the effect (in ice the pressure increases with depth by 10
>atmospheres every 110 metres).
>

It is true that reduced temperature tends to make ice more transparent
at IR wavelengths. It's also apparent from measurements down to -60 C
that the total effect can't be more than about one order of magnitude
-- i.e., from a penetration depth of 1 mm (at best) to one of about 1
cm (at best). This still won't compete with ordinary thermal
conduction.

As far as I know, nobody has measured infrared absorption by ice at
very high pressures, but there is no reason I know of to expect it
would make a serious difference for the purpose of this discussion.
To say that it might is grasping for straws.


>> Second, it make little difference what the transmissivity of
>> monocrystalline ice is. a) ice shelves are not monocrystalline b) ice
>> shelves are covered with snow. Snow, and polycrystalline ice, have much
>> higher absorptivities (lower transmissivities) than monocrystalline ice.
>
>Snow reflects and scatters light much more effectively than solid ice,
>because of the fact that it is made up of many tiny crystals separated
>by pockets of air. That is why fresh snow is a brilliant white colour -


This is only because ice exhibits negligible absorption at visible
wavelengths. If ice were even slightly absorbing, a snow field would
look noticeably gray, even if the relationship between wavelength and
particle size were unchanged.

>it can have an albedo as high as 85 percent (ie it reflects 85 percent of
>the light striking it). However, the efficiency of scattering depends
>strongly on wavelength - as long as the wavelength is smaller than the
>size of the ice crystals, as with light, efficient scattering occurs.
>However, long-wavelength infrared, as the name implies, has a much longer
>wavelength than visible light and so is much less susceptible to
>scattering. In fact, as Markus Kellerhaus pointed out earlier on, polar
>ice has an albedo of only 3 to 8 percent to longwave infrared, suggesting
>that the crystal size must be too small to have much effect.


The ice crystal size is not nearly as important in the latter case as
are the absorbing properties of the material. Also, even at the
typically ~10 micrometer wavelengths of thermal radiation, you're
still far from getting to the point where the grain size in pack ice
is negligible.


- Grant

cec hajf-flory

unread,
May 1, 1995, 3:00:00 AM5/1/95
to

: My understanding is that,

: although there is a lot of snow blowing around, the actual rate of
: precipitation in Antarctica is very low - a few centimetres a year.
: Even if the rate of precipitation doubled (and if it did I am sure
: someone would notice) it would take centuries to increase the pressure
: significantly.

My appologies in advance but .....

They told me that Antartica was a frozen desert too. It is pretty dry
most of the time, but don't forget there are thunderstorms in the desert
and Antarctica has heavy snow too. Deep heavy snow killed Scott. Data from
the Skelton Glacier (KIWI's during the Trans-Antarctic crossing)
and personal experience indicates that some areas seem to have fairly
regular heavy snows. I was on the Skelton Glacier in '69 and was buried
in 48" of snow in 48 hours + another 24" over the next 14 days. The
quarter sized smow flakes reminded me of skiing on Mt. Hood. Aerial
photos available show the same thing has happened in the past. We had an
aggregate of 30 some inches in 1970 too. Skiing was just great.

Ski the Skelton Glacier with the Kukri Hills Mountaineers.

--
Heaven is a "warm" sunny day on the "ICE"
Robert Flory,R.G.
oae6...@netcom.com

Paul Farrar

unread,
May 2, 1995, 3:00:00 AM5/2/95
to
In article p...@fu-berlin.de, den...@hamrun.met.fu-berlin.de (Dennis Schulze) writes:
>l...@schur.math.nwu.edu (Len Evens) writes:

>>My memory of the satellite data was that it showed an increase of about
>>2 mm/year, but I could have got that wrong.

>I am just curious... how satellites which orbit the Earth in 800-36000 km


>height can measure a length of a few millimeters.

Look in the December Journal of Geophysical Research (Oceans), which is a
special TOPEX/POSEIDON issue.

> Are these global data?

Yes.

>Have been taken into account that the wind force may press the water mass
>to one edge of the ocean and that this effect can result in a change of
>a magnitude (sorry, but that's what I learned at university, any corrections
>are welcome) higher than the mentioned 2 mm!?

Yes. That is one of the main things the data is used for: to determine
geographic variation of sea surface height due to circulation.

>One should be careful to draw quick conclusions from these data.

>Regards,

Hugh Easton

unread,
May 3, 1995, 3:00:00 AM5/3/95
to
In article <3nr8t5$4...@mozo.cc.purdue.edu>

gpe...@rain.atms.purdue.edu "Grant W. Petty" writes:

>
> Here are the facts:
>
> Thermal radiative transfer at terrestrial temperatures occurs
> primarily at wavelengths between 3 and 100 micrometers. Within this
> range, the imaginary part M_im of the complex index of refraction is
> between about 10^{-3} and nearly unity, according to Warren (1984;
> "Optical constants of ice from the ultraviolet to the microwave",
> Applied Optics).
>
> Since K_abs = 4*pi*M_im / wavelength ,

You do not say which end of the temperature scale the 10^-3 belongs to.
Let's try and work it out. The absorbtion coefficient of ice from 4 to
10um ranges from 10^4 to 10^3 cm^-1. Applying the formula you have given
above,

K_abs (10^4) = 4pi (about 10) * M_im / 10^-5m (or 10^-3 cm)

M_im = 1 (approximately)

So I guess the 10^-3 belongs to the 100um part of the spectrum.

K_abs = 4*pi*10^-3 / 100um (or 10^-2 cm)
= 1 cm^-1 (approximately)

At 10um K_abs is 10^3, at 20um it is 10^2 (see my earlier posts) and by
100um it has fallen to 1 cm^-1, giving an e-folding depth of 1 cm (not
the 1mm you state).

However, to have a significant effect on heat conduction the e-folding
depth must be greater than 1 metre, so a further improvement of 10^2 is
required.

> It is true that reduced temperature tends to make ice more transparent
> at IR wavelengths. It's also apparent from measurements down to -60 C
> that the total effect can't be more than about one order of magnitude
> -- i.e., from a penetration depth of 1 mm (at best) to one of about 1
> cm (at best). This still won't compete with ordinary thermal
> conduction.

(taken from your second message)

Are you saying that lowering the temperature increases the transparency
(1cm not 1mm) by a further factor of 10, to 10cm? So infrared heat
conduction in ice is only prevented from working by one final factor of
ten?

You have not stated whether the transparency improves further at longer
wavelengths. If it does, then it may be that infrared heat conduction in
ice does indeed become significant at sufficiently low temperatures and
over sufficiently long distances.

I'll try to find your reference.

>
> Hugh Easton's hypothesis of significant long-distance propagation of
> thermal energy via infrared radiation through polar ice thus seems to
> have been dealt a mortal blow...
>

Not quite yet.

>
> --
> Grant W. Petty gpe...@rain.atms.purdue.edu
> Asst. Prof. of Atmospheric Science
> Dept. of Earth & Atmospheric Sciences (317) 494-2544
> Purdue University, West Lafayette IN 47907-1397 FAX:(317) 496-1210
>

--
Hugh Easton <Hu...@daflight.demon.co.uk>

Grant W. Petty

unread,
May 3, 1995, 3:00:00 AM5/3/95
to
In article <799465...@daflight.demon.co.uk>,

Hugh Easton <hu...@daflight.demon.co.uk> wrote:
>
>However, to have a significant effect on heat conduction the e-folding
>depth must be greater than 1 metre, so a further improvement of 10^2 is
>required.
>

I'm not saying the above is wrong, because I haven't done the
calculations, but I'm wondering how you arrived at 1 meter. Does this
assume equal transparency over the entire blackbody spectrum? If ice
is effectively opaque in the vicinity of the peak of the blackbody
spectrum (which seems pretty clear to me from the numbers I have
seen), then even perfect transparency at some wavelength way out on
the longwave end of the spectrum isn't going to give you much heat
transfer, because not much thermal IR is being emitted at those
wavelengths.


Grant

Matthew Lybanon

unread,
May 4, 1995, 3:00:00 AM5/4/95
to
In article <3ng5qh$g...@access5.digex.net>
rm...@access5.digex.net (Robert Grumbine) writes:

> In article <3ng0dt$p...@fu-berlin.de>,
> Dennis Schulze <den...@hamrun.met.fu-berlin.de> wrote:

> >l...@schur.math.nwu.edu (Len Evens) writes:
> >
> >>My memory of the satellite data was that it showed an increase of about
> >>2 mm/year, but I could have got that wrong.
> >
> >I am just curious... how satellites which orbit the Earth in 800-36000 km

> >height can measure a length of a few millimeters. Are these global data?

It is remarkable to me also that satellites in orbits hundreds of
km above the Earth can actually measure sea level with a precision of a
few cm (not mm). Combined with numerical modeling, it is possible to
draw inferences at the mm level. Two special issues of the Journal of
Geophysical Research were devoted to results from the U.S. Navy's
GEOSAT mission. (GEOSAT, which was launched in 1985 and produced
useful data for several years, carried a microwave altimeter as its
single Earth-observing instrument.) They are:

Volume 95, Number C3, March 15, 1990
Volume 95, Number C10, October 15, 1990

A later issue of the same journal (JGR) is devoted to TOPEX/POSEIDON:

Volume 99, Number C12, December 15, 1994

Reading those three issues will give you a great deal of information
about altimetry and its uses, including the topic you asked about. You
could then also look for other papers by the same authors in other
issues of JGR, the Journal of Physical Oceanography, and the Journal of
Atmospheric and Oceanic Technology (to name the American journals most
likely to have papers on altimetry). Quite a bit of work is going on
in Europe as well, mainly in connection with the ERS-1 mission, which
also carries an altimeter. I am not sure where the best place is to
look for work by those people (the first name that comes to mind is
Chris Rapley in England).

For a simple introduction to the physics involved, I recommend:

M. Lybanon, "Satellite altimetry of the Gulf Stream,"
American
Journal of Physics, vol. 62, no. 7, pp. 661-665, July 1994,

which also contains some useful references.

> >Have been taken into account that the wind force may press the water mass
> >to one edge of the ocean and that this effect can result in a change of
> >a magnitude (sorry, but that's what I learned at university, any corrections
> >are welcome) higher than the mentioned 2 mm!?
> >

> >One should be careful to draw quick conclusions from these data.
> >

Hugh Easton

unread,
May 5, 1995, 3:00:00 AM5/5/95
to
On 14 April I posted the message which started this thread. In it I
mentioned the recent events in Antarctica - the breakup of the Wordie ice
shelf and the more recent partial disintegration of the Larsen ice shelf -
and put forward a possible explanation: that infrared heat radiation could
travel significant distances through ice. This would allow heat to travel
much more quickly through large volumes of ice (such as glaciers and polar
ice sheets) than might be expected from laboratory measurements of heat
conduction (which would, presumably, be made over comparatively short
distances of a few centimetres or less).

Last week, Grant Petty posted some data which appears to conclusively
disprove this hypothesis. Specifically, his figures show that infrared
radiation of the relevant wavelengths can travel at the most only 1-10cm
through ice before most of it is absorbed. A few simple calculations
(included in my original posting) show that infrared radiation would have
to be able to travel about 1 metre through ice before it transmitted as
much heat as ordinary thermal conduction does, so the actual distance it
can travel falls short by at least a factor of 10. Therefore these figures
effectively rule out the possibility that infrared heat transmission could
significantly speed up the overall rate of heat conduction through solid
ice.

However, those same figures indicate that it may have a significant effect
on one particular form of polar ice - snow. Because snow consists mainly
of air, infrared radiation will be able to travel a much longer distance
through it than through ice. For instance, for snow which is 10 percent ice
by volume, infrared would be able to travel 10 times further (ignoring the
effects of scattering, which are comparatively minor at long infrared
wavelengths). Therefore, some infrared radiation from a solid surface could
penetrate through a metre or more of snow above it.

Snow has all the properties of an excellent thermal insulator: a fluffy,
highly porous structure consisting mainly of air, trapped within a lattice
of tiny ice crystals. The thermal conductivity is presumably much lower
than that of solid ice, quite probably by a factor of ten or more. The
combination of a lower thermal conductivity and a higher transparency to
infrared radiation probably means that infrared heat transmission is
effective in snow, but that is not the point I wish to draw attention to.

A highly insulated, radiating surface can reach temperatures much lower
than the ambient air temperature: an insulated radiator high on a mountain
can reach temperatures nearly low enough to liquefy nitrogen. The limit is
set by the quality of the insulation and the amount of infrared radiation
reradiated from the atmosphere back to the surface. A snow-covered surface
is not a perfect insulated radiator because only part of the infrared
spectrum is transmitted, but nonetheless this effect could allow
temperatures beneath the snowpack to fall well below the air (and snow
surface) temperature. With one complication.

Snow's insulating properties have presumably not changed a great deal in
the last 150 years, but the quantity of infrared reradiated back from the
sky undoubtedly has. Infrared is emitted back to the surface by greenhouse
gases, by clouds and by anything else that tends to increase the general
murkiness of the atmosphere. Over the last 150 years CO2 levels have
increased by 25 percent and within the last 50 years a number of extremely
powerful manmade greenhouse gases have been added to the atmosphere. These
all emit infrared back to the surface, so that an insulated radiator cannot
reach as low a temperature now as it could 150 years ago. From what little
I know the effect is quite large, several tens of degrees C - perhaps
someone more knowledgeable in this area could comment.

Although my original theory was shown to be wrong, this modification to it
could go a long way towards explaining the recent events in Antarctica,
glaciers melting and "surging", the retreat of polar sea ice etc. If the
effect is of sufficient magnitude then it means that polar ice is indeed
much less stable than previously thought. That would greatly increase the
possibility of a catastrophic sea level rise in the near future, and
provide a compelling argument for taking action now to deal with the
problem of greenhouse gas emissions.


--
Hugh Easton <Hu...@daflight.demon.co.uk>

ejo

unread,
May 8, 1995, 3:00:00 AM5/8/95
to
>> This is not to say that the problem is easy, or that it has necessarily
>> been solved in the best possible way. Just an outline of some things
>> which are considered. What I've seen of the Topex/Poseidon work has
>> been very good, so I'm inclined to accept their figure as accurate (to
>> the limit they gave, I think it was +- 1 mm/yr).

Steve Nerem, Chet Koblinsky, Brian Beckley and I had an article in the
Topex Poseidon Special Issue of JGR oceans which appeared in December 1994.
(pages 24565-24583 Vol 99, No. C12 in JGR oceans)

The expected rate of 1.5 mm/yr is very hard to detect and currently still
obscured by noise (take a look at the formal error, our 1 sigma is 5 to 6
mm/year and we still see rather different rate estimates for different
periods in the data). Our conclusion is that we probably need 5 to 10
years of satellite altimeter data to detect a statistical significant trend,
although I must admit that opinions differ on this point.

Another estimate of global sea level rise comes from simple tide gauge
records that go back a few hunderd years in some cases. Along the Dutch coast
(and also on a global scale) we see a trend of the order of 10 cm per hunderd
year which may be caused by global sea level rise. However, there are also
many other phenomena playing a role such as post glacial rebound and land
subsidence which may hamper meaningful interpretation of tide gauge data.

In any case, I still don't think that we are in trouble here in the lowlands,
the sea walls are 0.5 meter above the highest water level (=spring tide +
storm surge combination). Even a 5 mm/year trend would allow +/- 100 years
to improve the infrastructure. IMHO the sea is not the problem, levies near
rivers used to be a second priority in the maintenance scheme until last
winter as you may have noticed in the press hysteria around this subject.

Hope this helps,

Ernst Schrama

----------------------------------------------------------------------
Ernst J.O. (Ejo) Schrama, Delft University of Technology, Faculty of
Geodetic Engineering, Thijsseweg 11, 2629 JA Delft, The Netherlands.
tel/fax : (31) 15 78 4975/3711, e-mail: sch...@geo.tudelft.nl
homepage : http://d11t.geo.tudelft.nl/~fmr/people/schrama.html

Dave Halliwell

unread,
May 10, 1995, 3:00:00 AM5/10/95
to
I've been leaving Grant and Hugh to argue this out for the last while,
as our news feed has been a bit slow. I want to address to points: one
regarding thermal conductivity that neither Grant nor Hugh have
considered, and one regarding radiation that Hugh brings up in this post.

Hugh Easton <Hu...@daflight.demon.co.uk> writes:

>On 14 April I posted the message which started this thread. In it I
>mentioned the recent events in Antarctica - the breakup of the Wordie ice
>shelf and the more recent partial disintegration of the Larsen ice shelf -
>and put forward a possible explanation: that infrared heat radiation could
>travel significant distances through ice. This would allow heat to travel
>much more quickly through large volumes of ice (such as glaciers and polar
>ice sheets) than might be expected from laboratory measurements of heat
>conduction (which would, presumably, be made over comparatively short
>distances of a few centimetres or less).

[further discussion of radiative properties of ice and snow deleted]

Both Grant and Hugh seem to have ignored the fact that IR radiation
transfer in snow or ice is not just a matter of how far incident
radiation will penetrate. The medium will also be _emitting_ IR
radiation, both upwards and downwards. The _net_ IR flux at any point is
the number that matters for overall energy transfer, not the
unidirectional transmission that has been the focus of the discussion.

What will the net IR flux be? Well, it depends on emissivities and
absorptivities, so the discussion hasn't beeen entirely irrelevant.
However, the net IR flux can be basically considered to be influenced by
temperature _gradient_. In an isothermal material of uniform properties,
net IR will be zero! As a temperature gradient is imposed, for whatever
reason, net IR will become non-zero, with energy movement from hot to
cold.

So what, you say? Well, it just so happens that energy movement along
a temperature gradient is also what happens with thermal conduction. Any
method of measuring thermal conductivity that I know of involves imposing
a temperature gradient and monitoring either time-dependent temperatures
or energy fluxes, UNDER THE PRESUMPTION THAT CONDUCTION IS THE PROCESS
TRANSFERING THE ENERGY. Typically, this will be referred to as "apparent
thermal conductivity" in situations where other energy transfer
mechanisms play a partial role (e.g. vapour distillation in wet soils).

The challenge in measuring thermal conductivity would be to do so _in_
_isolation_from_ the radiative effects that Hugh wants to impose. In
other words, published measurements of "thermal conductivity" for snow or
ice will already include a component that is possibly due to radiative
transfer rather than true conduction. I have never, in years of working
with thermal properties of things like snow and soil, encountered a
situation where any effort was put in to isolating the IR radiative
transfer from true conduction in measuring thermal conductivity.

Solar radiation penetation is a different matter, though, since it
normally won't be present in thermal conductivity measurements and it has
no reason to be related to an imposed temperature gradient. As a result,
penetration of *solar* radiation into ice and snow _is_ an important
additional factor in melt. Nobody that knows what they are doing in ice
and snow would ignore this factor. It is easily observed to cause
internal melting in ice.

>Snow's insulating properties have presumably not changed a great deal in
>the last 150 years, but the quantity of infrared reradiated back from the
>sky undoubtedly has. Infrared is emitted back to the surface by greenhouse
>gases, by clouds and by anything else that tends to increase the general
>murkiness of the atmosphere. Over the last 150 years CO2 levels have
>increased by 25 percent and within the last 50 years a number of extremely
>powerful manmade greenhouse gases have been added to the atmosphere. These
>all emit infrared back to the surface, so that an insulated radiator cannot
>reach as low a temperature now as it could 150 years ago. From what little
>I know the effect is quite large, several tens of degrees C - perhaps
>someone more knowledgeable in this area could comment.

I'm afraid that I would have to agree with the "what little I know"
part of your sentence.

Atmospheric counter-radiation is related to two things: atmospheric
temperature, and atmospheric radiative properties (amongst which we
include greenhouse gases as Hugh discusses, clouds, etc., as being
important variables). Atmospheric temperature is linked to ground surface
temperature by both radiative and convective heat transfer. In practical
terms, over large areas we won't see surfaces that are wildly different
in temperature from the overlying air. A net IR radiative flux at the
surface typically won't get worse than -100 to -150 W/m^2 (the negative
value indicating that the surface emits more than it receives from the
atmosphere).

For CO2 radiative changes we are talking about a few W/m^2 as
transient changes, BUT the net IR radiative changes at the surface are
negligible in the long term because of other links between surface and
atmospheric temperatures. Several tens of degrees C is way out of line.

Hugh's discussion of an insulated radiator has two characteristics
that make it different from the large ice sheet he wants to alter: the
insulated radiator is small enough that it doesn't affect local air
temperatures, and the insulation is good enough that the surface can't
extract energy from the body of the object to counteract its surface
cooling. There is no way to thermally uncouple an ice sheet from the
overlying atmosphere, and if a snow cover was as good an insulator as
Hugh wants it to be then it wouldn't be able to transfer its surface
temperature change to the depths of the ice sheet.

>Although my original theory was shown to be wrong, this modification to it
>could go a long way towards explaining the recent events in Antarctica,
>glaciers melting and "surging", the retreat of polar sea ice etc. If the
>effect is of sufficient magnitude then it means that polar ice is indeed
>much less stable than previously thought. That would greatly increase the
>possibility of a catastrophic sea level rise in the near future, and
>provide a compelling argument for taking action now to deal with the
>problem of greenhouse gas emissions.

This modification to it is just as speculative and unsupported as the
original hypothesis. Back to the drawing board, Hugh.

--

Dave Halliwell I don't speak for my employers, and you
Edmonton, Alberta shouldn't expect them to speak for me.

Grant W. Petty

unread,
May 12, 1995, 3:00:00 AM5/12/95
to
In article <3oqo1j$h...@minotaur.nofc.forestry.ca>,
Dave Halliwell <dhal...@nofc.forestry.ca> wrote:

...

> [further discussion of radiative properties of ice and snow deleted]
>
> Both Grant and Hugh seem to have ignored the fact that IR radiation
> transfer in snow or ice is not just a matter of how far incident
> radiation will penetrate. The medium will also be _emitting_ IR
> radiation, both upwards and downwards. The _net_ IR flux at any point is
> the number that matters for overall energy transfer, not the
> unidirectional transmission that has been the focus of the discussion.
>
> What will the net IR flux be? Well, it depends on emissivities and
> absorptivities, so the discussion hasn't beeen entirely irrelevant.
> However, the net IR flux can be basically considered to be influenced by
> temperature _gradient_. In an isothermal material of uniform properties,
> net IR will be zero! As a temperature gradient is imposed, for whatever
> reason, net IR will become non-zero, with energy movement from hot to
> cold.


I'm glad Dave raised this point, though I think it was already implicit
in both Hugh's and my arguments.

To elaborate on Dave's remark a little, one can easily derive an
approximate expression for IR heat transfer that is exactly analogous
to heat transfer by conduction, to wit:

net flux (power / unit area) = - C*dT/dx

In the case of "ordinary" heat conduction, C is just the thermal
conductivity (or diffusion coefficient).

In the case of thermal radiation, one can make some reasonable
approximating assumptions (e.g., weak, linear temperature change
on scales comparable to the e-folding length for radiative
propagation), in which case:


infty
/
C ~ | (1/k) (dB/dT) d-wavelength
/
0

where k is the wavelength-dependent absorption coefficient (units of
1/distance) and B is the Planck function (units power per area per
unit solid angle per unit wavelength) describing blackbody emission as
a function of temperature and wavelength. I think there is also
factor of pi (or 2*pi?) in front of the integral (I didn't try to
keep track of such details in my back-of-the-envelope derivation).

For the special case that k is constant over the important range of
wavelength, the above integral boils down to something like

(4/k)*sigma*T^3

where sigma is the Stefan-Boltzmann constant. Thus

net flux (power / unit area) ~ sigma*T^3 *(dT/dtau)

where tau = k*x = non-dimensional optical depth. In short, thermal IR
transfer is approximately proportional both to the temperature change
measured over one e-folding length for radiative absorption and to the
cube of the absolute temperature.

>
> So what, you say? Well, it just so happens that energy movement along
> a temperature gradient is also what happens with thermal conduction. Any
> method of measuring thermal conductivity that I know of involves imposing
> a temperature gradient and monitoring either time-dependent temperatures
> or energy fluxes, UNDER THE PRESUMPTION THAT CONDUCTION IS THE PROCESS
> TRANSFERING THE ENERGY. Typically, this will be referred to as "apparent
> thermal conductivity" in situations where other energy transfer
> mechanisms play a partial role (e.g. vapour distillation in wet soils).
>

This is completely true, and I am embarrassed that it didn't occur to
me to point this out myself.

In any event, it could still be interesting to compute the radiative
thermal diffusion coefficient defined by the above integral and
compare it with published values for the thermal conductivity of ice.
I would guess that the former will turn out to be a negligible
fraction of the latter.

It would also be interesting to find out whether there ARE substances
other than gases (since we *know* it is true for many of them) for
which the "radiative" component of the thermal conductivity is
comparable to, or greater than, the "kinetic" component. These would
have to be materials that are quite transparent to thermal IR
radiation.

>

...

>
>> Although my original theory was shown to be wrong, this modification to it
>> could go a long way towards explaining the recent events in Antarctica,
>> glaciers melting and "surging", the retreat of polar sea ice etc. If the
>> effect is of sufficient magnitude then it means that polar ice is indeed
>> much less stable than previously thought. That would greatly increase the
>> possibility of a catastrophic sea level rise in the near future, and
>> provide a compelling argument for taking action now to deal with the
>> problem of greenhouse gas emissions.
>
> This modification to it is just as speculative and unsupported as the
> original hypothesis. Back to the drawing board, Hugh.
>


I'm afraid I'd have to agree.


- Grant

btco...@iastate.edu

unread,
May 12, 1995, 3:00:00 AM5/12/95
to
In article <3ovr12$l...@mozo.cc.purdue.edu>,

Grant W. Petty <gpe...@rain.atms.purdue.edu> wrote:
>In article <3oqo1j$h...@minotaur.nofc.forestry.ca>,
>Dave Halliwell <dhal...@nofc.forestry.ca> wrote:
>
>> [further discussion of radiative properties of ice and snow deleted]
>>
>> Both Grant and Hugh seem to have ignored the fact that IR radiation
>> transfer in snow or ice is not just a matter of how far incident
>> radiation will penetrate. The medium will also be _emitting_ IR
>> radiation, both upwards and downwards. The _net_ IR flux at any point is
>> the number that matters for overall energy transfer, not the
>> unidirectional transmission that has been the focus of the discussion.
>>
>> What will the net IR flux be? Well, it depends on emissivities and
>> absorptivities, so the discussion hasn't beeen entirely irrelevant.
>
[MEGA-snip]

>
>In any event, it could still be interesting to compute the radiative
>thermal diffusion coefficient defined by the above integral and
>compare it with published values for the thermal conductivity of ice.
>I would guess that the former will turn out to be a negligible
>fraction of the latter.

I would also guess that based on my experience with UHV (ultra high
vacuum) gas phase chemistry (where radiative energy transfer becomes
important), and I would be backed up by roughly twenty years of
chemical physics literature.

>It would also be interesting to find out whether there ARE substances
>other than gases (since we *know* it is true for many of them) for

^^^^^^
Do we?

>which the "radiative" component of the thermal conductivity is
>comparable to, or greater than, the "kinetic" component. These would
>have to be materials that are quite transparent to thermal IR
>radiation.
>

[snip]

Please remember that the frequencies at which a material will emit
strongly are identically the frequencies at which a material will
*absorb* strongly, which precludes this as a long-range energy
transfer mechanism. Also, the T^3 dependence which my heavy-handed
editing just removed from the above discussion (sorry) can be
rationalized microscopically in terms of the frequency^3 dependence
of the Einstein spontaneous emission coefficient. Higher frequency
modes emit more strongly but are in the classical limit populated
in proportion to temperature.

Geez, and I was getting tired of this thread! ;-)

Cheers,
Brian
--
Brian Cooper
btco...@iastate.edu

howard rogers

unread,
May 13, 1995, 3:00:00 AM5/13/95
to
try.ca:>
Organization: California State University, Northridge
Distribution:

Dave Halliwell (dhal...@nofc.forestry.ca) wrote:
> Hugh Easton <Hu...@daflight.demon.co.uk> writes:

> >mentioned the recent events in Antarctica - the breakup of the Wordie ice
> >shelf and the more recent partial disintegration of the Larsen ice shelf -

lots deleted

I don't think that we have a long enough period of record to say that such
breakups are out of the ordinary.

If we accept that 'greenhouse warming' is going to produce widespread
reductions in sea ice cover and trigger instability in the marine based W.
Antarctic Ice Sheet and possibly E. Antarctic Ice Sheet, how do we
rationalize that with the orbital forcing theory which indicates
that we will (or at least should) soon be leaving our interglacial and
entering a cooler glacial period?

Hugh Easton

unread,
May 16, 1995, 3:00:00 AM5/16/95
to
In article <3oqo1j$h...@minotaur.nofc.forestry.ca>
dhal...@nofc.forestry.ca "Dave Halliwell" writes:

> I've been leaving Grant and Hugh to argue this out for the last while,
> as our news feed has been a bit slow. I want to address to points: one
> regarding thermal conductivity that neither Grant nor Hugh have
> considered, and one regarding radiation that Hugh brings up in this post.
>
>

> Both Grant and Hugh seem to have ignored the fact that IR radiation
> transfer in snow or ice is not just a matter of how far incident
> radiation will penetrate. The medium will also be _emitting_ IR
> radiation, both upwards and downwards. The _net_ IR flux at any point is
> the number that matters for overall energy transfer, not the
> unidirectional transmission that has been the focus of the discussion.

If you look back at my original posting, you will see that I have taken
this into account, although admittedly I could have explained it a little
more clearly:

=> for a 2.5K temperature difference at 260K the net heat transmission
^^^
=> is s.T2^4 - s.T1^4 = 269.2 - 259.1 or about 10 W/m^2
^^^^^ - notice the IR flux in the
reverse direction
=> (where s is the Boltzmann constant, 5.67 x 10e-8 W/(m^2.T^4), T1 is
=> 260K, T2 is 262.5K).

In any case, given the values for infrared transparency Grant posted,
infrared heat transmission can make at best only a small difference to
the overall rate of heat transfer in solid ice, and since it is only
effective over a relatively small distance it will most likely have
been (inadvertently) incorporated into existing laboratory measurements
anyway.

However, the second point you raise is important and needs further
clarification.

>
> Atmospheric counter-radiation is related to two things: atmospheric
> temperature, and atmospheric radiative properties (amongst which we
> include greenhouse gases as Hugh discusses, clouds, etc., as being
> important variables). Atmospheric temperature is linked to ground surface
> temperature by both radiative and convective heat transfer. In practical
> terms, over large areas we won't see surfaces that are wildly different
> in temperature from the overlying air.

True enough, but not particularly relevant. Surface temperatures in polar
regions (particularly the Arctic) have been closely monitored for the last
half century and no clear long-term warming trend has emerged (a 2.5 C
temperature rise has apparently taken place in the Antarctic peninsula
over the last 40 years, but this is a local, not a global, phenomenon).
Therefore we know that surface temperatures have not increased, and I was
not suggesting that they had.

Grant's figures indicate that longer wavelength infrared can travel several
centimetres at least through snow. As I suggested last week, provided that
snow has sufficiently good insulating properties this should allow a
snowdrift or a snow-covered surface to function as an 'insulated radiator'.
Temperatures inside an insulated radiator can fall far below the ambient
air temperature, and are ultimately limited only by the efficiency of the
insulation and the amount of infrared radiation reradiated back from the
atmosphere.

Given the fact that snow is an insulator and that it has some infrared
transparency, this effect must operate to an extent in snow. The physical
effect will be that the temperature some centimetres down in a snowpack
will be lower than the surface temperature, and the buildup of greenhouse
gases will have reduced that temperature drop. The two important questions
are: how large was the original temperature drop, and how much smaller is
it now?

>
> For CO2 radiative changes we are talking about a few W/m^2 as
> transient changes, BUT the net IR radiative changes at the surface are
> negligible in the long term because of other links between surface and
> atmospheric temperatures. Several tens of degrees C is way out of line.
>

CO2 levels have increased by about 25 percent since preindustrial times,
but there is a logarithmic rather than a linear relationship between CO2
levels and the strength of the greenhouse effect (due to saturation
effects in the absorbtion bands of CO2). Therefore, the overall effect
of the CO2 increase is a greenhouse effect strengthened by only a few
percent. Given the T^4 relationship between temperature and radiative
heat loss, only a small temperature rise (probably less than 1 C) is
necessary to offset the CO2 increase so far. Therefore I agree that the
CO2 increase so far is unlikely to have had much effect on snow's
efficiency as an insulated radiator.

However, that is by no means the whole story. Remember, we are not talking
about the normal infrared spectrum of a blackbody at 250 K (or thereabouts).
We are talking about the small part of that spectrum that can penetrate
through several centimetres of snow. Absorbtion by the snow prevents
wavelengths much shorter than 100um from penetrating through, and, while
longer wavelengths can penetrate easily, they carry too little energy to
be significant. What we have in effect is a fairly narrow 'window'
through which infrared radiation can escape.

CO2 has comparatively narrow absorbtion bands in the infrared, but it is
nonetheless a powerful greenhouse gas because it absorbs strongly near
Earths's peak emissivity of 10um. However, I doubt whether it absorbs much
radiation at wavelengths approaching 100um. That means that the infrared
which does manage to penetrate through snow could probably escape unimpeded
to space with very little radiated back from the atmosphere. Until about
50 years ago.

Since then, two manmade gases in particular have been added in ever
increasing quantities to the atmosphere: CFC-11 and CFC-12. Although they
are better known for their ozone-destroying qualities, these two gases are
also extremely efficient greenhouse gases. The reason is that they have much
broader absorbtion spectra than CO2 and absorb in parts of the infrared
spectrum which were previously free from interference. Also, since their
absorbtion bands are not saturated their greenhouse effect increases
linearly rather than logarithmically with concentration.

So... do CFCs absorb strongly near 100um? Unfortunately I just don't know,
but it would be interesting to find out.

>
> --
>
> Dave Halliwell I don't speak for my employers, and you
> Edmonton, Alberta shouldn't expect them to speak for me.
>

--
Hugh Easton <Hu...@daflight.demon.co.uk>

howard rogers

unread,
May 16, 1995, 3:00:00 AM5/16/95
to
William Connolley (w...@unixa.nerc-keyworth.ac.uk) wrote:

> In article p...@dewey.csun.edu, hbge...@huey.csun.edu (howard rogers) writes:
> >I don't think that we have a long enough period of record to say that such
> >breakups are out of the ordinary.

> How long do you want? We know those iceshelves have been there since the start of this
> century and are now (partially) gone.

The start of the century is just 95 short years. How can you possibly
infer that 'greenhouse warming is the cause of the breakup. We do not
know if this is the case.
> >If we accept that 'greenhouse warming' is going to ...cut... how do we


> >rationalize that with the orbital forcing theory which indicates

> >that we will ... soon be leaving our interglacial and


> >entering a cooler glacial period?

> By getting our timescales correct.
> Global warming is likely to occur within the next century.
> Orbital forcing won't significantly change for 1000 years.

There is strong evidence to suggest that temps. are rising, again the
cause is uncertain. It is also known that many of the worlds glaciers are
expanding - make of that what you will.

> - William Connolley


A J Mims

unread,
May 16, 1995, 3:00:00 AM5/16/95
to
In <3p75cg$f...@kwuz.nerc-keyworth.ac.uk> w...@unixa.nerc-keyworth.ac.uk

(William Connolley) writes:
>
>In article p...@dewey.csun.edu, hbge...@huey.csun.edu (howard rogers)
writes:
>>Dave Halliwell (dhal...@nofc.forestry.ca) wrote:
>>> Hugh Easton <Hu...@daflight.demon.co.uk> writes:
>>> >mentioned the recent events in Antarctica - the breakup of the
Wordie ice
>>> >shelf and the more recent partial disintegration of the Larsen ice
shelf -
>>I don't think that we have a long enough period of record to say that
such
>>breakups are out of the ordinary.
>
>How long do you want? We know those iceshelves have been there since
the start of this
>century and are now (partially) gone.
>
>>If we accept that 'greenhouse warming' is going to ...cut... how do
we
>>rationalize that with the orbital forcing theory which indicates
>>that we will ... soon be leaving our interglacial and
>>entering a cooler glacial period?
>
>By getting our timescales correct.
>Global warming is likely to occur within the next century.
>Orbital forcing won't significantly change for 1000 years.
>
Perhaps the "breakup"of the ice shelf is only a form of "calving" and
indicates a cooling instead of a warming. I believe that in the last
major cool period it was recorded that there were more icebergs further
south in the Atlantic. If the Earth were warming and the oceans rising
[as implied by the melting ice shelf theory] then we would surely know
it in Huntington Beach. Every relatively high tide overflows into the
traffic lanes of Pacific Coast Highway. Luckily the last ten years
have not shown a rise.

William Connolley

unread,
May 17, 1995, 3:00:00 AM5/17/95
to
In article 3...@dewey.csun.edu, hbge...@huey.csun.edu (howard rogers) writes:

>William Connolley (w...@unixa.nerc-keyworth.ac.uk) wrote:
>> In article p...@dewey.csun.edu, hbge...@huey.csun.edu (howard rogers) writes:
>> >I don't think that we have a long enough period of record to say that such
>> >breakups are out of the ordinary.
>> We know those iceshelves have been there since the start of this
>> century and are now (partially) gone.
>The start of the century is just 95 short years. How can you possibly
>infer that 'greenhouse warming is the cause of the breakup. We do not
>know if this is the case.
Don't put words in my mouth. Read my post - I said they have been around since the
start of the century and are now (partially) gone - nothing about cause.
For pictures and press release about the iceshelf breakup, see:
http://www.nbs.ac.uk/public/icd/bas_publ.html

>It is also known that many of the worlds glaciers are
>expanding - make of that what you will.

Quite frankly, guv, this is rubbish. *Some* glaciers are advancing, but the majority
are retreating. To quote from the IPCC II working group (March 95, marked
"do not cite" ;-):
During the last century there has been a massive loss and retreat of mountain
glaciers, a reduction in the depth of permafrost, and evidence of later freeze-up
and earlier break-up of river and lake ice in many northern countries.
See: http://www.usgcrp.gov/ipcc/grev/text/spm.txt
[ps - don't confuse IPCC II with the more famous IPCC I]

- William Connolley
w...@bas.ac.uk (not whatever the head of this post may say)
http://www.nbs.ac.uk/public/icd/wmc


William Connolley

unread,
May 17, 1995, 3:00:00 AM5/17/95
to
In article h...@ixnews3.ix.netcom.com, a...@ix.netcom.com (A J Mims) writes:
>Perhaps the "breakup"of the ice shelf is only a form of "calving" and
>indicates a cooling instead of a warming.
No.
1. There is a recorded temperature rise of 2.5 oC over the last 50 years in
the Antarctic Peninsula region.
2. The iceshelfs have not broken up in a way characteristic of calving.
3. You would not expect cooling to lead to contraction of the iceshelf - quite
the reverse.

>I believe that in the last
>major cool period it was recorded that there were more icebergs further
>south in the Atlantic.

Well, isn't this exactly what you expect in a cool period? The bergs can get
farther south before they melt 'cos its colder.

>If the Earth were warming and the oceans rising
>[as implied by the melting ice shelf theory] then we would surely know
>it in Huntington Beach. Every relatively high tide overflows into the
>traffic lanes of Pacific Coast Highway. Luckily the last ten years
>have not shown a rise.

Because of the motions of the continents, trying to infer sealevel rise
(or lack of it) from any one point is a waste of time. The shore of Southern
England is sinking at a rate of X (sorry, can't remember the number) into the
sea. Is this sea level rise? Well maybe a bit, but mostly its 'cos Scotland is
going upwards now the ice sheet has melted.

William Connolley - w...@bas.ac.uk


Dave Halliwell

unread,
May 17, 1995, 3:00:00 AM5/17/95
to
Hugh Easton <Hu...@daflight.demon.co.uk> writes:

>In article <3oqo1j$h...@minotaur.nofc.forestry.ca>
> dhal...@nofc.forestry.ca "Dave Halliwell" writes:

>> Both Grant and Hugh seem to have ignored the fact that IR radiation
>> transfer in snow or ice is not just a matter of how far incident
>> radiation will penetrate. The medium will also be _emitting_ IR
>> radiation, both upwards and downwards. The _net_ IR flux at any point is
>> the number that matters for overall energy transfer, not the
>> unidirectional transmission that has been the focus of the discussion.

>If you look back at my original posting, you will see that I have taken
>this into account, although admittedly I could have explained it a little
>more clearly:

>=> for a 2.5K temperature difference at 260K the net heat transmission
> ^^^
>=> is s.T2^4 - s.T1^4 = 269.2 - 259.1 or about 10 W/m^2
> ^^^^^ - notice the IR flux in the
> reverse direction
>=> (where s is the Boltzmann constant, 5.67 x 10e-8 W/(m^2.T^4), T1 is
>=> 260K, T2 is 262.5K).

This is still a drastic oversimplification. Downward-directed IR
flux is a combination of what is locally emitted downward plus what is
transmitted from above. The upward-directed IR flux is the amount locally
emitted upward plus the amount transmitted from below. A proper
evaluation requires combining the two, not looking at one part in
isolation. There are _four_ terms involved, not two: two upward, two
downward, one each of transmitted or emitted (or two transmitted and two
emitted, one in each direction; however you want to divide it).

Grant's e-folding approach is a reasonable *approximation*, which
divides the continuous vertical IR stream into layers thick enough that
assuming complete absorption allows a simplification. However, if you use
that approximation then you have to treat a fixed distance as a variable
number of absorption/reemission steps as radiative properties change. If
you don't understand it, then ask him or me to explain it to you.

>In any case, given the values for infrared transparency Grant posted,
>infrared heat transmission can make at best only a small difference to
>the overall rate of heat transfer in solid ice, and since it is only
>effective over a relatively small distance it will most likely have
>been (inadvertently) incorporated into existing laboratory measurements

>anyway.

"Most likely"? Can you give any experimental procedure that is capable
of seperating the IR flux from the "true conduction"?

>However, the second point you raise is important and needs further
>clarification.

>>
>> Atmospheric counter-radiation is related to two things: atmospheric
>> temperature, and atmospheric radiative properties (amongst which we
>> include greenhouse gases as Hugh discusses, clouds, etc., as being
>> important variables). Atmospheric temperature is linked to ground surface
>> temperature by both radiative and convective heat transfer. In practical
>> terms, over large areas we won't see surfaces that are wildly different
>> in temperature from the overlying air.

>True enough, but not particularly relevant. Surface temperatures in polar
>regions (particularly the Arctic) have been closely monitored for the last
>half century and no clear long-term warming trend has emerged (a 2.5 C
>temperature rise has apparently taken place in the Antarctic peninsula
>over the last 40 years, but this is a local, not a global, phenomenon).
>Therefore we know that surface temperatures have not increased, and I was
>not suggesting that they had.

Read what I wrote again. I am not talking about surface temperature
changes: I am talking about the difference between surface temperature
and near-surface air temperature. Are you using "surface temperature" to
mean "near-surface air temperature"? If so, then we need to clarify some
terminology before we can sort out your confusion.

When I speak of "surface temperature", I am talking about the
temperature at height 0 - the air/ground (or air/ice, or air/object)
interface. The sub-surface is within the material below the surface, the
air is the fluid above the surface. There is also no single sub-surface
or above-surface temperature: each is height-dependent and the gradients
in each medium drive the conductive fluxes.

>Grant's figures indicate that longer wavelength infrared can travel several
>centimetres at least through snow.

...and as something becomes less efficient at absorbing IR, it also
becomes less efficient at emitting IR (at the same wavelengths), so the
increased transmission of IR is at least partially offset by a decreased
emission of IR locally. The total IR flux in either direction is a
balance of these two effects, and this is why your overly-simplistic
analysis of IR fluxes is inappropriate.

> As I suggested last week, provided that
>snow has sufficiently good insulating properties this should allow a
>snowdrift or a snow-covered surface to function as an 'insulated radiator'.
>Temperatures inside an insulated radiator can fall far below the ambient

>air temperature, and are ultimately limited only by the efficiency of the
>insulation and the amount of infrared radiation reradiated back from the
>atmosphere.

Temperatures _inside_ the "insulated radiator", are, well, how can I
say it, INSULATED from what happens at the surface. The only possible way
that IR emission can lead to temperatures far below ambient is if all
other sources of energy (conduction from inside to the surface,
conduction or convection from the air to the surface, other radiative
fluxes, etc.) are cut off. A very thin layer of material in contact
with the surface cools substantially, because it is the sole source of
energy for the radiative IR flux that is required by whatever the surface
temperature currently is