# Fun diversion – How long until Antarctic ice touches South America?

Eric Worrall writes:

Based on the current rate of Antarctic ice growth, how long until an ice bridge forms between South America and Antarctica?

Lets start with a simplification – if you squint hard Antarctica is a circle. Antarctica, according to Wikipedia, is 14 million square miles. Sea ice this year covered 20 million square miles. So what is the radius of a 34 million square mile circle?

area = PI x radius ^ 2

so

(34,000,000 / PI) ^ 0.5 = 3289 miles

So the radius of our “circular” Antarctica is approximately 3289 miles.

According to Wikipedia, the distance between Antarctica and South America is 500 miles. http://en.wikipedia.org/wiki/Drake_Passage So we need to calculate, what is the perfectly circular volume of sea ice required to increase the radius by another 500 miles?

Using our area calculation,

Area = PI x radius ^ 2

Area = PI * (3289 + 500) ^ 2 = 45 million square miles.

Since 34 million square miles (the land area of Antarctica + sea ice) is already taken, to increase the radius of Antarctica enough to close the gap, ice growth needs to fill in another 11 million square miles.

At say 300,000 square miles growth per year (lets not forget, this year busted records by 600,000 square miles), and via my drastically simplified calculation, we could expect Antarctic ice to close the Drake passage in 36 years – by 2050.

Interestingly 2055 – 2060 is the peak of the coming Little Ice Age event predicted by Dr. Khabibullo Abdusamatov, head of the space research sector of the Russian Academy of Sciences’ astronomical observatory, in his press release in 2006.

http://en.ria.ru/russia/20060825/53143686.html

This is a very rough calculation, so please don’t take it as a firm prediction – I am most definitely not a polar ice or ocean expert. There are many other factors, such as the brutal winds and currents which blast through the Drake Passage, which would likely impede the formation of sea ice. On the other hand, the growth of ice would increase the albedo of an enormous area of ocean, causing more sunlight to be reflected back into space – though as we are talking about polar ocean, it doesn’t receive much sunlight to start with.

Story Title:

One line summary of story: The growth of Antarctic ice

5 1 vote
Article Rating
Inline Feedbacks
R. Shearer
September 23, 2014 7:36 pm

Sounds about right. More than close enough for government work.

ShrNfr
September 23, 2014 8:03 pm

Unfortunately, from my experience, our government does not work.

mike18xx
September 24, 2014 2:42 am

The government has been accomplishing its agenda with great efficiency.
— It’s just what *you* want.

joe crew
September 24, 2014 12:06 pm

At least not on this topic! AMEN

Claudius
September 25, 2014 2:42 am

Sure the government works. They’ve been busting their collective, Marxist/socialist backsides trying to saddle and ride this global warming hoax. ‘Er horse. And their backsides were already cracked.

Richard G
September 25, 2014 1:48 am

It’s sounds very chilling to me.

PaulC
September 23, 2014 7:41 pm

The closest part of Antarctica to South America may also be the warmest.
A number of active underwater volcanoes have been reported in this region and this may extend this estimate.

Jimbo
September 24, 2014 1:51 am

Let’s not go down the Warmist’s route. The problem with estimates / predictions like this is that they will most likely fail due to an ever changing climate. Dr. Peter Wadhams has said that the Arctic ocean will be ‘ice-free’ no later than 2016.

ROM
September 24, 2014 3:08 am

Jimbo
“Lets not go down the Warmist’s route”
I heartily concur!
.As the global temperatures have plateaued for a decade and a half and as this fact sinks in, the Skeptic, and I’m as skeptical as one gets, are increasingly showing signs of taking up the warmist theme of making what could easily be seen in the future as another science destroying bout of unsubstantiated predictions for a future cooling world where predictions, to gain increasing recognition for their proposers are constantly increased in volume and extent as to the new set of climatic dangers suposedly facing mankind all over again.
We’ve had enough of truly stupid and totally irrational planet dooming predictions from the rabid far left watermelon eco-loons including numerous so called scientists, or at least they have some letters after their names which they assume gives them the right to call themselves scientists, who have demonstrated their personal and mindless inability through the extremism of their predictions to think and behave in a rational, considered and thoughtful manner as befits a genuine scientist.
So as skeptics lets not also be sucked in to that prediction game as to do so will mean that those of us on the skeptic side who have tried to keep our beliefs and understandings firmly fixed in the realities of the great swings in climate that Nature regularly imposes on the planet are not eventually seen to be no better than the mindless, rabid and ultimately failed warmists and their catastrophic climate cult fixation.
To paraphrase Jimbo again;
Let us a skeptics not now also go down through the warmist prediction morass for there is nothing at the end except disappointment, despair, fear, dismay, distress, disparagement and complete denigration and ultimately a total loss of trust in the integrity and honesty and clear sighted-ness of those Skeptics who so openly and so forcefully and through the passing of many years, stood tall for truth and honesty in science and politics through all of the worst that could be thrown at them by the warmists over the past two decades

September 23, 2014 7:45 pm

I had previously predicted 2050, so 2055 seems entirely reasonable. Got me banned at Grist. LOL

Sun Spot
September 23, 2014 7:46 pm

Haven’t the GCM’s already model the Antarctic ice bridge to South America ?
/sarc

cdandy
September 23, 2014 7:50 pm

That only takes into account growth from one side certianly if ice formation is occuring from the Antartic side and it is cold enough to reach South America there will be ice formation form the South American side like happens in the shallower water every year in the Arctic.

RACookPE1978
Editor
September 23, 2014 8:19 pm

The Antarctic sea ice growth is actually very even all the way around the continent.

Truthseeker
September 23, 2014 8:27 pm

Actually … no. Look at the picture. The area in white (ice plus land) is roughly circular. However the land portion is not circular. That means that the sea ice growth is not very even at all.

RACookPE1978
Editor
September 23, 2014 8:40 pm

False.
The fixed shelf ice is NOT included in NSIDC’s sea ice calculations and records. The result is a nice, even circle around the total area of Antarctica + shelf ice.

Truthseeker
September 23, 2014 10:49 pm

“… even all the way around the continent.”
Continent is land, not shelf ice. The growth of the sea ice is very limited around the Trinity penisula compared to the rest of the continent.

Editor
September 23, 2014 7:50 pm

I think it’s too stormy there – winds and waves will break up new ice in that region and keep it well flushed.

TRM
September 23, 2014 7:57 pm

True. Maybe a better question is when will ships stop going through there?

upcountrywater
September 24, 2014 1:29 pm

Then the Panama Canal raises its rates 10 fold..
At the moment the canal saves a distance of 8,000 miles….
The bill for a standard fee for a container ship that fits the locks is about \$350,000.00 !

Richard G
September 25, 2014 1:59 am

The Chinese are working on a new canal through Central America. They must know something. Maybe they are planning on building bigger ships or they don’t want their access to the Atlantic cut off for political reasons or their expecting a lot of icebergs down there in the future.

September 25, 2014 11:55 am

Panama is working on a new Canal. Basically their economy depends upon the revenue from it, and as ships have gotten larger, the existing canal is getting less usage. China is probably a bit late to the party.

RACookPE1978
Editor
September 23, 2014 8:43 pm

Maybe, maybe not. We cannot tell.
The currents will likely keep part of the area clear of surface ice, but at the expense (greater area) of sea ice away from the narrow reaches between of Cape Horn and the Peninsula. Regardless, this is an assuming (amusing ?) exercise to tweak catastro-physicists who proclaim catastrophic loss of Arctic sea ice….

el gordo
September 23, 2014 8:57 pm

It was open during the LIA, probably because of the wild seas, but if it gets colder than the Dalton then all bets are off.

milodonharlani
September 24, 2014 5:48 am

It was open during the Maunder, too, which was the depth of the LIA and colder than the Dalton.

Streetcred
September 24, 2014 1:35 am

Agreed … hell of a Cape to sail though.

Baronstone
September 24, 2014 5:40 am

I managed the trip one time back in 1986 one a friends yacht. I vowed to never make the trip again because it was so brutal, but a few months later I was sailing through the very same stretch of ocean, but for the US Navy. Never again!

exSSNcrew
September 24, 2014 10:55 am

unless it’s done on a submarine, at ~ 400 feet depth! Even then you can feel hurricane strength wave action. The sub I served on went below a hurricane once and it was still a bit roller-coster’ish.

SIGINT EX
September 23, 2014 7:53 pm

Eric !
Not gona happen ! [Oh, your post is a funny funny, I agree. But I must add … ]
Why? Currents!
[Think of the movie ‘Master And Commander: The Far Side of the World’ of a few years ago. Yes, a fiction. And Yes, it gives a sense of sailing the oceans in the 19th century and the odds of survival.]
The southern ocean sea ice area extent took, just, a little pause before the “roll-over” to occur.
🙂

beng
September 24, 2014 8:32 am

Right. Currents are very strong in that area. Any sea-ice will be whisked away.

marvinshafer
September 23, 2014 7:57 pm

LOL, so I would expect to see the following headline in the media soon. “Antarctic Ice expected to collide with South America by 2050….Due to Global Warming”

Paris Paramus
September 23, 2014 7:59 pm

A lot more scientific than the IPCC’s methodology…

LeeHarvey
September 24, 2014 5:12 am

Per IPCC methodology, the estimator must first pull a number out of his posterior, then transpose two digits.
I predict the antarctic ice field will reach Tierra del Fuego by 2006.

TRG
September 23, 2014 8:00 pm

Has there been an ice bridge across that gap at any time in the past? How long ago?

noaaprogrammer
September 23, 2014 8:01 pm

Don’t confuse volume with area: “…what is the perfectly circular volume of sea ice required to increase the radius by another 500 miles?”

RACookPE1978
Editor
September 23, 2014 8:45 pm

Nope! you have to use the partial circular area formulas for a beanie cap.
NOT a flat circle.

noaaprogrammer
September 23, 2014 9:33 pm

You said it: “… partial circular area formulas …” – not “volume formula.”
Show me a “circular volume” formula. Spherical volume formulas – Yes; Spherical surface area formulas – Yes; Circular volume formulas – No! Well, maybe if you employ fractal transformations you can get dimensions higher than 2, but that’s not being done here.

RACookPE1978
Editor
September 23, 2014 10:05 pm

Volume? So, what thickness (depth) of sea ice are you going to assume?
The partial area of a surface of a sphere depends on the sphere’s radius and latitude (in this case) of the cap being analyzed.

noaaprogrammer
September 23, 2014 10:52 pm

Compared to the radius of the Earth and the small “beanie cap” extension of ice to the tip of S. America, the depth of the ice is negligible. In the spirit of the problem as presented, (“…if you squint hard Antarctica is a circle”), a simple projection from spherical 3d to Euclidean 2d is good enough for approximating a length of time.

James Strom
September 24, 2014 6:37 am

“Circular volume” seems like a neologism, but if you were forced to define it would you not perhaps equate it with “cylinder”?

noaaprogrammer
September 24, 2014 3:48 pm

Depending on the axis of movement (translation or rotation) for the circle, you could sweep out a cylinder, sphere, or torus. If scaling is employed while translating, then you can get a frustum, cone, ellipsoid, and any number of weird, unnamed objects.

Dave
September 23, 2014 8:01 pm

When M Mann abandons his climate models….in other words about the same time hell freezes over.

ferdberple
September 23, 2014 8:05 pm

http://en.wikipedia.org/wiki/History_of_Antarctica
snow-covered mountains” beyond the 64° S in 1603
in 1615, they proved that the Tierra del Fuego archipelago was … not connected to the southern land
the pack ice in 52° S in January 1700
ice-cumbered sea nearly in 55° S in 1730
none of them before 1770 reached the Antarctic Circle
On 17 January 1773 the Antarctic Circle was crossed for the first time
reached 67° 15′ S by 39° 35′ E, where their course was stopped by ice.
was stopped by ice in 61° 52′ S by 95° E
compelled after reaching 67° 31′ S to stand north again in 135° W
blocked by ice four days later at 71° 10′ S by 106° 54′ W
On 30 January 1820, Bransfield sighted Trinity Peninsula, the northernmost point of the Antarctic mainland

September 23, 2014 8:34 pm

“71° 10′ S by 106° 54′ W”
For anybody not familiar with Antarctic sea ice extent, map the above using your favorite mapping software.

Bruce Sanson
September 23, 2014 8:05 pm

I was thinking of saying ” 2019, the data is already written moderated and accepted for publication” but I sit on the wrong side of the fence for that.
Actually I think the solar hemispheric bias will drive the PDO negative thus promoting a more active arctic-both in sea-ice growth and hemispheric cooling. In my humble opinion.

beckleybud@gmail.com
September 23, 2014 8:17 pm

Mr Worrall is not using the proper formulas.

The area covered by the ice is not a circle, it is the cap of a sphere.
..
The correct formula is
.
A=2& pi;rh
..
As per this diagram.
..
http://en.wikipedia.org/wiki/Spherical_cap#mediaviewer/File:Spherical_Cap.svg

RACookPE1978
Editor
September 23, 2014 8:35 pm

Yeah – We fixed that.
It is worse than you think.
We only need 12 years to reach Cape Horn.

Travis Casey
September 23, 2014 8:17 pm

I understand albedo in the form of clouds, which do not allow sunlight to reach the earth’s surface, but I’m lost on ground level albedo. Wouldn’t the sunlight reflected off the ice be trapped by the greenhouse gases just the same as radiated heat? Thanks for the help.

September 23, 2014 8:24 pm

During winter in polar regions there is not much sunlight to reflect. At the south pole the sun has been away since March 21st and is just now back again since September 21st.

RACookPE1978
Editor
September 23, 2014 8:34 pm

False. Even at its minimum sea ice extents, the constantly increasing “excess” Antarctic sea ice is reflecting more and more solar energy. At its minimum sea ice extents, the edge of the Antarctic sea averages right at 67.2 south latitude. At that latitude, the Antarctic sea ice receives and reflects sunlight every day of the year.
Even today, at the equinox, the south pole is getting enough solar energy to reflect energy into space!
Not so in the Arctic. The vast majority of Arctic sea ice lays well north of 71 north latitude, and it IS hidden by darkness more than half of the year.
But it is even worse than you think!
When the Arctic sea ice is exposed to 24 hours of sunlight, it is receiving the LEAST solar energy of the entire year – less than 1315 watts/m^2 at top of atmosphere!
When the Antarctic sea ice is exposed to 24 hours per day of sunlight, it is receiving 1410 watts/m^2 at the top of atmosphere.

sleepingbear dunes
September 23, 2014 11:04 pm

RA
When you run through these numbers it makes me want to go out and buy a large globe. A lot easier than the flat maps in visualising what is going on and comparing latitudes in NH to the edges of Antarctic sea ice.

September 23, 2014 8:28 pm

Incoming sunlight is mostly shortwave. It doesn’t get absorbed by GHG’s regardless of which direction it happens to be going. When the shortwave is absorbed by earth surface on the other hand (as in absorbed, not reflected) the surface radiates that energy back out. But since the earth is no where near as hot as the sun, the energy is radiated out at a much longer wave length, and that’s the wavelength GHG’s absorb at.
Here is a graph that should help explain:
http://commons.wikimedia.org/wiki/File:Atmospheric_Transmission.png

Travis Casey
September 23, 2014 8:51 pm

Thank you for that reply davidmhoffer. I was ignorant of the main difference, which you explained clearly. That graph sure makes me wonder what all the CAGWers are in such a tizzie over. LOL.

RACookPE1978
Editor
September 23, 2014 8:49 pm

But Judith Curry measured the much dirtier, multi-year Arctic sea ice albedo as low as 0.38 in late July, with an average low of 0.43 for most oh July and early August. So, not as much energy is reflected from the Arctic as was previously thought.
The Antarctic sea ice is 90% fresh ice, covered with new snow. Its year-round albedo is 0,83 to 0.86 Much, much higher.

mobihci
September 24, 2014 12:44 am

so, you have the obligatory rolling stones reporter there stating half truths and treated as though nothing is wrong with what he says. the scientist is dragged down to this chaps level by using him as a prop, and you must question his motives. typical climate science piece.
the reality is regardless of rapid global co2 increases sea level rise is not accelerating, the arctic and antarctic are tied to natural cycles and while the arctic may be losing a fair bit of sea ice extent antarctica is gaining. sea ice volume losses are guess work, grace and other forms of modelled volume estimates are not available for any reasonable length of time. IPCC models of BOTH arctic and antarctic sea ice extent predict a NEGATIVE trend-
http://www.climatechange2013.org/images/report/WG1AR5_Chapter09_FINAL.pdf
page 789
so it is obvious that our ‘understanding’ of ice loss and sea ice extent is poor. with so many excuses for the cessation of global warming (the one predicted by climate scientists, not the alarmist make it up as you go version), you know the one where co2 in the atmosphere warms the surface and should result in more water vapour as a positive feedback, an upper tropospheric hot spot, INCREASING SURFACE TEMPS etc.. it is just too bloody hard to believe a word any of these snake oil salesmen.

Owen in GA
September 24, 2014 7:31 am

No, The reflected energy is in the shortwave bands that the atmosphere is transparent to. The Greenhouse problem only comes into effect when it is thermalized by absorption then re-emitted in the long wavelength IR bands.

RACookPE1978
Editor
September 23, 2014 8:18 pm

Eric!!!!
You can do better than this!
Now, let’s get serious here.
Radius of the earth = 6371 km.
Area of Antarctic land mass = 14.0 Mkm^2
Area of shelf ice = 3.5 Mkm^2 (NSIDC doesn’t include this in the sea ice extents nor area.)
Sea ice extents at minimum = 2- 2.5 Mkm^2
Minimum total area of ice at sea ice minimum = 14.0 + 3.5 + 2.5 = 20.0 Mkm^2
Today, at maximum sea ice extents = 20.5 Mkm^2,
Area_Maximum = 14.0 + 3.5 + 20.5 = 38.5 Mkm^2
(The usual Antarctic sea ice maximum is actually in 8 – 15 days from now!)
So, the actual latitude for a spherical earth for any Area_Total =
=DEGREES(ASIN(1-(Area_Total)*10^6/(2*PI()*6371^2)))
(using excel “arithmetic” notation)
So, at 2.5 Mkm^2 at minimum, the average latitude of the Antarctic sea ice extents = 67.2 latitude
(right at the southern polar circle.)
And, at the maximum antarctic sea ice record extents of 20.5 Mkm^2, total area = 38.5 Mkm^2, so
the average latitude = 58.1 degrees
Cape Horn = right at 56 degrees south latitude.
But, the ships go around it a little bit south (by about 20 kilometers to clear the rocks and allow for storm winds), so we can accurately use 56.0 degrees – and easily assume that the very narrow Straits of Magellan are frozen over also.
Reversing the above equation, latitude 56.2 requires 43.0 Mkmm^2 of total ice. (if you have a symmetric beanie cap over the south pole.)
43.0 – 14.0 -3.5 = 26.5 Mkm^2 of sea ice extents is needed when the Antarctic sea ice hits Cape Horn.
Net, we need only 6.0 million more kilometers of Antarctic sea ice.
But! Look at the increase in the Antarctic sea ice anomaly in the past 4 years.
2011 = -0.5 Mkm^2
2012 = +0.0 Mkm^2
2013 = +0.5 Mkm^2
2014 = +1.1 (In January)
2014 = +1.6 (in September)
At the recent rate of increase of 500,000 km^ per year, it will take less than 12 years to gain another 6.0 Mkm^2 …. And it is even faster if you include the recent acceleration …

September 23, 2014 8:24 pm

Yes, I should have calculated the area of Antarctica as a surface on a sphere instead of a flat circle – even scarier 🙂

PabloNH
September 23, 2014 9:11 pm

> Area of shelf ice = 3.5 Mkm^2 (NSIDC doesn’t include this in the sea ice extents nor area.)
The area of the ice shelves is about 1.6 million sq km.

RACookPE1978
Editor
September 23, 2014 11:12 pm

Good find. I agree.

PabloNH
September 23, 2014 10:57 pm

I also can’t find a reference claiming that the ice shelves are not included in the 14 million sq. km. Do you have one?

RACookPE1978
Editor
September 23, 2014 11:11 pm

September 23, 2014 8:23 pm

It seems to me that the ice is very close to South Georgia Island which is on the same latitude as the southern tip of South America. So you don’t rally need a perfect circle and I reckon 2025.

September 23, 2014 8:33 pm

Good thing all that ice is on the bottom, if it was on top I’d be afraid it might flip the world over. Good to have coutnerweight like that keeping us northerners up top where we belong… phew.

RACookPE1978
Editor
September 23, 2014 9:09 pm

But ice is lighter than the colder water that is sinking and flowing north so this means it WILL reach a tipping point faster! 8<)

TYoke
September 23, 2014 11:10 pm

Don’t tell Hank Johnson, we wouldn’t want him to get all wound up again.

PabloNH
September 23, 2014 8:35 pm

I know this is a fanciful calculation, but your units – and results are (almost) all wrong.
> Antarctica, according to Wikipedia, is 14 million square miles.
No, 14 million square kilometers.
> Sea ice this year covered 20 million square miles.
20 million square kilometers. And this is ice extent, not area, so “covered” is not accurate. (Antarctic sea ice area is about 16.6 million square kilometers.)
> So the radius of our “circular” Antarctica is approximately 3289 miles
Again, kilometers. And, not really – you’re not accounting for the curvature of the Earth.
> According to Wikipedia, the distance between Antarctica and South America is 500 miles.
This is the distance to the Livingston Island, not Antarctica – but what you’re really after is the area of a circle centered on the south pole and just touching South America. Let’s use Cape Horn, although it’s not part of the mainland. It’s at 56 deg south. The area of a spherical (we’ll assume the earth is a sphere) cap is 2 * pi * r * h = 2 * pi * 6378 km * (1 – sin(56 deg)) * 6378 = about 41 million square km, so we need another 21 million square km, or about twice as much as we have now.
> At say 300,000 square miles growth per year (lets not forget, this year busted records by 600,000 square miles)
Nope. This year’s record was 600,000 sq. km. higher. Assuming half that, 300,000 sq. km. per year, the Drake Passage will be (at least 15%) blocked in 70 years, not 36.

RACookPE1978
Editor
September 23, 2014 8:37 pm

Nope. Your numbers are incorrect. See above.
What formula are you using for latitude vs area?

PabloNH
September 23, 2014 8:45 pm

I forgot to add in the area of Antarctica (14 million sq km) – so we need 6 million, not 20 million sq km.
However, my point about area vs. extent stands. The 20 million sq km “extent” is at least 15% covered. The actual area is 16.6 million sq km.

csanborn
September 23, 2014 8:40 pm

Think of the catastrophic impact on resort beaches as ocean levels drop. Ferry docks throughout the world will be left high and dry. Whales will be beached, Venice will lose it flush waters.

PabloNH
September 23, 2014 8:52 pm

Sea ice does not affect sea levels.

RACookPE1978
Editor
September 23, 2014 9:26 pm

You don’t recognize sarcasm very well, do you? 8<)

Churning
September 23, 2014 8:41 pm

How long to get to Cape Agulhas? Maybe 2-2.5 times as long (eyeball estimate)?

September 23, 2014 8:49 pm

Albedo is more important at the South Pole than at the North as during the summer when that sun is shining on and melting the ice, the Earth is closer to the sun, the increase in albedo with all this extra ice must be huge.

RACookPE1978
Editor
September 23, 2014 9:22 pm

True:
When the Antarctic is exposed to 24 hours of solar energy per day, it is hit by 1407 watts/m^2 at top-of-atmosphere.
When the arctic is exposed to 24 hours of sunlight, that sunlight is only 1315 watts/m^2. Almost 100 watts/meter less.
We calculated that difference for today’s values – not even the mid-summer values you are assuming.
Today, 22-23 September, the 1.6 Million sq kilometers of “excess” Antarctic sea ice is reflecting five times the energy that the Arctic sea ice is receiving.
At 80 north latitude on September 22 at noon on a clear day, a flat surface only receives 106 watts/m^2
If sea ice, 22 watts is absorbed, 84 are reflected back into space
If open ocean, 72 watts are absorbed, and 33 are reflected and lost into space.
At 58 degrees south latitude the excess Arctic sea ice is hit by 515 watts/m^2
If open ocean (which was last year), 478 watts are absorbed, 37 watts are reflected.
if sea ice (this year!), 91 watts are absorbed, and 424 watts are reflected back into space.

PabloNH
September 23, 2014 11:17 pm

> At 80 north latitude on September 22 at noon on a clear day, a flat surface only receives 106 watts/m^2
Where do you get this number? Cos(80 degrees) = about .17. That would be well over 200 watts/m^s (at noon). Are you thinking of the average insolation over 24 hours?
> At 58 degrees south latitude the excess Arctic sea ice is hit by 515 watts/m^2
That would be Antarctic sea ice, I’m pretty sure the sea ice covers very little water this far north (see extent vs. area, and look at the map), and, again, is this an average or a peak value?

RACookPE1978
Editor
September 23, 2014 11:46 pm

No Pablo: You’re using the wrong approximation for air mass. Near the poles, you can’t just use the simple cosine that (almost) works close to the equator.
What attenuation factor are you assuming for your air mass? Polar or near-tropical?

William R.
September 23, 2014 9:01 pm

Haven’t we learned from the warmists about the perils of assuming current run rates continue indefinitely? We do not live in a linear world. More than likely the circumpolar current will keep the straight ice free until something more permanent, like a continent, blocks it’s path.

RACookPE1978
Editor
September 23, 2014 9:13 pm

Yeah. You’re right. But it is more fun to tweak their assumptions and linear scaling.

September 23, 2014 9:15 pm

Yeah. This recent uptick in Antarctic ice is unlikely to be any more significant than in the long term than was the 1998 super el nino. But boy is it fun to bring that graph up on your laptop, spin it around in a meeting, and ask people how that’s even possible….

Jack Hydrazine
September 23, 2014 9:05 pm

No one has mentioned this yet, but the increasing volcanic activity and thus the dust and other aerosols that are lifted into the atmosphere will help increase the growth of ice.
[Why would more dirt increase the growth of ice? .mod]

September 24, 2014 3:26 am

Please refresh my memory about “increasing volcanic activity.” I don’t recall that claim.

Owen in GA
September 24, 2014 8:46 am

I have the same problem skywolfe, I don’t remember global volcanism being any higher.
But as for the mod’s question, if sunlight is dimmed globally by high altitude particles there could be an increase in ice growth, of course it probably balances out later when those particles fall on the ice after a few years and cause hot spots to melt into the ice.

Doug
September 23, 2014 9:07 pm

The [strait] between Antarctica and South America has high winds are swift currents. I don’t think ice could form there and stay put for very long, unless we’re in an ice age.

September 23, 2014 9:14 pm

Good post, an amusing pastime tweaking the “Concerned Ones” noses with linear extrapolations from natural cycles.
But according to the Team solid ice from Antarctica to South America will just be weather.
Two hot days this Fall however will be Climate.

Travis Casey
September 23, 2014 9:26 pm

In response to the question asked in the title, I’m pretty sure we will need to model it in order to form a peer reviewed consensus answer. 🙂

September 23, 2014 10:25 pm

Oh yes, let’s! Albedo of snow/ice varies from 0.8 to 0.4 depending on age, roughness, accumulation of contaminants like dust, so those factors will all have to be modeled. Then there’s albedo of water which varies with angle of incidence anywhere from 0.08 to 0.65 so has to be modeled according to time of day AND time of year 24X365. Then there’s the amount of energy with is required to turn water into ice which is way different in salt water (versus fresh) since the entire water column must cool to the freezing point before ice forms at the top, so the energy calculation changes with distance from shore as the water gets deeper, so a lot more energy involved. We’ll need to include also the amount of energy radiated to space which is lower from ice than from water, so as water area turns to ice, that factor messes up the albedo corrections we did earlier…. and of course we have to take into account that the earth’s orbit is elliptical, and so the amount of TSI changes over the course of the year which has to get fed back into all the albedo adjustments. And with all that stuff going on, the temperature differential between arctic and temperate zones also changes which messes with prevailing winds, hadley cells, and all that. Modelling it should be a piece of cake….

RACookPE1978
Editor
September 23, 2014 10:40 pm

Well, I got all of the modeling done (except for the column of water bit). 8<)
I set latitude of the ice by changing the day-of-year (which uses the 2011-2013 average ice areas) and then allowing the user to assign an anomaly to match the total sea ice she or he wants to look at. Then you can look at all latitudes for the same day, or all of the times of the day for a single latitude.
Except ole davidmhoffer done did fergit the losses side.
Evaporation rate changes with humidity, air temperature, wind speed, and surface type, wave height, and surface temperature.
Conduction and convection losses change with most of them things too.
Yeppers, radiation losses change with air temperature, sky temperatures, sky clarity, surface type, and surface temperature.
He's almost got the going-in side;
Almost left off the change in sunlight at TOA over the year.
Got the change in water's albedo 'bout near right on.
Did leave off the change in atmosphere clarity as a function of latitude AND day-of-year.
Done did fergot to include the Air Mass change as a function of latitude and time of day.
Didn't change the albedo of arctic sea ice with day-of-year.

David A
September 23, 2014 10:53 pm

Its a climate science model, it does not have to be based on anything but the press conference. (emphasis on the “con” in conference)

David A
September 23, 2014 10:56 pm

RA and David, you are both good with numbers, and I bet you think the error estimates for the surface GAT are far larger then anyone admits. Here is a German paper that well supports that view. The error margins for surface GAT just increased 100 fold.

September 23, 2014 10:01 pm

I constantly spent my half an hour to read this weblog’s content daily along with
a mug of coffee.

September 24, 2014 3:11 am

Cheers! I do two cups, both extra bold, cream only.

September 23, 2014 10:25 pm

Antarctic sea ice isn’t evenly distributed by longitude. It extends far north of the Antarctic Circle south of the Atlantic and to a lesser extent Indian Ocean, and is well within the Antarctic Circle south of the Pacific Ocean. The difference is large, approaching 1,000 km.
There are likely several reason’s; the layout of the Antarctic continent, more heat transported southward by the Pacific ocean conveyor, distribution of katabatic winds, ++.
If sea ice does continue to increase, I’d bet on most of the increase being where the furthest northward extents exist already. Which is east of the Magellan Strait. Although sea ice does get blown eastward at a fairly rapid rate, so winds may distribute it fairly evenly.

Joel O'Bryan
September 23, 2014 10:28 pm

Antarctic plate drift should put it contact with the Cape of Good Hope in about 30 million years give take 10 million years.

johnmarshall
September 24, 2014 3:23 am

Unlikely because Africa is moving north east and Antarctica is fairly stationary. Cape Horn may be a different matter.

Michael D
September 23, 2014 10:48 pm

Isn’t that about when the rising ocean starts lapping at the Statue of Liberty ? 🙂
(Extrapolation of similar value).

King of Cool
September 23, 2014 10:49 pm

Forget about the mathematics, what we need is a computer model.
I vote that WUWT applies for a US government loan to begin this program with an initial report to be presented by the project manager at the Lima UN get together in Dec 2014. If Lima does not sound too inviting for whoever goes, don’t forget that there will be a few side trips for the troops up to Machu Picchu. And I believe the coast of Peru has some of the best seafood in the world.
But we should not just rely on a computer model. It must be backed up by actual measurements.
My suggestion is that Leonardo DiCaprio hires out the same mega yacht Topaz from Manchester City Football Club owner Sheikh Mansour which he and his buddies used to watch the World Soccer Cup in Rio de Janeiro.
The yacht should be positioned at Palmer Station on the Antarctic Peninsular at the beginning of winter for the next 5 seasons and be manned by a party of University of NSW volunteers led by Professor Chris Turney and an ABC journalist to take piccies and report progress of the ice.
To prevent boredom during measurement of the the slow daily increase of sea ice in the direction of South America, the team could be given the additional task of counting penguins. And especially for Leonardo there would be the odd opportunity of some soccer on ice with the crew of Palmer Station.
You never know, an ice bridge may be coming faster than we think and we need some dramatic action now.

Owen in GA
September 24, 2014 8:51 am

No loans! You aren’t thinking like a climate scientist…GRANTS! why pay back the money when you can get them to just give it to you.

RoHa
September 23, 2014 11:17 pm

And before long it will reach Australia. I’m a Queenslander, so I already think the Antarctic Circle runs through Tweed Heads. The prospect of actual Glaciers along the Gold Coast really gives me the shivers.

September 24, 2014 4:48 am

LOL – I hear you, last January (in the middle of SH Summer) I visited Brisbane, and shivered because I was cold.

Paul Martin
September 23, 2014 11:19 pm

If an ice bridge did form, disrupting the circulation of the Southern Ocean, it would have consequences for the established circulation patterns in the Atlantic and Pacific.

Nylo
September 23, 2014 11:45 pm

OMG, is this some kind of joke? Given a spherical cow…
I don’t understand the point of this article. To me, it looks totally worthless.

September 24, 2014 12:57 am

It is called ‘HUMOUR’ I believe.

Owen in GA
September 24, 2014 9:25 am

Hey now…a spherical cow makes the problem much easier, and when you change the model to 6 cylinders of appropriate size, the answer really doesn’t change much, but adds to the complexity by a factor of 6. Now we all know that a cow doesn’t resemble anything like 6 cylinders, but a much more complex shape which can be approximated as follow: the head: a cylinder 5cm X30cm (forms upper jaw and nasal part) a cylinder 5cm X 30cm (forms lower jaw) attached to a sphere of radius 10cm with two smaller hemispheres of 3cm (eyes), this is attached to a 10cmX50cm cylinder (neck) which is attached to a 150cmx250cm cylinder(body) etc. We can add to these any number of other shapes, each one adding a little to the total, but adding orders of magnitude to the calculations. The question is at what point does the spherical nature of our initial cow detract from the problem at hand. Of course I always found the part about placing that spherical cow into a vacuum at absolute 0 as the more problematic part of the problem.
The above was typed with tongue firmly planted in cheek. The problem really does illustrate something though. In a radiative physics problem the complexity of the shape does change the answer, but it depends on how much precision you need. For back of envelop estimates, that spherical cow is all the answer you need – it sets the upper limit on how long thermal equilibrium takes. However, if you are asking “how long can I safely expose a real cow to the cold of space (lets forget the vacuum for the moment)?” that is a different level of need for precision, and modeling it down to fractal shape matching may be required.
The problem as it applies to GCMs is they are essentially modeling a spherical cow and wanting an answer that tells us trends to tenths of a degree. I am afraid the spherical cow approach (5×5 degree grid cells?) doesn’t have the level of detail required to observe to the degree of temperature.
This whole article is poking fun at the “let’s take the last few years trend, linearize it and project it to infinity” approach that most climate alarmism is based on.

cnxtim
September 23, 2014 11:57 pm

Couldn’t the south island of NZ get there first? Go for it the Frosty Ferns !

jim wolf of Lewisham High Street.
September 23, 2014 11:57 pm

How long until Antarctic ice touches South America?
Answer when Leonardo Di Caprio can no longer sail around it.

Reply to  jim wolf of Lewisham High Street.
September 24, 2014 3:15 am

From the looks of him it looks like he just got back from training…in Syria!

johnmarshall
Reply to  jim wolf of Lewisham High Street.
September 24, 2014 3:21 am

Who the hell cares what this actor thinks?

September 24, 2014 12:02 am

Do you mean “Drake’s Passage” which is north of Tierra del Fuego or Cape Horn which is south of T. d. F.?

milodonharlani
September 24, 2014 6:14 am

Drake’s Passage is also south of Tierra del Fuego.

September 24, 2014 12:05 am

If the ice does touch South America the ocean currents are not necessarily blocked because the ice would float an the surface and the currents could still flow beneath it.

Sustainabally rogering Leo,s cabin boy
September 24, 2014 12:16 am

http://perezhilton.com/fitperez/2014-06-13-leonardo-dicaprio-takes-super-luxury-yacht-to-brazil-world-cup#.VCJuKRby3At
Here is Captain Leo,s Saudi owned CO2 polluting luxury private yacht .Picture courtesy of bitchy Hollywood celebrity blogger Perez Hilton.

September 24, 2014 12:34 am

Cool calculation. Of course it assumes the current increase is a long term trend. But that’s the same mistake that led the AGW supporters to think the arctic would soon be ice free.
Bob Clark

LeeHarvey
September 24, 2014 5:19 am

And therein lies the source of why such silliness is fun.

SanityP
September 24, 2014 12:48 am

“Hey, South America, is it ok if I touch you down there?”

September 24, 2014 1:43 am

I was just wondering what it would take for Antarctic Sea Ice and the tip of South America to touch. Thanks for the math. Did you notice how the tip of SA is getting a bit frostier with each image of late?
For other math along these lines please see my article, http://pathstoknowledge.net/2012/03/12/how-much-energy-is-required-to-melt-all-the-ice-in-greenland, that asks “How Much Energy Is Required To Melt All The Ice In Greenland?”

Farmer Gez
September 24, 2014 2:46 am

I have a question for the boffins of this blog. What is the climatic effect of the reduced wave action caused by such a large area of normally turbulent sea being ice covered? Colder ? Hotter? The Al Gore effect?

September 24, 2014 3:55 am

Approximately zero as a direct effect.
Secondary effects are mainly decreased heat loss from the oceans. Although ice albedo increases are significantly larger.
Net – increased sea ice causes substantial climate cooling.

Joe P. (in Baltimore where land is sinking and thus sea level rising as opposed to all to ice melting reasons)
September 24, 2014 3:06 am

Eric Opps, despite otherwise informative posts here you based on “[Antartic] Sea ice this year covered 20 million square miles.”
Really 20 million square kilometers by extent, 16.8 sq. km by area for winter max sea ice surrounding Antarctic last week.
http://nsidc.org/arcticseaicenews/charctic-interactive-sea-ice-graph/
http://arctic.atmos.uiuc.edu/cryosphere/antarctic.sea.ice.interactive.html
The metric system is great, we can confuse things in US with rest of planet, in any case, would like to see corrected redo of calculations in metric or standard.
It is also not a perfect circle either with a bit less west of Cape Horn and more everywhere else.
OZ on metric but still drive left side of road, but a good political turning point down under, no doubt sea ice data at recorded record had a turning point too heading North despite false global warming hot air.

johnmarshall
September 24, 2014 3:20 am

This scenario is unlikley because of the Antarctic Circumpolar Current. This powerful current effectively isolates Antartica from the northern warmer waters.
Nice try though.

September 24, 2014 3:44 am

The meme that bugs me most is “Antarctica is melting at an accelerated pace and the meltwater is freshening the salty seas causing increased sea ice extent because of the higher freezing point”…
Has the melt increased in any verifiable way? (Mass loss/gain argument)
Has the salinity of the Oceans changed to a point that is significant enough to increase the freezing point?
Does the fresh meltwater readily mix with the salt water or does it stay on the surface creating the sea ice?
Since most of the continent rarely gets above freezing (even in their Summer,Jan-Feb) is there a calculation to determine the “break even”melting point of land ice when it is below freezing given the amount of incoming solar radiation, the albedo and the ambient temperature? Given the known incoming amount of solar radiation, is there a point at which it is cold enough for the ice not to melt?
Is there a calculation to determine if combined solar radiation and pressure causes melt that overcomes the albedo and temperature constraints? (Is it regelation?) time for my second cup of Java!

RACookPE1978
Editor
September 24, 2014 5:30 am

No clima-catrastro-physicist has ever reported measurements of any of those values, nor – more importantly – the measured change in those values over time.

Richard M
September 24, 2014 8:23 am

Note that almost all of the claimed melting is in the Amundsen Sea. Now, check the picture and you will see the latitude of the sea ice is further south close to Amundsen Sea.
It would seem that particular area is the one that would be seeing the gain if melt-water really had any influence at all. Instead, it is likely the warmer water from the active vulcanism in that area has actually reduced the total amount of sea ice.
Also, note that since this area produces much of the ice that flows towards South America in the circumpolar current, continued geothermal activity would likely extend the time period for sea ice to reach South America. In fact, without this geothermal activity we could be seeing an even larger sea ice extent right now.

September 24, 2014 4:06 am

As a pure math problem, it is a good one. But if you gave it to a student to solve, there would be cries of alarm from the alarmists as to deafen all other news.
As an exercise in weather, it is a fascinating idea. Even during the height of the LIA (well from the 16th century at least), ice did not cover the distance. So the effect on temperatures? Scientists want to know. Alarmists want to politicize how ice forms because of record heat.

Timbo
September 24, 2014 4:19 am

I have a question. Why has no one used the word “unprecedented” yet?

RACookPE1978
Editor
September 24, 2014 5:28 am

We were afraid we were going to misspell it. 8<)

Richard G
September 25, 2014 2:24 am

That word is not in my vocabulary.

September 24, 2014 4:40 am

Ice growings and cold go hand in hand.
Therefore ice growing from the southern point of south America, mostly the eastern side, might reduce the time before south America and Antarctica “meets”.
In fact, considering also potential ice growth from south america makes the “bridge” a little less unrealistic?
Kind regards, Frank

September 24, 2014 4:41 am

But the curents in that spot make the area hard to “conquer” for the ice..

September 24, 2014 4:48 am

The albedo effect of additional ice in the polar daylight reflects energy – a positive feedback. The insulating effect of additional ice in the polar night prevents heat loss from the ocean surface – a negative feedback. Since the incominging sunlight is at a low angle, but the outgoing long wave radiation can go straight up, I suspect the negative feedback has dominance, and the rate of Antarctic ice growth would slow down.

phlogiston
September 24, 2014 5:24 am

Note that Antarctica led the warming leading up to the inception of the Holocene, beginning as early as 20,000 years ago, well in advance of the Bolling-Allerod.
http://onlinelibrary.wiley.com/doi/10.1029/97GL02658/pdf
Why could Antarctica not lead the Holocene termination also?

Richard M
September 24, 2014 8:31 am

This has been one of my thoughts as well. The start of an ice age might take the combination of the right Milankovitch cycle and an increase in the Antarctic sea ice. This is somewhat supported by the observations of more sea ice during the LIA. Just a little more sea ice might have pushed the planet into a glaciation mode.
If this is correct it means it wouldn’t be all that difficult to stop another ice age. Just add a couple of satellites that reflected more solar energy on the sea ice. Wouldn’t have much of an impact on anything else and could keep the sea ice from reaching a critical point.

jeff 5778
September 24, 2014 6:40 am

“This is a very rough calculation, so please don’t take it as a firm prediction – I am most definitely not a polar ice or ocean expert.”
Why would we let your lack of expertise get in the way of a perfectly good prediction. We must act now!

September 24, 2014 7:39 am

@ROM 3:08am.
But we know we jest.
The difference is no one here is demanding that taxpayers world wide surrender their wealth, liberty and future hope to mitigate the imaginary Doom.
Having read the comments I see most of us fail Climatology 101,lacking the prolific use of May.Might. Could and such weasel words, I guess we need the same help that Dr Fruitfly got from the PR firms.
The message must be emotional, appear to contain information and all predictions are to be forecast far enough into the future to avoid exposure.
However after all these years of listening to self professed “serious persons” babbling about the doom from CO2, extrapolated from the lefthand upper quadrant of a cyclic pattern,it is a lot of fun to use real world trends(however temporary) to mock the righteous fools.
The difference I trust, is most of us know we know very little of climate, that we are hardwired to see patterns where none may exist and that we are fully capable of being completely wrong about everything we think we know.
This being the reason I respect the constraints of the scientific method, while having no obligation to respect individual scientists, institutions or authorities.
Show me your work being the key to communication.

jayhd
September 24, 2014 9:34 am

Since the Drake Passage was open during the Little Ice Age, it appears nothing short of a full blown Ice Age would close it. But if you truly don’t mind another ice age, it would be funny.

Eliza
September 24, 2014 10:08 am

Oh XXXX I will be able to by car to Brisbane from here in Sao Paulo. Great won’t have to pay those ridiculously high airplane fares LOL (will use wind powered car)

Eliza
September 24, 2014 10:15 am

Seriously, this could be start of some sort of SH cooling but only in very Southern Latitudes. So far its had absolutely no effect on tropical, sub-tropical or temperate zone (ie Santiago) temperatures over the past 4 years. What is noticeable in my humble view is that it seems the cold air masses around Antarctica are larger but are not extending north (as they did when Antarctica extent was “normal”. It could be a compensating mechanism perhaps….

Eliza
September 24, 2014 10:29 am

Eric Worral :Yes temperatures on the East Coast of Australia do seem to be well below average (not much) but constantly during the past 3 years or so.. Brisbane (24C today), in particular is subject to westerly surface winds (850mb) from huge offshore highs fed by Antarctic air. This in fact may be a real cooler effect from a larger Antarctic, This is of course total suposition on my part. LOL

September 24, 2014 3:42 pm

Here in the SW of Australia, the main effect I’d look for is stronger Southern Ocean cold fronts, resulting in more heavy rainfall events. Although not necessarily more rain, due to several complicating factors.
My anecdotal observation is heavy rainfall events do seem to becoming more frequent. But maybe I didn’t take notice in the past.

F. Ross
September 24, 2014 11:24 am

“How long until Antarctic ice touches South America?”

How can you even ask this question?
I mean, what with all the manmade CO2 going to boil the oceans in the next 50-100 years.

Robert W Turner
September 24, 2014 11:25 am

We shouldn’t fall into the trap that the warmists are stuck in and have been since the 1980s, that of taking a short term trend and extrapolating it indefinitely into the future. But, this is an interesting question. What would the possible climate implications be if this did occur…

RH
September 24, 2014 11:29 am

How long before we can take a snowmobile from South America to New Zealand? That’s what I want to know.

Jukin
September 24, 2014 3:49 pm

Just an engineer that has done heat transfer, the real kind, all of my career, I doubt it will happen due to the massive water energy transfers around the cape. However if it does, it truly is bad news. Real global cooling and cooling is soooooooooooo much worse than warming. If AlGore says it can never happen buy coal futures.

Dirk Pitt
September 24, 2014 5:43 pm

As a taxpayer, I would gladly contribute a small portion of my income tax to building a 5 star resort on the southern tip of South America for climate alarmists to have a place to enjoy their hard earned vacation time. Me, … I’ll settle with Caribbean.

phlogiston
September 24, 2014 6:09 pm

Those arguing that Antarctica is isolated from the rest of the world by the circumpolar current overlook the deep ocean THC circulation. But we’re talking about century-millennial timescales. Colder Antarctica will – at first – increase southern deep water formation and influence global climate in the long term.
There are two stable states of global climate. One in which polar deep water formation energizes deep circulation resulting in more transport of equatorial water to the poles, resulting in smaller ice caps and warmer climate. The other state is when this deep circulation slows down – for instance the gulf stream stops. This state has much larger ice caps and colder (glacial) climate.
The real danger of expanding Antarctic sea ice is that it could interfere with deep circulation and deep water formation, pushing the system towards a switch from one state to the other.

crosspatch
September 24, 2014 10:29 pm

Should it freeze over all the way to S. America it could be a disruptive event. The removal of surface winds could change upwelling and have an impact on global circulation patters. I see that “phlogiston” has just addressed this. I concur.

Ian W
September 25, 2014 4:22 am

The assumption that the ice should expand to fill the Drake Passage is a linear projection that may or may not be valid. However, with a narrowed Drake Passage and volcanic or earthquake activity around the West Antarctic Ice Sheet a break away of a substantial portion of the WAIS perhaps in several large pieces, is possible indeed it is not such an unlikely event. If these large pieces of ice sheet were to be carried into the Drake Passage by ocean currents they could result in a partial blockage of the channel. Occurring at midwinter this could lead to a sea ice bridge. Whether the currents through that narrow passage would allow the blockage to form would be an interesting question. But as Phlogiston says “phlogiston September 24, 2014 at 6:09 pm” A blockage of the Drake Passage leading to disruption of the thermohaline circulation could have an immediate and indeterminate effect on world climate.

Richard G
September 25, 2014 10:39 am

I think the biggest danger would be in dodging high speed icebergs in 40 ft. seas.

Svend Ferdinandsen
September 25, 2014 10:52 am

The only reason that is has not grown to alarmism, is perhaps that it was not on the radar, because of “more ice” and not less. Anyway it seems to be a much more realistic near future than the constant predictions of ice sheets collapsing in a far far away future.
It is in fact worse than the north west passage, that has never really been open.

samAlochaka
September 26, 2014 12:36 am

Has there been any investigation on what has happened to the sum-total of ice? That is Arctic and Antarctic put together? Has the total remained constant, reduced, or increased? I am a lay person, so please answer in simple language.

Sciguy54
September 26, 2014 2:40 pm

BTW, Cryosphere Today seems to be mostly down. Whats Up (or down) With That?
arctic.atmos.uiuc.edu/cryosphere/

Tom Sullivan
September 30, 2014 6:57 pm

Some basic questions are begging for an answer:
1. How far from S Pole to S America islands, and mainland
2. How far does the ice extend already, in the winter
3. What is the remaining distance to be closed by ice expansion

Mike Rossander
October 1, 2014 1:52 pm

Wow, lots of errors in the original post – and they don’t seem to have been consistently corrected in the replies above.
1. As others have noted, the measurements in the article are reported as miles (or square miles) but are actually km (or km^2)
2. The assumption of a flat circle is significantly off from the spherical calculation.
3. Finally, I don’t think the measures of sea ice extent are actually all that good. You can get as good or better an estimate by eyeballing the map and visually estimating the “average” latitude of the sea ice extent.
With that in mind, I get:
average latitude of ice extent (deg): 60
current area under ice = 2*pi*r^2*(1-cos(90-lat)) = 34.2 million km^2
To match RACookPE1978’s estimate of total = 38.5 million km^2, the current sea ice extent would have to be wobbling around the 58th parallel. That does not match any recent image I can find.
Continuing…
approx latitude of the southern tip of SA: 56
target area under ice = 43.6 million km^2
needed ice growth: 9.4 million km^2
at 300k/yr: 31 years
Alternative:
If instead of eyeballing the average latitude of current sea ice extent, you use the real latitude of the ice now closest to Cape Horn, you might get a better approximation of the real needed growth since whatever currents or other factors are distorting the current ice extent from a perfect circle are likely to continue. That would change:
lat current: 61.5
current equivalent area: 31 million km^2
time: 42 years
This alternative is a really weak assumption, however, and is directly contradicted by observations. Antarctic ice extent is well above normal all around Antarctica EXCEPT right at the western peninsula where it is actually below normal. That observation also invalidates the ‘circular growth’ assumption in the main scenario. It was a fun little exercise, though.