Attention: The Arctic is to melt mostly by the summer of 2040

George,Y · 2006-12-14 18:46:56

The American Physics Society( or the Earth Physics Society) recently announced a report based on a computer model that the worst possibility for us is that the Arctic will melt except only some small pieces in Greenland by the summer of 2040. They warned that the Arctic only seems to melt at a constant speed only due to people's wrong interpretation of the expontial melting trend as a linear melting trend. So the danger is at some time in the future, the melting speed will get much larger than people's "constant" prediction and start to explode.

It is high time that we paid our sacrifice to curb the Global HEATING! (warming is only Too moderate)

By 2040, how old will you be?

2040, just the DAY AFTER TOMMORROW..............................................................

George,Y · 2006-12-14 18:53:40

I find it convincing for this example:
y=1.0001^n+some random variable with a variation of 0.001
draw y.
At early phase, constant model is best in explaining the graph.
then from some point, linear model is better.
At the end, you may realise it is in fact expontial, but it is toooooo late.

Toast · 2006-12-14 19:10:18

Oh Noes What About ``the Polar Bears!!!

George,Y · 2006-12-14 19:18:07

Yeah, the polar bears have already started to eat their fellows! - another recent report

LQ · 2006-12-14 22:53:51

In the same way that we stoped using freons, in the same way we should stop using carbons

Last edited by LQ (2006-12-14 22:54:19)

mathsyperson · 2006-12-14 23:57:18

This might be kind of unrelated, but I read somewhere that the ice at the Arctic melting wouldn't actually raise the sea level. All of that ice is floating, and because ice gets less dense when it melts, the amount of water that gets put into the ocean would be the same as the amount that was being displaced by the ice before it melted.

Not that that means that Global Warming isn't a huge problem, of course.

MathsIsFun · 2006-12-15 00:58:59

I, too, have heard that the ice melting will not raise sea levels, but that the increase in volume as sea water gets warmer will.

Also melting "land" ice such as glaciers will raise sea levels.

This is the kind of thing you would read about in fiction, and it seems to be coming true.

LQ · 2006-12-15 01:01:32

There is a continent under the ice, if the ice melts, it flows down into the water. Or so I've heard. I've also heard that dinosaurs lived there. Also, the ice might be thicker then the sea level etc. I don't know if that's the case.

Last edited by LQ (2006-12-15 01:04:18)

Patrick · 2006-12-15 02:58:23

How is this whole exponential melting happening? I mean, what makes it happen.

George,Y · 2006-12-15 03:42:32

news on yahoo
news on Times
news on Nationalgeographics

George,Y · 2006-12-15 14:18:16

From the 2nd page of the news on nationalgeographics:
Tremblay explains that the Arctic sea ice is like a giant mirror. It reflects the sun's energy back into space and prevents much of it from being absorbed by the ocean.

But as warmer average temperatures melt the ice, the mirror shrinks. A smaller mirror means that the ocean absorbs more of the sun's energy, which creates further warming.

This warming causes more ice to shrink, which causes more heat absorption.

"It goes into a positive feedback loopa very efficient way of getting rid of the ice cover," Tremblay said.

In addition, climate models suggest that global warming will alter ocean circulation patterns and drive warmer Atlantic waters into the Arctic.

"That is a positive feedback as well," he added. "It enhances the melting of the ice."

So here are the causes of expontial shrinking:

The less the ice, at a larger spead the heat is absorbed and at a larger speed the temperature rises.
The warmer the ocean(the higher the temperature), the more quickly the ice melts.

Let's denote t as time, T as the Temperature, LI to be the Lack of Ice from balance level.
It's fair to say that from some time, the Actic ice gets less than that is necessary to keep the Arctic anual average amount constant, and we can denote the initial lack LIo, while an initial temperature To.

Accordingly, we can translate the sentence sin boldface into the two formulae below:

where m and n are both constants.

Last edited by George,Y (2006-12-16 21:20:29)

George,Y · 2006-12-15 15:48:46

differentiate the second equation by t on both sides:

or

substitute dT/dt by the equivalent in terms of LI and t in the first equation, we can get

Note two functions equal to their 2nd derivative respectively, which are:
C sinh(t) and C cosh(t)

It is okay to conclude the function of Lack of Ice in terms of t shall be:

By knowing the initial condition of LIo and To( hence LI'o), we can determine the function.

Both Sinh(t) and Cosh(t) are more or less expontial

George,Y · 2006-12-15 16:12:20

Sinh'(t)=Cosh(t), Cosh'(t)=Sinh(t);
Sinh(0)=0, Cosh(0)=1

LIo=C[sub]2[/sub]

differentiating the formula of LI and evaluating both sides at t=0, we can solve C[sub]1[/sub] out:
nTo=√m√n C[sub]1[/sub]
C[sub]1[/sub]= (√n/√m)To

Let LIo=m=n=1% , To=300Kelvin(27°C) at some point on the earth.

C[sub]1[/sub]=300, C[sub]2[/sub]=0.01≈0, √m√n=0.01

We can get a function of the Lack of Ice in terms of time like this
LI(t)≈300Sinh(0.01t)=150exp(0.01t)-150exp(-0.01t)

Thus this function clearly illustrates how the Lack of Ice initially seems to grow steadily by the same annual increment then Explodes!!!

Last edited by George,Y (2006-12-15 16:23:25)

LQ · 2006-12-15 23:50:52

Yes, It's called termodynamics.

George,Y · 2006-12-16 21:22:29

MathsIsFun wrote:

I, too, have heard that the ice melting will not raise sea levels, but that the increase in volume as sea water gets warmer will.
Also melting "land" ice such as glaciers will raise sea levels.
This is the kind of thing you would read about in fiction, and it seems to be coming true.

After all, that was science-fiction.

George,Y · 2006-12-16 21:24:23

LQ wrote:

Yes, It's called termodynamics.

Yes, the interaction between ocean temparature and the Arctic Ice.

We may also note that the temperature rises in an expontial manner as well...

LQ · 2006-12-16 21:51:54

Yes, that is sad. What did I tell you? Stop with carbons as you stopped with freons

George,Y · 2006-12-17 15:02:11

LQ wrote:

Yes, that is sad. What did I tell you? Stop with carbons as you stopped with freons

But by what means? The technique to efficiently replace the carbon energy hasn't been invented.:(

LQ · 2006-12-17 20:58:07

For now, we can use wind and solar energy and hydrogen cells in our cars and steal the energy out of the air flow etc. Perhaps make our meatings on the internet. You know, simple things. Like "don't waste your waste in the sea, or the sea will become a waste" That sort of things. Should be fairly simple

Last edited by LQ (2006-12-17 21:03:40)

Toast · 2006-12-17 23:43:11

My science teacher told me that hydrogen fuel cells produce 1000x times the energy of fuel we use today. I'm not that savvy about what they've invented so far, but it would be good if they had an electrolysis engine built into the car so you can power your car with rainwater!
We have a myriad of options to make our future cleaner. I'm sure we will be able to somehow cope with this global warming issue.

LQ · 2006-12-18 01:39:01

Exactly! Not just continuing from wherever we were. Actually stop using carbons. Taking vehicle production into concern, that's like the only thing that we can do to stop this from going too far, right?

George,Y · 2006-12-18 16:22:17

Right, currently what we could do is reduce the use of energy as we can and opt fuel-efficient or non-gasoline vehicles.

Mommas Girl · 2007-03-10 12:59:18

So does this mean all Artic animals will be extinct?

Tigeree · 2007-03-10 13:09:55

that can't be good although they'll might move the polar bears to antarctica

Toast · 2007-03-10 14:39:28

Mass exodus of polar bears... wouldn't that be kinda hard?

Math Is Fun Forum

#1 2006-12-14 18:46:56

Attention: The Arctic is to melt mostly by the summer of 2040

#2 2006-12-14 18:53:40

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#3 2006-12-14 19:10:18

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#4 2006-12-14 19:18:07

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#5 2006-12-14 22:53:51

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#6 2006-12-14 23:57:18

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#7 2006-12-15 00:58:59

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#8 2006-12-15 01:01:32

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#9 2006-12-15 02:58:23

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#10 2006-12-15 03:42:32

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#11 2006-12-15 14:18:16

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#12 2006-12-15 15:48:46

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#13 2006-12-15 16:12:20

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#14 2006-12-15 23:50:52

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#15 2006-12-16 21:22:29

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#16 2006-12-16 21:24:23

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#17 2006-12-16 21:51:54

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#18 2006-12-17 15:02:11

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#19 2006-12-17 20:58:07

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#20 2006-12-17 23:43:11

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#21 2006-12-18 01:39:01

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#22 2006-12-18 16:22:17

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#23 2007-03-10 12:59:18

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#24 2007-03-10 13:09:55

Re: Attention: The Arctic is to melt mostly by the summer of 2040

#25 2007-03-10 14:39:28

Re: Attention: The Arctic is to melt mostly by the summer of 2040

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