## Thursday, August 11, 2011 ... /////

### CO₂ and ice-free Arctic Summer 2100

In recent 3 days, Andrew Revkin has pleased many climate skeptics by his opinions about the Arctic climate and ecosystems:

On Arctic Ice and Warmth, Past and Future

A Debate on Death Spirals and Arctic Resilience
Building on many recent papers that showed significant variations in the Arctic climate in the past (safely exceeding the recent changes), Revkin decided that there's no reason to be afraid of the Arctic ecosystems because they have survived similar or more dramatic changes in the past. I agree.

Swimming and getting some suntan in the warming Arctic

Nevertheless, I am probably going to repay debt to Revkin, shock some skeptics, and please by alarmists by this following opinion of mine:

I actually find it highly plausible that there will be an ice-free Arctic summer by 2100.

This opinion of mine stands on theoretical as well as empirical grounds. The observational support seems to be more robust among the two. At any rate, there seem to be many good reasons to believe that the Arctic climate is closely correlated with a very limited subset of forcings among which the carbon dioxide is an important one.

Let me start with some "theoretical" comments. First, there are differences between the polar regions on one side and the equatorial or moderate zones on the other side. Richard Lindzen believes that the equatorial temperatures have been constant - within a degree Celsius or so - for millions and maybe billions of years.

I am not sure whether such a bold statement is exactly right - or just an idealized slogan to promote the iris effect - but there surely exist many reasons to think that the variability of the temperature in the tropics is much smaller than it is in the extratropics. First of all, the recent observations show that the temperature variability near the equator is limited. Second of all, it's hotter over there and the same change of the temperature corresponds to a greater change in the energy fluxes. And the energy fluxes are somewhat likely to have the same variability over the globe which means that the temperature variability should be lower near the equator.

Also, there are lots of powerful negative feedbacks related to water vapor that are important exactly near the equator. And yes, the faint young Sun paradox also suggests that the Earth must be capable of regulating its equatorial temperatures much more than we would naively think. I could continue for a while but the main point I believe is that the variability of temperatures near the poles is higher than the variability of temperatures near the equator.

North vs South

Second, the North Pole seems to be different than the South Pole. Almost no temperature change in the recent 50 years has been detected around the Antarctica; on the other hand, the changes in the Arctic seem to be substantial. So it seems that only the Northern polar regions experience the variability we may clearly observe.

This difference between the North and the South impacts the global warming debate. It's perhaps unsurprising that it is always the North - and not the South - that the alarmists refer to. The Arctic just produces "more interesting data" for their case than the Antarctica.

However, it's not just the fearmongers' demagogy in which the North plays a more important role than the South. If you look at the details of the Milankovitch theory of glaciation cycles that was put on firm ground by Gerard Roe in 2006, you will see that it's the ice near the Arctic Circle that is being correlated, via the insolation near the Arctic circle, to the irregularities in the Earth's motion. Again, the North matters and the South doesn't. As far as I understand, if you calculated the Antarctic Circle's insolation, the Milankovitch theory wouldn't work too well.

This difference reduces to some circulations that exist near the North Pole - because of the free ocean over there - but not near the South Pole. Also, it may have something to do with the land near the Arctic Circle: there's a lot of continental ice that can grow and recede over there. On the other hand, almost all of Antarctica sits in the South from the Antarctic Circle (it is closer to the poles) so there's almost no land on the Antarctic Circle itself.

Antarctica is too cold - too close to the pole - to become ice-free; and the places which could grow large continental ice sheets aren't available in the South because there's no land over there. So for all these reasons, the fact that the interesting variability takes place in the North and not the South could be more than just a coincidence.

I almost forgot to say that the clouds in the Arctic are not "purely about cooling". In fact, they are more likely to have a warming effect. The fact that the solar radiation is arriving nearly horizontally most of the time is a part of the reason (especially in the winter): the clouds may reflect the solar radiation to the surface (down instead of up) and help to warm it up! So even if the cloud cover oscillates a lot, its average cooling effect on the surface is much smaller than it is in the mild zones. The same reasoning holds not only for clouds but even for aerosols and other players that are important away from the polar regions.

On the other hand, the greenhouse effect of $CO_2$ is always there in the Arctic because the $CO_2$ is always present and it always absorbs a part of the Earth's thermal radiation that is also there at all times. If you look at the situation, many effects "decouple" in the Arctic while the $CO_2$ greenhouse effect is among those that survive.

Also, the Arctic has some extra phenomena that are not important elsewhere - similar to the ice-albedo feedback. Those may amplify the initial perturbations (positive feedbacks) but on the other hand, they're really "close to being deterministic" (unlike things like the cloudiness): they don't carry "independent slow degrees of freedom". The shape of the sea ice may look complicated but it is almost exactly calculable from other things (air temperature above it) and it has a limited impact on the atmosphere above the ice. So the "turbulent phenomena" (hard to calculate ones) are suppressed near the poles. The polar environment is able to "cleanly amplify" a subset of forcings which is why the Milankovitch effects and even $CO_2$ may become visible in the Arctic temperature/ice data.

Empirical correlation

But let's look at the most important part of the story, the observed data. The graph below was created by Peter Hogarth for John Cook's blog.

Much of it takes the data from a paper by William Chapman and John Walsh. You may also download a gigabyte of bitmaps encoding historical data going back to 1870 from The Cryosphere Today. See the left upper corner of that page for many links.

Now, to be specific, look at the pink curve - the lowest one. It depicts the sea ice extent in millions of squared kilometers in July-August-September of various years; note that the minimum is reached around the mid September and this minimum is obviously even lower than the average of the adjacent 3-month period. (August-September-October would probably have even lower averages of the sea ice extent but it's not a conventional 3-month period.)

The pink curve does look like a hockey stick. More precisely, it is suggestively correlated with the carbon dioxide concentration. Let me be a bit more quantitative. I will assume the $CO_2$ concentrations to obey the "exponential business as usual". It is given by the following empirical formula of mine:
$C(y) = 280+22.3 \exp[(y-1920)/57]\,\,{\rm ppm}$ The formula says that the excess of the $CO_2$ concentration above 280 ppm is exponentially growing so that it reaches 280+22.3 in 1920, about 390 ppm in 2011, and the excess gets multiplied by $e\approx 2.718$ every 57 years so the annual increase of the $CO_2$ emissions is $100/57 = 1.75$ percent.

Of course, if the growth of the $CO_2$ emissions slows down in the future (which is pretty likely) - so that the multiplication of emissions (and excess carbon dioxide) by $e$ will take more than 57 years or we will even converge towards dropping emissions - all my estimates of the "speed of melting" below will become exaggerated (by a factor of two or so if you assume constant emissions from now).

Nevertheless, the sea ice area over the JAS 3-month period, as seen in the graph, may be approximated by
$A_{JAS,\,{\rm lin}} = 11.5 - [C(y)-280] / 27.$ Well, a more scientifically justifiable formula depends on the logarithm of the concentration (because the underlying theory is based on the nearly logarithmic greenhouse effect):
$A_{JAS,\,{\rm log}} = 11.5-11 \log [C(y)/280].$ In both cases, the units are millions of squared kilometers. The two formulae more or less agree before 2011 (and they agree with the pink graph) but the logarithmic formula predicts a less dramatic reduction of the sea ice extent in the future than the linear formula does.

The linear formula drops to zero around 2070 - we're talking about the ice-free average of July, August, and September in a given year - while the more realistic logarithmic formula drops to zero around 2100. So if you believe that the surprisingly convincing correlation between the $CO_2$ concentration and the sea ice extent that is seen on the graphs is more than a coincidence, it is very plausible that sometime in the 21st century, we will see an ice-free moment sometime in the Summer.

Just to be sure, it would take many, many centuries for the sea ice extent to drop to zero in the winter and I won't discuss those "more speculative" forecasts at all. Let me just cover them by the sentence that it is implausible that the Arctic will become ice-free throughout the year in any foreseeable future (even if we assume those persistently exponentially growing $CO_2$ emissions).

Fractal remainders of the temperature

People and Joe Romm make various bets about the ice-free Arctic. Yes, you're pretty safe if you bet that there won't be any ice-free moment in the Arctic in the next 20 years. I don't think that they will really see it in their "active lifetime", to enjoy the money they will win. But as I said, it's plausible that if they were living for 100+ years, they would see it. However, they would probably be too senile to be amazed by the observations (even more senile than Joe Romm is already today).

There is another subtlety that should be considered by all rational people who want to participate in similar bets: the behavior of the ice when its total area becomes very small. Imagine that the ice area drops to 0.5 million squared kilometers. Does it become easier to liquidate the remaining small amount of ice than to reduce ice from 6 to 5.5 million squared kilometers? Or does it become harder?

In other words, is the "most resilient ice" tougher and hard to be killed - which could mean that the Arctic will never be quite ice-free - or does the convergence towards $A=0$ accelerate when $A$ is very small?

I tend to think that the latter answer is correct. There are arguments in both directions and one must carefully compare them. First, there may be local variations of temperatures that make some "local islands of ice" very cold and almost indestructible. In the language of the normal distribution, 1/300 of the sea ice area has ice whose temperature is more than 3 sigma below what is needed for melting - and 3 sigma could be enough to beat the trend for many more decades or centuries.

On the other hand, when the sea ice area is very small, the remaining ice has a larger surface/volume ratio, so it's much easier to warm it up by its thermal contact with the warmer environment. I believe that this effect is probably more important than the previous, opposite one. So there probably won't be any important forces that will try to "preserve the last ice islands". Quite on the contrary, it seems plausible that the path towards "complete extinction" accelerates if the amount of sea ice becomes really small.

Of course, the tight observed correlation between the Arctic sea ice and the $CO_2$ concentration may be just a coincidence. If it's not, then the extrapolation is approximately legitimate. Within 50 years or so, there can be an ice-free moment sometimes in the Summer. Within 100 years or so, the whole 3-month period around the sea ice minimum may be ice-free, too.

Even if it is true, it will probably represent no threat for the ecosystems because similar things have happened in the past (Revkin mentions the end of the last ice age). The polar bear - a mammal, our relatively close cousin :-) - is indeed a rare exception of an animal who just pretends to prefer the life in the ocean but whose main bedroom is still on the land. ;-)

Just think about it: there is no "food" (carbon) richly available on the ice so there can't be any growing (reproducing) life forms living "on the ice" or "depending on the ice" except for life forms such as the polar bears that can quickly run over the ice (hundreds of kilometers), too. Ice is the ultimate lifeless zone (that's why we use fridges and freezers to protect meat against bacterial life) and polar bears are the exception among the "running animals" who boast that they can overcome this difficulty and use ice as a great ally that allows them to find some food beneath the ice. It makes no sense to dream about the "diversity of life" supported by ice itself.

Polar bears easily and logically move away from the pole when they find the sea ice around the poles too risky. If that's not the case, I believe that people in late August 2070 should spend a few million dollars and liberate the polar bears stuck on the shrinking (and, later, completely disappearing) last islands of ice near the pole. (I am less sure that today, we may effectively help the people in August 2070.)

While I view these considerations interesting from a scientific viewpoint - pure curiosity and speculations - and I think there's quite some evidence that the $CO_2$ could really be important for the Arctic climate, much like the Milankovitch (astrophysical) cycles, it's still important to realize that the Arctic is just a tiny (and for us nearly irrelevant, and too cold, anyway) piece of the globe and these insights obviously don't apply to warmer zones.

In the warmer zones, the internal variability of the atmosphere - and especially clouds (and everything that drives them internally or externally), water vapor, aerosols, and other things - are much more important for the climate and its evolution, so the warming trends are very noisy (a substantial portion of the Earth will be cooling) and their average may be between zero or slightly negative numbers (Lindzen's theory of the equator) and something comparable to the recently observed average trends (which are very small).

We shouldn't get carried away and of course, I am not suggesting that there's any climate threat. But still, the correlation between the Arctic ice and the $CO_2$ concentration looks much better than almost all other correlations that are claimed to be relevant.