Sea Ice anomalies

Since Jaxa resumed posting daily results of Arctic Sea Ice extent, I've been processing the data and posting plots here. I'm thinking of doing an interactive plotter for the various ice measures, similar to the climate plotter.You could choose which years to show.

So I started looking at means and anomalies, and thinking about trend calculations. The general method for anomalies seems to be to take a day-by-day average over some years and calculate discrepancies from that. The number of years is not huge, and there is a spike of variability near the maximum melt, so the daily mean is not free of the fluctuations from which an anomaly is sought. So I tried a multiple regression using trig functions and a secular trend.

An anomaly plot is useful for plotting in that it removes the seasonal oscillation, making the key information more visible. With the trig functions I can use a sidereal year, which gets rid of a minor but awkward leap year issue. I found four harmonics was sufficient as the magnitudes taper quite fast; using five made negligible difference.

I looked at the Jaxa data, and also the Arctic and Antarctic sea extent data from UIUC (Cryosphere Today).



There are two anomalies calculated - without and with trend adjustment. All curves have been very slightly smoothed, with a 5-point binomial filter.

JAXA IJIS

Here's the familiar Jaxa plot with the fitted periodic annual curve.

2012 is marked in black.

Here is the anomaly plot with trend, shown over the years from 2002:

The downtrend is about 65000 sq/m/year. Last years minimum was about 4500000sq km; at that rate of attrition it will be nearly 70 years before it disappears. However, there's no reason to expect that trend to apply over the period, and indeed the minima seem more variable than the general trend.

Now here is the same data plotted over a one year interval. Again 2012 is black. It shows that the anomaly so far this year is mid-range for the decade.


However, plotting the anomaly after allowing for trend shows that so far, 2012 is rather higher than expected.

UIUC Cryosphere Today Arctic

UIUC published data over a much longer period. They do their own anomaly calculations, which are in the data set and published on their website. But these are from the trig function regression. Here is the anomaly plot over years:

The trend is somewhat less than Jaxa, since the period is three times longer. Now the same plot superimposed.

There are now a lot of curves, so I've shown the last ten years with greater thickness.

Finally the trend-removed anomaly plot. Again 2012 is currently fairly high relative to recent years.

UIUC Cryosphere Today Antarctic

Finally, for completeness, the Antarctic data. They are of course six months out of phase, and the trend is up rather than down, though the magnitude is less than Arctic. Here are the anomalies:


The same over years:

and with trend removed:

I've been paged

Again
at WUWT

I responded there at about 7.30pm 29 May here (2.30 am PDST). My posts there now just disappear - I think into the spam bucket. We'll see if it appears.

Arctic Sea Ice - JAXA is back!

JAXA Arctic Sea Ice Extent is back, with a new satellite and a new style. In previous years I have kept a table and plots of the latest figures here. The page is supposed to be updated automatically daily at about 2pm Japan time. In the past JAXA updating has been irregular, and I've resorted to manual updating, which can be irregular at this end. We'll see how it goes this year.

I haven't yet adopted JAXA's new style, with just the current, past extreme years, and some decade averages. I'm still using the old style with the last ten years plotted and tabulated individually. This may change.

My impression so far is that the new data is jumpier than the old. 2012 is a mid-range year so far, but there was a huge melt yesterday. The previous day gained ice, so it may be just noisier.

The link to the data page is top right under pages, and also resources.

April GISS Temp up 0.1°C

TempLS showed a rise in global mean anomaly in April, 2012, from 0.32 °C to 0.52 °C. GISS showed a smaller rise, from 0.46 °C to 0.56 °C. This is the second month in which TempLS substantially exceeded GISS. The satellite indices showed rises comparable with TempLS. Time series graphs are shown here

As usual, I compared the previously posted TempLS distribution to the GISS plot.


Here is GISS:



And here is the previous TempLS spherical harmonics plot:

.

Previous Months

March
February
January
December
November
October
September
August

More data and plots

ANU emails - reactions?

They have been out now for over 24 hours, and in a word, blogwise, zilch.

Simon Turnill made the original FOI request for the emails. He was excitedly chronicling every step in the blogfuss based on reading meanings into comments of the Privacy Commissioner on what might be in the emails, made in the finding on his appeal.

Based on these speculations, WUWT pronounced BREAKING: “Death threats” against Australian climate scientists turn out to be nothing but hype and hot air. But I guess Anthony pronounced Game over.

So now they could actually read them and verify, right? Well, no. Simon Turnill has not posted them. Complete silence there. I posted a comment at WUWT - just one comment in response (we're all bedwetters).

My blog software lets me count how many people tuned in from other sites to link to the emails that I posted. From WUWT, just two. From Bishop Hill, where I also posted a notice and there was some discussion, there were four.

The Australian does have an article, which focusses on the "forced to release" angle. Very little about the outcome of their previous speculations. No mention of the main incident. And they haven't made the release accessible either.

Threats at ANU - emails released - UPDATE

Update 22 May

As Eli notes on the other thread, Deltoid has posted on the Media Watch report on this issue. This is the investigation trumpeted by the Australian headline:

"Media Watch eyes climate scientist death threat claims"

What did they find? The original Canberra Times reports seem well-based. They emphasised a generally threatening environment, with nasty stuff, and did particularly not emphasise death threats. The ABC amped that aspect up a bit. The V-C was reported as referring to death threats over the six month period of Simon Turnill's report, but it now isn't clear if he actually said that.

But they have independently investigated, and again found a definitely threatening environment for climate scientists. They too have a collection of emails received. And they emphasised that the Turnill six-months six scientists FOI request is very limited, and no basis for sweeping assertions that threats have been debunked.

"11 emails. To six scientists. In one university. In one six month period. How on earth do they debunk the Canberra Times's story?"

Their summary:

"One news outlet comes out of it, in our opinion, almost unscathed: Fairfax Media's The Canberra Times. The ABC doesn't look so great, and The Australian looks worst of all."

Eli has more

I have been involved in blog discussions at WUWT and Bishop Hill.

Indeed at WUWT I was honored with an award of crow pie. And told in no uncertain terms of the error of my ways:
You’ve earned troll bin moderation status me thinks because you’d rather believe this fantasy you’ve concocted than facts of the matter at hand. And, the facts are, that there’s no death threats. Game over. – Anthony

As Graham Readfearn notes, the ANU FOI request, on which the latest fuss is based, covers just six named staff at that one University, with threats that actually entered the email system, over a six month period. And ANU only sent around asking for them after a FOI request was received, so they don't include emails that the recipients deleted. So it's a very limited sample. I've summarised some more background here.

However, ANU has now released the emails. I've put a zip-file here. The Privacy Commissioner noted one particular email as:
“In my view, the exchange as described in the email could be regarded as intimidating and at its highest perhaps alluding to a threat.”

It's in Doc_5.pdf. It describes a conference/seminar organised by the University, at which, on the first day, someone "took exception" to a talk on climate change. Then:
"Moreover, before he left, he came to the Fri dinner and showed other participants his gun licence and explained to them how good a sniper he is."

Now I expect that at WUWT they'll say, well, he could be aiming low, or whatever. But it sure sounds like a death hint, at least.

Update
On the other thread a commenter "Colours" draws attention to a comment here where the poster identifies himself as the person who proffered the licence (in his version, a kangaroo culling licence) and gives an alternative non-threatening version of the circumstances.

Update So now that what was in the emails is known, what do we hear from WUWT and co? Nothing. And Simon Turnill, who demanded the emails under FOI, has not posted them. Not said anything. There is a story in the Australian. ANU "forced" to release emails - no mention of the main content.
Update: Simon Turnill has now (5pm Thu) posted the emails with his interpretation.

April 2012 temperatures up 0.2°C

The TempLS analysis, based on GHCNV3 land temperatures and the ERSST sea temps, showed a monthly average of 0.52°C for April, up from 0.32 °C in March. In fact, the March figure had also been revised upward by 0.03°C with late data, so the cumulative rise is 0.33°C since Feb. MSU-RSS satellite temp is also way up (by by 0.26°C).  There are more details at the latest temperature data page.

Update David Appell says that UAH rose even more, by 0.295°C
Further update - on re-reading, I'm not sure if the UAH figure was a rise or an absolute amount.
Latest - Roy Spencer has posted. The new value is 0.30°C, a rise of 0.19°C

Below is the graph (lat/lon) of temperature distribution for April. Still warm in the US, and pretty warm all over.

Update: I have added an interactive spherical projection map for the month. It's useful for seeing the Arctic warming in perspective. It's at the end of the post.






This is done with the GISS colors and temperature intervals, and as usual I'll post a comparison when GISS comes out.
And here, from the data page, is the plot of the major indices for the last four months:

Finally, here is the interactive worldview of April surface temperatures. Just click on the yellow squares to see different views of the Earth. The bottom square is the S pole view. The first click takes a second or two for loading.

Entropy and the greenhouse effect.

Efforts to explain the greenhouse effect are never-ending. Not that it's a hard concept, but the Second Law gets debated as well. In fact, entropy and its transport are very much part of the story.

Some will think that entropy is an abstract notion and can't clarify anything. But its something that can be tracked and budgetted, and that is a useful overlay on regular heat transfer talk. What I'm going to say here isn't any novel physics, and describes no unfamiliar mechanisms. But I found that it helped with my mental accounting.

A while ago I essayed an entropy budget for the Earth. We have a heat flux budget. Every time a heat flux Q arrives at or leaves a region, it carries a flux Q/T of entropy. Here T is absolute temperature at the transfer surface; if it isn't uniform, integration is needed. Entropy is created when sunlight is first absorbed by materials on the Earth, and leaves in the outgoing IR flux. Since it can't be destroyed, and isn't significantly accumulating, the IR must carry it all. That's a constraint worth investigating.

Entropy and heat conservation

We know that energy is conserved, and enters and leaves the Earth as electromagnetic radiation. After allowing for albedo reflection of sunlight, on average (time and space) about 238 W/m2 is absorbed. Since only a tiny fraction can accumulate without causing major warming, it is necessary that about the same flux is emitted as thermal IR. While the heat fluxes are the same, the entropy fluxes are not.

Entropy on entry

Entropy is tied up with free energy - the capacity to do work. Heat engines create entropy by transferring heat from hotter to cooler, increasing 1/T. You can reason backward and identify (not equate) entropy change with the work that could have been done by that heat transfer.

Entropy is created by many irreversible processes in the atmosphere. But the big one is the initial conversion of sunlight. In my earlier budget I attached an estimate of the entropy of the arriving flux. The sun is hot, but not infinitely so, and in principle more work could be extracted from 238 W/m2 arriving from an even hotter source. However, in fact the absorption process would be the same, so it might as well be said that the entropy of the arriving sunlight is zero.

An estimate of the entropy created is then 238/287 W/m2/K, where 287 is the average temperature of the earth. However, this is rough, and really it should be formed as an integral of arriving flux divided by arriving temperature. Note that warmer arrival means less entropy created - this will be important. It means the average estimate is not very good, since sunlight predominantly arrives during summer (and in daylight) - times of above average warmth.

Entropy on exit

That same 238 W/m2 leaves at much lower temperatures, on average. Much is emitted by GHG in the high troposphere, at temperatures about 225K. So it carries much more entropy than was created by the initial thermalisation. That is just as well, because all the happenings that make Earth interesting (eg life) create entropy, and that has to be removed.

Snowball Earth maximizes entropy flux

GHE discussions tend to start with a statement of the uniform temperature at which an Earth-sized spherical black (in IR) body would emit 238 W/m2. That temp is 255°K. This is about 33°K below the average Earth temp, and the difference is attributed to the greenhouse effect. The black body need not be in vacuo - and atmosphere of oxygen and nitrogen, which do not interact with IR, would not affect this calc. But greenhouse gases certainly do.

An interesting, rarely mentioned, significance of this "Snowball Earth", at uniform temperature is that it carries the maximum possible entropy that could be carried by a 238 W/m2 flux (proof appended). Maximum entropy removal. Any variation in space (latitude) or time (diurnal), or emissivity would detract from that.

But Murphy's Law intrudes - no interesting processes can create that entropy. The entropy creation at 255K is also a maximum, and they are equal.

Emerging budget constraints.

Snowball Earth already gives an indication of how an entropy budget affects global warming. Entropy export is bounded from above. Anything that reduces it must be balanced, and that must mean a reduction in entropy generation, ie surface warming. Also anything that generates entropy in other ways must cause warming at the point where sunlight is absorbed.

Inhomogeneous snowball

The very entry-level snowball has uniform irradiation etc which is very unrealistic. vatiation affects entropy transport. But there is one thing that can be said about a snowball Earth that has latitudinal variation, rotates, and even has seasons. None of these create substantial entropy (there is some local conduction, and with a nonb-GHG atmosphere, there may be more). So though export is reduced, export and import still pretty much balance.

There's an implication here if you're trying to maintain a cool Earth. While inhomogeneity on export hurts, on import it's your friend. You get less entropy at the same average temperature. Or at fixed entropy, can run at a lower average temperature.

Introduction of GHG's

GHG's do a number of things to impact the entropy budget. They raise the point of emission, which combines with the lapse rate to make emission from a cooler location. That helps with entropy export per unit flux, but the cold reduces the flux. That is made up from flux in atmospheric window frequencies, direct from the warm surface.

The nett result is a negative for entropy export. Remember, the optimum was uniform temperature, and anything that diverts from that, spatially, temporally, or in this case, spectrally, diminishes total entropy export. And the nett result is less entropy at thermalisation - ie warming.

But GHG's have another effect. A large part of the heat flux must now be transported from the surface to the emission point. In the IR-absorbing wavelength bands, that happens by repeated emission and absorption. Photons are more likely to be absorbed by gas cooler than their emission point - that's how the transport occurs. Each such pairing creates entropy. And again, this has to be compensated by surface warming.

In fact, this can be quantified. At frequencies where the optical depth is substantially greater than 1, the transport process follows a Fourier law - flux proportional to temperature gradient. Then entropy production per unit volume follows the rule:

E_V = (k/T²) ∇T • ∇T

where k is the effective conductivity.

Because entropy export is capped, that entropy production too has to be compensated by reduced entropy creation - ie warmer thermalisation.

Summary

It helps to add entropy accounting to the study of heat transfer underlying the Greenhouse Effect. Entropy export is constrained, and so any effects that limit it further or create extra entropy in other ways require a reduction in the main entropy generation, which is thernalisation of insolation. That means the thermalisation must take place at a higher temperature - ie warming.

Appendix - uniform temperature for black sphere is maximum entropy exporter.

Here's a proof re instantaneous spatial distribution using Lagrange multipliers. Suppose the world is divided up into areas A_i, each at temperature T_i. Then total flux is fixed at
F=ΣσA_iT_i⁴.

The rate of entropy export is
E=ΣσA_iT_i³.

The Lagrange formulation maximises
ΣσA_iT_i³+λΣσA_iT_i⁴-F)
over T_i and λ (the Lagrange multiplier)

This gives
3σA_iT_i²+4λσA_iT_i³=0

or T_i=-3/4λ for all i
ie uniform T.