## 05 August 2010

### Climate -- cycles 1

One of the things we expect about the weather is that it will change.  Following the dictum, as I do, that climate is what you expect and weather is what you get, change is part of climate.  But what changes do we expect?  One sort of change we -- those of us living in middle or high latitudes (above, say, 30 N, or 30 S) -- expect is that winter will be colder than summer.  Namely, we expect an annual cycle to temperature.

As part of a different project, I've computed the size of the annual cycle in the 2 meter air temperature.  (When meteorologists talk about 'surface air temperature', it really means the air 2 meters above the ground). The scale is degrees Celsius for the amplitude -- the difference between the average temperature and the warmest, or between average and coldest. If you want the range between the warmest part of the annual cycle and coldest, double this number. If you want the amplitude in Fahrenheit, double it (well, multiply by 1.8).

This is a beautiful scientific picture. Why, may not be immediately obvious, and there is more to the story than the annual cycle.

One thing is, remember that I like time series analysis, and some of the concepts from there, I'm using here.  In saying 'annual cycle', I actually mean a perfect sine wave that goes from peak to peak in exactly 1 year.  While the seasons do repeat on a 1 year basis, they don't do it precisely on a perfect sine wave.  In the sense of music, there are overtones.  Not just 1 cycle per year, but also 2 cycles and 3 cycles.  Those figures are below and I'll get to them in more detail later.

I confess that the beauty of the picture is not the color scheme or labelling, or pretty much any graphic arts aspect.  The beauty is in the science.  On seeing the picture, several ideas leap to mind:
• Annual cycle is higher over land than water
• Annual cycle is higher on eastern sides of continents than western
• Annual cycle is higher at high latitudes than low latitudes
All seem pretty reasonable at the casual eyeball level.  Putting them together, we'd expect the greatest annual cycle to be on the eastern side of a continent at high latitudes.  Siberia fits that bill well, and we do see the greatest annual cycle in eastern Siberia -- about 65 N, 130 E, 27 C!  (warmest to coldest of 54 C, 97 F!).  So that's a good start.

But here's the fun: let's try to get rigorous about it.  Is it always the case that the cycle is larger farther to the pole (still being on land, and just as far east)?  Well, no.  Antarctica is certainly farther to the pole than 65 degrees -- it goes all the way to 90, and poleward of 78 it is all land -- there's no western edge to the continent.  Yet its annual cycle is not as large as Siberia's.  More interesting, the largest annual cycles in the Antarctic are seen at the edge of the Ross Sce Shelf and the Filchner-Ronne ice shelf (Weddell Sea).  Edge of the continent rather than interior.  We also see that in southeastern Mongolia, the annual cycle is larger than in the part of Siberia to its immediate north, and for a good distance.

Hmm.  An idea of mine is that when you have a fairly decent general rule, if something breaks the rule, you can learn something interesting by studying it.  Exceptions are more interesting in science than rule-following.

Let's now take a look at the 2 cycles per year (semi-annual cycle) figure:

A quick look at the color bar tells us that the magnitudes are substantially smaller -- maximum is only 10 C instead of 27 C.  It's also quite striking, though, that the Arctic and Antarctic are the places with the largest amplitude for this cycle.  Also northernmost Siberia and Alaska, Hudson Bay, southern Baffin Bay and ... central India (!?).

Aside from India, the places with high amplitude semi-annual cycles a) are places that experience at least 1 day of no sun at all (namely, they're above the polar circles, 66.5 N or S) or b) have sea ice cover.  But some places that have sea ice cover (the Sea of Okhotsk, for instance) don't have a large annual cycle.  So probably we will wind up at a more complex rule.

The size of the semi-annual cycle in Antarctica is so great that it has a 'coreless winter' (van Loon's excellent term).  At the same time as the annual cycle is heading for its coldest temperatures, the semi-annual is heading for its warmest.  And with 8-10 C amplitude, that offsets a lot of the coldness you'd otherwise see.  Instead of steadily cooling off through the winter, the way, say, Siberia does (notice that Siberia doesn't have much of a semi-annual cycle), Antarctica gets cold soon, but then temperatures hold relatively steady until spring.

And we still don't know what's up with India.  (Actually, I do, but that's because I plotted some other figures.)  Some further research to be done.

At 3 cycles per year (ter-annual), the sizes are even smaller -- now reaching only up to 2.7 C.  Almost all the places with large ter-annual cycles are sea ice places, particularly the Ross Sea, Baffin Bay, north of Eastern Siberia and Western North America, and the Sea of Okhotsk.
Excluding the sea ice places, we see northern India and the Tibetan plateau as regions with large amplitudes.  What leads to that?

Since these are expectable features of temperatures -- getting warmer and colder on a regular schedule, by observable amounts -- they're climate.  (Yes, I used at least 30 years of data!).  If we want to understand climate, these are features to understand.  If we think we have a good model for climate, they're figures to compare against.  And ideally, you'll develop a theory that can predict all these observations.

No grand final answers.  Mostly just observations.  But they're observations that strongly invite you (me, anybody interested in science) to try to answer.  The annual cycle portion of this started being studied over 90 years ago -- C. E. P. Brooks, Continentality and temperature, Quarterly Journal of the Royal Meteorological Society, 43, 159-174, 1917.  (He examined more factors than just the three I mentioned.)

I do have the numbers, and will be happy to make them available once we figure out how.  They're on an irregular grid (the spacing in longitude is regular, but the edges of the boxes in latitude are different distances apart).  I prefer working with this because it is how the data were originally developed.  But I realize that most people don't like that sort of data, and it is certainly harder to work with.  I could also construct a best approximation data set that is on a regular grid.  It would be 2 degrees spacing in latitude and longitude.  What's best, though?  Spreadsheets with latitude and longitude in a column and row respectively?  Simply listing off latitude-longitude-amplitude (for each cycle) in a plain text file?

My analysis used as its input the NCEP/NCAR reanalysis from 1962 to 2007.  The reason for that odd set of years is my other project, which starts when the International Earth Rotation Service starts providing daily observations.

An aside: One of the thing people in my fields develop is a fair knowledge of geography.  Given the number of place names I mentioned above, you see why.  It basically amounts to another sort of vocabulary.  If you want to study the earth, it helps to be able to name the place you're looking at.

Arthur said...

This was a really nice overview, I had no idea there were such strong harmonics that were isolated in such a way. Also it illuminates a discussion I had on "deltoid" a few weeks ago about the magnitude of the annual cycle over the oceans. Thanks for this!

jacob l said...

a couple of months ago I tried plotting
the standard derivative of the past 130 years(1880-2009+) of monthly anomalies.
I created it from the data created from NASA's gistemp program.
any thoughts?
image

Penguindreams said...

arthur:
I knew ahead of time what the annual cycle looked like. And a fair notion of the 2 cycles per year, since I'd read van Loon 25 or so years ago. The 3 cycles per year was a surprise and makes me want to go back and compute 4 cycles per year as well. For my other project, I didn't need it. But, after we kick it around a little, I'll go back.

jacob:
I think you mean standard deviation.

It is indeed another interesting figure, though their color bar isn't very good. Also the lack of labels for latitude-longitude. If I'm guessing correctly, the left hand side is at 180 W, North and South America towards the left hand side of the figure.

What you have there is an interesting figure to compare with the annual cycle figure. Since you're looking at anomalies, the annual cycle has been removed. You're looking at how much variation there is away from the standard annual cycle.

The interesting parts (to me) are
a) Areas with large annual cycle also have large variability. Why would this be true?
b) ... except for the tropical Pacific ocean. Do we know of a climate process that occurs in that part of the world?

jacob l said...

Penguindreams: yes it should be standard deviation not derivative.
I'm still playing around and the left hand side is 180w.
The bright blue in the tropical pacific is around the el-nino region.
I'm just not sure where to go from here?
Thanks for noticing jacobl

Penguindreams said...

jacob:
"Where do we go from here?" is one of the great questions for science. Sometimes the answer is 'nowhere', and sometimes the answer turns out to be spectacular (invent quantum mechanics, general relativity, ...).

I don't know the answer here. I'll suggest a few things (even without answers, I can have ideas). One thing is to go back to what prompted you to look at the standard deviation of the monthly temperatures in the first place. I assume it was a question about some part of how climate works.

In looking at my figure for the annual cycle, then, you've added a second chunk of information. The first general rule I have is that if I get a second chunk of information, I try to see what's similar, and what's different, as compared to my first chunk.

The (to my eyes) first major similarity is that areas with high annual cycles also usually have large standard deviations. First points for further research are whether this is always true, how true is it (how strong is the correlation), and why should there be any connection at all? For some of these, you'll need my numbers for the size of the annual cycle, which I'll be happy to send you.

The first major difference is that the El Nino region shows up as an area of large standard deviation, but has a very low annual cycle. Why does the El Nino region break our previous rule? If it's broken in the El Nino region, are there any other regions that violate it? -- While eyeball inspection of plots is often a good way to start, plots can hide as much as they show, which might include other areas that violate the rule. Again, you'd want to get in to the numbers.

This last doesn't mean that it's worthless to work on the numbers yourself. First, if your goal is understanding, your work will certainly help you to that understanding. Second, even if the initial science was done a long time ago, you have far more data and computational resources available to you than anybody in the world had until extremely recently. That, plus a good question to answer, makes for good science.

It also leads to my offer: If you pursue this, I'll be happy to post your results as a guest post on the blog here. Whatever question you settle on as most interesting to you, is probably interesting to me and others, so I'd like to see the answer. And how you go about pursuing the answer will be interesting to readers here in the sense of my 'doing science' label.

S2 said...

"More interesting, the largest annual cycles in the Antarctic are seen at the edge of the Ross Ice Shelf and the Filchner-Ronne ice shelf (Weddell Sea). "

Altitude? Antarctica is generally pretty high, the Ross & the Ronne shelves are at a much lower elevation.

I am not sure how well that would work for Mongolia/Siberia, though. The Gobi desert is quite high, but there are some big mountain ranges to it's north.

i am intrigued by the semi-annual cycles - I would expect to see solar-driven cycles at the equator, since the sun crosses it twice a year - but not at the poles. Some kind of atmospheric effect driven by tropical insolation?

Penguindreams said...

S2:
Altitude tends to go the other way -- greater variability at higher elevations. Hence your observation of the Gobi. So probably not the source of the ice shelf edge cycle amplitude. (Plus Brooks found elevation to be significant in his paper). My bet is the sea ice.

You're right about the equatorial semi-annual cycle. It is indeed large compared to the annual cycle. That was one of my other unshown figures -- divide the semi-annual cycle amplitude by the annual cycle.

The reason you don't see it in my plots is that the tropics have small cycle amplitudes compared to the rest of the globe. This is an example of what I mentioned to jacob where graphics can hide interesting information. The larger amplitudes elsewhere swamp the interesting tropical behavior.

jacob l said...

guest post, But THANKYOU for noticing

http://www.flickr.com/photos/52782029@N06/4877550420/

ps: this time I used panoply to create the graph looking at the old code it was year to year NOT month to month, I was comparing gistemp to model E output and compressing to year to year was the easiest way I could think of
again Thankyou

Trakar said...

Is that a red streak through New Mexico as well?

Bayesian Bouffant, FCD said...

So far, 2010 is the world's hottest year on record, NOAA data show

Is the statistical outlier of 1998, so popular amongst climate change denialists, about to be sunk?

Penguindreams said...

jacob:
Much better figure!

Where to go from here ... pretty much the question I was working with in the previous answer. If you'd like to work with numbers, I can help you with the ones I made for the size of the annual cycle and such. Just write me at bobg AT radix dot net.

Bayesian:
I guess my days looking at ice ages have left me a little jaded. Tiny wiggles on the curves, like 1998 vs. 2005 vs. 2010, don't impress me. 2010 may be warmer than 1998, but it tells us little more than the converse answer. On the other hand, 1998 was during a massive El-Nino and extremely active sun, while 2010 includes a marginal El Nino (perhaps coming to a cool, La Nina phase) and a marginally active sun. For 2010 to be 'in the running' is a bit surprising, as the weather effects that normally matter are not in its favor.

The climate trend, 20-30 years, remains positive, and will pretty much regardless of what happens this year. Climate is (still) warming. (As you know, but I think the 20-30 year business can do with some repetition.)

Penguindreams said...

trakar:
The only red I see is in the Ross and Weddell seas, Antarctica, and in Siberia. New Mexico and Mexico are far to the low end of annual cycle amplitude.