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.