05 April 2011

Starting to work with data

Let's suppose you have no particular axe to grind and are wondering about what 2011's average temperature will look like.  What are some things you would do?  First, of course, is try to get some data to work with.  I'm choosing the NCDC global land and sea temperatures, annual average.  If you prefer some other source, go with that.  And if you're interested in something entirely different than this, have a go with that data source.  I'll be talking about methods of dealing with data, not anything unique to annual average global mean 2 meter air temperatures.

Next is to do some basic looking around the data.  That includes plotting it, finding the maximum, the minimum, the average, and the standard deviation.  Since you're thinking about making a prediction of 2011, you also want to take a look at how things change from year to year.  What does the plot of year to year change look like?  What are the maximum, minimum, average, and standard deviations of change?

 Anomaly Change Maximum 0.6183 0.2493 Minimum -0.4146 -0.2595 Average 0.0086 0.0058 Standard Deviation 0.252 0.098

The bulk statistics, as usual, aren't terribly informative, but they do give us a sense of what is going on and that is important for getting started with data.  The record high temperature was 0.6183 (in 2005, statistically indistinguishable from 2010's 0.6158).  The record fastest year to year warming was 0.2493 degrees, from 1976 to 1977.  0.2405 from 1956 to 1957, and 0.2024 from 1996 to 1997.  On the cold side, the record coldest year was -0.4146 degrees (below the 1901-2000 average) in 1911.  Record cooling was -0.2595 from 1963-1964; with -0.2482 from 1973-1974 and -0.2217 from 1953-1954.

The standard deviation tells us something about how much spread there is in the values away from their means.  We don't expect to see many that are more than 2 standard deviations away from the mean.

For all that I don't show many plots here, I do think it's important to look at them yourself.  Without looking at the plots to know better, you'd be tempted to forecast this year to be about the average, plus or minus a standard deviation.  So you'd call for an anomaly of 0.0086 plus or minus 0.252.  At that point, I'd be happy to take up a bet against you!  Because I've looked at the plot and done a little more math.  Here's the plot of temperatures:

One thing we see is that the temperatures are not random from year to year.  A cold year tends to be followed by a cold year, and a warm year tends to be followed by another warm year.  The easier way to be quantitative about this is to look at the year to year changes:

Although our table above assures us that the average change is not zero -- being +0.0058 degrees/year -- I defy anybody to pick that up from eyeball examination of the figure.  Likewise, it's hard to say by eye that there's a trend in these numbers.  The good part to that is that, unlike the temperatures themselves, the changes are (to eyeball inspection) pretty random.  They go up, they go down.  We see few changes more than 2 standard deviations away from the average, as expected for random numbers.  And negative values occur throughout the time period, as do positive values.

That means we can make a better-informed guess about 2011's temperatures -- that they'll be the same as last year, plus the average change (0.0058 K/year), and plus or minus the annual variability (0.098 K).  So, for 2011, our simple prediction is 0.6216 plus or minus 0.098.  That's both quite a bit warmer than the previous, even more simple, prediction of 0.0086, and quite a bit more confident -- variation of 0.098 vs. 0.252.

To make a serious prediction, of course, we'd want something more intelligent than the present simple methods.  For instance, you'd probably want to consider whether the current changes are represented well by the 130 year average.  You'd also want to include some knowledge about how La Nina and El Nino behave -- we're currently in La Nina conditions, which tend to be cold.  And you'd want to include in your uncertainty the possibility of a major volcanic eruption -- such as occurred with Mount Agung in 1963-1964.  You remember those years from above -- they're when the record year to year cooling occurred.

The simple methods give us a start to understanding the variable, and a bit about how it changes.  In this case, in looking at extreme changes tells us more than extreme values.  We do get a sense that the extreme warm values are all recent, and the extreme colds are some time back, which argues for a change of climate but not much beyond that.  The extreme changes, however, point us to some climate events -- volcanoes, El Nino, and La Nina.  The typical changes tell us that it's hard to change the earth's temperature by much very quickly.  0.1 degrees is a large change year to year, and 0.2 is very large.