And even if you ignore this guy's point about nonequilibrium and just accept the most straightforward definition - what most people think of as "average" - even that is very problematic. The straightforward definition would say something like: take the temperature of every point on the earth, add 'em up, and divide by the number of points. (Rather: take the normalized surface-integral of the temperature function over the earth's surface.)
But how in the heck do you do that? It's not like we have a thermometer sitting on each square-inch, square-foot, or even square-mile of the earth. We simple don't know what the temperature is in most places. What about out in the middle of the ocean? (Do you have any idea how HUGE the Pacific Ocean is?) We have to rely on shipping routes, or infer the temperature from satellite data, which relies on a model, which may be wrong.
In reality, we only measure "the temperature" on some tiny tiny fraction of the globe, at a bunch of points. So in practice what people have to do is interpolate what the temperature is likely to be in between those points. And then take the "average" of that. But that interpolation process embodies a model in itself.
In other words, even gauging something as seemingly straightforward as the "average temperature" relies upon models. Even if it's today's "average temperature", to say nothing of the "average temperature in 1900 or 1400.
This is something that few people apprehend.
And the change in the average that is measured is less than one unit of measure.
We still occupy only a tiny percentage of the Antarctic and Arctic cirlces. We only recently began to care what was the temperature in Africa, Asia, and South America, and even in rural areas of North America and Europe. Calibrated instruments are an essential part of any rigorous scientific study, and the discovery that a metrologist was careless casts doubt on the result of the study. Cold fusion is a good example of this.
We can not ascertain the precision of the thermometers in places where the temperature has been recorded for hundreds of years. Although many scientists were very careful in the years gone by, many ordinary people and some scientists were not careful. We can not even say with certainty that they actually read the thermometers. Prior to the cold war, what mattered was if it was 'hot' or 'cold.' Even if a person like a farmer did care, his thermometer may have been imprecise. Standardization is a relatively new concept. And who can blame generations past for keeping less than meticulous records? Few people would look at their data collections and think that in 2007, someone will be very concerned if it was 72 or 73 degrees. It feels like 72 and I have other things to do.
Exactly right. I am a seismic software engineer dealing with massive amounts of digital data to form images of the sub-ocean floor. We have to process traces, filter them, etc. An average just does not give much information whatsoever. The entire Earth could actually be cooling and in one location the temperature has spiked (outlier) causing the average to go up. In this case, a reason for the spike needs to be examined and not the average.
And I agree with you about the inherent riskiness of interpolation. Even when trying to interpolate trace data it is still a work in progress to get it "somewhat" correct.