How can the change of the Earth's temperature be determined with more than 1/10 K accuracy as IPCC suggests? How can one determine the extent of global warming (expressed as a temperature difference) with such precision? The latest IPCC report states temperature changes to fractions of one degree - without actually knowing the Earth’s absolute temperature! What is the statistical concept that allows for such precise determination of a temperature difference without having an absolute reference (i.e. the Earth’s absolute temperature)?
If we would know the earth`s effective heat capacity one could try and set up an energy balance (using data from space observation), but I doubt that this could be done with such precision? Some guidance would be most appreciated (note: I just entered high school, so please not too complicated). Thanks. Marie
 A: It is difficult to get a precise absolute measurement of the Earth's surface temperature because we don't have thermometers at every point on the Earth.  There are large swaths of the Earth that are largely uninhabited (the Sahara Desert, Antarctica, the oceans).  In mountainous regions of the Earth, the surface temperature can vary widely over a scale of a few kilometers, and to accurately measure the average temperature in such regions, we would have to blanket the area with stupidly large numbers of thermometers.  So while we could come up with an estimate of the Earth's average temperature in absolute terms, there would be a relatively large uncertainty on it because there are large portions of the world where we don't have enough data.
However, we do know that the temperature changes over large distances appear to be correlated with each other.  If it's a cold-than-average month in the valleys of a mountainous region, it's a colder-than-average month in the highlands as well.  Moreover, while a particular thermometer might have local effects that make it consistently read (say) 1°C too high relative to the surrounding area, it could still correctly report the changes in temperature from month to month or year to year.
It might help to think of the following analogy:  I'm sitting about 180 km from the Statue of Liberty right now.   My coffee cup is on the desk next to me.  It would be prohibitively difficult to measure the absolute distance between my coffee cup and the top of the Statue of Liberty's torch to within (say) 10 cm.  However, if I move my coffee cup across my desk, I can tell you how much the distance between my coffee cup and the torch has changed much more easily;  I just need to know the direction from my office to the Statue of Liberty, and a $2 plastic ruler.  In other words, it is much easier to measure the change in this quantity relative to a some baseline than it is to measure the absolute value of this quantity.
A: Temperatures are recorded at many weather stations in lots of countries.
This data has been recorded accurately for many years, then an average is done over 30 years, for example, to get the yearly change to $0.1K$ accuracy.
