If you've been following my posts you might have spotted an oddity: if you run the animation of gridding since 1850 it's pretty clear that there weren't many stations going into the mix up until the 1950s.
This introduces uncertainty when calculating the hemisphere and global figures. To get an idea about how little coverage there was, here's a graph showing the average number of stations used for calculating the monthly trend since 1850 (I've averaged over a year so that the graph is smaller).
In the 1850s there were around 50 stations to cover the whole world. By the 1990 there are over 1400. So the question is, how much uncertainty do the relative paucity of measurements in the 1850s introduce?
The answer in the published literature (see this paper section 6.1 for details) is 'very little'. If you take a look at the Figure 10 (below) from that paper the green error seems almost unchanged from the 1850s to today.
Since that's counter-intuitive that looks like a good place to start in checking the calculations performed. Would you expect 50 stations to give the same accuracy as 1400?
I really need to find the time to process the NCEP/NCAR 40-Year Reanalysis Project data and perform my own calculation of the uncertainty. If anyone else beats me to it, please let me know!