I've pushed an update to the script to the project. It adds reading, verifying and using the standard deviation data. The standard deviations are used to remove outlying temperature observations as defined in Brohan et al.
If an observation is greater than 5 sigma from the normal then it is dropped.
I've recomputed everything and it makes a very minor difference to the results. Here's a graph showing the northern and southern hemisphere and global trends smoothed from the new data. It's barely different from before. But at least I'm doing what's specified in the paper.
Red is northern hemisphere, green is southern and blue is global.
I'm still worried about the limited coverage error and I'm still don't fully get the Met Office response. Will post more when I hear from them.
Here's the updated trend chart for the northern hemisphere with the error bars for 95% confidence from the sub-sampling:
UPDATE: Since I only have land data the chart I should probably be comparing with in Brohan et al. is this one (top chart from Figure 12):
This looks a lot more like the errors shown in my chart, now it's just a question of accounting for the magnitude, since for the 1860s this chart shows an error of about 0.3C whereas my chart has more like 1.4C.
So need to track that down.
If you also look at Figure 12 you can see that the anomaly errors for the sea component of HadCRUT3 are really minimal. That probably explains why the global chart I was looking at before didn't have the same error range as my analysis. Need to stay just looking at the land data.