How should you calculate annual global temperature data? We start with Hadcrut4.5 gridded monthly data defined on a 5×5 degree grid and then form the global area weighted average in 3 different ways.

- Integrate the annual anomaly over month,lat & lon all in one go, weighting by cos(lat)
- First calculate the yearly averaged grid. Then integrate this over lat, lon grid points weighted by cos(lat)
- As 2. but first calculate the NH average and the SH average. Then calculate for GL = (SH+NH)/2

This is what I get

3 ways to calculate the global annual average from monthly data compared to the official 0) is H4 published annual series.

There is a systematic difference between the 3 methods. Hadcrut4.5 seems to be using the single pass average as this gives almost identical results to mine – but not quite. Most differences in the 3 methods are concentrated in the years before 1950, when the distribution of measurements was sparser, and mostly concentrated in the Northern hemisphere.

The Land only temperatures CRUTEM3 used the (NH+SH)/2 method until about 2011, but then switched to (2NH+SH)/3 for CRUTEM4, the argument being that the NH contains about twice the land surface of the southern hemisphere. If we now also apply second method to the latest GCHN V3C station data, then this is the result.

Comparison of V3C temperature anomalies calculated using CRU’s gridding and averging software to CRUTEM4 annual values.

Again before 1920 there are systematic differences between the two datasets. In my opinion this difference simply represents an underlying systematic error when calculating net warming from preindustrial times. This error is about ±0.15C and is in addition to statistical sampling errors. So I estimate that the earth has warmed by 0.85±0.25 C since 1850.