Here is the result of a Gaussian ‘kriging’ of Hadcrut4.5 temperature anomalies for February 2016. This is essentially what Cowtan & Way do.
Kriged result for February 2016
Hadcrut4.5 measured anomaly data (no kriging)
This clearly shows why the global average of the kriged data gives larger values than Hadcrut4.5 when anomalies at high latitudes are warmer.
However I still prefer Hadcrut4.5 because it makes less assumptions, which is especially important for early years.
Raw H4 values
One interesting possibility of kriging is that it can also handle irregular grids. This means that you don’t even need to average the data in grid cells first. I might even try this, if I find the time. I suspect this is more or less exactly what Berkeley Earth does.
The Cowtan & Way version of Hadcrut4 uses a kriging technique to extrapolate values into those parts of the world where there are no direct measurements. Originally I had assumed that this fit was guided by the use of UAH satellite tropospheric temperature data and therefore more valid than that say used by GISS. However this is not really true as kriging has been used on all Hadcrut4 gridded data back to 1850, and the difference between the Hybrid (satellite) and kriging only results since 1979 is minimal. The net effect of this is to airbrush away regional variability. This can be seen by comparing the meridional temperature profiles of the original Hadcrut4.5 data with those of Cowtan & Way.
Figure 1. All 117 meridional H4 temperature anomaly profiles from 1990 to 2016. They are coloured blue if the annual global anomalies < -0.2C, Blue,-0.2<grey<0.2, 0.2<yellow<0.4, red > 0.4. Traces are 80% transparent to view them all.
Figure2: Same as above but with Cowtan & Way regional profiles plotted with latitude (meridional)
All profiles have been nicely smoothed out with warming concentrated at the North Pole and the Antarctic. The Antarctic profiles are all sorted so that the warmest also agree with those at the North Pole. What a tidy picture – but is it true or just a by-product of the fit?
Here are the annual averaged anomalies calculated using the above profiles.
Figure 3: Comparison of the Hadcrut4.5 annual temperature anomalies with those calculated using the profiles in Figure 2.
The boost in warming from 2000 onwards is because the high latitude temperature profiles have been untangled by the algorithm. Kriging forces a smoothed ‘spline type’ dependence with latitude all the way to 90N.
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.