The “kriging” biases described in the previous post can be mostly avoided by using ‘spherical’ triangulation. This treats the earth as a sphere and triangulates all measurement points onto the earth’s surface. In this case vertex angles no longer add up to 180 degrees. The data are then re-gridded onto a regular 2 degree grid coving all latitudes and longitudes using an inverse distance weighting. The spatial average of measurements over all latitudes and longitudes is then calculated. The data used are all 7300 station data from GHCN V3C combined with HadSST3 ocean temperature data. Here is a comparison of this new method with all the other data.
Of particular interest is the extrapolation of data near the poles, which is where most warming has been observed. The problem though is that there are very few measurements in that region especially before 1940. Figure 2 shows triangulation grids for both poles in 1880 and 2016.
In 1880 there are no measurements further south than 70S or further north than 70N, and triangles cover huge distances. Therefore artefacts are likely introduced by krigging into these regions. The 2016 triangulation shows much better coverage but there are still no data inside 75N. Antarctica does a better job because stations now exist at research stations including one at the south pole.
Here is the full 167 year comparison.
My conclusions are that before 1940 it is best not to use any interpolation into unmeasured areas of the world because the coverage is so low, Hadcrut4 methodology is preferable. Recent warming is enhanced by interpolation because those empty lat,lon cells are filled by the influence of ‘warm’ nearby neighbours. Likewise natural warming cycles such as el Nino also get enhanced.
Next I will use the triangulation itself of measurement locations to calculate the global average, avoiding any interpolation.