Visualising Spherical Grids

I have found a much faster way to display spherical grids based on IDL object graphics. This uses OGL hardware support. I chose the warmest month ever recorded (March 2016) to show  results. First here is the grid rotated about the ‘y-axis’ which shows coverage from pole to pole. The intense gridding visible are the US stations in GHCNV3 and to a lesser extent also in Europe. Australia and Africa are also clearly visible.

The next animation shows the temperature anomalies calculated on the same grid, as described in the last post. I have to use the original aspect ratio this time otherwise the animated gif washes out the blue colour. Yes it is still abnormally cold in Antarctica.

The temperature scale for anomalies is ± 10C (blue to red). For comparison here is one of the coldest months in the last decade : January 2008. There was exceptional cold conditions over Siberia and the global average was about the same as the normalisation period 1961-1990.

Animations are all a bit of a gimmick, but I just can’t resist them. However I will  try to make some better quantitative visualisation for a given month.

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Spherical Triangulation

After 5 days on Heron Island and a narrow escape from Cyclone Debbie, I am now back to spherical gridding!

The most elegant method for spatial integration of irregular temperature data must surely be spherical triangulation over  the earth’s surface. This is because it treats each measurement equally by covering the earth’s surface with a triangular mesh of station & SST nodes. Unlike linear triangulation (described previously), spherical triangulation also spans polar regions. There is no need for any ‘kriging’ or linear interpolation into sparse polar regions, since they are naturally included. I finally deciphered IDL’s spherical triangulation output,  thanks to Nick Stokes.  Here then is the result in 3D for temperatures in January 2016. The shading for each triangle is the average of each node’s temperature anomaly (-5C – +5C).

Figure 1: Triangular mesh with temperature shading showing US stations in fine mesh. Transparency of 50% also shows ghosted the grid on the hidden hemisphere. Image currently takes 72 hours to render, so it is a little difficult to optimise!

I now need to find a better visualisation method as this one takes way too long, however at least it shows how triangulation now covers both poles.

Each triangular area shown in Figure 1 is calculated in 3D cartesian coordinates to derive the area weighting used for averaging. Figure 2 shows  how the final spherical results compare to the 2D (lat,lon) triangulation results.

Figure 2: Comparison of spherical triangulation temperature results with 2-D triangulation. Main difference is the handling of polar regions. In blue is shown  Cowtan & Way who use kriging to extrapolate data into polar regions

There is really very little difference in the annual temperature anomalies between the spherical results and the 2-D triangulation results. Based on these results it would seem that Cowtan & Way have exaggerated polar warming effects between 2005 and 2013. Figure 3 shows the monthly comparison and just how remarkably similar the 2-D and 3-D results are despite completely independent methods of integration.

Figure 3: Comparison of global monthly tempearture anomalies calculated using spherical triangulation and 2-d (lat,lon) triangulation. The difference proves that there are only small differences in final result.

Aesthetically the spherical triangulation grid is my favourite. Unfortunately, the extra effort makes only a tiny difference compared to the more easy 2D triangulation solution based on lat,lon coordinates. Despite this, both methods, in my opinion, are better than simple rectangular gridding as used by Hadcrut4 and (partially)  by GISS and NOAA. Furthermore they avoid interpolation.

I will post the code and the data soon.

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European Winters

The technique of triangulation of station data allows a neat way of visualising regional “climate change” and also the year to year variation.  Here are two animations for Europe. First a replay of 2016.

Monthly temperature anomalies over Europe for 2016 relative to the 1961-1990 average

The second animation shows all winter January temperatures from 1880 to 2016. Extreme winters of 1942, 1947, 1963 and even 2010 are particularly noticeable. Scale shown is Blue to Red -10C to +10C from normal. Black are extreme temperatures out of scale.

Posted in AGW, Climate Change | Tagged | 2 Comments