Spherical temperature averaging using Icosahedral grids

I reckon that Spherical triangulation of monthly global temperatures is by far the most honest way to present temperature data, but it has one drawback. You cannot make annual or longterm averages because the triangular mesh is forever changing from one month to another. To make such averages you really need a fixed grid. So does that mean that we have to give up and return to 2D fixed lat,lon grids such as  those used by CRU, NOAA  or NASA, in order to calculate annual distributions? The answer is no because there is a neat method of defining fixed 3D grids that maintains spherical symmetry.  This is based on subdividing an Icosahedron.

Figure 1. Annual average temperature anomalies for 2016 over the pole. Note the equal area triangles of an icosahedron grid.

Figure 1. shows  the annual average temperature anomalies for 2016 using this method, while here  and below is the WebGL (Nick Stokes) 3D interface.

An Icosahedron is a 20 sided object whose sides are equilateral triangles. The mesh is formed by dividing each triangle into 4 new triangles whose vertices are made to lie on a sphere. By repeating this procedure iteratively you generate an equal area mesh over the earth’s surface.

Generating a triangular mesh from an Icosahedron

I was lucky to find an IDL package to do this, and after quite a struggle managed to integrate it with the global temperature data.  I am using a level-4 mesh containing 2562 triangles which seems to be the best fit to the average density of global temperature measurements. Despite this there are still 94 empty triangles lying in remote regions. These have been assigned  zero anomaly and are visible as occasional single light blue triangles.

Another well known way to tesselate a sphere uses hexagons, as on a soccer ball. However it turns out that this is a just a truncated icosahedron!  Check out cutting off each vertex midway. It is just easier to make soccer balls that way.

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3D visualisation of Earth Science data

WebGL is a Javascript implementation of OpenGL which runs via your web browser locally on your graphics hardware. Nick Stokes has developed an interface to visualise 3D global  data such as temperatures on the earth. Here is an example for my March 2017 data. Click and drag on the sphere below to rotate it. Toggle buttons to add/remove triangular and point meshes.

To view the complete interface in a new window  click here

The great thing about such a 3D presentation is that you view distributions as they actually are, rather than through some distorted 2D map projection. Often such projections make polar regions appear far larger than they really are. Here are some more examples which I hope will show how useful 3D visualisations can be. To view Nick’s WebGL interface click on each title.

  1. Super El Nino January 2016

2. Cold winter of 2010

Europe experienced its coldest winter for 47 years. Cold Arctic air spread south over Europe and US under  a meandering Jet Stream.

3.Cold winter of 1963

The coldest winter in Europe for 100 years saw a similar pattern to 2010. There were twice as many weather stations active in 1963 than there are today. Compare the number of nodes in the grids to those visible in 2017, and you will see a huge reduction in stations.

VRML was originally proposed in 1995 as the 3D visualisation standard on the web but you always needed a plugin or SGI workstation. X3D grew out of XRML but has not been widely taken up. WebGL however has the advantage that it is supported by all modern HTML5 Browsers.

However, WebGL and Javascript are not for the faint hearted, as programming and debugging are rather difficult. Appreciations therefore go to Nick Stokes for doing most of the hard work to make a generic Earth Science interface, which is then relatively easy to adapt to new sets of data.

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Climate Change pattern similar to weather

These two animations show monthly global temperature anomalies from 1990 to 2017. There seems to be a multi-annual anticyclonic circulation of  air temperatures in the Northern Hemisphere with a stronger cyclonic circulation in the Southern Hemisphere.

NH anti-clockwise?

SH clockwise?

Multi-annual temperature distributions would appear to follow the same flow patterns as weather systems.

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