Analysis of ground magnetometer coverage Mervyn Freeman , UK

SuperMAG stations and nearest neighbour distances This shows a Behrmann projection of the world with 288 SuperMAG magnetometers (observatories and variometers) plotted as black dots (see http://supermag.jhuapl.edu/). Also shown by colour shading (blue large, red small) is the distance from any position to the nearest neighbouring magnetometer. As can be seen, spacing is non-uniform – the magnetometers are not optimally distributed for global data assimilation. Obvious gaps are over the oceans, but there are islands that could be exploited to improve this.

SuperMAG station coverage Each panel shows a polar stereographic projection of the world for the northern hemisphere (upper row) and southern hemisphere (lower row) with lines of constant latitude and longitude shown in black. In each panel, the Earth’s surface has been divided into equal area cells (light grey lines) with equal longitudinal spacing (and hence varying latitudinal spacing) for different horizontal resolutions – 100 km (first column), 500 km (second column), 1000 km (third column), and 2000 km (fourth column). Each equal area cell is coloured according to how many magnetometers it has within it (see colour bar. Note that no magnetometers corresponds to no fill.). Thus we readily see that the WMO goal and threshold horizontal resolutions of 100 km or 500 km, respectively, are far from being achieved for the world as a whole. Decent grid cell coverage only occurs at 2000 km resolution. 100 km 500 km 1000 km 2000 km

SuperMAG station coverage: comment Each panel shows a polar stereographic projection of the world for the northern hemisphere (upper row) and southern hemisphere (lower row) with lines of constant latitude and longitude shown in black. In each panel, the Earth’s surface has been divided into equal area cells (light grey lines) with equal longitudinal spacing (and hence varying latitudinal spacing) for different horizontal resolutions – 100 km (first column), 500 km (second column), 1000 km (third column), and 2000 km (fourth column). Each equal area cell is coloured according to how many magnetometers it has within it (see colour bar. Note that no magnetometers corresponds to no fill.). Thus we readily see that the WMO goal and threshold horizontal resolutions of 100 km or 500 km, respectively, are far from being achieved for the world as a whole. Decent grid cell coverage only occurs at 2000 km resolution.

SuperMAG coverage Maximum Actual The blue curve in the graph summarises how the percentage of equal area grid cells occupied by one or more magnetometers shown in slide 2 varies with horizontal resolution, from 0.5% at 100 km to 63% at 2000 km. The red curve shows the maximum possible percentage occupation. That is, for the set of M = 288 magnetometers, the maximum percentage occupation is equal to M/N*100, where N is the total number of equal area grid cells for a given resolution. We see that, for the current world’s (i.e., SuperMAG) supply of 288 magnetometers, 100% occupation can only be achieved at a resolution of more than 1270 km at which point N = M = 288. And in fact at this resolution the actual occupancy is only about 40% because of the non-optimal (i.e., uneven) distribution of magnetometers.  In fact, 100% occupancy of equal area grid cells would require M = N = 2030 magnetometers at the WMO threshold resolution of 500 km, and M = N = 51009 magnetometers at the WMO goal resolution of 100 km (!)

SuperMAG coverage: comment The blue curve in the graph summarises how the percentage of equal area grid cells occupied by one or more magnetometers shown in slide 2 varies with horizontal resolution, from 0.5% at 100 km to 63% at 2000 km. The red curve shows the maximum possible percentage occupation. That is, for the set of M = 288 magnetometers, the maximum percentage occupation is equal to M/N*100, where N is the total number of equal area grid cells for a given resolution. We see that, for the current world’s (i.e., SuperMAG) supply of 288 magnetometers, 100% occupation can only be achieved at a resolution of more than 1270 km at which point N = M = 288. And in fact at this resolution the actual occupancy is only about 40% because of the non-optimal (i.e., uneven) distribution of magnetometers.  In fact, 100% occupancy of equal area grid cells would require M = N = 2030 magnetometers at the WMO threshold resolution of 500 km, and M = N = 51009 magnetometers at the WMO goal resolution of 100 km (!)