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
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
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 nonoptimal (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 (!)