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# Geographical representation of unevenly sampled data

Posted 8 years ago

Mathematica 11 has the very useful function GeoHistogram. It is extremely useful to represent a huge variety of geospatial datasets. However, there is yet another way to represent that, which I would like to share. It is very simple and will allow us to generate plots like this one:

This plot represents the earthquake in the last month. The length of the green spikes corresponds to the strength of the earthquakes. In this post I will produce a simple function that allows us to process data of the form

{{lat1,long1},value1},{lat2,long2,value2},...,{latn,longn,valuen}}


to generate these spikes histograms. The first two functions are auxiliary only. The first calculates the latitude/longitude pairs into cartesian coordinates.

toCoordinates[coords_] :=
FromSphericalCoordinates[{#[[1]], Pi/2 - #[[2]], Mod[Pi + #[[3]], 2 Pi, -Pi]}] & /@ (Flatten[{1., #/360*2 Pi}] & /@coords)


The second one calculates the length of the spikes. It uses the max value to normalise the lengths.

lengths[inputdata_] := 2.*(inputdata/Max[inputdata])


The following then is the function needed to generate such plots:

myGeoHistogram[data_, radius_] :=
Show[SphericalPlot3D[radius, {u, 0, Pi}, {v, 0, 2 Pi}, Mesh -> None, TextureCoordinateFunction -> ({#5, 1 - #4} &),
PlotStyle -> Directive[Specularity[White, 10], Texture["~/Desktop/backgroundimage.gif"]], Lighting -> "Neutral",
Axes -> False, RotationAction -> "Clip", Boxed -> False, PlotPoints -> 100, PlotRange -> {{-3, 3}, {-3, 3}, {-3, 3}},
ImageSize -> Full], Graphics3D[Flatten[{Green, Thick, Line[{#[[1]], (radius + #[[2]])*#[[1]]}] & /@
Transpose[{toCoordinates[#[[All, 1]]], lengths[#[[All, 2]]]} & @data]}]]]


The first slot needs the data and the second one changes the radius of the earth. Reasonable values are from 0.5 to 2 or so. Let's generate some plots. First we need some data.

## Earthquakes

The data for the animation above is earth quake data. The Wolfram Language has everything built in.

earthquakedata = EarthquakeData[All, 4, {DateObject[{2016, 7, 1}], Today}];


This loads all the geopositions and magnitudes of the earthquakes (with magnitude larger 4) from 1 July 2016 to now. If you call:

myGeoHistogram[earthquakedata,2]


you obtain a representation of the earthquakes' magnitudes. If you use instead:

quakes = Normal[({#["Position"][[1]], 2.^#["Magnitude"]} & /@ earthquakedata)][[All, 2]];
myGeoHistogram[quakes, 2.]


you obtain the output shown above. You can easily see the geological fault lines and nicely aligned chains of earthquakes.

## Population of the world's capitals

Next we can look at the populations of the world's capital cities. The first function downloads a list of all capitals and the second one acquires the data of position and population size.

capitals = EntityClass["Country", "Countries"][EntityProperty["Country", "CapitalCity"]];
data = {#["Coordinates"], QuantityMagnitude[#["Population"]]} & /@ capitals;


Plotting

myGeoHistogram[Select[data, NumberQ[#[[2]]] &], 2]


(note that I filter out cities with unknown data) gives the following

Of course, this function is just a starting point. I should have wrapped it into Module and set a default value of 1 or two for the radius. But that is easy to do and I would love seeing suggestions of how to improve this or apply it to interesting data sets.

Cheers,

Marco

PS: This is not completely unrelated to another post of mine.

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