Skip to main content

plotting - How to ContourPlot a function of the coordinates on the Earth's surface on a map projection


There are two similar questions (this and this), but one is too specific and the other is apparently not clear and has no answers. I'll try to make the question more complete.


Suppose you have a vector field depending on the coordinates x,y,z of a point on the Earth's surface [Edit: I found a mistake on this expression but to keep discussions consistent I'll leave as is.]


field = With[{rl$ = 
    Transpose[{{1.45031*10^7, -1.46446*10^11}, {-3.86086*10^8, 
        2.25113*10^8}, {1.00319*10^8, 3.47297*10^10}} - 1. {##1}]}, 
  Total[({4.90254*10^12, 1.32705*10^20} rl$)/rl$^3] - 
   1. {-0.00569904, -0.0000209977, 0.00135953}] &


With some trick I can represent the Norm of this vector field on a map with the equirectangular projection. If I well understood the topic:


[Edit: I found another supposed mistake in the original code following. From what I now understand on a map usaully we represent the geodetic latitude. But the well known parametrization of an oblate spheroid (the one I originally used) refers to the geocentric latitude. The difference between the two expression is not more than about 0.2° for GRS80, but to be rigorous we need to take into account this difference. This is the reason for the function toGeocentric I added. Feel free to comment on this to confirm or to contradict my understanding of this topic.]


{a, b} = GeodesyData["GRS80", #] & /@ {"SemimajorAxis", 
     "SemiminorAxis"} // UnitConvert // QuantityMagnitude

toGeocentric = λ \[Function] 
  Evaluate[GeodesyData[
     "GRS80", {"GeocentricLatitude", λ}] /. λ -> λ °]


gg = GeoGraphics[GeoRange -> "World", 
  GeoProjection -> "Equirectangular", 
  GeoGridLines -> Quantity[15, "AngularDegrees"], ImageSize -> 800]

cp = ContourPlot[
  Norm[field[a Cos[toGeocentric @θ °] Cos[φ °], 
    a Cos[toGeocentric @θ °] Sin[φ °], 
    b Sin[toGeocentric @θ °]]], {φ, -180, 
   180}, {θ, -90, 90}, 
  ColorFunction -> (Opacity[0.6, ColorData["TemperatureMap"][#]] &)]


Show[Graphics @@ gg, cp]

Mathematica graphics


It is the "right" way to do that (I'm a bit concerned by Graphics@@gg for example, I read that on another question)?


It is possible to use many projections (ideally all map projections supported by Mathematica) in a consistent and general way without having to know and to input all the necessary projection transformations but taking advantage of the cartography framework in Mathematica?


I'm interested for example to "LambertAzimuthal", "Bonne", "Robinson"...




Comments

Post a Comment

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...
Post a Comment
Read more

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...
Post a Comment
Read more

list manipulation - Selecting multiple columns from a matrix?

Sample data: data = { {{2013, 1, 1}, 24.13, 167.67, 231.82}, {{2013, 1, 2}, 32.15, 170.92, 225.99}, {{2013, 1, 3}, 35.43, 172.68, 221.67}, {{2013, 1, 4}, 36.73, 173.05, 218.32}, {{2013, 1, 5}, 58.19, 165.96, 197.05}, {{2013, 1, 6}, 69.99, 163.50, 187.52}, {{2013, 1, 7}, 71.37, 154.21, 175.58}, {{2013, 1, 8}, 72.51, 149.66, 163.25}}; I want a DateListPlot with three graphs, so for a matrix formed by columns 1 and 2, one for columns 1 and 3, and 1 for columns 1 and 4. At the moment I'm using this code: data2 = Transpose[{data[[All, 1]], data[[All, 2]]}]; data3 = Transpose[{data[[All, 1]], data[[All, 3]]}]; data4 = Transpose[{data[[All, 1]], data[[All, 4]]}]; DateListPlot[{data2, data3, data4}, Joined -> True, Filling -> {3 -> {1}}] but I have a hunch that this can be done more efficiently. I don't like the Transpose s in particular. Any ideas? edit (for extra credit) What if I need to multiply the second column by 2, which in my solution is simp...
Post a Comment
Read more