How to assess GeoZoomLevel for GeoElevationData

Question

I'd like to fetch at most 10 000 points from GeoElevationData, regardless of the location's specification.

From my experience it usually fetches ~100-400k points or all available in case there are not so many.

GeoElevationData[
  GeoDisk[Here, Quantity[#, "Kilometers"]]
, "Geodetic"
, "GeoPosition"
] & /@ {.1, 1, 10, 50, 100, 500}

I prefer to have fewer points faster and not have to care about reducing the size as I really can't use 200k anyway.

Can this be set automatically?

Answer 1

Since zoom levels increase on the length scale by a factor of 2, we can estimate the number of data points in a lat-lon rectangle for a given zoom level, and choose the best one.

$maxZoomLevel = 12;

geoElevationRegionZoomLevel[loc_, target_] :=
  Block[{deltaDegree, count8, est},

    (* spacing of points (in degrees) at GeoZoomLevel -> 8 *)
    deltaDegree = 0.0054931640625`;

    (* Estimate the points GeoElevationData will return at zoom level 8 *)
    count8 = (Times @@ Subtract @@@ GeoBounds[loc])/deltaDegree^2;

    est = Log[4, target/(count8 + Boole[PossibleZeroQ[count8]])];
    Clip[Round[8 + est], {1, $maxZoomLevel}]
  ]

Here's the zoom level that gets us closest to 10000 points for Illinois:

loc = Entity["AdministrativeDivision", {"Illinois", "UnitedStates"}];

zoom = geoElevationRegionZoomLevel[loc, 10000]

5

This zoom level gives us 11375 points, so it's the closest to 10000 we can get:

GeoElevationData[loc, "Geodetic", "GeoPosition", GeoZoomLevel -> zoom]