[PROJ] Help with impossibly elusive horizontal datum

[Greg Troxel]

Landon Yarrington via PROJ <proj at lists.osgeo.org> writes:

> I am trying to georeference an US Army map of northern Haiti made from
> aerial photographs taken in 1942 and 1944 using `gdal_translate` and
> `gdalwarp`. I need a sanity check because this is impossible, and so I'm
> asking for help. Here is the map from Lib. of Congress (
> https://www.loc.gov/resource/g4940m.gct00206/?sp=160&r=0.365,0.623,0.281,0.173,0
> ).
>
> The map info states,

> Horizontal Datum is based on the following astronomic values:
> Fort Islet Lighthouse Lat. 18°33'31.33", Long. 72°20'59.03"
> Santo Domingo Lighthouse Lat. 18°27'53.64", Long. 69°52'52.74"
> Cape Dame Marie Astro Lat. 18°36'47", Long. 74°25'53"
> Extensions of control from Astronomic Positions have been made by multiplex
> triangulation.

This is remarkably clear and useful even if it is hard to understand.

The mapmaker is saying that they made astronomic determinations of
position at 3 named locations, presumably obvious on the map, and gives
the values.  These coordinates are not related to any particular datum.
Instead, they define a local datum.

Critically, there is absolutely no reason to expect that the coordinates
above match WGS84, other than that the time signals are consistent with
greenwhich, and latitude is physical.  But that doesn't get you the last
10s to 100s of meters.

Almost certainly they had the benefit of radio time signals, so their
longitudes should be pretty good.  Latitudes should be pretty good
without needing to think about time.  Without really thinking, 1000m for
a single determination strikes me as pretty good.  Before NAD83, which
used satellite/etc. data, NAD27 was different from modern ITRF by 40m
around me.  And that's a national datum that got to average multiple
observations, even if it was held to be somewhat consistent with
mid/late 1800s work.

Our current datums derive from averages of many astronomic observations,
straightened out with classical and satellite observations.  This "us
army northern haiti datum of 1942" to name it, is local only and not
connected to other datums.

Surely if the people making the map had the technical ability to connect
to NAD27, they would have done that.   However Haiti is a long way from
Florida :-)

> One thousand meter Universal Transverse Mercator grid, Clarke 1866
> spheroid, zone 18.

This is a projection, not a datum, and simply describes how to get
projected grid coordinates from geodetic (lat/lon) coordinates.
Indeed it is a projection typically used with NAD27.   NAD27 was the
standard datum for the mainland.

The "Thousand meter" pretty obviously refers to grid lines drawn on the
map.  UTM does not really have a scale like that.

> The very best accuracy to WGS84 I've been able to get with the 1st edition
> LOC map is ~1,000 meters offset. I think there must be some transformation
> involved, but it isn't clear to me at what point in the process. Should the
> Eastings and Northings in the map be transformed and use those transformed
> values as GCPs? Or should the GCPs use the grid values and some transform
> happen later? Or should is this just a really elusive horizontal datum...

There is no reason to expect this datum to be aligned with WGS84.

> I've tried everything I can think of. Here is a starter using lat long GCP
> points on the LOC map image.

You really aren't explaining where those points came from.

What I would do is:

  First, I'd probably try to do this in qgis, and use the georeferencer.

  Examine the map and find the 3 points where they have published
  coordinates.  Realize that these coordinates are in the map's (local)
  datum.  Guess at where they measured, but they only gave integer
  seconds.

  For those points, find their coordinates in WGS84/ITRF/NAD83 by using
  modern georeferenced imagery.  Much harder, go there and make 48h
  static dual-frequency GNSS observations.

  Compute distances from modern coordinates and also from local
  coordinates.  See if the distances match.  A sanity check.

  Understand how different these are.  I'm guessing there will be
  disagreement at the 0.01 degree level.

  Perhaps, compute a transform from the local to the modern coordinates.
  But, you'll need to transform in UTM, which means from haiti-local-UTM
  to NAD27-UTM.

  Accept that you really aren't going to be able to get an accurate
  transform from the above.  Assume that other than orientation and
  offset the map is pretty good quality (seems fair to me).  Assume that
  the distortion from nad27-utm to nad83-utm due to the differing
  ellipsoids is small compared to errors in the map (also seems fair to
  me, at least for a first step).

  Find about 10 features on the map that are still present today and
  that you can identify on modern georeferenced imagery.

  Add the 10 GCPs in the qgis georeferencer, based on modern
  WGS84/ITRF/NAD83 of the features and clicking on the map.

  Let the georeferencer estimate the transform, and see what it looks
  like.




  Most importantly, after asking for others to help you on the list,
  write up careful notes about what you did and what you found and
  report back to the list.  This is in my view the reciprocal obligation
  undertaken by asking.


Hope this helps!
Greg