[Proj] NAD83(Original) Transformation with Heights

[Rob Skelly]

> have you verified that the 54 cm is not within the limits of the
difference between HT2_0 and CGVD28?? if that is so then there is no error

Well, it turns out I made a math error: the difference is ~5cm, not 54cm.
That's a small error, but what we really want is for the outputs to match.

> another source of errors might be the path you go to that elevation..

The HT2_0 file is the grid shift file, so that's the mechanism proj is
using to get from the original orthometric heights to the ellipsoidal
heights. The HT2_0 file uses geographic coordinates, so proj must be doing
the horizontal transformation first, then the vertical shift -- so if the
horizontal coordinates are off, the elevation will be off.

So 5cm is obviously a small error, but it disagrees with GPS-H...

> make sure that "las2las" and GPS-H do the same assumptions

My working hypothesis was that, since GPS-H is using HT2_0 with the
NAD83(CSRS) reference frame, and our original data uses NAD83(Original),
there should be a +towgs84 argument in my original -> WGS84 transformation,
because WGS84 has changed between those two reference frames. However:

> how large was the horizontal difference?

My transformation from the original horizontal coordinates to WGS84 and
GPS-H's transformation are almost identical. Even if there is a reference
frame difference, the difference in shift values should be negligible.

So... we have just discovered that the grid shift files may be misaligned
by 8' to the East. Shifting them by that much provides almost perfect
results, at least for our study area.

Thanks for your time!
Rob
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