ArcMap-Projection Origin

[ChuckTurlington]

Hello,

I am using ArcMap 10.4.1.

I am looking for confirmation of my understanding of the below scenario. I am trying to understand what happens when two different coordinate systems do not align.  The concept appears simple but want to confirm that I am not missing something.  I have attached an image of the Lambert Conic Conformal projection model showing the Grid Origin and the Geodetic Origin, as an example.  It is my understanding that the grid origin (red X) would correspond to the cad/Esri program 0,0,0 (origin of northing-easting values).  While the geodetic origin corresponds to the projected ellipsoid origin, centered on the map (red square).  It appears that coordinate systems with different ellipsoids and units would shift the map false northing/easting to a different location, causing data to misalign.  By toggling the coordinate system alone is not enough to change the map data, but by performing a transformation-projection on the data allows the software to read the northing-easting coordinate values relative to the false northing/easting of the ellipsoid that is active in coordinate definition.

Does the above concept sound correct or could there be more to this concept that I am not aware?

[DanPatterson_Retired · Accepted solution]

I always like to think of it in these terms.

Take a big long rope that can't change length under any circumstances.

Your bud stands at some spot along the longitudinal origin (arbitrarily Greenwich... btw).

You unfurl the rope and go some place and record your longitude and latitude using the ellipsoidal model that you were using at the time.  You know the length of the rope because you measured it in planar units... the metre of course .  Now.. along comes the latest news that states that your prior knowledge of the equatorial and/or polar radii was all wrong and new values have been adopted.  Grief! The only thing that can happen if you bud hasn't moved and your rope is the same length... is that your coordinates have to change.  

Same principle applies when measuring anything relative to an arbitrary origin or know fixed distance and a relative coordinate system that depends on other properties (like radii)

[ChuckTurlington]

Dan,

If I understand correctly, your example applies to datums that remain the same but have different adjustments, and any differing datums with variations in physical properties like radius, etc.?

[DanPatterson_Retired]

My example was for changing datum... ie physical property changes... but if projections have different datum, then that is in addition to the differences associated with the projection geometry

[MelitaKennedy]

It's all relative to the "natural" projected coordinate system origin. That's usually central meridian / longitude of center and latitude of origin / latitude of center. Just to confuse things, technically, in a 2 standard parallel Lambert conformal conic case, The natural origin is almost halfway between the two standard parallels, so what Esri calls the latitude of origin is actually the latitude of false origin!

Anyway, let's think about a UTM zone like 11N. Its projection parameters are always the same:

central meridian: -117.0

latitude of origin: 0.0

scale factor: 0.9996

false easting: 500000.0

false northing: 0.0

If we compare the XY coordinates of a particular place in a NAD27-based zone versus a NAD83-based one, the coordinates will differ by up to 200 meters north-south and maybe 20 m east-west. The majority of the north-south offset is because NAD27 and NAD83 use ellipsoids that have different sizes and shapes. Some of the offsets are also because the two ellipsoids are oriented differently if you compare their positions relative to the earth's center. This all means that the latitude-longitude values of a position is almost always different when checked in different geographic coordinate systems (datums). The XY (easting-northing) values are derived from the latitude-longitude values so it all starts from there.

You could try this by creating some latitude-longitude points in a NAD83 shapefile.

1. Project the shapefile to the appropriate NAD83 UTM zone.

2. Copy the NAD83 shapefile and redefine it (Define Projection tool or data property page) to NAD27, then project it to NAD27 UTM.

3. Project the NAD83 UTM shapefile to NAD27 UTM.

The shapefile points from (2) should differ from (1) a bit, and both should differ more to (3).

Melita