How does ArcGIS project-on-the-fly in an Export Data task, to a different datum and custom projection?

Question

I need all my data in an equal area projection to for an analysis that will calculate area at the North American Scale. The projection I want is custom, it has the following settings. I will be using the Auxiliary Sphere setting 2 or 3 to improve the accuracy of the area calculations.

Sphere_ARC_INFO_Lambert_Azimuthal_Equal_Area Projection: Lambert_Azimuthal_Equal_Area False_Easting: 0.00000000 False_Northing: 0.00000000 Central_Meridian: -100.00000000 Latitude_Of_Origin: 45.00000000 Linear Unit: Meter

Geographic Coordinate System: GCS_Sphere_ARC_INFO Datum: D_Sphere_ARC_INFO Prime Meridian: Greenwich Angular Unit: Degree

The data I need to project and transform is in a couple of different formats: (1) ITRF92 Mexico and (2) Canada_Albers_Equal_Area_Conic with GCS_North_American_1983 and (3) USA_Contiguous_Albers_Equal_Area_Conic_USGS_version with GCS_North_American_1983

I have tried the project tool but there is no valid transformation in ESRI's transformation list that is valid to transform any of the three data sets into my custom projection and so it fails. However if I export the data that needs to be transformed and select the data frame which is set to my custom projection, it "seems" to work. How? Is project-on-the-fly through the Export Data operation reliable? Accurate?

Answer 1

If no transformation is set in ArcMap, the workflow to project between two projected coordinate systems (PCS) that are based on different geographic coordinate systems (GCS) is:

PCS1 - unproject - GCS1 - internally assign GCS2 - project - PCS2

So no transformation is occurring. You could set up a permanent custom transformation using the Create Custom Geographic Transformation tool, or a mxd-only custom transformation via the Transformations dialog in ArcMap.

For either case, you could either a null transformation (nothing happens) which is the same as ArcMap with no transformation set or use the geocentric translations method with the parameters set to zeroes. That will model the shape/flattening of the ellipsoid versus the sphere and change the latitudes. Longitude values will be unaffected.