Esri reprojection engine error: Specified geotransformation may be inappropriate

Symptom

 Reprojector: Specified geotransformation `' (forward) may be inappropriate for reprojection from `LL-WGS84' (GCS: `GCS_WGS_1984') to `UTM83-10' (GCS: `GCS_North_American_1983') using the ESRI reprojection engine 

Cause

This warning appears because you are transforming between two different datums without a specified transformation.

The original NAD 83 and WGS 84 reference frames were equivalent (to within a meter) but since NAD 83 is tied to the North American tectonic plate and WGS 84 is a global average, they have diverged over the years. The issue is addressed more fully in this article from NOAA: Transformations Between NAD83 and WGS84.

Resolution

Many still consider the two reference frames equivalent, so you may choose to ignore the warning. However, ArcGIS 10.1 and up has the transformation WGS_1984_(ITRF00)_To_NAD_1983 that you may wish to use for your reprojection.