Transformation Sign Convention


The NGS transformation grids for both NADCON (all releases from 5.0 on) and VERTCON (all releases from 3.0 on) use the same convention, that of “New coordinate minus Old coordinate”. This convention drives the sign of the transformation, that is, when the transformation value should be added or subtracted.

In generic terms:

  • Grid = Coordinate in New Datum – Coordinate in Old Datum
  • Coordinate in New Datum = Coordinate in Old Datum + Grid
  • Coordinate in Old Datum = Coordinate in New Datum – Grid

Said differently

  • If a new datum value is desired when an old datum value is given, ADD the model value to the old datum value.
  • If an old datum value is desired when a new datum value is given, SUBTRACT the model value from the new datum value.

Example: geometric transformation (NADCON 5.0 release 20160901), moving between NAD 83(NSRS2007) and NAD 83(2011)

The transformation between NAD 83(NSRS2007) and NAD 83(2011) consists of three grids (one for latitude, one for longitude, one for ellipsoid heights). The actual values found in those grids are of the form “NAD 83(2011) minus NAD 83(NSRS2007)”, meaning that the grids contain a model of “NAD 83(2011) minus NAD 83(NSRS2007)” differences. Therefore, to apply this transformation one should do the following:

  • Φ[NAD 83(2011)] = Φ[NAD 83(NSRS2007)] + ΔΦ[Grid]
  • λ[NAD 83(2011)] = λ[NAD 83(NSRS2007)] + Δλ[Grid]
  • h[NAD 83(2011)] = h[NAD 83(NSRS2007)] + Δh[Grid]

or

  • Φ[NAD 83(NSRS2007)] = Φ[NAD 83(2011)] + ΔΦ[Grid]
  • λ[NAD 83(NSRS2007)] = λ[NAD 83(2011)] + Δλ[Grid]
  • h[NAD 83(NSRS2007)] = h[NAD 83(2011)] + Δh[Grid]

Example: orthometric heights (VERTCON 3.0 release 20190601), moving between NGVD 29 and NAVD 88

The transformation between NGVD 29 and NAVD 88 consists of one grid (orthometric heights). The actual values found in that grid are of the form "NAVD 88 minus NGVD 29", meaning that the grids contain a model of "NAVD 88 minus NGVD 29" height differences. Therefore, to apply this transformation one should do the following:

  • H[NAVD 88] = H[NGVD 29] + ΔH[Grid]

or

  • H[NGVD 29] = [NAVD 88] - ΔH[Grid]