Are LiDAR datasets with same vertical datum, but based on different geoids comparable?

Question

I have two sets of LiDAR for the same region that I would like to compare. Both are in NAVD88. The older LiDAR set used GEOID03 for the transformation. The newer LiDAR set used GEOID09 for the transformation.

To accurately compare these two LiDAR datasets do I need to update the old dataset to use the new geoid?

The following ngs.noaa.gov link is relevant, but it is still a little unclear to me because in the first sentence it says use GEOID03 if it is from 2003, and then, goes on to say GEOID09 will be more accurate for data use. The gist sounds like that it should be converted to the same geoid. That is in line with my original thinking that it is a systematic error that should be corrected. I was hoping there would be someone out there that had experience with geoid transformations to confirm as it seems like it might add additional uncertainty.

NOAA's quote:

GEOID03 was fit to the data available in 2003. If you are still using data from 2003, the GEOID03 will fit better. However, NGS has changed the heights in the database for many of these points. Hence, GEOID03 will no longer fit the current values to (in some cases) better than the dm-level. GEOID09 was developed using current values. Hence, GEOID09 should be used now if you want to get results consistent with those showing on the NGS datasheets (our current best estimate of actual heights).

Answer 1

To accurately compare these two LiDAR datasets do I need to update the old dataset to use the new geoid?

Yes, the two geoid models will have different ondulation values for different same coordinates and so different orthometric height. So, you have to account for that or you will have systematic deviations.

Answer 2

1. LiDAR measurements are in the ellipsoidal height system. First, you have to see if the two sets use the same ellipsoidal system. I think the answer is yes and the system should be WGS84 (the GPS system).

2. I guess you have obtained your two sets of orthometric heights using:

   OH_2003 = h_2003 - N_geoid03
OH_2009 = h_2009 - N_geoid09

   where h_2003 and h_2009 are ellipsoidal heights in set1 and set2 from the LiDAR measurements and are used to compute orthometric heights using geoid03 and geoid09. Because the actual geoidal surface does not change over time (as low as few mm a year even in an area of huge glacier losses like Alaska), the differences in geoidal height between geoid03 and geoid09 are mainly due to model differences.

3. So if you want to see the temporal elevation changes in the same area, you should use ellipsoidal height changes (delta_h, the reference ellipsoid is the same), that it, compute:

   delta_h = h_2009 - h_2003

   But you just have OH_2003 and OH_2009, so you need to compute like this:

   delta_h = (OH_2009 + N_geoid09) - (OH_2003 + N_geoid03)
= (OH_2009 - OH_2003) + (N_geoid09 - N_geoid03)

   You have to find the original values from the models geoid03 and geoid09 to compute (N_geoid09 - N_geoid03).

The above analysis is applicable to any case of height change studies using different geoid models.