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.

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.