WGS84 Versus NAD83—What about the Vertical?

I am not a geodesist. I work for an agency that has some geodesists, but I don’t even play one on TV. That’s my disclaimer and I’m sticking to it. I do, however, have occasion to work with various horizontal and vertical datums in my day job (if the term datum is new to you, you might want to check out this tutorial on datums). One of the things I frequently come across is a confusion regarding WGS84 and NAD83. In particular, are they the same for mapping purposes or not?

If you do much searching on the Internet, you’ll find sites that tell you that “for mapping purposes,” these are the same. In a horizontal sense, and depending on your application, that’s not unreasonable. If a coordinate shift of somewhere between zero and about two meters doesn’t matter, then you’re good to go.

However, I work in the vertical a lot and you don’t find much on the web about that difference. It turns out that both NAD83 and WGS84 are 3D coordinate systems and the conversion between them happens along all three axes. In the U.S., most people don’t work with either NAD83 or WGS84 in the vertical. They work with NAVD88 orthometric heights. But, if you’re working with data derived from GPS (e.g. lidar), somewhere along the line someone applied a geoid model to ellipsoid values (e.g. NAD83 or WGS84) to get those orthometric heights.

NAD83 and WGS84 Ellipsoid Height Comparison

So, what does the spatial distribution of vertical change for the 3D transform between NAD83 and WGS84 look like? I ran a one-degree grid for the Northwest quadrant of the world through the NOAA/NGS HTDP program to have a look. That program is really meant to do a lot of other cool things related to the velocities of tectonic plates, but I used it for a simple change of coordinates without a time difference. Figure 1 shows the height in WGS84 coordinates for the zero elevation in NAD83 coordinates.

Figure 1. WGS84 minus NAD83 ellipsoid heights
Figure 1. WGS84 ellipsoid heights at zero NAD83 (equivalent to WGS84 minus NAD83). Click for larger image to read the scale.

For most of the conterminous United States the shift is around -1.0 to -1.5 meters, while in Alaska it’s somewhere around +0.5 meters. For many mapping purposes, a shift on that order isn’t a big deal, that’s usually not the case vertically. In a world where we strive for under 10 cm RMSE z accuracy for sea level rise studies, adding a meter shift when converting datums is something you’d better pay attention to.

NAVD88 and EGM08 Comparison

I did mention that people tend to work in orthometric heights like NAVD88, so what about those? You can get to orthometric heights by applying a geoid model to the ellipsoid heights, but you have to apply the geoid model that’s appropriate to your datum. How different are the orthometric heights that go with NAD83 (NAVD88) and WGS84 (EGM08)? Let’s take a look.

If I create surfaces in EGM08 and NAVD88 equivalent to my original NAD83 zero height and then subtract the NAVD88 surface from the EGM08 surface, I get a map that looks like Figure 2. Note that NAVD88 geoid grids only cover the U.S. while EMG08 is a global model. I also switched to an equal area projection just to give you a different perspective. There isn’t really a “truth” here. I’m comparing two models and as George E. P. Box noted, “Essentially, all models are wrong, but some are useful.”

EGM08 minus NAVD88 heights are shown in an Albers projection.
Figure 2. EGM08 minus NAVD88 heights are shown in an Albers projection.

The two are very close in much of Florida and Louisiana, and less than half a meter apart for much of the U.S. south and eastern regions. For any given location in most of the U.S. the NAVD88 height value will be larger than the EGM08 value. While the range of the difference is about the same between the ellipsoids and between the orthometric surfaces, the spatial pattern is very different. This is just another reason to pay close attention to which datum you’re in and how you got there. If you’re working in the vertical domain, it really does matter.