In Southern California, where I live, multiple sources of information seem to say that the conversion between NAD27 and NAD83 is almost purely in the east-west direction (about 80 meters), with almost no correction (only a few meters) along north-south. For example, the gdal utility cs2cs seems to verify this, by showing almost no change in the latitude and a much larger change in the longitude:

``````\$ echo "33.760268  -116.682251" | cs2cs -rsf "%.6f" +proj=latlong +datum=NAD27 +to +proj=latlong +zone=11 +datum=NAD83 -
33.760288   -116.683102 0.000032
``````

But I'm running into weird discrepancies that I don't understand. Here are the bottom left corners of two USGS topos, one from 1988 (left) and one from 2018 (right):

The text in the 1988 topo says:

1927 North American Datum. To place on the predicted North American Datum 1983 move the projection lines 80 meters east as shown by dashed corner ticks.

However, there is a clearly visible additional shift of about 200 meters in the y direction. For example, the y=35 km line coincides with a road in the old topo, but is far south of the same road in the new one.

I'm also seeing this with a handheld GPS unit. If I set it to read out in NAD27 and take the UTM coordinates on my front porch, I get this (x y):

``````0410910 3750091
``````

If I then set it to NAD83 and repeat, I get this:

``````0410830 3750288
``````

The sign and magnitude of the x offset are exactly as calculated by cs2cs and as claimed on the topo maps. However, there is an additional y offset of almost 200 meters.

What am I not understanding here?

If anyone can help me with this, feel free to come by my UTM coordinates for a beer. Just make sure to resolve the ambiguity first, or you'll end up at my neighbor's house up the street to the north.

[EDIT] It seems that each NAD datum has its own conversion between lat-lon and UTM:

``````\$ echo "33.760268  -116.682251" | cs2cs -rf "%.6f" +proj=latlong +datum=NAD83 +to +proj=utm +zone=11 +datum=NAD83 -
529425.663755   3735620.830534 0.000000
\$ echo "33.760268  -116.682251" | cs2cs -rf "%.6f" +proj=latlong +datum=NAD27 +to +proj=utm +zone=11 +datum=NAD27 -
529426.322142   3735427.157052 0.000000
``````

This can also be seen on the USGS maps, where the corners of the map are defined by lat-lon, but the UTM grid is shifted north-south relative to the corners.

So I guess this sort of clears it up for me, in the sense that it shows there are really four different coordinate systems: (NAD27,lat-lon), (NAD27,utm), (NAD83,lat-lon), and (NAD83,utm). I would still be happy to get an answer explaining this further. Are there two things that have to be specified, an ellipsoid and a projection?