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The default adjustment in LGO will be holding the WGS 84 positions of the control points, i.e. Latitude, Longitude and Ellispsoid Height. Below we see the values provided by such an adjustment.

To compute orthometric heights (elevations), the geoid separation is simply added to the adjusted ellipsoid height in Tools | Compute Geoid Separations. This may or may not provide good elevations on your points, depending on the accuracy of the model.
If you wish to hold the orthometric heights, we need to do a local adjustment. In order to do a local adjustment, you need to have a coordinate system attached to the project. In our example we are using MI S (Michigan South NAD83).
The first thing we need to do is configure the adjustment for a local adjustment.
Right-click on a blank area of the adjustment page, and select Configuration | General Parameters...

Select the Coordinate System tab and choose Local Geodetic for the coordinate system.

Select the Height Mode as Orhtometric.

If you do not have sufficient control, you may need to disable the computation of the rotations and scale. To do so, right-click on the YES for the value(s) you don't want to compute and double-click on NO to disable it as seen in the following two images.


However, two horizontal and three vertical controls are sufficient to solve for all the values.
Click OK to save your configuration.
Now, we need to modify our control values and specify that we want to use the local position and its orthometric height and, if needed, we will also enter the correct orthometric height.
Right-click on a control point on the adjustment page and select properties. Make sure the Control class is selected.
Click the radio button in front of Local.
Click the radio button in front of Orthometric.
Enter in the correct elevation in the height field.
Note: If you want to hold the local grid coordinates (i.e.. the state plane coordinates) instead of the latitude and longitude, change the Coordinate Type to Grid instead of Geodetic and verify or enter the correct values.

Click OK to save the changes.
Repeat the editing for each of the control points.
Re-adjust the network.
Re-compute the geoid separations. (LGO does not do this automatically).
Our local values are seen below.

You will see that the orthometric heights have been adjusted to the orthometric heights of the control, and the ellipsoid heights have been re-computed by applying the geoid separations to the orthometric heights.
In this example I held 300.00 meters at 54102, 296.63 meters at BULLDOG, and 292.02 meters at NORM.
Your project is now adjusted to the local orthometric heights, and in the adjustment results output you will have a new section of additional parameters shown below.

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