Converting from orthometric to ellipsoidal heights

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When imagery is collected via a satellite or aerial sensor, the locational information (specifically, height) is typically measured above an ellipsoidal model of the earth, whereas many available DEMs are modeled using an orthometric model. Basically, this results in two different elevation values for the same location because they are not measured from the same base location. Using a geoid correction, you can convert from one to another.

In ArcGIS, when you apply an orthorectification to a raster dataset, you can apply the geoid correction by checking a check box on the Layer Properties dialog box. This check box is also available when adding some imagery to a mosaic dataset using specific raster types. This will apply the geoid (EGM96) correction to the z-values. However, there may be cases where either you would like to insert your own geoid surface model or the check box isn't available.

Using the Arithmetic function (within a mosaic dataset) you can convert the orthometric height using a geoid before applying an orthorectification to your imagery.

To do this, apply the following equation:

h = H + N

Where

h = ellipsoidal height

H = orthometric (geoid) height

N = geoidal separation

The steps below guide you through creating a mosaic dataset containing elevation data. The Arithmetic function is applied to the entire mosaic dataset according to the equation above to generate a DEM with ellipsoidal heights.

Set up the mosaic dataset

1. Create a mosaic dataset.

   Use the Create Mosaic Dataset tool.

2. Add your elevation raster data to the mosaic dataset.

   Use the Add Rasters To Mosaic Dataset tool

   Be sure to build the overviews.

Add the Arithmetic function

1. Open the Catalog Window and navigate to the mosaic dataset.
2. Right-click the mosaic dataset and click Properties.
3. Click the Functions tab.

   You will see a function chain with the single Mosaic function listed. The Mosaic function is listed by default, because this is a mosaic dataset, and all rasters are being mosaicked. It is after the mosaicking that you will be applying your algorithm.

4. Right-click the Mosaic Function and click Insert > Arithmetic Function.

   When you insert a function, it is inserted above the function you've clicked.

   This opens the Raster Functions Properties dialog box, which allows you to set the options for this function.

5. Input Raster 1 is identified as the current contents of the mosaic dataset and will not be changed.

   This represents H in the equation above.

6. Click the Input Raster 2 browse button and navigate to the \pedata\geoid folder in the ArcGIS install location.
7. Choose the WGS84.img and click Add.

   This represents N in the equation above.

8. Click the Operation drop-down arrow and click Plus.
9. Click OK to close the Raster Functions Properties dialog box.
10. Click OK to close the Mosaic Dataset Properties dialog box.

These steps allow you to convert orthometric height to ellipsoidal. If you need to convert ellipsoidal height to orthometric, you can use the Arithmetic function to apply the H = h - N equation.

Once completed, the mosaic dataset can be used as the DEM input to orthorectify the imagery in another mosaic dataset.

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