The UTM scale factor for any point depends on three factors: 1) The base scale factor (which is a constant), the distance from the central meridian (81° West in the case of zone 17), and the ellipsoidal elevation of the point. There are simple calculations that can be done for any point to get a reasonably accurate (within a few PPM which can be thought of as a few mm per KM). results. Multiplying the three individual scale factors by each other results in what is shown on this map - the Combined Scale Factor.

One of the challenges in creating this map was determining the ellipsoidal elevation for a few million points. This was accomplished by starting with the digital elevation model (DEM) available from Ontario's open data. This was loaded in a GIS and converted to points on a grid. The elevation for each point was then converted using the HT2 geoid model from Natural Resources Canada. The resulting points were projected into the UTM-17 zone for the area of interest. The Easting (or X coordinate) of each point provides the distance to the central meridian (where the Easting is defined as 500,000). The individual scale factors for each point is then calculated, and product of the three factors is saved as the combined scale factor.

The results of the above process are then used to create a surface which interpolates values between the calculated points The combined scale factor is used Instead of elevations to define the surface, Contour lines were then generated to show the pattern of how the combined scale factor changes. As expected, the contour lines run north-south, somewhat parallel to the central meridian. They deviate from smooth lines where the elevation changes significantly.

The red line shows where the combined scale factor is equal to 1. If you are standing anywhere along this line, you could imagine seeing the UTM mapping plane emerging from being underground to the west and then proceeding to the east where it gradually gets higher above the ground surface.

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