Choosing the Correct Coordinate Transformation for Your Data

Datum transformations between two coordinate systems are often required to align geospatial data layers. When transformations are not required, you are likely thankful that your day is a little bit easier. But for all those other days, choosing the correct coordinate transformation can require careful consideration. 

Geographic Calculator will automatically generate a list of possible transformations based on your chosen source and target coordinate systems. Frequently, there are several transformations that can be applied with different results, making the selection a more artful step on the geodetic side of a geospatial workflow. The choices at hand may have different methods, Areas of Use, and, therefore, accuracies (or perhaps better said, inaccuracies or uncertainties, which vary by location). So why are there often multiple choices? The short answer is time and space. The longer answer is that transformations have been developed for different realizations of source and target reference frames (aka geodetic coordinate reference systems) through time, or for different areas of interest. In both cases, choosing the correct coordinate transformation comes down to different control networks on which the transformation parameters are fit.

Choosing a Transformation 

When presented with choices, an obvious question is “Which transformation is correct for my data?” There isn’t always a concrete answer, and perhaps a better question is “Which transformation is best for my data?” If you’re lucky, there will be only one valid choice between your source and target coordinate systems. This might mean that there is truly only one transformation defined, or that national standards, business rules, or Areas of Use dictate which of several choices to select. Metadata for the positions being transformed or historical information may also indicate which transformation is most appropriate. 

Geographic Calculator provides information and tools that support users in making better transformation selections, and can be configured to prevent users from making an unwanted choice. Examples of assistance include the display of accuracy/uncertainty estimates (where available), Area of Use filtering, and administrative settings to hide or disable some transformation objects from the selection interface. Deprecated definitions or those excluded by business rules are examples of settings that may be applied.

Example Transformation: NAD27 to WGS 84

To illustrate, let’s look at a case where multiple datum transformations exist between NAD27 and WGS 84. The sample position is on the goal line of a football field in the state of Maine, USA (Figure 1). The source projected coordinate system is NAD27 / UTM zone 19N and the target projected coordinate system is WGS 84 / UTM zone 19N. Note: The use of projected coordinate systems was chosen for display purposes and is immaterial to the usage or results of the datum transformations applied to the base geodetic systems.

Six NAD27 to WGS 84 transformations with different methods, Areas of Use, and published accuracies are compared in Table 1 below:

• Three methods are valid for the Area of Use of the sample point (green). 
• Two methods are invalid for the Area of Use and hidden by default with administrative settings in Geographic Calculator (red). 
• One older transformation is hidden by Geographic Calculator within the United States custom Area of Use (gray). 

These latter three invalid and hidden choices are included in Table 1 to show results if Geographic Calculator did not provide Area of Use and Custom Area Filtering tools to the user.

It is important to note that published accuracies have historically been reported as averages over the entire Area of Use, and are often somewhat different than the accuracy realized at a particular location. This can be seen in Table 1, which also shows measured accuracies for our sample point in Maine, in addition to the information mentioned above. The transformations are listed in order from highest to lowest measured accuracy.

Possible Transformation Choices

Figure 2 maps the spread and pattern of these six NAD27 to WGS 84 transformations, relative to the best estimate of the point’s position in WGS 84 (the original orthoimage is in NAD83, and several independent calculations were made from this to determine the best estimates of the NAD27 and WGS 84 coordinates).

A Closer Look at the Possible Transformations:

• • NADCON: The national standard transformation available between NAD27 and WGS 84 is NADCON (pre-v5.0). This grid-based transformation from the National Geodetic Survey is accurate to 13 cm, and is the most accurate of the six transformations in this example. Note: NADCON 5 does not include WGS 84 and, therefore, could not be included directly in this test case.
  • Multiple Regression Equation (MRE): Although MRE methods are filtered out by the United States Custom Area of Use, the NAD27 to WGS 84 MRE transformation performs quite well for this example in Maine. [To use this transformation, the “Ignore custom areas of use when selecting” option in Administrative Settings must be enabled.]
  • NTv2: The Area of Use for this NTv2 grid-based transformation is Canada and it is therefore filtered from use for the United States. Nevertheless, the grid extends southward to 40o N in this region (fully encompassing Maine in the United States) and performs very well, considering that it is outside its Canadian Area of Use polygon. [To use this transformation, the “Ignore datasource areas of use when selecting” option in Administrative Settings must be enabled.]
  • Geocentric Translations: Three Geocentric Translation transformations were included in this example:
    • Two of these are valid for this point in Maine. One has an Area of Use for the entire continental United States (CONUS) and a published accuracy of 10 m, while the other has an Area of Use for just CONUS east of the Mississippi River, with a published accuracy of 11 m. So, despite the slightly better published accuracy of the entire CONUS transformation, it performs roughly 20% better than the transformation specific to the eastern United States.
    • The third Geocentric Translation is for the CONUS area west of the Mississippi River. It is an invalid choice for this example but was included to make a point. Despite its published accuracy being better than the two valid geocentric translation choices above, it performs worse than them because it is very far from the area for which it was fit. This choice would be filtered out with the default settings of Geographic Calculator. [It could only be selected by enabling the “Ignore datasource areas of use when selecting” option in Administrative Settings.]

Chosen Transformation: NADCON

In this example, there are three reasons that make NADCON an easy choice: 1) it is the national standard transformation for these coordinate systems; 2) it has an appropriate Area of Use; and 3) it is the most accurate of the six choices presented.

Key Takeaways for Choosing a Transformation

The discussion and sample case presented here provide some insights into the nature of datum transformations, and criteria for arriving at a sensible and appropriate selection for any given dataset and location. In summary, there are several key takeaways:

1. For a pair of coordinate systems in a particular location, there may not be a unique choice of datum transformation.
2. All datum transformations introduce some level of inaccuracies on the resulting output positions.
3. Valid datum transformations for a location may be guided by national standards, business rules, areas of use, published accuracies, metadata, historical information, or other factors.
4. Published average accuracy is not always indicative of local accuracy.
5. Geographic Calculator provides information and filtering tools to help users select the best transformation for a location.
6. There are cases where technically invalid transformations (out of area or otherwise filtered) may turn out to be more accurate than otherwise valid choices for a location. However, these should be used with caution.
7. Ultimately, the best transformation for a location and dataset must be determined by the user based on all of the considerations above.

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