"Grid" versus "Ground": Optimized Design of Low-Distortion Projections Using Existing Projection Types Rigorously Georeferenced to the National Spatial Reference System

With the adoption of a new geometric datum in 2022, NOAA's National Geodetic Survey (NGS) will update the State Plane Coordinate System (SPCS). This update may consist simply of offsetting northings and/or eastings of existing SPCS projection zones. However, there is significant interest among NGS customers for another type of projected coordinate system: Low-Distortion Projections (LDPs). Although LDPs are presently not endorsed or supported by NGS, an assessment of LDP feasibility and performance is warranted within the context of updating the National Spatial Reference System (NSRS). LDPs are conformal map projections that minimize linear distortion at the topographic surface, manifested as a difference in distance between a pair of projected "grid" coordinates and the true horizontal "ground" distance. For SPCS, the differences can exceed a few hundred parts per million (ppm), and it can be problematic for engineering and surveying applications. Although such distortion cannot be eliminated, an LDP design method is presented that yields optimal results even for large areas of variable elevation. This approach can provide much lower distortion than the traditional method of scaling SPCS to ground, often called "modified" SPCS (MSPCS). MSPCS was included in training provided by NGS beginning in the 1960s, but it does not optimally minimize linear distortion. LDP systems have been adopted throughout the United States. One such system is the Oregon Coordinate Reference System (OCRS). Figure 1 compares distortion of an MSPCS for Bend, Oregon, to the OCRS zone for that area, where the green shading indicates distortion within ±20 ppm (2 cm/km or 0.1 ft/mile). The difference in performance is striking, even though both use the same projection type. Because LDPs cover larger areas, one can be used for many projects, whereas in most cases one MSPCS (and sometimes more) must be defined for every project. Importantly, the presented method for designing LDPs is based on common existing conformal projection types, so, unlike MSPCS, they are compatible with most engineering, surveying, and GIS datasets and software. Because they are rigorously georeferenced, LDPs facilitate appropriate use of the NSRS and directly represent conditions at ground without resorting to best-fit approximate transformations.