Approximations, Errors, and Misconceptions in the Use of Map Projections

Sergio Baselga,Michael J Olsen,Qianxin Wang

doi:10.1155/2021/1094602

Sergio Baselga, Michael J Olsen + Show 1 more

Open Access

https://doi.org/10.1155/2021/1094602

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Abstract

Global geodetic techniques currently can provide the user with worldwide millimeter accuracy. Preservation of this degree of accuracy in derived products is far from straightforward and may leave vast room for trouble in the different steps involved in the collection, storing, processing, analysis, and delivering of geospatial information. This paper is envisioned to serve as a guide for those utilizing map projections, in any possible form of application-cartography, GIS, remote sensing, photogrammetry, etc., to the common (and not so common) causes of error and misconception. This work also explores and questions the validity of some of approximations that are routinely implemented and quantifies the corresponding impact. These include the impact of neglecting meteorological corrections, reduction to ellipsoid and grid scale factors for distances, meridian convergence and arc-to-chord correction for angles, and mixing up with different frames and reference systems, height systems, or deceptively similar map projections. Correct indications are also given for accurately performing geospatial operations such as intersection of lines, determination of minimum point to line distance, and area determination for cadaster, which are often performed with suboptimal accuracy.

Highlights

Global geodetic techniques currently can provide the user with worldwide millimeter accuracy
Introduction e ever-increasing demands and capabilities of modern technologies and theoretical advances, with space geodetic techniques able to realize the International Terrestrial Reference Frame (ITRF) with accuracies of few millimeters [1], have brought many geodetic challenges that could be overlooked in the past
Another point to consider is the fact that in some applications, one can directly work in a 3D earthcentered earth-fixed (ECEF) coordinate system and avoid map projection distortion issues, whereas, for other applications, computations or visualization of data in ECEF can become overly complex and need to be simplified by working on a planar surface

Summary

Common Issues and Main Corrections

Is system will provide coordinates in NAD83 (2011) epoch 2010.00 (as well as preview coordinates in NATRF2022) after a conversion from ITRF When applying this coordinate to the base station coordinates to perform GNSS baseline computations to a rover, one rarely should reapply a reference frame transformation despite the software labelling of the coordinates as “WGS84” coordinates. It has to be noted that sometimes a handy scale coefficient k that includes both correction for length grid distortion equation (5) and reduction to the ellipsoid for a mean height in the area equation (3) can be provided. Referring to angles, they change when transformed or projected from the ellipsoid surface to a particular map projection. For details on these datums, please refer to https://tidesandcurrents.noaa.gov/datum_options. html

Additional Issues and Misconceptions

A Figure 3

Conclusion