University of Wisconsin–Madison

Wisconsin Geospatial News

Learning to Live with Five Different Kinds of Coordinates

As you probably already know, NGS (the National Geodetic Survey) is in the process of modernizing the NSRS (National Spatial Reference System). Originally planned for 2022, the rollout has been delayed for several years as described in this article. Despite this delay, NGS continues with its educational efforts and recently revised Part 3 of its Blueprint for the Modernized NSRS. This document is the subject of several recent webinars by NGS which are being made available to the public in recorded form.

There is a lot in the 125-page document, including case studies focusing on flood mapping, passive control for corridor projects, transitioning data to the modernized NSRS, and airport and infrastructure monitoring. My focus here, however, is the five different types of coordinates that users of the modernized NSRS will need to be aware of and use correctly.

NGS defines a coordinate as “one of a set of N numbers designating the location of a point in N-dimensional space.” This N-dimensional space is interpreted rather liberally, i.e., not just the horizontal components (latitude-longitude, Easting-Northing, x-y) but also “elevation, acceleration of gravity, geopotential, dynamic height, deflection of the vertical and other geodetic quantities.” (p. 4)

The need for multiple types of coordinates is the result of the NGS moving to a time-dependent model of location. The increased precision of surveying devices over the last few decades means that it is no longer possible to ignore the fact that locations on the surface of the earth are moving — both horizontally and vertically — with respect to the earth’s center of mass and to each other. The NGS’s solution to this problem is to provide a set of horizontal reference frames, defined by the boundaries between tectonic plates, which can be treated as internally rigid — at least over fairly short periods of time on the order of years or decades. Thus the North American Terrestrial Reference Frame (NATRF) that will be used in Wisconsin and the rest of the coterminous US, will effectively rotate at the average rate of the North American plate, thus alleviating the main source of latitude and longitude change over time for locations on the plate. Models of crustal motion then relate the coordinates of locations within these frames back to dynamic frames (such as ITRF, the International Terrestrial Reference Frame) that are not fixed to any plate.

As a result of time dependency, coordinates will now be differentiated to denote how they relate to crustal motion. An important concept here is the epoch. An epoch is “a particular instant of time from which an event or a series of events is calculated” (p. 5). NGS uses a decimal year notation for epoch. For example, 12:00 pm on March 29, 2020, would have an epoch of 2020.2418 since it is 88.5/366 of the whole year (2020 being a leap year).

The five kinds of coordinates identified by NGS are as follows:

Survey Epoch Coordinates (SECs). In earlier NGS documentation SECs were called Final Discrete Coordinates. An SEC marks the location of a point on the date when it was surveyed. Since observations are never truly instantaneous, SECs have an adjustment window, a span of time in which a series of observations will be adjusted to create the SEC.

As an example, a mark that has been occupied by a GNSS receiver numerous times over the years would have numerous sets of SECs, each associated with an epoch at or very near when the observations occurred. SECs will allow users to understand mark motion and underlying survey variations in a way they currently cannot.

SECs are computed by NGS using submitted data and metadata, and as such are are part of the NSRS. SECs represent the best estimates of the coordinates at any location at some specific point in time.

Reference Epoch Coordinates (RECs). These are coordinates estimated by NGS for one of the official reference epochs NGS will define (probably every five or ten years). RECs are similar to what most people now understand a coordinate to be. That is, they define a location on the earth’s surface that is considered stable, at least over a specific time period. RECs for various locations with the same epoch can be used together to build a polygon, compute a distance, or do spatial analysis. As these coordinates are computed by NGS they are considered part of the NSRS.

Since RECs come from observations that generally did not take place at the stated reference epoch, these coordinates require the use of a plate rotation model as well as an intra-frame velocity model (IFVM) that accounts for residual within-plate distortions not captured by the plate rotation model. This means RECs are subject to all of the uncertainties and assumptions of the IFVM. The IFVM accounts for both horizontal and vertical movement, while the plate rotation model only accounts for horizontal change.

RECs will provide a static, internally consistent set of coordinates at one fixed epoch (five or ten years, most likely). At those five or ten year intervals, the reference frame will be reset to a new epoch to “catch up” to plate and intra-frame movement. Another way of thinking about RECs is as “snapshots of geodetic control computed by NGS on a five or ten year basis, at reference epochs beginning with epoch 2020.00.” (p. 29)

(Note that the term IVFM may be changed in future documentation. The geodetic and geophysics communities are apparently split over a better term for “velocity” — the “V” in the acronym. Replacement candidates include “deformation” and “motion”.)

Active Coordinates (ACs). In earlier NGS documentation ACs were referred to as Final Running Coordinates. ACs are estimates of a point location continuously over time. The NGS defines ACs as synonymous with coordinate functions that are not associated with a specific epoch. As such they can only be generated by NGS at stations with active control, such as a Continuously Operating Reference Station (CORS).

Technically, a coordinate function is a function, in time, of the ITRF x, y and z values at a CORS, going back in time from when the CORS first went on-line up to the current moment. Each CORS coordinate function is a potentially discontinuous set of shorter-duration linear functions, each of which is continuous. Since ACs are collected by NGS they are included in the NSRS

Reported Coordinates. These are coordinates directly reported to NGS without the data necessary for NGS to replicate or evaluate them. As such they do not form part of the NSRS. Examples include coordinates from a map or smartphone. Reported Coordinates may or may not have a reliable date (or epoch) associated with them. Any coordinates transformed from one datum to another (such as through the use of NADCON or VERTCON) will also automatically be placed in the Reported Coordinate category. Reported Coordinates are useful for general mapping purposes but should not be used in high-accuracy applications.

OPUS Coordinates. In earlier NGS documentation NGS referred to these as Preliminary Coordinates. OPUS Coordinates are coordinates computed by OPUS that have not been evaluated by NGS. As such they are not considered to be part of the NSRS. However, if NGS-provided OPUS recommendations are followed, they will have a label of “tied to the NSRS” while if a user modifies any of the OPUS-recommended constraints, the coordinates will not carry this label. (OPUS is the NGS’s Online Positioning User Service, providing access to high-accuracy NSRS coordinates.)

Hopefully this summary has added some clarity rather than added to the confusion over NGS coordinate definitions! If you have an appetite for more information, please see the Blueprint Part 3 document, which provides much greater detail that can be covered here.

There’s more in the Blueprint Part 3 document I hope to cover in other SCO articles. Meanwhile, for more information on the modernization of the NSRS and its implications for Wisconsin see the WSRS2022 (Wisconsin Spatial Reference System 2022 task Force) webpage.