97 Apr 04

Updated 98 Jun 07 and again 02 04 18

Ecstasy, the word, comes from the Greek expression ek stasis: to stand outside of (one's body) ... for current pursuits: to visualize Earth as an object in space. Thus we begin an odyssey to establish the basis for geodesy.

Among astrophysical scientists, there is enough scientific basis for nearly all to conclude that the Universe began as a Big Bang. GOD. Clearly, based on observations, expansion continues. The solar system is one of billions in the Milky Way galaxy; the Milky Way is one of hundreds of billions of galaxies in the Universe for which observable evidence exists.

Earth is our chunk of Bang. Each of us is a product of Earth; each of us is a bag of Bang. Earth is an object that bears us and one that we must manage. As a part of management, we must apply metrics: for space and for time. Fortunately, humans are capable of abstractions of viewpoint and of form.

For example, abstraction of viewpoint from outside the solar system provides the context for construction of a mathematical model representing the surface of Earth (abstraction of form). This is the basis for the GRS80 ellipsoid.

A prior level of abstraction was based on two notions not tenable today:

- the surface of Earth is flat
- sea-level is a suitable reference elevation (plane)

Today we have a more reliable abstraction based on observable realities of time and space. First, time: Time is partition of a cycle. For example, the rotational cycle of Earth in space. This is best marked in relation to Sun. There are two basic phases: Sun and NoSun.

For convenience the number 12 is chosen to partition each of these phases into hours. 12 is again applied to partition the hour into 12 chunks; each divided by 5 resulting in minutes. Minutes are again divided by the product of 12 and 5 into seconds. This defines time as a clock.

Another cycle is the revolution of Earth around Sun, the basis for our calendar. This is an orbital cycle. There are 365.25 rotations of Earth during each orbit of Sun; so we have 365 days per year, then add a day every 4 years.

Now we have time defined. On to space

Space, like time, can be defined relative to any of 3 primary systems within the volumetric Universe:

- Milky Way Galaxy
- Solar System
- Earth

Earth is essentially a single-body system however affected by its moon. The other two systems are multi-bodied. The Milky Way Galaxy is a disc-shaped volume of objects including the Solar System, located about 2/3 out from galactic center. The Solar system is a disc-shaped volume of planets including Earth. Earth may be modeled as either: (1) volumetric body, or (2) non-volumetric surface.

1. Volumetrically, Cartesian reference axes are fixed relative to Earth. The initial reference is the axis of rotation of Earth. This Z axis is, by definition, orthogonal to, and determines, the equatorial plane. The intersection of this Z axis with the equatorial plane is the point 0,0,0 at the Center Of Mass of Earth (C.O.M.).

Arbitrarily, we define the X axis intersecting the Greenwich meridian at the equator. The Y axis is determined by a 90° rotation from the X axis (roughly, the eastern boundary of India). The resulting 3D coordinate system is termed a Conventional Terrestrial Reference Frame.

Today, the International Terrestrial Reference Frame is maintained by the International Earth Rotation Service (IERS) based in France. It is updated yearly, as in ITRF96. This is the reference frame within which GPS is currently defined and reported.

2. As a surface, Earth is best approximated by an ellipsoid centered at C.O.M. As stated above, the conventional spec is the GRS80 ellipsoid, a plate of which is NAD83.

The combination of the ITRF and the GRS80 comprise the World Geodetic System (WGS84). Currently, WGS 84 (G873) is declared, by DoD, to be the definitive coordinate system for earth modeling consistent with the Global Positioning System. Conversions are direct between ITRF XYZ to a point radially extended from the surface of the ellipsoid. Conventional projections also are directly derived.

GPS receivers make all computations using the ITRF coordinate system. But, typically, receivers do not provide display of these XYZ coordinates. Instead, coordinates are displayed as geographic coordinates on the ellipsoid, i.e. lat/long, with an accompanying orthometric height over the GRS80 ellipsoid.

Thus we have a common coordinate system, with global integrity, to use world-wide for base maps supporting Geographic Information Systems and ad hoc projects. But likely because this coordinate system is relatively new, and tools for reliably measuring within this system are even newer, common practice is to use some other, less perfect, coordinate system for the base map. So the current status is a relative Tower of Babel most troublesome at state boundaries or in areas straddling state planes, for example around Cincinnati and Columbus, OH.

We are advocating movement to universal acceptance of the best system for measuring space and time. This movement is greatly facilitated by the work of the National Geodetic Survey in evolving the network of HARN stations and CORS sites which record ITRF XYZ coordinates with increasing accuracy.

Additionally, tools are evolving to enable computations in the simplified 3D space of ITRF. One of these tools is BURKORD by Global COGO, Inc. This program also addresses another critical factor in spatial data management, the quality or accuracy of a measurement. As GIS provides integration of spatial measurements from GPS, EDM, and proliferating other measuring tools, it is increasingly important to qualify a reported location with probable error information.

BURKORD is a 3-dimensional coordinate geometry program which supports manipulation of spatial data using a Global Spatial Data Model (GSDM). By combining horizontal and vertical survey information into the same BURKORD data base, the geometrical integrity of all three spatial data components is preserved and can be described by standard deviations and error propagation. Based upon rules of solid geometry, the BURKORD computation system is equally applicable world-wide. Output includes XYZ coordinates, GRS80 locations, and local plane inverses.

We anticipate a new era in computer-based modeling (CAD and GIS software) that utilizes the ITRF coordinate system as the basis for the geometric engine to facilitate globally-consistent modeling and design, even managing positional error components. All the while, the User works with a correct model of the Earth, and may select the preferred projection as a part of the GUI or for map-making.

At our seminar, we will provide an AutoCAD drawing of the ITRF and NAD83 in the context of the solar system, enabling a clearer understanding and direct use of the Geodetic basis for positional metrics with today's tools. For more background browse to NCAD.net. Hope to see you on Friday, 98 Jun 19.