GPS Q&A-Andy Carbognin

Q.I have a very basic surveying question. Are latitude and longitude independent of the spheroid? When you use differential GPS to survey an area the Lat. and Long. define the horizontal position and z defines position above and or below the chosen spheroid. As I understand it, this would indicate that the spheroid is only involved in the z value. Please enlighten me on this very basic question. John Jordan E-mail

A.This is a very good question, and the reader is correct stating the "z" (or ellipsoid height) will change. Let me explain the relation of latitude and longitude to the chosen spheroid with some simple definitions first.

    A spheroid (also called an ellipsoid) is a mathematical surface which approximates the surface of the Earth and allows us a measurement reference (usually called a datum) to mathematically define points on Earth. To do this, we need to know the size and shape of the spheroid, and the orientation of it relative to our planet. To define the size and shape, we can picture an ellipse with axis lengths, "a" and "b".
    To create a 3-dimensional surface, we rotate this ellipse around the "b" axis and call the resulting surface an ellipsoid. Now, for the orientation, let's put the center of the ellipsoid at the center of the Earth, and the "b" axis of the ellipsoid extending through the rotational axis of the Earth (the north pole). This defines our surface and places it on the Earth where we need it, and if we have the right numbers for "a" and "b", we have the correct distances from the center of the Earth to the equator, and the center of the Earth to the north pole, respectively.
    Now we have one more parameter to define before we can get coordinates from our ellipsoid. Our latitude can be defined as the number of degrees north of the equator (or, in our case, the "b" axis), but a point needs to be selected for the longitude starting point. Historically, this starting point was widely disputed in the 18th and 19th centuries, but was finally agreed on as the Observatory at the Royal Naval Academy in England, known as Greenwich. This is our starting point for longitude and any position on Earth can be described as east or west of Greenwich.
    Now that our ellipsoid is defined, we have to look a little deeper. The ellipsoid is at the center of the Earth, but how is the center of the Earth defined? To see how ellipsoids are centered on the Earth, we need to look at how ellipsoids were defined in the past.
    With the need for maps came the need for accurate land surveys for map production. These large-scale triangulation surveys connected continuous coordinate systems across continents and, with spherical geometry, allowed the calculation of the size and shape of the Earth. For example, the NAD27 datum (based on the Clarke 1866 ellipsoid parameters) is based on land measurement - a survey across North America. Measurements and spherical geometry were used to determine the shape of the Earth and the center of Earth relative to the control points measured. The ellipsoid is therefore placed for the best possible fit for the continent.
    In contrast, the development of satellite geodesy led to additional datum definitions. Satellites orbit around the center of mass of the Earth, and therefore a new datum was required. For GPS this is known as WGS84, with "a" and "b" selected to best fit the entire Earth, and the center of the ellipsoid corresponding to the center of mass of the Earth. This continental vs. global disparity results in a difference in the centers of the NAD27 datum vs. the WGS84 datum of hundreds of meters. This value also changes slightly with anomalies in the NAD27 reference coordinates across North America, so the value for Los Angeles will be different than the value for Atlanta or New York.
    For example, a coordinate expressed in the NAD27 datum will need to be adjusted in several ways to show the same location in the WGS84 reference. The coordinates need to be shifted to the new datum origin, and rotations and scale shifts may be required to orient the axes of both systems in the same directions.
    So, changing ellipsoids will affect all three coordinate components. Latitude, longitude and height need to be transformed in rotation (axis directions), translation (origin shift), and ellipsoid dimensions to obtain correct coordinates in the new datum.

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