Reference Ellipsoid and the Geodetic Coordinate System - Geodesy: Introduction to Geodetic Datum and Geodetic Systems - page 211

Fig. 5.29 Diagram for solving horizontal coordinates using observed values
Reduction of the elements on the Earth's surface to the surface of the ellipsoid
means that appropriate corrections are applied to the terrestrial observation ele-
ments. In this case, the terrestrial observation elements will be transformed into the
corresponding elements on the ellipsoid, making geodetic computations on the
ellipsoid possible. The degree of accuracy of reductions should not jeopardize the
accuracy of field observations.
There are three fundamental requirements for reducing the elements of terrestrial
triangulateration to the ellipsoid surface.
1. The ellipsoidal normal is referred to as the reference line. The direction of the
plumb line at the observation point usually does not coincide with the
corresponding normal to the ellipsoid. The angle between the plumb line and
the line normal to the ellipsoid at the same point is called deflection of the
vertical. The ellipsoidal normal is made the datum, which means that the values
observed referring to the plumb line will be converted to the values that are
referred to the ellipsoidal normal. In this case, the effect of deflection of the
vertical will be removed.
2. The ellipsoid is taken as the reference surface. We project the point from the
physical surface of the Earth onto the ellipsoid along the ellipsoidal normal and
reduce the observed values at a certain height above the Earth's surface to those
on the surface of the ellipsoid. In this case, the effect of the ellipsoidal height will
be eliminated.
3. The geodesic is taken as the connection between two points on the ellipsoid.
Reduce the observed values in the direction of the normal section to the observed
values in the direction of the geodesic, and the effect of the normal section-
geodesic separation will be removed.
Through the above reductions, the terrestrial triangulateration network will be
reduced to the ellipsoid, as shown in Fig. 5.30 . It thus follows that the reduction
essentially achieves transformations between elements on the Earth's surface and
elements on the surface of the ellipsoid.