# Geodesy and its applications and the importance of reference surface

### What is Geodesy?

Geodesy is the science which deals with the methods of precise measurements of elements of the surface of the earth and their treatment for the determination of geographic positions on the surface of the earth. It also deals with the theory of size and shape of the earth.

Geodesy may be broadly divided into two branches, namely,
(i) Geometric Geodesy
(ii) Physical Geodesy

There is a third one also, known as Satellite Geodesy. Dictionary meaning of Geodesy is ‘dividing the earth and measurement of the earth’ of Geometry. Thus Geometric Geodesy appears to be purely geometrical science as it deals with the geometry (shape and size) of the earth.

Determination of geographical positions on surface of earth can be made by observing celestial bodies, and thus comes under geodetic astronomy, but this can also be included under Geometric Geodesy.

Earth gravity field is a physical entity and is involved in most of the geodetic measurements, even the purely geometric ones. The measurement of geodetic astronomy, triangulation and leveling, all make essential use of plumb line being the direction of gravity vector.

Thus, astro-geodetic methods which use astro determination of latitude, longitude, and azimuth and geodetic operations e.g. triangulation, trilateration, base measurement etc., may be considered as belonging to Physical Geodesy fully as much as the gravimetric methods.

As a general distinction astro-geodetic methods come under geometric geodesy which use the direction of gravity vector, employing geometrical techniques, where as the gravimetric methods come under Physical geodesy, which operate with the magnitude of ‘g’ using potential theory. A sharp demarcation is impossible and there are frequent overlap.

Satellite Geodesy :-
Satellite geodesy comprises the observational and computational techniques which allow the solution of geodetic problems by the use of precise measurements to, from or between artificial, mostly near the earth satellite.

Application of Geodesy:

(a) Primary or Zero order triangulation, trilateration and traverse.

(b) The measurement of height above sea-level by triangulation or sprit leveling.

(c) Astronomical observations of latitude, longitude and azimuth to locate origins of Surveys, and to Control their direction.

(d) Crustal Movements. To detect changes in the relative positions on the ground, and in their heights above sea level.

(e) Observation of the direction of Gravity by astronomical observations for latitude and longitude.

(f) Observation of the intensity of Gravity by the pendulum and other apparatus.

(g) To deduce the exact form of earth’s sea level equipotential surfaces at all heights.

(h) Polar motion studies.

(i) Earth tides.

(j) The separation between the Geoid and the mean sea level.

(k) Engineering Surveys.

(l) Satellite Geodesy: which includes Modern techniques of Positioning by space methods e.g. GPS, SLR, VLBI etc.

#### The Important Reference Surfaces in Geodesy:

To understand how the size and shape of the earth is determined, three surfaces which are of interest to the geodesists have to be understood clearly.

These three surfaces are :
1. Physical Surface of the Earth
2. Geoid
3. Reference Ellipsoid

The Physical Surface of the Earth :
The Physical surface of the earth is with all undulations (mountain and depressions). This is roughly an oblate ellipsoid (obtain by revolving an ellipse about its minor axis). It the actual topographical surface on which earth measurements are to be made. It is not suitable for exact mathematical computation, because the formula which would be required to take the irregularities in the account would necessitate a prohibitive amount of computations.

Geoid :
On the other hand, the ellipsoid is much less suitable as a reference surface for vertical coordinates (heights). Instead, the geoid is used. It is defined as that level surface of the gravity field which best fits the mean sea level, and may extend inside the solid body of the earth.

The vertical separation between the geoid and particular reference ellipsoid is called geoidal undulation N.

The geoid is an equipotential surface of Earth’s attraction and rotation. It is nearly ellipsoidal but a complex surface. The geoid is almost same as mean sea level, i.e., it may be described as a surface coinciding mean sea level in oceans and lying under the land at the sea level to which the sea would reach if admitted by small friction less channels. The geoid is a physical reality. At sea level (geoid) the direction of gravity and axis of a level theodolite is perpendicular to it.

The mean sea level or geoid is the datum for height measurement. The geoid may depart from ellipsoidal shape by varying amounts, up to 100m or even more.

The geoid unfortunately has rather disagreeable mathematical properties. It is a complicated surface with discontinuities of curvature, hence not suitable as a surface to perform mathematical computations. That is why an ellipsoid of revolution used as reference system for horizontal control.

Reference Ellipsoid:
The ellipsoidal surface is smooth and convenient for mathematical operations. This is why the ellipsoid is widely used as the reference surface for horizontal coordinates in geodetic network. It is a mathematical surface with arbitrarily defined geometrical figure. It is closely approximate to the geoid or actual topographical surface. Since the reference ellipsoids are smooth mathematical surfaces (user defined), computations are quite easy to be performed on this surface. It is an ideal surface for referencing the horizontal position of the points on the surface of the earth. The reference ellipsoid are of two categories:

1. In the first category the reference ellipsoid is chosen in such a way that the center of gravity of the actual earth coincide with the center of the ellipsoid. This type of ellipsoid are called geocentric ellipsoids. For Example – WGS-72, WGS-84 etc.

2. In the second category, the ellipsoid are chosen in such a way, that it fits with the local datum of interest as closely as possible. For example Everest, Bessel etc.

The MSL is differ from the geoid due to the following reason-

1.The MSL surface overlain by air, whose pressure varies. It is not quite a free surface.

2. The wind applies horizontal force to the surface.

3. The density of water varies with temperature and salinity.

4. The sources of water, rain, river and melting of ice, do not coincide with the areas where water is lost by evaporation.