Exploring Geodesy

Exploring Geodesy

Survey of India is in the process of developing a geoid model. In practice, geodesy uses the principles of mathematics, astronomy and physics and applies them within the capabilities of modern engineering and technology.

From the very beginning of civilizations, man has strived to learn about planet earth. For many centuries, the only way to learn about the geometry of the earth was through astronomy. The first documented ideas about geodesy date back to Thales of Miletus (625-547 BC), recognised as the founder of trigonometry, who conceptualized a disk like earth floating on an infinite ocean. The school of Pythagoras (580-500 BC) was the first to believe in a spherical earth. Around the end of the Sixth Century BC, Hecataeus compiled one of the first known maps of the world. Anaxagoras (500-438 BC) recognised the spherical form of the moon and explained the diurnal motions of the sun and moon. Eudoxus of Cnidus (408-355 BC) prepared the star map and accurately calculated length of the solar year to be almost exactly 365.25 days. The first hint towards the possibility of gravity was made by Aristotle (384-322 BC) who in addition, formulated a plausible argument for the sphericity of the earth. Eratosthenes (276-194 BC) from the geodetic point of view, can be called the proper founder of geodesy. The results of his determination of the size of the earth are comparable in the context of some at the more modern results.

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Explaining concepts

The surface or topography of landmasses shows large vertical variations between mountains and valleys which make it impossible to approximate the shape of the earth with any reasonably simple mathematical model. If ocean water is allowed to pass below landmasses with the assumption that the water can flow freely and assume that the resultant water surface is affected by gravity only, the surface generated by this global ocean is undulating. This surface is called geoid or the ‘physical figure of the earth’ and the plumb line through any surface is always perpendicular to it.

The earth, is in fact, flattened slightly at the poles and bulges at the equator. For this purpose we need a mathematical reference frame. The mathematical figure used in geodesy that nearly approximate the shape of the earth is an ellipsoid of revolution. The ellipsoid of revolution is the figure which would be obtained by rotating an ellipse about its shorter axis. This is defined by specifying two dimensions i.e semi major axis and flattening. The radius at the equator, semi major axis, is designated by letter ‘a’ and the shape of ellipsoid given by the flattening ‘f ‘indicates how closely an ellipsoid approaches a spherical shape.

Every country had adopted its own locally best fitting ellipsoid for cartographic mapping purposes. At present more than hundreds of such ellipsoids exist. Locally best fitting ellipsoid for India and its adjacent countries is the Everest spheroid. However, with the advent of satellite technology it has become possible to realise the globally best fitting ellipsoid such as WGS-84, which is geo centric in nature (the centre of earth and centre of ellipsoid coincide). It is being utilised by most of the countries of the world.

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Applying the principles of Geodesy

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The pioneering work done by Snell and Picard showed that terrestrial geodetic measurements (angles and distances) are the main tools for the task of relative positioning. The technique of triangulation, astronomical determination of positions and azimuths, as well as levelling were started in the mid seventeenth century. In India, the beginning of scientific geodesy started with Major William Lambton, who conceived a project for the measurement of an arc of the meridian through a network of trigonometric surveys covering the Indian peninsula. Sir George Everest, the then Surveyor General of India was also responsible for measurement of the Great Indian Arc. Until a decade or two ago, geodesy was thought as a science of measuring and portraying the earth’s surface. The science of geodesy has since undergone significant changes and search for a new framework culminated in a new definition of geodesy.  Accepted by the National Research Council of Canada (NRC) and the associated committee of Geodesy and now Geophysics the definition says, “Geodesy is the discipline that deals with the measurement and representation of the earth, including its gravity field, in a three dimensional time varying space”. The scientific activities of geodesy can be arranged into sub-disciplines. The classical sub-disciplines are geometrical geodesy, physical geodesy, mathematical geodesy and dynamic geodesy. While new technology and applications have given rise to several more geodesies, for example, satellite geodesy, inertial geodesy, marine geodesy and space geodesy. The US committee on Geodesy states that the major goals of geodesy can be summarised as:

  • Establishment and maintenance of national and global three dimensional geodetic control network on land, recognising the time variant aspects of these networks
  • Measurement and representation of geodynamic phenomena (polar motion, earth tides and crustal motion)
  • Determination of the gravity field of the earth including temporal variations.

Geodesy is a specialised application of several familiar facts of basic mathematical and physical concepts. In practice, geodesy uses the principles of mathematics, astronomy and physics and applies them within the capabilities of modern engineering and technology. Geodesy was largely involved with the practical aspect of determination of exact positions of points on the earth’s surface for mapping and scientific determination of the precise size and shape of the earth. Modern requirements for distance and direction need both practical and scientific applications to provide answers to problems in fields such as satellite tracking, global navigation and defense missile operations. The position of a survey point is defined in terms of horizontal positioning and vertical positioning.

Horizontal positioning

Horizontal position of a point is defined by the values of longitude and latitude. Longitude is the angle between the plane of two meridians i.e. meridian passing through Greenwich (Prime meridian or standard meridian) and the meridian of the point, measured in the equatorial plane. Latitude is defined as the angle between the perpendicular to the ellipsoid and the plane of the equator, measured in meridian plane of the point. The line perpendicular to the ellipsoid at a point is called ellipsoidal normal.

Vertical positioning

Vertical surveying is the process of determining heights/elevations above the mean sea level surface. The geoid corresponds to the mean sea level in the open sea. These heights are known as orthometric heights. The ellipsoidal height is measured along the ellipsoidal normal and the orthometric height along the plumb line Ellipsoidal heights have to be adjusted before they can be compared to the orthometric heights. The deviation between the geoid and a reference ellipsoid is called geoidal undulation. Geoidal undulation can be used to adjust the ellipsoidal heights.

In recent years, modern technological developments have added several new methods utilising artificial earth satellites and other methods relevant to geodetic surveying. There are however four traditional surveying techniques of horizontal and vertical positioning of a point – astronomical positioning; triangulation; trilateration and traverse.  Historically, the geodetic reference system in each country was defined as two separate datums i.e. horizontal and vertical datums. Normally vertical datum is established through the observation of Local Mean Sea Level (LMSL) at a number of tide gauge sites over a sufficient long period of years. To establish a vertical network origin it is only necessary to define a point to have an elevation zero. That ‘zero’ definition is then usually transported with high precision levelling techniques via closed polygons for the rest of country. In India the vertical datum was defined in 1909 using the MSL data furnished from nine tide gauge stations located at Karachi, Bombay, Karwar, Beypore, Cochin, Nagapattinam, Madras, Visakhapatnam and False Point. The datum defined in 1909 is still in use and suffice most of the practical applications.

During the last few years the widespread adoption of GPS technique with an equivalently vibrant range of accuracy requirements has been witnessed globally. However, it becomes apparent that the ability to derive precise, and perhaps more importantly, accurate and meaningful elevation, is the most difficult component to accomplish from GPS technology. The ellipsoidal heights derived from GPS observations do not have any physical meaning unless it is transformed to levelled heights of local reference datum. Thus the satellite techniques necessitate the requirements of a precise model of geoid at global, regional and local scales in the practical world (engineering surveys) as well as for the geodetic applications.

Survey of India, the national mapping and surveying organisation of India is in the process of developing a geoid model. In the absence of this important geodetic infrastructure the use of GPS has only been limited to provide horizontal positions and deriving precise vertical positions is still a distant dream. The present day nation-wide geoid available in graphical form was computed a long time back and based on astrogeodetic observations and refers to non-geocentric datum ‘Everest spheroid’. It has only limited applicability and does not hold any significance as far as GPS applications for determination of orthometric heights are concerned.

Inputs from Survey of India, Business and Publicity Division, Dehradun. (2007-08/3)

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