Geodetic systems (earth, ellipsoid)

Geodetic Systems (Earth, Ellipsoid)

Prepared by: Md Tamim Haider

Overview

Geodetic Systems

Surveying

Geodesy

The Geoid

Reference Ellipsoids

Local and Global Ellipsoids

Some Common Datums

World Geodetic System 1984 (WGS 84)

Geographic Coordinate Systems

Geodetic Systems

Geodetic systems is the mathematical representation of Earth. It s used in geodesy, navigation, surveying. A datum is a set of values used to define a specific geodetic system. The North Pole, South Pole and Equator may be assumed to be in different positions on different datums, so the true points may be vary slightly different. Different datums use different estimates for the precise shape and size of the Earth (reference ellipsoids).

Horizontal datums are used for describing a point on the earth's surface e.g. latitude and longitude. And Vertical datums are used to measure heights or underwater depths.

Geodetic Systems (Earth, Ellipsoid)

Surveying:

The art of making measurements of the relative positions of natural and man-made features on the Earth’s surface. And the presentation of this information either graphically or numerically.

Geodesy:

Geodesy is the discipline that deals with the measurements and representation of the Earth, including its gravity field, in a three-dimensional time varying space.

Geodesy focus on the Earth and neglect any man-made features on it (e.g. buildings, public utilities, etc.), while surveying use the results of

geodesy for positioning and mapping of these features.

Geodetic Systems (Earth, Ellipsoid)

Geodetic Systems (Earth, Ellipsoid)

The Geoid:

This is defined as the ‘equipotential surface that most closely corresponds to mean sea level’.

An ellipsoid may not be sufficiently accurate for detailed measurements at large scale. The Earth is actually slightly ‘pear-shaped’. It also has ‘bumps’ and ‘hollows’. For geodetic measurements, the Geoid is used. It is modeled from gravity data. We can’t see the surface or measure it directly.

The geoid surface is irregular, unlike the reference ellipsoid which is a mathematical idealized representation of the physical Earth, but considerably smoother than Earth's physical surface. Although the physical Earth has excursions of +8,000 m (Mount Everest) and −418 m (Dead Sea), the geoid's variation ranges from −106 to +85 m, less than 200 m total compared to a perfect mathematical ellipsoid.

Geodetic Systems (Earth, Ellipsoid)

Reference Ellipsoids:

A Reference Ellipsoid is a mathematically-defined surface that approximates the geoid, the truer figure of the Earth. The semi-major axis, semi-minor axis of the ellipse and flattening completely specify the shape of the ellipsoid.

Some of the most popular reference Ellipsoids are: Clarke 1866, International 1924, and WGS 1984. Currently the most common reference ellipsoid used, and that used in the context of the Global Positioning System, is WGS 84.

Local and Global Ellipsoids

Many ellipsoids have been defined in the world. Local ellipsoids have been established to fit the Geoid (mean sea level) well over an area of local interest, which in the past was never larger than a continent.

With increasing demands for global surveying, work is underway to develop global reference ellipsoids. In contrast to local ellipsoids, which apply only to a specific country or localized area of the Earth’s surface, global ellipsoids approximate the Geoid as a mean Earth ellipsoid. The International Union for Geodesy and Geophysics (IUGG) plays a central role in establishing these reference figures.

North American Datum 1927 (NAD27) Uses the Clarke 1866 spheroid Reference point is located at Meades Ranch, Kansas Based on ground survey information in the 1800’s

North American Datum 1983 (NAD83) Uses GRS80 (Geodetic Reference System) spheroid using the Earth’s center as a reference point rather than the

surface. Based on ground surveys and satellite information

WGS 1984 Most recently developed datum framework for measurements worldwide Earth centered, or geocentric, perspective US military & the GPS system uses WGS84

Common Datums

Earth-centered, Earth-fixed terrestrial reference system & geodetic datum.

WGS 84 is based on a consistent set of constants and model parameters that

describe the Earth's size, shape, gravity and geomagnetic fields.

WGS 84 is the standard U.S. Department of Defense definition of a global

reference system for geospatial information.

World Geodetic System 1984 (WGS84) spheroid, which is more or less identical

& mathematically refined to Geodetic Reference System 1980 (GRS80)

It is compatible with the International Terrestrial Reference System

(ITRS).

National Geospatial-Intelligence Agency is the responsible organization

for WGS 84.

WGS 84 is the reference system for Global Positioning System (GPS).

World Geodetic System 1984 (WGS 84)

Ellipsoid referenceSemi-major

axis aSemi-minor axis b

Inverse flattening (1/f)

WGS 84 6378137.0 m 6356752.314245 m 298.257 223 563

Geographic Coordinate Systems

A geographic coordinate system is a coordinate system that enables every location on the Earth to be specified by a set of numbers or letters.

A common choice of coordinates is latitude, longitude and elevation. The Prime Meridian and the Equator are the reference planes used to define latitude and longitude.

Latitude, Longitude, and Height

The geodetic latitude of a point is the angle from the equatorial plane to the vertical direction of a line normal to the reference ellipsoid.

The geodetic longitude of a point is the angle between a reference plane and a plane passing through the point, both planes being perpendicular to the equatorial plane.

The geodetic height at a point is the distance from the reference ellipsoid to the point in a direction normal to the ellipsoid.

Cartesian coordinates

Every point that is expressed in ellipsoidal coordinates can be expressed as an x y z (Cartesian) coordinate.

Z-axis points toward the North Pole. X-axis defined by the plane that goes through the intersection

of the prime meridian and the equatorial plane. Y-axis is orthogonal to X and Z axis created a right handed

system.

Geographic Coordinate Systems

Geographic Coordinate Systems