Geodesy md. yousuf gazi

Geodesy
Md. Yousuf Gazi, Lecturer, Department of Geology, University of Dhaka (yousuf.geo@du.ac.bd)
GIS

❖ Geodesy is the division of science associated
with the measurement and portrayal of the
Earth.
❖ Geodesy, known also as geodetics, is intimately
concerned with the determination of the size
and shape of the Earth, as well as its elements.
❖ These Earth-based elements include its
terrestrial gravity, magnetic field, tides,
geologic and crustal movement, and polar
motion.
❖ GIS employs these forms of terrestrial
measurement through various data sources,
such as satellite, GPS, and field measurements.
Ocean
Geoid
Earth surface
Gravity Anomaly
Basics of Geodesy
GIS

❖ To adequately represent the shape of the Earth in scientific and
real-life applications, a calculable, formula-driven figure of the
Earth is needed.
❖ In its most basic sense, an Earth ellipsoid is a flattened sphere that
bulges in the middle and has two imaginary lines traversing its
core: one from north to south and one from east to west. Each
imaginary line is called an axis.
❖ The ellipsoid’s flattening causes two unequal axes: a longer axis
and a shorter axis
❖ The north-to-south axis through the Earth’s core is the shorter axis
and, as such, is called the minor axis or polar axis.
❖ The east-to-west axis through the Earth’s core is longer and is
called the major axis or equatorial axis
Mathematical Model of the Earth GIS

❖ The Earth’s ellipsoid is an ellipse rotated upon its
minor axis, which is functionally called the axis of
rotation or axis of revolution. The purpose of a
mathematical model is to simplify calculations.
❖ Due to the Earth’s symmetry and to minimize
complexity, the mathematical model targets one
quadrant in the ellipse and imparts six key
parameters for calculation.
GIS

❖ The six parameters are the
• Semi major axis
• Semi minor axis
• Flattening
• Inverse flattening
• Eccentricity,
• and second eccentricity.
❖ In brief, the flattening of the ellipse is directly related to
the differences in both the semi major and semi minor
axes. It is represented by the formula
Flattening f= (a-b)/a
GIS

❖ Earth’s flattening is sometimes displayed as a reciprocal
called the inverse flattening.
❖ For instance, a flattening of 0.003389831 (or 1/295) can
be portrayed as an inverse flattening of 295.
❖ Eccentricity e is the first eccentricity, whereby the
descriptor first is typically implied. It measures the degree
of flattening as the relationship between the focal radius,
or radius from the center point to the foci (i.e., F1, F2),
and the semimajor axis.
GIS

❖ Second eccentricity e ′ measures the degree of flattening
as a relationship between the focal radius and the
semiminor axis.
❖ Eccentricity (first and second) is constant throughout the
entire ellipse and ranges from 0 to 1, or more simply from
an ellipsoid with no flattening (circle) to one totally flat
(line). Since a circle has no flattening, its eccentricity
equals zero (e = 0). As e becomes larger and approaches
1, the ellipse becomes flatter until it is a straight line (e =
1).
GIS

GIS

❖ Basically, every GIS and geographic information product is based upon
a reference ellipsoid, which is defined as a standard ellipsoid with
proven and measured parameters.
❖ The reference ellipsoid enables GIS to define point locations with
regional accuracy.
❖ Throughout the years, numerous reference ellipsoids have been
developed by various geodesists with measurements taken at different
source points on Earth.
❖ These reference ellipsoids are only slightly dissimilar. Because of this
differentiation in source data locations, certain reference ellipsoids
work better than others for certain applications and for certain regions.
❖ Unlike Bessel 1841 and other major area-specific ellipsoids, WGS84 is
much more universal and, as a result, is one of the most widely used
reference ellipsoids available.
Reference Ellipsoids
GIS

Primary Types of Geodetic Datums
▪ Geodetic datum's empower the user
with a referenced-based geographic
coordinate system within which
accurate point positions can be
determined.
▪ In a two-dimensional space, point
positions are defined by a coordinate pair
(x, y) on a uniform plane.
▪ In the real three-dimensional world,
height (z) is as important a distinguisher as
the x and y coordinates.
GIS

• Geodetic datum's, both local and geocentric,
offer the opportunity to manage these
horizontal and vertical levels for greater
positional accuracy.
• This leads us into the two primary types of
geodetic datum's:
- horizontal control datum's
- and vertical control datum's.
GIS

▪ A horizontal control datum (or horizontal datum) is used to manipulate and set a position in the x and y
directions. Horizontal datum's are often defined by a reference ellipsoid and a coordinate origin.
▪ Alternately, a vertical control datum (or vertical datum) is used to manipulate and set a positional height in the z
direction.
▪ Vertical datum's provide a level from which positional heights can be determined. Both primary types of
geodetic datum's provide a favorable degree of positional control.
GIS

World Geodetic System 1984
• The World Geodetic System 1984 (WGS84) is considered a
global datum that defines an Earth-fixed global reference frame
for the Earth.
• WGS84 is based upon the ellipsoidal parameters of the
Geodetic Reference System of 1980.
• WGS84 is used for GPS satellites and is defined by a gravity
model of the Earth.
• WGS is a geocentric datum that made its first appearance in
1960.
• A product of the U.S. Defense Mapping Agency (DMA) for
mapping and charting, the WGS has evolved from the
primitive satellite measurements of 1960 (WGS60) to the
sensitive Doppler satellite data and satellite data altimetry used
in the latest and highly accurate WGS84.
• With its satellite-driven precision, WGS84 has proved to be a
satisfactory reference datum for nearly every Earth location.
GIS

• Given its Earth-fixed nature, WGS84 offers a
standard reference ellipsoid with base
parameters being:
Semimajor axis a =6 378 137 meters
Semiminor axis b=6 356752 .314 meters
Flattening f= 0.003352811
Inverse flattening 1/f = 298.2572236
• Due to its general accuracy worldwide,
WGS84 is a highly used, worldwide datum
(and reference ellipsoid). In fact, due to its
global appeal, many applications require local
datums to be converted to WGS84.
World Geodetic System 1984
GIS

The Vertical Datum
• Today, vertical datums provide just such a
reference from which positional heights on
the Earth’s topographical surface can be
determined with reasonable accuracy.
• There are two primary reference surfaces
used by leading vertical datums: sea levels
(tidal) and standard ellipsoids (geodetic).
• References for sea level–based datums vary
from high and low tide levels to an average
sea level.
• Ellipsoid-based datums generally reference
the same ellipsoid model used for
calculating horizontal datums.
• By function, GIS utilizes these same
reference surfaces when defining general and
specific point heights.
GIS

The orthometric height of a point is the distance H along a plumb line from the point to a reference height.
When the reference height is a geoid model, orthometric height is for practical purposes "height above sea
level".
Orthometric Height:
GIS

Standard Vertical Datums
• The heights or depths of terrestrial points are
determined through referencing the defined
elevation surface of a vertical datum.
• Like the horizontal datum, the need for
positional accuracy has prompted the
development of standardized vertical datums.
• Once again, each major province or country
has its own national standard datum of choice
or design. They are used throughout the world
for elevation-related reference and precision
along the z axis.
• Four commonly used vertical control datums
for the Earth model, namely the Earth
Gravitational Model of 1996, the GEOID03
reference family, the National Geodetic
Vertical Datum of 1929, and the North
American Vertical Datum of 1988.
GIS

Earth Gravitational Model of 1996
• The Earth Gravitational Model of 1996 (EGM96) is the accurate collaborative product of the National
Imagery and Mapping Agency (NIMA), the NASA Goddard Space Flight Center, and the Ohio State
University.
• EGM96 is a geopotential model of the Earth, which means that orthometric height (height above
MSL) is adjusted using the differential of gravity with latitude and elevation.
• Therefore, EGM96 offers heights that are influenced and adjusted by the Earth’s gravity.
• As a well-defined global vertical datum, EGM96 is used as a modern reference for numerous
applications worldwide, such as bathymetrical and geophysical studies.
GIS

GIS

Geodesy md. yousuf gazi

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