basic geodesy

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1/27 Merriam-Webster: a branch of applied mathematics concerned with the determination of the size and shape of the earth and the exact positions of points on its surface and with the description of variations of its gravity field

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Basic Geodesy. Merriam-Webster:   a branch of applied mathematics concerned with the determination of the size and shape of the earth and the exact positions of points on its surface and with the description of variations of its gravity field. Basic Geodesy. - PowerPoint PPT Presentation

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Merriam-Webster:  a branch of applied mathematics concerned with the

determination of the size and shape of the earth and the exact positions of points on

its surface and with the description of variations of its gravity field

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Basically it is what we use to geo-reference or position our civil works projects with respect to other related

projects such as SLOSH models, historical high water marks, ADCIRC

models, DFIRMS, Bridges, etc.

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EratosthenesEgypt about 240 BC

Syene

Alexandria

500mi

7 º 12’

or

1/50th

of a circle

Eratosthenes had observed that on the day of the summer solstice, the midday sun shone to the bottom of a well in the Ancient Egyptian city

of Swenet (known in Greek as Syene).

Sun not directly overhead

To these observations, Eratosthenes concluded that

the circumference of the earth was 50 x 500 miles, or

25000 miles.

The accepted value along the equator is 24,902 miles, but, if you

measure the earth through the poles the value is 24,860 miles

He was within 1% of today’s accepted value

Eratosthenes' conclusions were highly regarded at the time, and his estimate of the Earth’s size was accepted for hundreds of

years afterwards.

He knew that at the same time, the sun was not directly overhead at

Alexandria; instead, it cast a shadow with the vertical equal to

1/50th of a circle (7° 12').

He also knew that Alexandria and Syene were 500 miles apart

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Gravity: Local Attraction

Unfortunately, the density of the earth’s crust is not uniformly the same. Heavy rock, such as an iron ore deposit, will have a stronger attraction than lighter materials. Therefore, the geoid (or any equipotential surface) will notnot be a simple mathematical surface.

Vertical DatumsVertical DatumsThe GeoidThe Geoid

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What is the GEOID?• ““The The equipotential surfaceequipotential surface of the Earth’s of the Earth’s

gravity field which best fits, in the least gravity field which best fits, in the least squares sense, global mean sea level.”squares sense, global mean sea level.”

• Can’t see the surface or measure it Can’t see the surface or measure it directly.directly.

• Modeled from gravity data.Modeled from gravity data.

Vertical DatumsVertical DatumsThe GeoidThe Geoid

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Equipotential Surfaces

Reference Surface (Geoid)

Topography

The GeoidThe GeoidVertical DatumsVertical Datums

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An ellipsoid of revolution is the figure which would be obtained by rotating an ellipse about its shorter axis. The GRS80 ellipsoid is used for the NAD83.

a= 6378137.00000 metersb= 6356752.31414 meters

f= 1/(a-b)/a = 298.2572220972

So we squash the sphere to fit better at the poles.

This creates a spheroid

a = 6,378,137.00000 m

b =

6,3

56,7

52.3

1414

m

Close Fit At The Equator

But The Poles Are Out

NAD83 uses the

GRS80 Ellipsoid

GRS80 fits geoid to about +/- 300’

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9/27

h

Ear

th’s

S

urf

ace

P

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A point, line, or A point, line, or surface used as a surface used as a reference, as in reference, as in

surveying, mapping, surveying, mapping, or geology. or geology.

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GRS80-WGS84CLARKE 1866

GEOID

Earth Mass Center

Approximately 236 meters

Local vs. Global Reference Ellipsoid

Basic GeodesyBasic Geodesy

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UNITED STATESELLIPSOID DEFINITIONS

CLARKE 1866 a = 6,378,206.4 m 1/f = 294.97869821

GEODETIC REFERENCE SYSTEM 1980 - (GRS 80)a = 6,378,137 m 1/f = 298.257222101

WORLD GEODETIC SYSTEM 1984 - (WGS 84) a = 6,378,137 m 1/f = 298.257223563

BESSEL 1841 a = 6,377,397.155 m 1/f = 299.1528128

Basic GeodesyBasic Geodesy

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Ellipsoid vs. Geoid

• Ellipsoid– Simple Mathematical Definition– Described by Two Parameters– Cannot Be 'Sensed' by Instruments

• Geoid– Complicated Physical Definition– Described by Infinite Number of Parameters– Can Be 'Sensed' by Instruments

Vertical DatumsVertical Datums

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Ellipsoid vs. Geoid

Vertical DatumsVertical Datums

High Density

Low DensityellipsoidgeoidEarth’s surface

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N = separation between geoid and ellipsoid

(Geoid03)

h = elevation relative to ellipsoid (GRS80)

This is what we reference our project elevations to. These are the

elevations you get from the NGS datasheets and traditionally were obtained from geodetic leveling

h = H + N

The geoid is the equipotential surface of the earth’s attraction and rotation which, on the average, coincides with mean sea level in the open ocean.

They are instead referenced to the GRS80 ellipsoid, that squashed sphere that best fits the earth and is used for NAD83

Let’s take a look at the difference between NAVD88 elevations (orthometric heights) and the ellipsoid heights from GPS

H

GPS heights are not related to either orthometric or hydraulic/tidal elevations.

h

N

To convert GPS derived heights to NAVD88 you must use the latest geoid model (currently Geoid03)

H = elevation relative to geoid (orthometric or NAVD88)

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Geoid ModelGeoid Model

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H is measured traditionally h is measured with GPS ObservationsN is modeled using Gravity Models

Vertical DatumsVertical Datums

hh = H + N = H + N

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NSRS Coordinate Systems

Latitude & Longitude State Plane Coordinates

UTM Coordinates

NAD 83NAD 27

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Surfaces Used In State Plane Coordinate Systems

Lambert Projection Transverse Mercator Projection

East-West North-South

EARTH

IMAGINARY CYLINDER

A

C

B

D

A

C D

B

IMAGINARY CONE

EARTH

•Conformal (preserve distances and directions within defined limits)Conformal (preserve distances and directions within defined limits)158 miles for 1:10,000158 miles for 1:10,000

Basic GeodesyBasic Geodesy

158 miles wide

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Conic ProjectionsConic Projections(Lambert)(Lambert)

The lines where the cone is tangent or

secant are the places with the least distortion.

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Cylindrical ProjectionsCylindrical Projections(Mercator)(Mercator)

Transverse

Oblique

The lines where the cylinder is tangent or secant are the places

with the least distortion.

Panhandle of Alaska

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2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 222 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

168W 162 156 150 144 138 132 126 120 114 108 102 96 90 84 78 72 66 60 54W

UTM Zones

Basic GeodesyBasic Geodesy

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UTM Zone 14

Equator-120° -90 ° -60 °

-102° -96°

-99°

Origin

Basic GeodesyBasic Geodesy

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NAD83 State Plane Coordinate ZonesNAD83 State Plane Coordinate ZonesState Plane Coordinate System - 1983State Plane Coordinate System - 1983

Basic GeodesyBasic Geodesy

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NAD83 State Plane Units of MeasureNAD83 State Plane Units of Measure

Basic GeodesyBasic Geodesy

2007

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Additional Information Available at:

http://crunch.tec.army.mil/information/SM_CoP/ndsp

[email protected]