Transcript geodesyattamucc.pbworks.com

Lecture 1(Class 2)
GISC3325-Geodetic Science
20 January 2009
Course Update
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Reading assignment for this week: Chapters 13 of the text.
Lab 1 must be received by midnight 21 January
2009.
Next two labs deal with NGS monument
recovery. Details are posted to the class web
page. It involves on-line research and field
work. Points recovered will be used in
subsequent labs.
Topics for today
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Definitions of geodesy
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Divisions of geodesy
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Reference surfaces
for heights
Experiment of
Eratosthenes, the
Father of Geodesy
Geodesy defined
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The discipline that deals with the measurement
and representation of the earth, including its
gravity field, in a three-dimensional time-varying
space. (Vanicek and Krakiwsky)
The problem of geodesy is to determine the
figure and the external gravity field of the earth
and of other celestial bodies as functions of
time; as well as ,to determine the mean earth
ellipsoid from parameters observed on and
exterior to the earth's surface. (Torge)
Why is geodesy important to
land surveyors?
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Surveyors often required to establish vertical
and horizontal control project.
Use of GPS fundamentally linked to geodetic
issues of coordinates, reference frames, etc.
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GIS should have as base layer geodetic control.
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SPCS based on reference ellipsoid
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Coordinate transformations (e.g. between NAD
27 and NAD 83) are geodetic problems.
Datum
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A geodetic datum is represented by a set of
physical monuments on the earth's surface,
published coordinates for these monuments,
and a reference surface upon which the spatial
relationships between the monuments are
known. (textbook)
Another and better definition
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Geodetic datums define the size and shape of
the earth and the origin and orientation of the
coordinate systems used to map the earth.
Hundreds of different datums have been used
to frame position descriptions since the first
estimates of the earth's size were made by
Aristotle. Datums have evolved from those
describing a spherical earth to ellipsoidal
models derived from years of satellite
measurements.
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From Peter Dana's site:
http://www.colorado.edu/geography/gcraft/notes/datum/datum.htm
l
Divisions of Geodesy
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Areas of emphasis in geodesy include:
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Geometric
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Physical
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Satellite
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Astronomy
Getting positions and heights from GPS
involves all these areas.
Remember: h – H – N = 0 plus errors in h,H,
and N
Reference Surfaces
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Topographic surface
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Geometric reference surface
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Physical reference surface
Their Characteristics
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Topographic surface is where we live and work.
It usually corresponds with neither the geometic
nor physical reference surface.
Geometric reference surface is the
mathematical reference system used for making
calculations.
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Sphere – used in astronomical computations and
for approximate results.
Ellipse – more precise but more complex. The
Earth as an ellipsoid of revolution takes into
account for flattening of the sphere.
Physical reference Surface
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Geoid, is from the Greek for "Earth-shaped", is
the common definition of our world's shape.
This recursive description is necessary because
no simple geometric shape matches the Earth.
Our definition: The equipotential surface of the
Earth's gravity field which best fits, in a least
squares sense, global mean sea level.
Geoid model from GRACE data
Heights
Heights
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Point on topographic surface (terrain)
Ellipsoid height (h) is the distance from the
ellipsoid reference surface to the terrain.
H – Orthometric height (NAVD88) is the
distance from the geoid to the terrain.
N – Geoid height is the distance between the
geoid and the ellipsoid reference surface.
From below: -23.949(h) – 1.83(H) (-25.75)(N) = 0.029 error
AH1762 ***********************************************************************
AH1762 HT_MOD
- This is a Height Modernization Survey Station.
AH1762 CBN
- This is a Cooperative Base Network Control Station.
AH1762 TIDAL BM - This is a Tidal Bench Mark.
AH1762 DESIGNATION - 877 5870 H TIDAL
AH1762 PID
- AH1762
AH1762 STATE/COUNTY- TX/NUECES
AH1762 USGS QUAD - CRANE ISLANDS SW (1975)
AH1762
AH1762
*CURRENT SURVEY CONTROL
AH1762
___________________________________________________________________
AH1762* NAD 83(2007)- 27 35 17.26666(N) 097 13 22.29500(W) ADJUSTED
AH1762* NAVD 88 1.83 (meters)
6.0 (feet) GPS OBS
AH1762
___________________________________________________________________
AH1762 EPOCH DATE 2002.00
AH1762 X
- -711,246.902 (meters)
COMP
AH1762 Y
- -5,612,090.901 (meters)
COMP
AH1762 Z
- 2,936,118.126 (meters)
COMP
AH1762 LAPLACE CORR0.94 (seconds)
DEFLEC99
AH1762 ELLIP HEIGHT-23.949 (meters)
(02/10/07) ADJUSTED
AH1762 GEOID HEIGHT-25.75 (meters)
GEOID03
Experiment of Eratosthenes
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Measured earth's radius/circumference in 220
BCE
At local noon on the summer solstice it was
possible to see to the bottom of a well in Syene.
On the same day/time he measured the angle
of sun's rays in Alexandria.
He then measured the distance between Syene
and Alexandria.
Using simple geometry, he calculated the radius
and the circumference of the Earth.
Details
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The angle was measured by solving the right
triangle using the known height of a staff and
the shadow formed by the sun.
The angle was found to be 7.2 degrees.
The distance (S) between the two cities was
5000 stade (1 stade ≈ 160 m)
Use equivalent fractions to solve.
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(7.2deg/360deg) = (S / circumference of earth(C))
How good was the result?
Scilab Code - http://www.scilab.org/
Complications
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We don't really know the length of a stade.
Syene and Alexandria are not on the same
meridian making the angle inaccurate.
Angle seems surprisingly convenient (7.2
degrees is 1/50 of a circle).
Unit questions
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We still see problems with unit conversions.
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US Survey foot is equal to 3927/1200 exactly
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International foot is based on relationship of 2.54
cm = one inch.
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Or 3.2808333333... approximately
i.e. (0.0254 * 12) = 0.3048 cm/ft
Or 3.28083989501 meters in one foot
If we confuse the two we get bad results converting
SPCS values.