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NATIONAL SPATIAL REFERENCE SYSTEM

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Title: NATIONAL SPATIAL REFERENCE SYSTEM


1
State Plane Coordinates and Datum Transformations
Michigan Society of Professional Surveyors Iron
Mountain and Novi May 20 22, 2008
David Doyle Chief Geodetic Surveyor National
Geodetic Survey Dave.Doyle_at_noaa.gov, (301)
713-3178 (ftp//ftp.ngs.noaa.gov/dist/DaveD/MSPS/)

2
PROGRAM OUTLINE
Geodetic Reference Systems (Horizontal and
Vertical) New Adjustment of NAD 83 Map
Projection Concepts Scale Factor Ellipsoid
Reduction Factor Mapping/Convergence
Angle Datum Transformation Methods
3
ACRONYMS US
R
ITRF 00
NAD 27
GRS 80
FBN/CBN
NSRS
CORS
WGS 84
NAVD 88
HPGN
HARN
NGVD 29
NAD 83
4
http//www.ngs.noaa.gov
5
Our Positioning History
Whats In a Name?
1807 - Survey of the Coast
1836 - Coast Survey
1878 - US Coast and Geodetic Survey
1970 - National Ocean Service National
Geodetic Survey
1970 - National Geodetic Survey (NOS geodetic
functions)
6
1807 President Thomas Jefferson signs
legislation establishing the Survey of the Coast
7
Ferdinand Hassler (1770-1843)
8
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9
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10
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11
Coordinate Systems
  • Latitude Longitude
  • State Plane Coordinates
  • UTM Coordinates
  • NAD 83
  • NAD 27
  • NAVD 88
  • NGVD 29
  • WGS 84
  • ITRF
  • ….. Having trouble deciding what to use?

12
NATIONAL SPATIAL REFERENCE SYSTEM(NSRS)
  • Consistent National Coordinate System
  • Latitude
  • Longitude
  • Height
  • Scale
  • Gravity
  • Orientation
  • and how these values change with time

13
NSRS COMPONENTS
14
METADATA??
Horizontal Datum??
Plane Coordinate Zone ??
Units of Measure ??
How Accurate ??
15
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16
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17
GEODETIC DATUMS
  • HORIZONTAL
  • 2 D (Latitude and Longitude) (e.g. NAD 27, NAD 83
    (1986))
  • VERTICAL
  • 1 D (Orthometric Height) (e.g. NGVD 29, NAVD 88,
    Tidal)
  • GEOMETRIC
  • 3 D (Latitude, Longitude and Ellipsoid Height)
  • Fixed and Stable - Coordinates seldom change
  • (e.g. NAD 83 (1994), NAD 83 (2007))
  • also
  • 4 D (Latitude, Longitude, Ellipsoid Height,
    Velocities) Coordinates change with time
  • (e.g. ITRF00, ITRF05)

18
HORIZONTAL DATUMS
  • 8 Constants
  • 3 specify the location of the origin of the
    coordinate system.
  • 3 specify the orientation of the coordinate
    system.
  • 2 specify the dimensions of the reference
    ellipsoid

19
HORIZONTAL DATUMS
  • NAD 27
  • 39o 13 26.686
  • ? 98o 32 30.506
  • h 0.000 m

Azimuth a 255o 28 09.63 Deflection N-S
0.00 Deflection E-W 0.00
20
Earth-Centered Earth-Fixed (ECEF)
Coordinate System
Z
XA, YA,ZA
Conventional Terrestrial Pole 1984.0 Bureau
International de l'Heure (BIH) now the IERS
-X
-Y
Greenwich Meridian
Earth Mass Center
X, Y, Z 0
Y
X
-Z
21
3-D Coordinates derived from GPS
X1 Y1 Z1
X2 Y2 Z2
X3 Y3 Z3
X4 Y4 Z4
Z
XA YA ZA
NA EA hA
A
Greenwich Meridian
Earth Mass Center
GEOID03
ZA
- Y
- X
NA EA HA
YA
XA
Y
X
- Z
Equator
22
THE ELLIPSOID A MATHEMATICAL MODEL OF THE EARTH
N
b
a
a Semi major axis b Semi minor axis f
a-b Flattening a
S
23
UNITED STATES ELLIPSOID 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
24
VERTICAL DATUMS
  • A set of fundamental elevations to which other
    elevations are referred
  • Datum Types
  • Tidal Defined by observation of tidal
    variations over a specified epoch of time
  • Geodetic Typically based on Local Mean Sea
    Level at one or more points for a specified epoch
    of time

25
NGVD 29 TIDE CONTROL
26
NGVD 29 and NAVD 88
27
ELLIPSOID - GEOID RELATIONSHIP
H Orthometric Height (NAVD 88)
h Ellipsoidal Height (NAD 83)
N Geoid Height (GEOID 03)
H h N

h
H
N
GEOID03
Geoid
Ellipsoid GRS80
28
International Earth Rotation and Reference System
Service (IERS)
The International Terrestrial Reference System
(ITRS) constitutes a set of prescriptions and
conventions together with the modeling required
to define origin, scale, orientation and time
evolution ITRS is realized by the
International Terrestrial Reference Frame (ITRF)
based upon estimated coordinates and velocities
of a set of stations observed by Very Long
Baseline Interferometry (VLBI), Satellite Laser
Ranging ( SLR), Global Positioning System and
GLONASS (GNSS), and Doppler Orbitography and
Radio- positioning Integrated by Satellite (
DORIS). ITRF89, ITRF90, ITRF91, ITRF92, ITRF93,
ITRF94, ITRF95, ITRF96, ITRF97, ITRF2000,
ITRF2005 (Released two weeks ago)
29
International Terrestrial Reference Frame 4
Global Independent Positioning Technologies
International Global Navigation Satellite Systems
Service (IGS)
International Laser Ranging Service (ILRS)
International Very Long Baseline Service (IVS)
International DORIS Service (IDS)
30
ARE NAD 83 WGS 84 THE SAME?
Federal Register Notice Vol. 60, No. 157, August
15, 1995, pg. 42146 Use of NAD 83/WGS 84 Datum
Tag on Mapping Products
31
WORLD GEODETIC SYSTEM 1984
DATUM WGS 84(G873) 5 USAF GPS Tracking
Stations 7 NIMA Evaluation Stations Datum
redefined with respect to the International
Terrestrial Reference Frame of 1994 (ITRF94) /-
10 cm in each component (Proceedings of the ION
GPS-97 pgs 841-850)
DATUM WGS 84(G730) 5 USAF GPS Tracking
Stations 5 DMA Evaluation Stations Datum
redefined with respect to the International
Terrestrial Reference Frame of 1992 (ITRF92) /-
20 cm in each component (Proceedings of the ION
GPS-94 pgs 285-292)
DATUM WGS 84 RELEASED - SEPTEMBER 1987 BASED ON
OBSERVATIONS AT MORE THAN 1900 DOPPLER STATIONS
DATUM WGS 84(G1150) Datum redefined with
respect to the International Terrestrial
Reference Frame of 2000 (ITRF00) /- 2 cm in
each component (Proceedings of the ION GPS-02)
http//earth-info.nima.mil/GandG/sathtml/IONRepor
t8-20-02.pdf
HOW MANY WGS 84s HAVE THERE BEEN????
32
MY SOFTWARE SAYS IM WORKING IN
WGS-84
Unless you are doing autonomous positioning
(point positioning /- 6-10 meters) youre
probably NOT in WGS-84
Project tied to WGS-84 control points obtained
from the Defense Department -- Good Luck!
Youre really working in the same reference frame
as your control points -- NAD 83?
33
EARLY NAD 83 NETWORK PROBLEMS
  • NOT GPSABLE

POOR STATION ACCESSIBILITY
IRREGULARLY SPACED
POSITIONAL ACCURACY
34
HIGH ACCURACY REFERENCE NETWORK
(HARN) 1989 - 1997
  • GPSABLE
  • Clear Horizons for Satellite Signal Acquisition
  • EASY ACCESSIBILITY
  • Few Special Vehicle or Property Entrance
    Requirements
  • REGULARLY SPACED
  • Always within 20-100 Km
  • HIGH ACCURACY
  • A-Order (5 mm 110,000,000) (3 5.5 hr sessions)
  • B-Order (8mm 11,000,000) (2 5.5 hr sessions)

35
FEDERAL COOPERATIVE BASE
NETWORKS (FBN/CBN) 1997
- 2004
  • MORE STATE PARTNERSHIPS
  • REMOVE DISTORTIONS IN EARLY HARNS
  • (3-10 CM)
  • ENSURE CONNETIONS TO CORS
  • IMPROVE ELLIPSOID HEIGHT ACCURACY
  • (Not more than 2 cm)

36
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37
MICHIGAN HARN 1994 2003
38
HPGN HARN FBN - CBN
39
THE GEOID
An equipotential surface to which gravity is
normal that most closely approximates mean sea
level on a global basis
A level surface that is everywhere perpendicular
to the plump line
A lake is an equipotential surface
40
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41
NAD 27 GEOID HEIGHTS
MEADES RANCH 1891
42
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43
FUTURE GEOID MODELS
National Geospatial-Intelligence Agency
(NGA) EGM08 Mid 2008 Estimate globally 20-50 cm
National Geodetic Survey GEOID08 Winter 2008
Goal 2-4 cm (conterminous U.S.)
44
National Geodetic Survey, Retrieval Date
APRIL 25, 2008 QL0101

QL0101 FBN - This is a Federal Base
Network Control Station. QL0101 DESIGNATION -
ISABELLA QL0101 PID - QL0101 QL0101
STATE/COUNTY- MI/DELTA QL0101 USGS QUAD -
GARDEN CORNERS (1985) QL0101 QL0101
CURRENT SURVEY CONTROL QL0101
__________________________________________________
_________________ QL0101 NAD 83(2007)- 45 53
41.73795(N) 086 36 59.89990(W) ADJUSTED
QL0101 NAVD 88 - 192.881 (meters)
632.81 (feet) ADJUSTED QL0101
__________________________________________________
_________________ QL0101 EPOCH DATE -
2002.00 QL0101 X - 262,435.849
(meters) COMP QL0101 Y
- -4,439,072.424 (meters)
COMP QL0101 Z - 4,557,239.950
(meters) COMP QL0101
LAPLACE CORR- 1.07 (seconds)
DEFLEC99 QL0101 ELLIP HEIGHT-
157.275 (meters) (02/10/07) ADJUSTED
QL0101 GEOID HEIGHT- -35.62 (meters)
GEOID03 QL0101 DYNAMIC HT -
192.883 (meters) 632.82 (feet) COMP
QL0101 QL0101 ------- Accuracy Estimates (at
95 Confidence Level in cm) -------- QL0101
Type PID Designation
North East Ellip QL0101 ---------------------
----------------------------------------------
QL0101 NETWORK QL0101 ISABELLA
0.55 0.39 1.65 QL0101
--------------------------------------------------
----------------- QL0101 MODELED GRAV-
980,621.3 (mgal) NAVD 88
QL0101 QL0101 VERT ORDER - FIRST CLASS 0
QL0101 QL0101.The horizontal coordinates were
established by GPS observations QL0101.and
adjusted by the National Geodetic Survey in
February 2007. QL0101 QL0101.The datum tag of
NAD 83(2007) is equivalent to NAD 83(NSRS2007).
QL0101.See National Readjustment for more
information. QL0101.The horizontal coordinates
are valid at the epoch date displayed above.
QL0101.The epoch date for horizontal control is a
decimal equivalence QL0101.of Year/Month/Day.
H h - N 192.88 157.28 - (-
35.62) 192.88 ? 192.90
45
QL0101 North East
Units Scale Factor Converg. QL0101SPC MI N
- 123,619.298 8,029,750.259 MT 0.99992591
0 16 37.5 QL0101SPC MI N - 405,575.12
26,344,325.00 iFT 0.99992591 0 16 37.5
QL0101UTM 16 - 5,082,444.737 529,740.672
MT 0.99961087 0 16 31.0 QL0101 QL0101!
- Elev Factor x Scale Factor
Combined Factor QL0101!SPC MI N -
0.99997534 x 0.99992591 0.99990126
QL0101!UTM 16 - 0.99997534 x
0.99961087 0.99958622 QL0101
QL0101-------------------------------------------
-------------------------- QL0101 PID
Reference Object Distance
Geod. Az QL0101
dddmmss.s
QL0101 QL0100 ISABELLA RM 1
21.763 METERS 08613 QL0101 QL0103
ISABELLA AZ MK
2483759.2 QL0101 QL0102 ISABELLA RM 2
19.014 METERS 25629
QL0101-------------------------------------------
-------------------------- QL0101 QL0101
SUPERSEDED SURVEY CONTROL
QL0101 QL0101 ELLIP H (06/11/02) 157.268 (m)
GP( ) 4 1 QL0101 NAD
83(1994)- 45 53 41.73838(N) 086 36
59.89939(W) AD( ) B QL0101 ELLIP H
(09/20/95) 157.271 (m)
GP( ) 1 2 QL0101 NAD 83(1986)- 45 53
41.72963(N) 086 36 59.89454(W) AD( ) 2
QL0101 NAD 27 - 45 53 41.83000(N) 086
36 59.37200(W) AD( ) 2 QL0101 NAVD 88
(09/20/95) 192.88 (m) 632.8 (f)
LEVELING 3 QL0101 NGVD 29 (??/??/92)
192.87 (m) 632.8 (f) COMPUTED 1
0 QL0101 QL0101.Superseded values are not
recommended for survey control. QL0101.NGS no
longer adjusts projects to the NAD 27 or NGVD 29
datums. QL0101. QL0101_MARKER DS
TRIANGULATION STATION DISK QL0101_SETTING 7
SET IN TOP OF CONCRETE MONUMENT QL0101_SP_SET
SET IN TOP OF CONCRETE MONUMENT QL0101_STAMPING
ISABELLE 1954 QL0101_MARK LOGO CGS
46
CONTINUOUSLY OPERATING REFERENCE STATIONS (CORS)
  • 1300 Installed and Operated by various
    Federal-State-local Agencies
  • NOAA/National Geodetic Survey
  • NOAA/OAR Global Systems Division
  • U.S. Coast Guard - DGPS/NDGPS
  • Corps of Engineers - DGPS
  • FAA - WAAS/LAAS
  • State DOTs
  • County and City
  • Academia
  • Private Companies

47
CONTINUOUSLY OPERATING REFERENCE STATIONS (CORS)
  • Dual-Frequency
  • Antennas and Receivers
  • Allen-Osborne
  • Ashtech/Thales
  • Leica
  • Topcon
  • Trimble

48
CONTINUOUSLY OPERATING REFERENCE STATIONS (CORS)
  • NGS PROVIDES
  • Horizontal and Vertical NSRS Connections
  • NAD 83 and ITRF00 Coordinates
  • Network Data Collection - Hourly Daily
  • Daily 3D Network Integrity Adjustment
  • Public Data Distribution - Internet
  • 13 Year On-Line Data Holding

49
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50
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51
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52
NORWAY (MINW), MICHIGAN _______________________
__________________________________________________
____

Antenna Reference Point(ARP) NORWAY CORS ARP
--------------------
-------------------------
PID DH7129




ITRF00 POSITION (EPOCH 1997.0)
Computed in
November 2005 using 53 days of data.
X 161837.249 m
latitude 45 47 24.35889 N
Y -4452310.855 m longitude 087
55 05.77063 W Z
4549193.690 m ellipsoid height 255.888 m


ITRF00 VELOCITY
Predicted with
HTDP_2.7 November 2005.
VX -0.0185 m/yr
northward -0.0010 m/yr
VY -0.0016 m/yr eastward
-0.0185 m/yr VZ
-0.0005 m/yr upward 0.0003 m/yr



NAD_83 (CORS96)
POSITION (EPOCH 2002.0)
Transformed from ITRF00 (epoch
1997.0) position in Nov. 2005.
X 161837.786 m latitude 45 47
24.32840 N Y
-4452312.197 m longitude 087 55 05.74803
W Z 4549193.738 m
ellipsoid height 256.871 m

NAD_83 (CORS96)
VELOCITY
Transformed from ITRF00 velocity in
Nov. 2005.
VX -0.0000 m/yr northward 0.0000 m/yr
VY 0.0000 m/yr
eastward 0.0000 m/yr
VZ -0.0000 m/yr upward
0.0000 m/yr
_______________________________________________
______________________________
53
WILLOW RUN (WRUN), MICHIGAN Retrieved from NGS
DataBase on 04/15/05 at 205637.
__________________________________________________
___________________________

Antenna Reference Point(ARP)
WILLOW RUN CORS ARP
-------------------------------------------------

PID DG9787



ITRF00 POSITION (EPOCH 1997.0)

Computed in April 2005 using 30 days of data.
X
531992.164 m latitude 42 14 05.17869 N
Y -4699633.726 m
longitude 083 32 30.07427 W
Z 4265072.758 m ellipsoid height
186.603 m

ITRF00 VELOCITY

Predicted with HTDP_2.7 April 2005.
VX -0.0174
m/yr northward 0.0008 m/yr
VY -0.0017 m/yr eastward
-0.0175 m/yr VZ
0.0008 m/yr upward 0.0003 m/yr



NAD_83 (CORS96)
POSITION (EPOCH 2002.0)
Transformed from ITRF00 (epoch
1997.0) position in Apr. 2005.
X 531992.700 m latitude 42 14
05.14941 N Y
-4699635.124 m longitude 083 32 30.05787
W Z 4265072.855 m
ellipsoid height 187.742 m

NAD_83 (CORS96)
VELOCITY
Transformed from ITRF00 velocity in
Apr. 2005.
VX 0.0000 m/yr northward 0.0000 m/yr
VY -0.0000 m/yr
eastward 0.0000 m/yr
VZ 0.0000 m/yr upward
0.0000 m/yr
_______________________________________________
______________________________
54
CORS DATA QUALITY
55
What is OPUS?
  • On-Line Positioning User Service
  • Processes GPS data
  • Global availability (masked)
  • 3 goals
  • Simplicity
  • Consistency
  • Reliability

56
How Does OPUS Compute Position?
NGS-PAGES software used L3-fixed solution w/
tropo adjusted 3 best CORS selected 3 separate
baselines computed 3 separate positions
averaged Position differences also include any
errors in CORS coordinates
57
http//www.ngs.noaa.gov/OPUS
58
WHAT CAN I EXPECT FROM OPUS
NGS OPUS SOLUTION
REPORT
USER
dave.doyle_at_noaa.gov DATE
April 25, 2008 RINEX FILE minw092k.08o
TIME 161542 UTC SOFTWARE
page5 0612.06 master2.pl START
2008/04/01 100000 EPHEMERIS igs14732.eph
precise STOP 2008/04/01
130000 NAV FILE brdc0920.08n
OBS USED 6185 / 6543 95 ANT
NAME LEIAT504 LEIS FIXED
AMB 40 / 40 100 ARP HEIGHT 0.0
OVERALL RMS 0.011(m)
REF FRAME NAD_83(CORS96)(EPOCH2002.0000)
ITRF00 (EPOCH2008.2499) X
161837.777(m) 0.023(m)
161837.032(m) 0.023(m) Y
-4452312.198(m) 0.015(m)
-4452310.875(m) 0.015(m) Z
4549193.735(m) 0.009(m)
4549193.682(m) 0.009(m) LAT 45 47
24.32830 0.009(m) 45 47 24.35843
0.009(m) E LON 272 4 54.25153
0.022(m) 272 4 54.21929 0.022(m)
W LON 87 55 5.74847 0.022(m) 87
55 5.78071 0.022(m) EL HGT
256.869(m) 0.015(m) 255.891(m)
0.015(m) ORTHO HGT 291.387(m)
0.029(m) Geoid03 NAVD88
UTM COORDINATES STATE PLANE COORDINATES
UTM (Zone 16) SPC
(2111 MI N) Northing (Y) meters 5071135.583
112309.325 Easting (X) meters
428628.421 7928605.666 Convergence
degrees -0.65822977
-0.66371159 Point Scale 0.99966262
0.99993995 Combined Factor
0.99962237 0.99989969
BASE STATIONS USED PID
DESIGNATION LATITUDE
LONGITUDE DISTANCE(m) DI0208 MIIR IRON RIVER CORS
ARP N460449.372 W0883800.111
64165.2 DG9743 MIMQ MARQUETTE CORS ARP
N463243.941 W0872243.276 93744.2 AJ5569 SUP2
ESCANABA CORS ARP N454458.109
W0870424.599 65865.5
MINW PUBLISHED NAD 83 Lat 24.32840 (0.003
m) Long 05.74803 (0.010 m) h 256.871
(0.002 m)
59
Many Flavors of OPUS Planned
  • OPUS
  • receiver, hours of data
  • OPUS-DB
  • receiver, hours of data, share results
  • OPUS Rapid Static
  • receiver, minutes of data
  • OPUS Projects
  • Multiple receivers, hours, share results
  • OPUS MAPPING
  • receiver, minutes of data

60
OPUS-DB OBSERVATION DATA STREAM
description form
photo(s)
GPS data
Observation log
NGS website OPUS-DB
NGS magic
DATASHEET
61
OPUS DB
62
OPUS DB
63
OPUS DB
64
OPUS DB Simple Shared Data NGS Archived
65
NAD 83 National Readjustment
  • Early GPS observations (prior to 1992) did not
    benefit from high accuracy GPS orbit data.
  • Early GPS observations (prior to 1995) did not
    have access to CORS.
  • HARN observations prior to 1997 did not focus on
    the vertical.
  • Some HARNs exhibit 4 7 cm difference with CORS
  • Different NAD 83 adjustment tags (e.g., NAD 83
    1994) in adjoining states causes confusion.

66
NAD 83 National Readjustment
  • NOT a new datum. A readjustment within the
    original NAD 83 framework
  • GPS only Classical (triangulation) was not be
    included
  • National CORS used as control
  • All GPS data submitted to NSRS was included
  • Network and Local Accuracies computed
  • No changes to NAD 83 State Plane Coordinate
    System parameters

67
NAD 83 National Readjustment
  • 3065 Projects included
  • Free Adjustment
  • Outliers Rejected
  • Connectivity to CORS, A/B Order Network verified
  • 67,693 total stations
  • 1,090 stations in Michigan
  • No national transformation model (e.g. NADCON)

68
NAD 83 TRASH
  • Projects Not Recommended for Inclusion
  • 149 projects with 9903 stations
  • Many Third-Order FAA Projects from 1980s
  • Some projects that have no ties to the Network
  • Includes original TN HARN (Macrometer Data)
  • Included original Eastern Strain Network project

69
NEW STANDARDS FOR GEODETIC CONTROL
  • TWO ACCURACY STANDARDS
  • local accuracy ------------- adjacent
    points
  • network accuracy ---------- relative to CORS
  • Numeric quantities, units in cm (or mm)
  • Both are relative accuracy measures
  • Do not use distance dependent expression
  • Horizontal accuracies are radius of 2-D 95 error
    circle
  • Ellipsoidal/Orthometric heights are 1-D (linear)
    95 error

70
NAD 83 NATIONAL READJUSTMENT
  • NAD 83 data that is NOT part of NSRS must be
    readjusted by contractor/user with original
    observations

71
WHAT YOU NEED TO USE THE STATE PLANE COORDINATE
SYSTEMS
  • N E State Plane Coordinates for Control
    Points
  • AZIMUTHS
  • - True, Geodetic, or Grid
  • - Conversion from Astronomic to Geodetic
  • - Conversion from Geodetic to Grid (Mapping
    Angle)
  • DISTANCES
  • - Reduction from Horizontal to Ellipsoid
  • Sea-Level Reduction Factor
  • - Correction for Grid Scale Factor
  • - Combined Factor

72
STATE PLANE COORDINATE MANUALS (http//www.ngs.noa
a.gov/PUBS_LIB/pub_index.html)
73
MAP PROJECTIONS
Lambert Conformal Conic
Transverse Mercator
74
LAMBERT CONFROMAL CONIC WITH 2 STANDARD PARALLELS
75
TRANSVERSE MERCATOR
76
CONVERGENCE ANGLE (Mapping Angle)
The Convention of the Sign of the Convergence
Angle is Always From Grid To
Geodetic
Convergence angles (?) always positive ()
East
Convergence angles (?) always negative (-) West
?O
CENTRAL MERIDIAN
77
CONVERGENCE ANGLE (Mapping Angle)
78
LAMBERT CONFROMAL CONIC WITH 2 STANDARD PARALLELS
Grid Scale Factor
SCALE gt 1
?N
SCALE EXACT
STANDARD PARALLELS
SCALE lt 1
?S
SCALE EXACT
SCALE gt 1
?O
CENTRAL MERIDIAN
79
d
GEODETIC vs. GRID DISTANCE
c
d
c
b
b
a
a
80
Michigan State Plane Coordinate System NAD 83
Geometic Parameters remain the same Zone
Boundaries Central Meridian North/South Standard
Parallels Latitude/Longitude of Origin
False Northing and Easting Changed and defined in
meters Conversion to Feet left up to individual
states U.S. Survey or International Feet
81
NORTH STANDARD PARALLEL
CENTRAL MERIDIAN
SOUTH STANDARD PARALLEL
ORIGIN 44o 47 00 87o 00 00
N 0 m E 8,000,000 m
82
COORDINATE CHANGES (STATE PLANE)
  • STATION ISABELLA
  • MICHIGAN NORTH ZONE (NAD 27/NAD 83)
  • Northing Easting Converg
    Angle Scale Factor
  • 405,596.34 ft. 2,097,649.60 ft. 0o 16
    37.9 0.99996411
  • 123,619.298 m. 8,029,750.259 m. 0o 16 37.5
    0.99992591
  • (405,574.31 ft) (26,344,272.31 ft)
  • (405,575.12 ft) (26,344,325.00 ft)
  • (0.81) (52.69)
  • Converted using U.S. Survey Foot, 1 M
    3.2808333333 Ft.
  • Converted using International Foot, 1 M
    3.2808398501 Ft.

83
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84
STATE PLANE COORDINATE COMPUTATION
  • ISABELLA
  • N 405,575.12 International Feet
  • E 26,344,325.00 International Feet
  • Orthometric Height (H) 632.81 Feet
  • Geoid Height (N) - 116.86 Feet
  • Laplace Correction 1.07
  • Grid Scale Factor (k) 0.99992591
  • Meridian Convergence (g) 0o 16 37.8
  • Observed Astro Azimuth (aA) 253o 26 14.9
  • Horizontal Distance (D) 3,314.91 Feet

85
STATE PLANE COORDINATE COMPUTATION
  • N1 N (Sg x cos ag)
  • E1 E (Sg x sin ag)
  • Where
  • N Starting Northing Coordinate
  • E Starting Easting Coordinates
  • Sg Grid Distance
  • ag Grid Azimuth

86
REDUCTION TO THE ELLIPSOID
D
h
H
S
N

R Earth Radius
6,372,200 m 20,906,000 ft.
S D x ___R__ R h
h H N
87
REDUCTION TO THE ELLIPSOID
  • N the Radius of Curvature in
  • the Prime Vertical, NOT
  • Geoid Height
  • a Ellipsoid semi-major axis
  • b Ellipsoid semi-minor axis
  • Azimuth of the line
  • F Latitude of the Station


WHERE
e (a2 b2)1/2 / a
88
REDUCTION TO ELLIPSOID with and w/o Geoid Height
  • S D x R / (R h)
  • D 3,314.91 ft (Measured Horizontal Distance)
  • R 20,906,000 ft (Mean Radius of the Earth)
  • h H N (H 633 ft, N - 117 ft)
  • 516 ft (Ellipsoid Height)
  • S 3,314.91 20,906,000 / 20,906,000 516
  • S 3,314.91 x 0.99997532
  • S 3,314.83 ft
  • S 3,314.91 20,906,000 / 20,906,000 633
  • S 3,314.91 x 0.99996972
  • S 3,314.81 ft
  • Diff 0.02 ft or 1166,000

89
GRID SCALE FACTOR (k) OF A LINE
  • k 12 (k1 4km k2) / 6
  • (m mean of k1 k2)
  • Typically the Average Value Works Fine
  • k 12 (k1 k2) / 2

90
REDUCTION TO GRID
  • Sgrid S (Geodetic Distance) x k (Grid Scale
    Factor)
  • Sgrid 3,314.83 x 0.99992591
  • Sgrid 3,314.58 meters

91
COMBINED FACTOR (CF)
  • CF Ellipsoidal Reduction x Grid Scale Factor
    (k)
  • 0. 0.99997532 x 0.99992591
  • 0.99990123
  • CF x D Sgrid
  • 0.99990123 x 3,314.91 3,214.58 ft

92
AZIMUTH RELATIONSHIP
  • True Azimuth Derived from astronomic
    observations (e.g. Solar/Polaris)
  • Geodetic Azimuth Derived from the inverse
    between two points of known latitude and
    longitude, or from a LaPlace corrected astronomic
    observation
  • Grid Azimuth Derived from the inverse between
    two points defined in northing easting
  • (e.g. State Plane, UTM, local grid coordinates)

93
GRID AZIMUTH COMPUTATION
  • agrid aAstro Laplace Correction
    Convergence Angle (g)
  • 253o 26 14.9 (Observed Astro Azimuth)
  • 1.1 (Laplace
    Correction)
  • 253o 26 16.0 (Geodetic Azimuth)
  • - 0 16 37.5 (Convergence Angle)
  • 253o 09 38.5 (Grid Azimuth)
  • The convention of the sign of the convergence
    angle is always from Grid to Geodetic

94
STATE PLANE COORDINATE COMPUTATION
  • N1 N (Sgrid x cos agrid)
  • E1 E (Sgrid x sin agrid)
  • N1 405,575.12 (3,214.58 x Cos 253o 09 38.5)
  • 405,575.12 (3,214.58 x 0.289688462)
  • 405,575.12 (- 931.23)
  • 404,643.89 International Feet
  • E1 26,344,325.00 (3,214.58 x Sin 253o 09
    38.5)
  • 26,344,325.00 (3,214.58 x - 0.957120993)
  • 26,344,325.00 (- 3,076.74)
  • 26,341,248.26 International Feet

95
GROUND LEVEL COORDINATES SURFACE LEVEL
COORDINATES PROJECT DATUM COORDINATES
  • I WANT STATE PLANE COORDINATES RAISED TO GROUND
    LEVEL
  • GROUND LEVEL COORDINATES ARE NOT STATE PLANE
    COORDINATES!!!!!

96
GROUND LEVEL COORDINATES PROBLEMS
  • RAPID DISTORTIONS
  • PROJECTS DIFFICULT TO TIE TOGETHER
  • CONFUSION OF COORDINATE SYSTEMS
  • LACK OF DOCUMENTATION

97
GROUND LEVEL COORDINATES IF YOU DO
  • TRUNCATE COORDINATE VALUES
  • SUCH AS
  • N 404,648.89 ft becomes 4,648.89
  • E 26,341,246.75 ft becomes 1,246.75
  • AND

DOCUMENT DOCUMENT DOCUMENT !!
98
DATUM TRANSFORMATIONS
  • 1. WHAT DATUM ARE THE EXISTING COORDINATES ON?
  • 2. WHAT DATUM DO I WANT THE NEW COORDINATES ON?
  • 3. HOW LARGE A GEOGRAPHICAL AREA DO I WANT TO
    CONVERT AT ONE TIME?
  • 4. HOW MANY POINTS ARE COMMON TO BOTH DATUMS?
  • 5. WHAT IS THE DISTRIBUTION OF THE COMMON
    POINTS?
  • 6. HOW ACCURATE ARE THE EXISTING COORDINATES?
  • 0.1 Foot
  • 1.0 Foot
  • 10. Feet
  • 7. HOW ACCURATE DO I WANT THE NEW COORDINATES?

99
DATUM TRANSFORMATIONS
  • MOLODENSKY
  • Converts latitude, longitude and ellipsoidal
    height to X,Y,Z Earth-Centered Coordinates.
  • Applies a 3-dimensional change in the origin
  • (dX, dY,dZ)
  • Applies a change in the size and shape of the
    reference ellipsoid
  • Converts new X,Y,Z Earth-Centered Coordinates
    back to latitude, longitude and ellipsoidal
    height

100
DATUM TRANSFORMATIONS
  • MOLODENSKY
  • For continental regions accuracy can be /- 8
    to 10 meters
  • Does not model network distortions very well.
  • Assumes heights in both systems are ellipsoidal
    (NAD 27 did not have ellipsoidal heights).

101
MOLODENSKY TRANSFORMATION
102
DATUM TRANSFORMATION IDEAL METHOD
  • SATISFIES ALL USERS REQUIREMENTS
  • CAPABLE OF TRANSFORMING LARGE HOLDINGS OF
    COORDINATE DATA
  • NEAR-REAL TIME APPLICATIONS
  • SIMPLE - METHOD SHOULD NOT REQUIRE AN EXPERT OR
    DECISIONS TO BE MADE
  • ACCURATE

103
NADCON
d? 0.12344 d? -1.87842
d? 0.12249 d? -1.88963
d? 0.12396 d? -1.85209
? 0.12423 ? -1.81246
d? 0.12568 d? -1.83364
d? 0.12449 d? -1.88905
d? 0.12640 d? -1.85407
d? 0.12499 d? -1.86543
104
COORDINATE COMPARISON NAD 27 to NAD 83(2007)
  • MOLODENSY
  • ADJUSTED vs. TRANSFORMED
  • Station ISABELLA
  • LATITUDE
    LONGITUDE
  • 45-53-41.73795
    086-36-59.89990 - PUBLISHED
  • 45-53-41.91245
    086-36-59.34798 - MOLODENSKY
  • .17450
    .55192
  • 5.388 m
    11.898 m
  • THIS CORRESPONDS TO A POSITIONAL
  • DIFFERENCE OF 13.061 m (42.85 ft)

105
COORDINATE COMPARISON NAD 27 to NAD 83(2007)
  • NADCON
  • ADJUSTED vs. TRANSFORMED
  • Station ISABELLA
  • LATITUDE
    LONGITUDE
  • 45-53-41.73795
    086-36-59.89990 - PUBLISHED
  • 45-53-41.73327 086-36-59.89262 -
    NADCON
  • .00468
    .00737
  • 0.144 m
    0.157 m
  • THIS CORRESPONDS TO A POSITIONAL
  • DIFFERENCE OF 0.213 m (0.70 ft)

106
GOOD COORDINATION BEGINS WITH GOOD COORDINATES
GEOGRAPHY WITHOUT GEODESY IS A FELONY
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