Terrestrial Data Structures
Representing the Earth:
From the 3D Globe to the 2D map
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GISC 6381 GIS Fundamentals
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Course Content
Part I: Overview
• Fundamentals of GIS
• Hands-on Intro to ArcGIS
– (lab sessions @ 4:00-7:00pm
or 7:00-10:00pm)
Part II: Principles
• Terrestrial data structures
Part III: Practice
• Data Input:
preparation and
integration
• Data analysis and
modeling
• Data output and
application examples
– representing the real world
• GIS Data Structures
– representing the world in a
computer
Part IV: The Future
• Future of GIS
• Data Quality
– An essential ingredient
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Terrestrial Data Structures
Pop Quiz or Cocktail Conversation
• name the states containing the most northerly,
easterly, westerly and southerly points of the US.
• land area of Canada is about:
(a) twice (b) same ( c) half
that of US?
• a degree of latitude is
(a) slightly longer (b) same ( c) slightly shorter
at the poles than at the equator ?
Some Light Reading
– Sobel, Dava Longitude: The True Story of a Lone Genius Who Solved the Greatest
Scientific Problem of His Time London: Fourth Estate, 1996 (paperback 1998)
– Linklater, Arlo Measuring America Peguin Books, 2002 (a fascinating history of
surveying, the Public Land Survey System, measurement and its standardization)
Some Light Viewing (movie)
– The Englishman Who Went Up a Hill and Came Down a Mountain
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…the most southerly point in the US
Where am I?
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Canada twice area of US
Greenland biggest island
Which is correct?
Canada same area as US
Australia biggest island
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Representing the Earth: Topics
•
•
•
•
•
Geoid and Spheroids: modeling the earth
Latitude and Longitude: position on the model
Datums and Surveying: measuring the model
Map Projections: converting the model to 2 dimensions
Scale: sizing the model
– cover under Data Quality
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The Shape of the Earth
• topographic surface
3 concepts
– the land/air interface
– complex (rivers, valleys, etc) and difficult to model
• geoid
– a continuous surface which is perpendicular at every point to the direction of gravity
---surface to which a plumb line is perpendicular
– approximates mean sea-level in open ocean without tides, waves or swell
– “that surface to which the oceans would conform over the entire earth if free to adjust
to the combined effect of the earth's mass attraction and the centrifugal force of the
earth's rotation.” Burkhard 1959/84
– satellite observation (after 1957) showed it to be somewhat irregular ‘cos of local
variations in gravity resulting from the uneven distribution of the earth’s mass.
• Spheres and spheroids (3-dimensional circle and ellipse)
– mathematical models used to approximate the geoid and provide the basis for accurate
location (horizontal) and elevation (vertical) measurement
– sphere (3-dimensional circle) with radius of 6,370,997m considered ‘close enough’
for small scale maps (1:5,000,000 and below - e.g. 1:7,500,000)
– spheroid (3-dimensional ellipse, flattened at the poles) should be used for larger scale
maps of 1:1,000,000 or more (e.g. 1:24,000)
– the issue is, which spheroid?
GPS (global positioning system) measures elevation relative to spheroid.
Traditional surveying via leveling measures elevation relative to geoid.
Land
surface
Spheroid
b -- semi-minor axis
Relationship of Land Surface to Geoid and Spheroid
a=b=sphere (3D circle)
a>b=spheroid (3D ellipse)
>
<
a-- semi-major axis f=flattening=a-b
a
mean sea surface
(geoid)
Perpendicular
to Spheroid
Perpendicular
to Geoid
(plumbline)
Spheroid
(math model)
Geoid
(undulates due to
gravity)
Note that elevation causes distances
measured on ground to be greater than
on the spheroid. Corrections may be applied.
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Which Spheroid?
Hundreds have been defined
depending upon:
Most commonly encountered are:
•
– available measurement technology
– area of the globe (e.g North America,
•
Africa)
– map extent (country, continent or
global)
•
– political issues (e.g Warsaw pact
versus NATO)
• ARC/INFO supports 26 different
spheroids!
– conversions via math. formulae
Earth measurements (approx.):
equatorial radius: 6,378km 3,963mi
polar radius:
6,357km 3,950mi
(flattened about 13 miles at poles)
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•
Everest (Sir George) 1830
– one of the earliest spheroids; India
– a=6,377,276m b=6,356,075m f=1/300.8
Clarke 1886 for North America
– basis for USGS 7.5 Quads
– a=6,378,206.4m b=6,356,583.8m f=1/295
GRS80 (Geodetic Ref. System, 1980)
– current North America mapping
– a=6,378,137m b=6,356,752.31414m
f=1/298
Hayford or International (1909/1924)
– early global choice
– a=6,378,388 b=6,356,911.9m f=
•
WGS84 (World Geodetic Survey, 1984)
– current global choice
– a=6,378,137 b=6,356,752.31m f=
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Latitude and Longitude: location on the spheroid
W 180°
Prime
Meridian
180° E
90° N
Distance between two points on the globe
(great circle or spherical distance):
Cos d = (sin a sin b) + (cos a cos b cos P)
where: d = arc distance
a = Latitude of A
b = Latitude of B
P = degrees of long. A to B
0° Equator
Longitude meridians
Prime meridian is zero: Greenwich, U.K.
International Date Line is 180° E&W
circ.: 40,008km 24,860mi
(equator to pole approx. 10,000,000 meters,
actually 10,001,965.7 meters )
1 degree=69.17 mi at Equator
48.99 mi at 45N/S
0 mi at 90N/S
length long.=cosine of lat * length of 1° of lat.
(1/2 at 60° not 45°)
(distances based on WGS84 spheroid)
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90° S
lat./long coords.
for a location will
change depending
on spheroid chosen!
Latitude parallels
equator is zero
circ.: 40,076km 24,902mi
1 degree=68.71 mi at equator (110,567m.)
69.40 mi at poles
(1 mile=1.60934km=5280 feet)
1 nautical mile=length of 1 minute
6080 ft=1853.248m (Admiralty)
6076.115ft=1852m (international)
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Latitude and Longitude Graticule
Prime
Meridian
NW
+ -
NE
+ +
SW
- -
SE
- +
When entering data, be sure to include negative signs.
Longitude sometimes recorded using 360° to avoid
negatives.
Lat and long measured in:
degrees° minutes” seconds’
(60’=1” & 60”=1°)
UTD: 32° 59” 16.0798N 96° 44” 56.9522W
1 second=100ft or 30m. approx.
(lat., or long. at equator)
Decimal degrees, not minutes/seconds,
best for GIS.
dd= d° + m”/60 + s’/3600
Carry enough decimal points for accuracy!
6 decimals give 4 inch (10cm) accuracy
(but must use double precision storage-single precision accurate to only 2m)
UTD: 32.98779994N 96.74915339W
(8 decimals-->1 millimeter accuracy!)
(note: 1 meter= 3.2808 feet)
graticule: network of lines on globe or map representing latitude and longitude.
Origin is at Equator/Prime Meridian intersection (0,0)
grid: set of uniformly spaced straight lines intersecting at right angles.
(XY Cartesian coordinate system)
Latitude normally listed first (lat,long), the reverse of the convention for X,Y Cartesian coordinates
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Measuring Latitude
geodetic latitude (d):
angle of vector
perpendicular to
ellipsoid surface
b -- semi-minor axis
geodetic latitude is
always used.
a-- semi-major axis
Ellipsoid
f=flattening=a-b
a
tangent
c
d
Because the earth is flatter at the poles,
close to poles tangent must ‘move’ further
to change by 1 degree, hence 1 degree of
lat. is longer at poles than at the equator.
geocentric or authalic latitude (c):
angle of vector thru center of ellipsoid
For a sphere, geodetic and geocentric
are the same. On authalic sphere used
for small scale mapping 1° lat = 1° long
= 69.11 miles (both Clark & WGS84)
N
0°
S
E
W
Bisected by a hemisphere!
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Geodesy & Surveying
Process of measuring position (horizontal control) and
elevation (vertical control) of points on earth’s surface (spheroid)
•
Geodetic Surveying: incorporates earth’s shape and curvature
–
–
•
used to establish location of survey monuments which provide basis for all measurements.
conducted in US by the National Geodetic Service (previously the US Coast and Geodetic Survey) in the
Dept. of Commerce.
Plane Surveying: assumes earth is flat
– employed by local surveyors for small geographic area (building site, sub-division, etc.)
– usually uses survey monuments as starting point.
Techniques:
– all employ ‘triangulation:’ using geometry to impute unknown positions and distances based
on certain measured angles or distances between other known locations.
– earlier techniques based on visual sighting (from starting point, then back to it) using:
• invar-tape (very small coefficient of expansion) for distance measurement
• theodolites (or less accurate transits in local surveys) to measure angles for horizontal positioning (also
measure vertical angles for elevation)
• levels and graduated rods for accurate vertical measurement.
– modern techniques use:
• laser based instruments to measure distances
• gps (global positioning system) receivers to establish location and elevation
• cost one fifth as much as traditional approaches!
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Datums:
--any numerical or geometrical quantity or set of such quantities
which serve as a reference or base for other quantities
--all horizontal or vertical positions are relative to a specific datum
For the Geodesist (and for GIS)
• a set of parameters defining a coordinate system, including:
– the spheroid (earth model)
– a point of origin and an orientation relative to earth’s axis of rotation (ties
spheroid to earth)
For the Local Surveyor
• a set of points whose precise location and /or elevation has been determined,
which serve as reference points from which other locations can be determined
(horizontal datum)
• a surface to which elevations are referenced usually ‘mean sea level’ (vertical
datum)
• points usually marked with brass plates called survey markers or monuments
whose identification codes and precise locations (usually in lat/long) are
published.
Unlike with spheroids and map projections, there is not necessarily a math. formulae
for conversion between datums, although ‘equivalency tables’ may be available15
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•
Original North
American
Datums
NAD83
1900 US Standard Datum
– first nationwide datum
– Clark 1866 spheroid
– origin Meades Ranch,
Osborne Cnty, KS
(39-13-26.686N 98-32-30.506W)
– determined by visual triangulation
– approx. 2,500 points
– renamed North American Datum
(NAD) in 1913 when adopted by
Mexico and Canada
•
NAD27
–
–
–
–
–
Clark 1866 spheroid
Meades Ranch origin
visual triangulation
25,000 stations (250,000 by 1970)
NAVD29 (North American Vertical
Datum, 1929) provided elevation
– basis for most USGS 7.5 minute
quads
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– satellite (since 1957) and laser distance data
showed inaccuracy of NAD27
– 1971 National Academy of Sciences report
recommended new datum
– used GRS80 spheroid (functionally equivalent to
WGS84 altho. not identical)
– origin: Mass-center of Earth
– 275,000 stations
– “Helmert blocking” least squares technique fitted
2.5 million other fed, state and local agency points.
– NAVD88 provides vertical datum
– points can differ up to 160m from NAD27, but
seldom more than 30m, (and data from a digitized
map more inaccurate than datum difference)
– no mathematical formulae for conversion from
NAD27: See USGS Survey Bulletin # 1875 for
conversion tables (in ARC/INFO)
– completed in 1986 therefore called NAD83
(1986)!
– but new data coming from gps was more accurate!
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Current US Datum Programs:
National Geodetic Reference System(NGRS)/
National Spatial Reference System(NSRS)
Continuously Operating Reference
Stations (CORS)
( first called HPGN-High Precision GPS Network)
– NAD83 not ‘gps-able’
• continuos measurement of location
• inaccessible monuments (hill tops)
from GPS satellites
• irregular spacing of monuments
• 500 km spacing
– get destroyed
• DFW site in Arlington run by
– too many (275,000) to maintain
TXDOT (about 70 in TX as of 2007)
• insufficient accuracy for precision work (at 1m or less)
– 3-Tier Plan
• posted hourly on the Internet
• federal base network (FBN)
• Use for differential GPS, calibrating
– ~1,600-2,000 monuments
gps instruments, monitor crustal
– 5-8 mm accuracy (A or B order)
movement, etc.
– evenly spaced 1 degree by 1 degree (75-125 kms);
– 3 year visitation cycle
• datum revision know as NAD83
• cooperative base network (CBN-states)
(CORSxx) since several been
– ~16,000 monuments
released (‘93, ‘94, ’96, etc)
– 25-30km spacing; B-order accuracy
High Accuracy Reference Network (HARN)
–
no coop agreement with Texas!
• user densification network
– Diff. from NAD83 (HARN) <10cm
Reference
– local points connected to FBN/CBN
Lapine, Lewis A. National Geodetic Survey: Its
Mission, Vision, and Goals, US Dept of
– Revision known as NAD83(HARN)
Commerce, NOAA, October, 1994
• Issued on a regional basis from 1989 thru 1997
Snay and Soler Professional Surveyor Dec 1999,
• Differs from NAD83 (1986) by <=1m (horizon.)
Feb 2000
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Measuring Elevation
• so far focused on horizontal location (“x,y”)
• vertical location or elevation (z) also important
• Traditional surveying uses “leveling” to measure elevation relative to mean sea level
(MSL)
–
–
–
–
–
published on standard paper maps based on NAVD1929 or NAVD88 for US
MSL is arithmetic mean of hourly water elevations observed over a 19 year cycle
MSL is different for different countries or locations
NAVD88 based on mean sea level at Rimouski, Quebec, Canada on St Laurence gulf
Leveling follows geoid, thus elevations (orthometric height) are relative to geoid
• GPS (global positioning systems) knows nothing about geoid so its elevations
(called ellipsoid height) are relative to a spheroid (usually WGS84)
• The two may be (and usually are) different—by as much as 87 meters worldwide
– in Texas ellipsoid heights about 27 meters less (lower) than orthometric (geoid) ht.
– Spheroid (ellipsoid) above geoid everywhere in US
Land surface
Geoid03 is a gravity model of the geoid for the
US and may be used to “correct” GPS
Geoid height
elevations (ellipsoid height) to correspond to
traditional surveyed heights above geoid
Geoid
(orthometric height)
http://www.ngs.noaa.gov/GEOID
Spheroid
Ellipsoid height
U.S.
Orthometric height
Geoid
heights
for U.S.
(relative to
WGS84
spheroid)
Texas average about -27m
Source:
http://www.ngs.noaa.gov/GEOID/
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--values negative since geoid is below
WGS84 spheroid
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GISC 6381 GIS Fundamentals
Measuring Area (reference)
Acre is the standard measurement of land area in the US
• Originally, the area that could be worked by a team of oxen in a
day (approximately!), and varied from state to state in Ben
Franklin’s days!
• Equals 43,560 sq. feet, 4,840 sq. yards, or 10 sq. chains
• A surveyor’s chain (or Gunter’s Chain) is 66 feet long
– A rod, pole or perch is 16.5 feet, thus 4 rods equals a chain
• An acre is 1 chain by 10 chains, or 66 feet by 660 feet
• 640 acres in a square mile
Hectare
• Standard measurement of land area in metric system
• Equals 100 meters by 100 meters, or 10,000 square meters
– 100 hectares in a square kilometer
• Equivalent to 2.471 acres or 107,639 square feet.
For fascinating detail, see A. Linklater, Measuring America Peguin Books, 2002
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Map Projections: the concept
• A method by which the curved 3D surface of the earth is
represented on a flat 2D map surface.
• a two dimensional representation, using a plane coordinate
system, of the earth’s three dimensional sphere/spheroid
• location on the 3D earth is measured by latitude mad longitude;
• location on the 2D map is measured by x,y Cartesian coordinates
• unlike choice of spheroid, choice of map projection does not
change a location’s lat/long coords, only its XY coords.
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Map Projections:
the inevitability of distortion
• because we are trying to represent a 3-D sphere on a 2-D
plane, distortion is inevitable
• thus, every two dimensional map is distorted (inaccurate?)
with respect to at least one of the following:
–
–
–
–
area
shape
distance
direction
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We are trying to represent
this amount of the earth on
this amount of map space.
GISC 6381 GIS Fundamentals
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Map Projections: classification
Classified by property preserved or by geometrical model
Property Preserved
Geometric Model Used
•
•
•
•
Equal area projections preserve the
area of features (popular in GIS)
Conformal projections preserve the
shape of small features (good for
presentations) , and show local
directions (bearings) correctly
(useful for coastal navigation!)
Equidistant projections preserve
distances (scale) to places from
one point, or along a one or more
lines
True direction projections preserve
bearings (azimuths) either locally
(in which case they are also
conformal) or from center of map.
Azimuth: angle between a great circle (line on
globe) and a meridian.
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–
–
along one line (tangent) or
cuts thru globe along two lines (secant)
(usually parallels of latitude)
cone is then unfolded to create “flat map”
•
– Scale can never be correct
everywhere on any map
•
•
Planar/Azimuthal/Zenithal: image of
spherical globe is projected onto a map
plane which is tangent to (touches) globe
at single point
conical: image of spherical globe is
projected onto a cone which touches
cylindrical: image of spherical globe is
projected onto a cylinder which again
– may be tangent along one line,
– or secant along two lines
– again, cylinder is unfolded to create a
“flat map”
See Apppendix for detail
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Azimuthal Projections
Possible Light sources for Azimuthal Polar Projections
Conic and Cylindrical Projections
Great circle
Central meridian
Geometric Models and Projection Parameters
• Knowing simply the type of projection is usually insufficient in GIS
• Projections parameters must also be known for any set of projected data
• These describe the exact transformation used and depend on geometric model
Azimuthal
• The lat/long coordinates for
the point of tangency
• May be
– Polar (north or south)
– Equatorial (point on equator)
– Oblique (any other point)
• Note that light source may
– Earth center (gnomonic)
– Earth opposite (stereographic)
– Parallel rays (orthographic)
Conic
• Standard Parallel(s)
– Where cone touches/cuts thru globe
– One if tangent, two if secant
• Central meridian
– Down center of cone
Cylindrical
– Normal: tangent at equator
– Transverse, therefore must know
• Central meridian
– Oblique, therefore must know
• Great circle
Additionally must always know:
--origin of axis of coordinate system (‘false origin’ often used)
--measurement units of coordinate system (feet, meters, etc..)
Commonly Encountered Map Projections in GIS
• American Polyconic
– early projection used by USGS; usually only encountered on older maps; replaced
by transverse mercator.
– “Neither conformal nor equivalent, it minimizes distance distortion on large scale
maps” (quote from Monmonier: http://www.markmonmonier.com/work6.htm)
• Albers Conic Equal-Area
– often used for US base maps showing all of the “lower 48” states
– standard parallels set at 29 1/2N and 45 1/2N
• Lambert Conformal Conic
– often used for US Base map of all 50 states (including Alaska and Hawaii), with
standard parallels set at 37N and 65N
– also for State Base Map series, with standard parallels at 33N and 45N
– also used in State Plane Coordinate System (SPCS)
– Great circles (shortest distance point to point on globe) are straight lines
• Transverse Mercator (conformal cylindrical)
– used in SPCS for States with major N/S extent
– Basis for Universal Transverse Mercator (UTM) systems used for standardized
mapping worldwide and for United States National Grid (USNG)
Most commonly, for relatively large scale maps, you encounter the last 3
projections, along with the SPCS and UTM projections systems which use them.
27
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GISC 6381 GIS Fundamentals
Universal Transverse Mercator (UTM)
•
•
•
first adopted by US Army in 1947 for large scale maps worldwide
used from lat. 84°N to 80°S; Universal Polar Stereographic (UPS) used for polar areas
globe divided into 60 N/S zones, each 6° wide; these are numbered from one to sixty going
east from 180th meridian
– Conformal, and by using transverse form with zones, area distortion significantly reduced
•
each zone divided into 20 E/W bands (or “belts”), each 8° high lettered from the south
pole using C thru X (O and I omitted) thus north Texas in “S” belt from 32° (thru
Hillsboro) to 40° (Nebraska/Kansas line).
– These belts of no real relevance for UTM, but important for MGRS and USNG (next slide)
•
the meridian halfway between the two boundary meridians for each zone is designated as
the central meridian and a secant cylindrical projection is done for each zone
– Central meridian for zone 1 is at 177° W
– Standard meridians (secant projection) are approx.150 km either side of this; scale correct here
•
•
scale of central meridian reduced by .9996 to minimize scale variation in zone resulting
in accuracy variation of approx. 1meter per 2,500 meters
coordinate origins are set:
– For Y: at equator for northern hemisphere; at 10,000,000m S. of equator for southern hemi.
– For X: at 500,000m west of central meridian
– thus no negative values within zone, and central meridian is at 500,000m East
40N KS/NE line
102W
96W
UTM in Texas: 13
14
Midland
3 zones
15
Lake
Tawakoni
Dallas is
in 14S
Definitive documentation: http://earth-info.nga.mil/GandG/publications/tm8358.2/TM8358_2.pdf
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Band “S”
32N Hillsboro
28
UTM and SPCS Zones
UTM (and USNG) Grid Zones Worldwide
Prime Meridian
(includes Washington, D.C.)
Zone numbering begins at 180th
meridian and proceeds east in 6° bands
Source: FGDC-STD-001-2001 United States National Grid
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Greenwich Meridian
GISC 6381 GIS Fundamentals
Equator
Vertical belts,
8° tall. Used only in
military and USNG
30
Prime Meridian
Equator
UTM (and USNG) Grid Zones Worldwide
Superimposed on world map
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Source: Wikipedia
31
Military Grid Reference System (MGRS
& United States National Grid (USNG)
•
MGRS developed initially by US military and then adopted by the FGDC (Federal Geographic Data
Committee) as the USNG formal standard in 2001 (FGDC-STD-011-2001)
–
•
Goals is to provide standard coordinate based “address locator” applicable to both analog and digital
maps, supporting
–
–
•
Consequently MGRS and USNG are the same within the US
Disaster response
Location based services (where is closest MacDonalds?)
Based on UTM.
– Each primary UTM Grid Zone Designation (GZD) (the 6 ° long. by 8 ° lat. areas) identified by a
number/letter combination (e.g 14S for north Texas, 18S for central east coast of US)
– Each GZD divided into 100,000 meter by 1000,000 meter (100km x 100km) squares each
identified by two letters (QB for DFW, UJ for Washington, D.C.)
– Within each 100,000-meter-square, points locations are based on UTM east/north coordinates
• Easting (“read across”) and northing (“then go up”) must always have the same number of digits.
• number of digits used depends on precision requirements
– Example for Washington monument
–
–
–
–
–
–
–
18S--locates within the 6 ° long. by 8 ° lat. zone
18SUJ—locates within a 100km by 100km square
18SUJ20--Locates with a precision of 10 km (within a 10km square)
18SUJ2306 - Locates with a precision of 1 km (uses 2 digits)
18SUJ234064 – Locates with a precision of 100 meters (3 digits—within a city block)
18SUJ23480647 - Locates with a precision of 10 meters (4 digits—a single house)
18SUJ2348306479 - Locates with a precision of 1 meter (5 digits—a parked vehicle)
– Founders Bldg UTD: 14S QB 10316 52184 (1 meter precision)
for more info: http://www.fgdc.gov/usng/
http://usgrid.gmu.edu/resources.html
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Global
Locating the
Washington
Monument: USNG
14S
18S UJ 23483 06479
(NAD83)
Regional
483 meters
Source: How to Read a United States National Grid
(USNG) Spatial Address The Public XY Mapping Project
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479 meters
33
(NAD83)
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Example USN
34
US 75 @ 15th
USNG 100km Grid Squares
Source: FGDC-STD-001-2001 United States National Grid
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State Plane Coordinate System (SPCS)
•
•
began in 1930s for public works projects; popular with interstate designers.
states divided into 1 or more zones (~130 total for US)
– each zone designed to maintain scale distortion to less than 1 part per 10,000
•
•
Texas has 5 zones running E/W: north (5326/4201), north central (5351/4202), Central
(5376/4203), south central (5401/4204), south (5426/4205) (datumID/fipsID)
Different projections used:
– transverse mercator (conformal) for States with
large N/S extent
– Lambert conformal conic for rest (incl. Texas)
– some states use both projections (NY, FL, AK)
– oblique mercator used for Alaska panhandle
•
each zone also has:
– unique standard parallels (2 for Lambert) or central meridian (1 for mercator)
– false coordinate origins which differ between zones, and use feet for NAD27
and meters for NAD83
– (1m=39.37 inches exact used for conversion; differs slightly from NBS 1”=2.54cm)
– scale reduction used to balance scale across entire zone resulting in accuracy
variation of approx. 1 per 10,000 thus 4 times more accurate than UTM
•
See Snyder, 1982 USGS Bulletin # 1532, p. 56-63 for details
easting
Co-ordinate Values for
Selected Coordinate Systems -96.52
northing
Coords for NE Corner
32.99 long/lat
Dallas County (NE & SW corners)
731,900 3,652,850 UTM
SPCS (5351)
NAD27 NAD83
785,000 2,148,400 SPCS meters
spheroid
Clarke 1886
GRS80
2,575,000 7,048,000 SPCS feet
central meridian: 97.5W
98.5W
reference latitude*: 31.67N 31.67N 2,300,000
482,000 SPCS ft (NAD27)
stan. parallel 1:
32.13
32.13
stan. parallel 2:
33.96
33.96
false easting: 2,000,000ft 600,000m
false northing:
0
2,000,000m
* origin point for coordinates
Note: by default AV displays in meters
Coords for SW Corner
easting
northing
Dallas County
(all coordinates NAD83
unless otherwise noted)
Meters north
of equator
Note: coords derived
graphically so feet/meter
conversions not exact
(1m = 3.281ft)
1 degree of lat approx.=
10,000,000m/90° =
111,111m
UTM zone 14 (NAD83)
bounding meridians: 102W & 96W
-97.03
32.56
long/lat
central meridian:
99W
684,800 3,603,800 UTM meters
false easting:
500,000 m
737,800 2,099,650 SPCS meters
false northing:
0
2,420,000 6,888,000 SPCS feet
2,144,200 324,000 SPCS feet (NAD27)
37
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Parameters for SPCS in Texas
Source: ARCDoc--SPCS, derived from Snyder
State & Zone Name
Texas, North
Texas, North Central
Texas, Central
Texas, South Central
Texas, South
Abbrev. Datum ZONE
TX_N
5326
TX_NC
5351
TX_C
5376
TX_SC
5401
TX_S
5426
FIPSZONE
4201
4202
4203
4204
4205
State Plane Zones - Lambert Conformal Conic Projection (parameters in degrees, minutes, seconds)
Zone 1st Std.Parallel 2nd Std.Parallel CentralMeridian Origin(Latitude) False Easting (m) False Northing(m)
NAD83
TX_N
TX_NC
TX_C
TX_SC
TX_S
NAD27
TX_N
TX_NC
TX_C
TX_SC
TX_S
34 39 00
32 08 00
30 07 00
28 23 00
26 10 00
36 11 00
33 58 00
31 53 00
30 17 00
27 50 00
-101 30 00
-98 30 00
-100 20 00
-99 00 00
-98 30 00
34 00 00
31 40 00
29 40 00
27 50 00
25 40 00
200000
600000
700000
600000
300000
1000000
2000000
3000000
4000000
5000000
34 39 00
32 08 00
30 07 00
28 23 00
26 10 00
36 11 00
33 58 00
31 53 00
30 17 00
27 50 00
-101 30 00
-97 30 00
-100 20 00
-99 00 00
-98 30 00
34 00 00
31 40 00
29 40 00
27 50 00
25 40 00
609601.21920
609601.21920
609601.21920
609601.21920
609601.21920
0
0
0
0
0
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38
Texas Statewide Mapping System (TSMS)
http://www.tnris.state.tx.us/DigitalData/projections.htm
•
•
•
•
•
•
•
•
•
•
•
Mapping System Name: Texas State Mapping System
Abbreviation: TSMS
Projection: Lambert Conformal Conic
Longitude of Origin (central meridian): 100° West (-100)
Latitude of Origin: 31° 10’ North (31.16)
Lower Standard Parallel: 27° 25’ (27.416)
Upper Standard Parallel: 34° 55’ (34.916)
False Easting: 1,000,000 meters
False Northing: 1,000,000 meters
Datum: North American Datum of 1983 (NAD83)
Unit of Measure: meter
This is the standard (set, 1992) for a map covering all of Texas.
see: http://www.dir.state.tx.us/tgic/pubs/gis-standards-1992.htm
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Texas Map Projections
Texas Department of Information Resources, 2001
Conformal
Equal Area
•
•
•
•
•
•
•
•
•
•
•
•
Mapping System Name: Texas Centric
Mapping System/Lambert Conformal
Abbreviation: TCMS/LC
Projection: Lambert Conformal Conic
Longitude of Origin (central meridian):
100° West (-100)
Latitude of Origin: 18° North (18)
Lower Standard Parallel: 27° 30’ (27.5)
Upper Standard Parallel: 35° (35.0)
False Easting: 1,500,000 meters
False Northing: 5,000,000 meters
Datum: North American Datum of 1983
(NAD83)
Unit of Measure: meter
•
•
•
•
•
•
•
•
•
•
Mapping System Name: Texas Centric
Mapping System/Albers Equal Area
Abbreviation: TCMS/AEA
Projection: Albers Equal Area Conic
Longitude of Origin (central meridian):
100° West (-100)
Latitude of Origin: 18° North (18)
Lower Standard Parallel: 27° 30’ (27.5)
Upper Standard Parallel: 35° (35.0)
False Easting: 1,500,000 meters
False Northing: 6,000,000 meters
Datum: North American Datum of 1983
(NAD83)
Unit of Measure: meter
These projections are also used!
“The nice thing about standards is that there are so many to choose from.”
John Quartermain The Matrix
They are all available as defined projections in ArcGIS 9 under State Systems (not the same as State Plane!)
Coordinate Systems: critical required information
To correctly use any set of projected data in GIS, the following
critical information (metadata) is required at minimum
• Datum (required also for data in lat./long coordinates)
• Projection type (Mercator, Lambert conformal conic, etc.)
• Projection parameters
For conic and cylindrical
– Central meridian
– Standard parallel (for tangent)
• both standard parallels for secant
For azimuthal
• Point of contact
– Point of origin for coordinate system
(often expressed as false easting & northing)
• Unit of measurement
– Feet, meters, etc.
Note: The term geographic projection often used to
refer to data in lat/long units.
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All this info. should
be recorded on every
printed map, and
stored in metadata
for digital files!
41
Choosing a Map Projection
• Issues to Consider:
– extent of area to map: city, state, country, world?
– location: polar, mid-latitude, equatorial?
– predominant extent of area to map: E-W, N-S, oblique?
}
detail in Appendix
• Rules of thumb
– Choose a standard for your organization and keep all data that way.
– Also retain lat/long coords in the GIS database if possible
– for small areas, projection is less critical and datum is more critical; reverse
for large areas
– check contract; does it specify a required projection? State Plane or UTM
often specified for US gov. work.
– use equal-area projections for thematic or distribution maps, and as a general
choice for GIS work
– use conformal projections in presentations
– for navigational applications, need true distance or direction.
– Even though modern GIS systems are sophisticated in their handling of
projections, you ignore them at your peril!!!
42
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The US displayed using a
“Geographic Projection”
• treats lat/long as X,Y
• has no desirable properties
other than convenience
• don’t do it!
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Map of State Plane zones
Do not do it!
GISC 6381 GIS Fundamentals
43
How ArcGIS Handles
Coordinates and Projections
• The coordinate reference
system of the display view is
determined by the first layer
opened in the view
•
•
– projection assoc. with entire view, not
any one layer
– Once ArcMAp has been informed of the
original projection of the data, you can
re-project the view.
– this applies to the display only. The
underlying data files are not changed in
any way
– To change the underlying data files, use
ArcCatalog
• Geographic (lat/long)
• Projected (by type and
parameters)
– This may or may not be known
• As other layers are added, they
are:
– Re-projected “on-the-fly” to that
of the view if their reference
system and reference system of
first layer is known
– Displayed “as is” (and thus
potentially incorrectly) if either is
not know (warning issued)
If the projection of the first layer was
not already recorded, you must select
View/Data Frame Properties and either
select Coordinate System tab to specify
projection of View
•
For correct measurement only, you can
select General tab
– Map Units: may be “unknown” when
data read in
–
• user sets it based on actual units for raw
data (e.g decimal degrees)
Display units (distance units in AV 3.2): for
reporting measurements (e.g. miles)
• map units must be specified before display
units can be set
• if map units specified incorrectly, distance
measures will be wrong!
Summary: Measuring Position on Earth
X-Y coordinates
--derived via projection from lat/long
--represent position on 2-D flat map
surface
Lines of latitude and Longitude
Where am I?
This guy’s latitude and
longitude (and elevation)
differ depending on
spheroid used.
Elevation of land surface may be:
--above geoid
(traditional surveying)
--above spheroid (GPS)
--are drawn on the spheroid
--establish position on 3-D spheroid
Spheroid: “math model
representing geoid”
Spheroid+tiepoint=datum
Geoid:
Land Surface:
--line of equal gravity
--mean sea level with no
wind or tides
References on Map Projections and Related Topics
•
•
•
•
•
•
•
•
•
Smith, James R. Introduction to Geodesy: The History and Concepts of Modern Geodesy
New York, John Wiley, 1997
Yang, Snyder, Tobler Map Projection Transformation: Principles and Applications,
Taylor and Frances, 2000
Lev M Bugayevskiy, J. P Snyder Map Projections: A Reference Manual Taylor and
Frances, 1995
Snyder, John P. Map Projections--A Working Manual US Geological Survey Professional
Paper #1395, 1987
Snyder, John P. Map Projections Used by the US Geological Survey, USGS Bulletin
#1532, 2nd. ed., 1983
Melita Kennedy and Steve Kopp. Understanding Map Projections: Redlands, CA, ESRI,
Inc, 1994
Maling, D.H. Coordinate Systems and Map Projections, London, George Philip, 1973
Robinson, Arthur H. et. al. Elements of Cartography. New York: John Wiley, 5th ed.,
1995
White, C. Albert A History of the Rectangular Survey System Washington, D.C. USGPO,
1982
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Appendix
Projection Reference Materials
Useful articles on ESRI's Support Site:
FAQ: Where can I find more information about coordinate systems, map
projections, and datums?
http://support.esri.com/index.cfm?fa=knowledgebase.techarticles.articleShow&d=17420
FAQ: Projection Basics: What the GIS professional needs to know
http://support.esri.com/index.cfm?fa=knowledgebase.techarticles.articleShow&d=23025
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Map Projections by Property Preserved:
Shape and Area
• Conformal (orthomorphic)
–
–
–
–
–
–
preserves local shape by using correct angles; local direction also correct
lat/long lines intersect at 90 degrees
area (and distance) is usually grossly distorted on at least part of the map
no projection can preserve shape of larger areas everywhere
use for ‘presentations’; most large scale maps by USGS are conformal
examples: mercator, stereographic
• Equal-Area (Equivalent or homolographic))
–
–
–
–
–
area of all displayed features is correct
shape, angle, scale or all three distorted to achieve equal area
commonly used in GIS because of importance of area measurements
use for thematic or distribution maps;
examples: Alber’s conic, Lambert’s azimuthal
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Map Projections by Property Preserved:
Distance and Direction
• Equidistant
– preserves distance (scale) between some points or along some line(s)
– no map is equidistant (i.e. has correct scale) everywhere on map (i.e. between all
points)
– distances true along one or more lines (e.g. all parallels) or everywhere from one point
– great circles (shortest distance between two points) appear as straight lines
– important for long distance navigation
– examples: sinusoidal, azimuthal
• True-direction
–
–
–
–
–
provides correct direction (bearing or azimuth) either locally or relative to center
rhumb lines (lines of constant direction) appear as straight lines
important for navigation
some may also be conformal, equal area, or equidistant
examples; mercator (for local direction), azimuthal (relative to a center point)
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Map Projections by Geometry
Planar/Azimuthal/Zenithal
• map plane is tangent to (touches) globe at single point
• accuracy (shape, area) declines away from this point
• projection point (‘light source’) may be
– earth center (gnomic): all straight lines are great circles
– opposite side of globe (stereographic): conformal
– infinitely distant (orthographic): ‘looks like a globe’
• good for polar mappings: parallels appear as circles
• also for navigation (laying out course): straight lines from tangency
point are all great circles (shortest distance on globe).
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Map Projections by Geometry
Conical
• map plane is tangent along a line, most commonly a parallel of latitude
which is then the map’s standard parallel
• cone is cut along a meridian, and the meridian opposite the cut is the
map’s central meridian
• alternatively, cone may intersect (secant to) globe, thus there will be
two standard parallels
• distortion increases as move away from the standard parallels (towards
poles)
• good for mid latitude zones with east-west extent (e.g. the US), with
polar area left off
• examples: Alber’s Equal Area Conic, Lambert’s Conic Conformal
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Map Projections by Geometry
Cylindrical
• as with conic projection, map plane is either tangent along a single
line, or passes through the globe and is thus secant along two lines
• mercator is most famous cylindrical projection; equator is its line of
tangency
• transverse mercator uses a meridian as its line of tangency
• oblique cylinders use any great circle
• lines of tangency or secancy are lines of equidistance (true scale), but
other properties vary depending on projection
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Best Map Projections by Size of Area
World/Hemisphere
• World - Conformal
MERCATOR, TRANSVERSE,
OBLIQUE_MERCATOR
• World - Equal Area
CYLINDRICAL, ECKERTIV, ECKERTVI,
FLAT_POLAR_QUARTIC
MOLLWEIDE, SINUSOIDAL
• World - Equidistant:
AZIMUTHAL
• World - straight rhumb line:
MERCATOR
• World - Compromise:
MILLER, ROBINSON
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• Hemisphere - Conformal
STEREOGRAPHIC, POLAR
• Hemisphere - Equal Area
LAMBERT_AZIMUTHAL
• Hemisphere - Equidistant
AZIMUTHAL
• Hemisphere - Global look
ORTHOGRAPHIC
NAMES correspond to ARC/Info commands
GISC 6381 GIS Fundamentals
53
Best Map Projections by Size of Area:
continent or smaller
• E/W along equator
MERCATOR (conformal)
CYLINDRICAL (equal area)
• E/W away from Equator
LAMBERT (conformal)
ALBERS (equal area)
• North/South
TRANSVERSE, UTM (conformal)
• Oblique region
OBLIQUE_MERCATOR (conformal)
• Equal extent all directions
POLAR, STEREOGRAPHIC< UPS
(conformal)
LAMBERT_AZIMUTHAL (equal
area)
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• Straight Great Circle
GNOMIC
• Correct Scale- between points:
TWO_POINT_EQIDISTANT
• Correct Scale- along
meridians
AZIMUTHAL(polar),
EQUIDISTNAT,
SIMPLE_CONIC
• Correct Scale - along parallels
POLYCONIC, SINUSOIDAL,
BONNE
Source: Snyder, 1987 Map Projections - A Working Manual.
Workshop Proceedings, 1995 ESRI User Conference, p. 552
GISC 6381 GIS Fundamentals
54
How ArcView 3.2 Handles •
Coordinates and Projections
• all themes in a view must be in same
coordinate system (lat/long or projected)
• you must know it‘cos ArcView will read
raw data and overlay even if projections
differ
• A View can be projected only if original
data is in Lat/Long decimal degrees
– All themes must be in lat/long decimal
degrees, and in same datum
– always try to get data in that format
•
– for US “lower 48” states these will range
from -125 to -65 (W-E) and 25 to 49 S-N
• exception for images: if image is
projected, and vector data is in decimal
degrees, can set view projection to match
image projection and data will overlay
correctly
•
• If raw data in different coord systems, use
projection utility external to AV (new in
3.2) to convert to common coord. system
View, Properties used to specify
projections and related issues
– projection assoc. with view not a theme
– Map Units will be “unknown” when data
read in
• user sets it based on actual units for raw
data (e.g decimal degrees)
– Distance units are units in which
measurements will be reported (e.g.
miles)
• map units must be specified before
distance units can be set
• if map units specified incorrectly, distance
measures will be wrong!
To Project a View
– All data must be in decimal degrees and
Map Units should be set to this
– a variety of projections are available with
preset parameters (stan. parallels, etc)
• Custom check box available if wish to
specify own parameters
– re-specify decimal degrees in Map Units
to 'cancel' a projection
If data already projected, do not specify
projection in AV. View won’t draw! To cancel
mistake, select Projections of the World, Type:
unknown, then click Zoom to Full Extent icon