Terrestrial Data Structures

1
Terrestrial Data Structures

• Representing the Earth
• From the 3D Globe to the 2D map

2
Course Content

• Part III Practice
• Data Input preparation and integration
• Data analysis and modeling
• Data output and application examples
• Part IV The Future
• Future of GIS

• Part I Overview
• Fundamentals of GIS
• Hands-on Intro to ArcGIS
• (lab sessions _at_ 400-700pm or 700-1000pm)
• Part II Principles
• Terrestrial data structures
• representing the real world
• GIS Data Structures
• representing the world in a computer
• Data Quality
• An essential ingredient

3
Terrestrial Data StructuresPop 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) halfthat 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

4
the most southerly point in the US
Where am I?
5
Canada twice area of US Greenland biggest island
Which is correct?
Canada same area as US Australia biggest island
6
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

7
The Shape of the Earth3 concepts

• topographic surface
• 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 earths 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 (15,000,000 and below - e.g.
  17,500,000)
• spheroid (3-dimensional ellipse, flattened at
  the poles) should be used for larger scale maps
  of 11,000,000 or more (e.g. 124,000)
• the issue is, which spheroid?

8
Relationship of Land Surface to Geoid and Spheroid
GPS (global positioning system) measures
elevation relative to spheroid. Traditional
surveying via leveling measures elevation
relative to geoid.
Land surface
mean sea surface (geoid)
ocean
Perpendicular to Geoid (plumbline)
Spheroid (math model)
Perpendicular to Spheroid
Geoid (undulates due to gravity)
Note that elevation causes distances measured on
ground to be greater than on the spheroid.
Corrections may be applied.
9
Which Spheroid?

• Most commonly encountered are
• Everest (Sir George) 1830
• one of the earliest spheroids India
• a6,377,276m b6,356,075m f1/300.8
• Clarke 1886 for North America
• basis for USGS 7.5 Quads
• a6,378,206.4m b6,356,583.8m f1/295
• GRS80 (Geodetic Ref. System, 1980)
• current North America mapping
• a6,378,137m b6,356,752.31414m f1/298
• Hayford or International (1909/1924)
• early global choice
• a6,378,388 b6,356,911.9m f
• WGS84 (World Geodetic Survey, 1984)
• current global choice
• a6,378,137 b6,356,752.31m f

• Hundreds have been defined depending upon
• 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)

10
Latitude and Longitude location on the spheroid
Prime Meridian
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
90 N
Equator
0
lat./long coords. for a location will change
depending on spheroid chosen!
Longitude meridians Prime meridian is zero
Greenwich, U.K. International Date Line is 180
EW circ. 40,008km 24,860mi (equator to pole
approx. 10,000,000 meters, actually 10,001,965.7
meters ) 1 degree69.17 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)
90 S
Latitude parallels equator is zero circ.
40,076km 24,902mi 1 degree68.71 mi at equator
(110,567m.) 69.40 mi at poles (1
mile1.60934km5280 feet) 1 nautical milelength
of 1 minute 6080 ft1853.248m (Admiralty)
6076.115ft1852m (international)
(distances based on WGS84 spheroid)
11
Latitude and Longitude Graticule
Lat and long measured in degrees minutes
seconds (601 601) UTD 32 59
16.0798N 96 44 56.9522W 1 second100ft 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--gt1 millimeter
accuracy!) (note 1 meter 3.2808 feet)
When entering data, be sure to include negative
signs. Longitude sometimes recorded using 360 to
avoid negatives.
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
12
Measuring Latitude
geodetic latitude (d) angle of vector
perpendicular to ellipsoid surface
geodetic latitude is always used.
tangent
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.
b -- semi-minor axis
d
c
geocentric or authalic latitude (c) angle of
vector thru center of ellipsoid
a-- semi-major axis
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)
fflatteninga-b a
13
N
0
S
E
W
Bisected by a hemisphere!
14
Geodesy SurveyingProcess of measuring position
(horizontal control) and elevation (vertical
control) of points on earths surface (spheroid)

• Geodetic Surveying incorporates earths 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!

15
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
  earths 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 available

16
Original North American Datums

• NAD83
• 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!

• 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

17
Current US Datum ProgramsNational Geodetic
Reference System(NGRS)/ National Spatial
Reference System(NSRS)

• High Accuracy Reference Network (HARN)
• ( first called HPGN-High Precision GPS Network)
• NAD83 not gps-able
• inaccessible monuments (hill tops)
• irregular spacing of monuments
• get destroyed
• too many (275,000) to maintain
• insufficient accuracy for precision work (at 1m
  or less)
• 3-Tier Plan
• federal base network (FBN)
• 1,600-2,000 monuments
• 5-8 mm accuracy (A or B order)
• evenly spaced 1 degree by 1 degree (75-125 kms)
• 3 year visitation cycle
• cooperative base network (CBN-states)
• 16,000 monuments
• 25-30km spacing B-order accuracy
• no coop agreement with Texas!
• user densification network

• Continuously Operating Reference Stations (CORS)
• continuos measurement of location from GPS
  satellites
• 500 km spacing
• DFW site in Arlington run by TXDOT (about 70 in
  TX as of 2007)
• posted hourly on the Internet
• Use for differential GPS, calibrating gps
  instruments, monitor crustal movement, etc.
• datum revision know as NAD83 (CORSxx) since
  several been released (93, 94, 96, etc)
• Diff. from NAD83 (HARN) lt10cm
• Reference
• Lapine, Lewis A. National Geodetic Survey Its
  Mission, Vision, and Goals, US Dept of Commerce,
  NOAA, October, 1994
• Snay and Soler Professional Surveyor Dec 1999,
  Feb 2000

18
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) differentby 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 elevations
(ellipsoid height) to correspond to traditional
surveyed heights above geoid (orthometric height)
Geoid height
Ellipsoid height
Geoid
Orthometric height
U.S.
Spheroid
http//www.ngs.noaa.gov/GEOID
19
Geoid heights for U.S. (relative to WGS84
spheroid)
Texas average about -27m
Source http//www.ngs.noaa.gov/GEOID/
--values negative since geoid is below WGS84
spheroid
20
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 Franklins
  days!
• Equals 43,560 sq. feet, 4,840 sq. yards, or
  10 sq. chains
• A surveyors chain (or Gunters 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

21
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 earths 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 locations lat/long
  coords, only its XY coords.

22
Map Projectionsthe 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

We are trying to represent this amount of the
earth on this amount of map space.
23
Map Projections classification
Classified by property preserved or by
geometrical model

• Geometric Model Used
• 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
• along one line (tangent) or
• cuts thru globe along two lines (secant)
  (usually parallels of latitude)
• cone is then unfolded to create flat map
• 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

• Property Preserved
• 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
• Scale can never be correct everywhere on any map
• 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.
See Apppendix for detail
24
Azimuthal Projections
Possible Light sources for Azimuthal Polar
Projections
25
Conic and Cylindrical Projections
Great circle
Central meridian
26
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..)
27
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.
28
Universal Transverse Mercator (UTM)

• first adopted by US Army in 1947 for large scale
  maps worldwide
• used from lat. 84N to 80S 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
Dallas is in 14S
Definitive documentation http//earth-info.nga.mi
l/GandG/publications/tm8358.2/TM8358_2.pdf
29
UTM and SPCS Zones
30
UTM (and USNG) Grid Zones Worldwide
Zone numbering begins at 180th meridian and
proceeds east in 6 bands
Vertical belts, 8 tall. Used only in military
and USNG
Source FGDC-STD-001-2001 United States
National Grid
31
UTM (and USNG) Grid Zones Worldwide Superimposed
on world map
Source Wikipedia
32
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)
• Consequently MGRS and USNG are the same within
  the US
• Goals is to provide standard coordinate based
  address locator applicable to both analog and
  digital maps, supporting
• 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
• 18SUJlocates 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 digitswithin a city block)
• 18SUJ23480647 - Locates with a precision of 10
  meters (4 digitsa single house)
• 18SUJ2348306479 - Locates with a precision of 1
  meter (5 digitsa parked vehicle)

33
Global
Locating the Washington Monument USNG
14S
18S UJ 23483 06479
(NAD83)
Regional
Source How to Read a United States National Grid
(USNG) Spatial Address The Public XY Mapping
Project
34
(No Transcript)
35
USNG 100km Grid Squares
Source FGDC-STD-001-2001 United States
National Grid
36
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
• (1m39.37 inches exact used for conversion
  differs slightly from NBS 12.54cm)
• 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

37
Co-ordinate Values for Selected Coordinate
Systems Dallas County (NE SW corners)
easting northing
Coords for NE Corner
-96.52 32.99 long/lat 731,900
3,652,850 UTM 785,000 2,148,400 SPCS
meters 2,575,000 7,048,000 SPCS feet 2,300,000
482,000 SPCS ft (NAD27)
SPCS (5351) NAD27 NAD83 spheroid
Clarke 1886 GRS80 central meridian
97.5W 98.5W reference latitude 31.67N
31.67N 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
parameters
Note coords derived graphically so feet/meter
conversions not exact (1m 3.281ft) 1 degree of
lat approx. 10,000,000m/90 111,111m
origin point for coordinates Note by default
AV displays in meters
Coords for SW Corner
easting northing
UTM zone 14 (NAD83) bounding meridians 102W
96W central meridian 99W false easting
500,000 m false northing
0
Meters north of equator
-97.03 32.56 long/lat 684,800
3,603,800 UTM meters 737,800 2,099,650
SPCS meters 2,420,000 6,888,000 SPCS feet
2,144,200 324,000 SPCS feet (NAD27)
parameters
38
Parameters for SPCS in TexasSource
ARCDoc--SPCS, derived from Snyder
State Zone Name Abbrev. Datum ZONE
FIPSZONE
Texas, North TX_N 5326 4201 Texas, North
Central TX_NC 5351 4202 Texas,
Central TX_C 5376 4203 Texas, South
Central TX_SC 5401 4204 Texas,
South TX_S 5426 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 34 39 00 36 11 00 -101 30 00 34 00 00
200000 1000000 TX_NC 32 08 00 33 58 00 -98 30
00 31 40 00 600000 2000000 TX_C 30 07 00 31
53 00 -100 20 00 29 40 00
700000 3000000 TX_SC 28 23 00 30 17 00 -99 00
00 27 50 00 600000 4000000 TX_S 26 10 00 27
50 00 -98 30 00 25 40 00 300000 5000000
NAD27
TX_N 34 39 00 36 11 00 -101 30 00 34 00 00
609601.21920 0 TX_NC 32 08 00 33 58 00 -97 30
00 31 40 00 609601.21920 0 TX_C 30 07 00 31
53 00 -100 20 00 29 40 00
609601.21920 0 TX_SC 28 23 00 30 17 00 -99 00
00 27 50 00 609601.21920 0 TX_S 26 10 00 27
50 00 -98 30 00 25 40 00 609601.21920 0
39
Texas Statewide Mapping System (TSMS)http//www.t
nris.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
40
Texas Map ProjectionsTexas Department of
Information Resources, 2001

• Conformal
• 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

• Equal Area
• 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!)
41
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
• Point of origin for coordinate system(often
  expressed as false easting northing)
• Unit of measurement
• Feet, meters, etc.

• For azimuthal
• Point of contact

All this info. should be recorded on every
printed map, and stored in metadata for digital
files!
Note The term geographic projection often used
to refer to data in lat/long units.
42
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?
• 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!!!

detail in Appendix
43
The US displayed using a Geographic Projection

• treats lat/long as X,Y
• has no desirable properties other than
  convenience
• dont do it!

Map of State Plane zones
Do not do it!
44
How ArcGIS Handles Coordinates and Projections

• 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
• 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
• 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!

• The coordinate reference system of the display
  view is determined by the first layer opened in
  the view
• 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)

45
Summary Measuring Position on Earth
X-Y coordinates --derived via projection from
lat/long --represent position on 2-D flat map
surface
Projection
Lines of latitude and Longitude --are drawn on
the spheroid --establish position on 3-D spheroid
Where am I? This guys latitude and longitude
(and elevation) differ depending on spheroid used.
Spheroid math model representing
geoid Spheroidtiepointdatum
Geoid --line of equal gravity --mean sea level
with no wind or tides
Elevation of land surface may be --above geoid
(traditional surveying) --above spheroid (GPS)
Land Surface
46
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

47
AppendixProjection 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?faknowledgebase
  .techarticles.articleShowd17420
• FAQ  Projection Basics What the GIS
  professional needs to know http//support.esri.co
  m/index.cfm?faknowledgebase.techarticles.articleS
  howd23025

48
Map Projections by Property PreservedShape 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 Albers conic, Lamberts azimuthal

49
Map Projections by Property PreservedDistance
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)

50
Map Projections by Geometry Planar/Azimuthal/Zeni
thal

• 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).

51
Map Projections by GeometryConical

• map plane is tangent along a line, most commonly
  a parallel of latitude which is then the maps
  standard parallel
• cone is cut along a meridian, and the meridian
  opposite the cut is the maps 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 Albers Equal Area Conic, Lamberts
  Conic Conformal

52
Map Projections by GeometryCylindrical

• 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

53
Best Map Projections by Size of
AreaWorld/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

• Hemisphere - Conformal
• STEREOGRAPHIC, POLAR
• Hemisphere - Equal Area
• LAMBERT_AZIMUTHAL
• Hemisphere - Equidistant
• AZIMUTHAL
• Hemisphere - Global look
• ORTHOGRAPHIC

NAMES correspond to ARC/Info commands
54
Best Map Projections by Size of Areacontinent
or smaller

• 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

• 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, STEREOGRAPHIClt UPS (conformal)
• LAMBERT_AZIMUTHAL (equal area)

Source Snyder, 1987 Map Projections - A Working
Manual. Workshop Proceedings, 1995 ESRI User
Conference, p. 552
55
How ArcView 3.2 Handles Coordinates and
Projections

• 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 wont draw! To cancel
  mistake, select Projections of the World, Type
  unknown, then click Zoom to Full Extent icon

• all themes in a view must be in same coordinate
  system (lat/long or projected)
• you must know itcos 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