1 8/1/2015 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals Terrestrial Data Structures Representing...

104/19/23 Ron Briggs, UTDallas GISC 6381 GIS Fundamentals

Terrestrial Data Structures

Representing the Earth:

From the 3D Globe to the 2D map


Course ContentPart 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

– representing the real world

• GIS Data Structures– representing the world in a computer

• Data Quality– An essential ingredient

Part III: Practice• Data Input:

preparation and integration

• Data analysis and modeling

• Data output and application examples

Part IV: The Future• Future of GIS


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) 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


…the most southerly point in the US

Where am I?


Canada twice area of USGreenland biggest island

Canada same area as USAustralia biggest island

Which is correct?


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

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 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?


Relationship of Land Surface to Geoid and Spheroid

ocean

Land surface

Geoid(undulates due togravity)

Spheroid (math model)

mean sea surface (geoid)

Perpendicularto Geoid(plumbline)Perpendicular

to Spheroid

Note that elevation causes distances measured on ground to be greater than on the spheroid. Corrections may be applied.

GPS (global positioning system) measures elevation relative to spheroid.Traditional surveying via leveling measures elevation relative to geoid.

a-- semi-major axis

b -

- se

mi-

min

or a

xis

Spheroid

f=flattening=a-b a

a=b=sphere (3D circle)a>b=spheroid (3D ellipse)

< >


Which Spheroid?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)

Most commonly encountered are:• 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=


Latitude and Longitude: location on the spheroid

Longitude meridiansPrime 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/Slength long.=cosine of lat * length of 1° of lat.

(1/2 at 60° not 45°)

W 180° 180° E

Latitude parallels equator is zerocirc.: 40,076km 24,902mi1 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)

90° N

lat./long coords.for a location willchange dependingon spheroid chosen!

0°

90° S

Equator

PrimeMeridian

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 BP = degrees of long. A to B

(distances based on WGS84 spheroid)


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

Lat and long measured in:degrees° minutes” seconds’ (60’=1” & 60”=1°)UTD: 32° 59” 16.0798N 96° 44” 56.9522W1 second=100ft or 30m. approx. (lat., or long. at equator)Decimal degrees, not minutes/seconds, best for GIS. dd= d° + m”/60 + s’/3600Carry 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)

Latitude and Longitude Graticule

N E+ +

N W+ -

S E- +

S W- -

PrimeMeridian

When entering data, be sure to include negative signs.Longitude sometimes recorded using 360° to avoid negatives.

Measuring Latitude

geocentric or authalic latitude (c):angle of vector thru center of ellipsoid

geodetic latitude (d):angle of vector perpendicular to ellipsoid surface

geodetic latitude isalways used.

a-- semi-major axis

b --

sem

i-m

inor

axi

s

dc

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)

Ellipsoid

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.

tangent

f=flattening=a-b a


E W

N

0°

S

Bisected by a hemisphere!


Geodesy & SurveyingProcess 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!


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 available


Original North American Datums• 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

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!


Current US Datum Programs:National 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– local points connected to FBN/CBN

– Revision known as NAD83(HARN)• Issued on a regional basis from 1989 thru 1997• Differs from NAD83 (1986) by <=1m (horizon.)

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) <10cmReferenceLapine, 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

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

GeoidOrthometric height

Spheroid

Land surface

Ellipsoid height

http://www.ngs.noaa.gov/GEOID

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) U.S.

Geoid height





Source: http://www.ngs.noaa.gov/GEOID/ --values negative since geoid is below WGS84 spheroid

Geoid heights for U.S.(relative to WGS84 spheroid)

Texas average about -27m

http://www.ngs.noaa.gov/GEOID/




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 mileHectare• 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


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.


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

We are trying to represent this amount of the earth on this amount of map space.


Map Projections: classification

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.

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”

Classified by property preserved or by geometrical model

See Apppendix for detailAzimuth: angle between a great circle (line on globe) and a meridian.

Azimuthal Projections

Possible Light sources for Azimuthal Polar Projections

Conic and Cylindrical Projections

Central meridian

Great circle

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.

http://www.markmonmonier.com/work6.htm


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

102W 96W

LakeTawakoni

13 14 15Midland

UTM in Texas: 3 zones

40N KS/NE lineDallas is in 14S

Band “S”

32N HillsboroDefinitive documentation: http://earth-info.nga.mil/GandG/publications/tm8358.2/TM8358_2.pdf

UTM and SPCS Zones


Greenwich Meridian

Equator

(includes Washington, D.C.)

Pri

me

Mer

idia

n

UTM (and USNG) Grid Zones Worldwide

Source: FGDC-STD-001-2001 United States National Grid

Zone numbering begins at 180th meridian and proceeds east in 6° bands Vertical belts,

8° tall. Used only in military and USNG


Equator

Prime Meridian

UTM (and USNG) Grid Zones WorldwideSuperimposed on world map Source: Wikipedia


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– 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

http://www.fgdc.gov/usng/


14S

Global

Regional

Source: How to Read a United States National Grid (USNG) Spatial Address The Public XY Mapping Project

18S UJ 23483 06479

483 meters

479 meters

Locating the Washington Monument: USNG

(NAD83)


Example USNGUS 75 @ 15th

(NAD83)


USNG 100km Grid Squares

Source: FGDC-STD-001-2001 United States National Grid

• 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

State Plane Coordinate System (SPCS)


Co-ordinate Values for Selected Coordinate Systems Dallas County (NE & SW corners)

-96.52 32.99 long/lat731,900 3,652,850 UTM785,000 2,148,400 SPCS meters2,575,000 7,048,000 SPCS feet2,300,000 482,000 SPCS ft (NAD27)

-97.03 32.56 long/lat 684,800 3,603,800 UTM meters 737,800 2,099,650 SPCS meters2,420,000 6,888,000 SPCS feet 2,144,200 324,000 SPCS feet (NAD27)

UTM zone 14 (NAD83)bounding meridians: 102W & 96Wcentral meridian: 99Wfalse easting: 500,000 mfalse northing: 0

Dallas County(all coordinates NAD83 unless otherwise noted)

SPCS (5351) NAD27 NAD83spheroid Clarke 1886 GRS80central meridian: 97.5W 98.5Wreference latitude*: 31.67N 31.67Nstan. parallel 1: 32.13 32.13stan. parallel 2: 33.96 33.96false easting: 2,000,000ft 600,000mfalse northing: 0 2,000,000m

* origin point for coordinatesNote: by default AV displays in meters

Note: coords derived graphically so feet/meter conversions not exact(1m = 3.281ft)1 degree of lat approx.=10,000,000m/90° =111,111m

Meters northof equator

easting northing

easting northing

Coords for NE Corner

Coords for SW Corner

para

met

ers

para

met

ers


Parameters for SPCS in TexasSource: ARCDoc--SPCS, derived from Snyder

State & Zone Name Abbrev. DatumZONE FIPSZONE

Texas, North TX_N 5326 4201Texas, North Central TX_NC 5351 4202Texas, Central TX_C 5376 4203Texas, South Central TX_SC 5401 4204Texas, 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 1000000TX_NC 32 08 00 33 58 00 -98 30 00 31 40 00 600000 2000000TX_C 30 07 00 31 53 00 -100 20 00 29 40 00 700000 3000000TX_SC 28 23 00 30 17 00 -99 00 00 27 50 00 600000 4000000TX_S 26 10 00 27 50 00 -98 30 00 25 40 00 300000 5000000

TX_N 34 39 00 36 11 00 -101 30 00 34 00 00 609601.21920 0TX_NC 32 08 00 33 58 00 -97 30 00 31 40 00 609601.21920 0TX_C 30 07 00 31 53 00 -100 20 00 29 40 00 609601.21920 0TX_SC 28 23 00 30 17 00 -99 00 00 27 50 00 609601.21920 0TX_S 26 10 00 27 50 00 -98 30 00 25 40 00 609601.21920 0

NAD27


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

http://www.tnris.state.tx.us/DigitalData/projections.htm

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 MatrixThey are all available as defined projections in ArcGIS 9 under State Systems (not the same as State Plane!)


Coordinate Systems: critical required informationTo 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.


• 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!!!

Choosing a Map Projection

}detail in Appendix


The US displayed using a “Geographic Projection”

• treats lat/long as X,Y

• has no desirable properties other than convenience

• don’t do it!

Map of State Plane zones

Do not do it!

How ArcGIS Handles Coordinates and Projections

• 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)

• 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!

Summary: Measuring Position on Earth

Land Surface:

Geoid: --line of equal gravity--mean sea level with no wind or tides

Spheroid: “math model representing geoid”Spheroid+tiepoint=datum

Lines of latitude and Longitude--are drawn on the spheroid--establish position on 3-D spheroid

Where am I?Where am I?This guy’s latitude and longitude (and elevation) differ depending on spheroid used.

X-Y coordinates--derived via projection from lat/long--represent position on 2-D flat map surface

Elevation of land surface may be: --above geoid (traditional surveying)--above spheroid (GPS)

Projection


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


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?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

http://support.esri.com/index.cfm?fa=knowledgebase.techarticles.articleShow&d=23025


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


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)


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).


Map Projections by GeometryConical

• 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


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


Best Map Projections by Size of AreaWorld/Hemisphere

• World - ConformalMERCATOR, TRANSVERSE,

OBLIQUE_MERCATOR

• World - Equal AreaCYLINDRICAL, 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


Best Map Projections by Size of Area:continent or smaller

• E/W along equatorMERCATOR (conformal)

CYLINDRICAL (equal area)

• E/W away from EquatorLAMBERT (conformal)

ALBERS (equal area)

• North/South TRANSVERSE, UTM (conformal)

• Oblique regionOBLIQUE_MERCATOR (conformal)

• Equal extent all directionsPOLAR, STEREOGRAPHIC< UPS

(conformal)

LAMBERT_AZIMUTHAL (equal area)

• 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

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

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