technical issues in gis

7/28/2019 Technical Issues in Gis

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http://www.geog.ucsb.edu/~good/176b/a05.html#7.%20

UNIVERSAL%20TRANSVERSE%20MERCATOR

GEOGRAPHY 176B: TECHNICAL ISSUES IN GIS

LECTURE 5: GEOREFERENCING

1. THE PROBLEM

2. PLACENAMES

3. ADDRESSES, POSTCODES, AREA CODES

4. THE CADASTER AND PUBLIC LAND SURVEYSYSTEM

5. LATITUDE AND LONGITUDE

6. PROJECTIONS AND COORDINATES

7. UNIVERSAL TRANSVERSE MERCATOR

8. STATE PLANE COORDINATES

Credit: many of the illustrations in this unit were prepared by Peter Dana, University of Texas, Austin, for

the Geographer's Craft project

1. THE PROBLEM

The atom of geographic information

<location, time, attribute>

to communicate, we need standard ways of

dealing with all three

http://www.geog.ucsb.edu/~good/176b/a05.html#7.%20UNIVERSAL%20TRANSVERSE%20MERCATOR


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http://www.geog.ucsb.edu/~good/176b/#2.

http://www.geog.ucsb.edu/~good/176b/#3.%20ADDRESSES,%20POSTCODES,%20AREA

http://www.geog.ucsb.edu/~good/176b/#4.%20THE%20CADASTER%20AND%20PUBLIC%20LAND%20SURVEY%20SYSTEM


http://www.geog.ucsb.edu/~good/176b/#5.%20LATITUDE%20AND

http://www.geog.ucsb.edu/~good/176b/#6.%20PROJECTIONS%20AND

http://www.geog.ucsb.edu/~good/176b/#7.%20UNIVERSAL%20TRANSVERSE%20MERCATOR

http://www.geog.ucsb.edu/~good/176b/#8.%20STATE%20PLANE%20COORDINATES

http://www.utexas.edu/depts/grg/gcraft/notes/mapproj/mapproj.html



http://www.geog.ucsb.edu/~good/176b/#1.%20THE

http://www.geog.ucsb.edu/~good/176b/#2.

http://www.geog.ucsb.edu/~good/176b/#3.%20ADDRESSES,%20POSTCODES,%20AREA



http://www.geog.ucsb.edu/~good/176b/#5.%20LATITUDE%20AND

http://www.geog.ucsb.edu/~good/176b/#6.%20PROJECTIONS%20AND

http://www.geog.ucsb.edu/~good/176b/#7.%20UNIVERSAL%20TRANSVERSE%20MERCATOR

http://www.geog.ucsb.edu/~good/176b/#8.%20STATE%20PLANE%20COORDINATES

http://www.utexas.edu/depts/grg/gcraft/notes/mapproj/mapproj.html



time

Gregorian calendar

attribute

depends on application

temperature scales

vegetation classifications

highway classifications

location

many ways of referencing

how to specify the

locations of a polygon's points?

120.12456 W, 34.89176 N

909 West Campus Lane,Goleta, CA 93117, USA

5789654N, 314654E

NE 1/4, Section 12,

Township 23 Range 5 of

the Second Principal

Meridian

How to reference a location on the Earth's surface?

in a way that others can understand

with sufficient accuracy for the application

many methods

The act of assigning locations to things



georeferencing

geocoding

geolocating

within the geographic frame of reference

other frames of reference?

Requirements of a georeferencing system

uniqueness

one code per location

every location gets its own code

over what domain?

the entire globe

universal systems

latitude/longitude

over a limited domain

e.g. unique in the U.S.

e.g. unique to a zone

same geocode repeats in

different places

7-digit phone

number repeats

in every area

code

10-digit phone

number unique in

the U.S. andCanada



11-digit phone

number (add 1)

unique in the

world

placenames repeat

at least 18 stateshave a city of

Springfield

shared meaning

sender and receiver must both

understand

latitude/longitude is

universally understood

Tobler's postcardmail a letter from China to

909 West Campus Lane,

Goleta, CA 93117, USA

persistent through time

latitude/longitude since the 1890s

area codes often change

spatial resolution

how big is the area covered by a

single georeference?

Rhode Island pins location

down to 3000 sq km

http://www.geog.ucsb.edu/~good/176b/tobler.jpg

http://www.geog.ucsb.edu/~good/176b/tobler.jpg



California only to 410,000

sq km

area or linear measure?

a rectangle of

3000 sq km is

about 55 kmacross

a rectangle of

410,000 sq km is

about 650 kmacross

we tend to work

with both

metric georeferences

measure position with respect tofixed points

can be used to measure distances

between points

coordinates

e.g. Salt Lake City street

addresses

ordered allocation

e.g. New York avenues

2. PLACENAMES

Locations identified by name



likely the first type of georeference

littering the surface of the Earth

Placename authorities

state, national boards

official authorization

Board on Geographic Names

Geographic Names Information

System

Alexandria Gazetteer

Relative names

e.g. 5 miles west of Greenfield, CA

e.g. between Salinas and Greenfield

the museum collection problem

collected 1 mile north of Cachuma

Saddle

metes and bounds property description

from the big maple tree, 100 ft in a

southerly direction to the crossing of

the creek

Problems with placenames

variable spatial resolution

e.g. Asia

e.g. Eiffel Tower

lost through time

http://mapping.usgs.gov/www/gnis/bgn.html

http://mapping.usgs.gov/www/gnis/gnisform.html


http://webclient.alexandria.ucsb.edu/

http://mapping.usgs.gov/www/gnis/bgn.html



http://webclient.alexandria.ucsb.edu/



Where was Camelot?

Only locally defined

The Riviera

downtown

Not officially recognized

The Midwest

Fuzzy or crisp

The Atlantic Ocean

Context-specific

LA

If you live in New York

if you live in RiversideAlphabets

Chinese place names

3. ADDRESSES, POSTCODES, AREA CODES

Devised for specific purposes

Used for many other purposes

Addresses

Delivering mail

registering property

place of residence



spatial resolution

one mailbox

one property

domain

local area

assumptions

dwelling is a destination for mail

dwellings arrayed along streets

streets have names that are unique

within local area

local areas have names that are

unique within state/country

violations?

give your street address to911?

where do they not work?

Postal codes

ZIP - 93117-4338

unique in US

spatial resolution <1 block

changes made frequently

UK postcode - SE3R 1KW

Canadian postcode - N6G 1R1

widely known and accessible

http://www.geog.ucsb.edu/~good/176b/zip_example.gif

http://www.starmanager.com/newzip.htm

http://www.geog.ucsb.edu/~good/176b/zip_example.gif

http://www.starmanager.com/newzip.htm



mailing lists

widely used for marketing, analysis

Area codes

4. THE CADASTER AND PUBLIC LAND SURVEY

SYSTEM

Cadaster

the map of land ownership

field-like

at any point there is exactly one

owner

not an effective georeference

Public land survey system

devised circa 1830 for surveying the western

lands acquired by the U.S.

extended to Canada

a regular basis for allocating land to new

owners

used for georeferencing in land management

oil and gas

BLM

Elements of the PLSS

the principal meridian



a north-south line laid out very

accurately

ranges

at 6 mile intervals

townships

6 mile blocks east and west of the

principal meridian

sections

36 blocks of 1 square mile each (640

ac)

regularly numbered

numbering east of the principalmeridian

1 2 3 4 5 6

12 11 10 9 8 7

13 14 15 16 17 18

24 23 22 21 20 19

25 26 27 28 29 30

36 35 34 33 32 31

Reversed west of the principal

meridian

4 quarter sections of 1/4 sq mile (160 ac)

NW NE



SW SE

quarter-quarter sections of 1/16 sq mi (40 ac)

fixed spatial resolution

can go as fine as needed

hierarchical system

Applications

locations of oil and gas leases

locations of public land locations of agricultural land

Problems

the Earth isn't flat

surveying errors

steep terrainother irregularities

Santa Barbara county

5. LATITUDE AND LONGITUDE

Earth's axis

5 m wobble

Center of mass

Equator

90 degrees to axis, through the center of mass



Prime meridian

Royal Observatory at Greenwich

plane through the axis and the prime meridian

Longitude

plane through the axis and a point

angle between the two planes

180 W to 180 E

360 degrees in 24 hours

15 degrees per time zone

-180 to +180

history of longitude

Longitude by Dava SobelFigure of the Earth

geoid

isosurface

sea level if continents were porous

accurately measured with satellites

ellipsoid

mathematical surface

rotate an ellipse around the axis

some ellipsoids

WGS84

http://www.geog.ucsb.edu/~good/176b/line.jpg

http://www.geog.ucsb.edu/~good/176b/ellipse.jpg

http://www.geog.ucsb.edu/~good/176b/line.jpg

http://www.geog.ucsb.edu/~good/176b/ellipse.jpg



NAD83

a=6,378,137 m

b=6,356,752 m

f =1/298.257

Clarke's ellipsoid of 1866

NAD27

List of ellipsoids

Ellipsoid Semi-major axis 1/flattening

Airy 1830 6377563.396 299.3249646

Modified

Airy6377340.189 299.3249646

Australian

National6378160 298.25

Bessel 1841(Namibia)

6377483.865 299.1528128

Bessel 1841 6377397.155 299.1528128

Clarke 1866 6378206.4 294.9786982

Clarke 1880 6378249.145 293.465

Everest

(India 1830)6377276.345 300.8017

Everest

(Sabah

Sarawak)

6377298.556 300.8017

Everest

(India 1956)6377301.243 300.8017

Everest(Malaysia 6377295.664 300.8017



1969)

Everest

(Malay. &

Sing)

6377304.063 300.8017

Everest

(Pakistan)6377309.613 300.8017

Modified

Fischer 19606378155 298.3

Helmert

1906

6378200 298.3

Hough 1960 6378270 297

Indonesian

19746378160 298.247

International

19246378388 297

Krassovsky

1940 6378245 298.3

GRS 80 6378137 298.257222101

South

American

1969

6378160 298.25

WGS 72 6378135 298.26

WGS 84 6378137 298.257223563

Latitude

angle between the Equator and a line drawn

perpendicular to the ellipsoid

not necessarily through the center of

mass



90 S to 90 N

-90 to +90

parallel

line of constant latitude

Precision of latitude and longitude

degrees, minutes, seconds

decimal degrees

1 second latitude about 30 m

1 minute latitude = 1 nautical mile

1 degree latitude about 70 miles or 110 km

longitude degrees shorter on the Earth

except at the Equator

depending on latitude

at 30 degrees 0.866

at 45 degrees 0.707

at 60 degrees 0.500

at 90 degrees 0.000

great circle

slice through the center of mass

divides the Earth into two equal

hemispheres

small circle

slice not through the center of mass

Approximate figures of the Earth



larger than 1:10,000, assume a flat Earth

from 1:10,000 to 1:10,000,000 assume a

spheroid

smaller than 1:10,000,000 assume a sphere

Distances on the sphere

latitude φ

longitude λ

R arccos (sin φ1 sin φ2 + cos φ1 cos φ2 cos(λ1 - λ2))

circumference 2π R

distance from Equator (0,0) to N Pole (90,0)

R arccos (0x1 + 1x0 cos (0 - 0))

R arccos (0)

Rπ/2

WGS84

R = (a+b)/2 = 6,367,444 m

Rπ/2 = 10,039,173 m

6. PROJECTIONS AND COORDINATES

Why flatten the Earth?

paper is flat

input and output

easily printed, copied

rasters are flat



can't cover a curved surface with

squares

use of rasters in analysis, modeling

photographs are flat

to see all of the Earth at once

Map projection

a transformation from (φ,λ) to ( x, y)

Mercator projection

x = λ

y = ln tan (φ/2 + π/4)

inverse transformations

λ = x

φ = 2(arctan e y - π/4)

How does a GIS make the calculations?

often by expanding functions as series

e.g., e y = 1 + y + y2/2! + y3/3! + ...

make forward transformation followed byinverse

are the results exactly the same?

errors may accumulate

Distortion properties

http://www.geog.ucsb.edu/~good/176b/mercator.gif

http://www.geog.ucsb.edu/~good/176b/mercator.gif



angles, areas, directions, shapes and distances

become distorted when transformed from a

curved surface to a plane

examples

all these properties cannot be kept undistorted

in a single projection

usually the distortion in one property

will be kept to a minimum while

other properties become very

distorted

Tissot's Indicatrix

is a convenient way of showing distortion

imagine a tiny circle drawn on the surface of the globe

on the distorted map the circle will

become an ellipse, squashed or

stretched by the projection

height changed by the

vertical scale (k )

width changed by the

horizontal scale (h)

the size and shape of the Indicatrix

will vary from one part of the map to

another

http://www.geog.ucsb.edu/~good/176b/threepro.gif

http://www.geog.ucsb.edu/~good/176b/threepro.gif



we use the Indicatrix to display the

distorting effects of projections

Conformal (Orthomorphic)

a projection is conformal if the angles in the

original features are preserved

over small areas the shapes of objects

will be preserved

preservation of shape does not holdwith large regions (e.g. Greenland in

Mercator projection)

a line drawn with constant

orientation (e.g. with respect to

north) will be straight on a conformal

projection, is termed a rhumb line or

loxodrome

conformal projections are good for navigation

parallels and meridians cross each other at

right angles (note: not all projections with thisappearance are conformal)

the Tissot Indicatrix is a circle everywhere, but

its size varies

conformal projections cannot have equal area

properties, so some areas are enlarged

generally, areas near margins have a

larger scale than areas near the center



Equal area (Equivalent)

the representation of areas is preserved so that

all regions on the projection will be

represented in correct relative size

equal area projections are good for

GIS analysis

equal area maps cannot be conformal, so mostEarth angles are deformed and shapes are

strongly distorted

the Indicatrix has the same area everywhere,

but is always elliptical, never a circle (except at

the standard parallel)

Equidistant

cannot make a single projection over which alldistances are maintained

thus, equidistant projections maintain relative

distances from one or two points only

e.g., in a conic projection all

distances from the center arerepresented at the same scale

Geometric analogy: Developable surfaces

the most common methods of projection can beconceptually described by imagining the

developable surface, which is a surface that can

be made flat by cutting it along certain linesand unfolding or unrolling it



the points or lines where a developable surface

touches the globe in projecting from the globe

are called standard points and lines, or points

and lines of zero distortion.

at these points and lines, the scale isconstant and equal to that of the

globe, no linear distortion is present

if the developable surface touches

the globe, the projection is called

tangent

e.g. cylindrical

if the surface cuts into the globe, it is

called secant

where the surface and the

globe intersect, there is nodistortion

where the surface is

outside the globe, objects

appear bigger than in

reality - scales are greater

than 1

where the surface is insidethe globe, objects appear

smaller than in reality and

scales are less than 1

note: symbols used in the following: λ - longitude φ -

latitude χ - colatitude (90 - lat)

http://www.geog.ucsb.edu/~good/176b/cylinder.gif

http://www.geog.ucsb.edu/~good/176b/scylind.gif

http://www.geog.ucsb.edu/~good/176b/cylinder.gif

http://www.geog.ucsb.edu/~good/176b/scylind.gif



h - distortion introduced along lines of

longitude

k - distortion introduced along lines of latitude

(h and k are the lengths of the minor

and major axes of the Indicatrix)

commonly used developable surfaces are:

1. Planar or azimuthal

a flat sheet is placed in contact with a globe,and points are projected from the globe to the

sheet

mathematically, the projection is easily

expressed as mappings from latitude and

longitude to polar coordinates with the origin

located at the point of contact with the paper

formulas for stereographic projection

(conformal) are:

r = 2 tan(χ / 2)

q = λ

h = k = sec2(χ / 2)

Examples:

stereographic projection

gnomic projection

Lambert's azimuthal equal-area projection

orthographic projection

http://www.geog.ucsb.edu/~good/176b/splane.gif

http://www.geog.ucsb.edu/~good/176b/splane.gif



2. Conic

the transformation is made to the surface of a

cone tangent at a small circle (tangent case) or

intersecting at two small circles (secant case)

on a globe

mathematically, this projection is alsoexpressed as mappings from latitude and

longitude to polar coordinates, but with the

origin located at the apex of the cone

formulas for equidistant conical projection with one

standard parallel (φ0 , colatitude χ0) are:

r = tan(χ0) + tan(χ - χ0)

q = n λ

n = cos(χ0)

h = 1.0

k = n r / sin(χ)

Examples

Alber's conical equal area projection with twostandard parallels

Lambert conformal conic projection with two

standard parallels

equidistant conic projection with one standard parallel

3. Cylindrical

http://www.geog.ucsb.edu/~good/176b/scone.gif

http://www.geog.ucsb.edu/~good/176b/nalccna.gif

http://www.geog.ucsb.edu/~good/176b/scone.gif

http://www.geog.ucsb.edu/~good/176b/nalccna.gif



developed by transforming the spherical

surface to a tangent or secant cylinder

mathematically, a cylinder wrapped around the

equator is expressed with x equal to longitude,

and the y coordinates some function of latitude

formulas for cylindrical equal area projectionare:

x = λ

y = sin(φ)

k = sec(φ)

h = cos(φ)

Examples

Mercator Projection

meridians and parallels intersect at

right angles

straight lines are lines of constant

bearing - projection is useful for

navigation

great circles appear as curves

Plate Carree or unprojected or cylindrical

equidistant

4. Non-Geometric (Mathematical) projections

http://www.geog.ucsb.edu/~good/176b/naunproj.gif

http://www.geog.ucsb.edu/~good/176b/naunproj.gif



some projections cannot be expressed

geometrically

have only mathematical descriptions

Examples

Molleweide

Eckert

7. UNIVERSAL TRANSVERSE MERCATOR (UTM)

UTM is the first of two projection based coordinate

systems to be examined in this unit

UTM provides georeferencing at high levels of

precision for the entire globE

established in 1936 by the International Unionof Geodesy and Geophysics

adopted by the US Army in 1947

adopted by many national and

international mapping agencies,

including NATO

is commonly used in topographic and

thematic mapping, for referencingsatellite imagery and as a basis for

widely distributed spatial databases

Transverse Mercator Projection

results from wrapping the cylinder around the poles rather than around the equator

http://www.geog.ucsb.edu/~good/176b/transcyl.gif

http://www.geog.ucsb.edu/~good/176b/transcyl.gif



the central meridian is the meridian where the

cylinder touches the sphere

theoretically, the central meridian is the line of

zero distortion

by rotating the cylinder around the poles the

central meridian (and area of least distortion)can be moved around the earth

Zone System

in order to reduce distortion the globe is

divided into 60 zones, 6 degrees of longitude

wide

zones are numbered eastward, 1 to 60,

beginning at 180 degrees (W long)

the system is only used from 84 degrees N to80 degrees south as distortion at the poles is

too great with this projection

at the poles, a Universal Polar

Stereographic projection (UPS) is

used

each zone is divided further into strips of 8degrees latitude

beginning at 80 degrees S, are

assigned letters C through X, O and I

are omitted

picture

Distortion

http://www.geog.ucsb.edu/~good/176b/utmzones.gif

http://www.geog.ucsb.edu/~good/176b/utmzones.gif



to reduce the distortion across the area covered

by each zone, scale along the central meridian

is reduced to 0.9996

this produces two parallel lines of zero

distortion approximately 180 km away fromthe central meridian

scale at the zone boundary is approximately

1.0003 at US latitudes

Coordinates

coordinates are expressed in meters

eastings ( x) are displacements

eastward

northings ( y) express displacement

northwardthe central meridian is given an easting of

500,000 m

the northing for the equator varies depending

on hemisphere

when calculating coordinates for

locations in the northern hemisphere,

the equator has a northing of 0 m

in the southern hemisphere, the

equator has a northing of 10,000,000

m

UTM zone 14

http://www.geog.ucsb.edu/~good/176b/utm14.gif

http://www.geog.ucsb.edu/~good/176b/utm14.gif



Advantages

UTM is frequently used

consistent for the globe

is a universal approach to accurate

georeferencing

Disadvantages

full georeference requires the hemisphere, zone

number, easting and northing (unless the areaof the data base falls completely within a zone)

rectangular grid superimposed on zones

defined by meridians causes axes on adjacentzones to be skewed with respect to each other

problems arise in working across zone

boundaries

no simple mathematical relationship exists

between coordinates of one zone and an

adjacent zone

8. STATE PLANE COORDINATES (SPC)

SPCs are individual coordinate systems adopted by U.S.

state agencies

originated in the 1930s based on NAD27

revised in 1983 based on NAD83

each state's shape determines which projectionis chosen to represent that state



e.g. a state extended N/S may use a

Transverse Mercator projection

while a state extended E/W may use

a Lambert Conformal Conic projection (both of these are

conformal)

projections are chosen to minimize distortion

over the state

a state may have 2 or more

overlapping zones, each with its own projection system and grid

Texas zones

units are generally in feet

Advantages

SPC may give a better representation than the

UTM system for a state's area

SPC coordinates may be simpler than those of

UTM

Disadvantages

SPC are not universal from state to state

problems may arise at the boundaries of

projections

Use in GIS

http://www.geog.ucsb.edu/~good/176b/tspzones.gif

http://www.geog.ucsb.edu/~good/176b/tspzones.gif



many GIS have catalogs of SPC projections

listed by state which can be used to choose the

appropriate projection for a given state

REFERENCES

Maling, D.H., 1973. Coordinate Systems and Map

Projections, George Phillip and Son Limited, London.

Robinson, A.H., R.D. Sale, J.L. Morrison and P.C.

Muehrcke, 1984, Elements of Cartography, 5th edition,

John Wiley and Sons, New York. See pages 56-105.

Snyder, J.P., 1987. Map Projections - A Working

Manual , US Geological Survey Professional Paper 1395,

US Government Printing Office, Washington.

Strahler, A.N. and A.H. Strahler, 1987. Modern Physical

Geography, 3rd edition, Wiley, New York. See pages 3-8for a description of latitude and longitude and

various appendices for information on coordinate

systems.

REVIEW QUESTIONS

1. Define the three standard properties of map projections: equal-area, equidistant and conformal.

Discuss the relative importance of each for different

applications. What types of applications require which

properties?

2. What type of projection would you expect to be used

in the following circumstances, and why?



a. an airline pilot flying the North Atlantic between New

York and London.

b. a submarine navigating under the ice of the North

Pole.

c. an agricultural scientist assembling crop yield data for

Africa.

d. an engineer planning the locations of radiotransmitters across the continental US.

3. What map projections would you choose in designing

a workstation to be used by scientists studying various

aspects of global environmental change?

4. By examining the list of SPC systems adopted by the

states, what can you deduce about the criteria used to

determine the projection adopted and the number of

zones used? You will need a map of the US showing the boundaries of states. Are there any surprising choices?

technical issues in gis

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