Chapter 2 Basic Mapping Processes | Introduction |

I. Defining an Object’s Location in the World

II. Geographical Coordinate System

III. What is the Earth’s Shape?

IV. Impact of Earth’s Shape on Location

Determination

V. A Datum as a Mapping Framework

I. Horizontal Datum

II. Vertical Datum

How do we define the location of an object in the world?

40.625106o, -73.961446o

40o 37’ 30.3816”, -73o 57’ 41.2056”

40.606789o, -74.044016o

40o 36’ 24.4404”, -74o 2’ 38.4576”

Chapter 2 Basic Mapping Processes

Geographical Coordinate

System

Chapter 2 Basic Mapping Processes

Types of Coordinate Systems

Geographical Coordinate System

(Spherical Coordinates)

Projected Coordinate System

(Cartesian Coordinates)

Chapter 2 Basic Mapping Processes

source: http://courses.washington.edu

What differences do you see between these?

Types of Coordinate Systems

Projected Coordinate System

(Cartesian Coordinates)

Chapter 2 Basic Mapping Processes

source: http://courses.washington.edu

Geographic Coordinate System

Source: Extracted from PDF version of the

http://www.disam.dsca.mil/pubs/archives.htm Vol 26-4 2004

DISAM Journal

Graticule

The pattern of meridians

and parallels on the earth.

Great Circle

A circle that divides the

earth into two equal halves.

Small Circle

A circle that divides the earth

into two unequal halves.

Chapter 2 Basic Mapping Processes

Latitude is the angular distance north or

south of the equator.

Geographic Coordinate System

Image Source: Christopherson, Geosystems 6th edition

Parallels connect points of equal latitude. Meridians connect points of equal longitude.

Longitude is the angular distance east or

west of the Prime Meridian.

Chapter 2 Basic Mapping Processes

Geographic Coordinate System

A degree of latitude or longitude can be subdivided further into minutes and seconds…

One degree is divided into 60

minutes (60’)…

One minute is divided into 60

seconds (60”)….

Example: 44o42’06”E

This reads 44 degrees, 42 minutes,

6 seconds East of the Prime

Meridian.

44th degree divided into 60 minutes

42nd minute divided into 60 seconds

42nd minute of 44th degree

6th second of 42nd minute

44oE 45oE

44o43’E

44o42’E

So, how do you convert between DMS and Decimal Degrees?

Chapter 2 Basic Mapping Processes

What is the Earth’s Shape?

Chapter 2 Basic Mapping Processes

Chapter 2 Basic Mapping Processes

Three Important Shapes of the Earth

“Good Enough” For

General Mapping Purposes

Need to Consider Both in

Detailed Mapping Efforts

Impact of the Earth’s Shape

on Location Determination

Chapter 2 Basic Mapping Processes

An accurate and precise calculation of “the vertical” is required in order to accurately

calculate a locations’ latitude and longitude using traditional methods.

Deflection of the vertical – the

difference between a vertical line

passing through the earth’s center

of gravity (geoid) and a vertical line

passing through the earth’s

geometric center (ellipsoid).

Chapter 2 Basic Mapping Processes

Impact of Earth’s Shape on Latitude / Longitude

Determination

What About a Point’s Elevation Value?

Different elevation values are obtained based on which shape is used.

Which surface do you use?

Chapter 2 Basic Mapping Processes

Horizontal Datum

Chapter 2 Horizontal Datum

Horizontal Datums

Local Horiz. Datum – ellipsoid is constructed as a best fit with the geoid in a specific area.

Global Horiz. Datum – ellipsoid is constructed as a best fit with the geoid globally

Source: http://www.kartografie.nl/geometrics/Reference%20surfaces/body.htm

Chapter 2 Horizontal Datum

A Selection of Ellipsoids Used for Mapping Purposes

Name | Date | Equatorial Radius (m) |
Polar Radius (m) |
Area of Use |

WGS84 | 1984 | 6,378,137 | 6,356,752.31 | Worldwide |

GRS 80 | 1980 | 6,378,137 | 6,356,752.3 | Worldwide (Nad83) |

Australia | 1965 | 6,378,160 | 6,356,774.7 | Australia |

Clarke 1880 | 1880 | 6,378,249.1 | 6,356,514.9 | France, most Africa |

Clarke 1866 | 1866 | 6,378,206.4 | 6,356,583.8 | North America (Nad27) |

Airy | 1849 | 6,377,563.4 | 6,356,256.9 | Great Britain |

Chapter 2 Horizontal Datum

North American Datum of 1927 (NAD27)

Meades Ranch-Center of the Contiguous US

The base point was the reference point for almost all land survey measurements in the

United States from 1927 until the establishment of the North American Datum of 1983

(NAD 83) and the World Geodetic System of 1984 (WGS84).

Chapter 2 Horizontal Datum

Effect of the Datum Change

The North American Datum of

1983, contains fewer inherent

local distortions than the North

American Datum of 1927

The datum change resulted in the

adjustment (0-250 meters) of most

latitude and longitude locations

throughout the North America.

Chapter 2 Horizontal Datum

Chapter 2 Vertical Datum

Vertical Datum

Chapter 2 Vertical Datum

Vertical Datums and Elevation Measurements

Traditionally, vertical measurements are referenced to a local vertical

datum that has a starting point at a tidal station.

North American Vertical Datum of 1988

Many elevation measurements in North

America are tied to the North American

Vertical Datum of 1988 (NAVD 88)

The zero surface for this datum is defined

by Mean Sea Level at the Rimouski tidal

station in Canada

Mean Sea Level (MSL) is defined by

surveyors as the average of all low and

high tides at a particular starting location

over a 19 (18.6) year lunar period called

Metonic cycle.

Chapter 2 Vertical Datum

Vertical Datums and

Elevation Measurements

A local vertical datum is

implemented through a vertical

control network.

Example: Geodetic leveling in the

Netherlands using the vertical datum

defined by the Amsterdam tidal station

Source: http://www.kartografie.nl/geometrics/Reference%20surfaces/body.htm

NO CLASS – Classes Follow MONDAY Schedule Chapter 2 Vertical Datum

Important Dates!

Added to the Calendar on Blackboard:

Tuesday Feb 7th (that’s today) – last

day to drop with 50% refund

Tuesday Feb 14th (one week from

today) – last day to drop with 25%

refund and not receive a “W”

Tuesday Feb 21st – Classes follow the

Monday schedule – No Class Meeting

Thursday Feb 23rd – I will be traveling, I

will pre-record and send out a lecture, I

will be available via email for questions

during our class time (up until the plane

takes off)

After that, no schedule disruptions until

SPRING BREAK

The UTM Zones

Chapter 2 Coordinate Systems Grid Systems: UTM

840N

800S

00

There are total 60 North-South Zones, starting

from 180ºW and each being 6º wide in longitude

1800W

1800W

1800E

1800E

00

00

00

Chapter 2 Coordinate Systems Grid Systems: UTM

NAD_1983_UTM_Zone_17N

Projection: Transverse_Mercator

False_Easting: 500000.000000

False_Northing: 0.000000

NAD_1983_UTM_Zone_18N

Projection: Transverse_Mercator

False_Easting: 500000.000000

False_Northing: 0.000000

Two UTM zones

for New York

But what’s the deal

with this falseness?

Chapter 2 Coordinate Systems Grid Systems: UTM

source: http://www.vidiani.com

Let’s use Manhattan as a model

UTM does not use use negative numbers.

UTM North zones doesn’t use false northing, it uses the equator (black line)

UTM Southzones, rather than measuring south from the equator (negative

numbers) instead it measures up from an imaginary false north (red line)

500k

UTM Meridian UTM Meridian

False Easting

Transverse Mercator

Projection

Used for North – South

trending states

Used for East – West

trending states

Lambert Conformal Conic

Projection

Chapter 2 Coordinate Systems Grid Systems: UTM

Chapter 2 Coordinate Systems Grid Systems: UTM

State Plane Systems

• Lambert Conformal Conic

• Transverse Mercator

• Oblique Mercator (Alaska)

NAD_1983_StatePlane_New_York_West

Projection: Transverse_Mercator

False_Easting: 350000.000000

False_Northing: 0.000000

Chapter 2 Coordinate Systems Grid Systems: UTM

• A systematic rendering of a

graticule of lines of latitude and

longitude on a flat sheet of paper.

• A mathematic transformation of

the curved earth surface to a flat

sheet of paper

Curved Earth

Geographic coordinates

(Latitude & Longitude)

Flat Map

Cartesian coordinates: x,y

(Easting & Northing)

A Map Projection is …

Chapter 2 Map Projections What is a map projection?

Maps can’t or don’t show

the whole world

• Examples:

– Mercator: usually extends

to 80o N and 80o S

– Gnomonic, limited

mathematically to cover

less than a hemisphere.

Although maps are useful, they have limitations…

Chapter 2 Map Projections

0 30W |
60E 30E |

90E 150E 120E |
30N 180E 180W 120W 150W 60N |

60W

90W

150N

What is a map projection?

1800W

1800W

1800W

900N

Point to

Point

Point to line

Continuity

Loss

Breaks in continuity (where the same line forms two edges of the map)

(World from space, modified) (World Miller Cylindrical Projection)

Correspondence and continuity are lost and geographic distortions occur.

Chapter 2 Map Projections

Although maps are useful, they have limitations…

What is a map projection?

(Azimuthal) Plane Cylinder Cone

Developable Surface of Map Projection

Chapter 2 Map Projections Creation of a Map Projection

Choose based on scale, place, other considerations

Plane Projection Orientations

Normal

(Polar)

Transverse (Equatorial)

Oblique

Chapter 2 Map Projections Creation of a Map Projection

Cylindrical Projection Orientations

Transverse

(Along a Meridian)

Oblique

Normal

(Equatorial)

Chapter 2 Map Projections Creation of a Map Projection

Light source at the

center of the earth

Light source at the

infinite distance

Light source sits

exactly opposite the

developable surface’s

point of tangency

Gnomonic Projection

Orthographic Projection

Stereographic Projection

Chapter 2 Map Projections Creation of a Map Projection

Light Type for Map Projections

• Two Major Properties

Properties that can exist at all

points on certain projections.

Earth Properties to Preserve or Distort

• Two Minor Properties

Properties that can exist in

relation to only one or two

points or lines on certain

projections.

12

12 |

12 12

50°

50°

40°

–Conformality: Shape (Angle)

–Equivalence: Area (Size)

–Distance (Scale)

–Direction (Azimuth)

Chapter 2 Map Projections Earth’s Properties S.A.DD

Mercator Conformal Projection

Generating Globe

Chapter 2 Map Projections Earth’s Properties Conformality (Shape)

Another Example: Lambert’s Conic Conformal Projection

Example of a Conformal Projection – preserves shape

Mollweide Equal-area Projection

Chapter 2 Map Projections Earth’s Properties Equivalence (Area)

Sinusoidal Projection

Albert’s Conic Equal-Area Projection

Lambert’s Azimuthal Equal Area

Other Examples:

Generating Globe

Example of an Equal-Area Projection – preserves area

• Conformality (Shape) and Equivalence (Area) are mutually

exclusive, you CANNOT preserve both on one map.

• However, a map can be both azimuthal (preserving

direction) and equivalent (preserving area) or both

azimuthal and equidistant (preserving scale).

Azimuthal equidistant projection Azimuthal equal-area projection

Chapter 2 Map Projections Earth’s Properties S.A.D.D.

Compromise projections are projections that do not preserve

any of the globe properties but also does not result in extreme

distortion of any property.

• It is impossible and

unnecessary to keep all

or none of the properties

precisely.

• Compromise projections

have better visual

effects as used for the

education purpose.

• Commonly used ones

include Miller

Cylindrical, Robinson,

and Winkel Tripel.

Chapter 2 Map Projections Earth’s Properties Compromise Projections

Chapter 2 Map Projections Earth’s Properties Compromise Projections

Projection Selections

• Purpose of the map

Are aesthetics important?

Are density calculations being made?

Are distance and / or direction calculations being made?

• Size of the area being mapped

Is an entire continent being mapped?

f

• Shape of the area being mapped

Does the area being mapped have a “skinny” shape? (e.g. Chile)

Does the area being mapped have a rectangular shape? (e.g. United

States)

• Latitudinal location of the area being mapped

Polar Location?

Mid-Latitude Location?

Equatorial Location?

What considerations do we need to make when selecting

a map projection?

Great Website: http://egsc.usgs.gov/isb/pubs/MapProjections/projections.html