GIS Exam 1: Map Projections and Classes of Maps

Mollweide Map Projection

An equal-area, pseudocylindrical map projection. The projection trades accuracy of angle and shape for accuracy of proportions in area, and as such is used where that property is needed, such as maps depicting global distributions.

True North or Geographic North

Is the direction of northern pole of the Earth's axis of rotation.

Azimuthal

True direction is shown from one central point to all other points.

A polar area asks for a

Azimuthal Projection

Classes of Maps

Equal Area Conformal Equidistant Azimuthal

Projection properties

Equal area, conformal (shape), equidistance, azimuthal (direction)

The different Norths

Grid North True North Magnetic North

Grid North

Is the direction of the Eastings on a Map. OR direction of the y axis in the projection.

In Search of a Good Projection

Need to consider Location, Size and Shape A country in the tropics asks for a cylindrical projection A country in the temperate zone asks for a conical projection A polar area asks for a azimuthal projection

Tangent Line

Plane JUST TOUCHES globe at a single point. The farther from this line, the more distortion.

Oblique Tangent

Tangent at some intermediate latitude.

Polar Tangent

Tangent at the poles

Horizontal datum transformation

Transformed to another datum for the purposes of compatibility with existing data. The transformation method shall directly use, or be directly traceable to the North American Datum Conversion (NADCON) algorithm. The transformation shall not be performed on positions obtained through high accuracy survey techniques unless the transformation method employs a closed mathematical formula.

False Northing

UTM origin value 10,000,000 meters as a y unit instead of (0,0) so that all values of the equator are positive.

False Easting

UTM origin value 500,000 meters as a x unit and instead of (0,0) so that all values of the central meridian are positive.

Transverse Mercator

Very popular. Project onto a cylinder tangent to a central meridian Good for areas with longer N-S than E-W extent Distortion increases with distance from the central meridian Universal Transverse Mercator (UTM) is one example

False Easting and False Northing origin

(500,000, 10,000,000) = UTM origin

TGIS: Mapping Datums

- Horizontal Datum - Vertical Datum - Horizontal Datum Transformation - Vertical datum transformation

The Map Projection Process

- Projecting GIS data from one map projection to another is accomplished via exact mathematical transformations - Vector data can be projected "on the fly" that is to say in real time and does not necessarily result in loss of information - Projecting raster data is computationally intensive and can result in loss of information

Important Projections in GIS

- Universal Transverse Mercator (UTM) - Military Grid Coordinate System - State Plane Coordinate System (SPCS) - Texas Public Land Rectangular Survey System - Web Mercator - ESPG Projection Definitions

Military Grid Zones

A 6°x8° cell divided into squares 100,000 meters on a side and is assigned a two letter designation. In the east-west direction A-Z (I, O omitted) In the north-south direction A-V (I, O out) This identifies a single 100,000 meter grid square in a 4 alphanumeric identifier More accuracy is done by then giving UTM coordinates (often without trailing zeros)

Pseudocylindrical Maps

Are distinguished by the fact that in their simplest form, lines of latitude are parallel straight lines and meridians are curved lines (only the central meridian is straight, all others are curved). Another trade-off of shape vs. area.

The Important Properties of a Globe

Area Shape Distance Direction

Oblique Aspect Orthographic Projection

Area and shape are distorted Distances are true along equator and other parallels

Equal Area

Areas are preserved at the expense of other properties. Show parallels and the equator as straight lines and other meridians as curved; used to map tropical latitudes

Properties of Cylindrical Maps

Areas of least distortion are bands parallel to the line(s) of tangency. Exaggeration increases toward the outer edges of the map. Distortion may appear in: area angle direction distance

Projections consider lat and long as rectangular coordinates systems. True/False

False

Examples of Cylindrical Maps

Mercator Miller Gall's Stereographic Cylind. Gall-Peters Transverse Mercator Oblique Mercator Psuedocylindrical Mollweide Robinson

Families: Azimuthal

North/South Pole contact (plane)

Public Land Survey System (PLSS)

Not a coordinate system, but a standardized method for for designating and describing the locations of land parcels based on regularly spaced survey lines in approx. north-south and east-west directions. Often used as reference grid for further surveys or land subdivisions.

What is a map projection?

The systematic representation of all or part of the surface of a round body, especially the earth, onto a flat or plane surface OR simply going from the round Earth to a flat piece of paper.

Cost

When asking yourself is the acquisition of the projection cost effective? Is there already one available or must a projection be developed? Not so much an issue today

Deformational patterns

When asking yourself, does the deformation pattern accommodate the base map shape to minimize scale distortion?

Projection center

When asking yourself, is the projection center at or near the optimum location on the base map?

Familiarity

When asking yourself, will the arrangement of lines of longitude and latitude be familiar to the reader or will it distract from the cartographic presentation? However, sometimes something slightly different is refreshing...

About the Classic Orange Peel

When going from a 3-D sphere to a 2-D piece of paper it is inevitable that distortion will occur To maintain one of the properties, you have to give up the others Selection of a map projection means deciding what to save and what to give up.

Distortion is usually ____________ near the points or lines of intersection.

Less

Loxodromes

Line drawn on a globe possessing a constant compass bearing (posture, stance).

Parallels

Lines of constant latitude. Run parallel to each other in the east and west direction around the Earth.

Meridians

Lines of constant longitude. Geographic north and south lines that converge at the poles.

Tissot's Indicatrix

A mathematical approach to characterizing the distortions present on a map due to its map projection. It was first presented by Nicholas August Tissot in 1859. It represents distortion at a singular point, therefore many indicatrices are placed across a map to show distortions.

State Plane Coordinate System (SPCS)

A standard set of projections for the U.S. There are one or more zones in each state with slightly different projections in each State Plane zone to limit distortion which are kept below 1 part in 10,000. They greatly facilitate surveying, mapping subdivisions and spatial data development in GIS. Use to be NAD 27, now NAD 83.

Robinson Map Projection

A tabular(flat at the poles) projection designed to 'look right'but distorts: shape area scale distance

Military Grid

Adopted by U.S. Army in 1947 uses a lettering scheme to reduce the number of digits needed to isolate a location There are 60 zones like the civilian system, but going from south to north there are 8° strips of latitude going from C to X (no I and O to prevent confusion)

Universal Transverse Mercator Coordinate System

Based on the transverse mercator projection. This system divides the Earth into sones that 6 degrees wide in longitude and extend from 80 degrees south latitude to 84 degrees north latitude. UTM zones are numbered from 1 to 60 in an easterly direction. Has different origins in it's coordinate system so that all coordinates are positive. (500,000, 10,000,000) It is a common system for data and study area spanning large regions.

Lambert Azimuthal Equal Area

Central meridian is straight line (azimuthal) and all others curved (equal area). A straight line through the center point is a great circle.

A country in the temperate zone asks for a

Conic Projection

Geographic Coordinate System (GCS)

Consists of angular measurements of latitude, which varies from north to south, and longitude, which varies from east to west.

Families: Cylindrical

Contact w/ Prime Meridian or equator. (cylinder)

Families: Conic

Contact w/ a small circle. (cone)

Vertical datum transformation

Coordinates obtained in a specific vertical datum may be transformed to another datum for the purposes of compatibility with existing data. The transformation method shall directly use, or be directly traceable to the North American Vertical Datum Conversion (VERTCON) algorithm.

A country in the tropics asks for a

Cylindrical Projection

Mercator Projection

Cylindrical map projection. It became the standard map projection for nautical purposes because of its ability to represent lines of constant course, known as rhumb lines or loxodromes, as straight segments that conserve the angles with the meridians.

Miller Projection

Cylindrical projection is a modified mercator projection. This projection has straight meridians and parallels Shapes and areas are distorted, but areas not as much as the Mercator

Projected Coordinate System (PCS)

Data stored in a certain map projection.

Lambert Conformal Conic

Designed to preserve shapes. Areas are distorted away from the standard parallels, so as distance increases so does the distortion. Directions true in limited areas Commonly used for North America

Polar Stereographic

Directions are true from the center point scale increases away from the center point as does distortion and shape

Equidistant Map

Distance along designated great circles are true OR distances from one point to all others is true.

Equidistant Conic

Distances along the meridians are proportionately correct, and distances are also correct along two standard parallels that the mapmaker has chosen. The two standard parallels are also free of distortion. The map projection is used most often in maps of regions elongated east-to-west. Direction, area, and shape distorted away from standard parallels.

Azimuthal Equidistant

Distances and direction from the center are true.

Properties of an Azimuthal Projection

Distortion increases with distance from the standard point or line Distortion increases in concentric bands around that point Distortion reaches a maximum at the edges Distortion can appear in area angle distance direction

A little bit about Alaska

Each state, except Alaska is based upon a different map projection (Alaska uses all three) Transverse Mercator Projection used for states elongated North-South Lambert Conformal Conic Projection used for states elongated East-West Southeastern Alaska uses an oblique Mercator Projection States are then divided into a number of zones This is done to assure that the required level of accuracy can be maintained by selecting local standard parallels, etc.

Why map projections matter?

Impact how we view the world.

Distortion usually _____________ with ________________ distance from the intersection points or lines. Increases, Decreasing Decreases, Increasing Increases, Increasing Decreases, Decreasing

Increases, Increasing

Albers Equal Area Conic I

Is a conic, equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels.

Great Circle

Is a line that connects two points on the surface of a globe and divides the globe into two halves. It (or a portion of it) is also the shortest distance between two points.

SPCS 83

Is based on NAD83 and these coordinates are in meters Spheroid is different between the two SPCS as well Some states have changed the definitions of their zones some values of latitude and longitude have changed. The two datums do not share a common datum transformation method

Gall-Peter's Projection

Is one specialization of a configurable equal-area map projection known as the equal-area cylindric or cylindrical equal-area projection. De-emphasizes area exaggerations by shifting the standard parallels to 45° or 47°

Magnetic North

Is the direction towards which a compass points.

Oblique Mercator

It is conformal but not equal area. It's equivalent to a regular Mercator projection that has been altered by wrapping a cylinder around the sphere so that it touches the surface along the great circle path chosen for the central line instead of along the Earth's Equator. Good for areas that do not run N-S or E-W

Gall's Stereographic Cylindrical

It is neither equal-area nor conformal but instead tries to balance the distortion inherent in any projection. Results from projection onto a cylinder that is secant to the earth at 45° N and S Moderately distorts distance, shape, direction and area

Polyconics

Projection made of a series of stacked cones. Used for USGS topographic quadrangles until the 1950's apparently some USGS quadrangles produced after about 1957 are mislabeled as polyconic central meridian is straight other meridians complex curves parallels are non-concentric circles scale is true along each parallel and the central meridian

Factors that must be taken into consideration when selecting a Map projection

Projection properties Deformational patterns Projection Center Familiarity Cost

Conformal Map

Shape (of small areas) are preserved. Lines of longitude and latitude cross at right-angles

Properties of a Conic Projection

Straight or curved meridians Parallels are arcs In tangent case scale is true along arc forming contact between cone and sphere In secant case scale is true along the two arcs in contact and distortion minimized in area between the two arcs

Equatorial Tangent

Tangent at the equator

Texas Geographic Information Standards

The Texas Legislature has legislatively defined some Geographic Information Standards, including specifying a Datum and several map projections for statewide use.

Families of Projections

The different ways a two dimensional surface can be brought into contact with a sphere.

Why are properties of a globe are important?

There are four general classes of map. Each of these four types is designed to preserve one of the four major properties of a globe, but to accomplish this it is necessary to make accommodations in the other three The art of selecting an appropriate map projection is determining which property of the globe is most important to preserve while striving to minimize distortions in the others for your area of interest.

Secant Line

This line is the only part of the projection plane without distortion. Projection distortion inside this line makes features slightly smaller. Projection distortion outside this line makes features slightly larger.