GST 101 Introduction to Geospatial Technology��Unit 3 – Displaying Geospatial Data�Module 3.2 – Map Projections and Datums������ � �

Ann Johnson

Associate Director

ann@baremt.com

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Based upon work supported by the National Science Foundation under Grants DUE 1304591, DUE 164409, DUE 1700496, DUE 1937177, Due 1938717 DUE 1937237, 2030206 and 2015927. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Poster from USGS

In Module 3.1 we defined how to specify locations on a globe using a Geographic Coordinate System

In this Unit we will see how different types of Map Projections and its Datum are created and used to take a location on a 3D sphere and specify the same location on a 2D map (flat plane)

We will also review a few other Coordinate Systems used in the US

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http://thepioneerwoman.com/homeschooling/2010/11/choosing-a-globe-for-your-home-school/

Map Projections mathematically calculate locations of features from a 3D Geographical Coordinate System using Latitude and Longitude to locations on a flat plane�

• The process must include the values from a Datum (Earth’s size, shape and reference point) used in the original location and applied to the newly projected Map
• Watch the video from NOAA about Geodetic Datums and why it is important to use them

https://www.youtube.com/watch?v=kXTHaMY3cVk&list=PLfC6QYs6OC2qEJrfwx4eJvhBFNAZS7H_E

Analysis - Reprojection and Datum Transformation

1. From one projection to another – same Datum and version

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• From one projection to another – different Datums

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Why Create 2D Maps?

• There are many reasons for wanting to project the Earth’s surface onto a flat plane
• The Earth has to be projected to see all of it at once
• It’s much easier to measure distance on a flat plane rather than a sphere
• Its not practical to carry around a spherical map, especially to show a lot of detail in a small area and keep the map and sphere at the same scale!

Map Projection Poster From USGS

Projection of a 3D Object Onto a Flat Plane

The process of going from an ellipsoidal earth onto a flat map is called a map projection

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The map projection can be onto a flat surface or a surface that can be made flat by cutting, such as a cylinder or a cone

Map Projections and Distortions

• All map projections distort features in some way – shape, area, direction, distance
• Two types of projections are important:
• Conformal: Shapes of small features are preserved; anywhere on the projection the distortion is the same in all directions
• Equivalent (Equal Area): Shapes are distorted, but features have accurate areas
• Both types of projections will generally distort distances
• No flat map can be both equal area and conformal
• Most fall between the two as compromises
• To compare or edge-match maps, both maps MUST be in the same projection using the same Datum

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�������Map Projections – Regions where there is least distortion

• If the 2D surface cuts the globe, the projection is called secant
• If the 2D surface just touches one point on the globe, the project is called tangent
• Lines where the cuts take place or where the surface touches the globe have no projection distortion

From: http://nationalatlas.gov/articles/mapping/a_projections.html

Secant is a term in mathematics derived from the Latin secare ("to cut")�

The tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point

Map Projections

Features are projected onto one of three “developable” surfaces

https://en.wikipedia.org/wiki/Map_projection

Conic: a map projection where the earth’s surface is projected onto a tangent or secant cone, which is then cut from apex to base and laid flat

Cylindrical: a map projection where the earth’s surface is projected onto a tangent or secant cylinder, which is then cut lengthwise and laid flat

Planar: a map projection resulting from the conceptual projection of the earth onto a tangent or secant plane

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Bolstad, Fig. 3-38

Conformal Projection

• Cylindrical projection

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• Parallels and meridians at right angles
• Angles and shapes of small objects preserved (at every point, east–west scale same as north–south scale)
• The size/shape/area of large objects distorted
• Often used for online world maps

Example: Mercator projection (1569)

used for nautical purposes (constant courses are straight lines)

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Cylindrical Projections

• Conceptualized as the result of wrapping a cylinder of paper around the Earth.
• The Mercator projection is the best-known cylindrical projection.
• The projection is conformal.
• At any point scale is the same in both directions.
• Shape of small features is preserved.
• Features in high latitudes are significantly enlarged.

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Statue of Mercator on the Government House In Leuven, Belgium – where he lived and taught

Conic Projections

• Conceptualized as the result of wrapping a cone of paper around the Earth
• Standard Parallels occur where the cone intersects the Earth
• The Lambert Conformal Conic projection is commonly used to map North America
• On this projection lines of latitude appear as arcs of circles, and lines of longitude are straight lines radiating from the North Pole

Equivalent or Equal Area Projection

• Conic projection

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• Preserves accurate area
• Scale and shape are not preserved

Example: Albers Equal Area

standard projection for US Geological Survey, US Census Bureau

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The Universal Transverse Mercator (UTM) Projection

• A type of cylindrical projection
• Implemented as an internationally standard coordinate system
• Initially devised as a military standard
• Uses a system of 60 zones
• Maximum distortion is 0.04%
• Transverse Mercator because the cylinder is wrapped around the Poles, not the Equator

Universal Transverse Mercator (UTM)�Zones are each six degrees of longitude, numbered West to East from 180 (International Dateline) and extend from 80°S to 84°N

UTM Coordinates Use Meters as Distance Units

• The Equator is defined as 0 meters North
• In the northern hemisphere the Central Meridian of each zone is given a false easting of 500,000 meters East
• UTM locations consist of a zone number, a hemisphere, a six-digit easting and a seven-digit northing.
• For example: 14N 468324E 5362789N is:

Zone = 14 Hemisphere = N

Easting = 468324E Northing = 5362789N

• Eastings and northings are both in meters allowing easy estimation of distance using this projection
• Different countries may adjust northings and easting values depending on the country's geography

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Implications of the UTM Zone Coordinate System

• Each zone defines a different Central Meridian
• Two maps of adjacent zones will not fit along their common border
• For Example: Italy spans UTM Zones 32 and 33 and

California spans UTM Zones 10 and 11

• Jurisdictions that span two zones must make special adjustments such as:
• Use only one of the two projections and accept the greater-than-normal distortions in the other zone
• Use a third projection spanning the jurisdiction

UTM zones in the lower 48 States

UTM uses a modified Mercator projection with codes based on 6-degree Zones creating narrow north-south regions with minimal distortion within each zone

Over time UTM data has been based on different Datums, with current UTM codes generally based on a WGS 84 Datum

Caution: when using UTM data based on older Datums with current UTM data, the Datum should be transformed to the same Datum or location may be off by several 10s to 100s of meters

Compromise Projections

• Neither equivalent nor conformal
• Meridians curve gently, avoiding extremes
• Doesn’t preserve properties, but visually looks correct

Example:�Robinson projection (1961)

• Good compromise projection for viewing entire world

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• Used by Rand McNally and the National Geographic Society

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When the Correct Projection is Important

• Small-scale maps
• Comparing shapes, areas, distances, or directions of map features
• When natural appearance is desired

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New York

New York

Los Angeles

Los �Angeles

Projection: Mercator�Distance: 3,124.67 miles

Projection: Albers Equal Area�Distance: 2,455.03 miles

Actual distance: 2,451 miles

Los Angeles

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When Projection Is Less Important

• Many business, policy, and management applications.
• On large-scale maps.
• Error is negligible

when a small region is

being mapped such

as a neighborhood

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GIS Software and Web Mapping

• Many desktop software options can “reproject” data on the fly but Datum transformation generally must be done by the user and should be done before using the data
• Even though data may be reprojected, it is still advisable for important projects to have data reprojected into the same format (projection and datum) prior to carrying out any spatial analysis
• See this vido for more details and a link to a PDF of transformation information
• Datums and transformation: https://www.youtube.com/watch?v=-2z_WP7N7to
• Web Mercator is used by many online mapping applications (Google, Bing, ArcGIS Online, etc.)
• Web Mercator is NOT truly equal area
• Distortion increases as the map location moves north or south of the equator
• Polar regions are not included
• Some users (DoD) to not allow these projections to be used in their organization

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Online or Web Maps and Map Projection

• Some browser-based online mapping applications use a Web Mercator projection to visualize the Earth
• Care should be taken when doing basic analysis using these maps for calculating distance and areas
• While some applications use Web Mercator for displaying features, they may be calculating areas and distance based on appropriate map projections and providing the answer on the unseen projection
• Check carefully when relying on these values

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Examples of Other Coordinate Systems

• A coordinate system is a standardized method for assigning codes to locations so that locations can be defined by the codes
• One such system is the Universal Transverse Mercator (UTM) Coordinate System
• UTM uses a modified Mercator projection with codes based on 6-degree Zones creating narrow north-south regions with minimal distortion within each zone
• Over time UTM data has been based on different Datums, with current UTM codes generally based on a WGS 84 Datum
• Caution: when using UTM data based on older Datums with current UTM data, the Datum should be transformed to the same Datum or location may be off by several 10s to 100s of meters

Military Grid Reference System (MGRS) Coordinates Add Additional Locational Information to Each UTM Zone Code

• The MGRS adds 20 “latitude” bands (8° high bands using letters C to X) that are:
• Divided into 100,000 m cells identified by column and row letters
• Each of these cells are further divided into 1,000 m squares by columns and rows using numbers
• And can be further divided, if needed, into 10 and 1 m zones with additional codes

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By cmglee, STyx, Wikialine and Goran tek-en - World map nations.svg, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=84366980

Its Code for Location is: 18TWC8713. For more information see: https://en.wikipedia.org/wiki/Military_Grid_Reference_System

State Plane Coordinate System

• State Plane System - Defined in the US by each state
• Some states use multiple zones
• Several different types of projections are used
• Different Datums may cover different regions within a state
• Most states that are generally longer east-west have zones layered out horizontally (east/west), where states that are generally longer north-south have zones layered out vertically (north/south)
• Generally, provides less distortion than UTM
• Preferred for applications needing very high accuracy, such as surveying

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Bolstad Fig. 3-41

Public Land Survey System

• A grid system that divides some states into approximately 36 square-miles grid cells with columns identified as a Townships and rows as Ranges
• Townships and Range grids are divided by Principal Meridians and Baselines that help define the location (Range East or West of a Meridian or Township North or South of a Baseline)
• Many cities have streets that get their name of Baseline from this system
• Each Township/Range block is further divided into 6 square mile blocks numbered starting in the upper right corner
• Blocks can then be further divided into one-mile sections and sections further divided into smaller grid cells
• The Stared location would have a location of:
• The SE ¼ NE ¼, S13,T2S, R2W

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Tutorial on Public Lands Survey System

https://dnr.wisconsin.gov/sites/default/files/topic/ForestManagement/PLSSTutorial.pdf

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Videos to Watch

Please watch each of the following YouTube Videos. They range in time from 1 to 3 minutes

• Why We Have Map Projections (1 min)

https://www.youtube.com/watch?feature=player_embedded&v=2LcyMemJ3dE

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• Distortions From Map Projections (1 min)

https://www.youtube.com/watch?feature=player_embedded&v=e2jHvu1sKiI

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• Map Projection of Earth (2 min)

https://www.youtube.com/watch?feature=player_embedded&v=gGumy-9HrSY

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• Map Projection – Reading Lessons for Kids (2 min)

https://www.youtube.com/watch?feature=player_embedded&v=Y0T05iuaH-A

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• Projection and Other Methods for Making Maps (2 min)

https://www.youtube.com/watch?feature=player_embedded&v=oUUuGh7zaiY

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• What is Sea Level? (3 min)

https://www.youtube.com/watch?feature=player_embedded&v=q65O3qA0-n4

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See GeoTech Center website (https://geotechcenter.org) �for additional Model Courses and other curriculum resources. ���������Note: some content is a derivative of other authors���

Ann Johnson

Associate Director

ann@baremt.com

2-15-2021 V8