L 5 Map Projections Lecture 51

2 Map projections are used to transfer or “project” geographical coordinates onto a flat surface.. There are many projections: Maine example: NAD 27 Universal Transverse Mercator – Zone 19N NAD 27 Maine State Plane –East Zone –West Zone NAD 83 Universal Transverse Mercator– Zone 19N NAD 83 Maine State Plane –East Zone –Central Zone –West Zone

Lecture 53 Many Projections: Minnesota example

Lecture 54 Projections may be categorized by : 1.The location of projection source 2.The projection surface 3.Surface orientation 4.Distortion properties

Lecture 55 Gnomonic - center of globe Stereographic - at the antipode Orthographic - at infinity Source: Categorized by the Location of Projection Source

Lecture 56 Cone – Conic Cylinder - Cylindrical Plane - Azimuthul The projection surface:

Lecture 57 Projection Surfaces – “developable”

Lecture 58 The Tangent Case vs. The Secant Case In the tangent case the cone, cylinder or plane just touches the Earth along a single line or at a point. In the secant case, the cone, or cylinder intersects or cuts through the Earth as two circles. Whether tangent or secant, the location of this contact is important because it defines the line or point of least distortion on the map projection. This line of true scale is called the standard parallel or standard line.

Standard Parallel The line of latitude in a conic or cylindrical projection where the cone or cylinder touches the globe. A tangent conic or cylindrical projection has one standard parallel. A secant conic or cylindrical projection has two standard parallels. Lecture 59

10 The Orientation of the Surface

Lecture 511 Projections Categorized by Orientation: Equatorial - intersecting equator Transverse - at right angle to equator

Lecture 512 Specifying Projections 1.The type of developable surface (e.g., cone) 2.The size/shape of the Earth (ellipsoid, datum), and size of the surface 3.Where the surface intersects the ellipsoid 4.The location of the map projection origin on the surface, and the coordinate system units

Lecture 513 Defining a Projection – LCC (Lambert Conformal Conic) The LCC requires we specify an upper and lower parallel An ellipsoid A central meridian A projection origin central meridian origin

Lecture 514 Locally preserves angles/shape. Any two lines on the map follow the same angles as the corresponding original lines on the Earth. Projected graticule lines always cross at right angles. Area, distance and azimuths change. Conformal Projections

Lecture 515 Equidistant Projections A map is equidistant when the distances between points differs from the distances on Earth by the same scale factor.

Lecture 516 Equivalent/Equal Area Projection Equivalent/equal area projections maintain map areas proportional to the same areas of the Earth. Shape and scale distortions increase near points 90 o from the central line.

Lecture 517 “Standard” Projections Governments (and other organizations) define “standard” projections to use Projections preserve specific geometric properties, over a limited area Imposes uniformity, facilitates data exchange, provides quality control, establishes limits on geometric distortion.

Lecture 518 National Projections

Lecture 519

Lecture 520 Map Projections vs. Datum Transformations A map projections is a systematic rendering from 3-D to 2-D Datum transformations are from one datum to another, 3-D to 3-D or 2-D to 2-D Changing from one projection to another may require both.

Lecture 521 From one Projection to Another

Lecture 522

Lecture 523 Common GIS Projections Mercator- A conformal, cylindrical projection tangent to the equator. Originally created to display accurate compass bearings for sea travel. An additional feature of this projection is that all local shapes are accurate and clearly defined. Transverse Mercator - Similar to the Mercator except that the cylinder is tangent along a meridian instead of the equator. The result is a conformal projection that minimizes distortion along a north-south line, but does not maintain true directions. Universal Transverse Mercator (UTM) – Based on a Transverse Mercator projection centered in the middle of zones that are 6 degrees in longitude wide. These zones have been created throughout the world.

Lecture 524 Lambert Conformal Conic – A conic, confromal projection typically intersecting parallels of latitude, standard parallels, in the northern hemisphere. This projection is one of the best for middle latitudes because distortion is lowest in the band between the standard parallels. It is similar to the Albers Conic Equal Area projection except that the Lambert Conformal Conic projection portrays shape more accurately than area. Lambert Equal Area - An equidistant, conic projection similar to the Lambert Conformal Conic that preserves areas. Albers Equal Area Conic - This conic projection uses two standard parallels to reduce some of the distortion of a projection with one standard parallel. Shape and linear scale distortion are minimized between standard parallels. State Plane – A standard set of projections for the United States –based on either the Lambert Conformal Conic or transverse mercator projection, depending on the orientation of each state. Large states commonly require several state plane zones.

Lecture 525 Map Projections Summary Projections specify a two-dimensional coordinate system from a 3-D globe All projections cause some distortion Errors are controlled by choosing the proper projection type, limiting the area applied There are standard projections Projections differ by datum – know your parameters

Lecture 526 Coordinate Systems Once map data are projected onto a planar surface, features must be referenced by a planar coordinate system. Coordinates in the GIS are measured from the origin point. However, false eastings and false northings are frequently used, which effectively offset the origin to a different place on the coordinate plane. The three most common systems you will encounter in the USA are: –State Plane –Universal Transverse Mercator (UTM) –Public Land Survey System (PLSS) – non-coordinate systems Coordinate systems

Lecture 527 State Plane Coordinate Systems Uses Lambert conformal conic (LCC) and Transverse Mercator (TM, cylindrical) LCC when long dimension East-West TM when long dimension N-S May be mixed, as many zones used as needed

Lecture 528 State Plane Coordinate System Each state partitioned into zones Each zone has a different projection specified Distortion in surface measurement less than 1 part in 10,000 within a zone California State Plane Zones

Lecture 529 State Plane Coordinate System Zones

Lecture 530 Maine State Plane

Lecture 531 State Plane Coordinate System e.g., Maine East State Plane Zone Projection: Transverse_Mercator False_Easting: False_Northing: Central_Meridian: Scale_Factor: Latitude_Of_Origin: Linear Unit: Meter ( ) Geographic Coordinate System: GCS_North_American_1983 Angular Unit: Degree ( ) Prime Meridian: Greenwich ( ) Datum: D_North_American_1983 Spheroid: GRS_1980 Semimajor Axis: Semiminor Axis: Inverse Flattening:

Lecture 532 UTM – Universal Transverse Mercator UTM define horizontal positions world- wide by dividing the surface of the Earth into 6 o zones. Zone numbers designate the 6 o longitudinal strips extending from 80 o south to 84 o north. Each zone has a central meridian in the center of the zone.

Lecture 533 Universal Transverse Mercator – UTM System

Lecture 534 UTM Zone Details Each Zone is 6 degrees wide Zone location defined by a central meridian Origin at the Equator, 500,000m west of the zone central Meridian Coordinates are always positive (offset for south Zones) Coordinates discontinuous across zone boundaries

Lecture 535 Universal Transverse Mercator Projection – UTM Zones for the U.S.

Lecture 536 UTM Zone 19N Projection: Transverse_Mercator False_Easting: False_Northing: Central_Meridian: Scale_Factor: Latitude_Of_Origin: Linear Unit: Meter ( ) Geographic Coordinate System: GCS_North_American_1983 Angular Unit: Degree ( ) Prime Meridian: Greenwich ( ) Datum: D_North_American_1983 Spheroid: GRS_1980 Semimajor Axis: Semiminor Axis: Inverse Flattening:

False Easting/Northing False easting – the value added to the x coordinates of a map projection so that none of the values being mapped are negative. False northing are values added to the y coordinates. Lecture 537

Central Meridian Every projection has a central meridian. The line of longitude that defines the center and often the x origin of the projected coordinate system. In most projections, it runs down the middle of the map and the map is symmetrical on either side of it. It may or may not be a line of true scale. (True scale means no distance distortion.) Lecture 538

Central Meridian Lecture /concepts/Map%20coordinate%20systems/Projection%20parameters.htm

Scale Factor 0 > scale factor < =1 The ratio of the actual scale at a particular place on the map to the stated scale on the map. Usually the tangent line or secant lines. Lecture 540

Lecture 541 Coordinate Systems Notation Latitude/Longitude Degrees Minutes Seconds45° 3' 38" N Degrees Minutes (decimal) 45° ' N Degrees (decimal) ° N State Plane (feet)2,951, N UTM (meters)4,996, N

ArcGIS Datums and Projections Lecture 542

Datum Transformations Lecture 5 43 Moving your data between coordinate systems sometimes includes transforming between the geographic coordinate systems. Because geographic coordinate systems contain datums that are based on spheroids, a geographic transformation also changes the underlying spheroid ArcGIS Help

Datum Transformations Lecture 544 A geographic transformation is always defined in a particular direction. When working with geographic transformations, if no mention is made of the direction, an application or tool like ArcMap will handle the directionality automatically. For example, if converting data from WGS 1984 to NAD 1927, you can pick a transformation called NAD_1927_to_WGS_1984_3 and the software will apply it correctly. (ArcMap automatically loads one geographic transformation. It's designed for the lower 48 states of the United States and converts between NAD 1927 and NAD 1983.) ArcGIS Help

Graph the Following Lecture 545 DistanceTime DistanceTime

Graph the Following Lecture 546 Distance Km Time Hr Distance M Time Min

Lecture 547

Define The Projection Predefined Custom Import Lecture 548

Predefined Lecture 549

Custom & Import Lecture 550

Custom & Import Lecture 551

Reproject “On the Fly” Two or more layers with different DEFINED projections. First layer in the data frame defines the projection for the data frame. Next layer added, ArcGIS will automatically reproject it to the data frame. Lecture 552

Defining The Projection for A Data Frame Lecture 553

Project Lecture 554

Project Lecture 555