Georeferencing. datum. projection. scale. The next few lectures will introduce you to these elements. on the Earth, you ll need to understand how

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1 Georeferencing GOAL: To assign a location to all the features represented in our geographic information data In order to do so, we need to make use of the following elements: ellipsoid/geoid To determine a position datum on the Earth, you ll need to understand how projection these elements relate to coordinate system each other in order to scale specify a position The next few lectures will introduce you to these elements

2 Using Projections to Map the Earth We have discussed geodesy, and we now know about modeling the shape of Earth as an ellipsoid and geoid We are ready to tackle the problem of transforming the 3- dimensional Earth 2-dimensional representation that suits our purposes: Earth surface Paper map or GIS map

3 Why Use Projections at All? There are many reasons for wanting to project the Earth s surface onto a plane, rather than deal with the curved surface: The paper used to output GIS maps is flat, and paper maps are more convenient than 3D models like globes for most large-scale applications Scanning and digitizing flat maps is a significant source of spatial data that is used in a GIS The raster spatial data model representation of the Earth s surface is flat, and it is impossible to create a raster on a curved surface The Earth has to be projected to see all of it at once It is much easier to measure distance on a plane

4 What is a Projection? Map projection - The systematic transformation of points on the Earth s surface to corresponding points on a planar surface The easiest way to imagine this is to think of a light bulb inside of a semi-transparent globe, shining features from the Earth s surface onto the planar surface

5 Projections Distort Because we are going from the 3D Earth 2D planar surface, projections always introduce some type of distortion When we select a map projection, we choose a particular projection to minimize the distortions that are important to a particular application

6 Three Families of Projections There are three major families of projections, each tends to introduce certain kinds of distortions, or conversely each has certain properties that it used to preserve (i.e. spatial characteristics that it does not distort): Three families: 1. Cylindrical projections 2. Conical projections 3. Planar projections 3 2 1

7 Developable Surfaces We refer to the 2-dimensional surface upon which the map information is projected as a developable surface The developable surface is a geometric surface that can be unrolled without distortion, although the projected information will contain distortions

8 Standard Points and Lines We can identify the locations where the developable surface contacts the ellipsoid s surface these locations are standard points and lines Standard point/lines: On a projected map, these are location(s) free of all distortion at the exact point or lines where the developable surface (cylinder, cone, plane) touches the globe

9 Tangent Projections Tangent projections have a single standard point (in the case of planar projection surfaces) or a standard line (for conical and cylindrical projection surfaces) of contact between the developable surface and globe

10 Secant Projections Secant projections have a single standard line (in the case of planar projection surfaces) or multiple standard lines (for conical and cylindrical projection surfaces) of contact between the developable surface and the globe

11 The Graticule The parallels and meridians of latitude and longitude form a graticule on a globe, a grid of orthogonal lines

12 The Graticule Picture a light source projecting the shadows of the graticule lines on the surface of a transparent globe onto the developable surface

13 The Graticule, Projected

14 Cylindrical Projections To create a cylindrical projection, the meridians are projected geometrically while the parallels are projected mathematically to produce 90 intersections throughout the graticule The meridians are equally spaced on a regular cylindrical projection, while the parallels are not The distortions have a linear pattern moving away from the standard lines

15 Cylindrical Projection Distortion Tangent Secant Standard Line Increasing Distortion Standard Lines

16 Mercator Projection The Mercator projection is a well known cylindrical projection (commonly used for world maps) The Equator is the standard line The spacing between parallels increases towards poles True-direction along graticule lines Great circles are not straight lines on this map projection

17 Transverse Mercator Projection You are likely less familiar with the transverse Mercator projection, although it is one of the most popular projections in current use It uses a cylindrical developable surface, oriented transversely with respect to the regular Mercator projection Meridians are tangential contacts The standard lines run north-south Used in the Universal Transverse Mercator (UTM) coordinate system

18 Plate Carrée (or Cylindrical Equidistant) Projection The Plate Carrée projection can be thought of as an unprojected projection, because latitude and longitude are simply mapped to an x-y grid by assigning latitude to the y-axis and longitude to the x-axis On the globe, meridians converge towards the poles, but using this projection they are parallel everywhere By default, a View in ArcView shows geographic data using this projection until the user specifies that the data should be displayed using some other projection

19 Conical Projections The simplest conical projection has a standard line called the standard parallel, because it contacts the globe along a line of latitude Meridians meet at the apex of the cone, and the distance between them increases as they move away from the apex Distortion increases north and south from the standard parallel along concentric arcs

20 Conical Projection Distortion Tangent Secant Standard Line Increasing Distortion

21 Lambert Conformal Conic Projection The Lambert Conformal Conic projection preserves the shape of geographic features Parallels are unequally spaced arcs that get further apart as they move away from the pole, and are portions of concentric circles Meridians are the radii of the same circles, that meet at the pole, which is represented by a single point It is a useful projection for mapping the middle latitudes It is typically used in applications where the accurate depiction of shape is important

22 Albers Equal Area Conic Projection The Albers Equal Area Conic projection preserves the area of geographic features Parallels are again unequally spaced arcs that get further apart as they move away from the pole, but they are not concentric circles as in the Lambert Conformal Conic The pole is not represented as a point, but instead as another arc It is a useful projection for producing maps where the area of features is important, and is often used for maps of the lower 48 states (a.k.a. the conterminous United States)

23 Planar Projections These are also called azimuthal projections The standard point acts as a focus for projection When describing an azimuthal projection, you specify a central latitude and longitude There is a 90 intersection of graticule lines at the center point All directions from the center point are true directions The patterns of distortion are circular around center point

24 Planar Projection Distortion Tangent Secant Standard Point Increasing Distortion Standard Line

25 Planar Projections We can describe planar projections by their orientation, which varies between the extremes of polar and equatorial orientations, and oblique orientations anywhere in between

26 Lambert Azimuthal Projection The Lambert Azimuthal projection preserves the direction and the area of geographic features to some extent The center of the projection is the only point with no distortion, as scale decreases as features get further from the center Directions are true with respect to the center Great circles (which denote the shortest route between two points on the surface of the Earth) are straight lines when using this projection

27 Planar Projections We can also describe planar projections in terms of the position of the light source used to project: Gnomonic all great circle arcs are straight lines Stereographic distortion compacted around center Orthographic perspective view; the distortion of areas and angles is not obvious

28 Preservation of Properties Every map projection introduces some sort of distortion because there is always distortion when reducing our 3- dimensional reality to a 2-dimensional representation Q: How should we choose which projections to use? A: We should choose a map projection that preserves the properties appropriate for the application, choosing from the following properties: 1. Shape 2. Area 3. Distance 4. Direction Note: It may be more useful to classify map projections by the properties they preserve, rather than by the shape of their developable surfaces

29 Preservation of Properties - Shape If a projection preserves shape, it is known as a conformal projection preserves local shape (i.e. angles of features) graticule lines have 90 intersection distortion of shape, area over longer distances rhumb lines lines of constant direction Greenland (Globe) Greenland (Mercator)

30 Preservation of Properties - Area Equal Area Projections preserve the area of displayed features however, shape, distance, direction, or any combination of these may be distorted on large-scale maps, the distortion can be quite difficult to notice Albers Equal-Area Conic A projection cannot preserve both shape and area!

31 Preservation Properties - Distance Equidistant Projections preserve the distance between certain points they maintain scale along one or more lines display true distances Sinusoidal A projection cannot preserve distance everywhere!

32 Preservation Properties - Direction Azimuthal Projections preserve directions, or azimuths, of all points on the map with respect to the center They can also be conformal equal-area equidistant Lambert Equal-Area Azimuthal A projection cannot preserve direction everywhere!

33 Tissot s Indicatrix Tissot s Indicatrix is a graphical tool which we can use to assess the properties preserved by a projection Tissot s Indicatrix allows us to take a feature that is a perfect circle before projection, and then see how it looks once projected (usually the distortion causes it to be elliptical in shape) We can calculate s = "area scale" = the product of semimajor and semi-minor axes of the ellipse

34 Tissot s Indicatrix