Maps Base maps Coordinate Systems, Datums, Projections Lat-long, Township-Range, UTM NAD27, WGS84 Topographic Maps Contours Distance Scale Declination Location and Navigation

Types of Maps Shaded-relief map Topographic map with elevation contours Satellite image Observe the four maps, which show the same area in different ways MEDIA 0206a4_sp_crater_maps.mov INSTRUCTIONS TO STUDENTS Observe these four maps, which show the same area in different ways EXPLANATION Shaded relief map shows shape of the land by simulating light and shadows on the hills and valleys Topographic map shows the elevation above sea level of the land surface using contour lines Satellite image using different wavelengths to show the distribution of different types of plants, rocks and other features Geologic map shows the distribution of rock units and geologic features Geologic map (ages and types of rocks and features) Center of area 02.06.a1-4

Base Maps Starting point for depicting or recording spatial data. Shows geographic, cultural, topographic features that are references to the data plotted. Typically airphotos, satellite images, and topographic maps are used as bases.

Base Maps Need to have a minimum of distortion e.g. they need to be planimetrically correct. Since Earth is curved, this requirement leads to map projections, etc. as ways to depict a curved surface on a flat map.

Base Maps Topographic maps (1:250k to 1:24k or larger) Aerial photographs Oblique – substantial distortion (perspective) Vertical – less distortion (lens and topography effects) Othorectified – planimetrically corrected

Coordinate Systems Ellipsoid (spheroid): define the shape of the physical Earth. Geoid: defines the shape of the Earth’s gravitational field e.g. the shape of surfaces of equipotential.

Coordinate Systems Datum: defines a reference for the shape and size of the earth, based on specific parameterizations of the ellipsoid and geoid. Many, some for local use, some for global use. Common ones are NAD27, NAD83, and WGS84

Coordinate Systems Any particular datum is based on a model for the shape of the Earth. Flat models for local surveying Spherical models for airplane radio navigation aids (VOR-DME-TACAN) Ellipsoidal models for precision, global ranging using radio Loran and GPS.

Coordinate Systems For maps, datums set the “zero point” for horizontal and vertical measurements. Converting between datums is a transformation of coordinates e.g. shifting the origin. Very important to use the correct datum or you will mislocate yourself and your data!

Coordinate Systems Earth is divided into a spherical grid system of latitude and longitude. Planes through the equator and the poles define circular intersections with the Earth’s surface.

Coordinate Systems Longitude: Intersection circles defined by set of all planes parallel to the rotation axis. North-south, NON-parallel lines (meridians). Origin (zero point) is the Greenwich Prime Meridian. Longitude measured in degrees East or West of Greenwich.

Coordinate Systems Latitude: Intersection circles defined by set of all planes perpendicular to rotation axis (parallel to equator). East-west, NON-intersecting lines (parallels). Origin (zero point) is the Equator. Latitude measured in degrees North or South of the Equator.

Coordinate Systems Township and Range: Old system to subdivide US for survey purposes. Origin (initial point or IP) is intersection of a principal meridian and a base line. Gridded in 6 mile increments. N-S increments are townships. E-W increments are ranges. Grid further subdivided by quartering…

Map Projections Curved surfaces are hard to depict on flat surfaces. No matter what you do, there will always be some distortion of… Areas Angles/Directions You can fix one or the other, but not both.

Map Projections Just what it sounds like…imagine you are projecting an image of the Earth onto a flat plane. The trick is figuring out how to do it to achieve the result you want. Mathematically, projections are a class of geometric transformation of coordinate systems.

Map Projections Images and maps contain inherent distortion  display of a curved surface on a flat medium. Projections are systematic representations of curved surfaces on planes: Perspective – projection through a projection center onto a plane Conic – projection through object center onto enveloping cone Cylindrical – projection through object center onto enveloping or intersecting cylinder Projections can be conformal (preserve shape and angles) or equivalent (preserve areas and distances)

Map Projections Question to ask: What kind of distortion do you need to minimize? Areas? Angles? Both? Neither? Purpose of the map dictates the answer and the answer dictates the appropriate projection to use. Scale of the map and location on Earth’s surface also affects the magnitude of the potential distortions.

Map Projections Mercator: Projection onto a circumscribing vertical cylinder results in rectangular maps with latitude and longitude in a grid pattern. Since longitude lines are not parallel, this results in distortion in polar areas (where meridians converge). Useful because directions and angles are preserved. But at the cost of distorting areas. Conformal. Scale changes with latitude.

Map Projections Transverse Mercator: Projection onto a horizontal circumscribing cylinder. One meridian line (central meridian) is tangent to the cylinder (compare to regular Mercator where the equator is tangent). This results in minimal area distortion along that tangent line and +/- 15° to either side (just as distortion is minimal near the equator in the regular Mercator projection). Conformal projecton.

Map Projections Universal Transverse Mercator (UTM): grid system for numbering maps produced in a Transverse Mercator projection. Grid covers globe from 84° N to 80° S. Grid divided into 60 N-S zones (each 6° wide) numbered from E to W starting at 180° longitude. Zones divided into 20 quadrangles 8° high Each quadrangle has its own grid with separate origin. Origin is intersection of central meridian and equator. UTM coordinates are distance in meters in N-S (“northing”) and E-W (“easting”) directions from the origin.

Map Projections Polyconic: Cut globe into strips. Flatten and stretch out to form a continuous surface. Scale constant along given line of latitude. Scale changes in N-S direction. Portion in center has minimal area distortion.

Map Projections Lambert Conformal Conic: Useful for areas that are elongated in E-W direction. Latitude and longitude grid projected onto a cone. Distance is preserved only along two standard parallels tangent to cone . Shapes and directions are preserved. Conformal. Projection used in most quadrangle maps.