Maps

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Maps

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

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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.

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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.

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Base Maps

• Topographic maps (1250k to 124k or larger)
• Aerial photographs
• Oblique substantial distortion (perspective)
• Vertical less distortion (lens and topography
  effects)
• Othorectified planimetrically corrected

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Coordinate Systems

• Ellipsoid (spheroid) define the shape of the
  physical Earth.
• Geoid defines the shape of the Earths
  gravitational field e.g. the shape of surfaces of
  equipotential.

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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

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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.

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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!

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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 Earths surface.

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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.

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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.

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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

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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.

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Map Projections

• Just what it sounds likeimagine 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.

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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)

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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 Earths surface
  also affects the magnitude of the potential
  distortions.

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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.

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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.

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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.

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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.

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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.

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Topographic Maps

• Depicts the shape of the earth by showing lines
  of constant elevation (contours).
• Contours are shown at regular intervals of
  elevation (on USGS maps typically 20 ft).
• Understanding shape and density of contours is
  critical skill for effective use of topographic
  maps.

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Topographic Maps

• Rule of Vs
• Spacing of contours.
• Hatched contours.
• Contours cant cross.
• Saddles, peaks, valleys

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Topgraphic Maps

• Closely-spaced contours steep topography.
• Hatched contour lines are closed contours
  (depressions).
• Contour lines can never cross!
• Peaks, valleys, and saddles are useful for
  locating yourself

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Topographic Maps

• Ground distance vs. Map distance
• Ground distance is the total distance you would
  have to walk from point A to point B. Takes into
  account that terrain isnt flat.
• Map distance is the straight line distance you
  could take if you could fly from point A to point
  B. Assumes flat surface (no relief).
• In general Map distance lt Ground distance.

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Topographic Maps

• Map scale the relationship between the size of a
  feature on the map and the actual size on the
  ground.
• Indicated on maps by a scale bar, a verbal scale,
  or a fraction.

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Topographic Maps

• Large scale vs. small scale not intuitive!!!
• Large-scale maps show details of small areas.
  Large scale-fractions e.g. 11000.
• Small-scale maps show large areas. Small
  scale-fractions e.g. 11000000.

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Topographic Maps

• Declination angular measure of the difference
  between true and magnetic north.
• USGS maps are aligned with true north (rotation
  axis of Earth).
• Magnetic north is not at the rotation axis AND it
  changes!
• But our compasses point to magnetic NOT true
  north

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Topographic Maps

• Thankfully, we can correct for declination on our
  Brunton compass.
• Within a map area, declination is constant
  (essentially).
• Declination changes slowly (decade timescale).

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Topographic Maps

• Locating yourself takes practice! We will start
  practicing on Friday.
• Need to use the contours on the map and careful
  observation of your surroundings.
• Need to be aware of scale and distance.
• Using a compass to take bearings to landmarks
  helps

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Topographic Maps

• Bearing direction of a straight line between two
  points in terms of angular distance E or W of N-S
  line. Example N70W.
• Azimuth direction given in terms of clockwise
  angular distance from North. Example 290.
• Brunton compasses use either convention.

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Topographic Maps

• Profiles can be made using the contour data on a
  map
• Draw the profile line on the map.
• Mark the intersection of each contour line on the
  profile line.
• On a separate paper, draw the profile line to the
  same scale and transfer the intersection points.
• Select an appropriate vertical scale (with or
  without vertical exaggeration) and for each
  intersection point, plot the appropriate
  elevation on the vertical scale.
• Connect the dots.

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Topographic Map Rules

• Contours never cross.
• Contours never branch/merge.
• Contours dont disappear (except at edge of the
  map).
• Also

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Location and Navigation

• Locating yourself takes practice! We will start
  practicing on this afternoon
• Need to use the contours on the map and careful
  observation of your surroundings.
• Need to be aware of scale and distance.
• Using a compass to take bearings to landmarks
  helps

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Location and Navigation

• Bearing direction of a straight line between two
  points in terms of angular distance E or W of N-S
  line. Example N70W.
• Azimuth direction given in terms of clockwise
  angular distance from North. Example 290.
• Brunton compasses use either convention.

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Location and Navigation

• Vertical accuracy of USGS maps is within ½
  contour interval.
• Horizontal accuracy of USGS maps is to within 40
  feet on the ground for 124k maps. This is about
  0.5 mm on the map
• so you must learn to locate yourself and
  features to within the size of a pencil point!

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Location and Navigation

• Find north with the compass.
• Orient yourself and the map with north.
• Locate yourself by comparing the map with the
  surrounding terrain.
• Mark approximate location.
• Refine the location

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Location and Navigation

• Find yourself at a unique feature (intersections,
  bends, hilltops, etc.)
• Locate yourself along a linear feature by taking
  a bearing
• Locate yourself along a linear feature by
  determining your elevation
• Take a bearing and distance to a nearby landmark
• Triangluate to three or more landmarks
• Take a bearing to a landmark and determine your
  elevation

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Brunton Compass
Good to w/in ca. ½ degree. Metal is bad!
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Brunton Compass
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Brunton Compass
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Brunton Compass
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Shooting a Bearing
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Shooting a Bearing
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Triangulation
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Triangulation
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Triangulation
angle should be ca 60-90 degrees.
Triangulation Finding a feature
Resection Finding yourself
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Topographic Map Symbology
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Topographic Maps
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Topographic Map Symbology
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Topographic Map Symbology
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Topographic Map Symbology
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Topographic Map Symbology
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Topographic Map Symbology
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Topographic Maps

• How are they made?
• Ground surveys
• Stereo air photographs
• How can you make one (as we all will a few weeks
  from now)?

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Topographic Maps

• Collect elevations at a set of spaced points.
  Take some on ridge crests and in stream bottoms.
• Mark ridges with dashed lines along ridges toward
  stream intersections.
• Decide on appropriate contour interval (depends
  on relief and scale and number of control
  points).
• Mark points on ridges and streams corresponding
  to contour interval.
• Connect the dots smoothly and realistically.

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Topographic Maps

• Profiles can be made using the contour data on a
  map
• Draw the profile line on the map.
• Mark the intersection of each contour line on the
  profile line.
• On a separate paper (or below the map), draw the
  profile line to the same scale and transfer the
  intersection points.
• Select an appropriate vertical scale (with or
  without vertical exaggeration) and for each
  intersection point, plot the appropriate
  elevation on the vertical scale.
• Connect the dots.

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