Module 3

Question 1

Comments on longitude

Answer 1

• Location of prime meridian is arbitrary = Greenwich observatory in UK 1 Degree of
• Lines of longitude converge at the north and south poles
• To find longitude typically requires a clock, although there is a technique, called the lunar method that relies on the fact that the moon moves ½ of a degree per hour.

Question 2

Magnetic Declination

Answer 2

sometimes called magnetic variation, is the local angle between magnetic north and true north. Declination is considered positive east of true north and negative when west.

Question 3

The geomagnetic field

Answer 3

field is a combination of several generated magnetic fields sources (Magnetosphere, currents in Ionosphere, and the Earth’s internal magnetic
field)
These fields are superimposed on and interact with each other. More than 90% of the field measured is generated INTERNAL to the planet in the Earth’s outer core. This portion of the geomagnetic field is often referred to as the Main Field.

Question 4

The magnetic field varies across the Earth

Answer 4

the magnetic field changes with location, time and rate. It is so irregular that it must be measured in many places

At the magnetic poles, a dip needle stands vertical (dip=90 degrees; north magnetic pole, the north end of the dip needle is down), the horizontal intensity is zero, and a compass does not show direction At the magnetic equator the inclination is zero. Unlike the Earth’s geographic equator, the magnetic equator is not fixed, but slowly changes.

Question 5

Coordinate Systems

Answer 5

There are many different coordinate systems, based on a variety of geodetic datums, projections, and units in use
Geographic coordinate systems (no projection): Spheroid or Ellipsoid-based systems. •
Projected coordinate systems: examples UTM, state plane. BASED ON MAP PROJECTIONS

Question 6

Classes of Map projections

Answer 6

Physical models:
• Cylindrical projections (cylinder) -
• Conic Projections (cone)
• Stereo planar (Azimuthal) projections (plane)

Distortion properties:
• Conformal (preserves local angles and shape)
• Equal area or equivalent (area)
• Equidistant (scale along a center line)
• Azimuthal (directions)

Question 7

Basics of Map Projections

Answer 7

• A map projection is a mathematical model for conversion of locations from a three-dimensional earth surface to a two-dimensional map representation. This conversion necessarily distorts some aspect of the earth’s surface - area, shape, distance, or direction.
• Every projection has its own set of advantages and disadvantages. There is no “best” projection.
• Distortions of conformality (shape), scale, distance, direction, and area
• Some projections minimize distortions in one properties at the expense of maximizing errors in others.
• Some projection are attempts to only moderately distort all of these properties
• The mapmaker must select the one best suited to the needs, reducing distortion of the most important features.

Question 8

Cylindrical projections

Answer 8

• the meridians are straight, parallel, and equally spaced. The parallels are straight, parallel, and perpendicular to the meridians. The projection outline is rectangular.
• Ex: The Plate Carree, Mercator, Equidistant Cylindrical, Lambert Equal Area Cylindrical

Question 9

Mercator Projection (1569)

Answer 9

Directions are true along straight line of any two points,

Distances are true only along equator, and reasonable correct within 15° of equator.

In secant model, distance along two parallels are correct in scale instead of the Equator.

Areas and shapes of large area are distorted.

Distortion increases away from Equator and is extreme in polar regions. However, map is conformal in that angles and shapes within any small area is essentially true. -

Used for navigation or maps of equatorial regions.

Question 10

Transverse Mercator Projection (Lambert 1772)

Answer 10

• Distances are true only along the central meridian selected by the mapmaker or else along two lines parallel to it, but all distances, directions, shapes, and areas are reasonably accurate within 15° of the central meridian.

Distortion of distances, directions, and size of areas increases rapidly outside the 15° band.

Because the map is conformal, however, shapes and angles within any small area (such as that shown by a USGS topographic map) are essentially true

Question 11

Universal Transverse Mercator (UTM)

Answer 11

• 60 zones, 6° wide, 80°S-84°N.
• Each zone uses a Transverse Mercator projections with its own central meridian and is further divided into North and South.
• The central meridian in each UTM zone has a scale factor of 0.9996, which means that measurements along it fall short of true scale by 4 units in 10,000 (or 1 unit in 2,500). This is the maximum scale error anywhere within the zone.

North Zones: false easting of 500,000 m
South Zones: false easting of 500,000 m, false northing of 10,000,000 m

Question 12

Secant slices should be

Answer 12

close to surface to minimize SF distortion.

Question 13

Gnomonic model:

Answer 13

The gnomonic projection displays great circles as straight lines. Can be constructed by using a point of perspective at the center of the Earth. r(d) = c tan(d/R); so that even just a hemisphere is already infinite in extent. Preserving shortest route, a trait preserved only by the gnomonic projection

Question 14

Conic Projections

Answer 14

• the parallels (latitudes) are partial concentric circles.
• The meridians are straight, equally spaced radii of the circles.
• Conic projections usually don’t show the entire world
• the projection outline is fan-shaped.
• Ex: The Albers Equal Area Conic, Lambert Conformal* Conic, and Equidistant Conic

Question 15

Planar (Azimuthal) Projections

Answer 15

• In planar (azimuthal) projections, the parallels are full concentric circles centered on a pole.
• As with conics, the meridians are straight, equally- spaced radii of the circles.
• Some planar projections show the whole world; others show just a hemisphere.
• The normal aspect for planar projections is polar.
• Ex: The Stereographic, Orthographic, Gnomonic, Lambert Azimut Equal Area, and Azimuthal Equidistant

Question 16

Conformal Map Uses Conformal

Answer 16

• a map projection preserving the correct angles between directions within small areas, though distorting distances.
• Use a conformal projection when the map’s main purpose involves measuring angles, showing accurate local directions, or representing the shapes of features, such as:
(i) Topographic maps and cadastral (land parcel) maps
(ii) Navigation charts (for plotting course bearings and wind direction)
(iii) Civil engineering maps
(iv) Military maps
(v) Weather maps (for showing the local direction in which weather systems are moving)

Question 17

Equal Area Maps

Answer 17

An equal area map preserves the property of area.
[1] the total area of the scaled map is the same as the total surface area of the Earth,
[2] any area on the Earth’s surface will have the same scaled area on the map, although the shape of that expanse will most likely change.

Question 18

Equidistant Distance (scale)

Answer 18

An equidistant map preserves the property of distance for all lines passing through (or radiating from) a single, specific point

Question 19

Equidistant Map Uses

Answer 19

• Airline distances from a single city to several other cities
• Seismic map showing distances from the epicenter of an earthquake
• Maps used to calculate costs or charges based on straight-line distance from a source
• Maps used to calculate ranges; for example, the cruising ranges of airplanes or the habitats of animal species

Question 20

Direction (Azimuth)

Answer 20

• On an azimuthal map, azimuths are true for all lines that pass through a single, specified point.
• These straight lines are actually arcs of great circles
• Note how an azimuthal map, distorts latitude and longitude lines

Question 21

The concept of direction is complicated by that fact that

Answer 21

azimuth, or true direction, is one thing and constant direction is another. A line of constant direction (also called a rhumb line or loxodrome) On an azimuthal map, lines of constant direction are projected as curves.

Question 22

Azimuth values are measured

Answer 22

clockwise from the meridian on which the center point lies to a great circle that connects the center point to another point.

Question 23

Tissot’s Indicatrix

Answer 23

When a circle on a sphere is projected onto a flat surface, it is deformed into an ellipse.

The size, shape, and orientation of this ellipse (which is called an indicatrix) describe the spatial distortion at that location.

By placing indicatrices at regular intervals, you can see the distortion pattern across the surface.

Question 24

Mercator (equatorial aspect)

Answer 24

Central meridian: 0
Standard parallel: 0
Graticule spacing: 30 degrees
Type: Cylindrical
Graticule: Meridians are straight parallel lines. Parallels are unequally spaced straight parallel lines.
Scale: True on the equator; increasing toward the poles. Constant along any parallel.
Properties: Conformal.
Distortion: Severe area distortion near poles.
Uses: Marine charts and navigation; conformal mapping of equatorial regions.
Notes: Best within 15 degrees of the equator; any straight line is a true compass bearing; area distortion makes it a poor world map.

Question 25

Lambert Azimuthal Equal Area

Answer 25

Central meridian: 0
Latitude of origin: 90N
Graticule spacing: 20 degrees
Type: Planar Graticule: Meridians are equally spaced straight lines intersecting at the pole. Parallels are unequally spaced circles centered on the pole. Spacing of parallels decreases with distance from the pole.
Scale: True at the center. Decreases with distance from the center along radii. Increases with distance from the center in a direction perpendicular to radii.
Properties: Azimuthal and equal area.
Distortion: Zero distortion at the center. Distortion increases with distance from the center but remains moderate within one hemisphere (the limits of the projection).
Uses: Atlas maps of polar regions and northern and southern hemispheres.
Notes: Excellent equal-area map for approximately round areas. Lambert Azimuthal Equal Area (polar aspect)

Question 26

Equidistant Conic

Answer 26

Central meridian: 90W
Standard parallels: 0, 60N
( no distortion at 60°,-90°; 0°, -90) Graticule spacing: 30 degrees
Type: Conic
Graticule: Meridians are equally spaced straight lines that converge beyond the poles. Parallels are equally spaced concentric circular arcs.
Scale: True along all meridians and the standard parallels. Constant along all parallels.
Properties: Compromise between equal area and conformal.
Distortion: Increases with distance from standard parallels.

Question 27

• Albers Equal-Area Conic Projection (1805)

Answer 27

All areas on the map are proportional to the same areas on the Earth. Directions are reasonably accurate in limited regions. Distances are true on both standard parallels. Maximum scale error is 1 1/4% on map of conterminous States with standard parallels of 29 1/2°N and 45 1/2°N. Scale true only along standard parallels - Used for maps showing the conterminous United Stated

Question 28

• Lambert Conformal Conic Projection (1772

Answer 28

Distances true only along standard parallels; reasonably accurate elsewhere in limited regions. Directions reasonably accurate. Distortion of shapes and areas minimal at, but increases away from standard parallels. Shapes on large-scale maps of small areas essentially true Used for maps of North America. USGS Base Maps for 48 conterminous States with standard parallels 33 N, and 45 N (maximum scale error 2 ½ %). for TOPO maps, standard parallels vary. - Used for many topographic maps and for State Base Map series.

Question 29

State Plane Coordinate System

Answer 29

To support high-accuracy applications, all US states have adopted their own specialized coordinate systems: State Plane Coordinates. For example, Texas has five zones based on the Lambert Conformal Conic projection, while Hawaii has five zones based on Transverse Mercator projection

Question 30

Universal Polar Stereographic (UPS) Coordinate System

Answer 30

• UPS azimuthal equidistant projection - all points on the map are at proportionately correct distances from the center point, and all points on the map are at the correct azimuth (direction) from the center point. A polar projection shows all lines of longitude as straight, with distances from the north or south pole represented correctly.
• The UPS is defined above 84 degrees north latitude and south of 80 degrees south latitude.
• The eastings and northings are computed using a polar aspect stereographic projection.
• Zones are computed using a different character set for south and north Polar regions.