GIS Through Quiz 3

Certain map projections can preserve all properties (i.e., area, distance, direction, and shape) simultaneously. a) True b) False

b

Which order is from most complex to least complex? a) Sphere > Ellipsoid > Geoid > Earth b) Earth > Geoid > Ellipsoid > Sphere c) Earth > Ellipsoid > Geoid > Sphere d) Geoid > Earth >

b

Secant

cuts through the earth

A geographic coordinate system uses a three-dimensional spherical surface to define locations on Earth whereas a projected coordinate system project locations from the spherical surface onto a two-dimensional flat surface. a) True b) False

a

The geoid is the equipotential surface of the Earth's gravity field which best fits, in a least square sense, global mean sea level a) True b) False

a

While latitude and longitude can accurately locate exact positions on the surface of the globe, they are not convenient units for measuring distance, area, and angle. a) True b) False

a

Tangent

lies flat at a tangent to some point on the globe

Map projections

- A projection is a mathematical means that transforms information from the Earth's curved surface to a two-dimensional medium—paper or a computer screen - Transforming a globe surface to a flat surface always results in distortion (e.g., area, distance, direction, and shape—ADDS) - Cannot preserve all properties simultaneously -Map projections can be constructed in different ways. Each map projection has some unique characteristics. One needs to select the map projection carefully according to application needs. - Projections can be developed in any shape that is desired - A combination of projections can be used

UTM

- A secant projection - Applied for each 6-degree zone (altogether 60 zones) - Each zone is further divided into the northern and southern hemispheres - Limited between 84 ̊N and 80 ̊S - UTM zone is labeled by a number and a letter. For example, UTM zone 10N refers to the zone between 126°W and 120°W in the northern hemisphere. - Standard line is across the poles - UTM grid system may be based on NAD27, NAD83, or WGS84

Datum

- A system for anchoring an ellipsoid to known location - How we approximate the surface of the Earth "best fit" - The center and orientation of the chosen ellipsoid = DATUM - Different datums -> different estimates of Earth's shape/size - Horizontal and vertical datums

SPC vs UTM

- Both have unique parameters for each zone - SPC is more accurate than UTM, however, SPC is less universal - SPC is often used in legal description of properties and engineering applications.

Vertical Datums

- Collection of points on the Earth according to their height - Either according to MSL or the geoid - NGVD 29 (National Geodetic Vertical Datum of 1929) - NAVD 88 (North American Vertical Datum of 1988)

Horizontal Datums

- Collection of points on the Earth according to their latitude and longitude - Triangulation, GPS - NAD 27 (North American Datum of 1927, NAD 83

Azimuthal (Planar) Projections

- Direction between all points cannot be shown without distortion - Azimuthal (planar) projection - true directions from one central point to all other points Ex: Azimuthal equidistant and Lambert azimuthal equal area

Ellipsoid vs Geoid

- Ellipsoids are mathematically simpler to calculate that geoids - Geoids require more computational power to calculate - Geoids are typically used to define the vertical distance (z-value) above mean sea level (MSL)

Albers Conic Equal Area Projection

- It preserves areas (i.e., sizes of landmasses) - It is also used for mapping countries and regions of primarily east-west extent (such as the U.S. and Russia) - Equal-area projections like this one are preferred for thematic maps that show statistical attributes like population density.

Commonly used Projected Coordinate Systems

- Universal Transverse Mercator (UTM) - State Plane Coordinate System (SPC) - A projected (plane) coordinate system is based on a map projection - A map projection is derived from a sphere - A sphere is a approximation of an Ellipsoid (datum) Therefore, a projected coordinate system is both a map projection and a datum.

Datums: Global and Local

- WGS84 - "best fit" for whole Geoid - NAD27/83 - fitted to a particular region of the Earth (North America) where reference ellipsoid best fits that part

SPC

- created in the 1930s to permanently record original land survey monument locations in the United States. - completely covers the US with a flat grid network at a constant scale - Maximum scale distortion error wouldn't exceed 1 in 10,000 - Lambert Conformal Projection was used for zones of east-west extent. - Transverse Mercator Projection was used for zones of north-south extent. - Because of the switch from NAD27 to NAD83, there are SPC27 and SPC83.

Summary: Classification of Map Projections

- cylindrical, conic, planar - secant, tangent - normal (equatorial), transverse, oblique - Equal area (equivalent), conformal, equal-distance, azimuthal (planar)

How to choose a map projection?

1. What map properties you want to preserve? a) Area (equivalent) b) Distance (equidistance) c) Direction (azimuthal) d) Shape (conformal) 2. What is the size and shape of the study area? a) North-South extent (Universal Mercator) b) East-West (Lambert Conformal Conic)

Aspect

How the earth is viewed when projected - normal - transverse - oblique

Parallels

Lines of equal latitude. Using the equator as the 0° latitude, we can measure the latitude of a point as 0 to 90° north or south of the equator. Similarly, We may also use negative values represent latitudes to the south of equator, in which case latitudes can range from -90° to 90°.

Meridians

Lines of equal longitude. The prime meridian passes through Greenwich, England, and is of 0° longitude. Using the prime meridian as a reference, the longitude of a point on the Earth surface can range from 0 to 180° degree, east or west of the prime meridian. We may also use negative values represent longitudes to the west, in which case longitudes can range from -180° to 180°.

Longitude

Measure of how far east or west a place is from the Prime Meridian (Greenwich England)

Latitude

Measure of how far north or south a location is from the equator

Lambert Conformal Conic Projection

Preserves angles - used for mapping countries and regions of primarily east-west extent (such as the U.S. and Russia). - sed as the basis of the U.S. State Plane Coordinate System

Mercator Projection

Preserves shapes and angles, aka a conformal projection - distorts areas and distance - lots of distortion towards the poles

Geographic Projection

Simplest of the projections - Uses latitude and longitude as 2D coordinates, although they are defined on a 3D globe - Both areas and angles are distorted

Projected (Plane) Coordinate System

Superimposes a square grid on a flat map after a map projection. Less accurate but more convenient. A projected coordinate system is built on a map projection - Only a few projections can be used to create a plane coordinate system - provide accurate measurements for area, shape, distance, and direction, especially for large-scale maps - Projected coordinate systems are designed for detailed calculations and positioning, and are typically used in large-scale mapping such as at a scale of 1:24,000 or larger. - To maintain the level of accuracy desired for measurements, a projected coordinate system is often divided into different zones, with each zone defined by a different projection center.

Geoid

The equipotential surface of the Earth's gravity field which best fits, in a least squares sense, global mean sea level

Equal Area Projection

When a projection preserves area - Represent the area of regions is correct or constant proportion to earth reality - Each square inch on a flat map represents the same number of square units (miles, km, etc) anywhere else on the earth - Shape is distorted: A square on earth may become rectangle on the flat map - ex: Cylindrical Equal Area, Albers Equal Area

Equal Distance Projection

When a projection preserves distance - Equidistant when it portrays distances from the center of the projection to any other place on the map. - A map CANNOT be both equidistant and equal area Ex: simple conic and azimuthal equidistant projections

Conformal Projection

When a projection preserves shape and angles - Show accurate shapes for small areas by preserving correct angular relationships (directions) - No projection can provide correct shapes for large areas - Parallels and meridians intersect at right angles, as they do on the globe, but the size is distorted Ex: Mercator, Lambert Conformal Conic

Select the basic surfaces that are commonly used in map projections? a) Cylindrical b) Ellipsoidal c) Planar (azimuthal) d) Conical

a, c, d

Calculations using Geoids are mathematically simpler than calculations on ellipsoids. a) True b) False

b

Which of the below is INCORRECT? a) Each map projection is a mathematical means that transforms information from the Earth's curved surface to a two dimensional medium b) The most common surfaces to construct map projections onto are flat, cylindrical or conical surfaces c) There are map projections that can preserve all properties simultaneously (area, distance, angle) d) Each map projection has some unique characteristics

c

Projected Coordinate System

project locations from the sphere (globe) onto a two-dimensional flat surface - All will compromise on at least one dimension

Geographic Coordinate System (GCS)

the location reference system for spatial features on the Earth's surface - Longitude and latitude can accurately locate exact positions on the surface of the globe. However, they are not convenient units for measuring distance, area, and angles. Distance between two positions cannot be easily get from latitude/longitude coordinates