GIS/GPS Chapter 4

Spatial reference

datum, coordinate system, project

Types of coordinate systems

global.spherical coordinate system for the whole earth, geographic coordinate system, projected coordinate system based on a local area of the earth surface

Projected coordinate system based on a local area of the earth’s surface

Z-coordiante in 1 and 3 is geometrically defined, Z-coordinate in 2 is gravity defined

Geographic coordinates

latitude and longitude defined using an ellipsoid w/ ellipse about an axis, elevation defined using geoid w/ surface of constant gravitational potential, earth datums define standard values of the ellipsoid and geoid

Simple sphere

latitude based off of plan of equator, line from point of origin from the equator for latitude, go east and west either way for longitude

Latitude

take a point S on the surface of the ellipsoid and define there the tangent plane (mn), define teh line pq through S and normal to the tangent plan, angle pqr which this line makes w/ the equatorial plan is the latitude of point S

Longitude

angle between a cutting plan on the prime meridian and the cutting plan on the meridian through the point P

When converting what ways are positive and negative?

W and S are negative, N and E are positive

Length on a meridian

AB = Re (0), same for latitudes

Length on a parallel

CD = R, deltawavelength = Re deltawavelength Cos (0), varies with latitude

What happens to parallels as they approach poles?

converge together

Where is the shortest distance?

along the great circle

Great circle

intersection of a sphere with a plane going through its center, earth always changing

Steps of the great circle

spherical coordinates converted to Cartesian coordinates, calculate angle frequency from latitude and longitude, great circle distance is Rfrequency where R = 6370 km

Map projections

method for converting 3D surface to 2D surface, cartographers use it to describe the process of converting coordiantes from a 3D spherical coordinate system to a 2D dimensional planar coordinate system to make everything look distorted, spatial properties but no map can have all 4 only 2 at a time and no map has a true scale in all directions

Spatial properties subject to distortion in a projection

shape (conformality), area (equivalence), distance (equidistance), direction (azimuthality)

Shape

if a map preserves shape then feature outlines (country boundaries) look the same ont he map as they do on Earth, preserving shape is conformal, conformal map distorts are with most features are depicted too large/small

Area

if a map preserves area than the size of a feature on a map is the same relative to its size on the earth, equal area world map Norway takes up the same percentage of map space that actual Norway takes up on earth and in equal-area map the shapes of most features are distorted and no map can rpeserve both shape and area for the whole world

Distance

if a line from a to b on a map is the same distance (accounting for scale) that it’s on the earth then the map line has true scale, no map has trule scale everywhere, most map have at least ½ lines of true scale

Direction (azimuth)

measured in degrees of angle from N, on earth this means that the direction from a to b is the angle between the meridian on which a lies and the great circle arc connecting to b

Compromise

some maps projects preserve none of the properties described above but instead seek a compromise that minimizes distortion of all kinds, US uses a lot

What do good maps preserve?

direction and distance, direction and shape, direction and area

What do bad maps preserve?

shape and distance, area and distance, shape and area

Cylindrical

top light rays are perpendicular to the earth’s polar axis and parallel spacing decreases toward the poles, bottom light rays emanate from the center of the globe and parallel spacing increases toward the poles and get exaggerated latitudinal lines with drawing lines from center to each latitude, mercator projection with any straight line drawn has true direction with scaling issues and only true along the equator, cylinder secant to a sphere adds the low distortions further to the others and tangent adds the low distortions closer to the equator with north not preserved, universal transverse mercator (UTM) in 18N and 17N where we are and as go further out then it gets more distorted and can be broken up into 60 zones most of the times but can be other ways, mollweide pseudocylindrical is equal-area not equal shape

Conic

distortion increases north and south of the standard parallel, distortion at the poles is so extreme that many maps that use conic projections remove the polar regions, typically used for mid-latitude zones with an east-west orientation, map projection can look like a half eaten donut, showing usually use albers equal-area conic, not equidistant and direction kept for a little bit and preserves nothing equally, lambert conformal conic is used by the USGS, further west and biggest state in US is Alaska

Planar

azimuthal projections, project map data onto a flat surface, simplest planar projection is tangent to the globe at one point, gnomonic, stereographic, orthographic, azimuthal equidistant can be equal with distance if go through the center point

Gnomonic

from center than exerted out

Stereographic

from one end than exerted out

Orthographic

light source is infinite distance away from the globe

Few projections with different properties

lambert conformal conic preserves shape, mollweird preserves area with comparing the relative sizes of Greenland and South America in one and then the other, orthographic projection preserves direction, azimuthal equidistant preserves both distance and direction, winkel tripel is a compromise projection

What’s the map purpose?

when you choose a projection the first thing to consider is the purpose of the map, general reference and atlas maps you usually want to balance shape and area distortion, map has a specific purpose and may need to preserve a certain spatial property most commonly shape/area to achieve that purpose

Mapping tropical regions

cylindrical

Mapping middle latitudes

conic

Mapping polar region

azimuthal

Coordinate system

UTM, custom, state plane coordinate system

State plane coordinate system

reference system composed of zones with custom projections, assigns precise x, y coordinates to locations and is used for large-scale mapping and spatial analysis, unlike UTM the state plane system applies only to the US, very confusing with not staying consistent by state

Universal transverse mercator

17W and 18E in PA, Maryland and West Virginia each have their own system

Tissot’s indicatrix

circles drawn on a map to show what’s distorted, developed ot measure and graphically illustrate the geometric distortion associated with various map projections, geometric deformation indicator that’s an infinitely small circle on a surface of the earth projected as a small ellipse on a map projection plane, ellipse describes characteristics locally at and near the small ellipse

Why is the northern hemisphere on the top of the earth?

used purposely to get people’s bias

Where does east begin/end and what about west?

geographically, culturally

Does a map influence cultural/societal/etc perceptions and saying do maps influence bias?

yes people love their country and want to represent it

Maps being created

sea by the european meaning, archetypes area symbols since it was a universally meaning, nature being a green color