Geodesy

Large Scale

"zoomed in"; approach 1:1; small area coverage - both distances and direction on map remain approximately true. Line features can be more precise and intricate. Less generalized.

Small Scale

"zoomed out" maps of large areas. projection distortions means that scale ratio will only apply to certain points, lines , and areas. More generalized.

Earth's Graticule

1) All parallels of latitude are parallel 2) All parallels are equally spaced along meridians 3) All meridians are equally spaced along parallels 4) Meridians of longitude are half great circles and converge at the poles 5) Meridians and parallels intersect at right angles 6) Quadrilaterals formed by same two parallels and having same longitudinal dimensions have same areas. 7) Area scale is uniform and distance scale is uniform.

Classification of Map Projections

1) Class (cylinder, cone, azimuth) 2) Secancy (tangent, secant) 3) Aspect (Normal, transverse, oblique) 4) Distortion Property (equivalent, equidistant, conformal)

Results of VLBI

1) Motion of tectonic plates 2) Deformation and local uplift 3) Variation in Earths orientation and time of day

3 Methods of Map Scale

1) RF 2) Scale / Word Statement 3) Graphic Scale

Choosing a Map Projection

1) Shape of Area 2) Location of area 3) Purpose of Map (is distortion okay?)

Steps in the Earth to Map Process

1) Study and estimate geoid 2) Define Earth positions 3) Transform spheroid into a plane (3D to 2D)

Three steps in the Earth to Map Process

1) Study and estimate the geoid 2) Define Earth positions 3) Transform spheroid onto a plane

3 parts of a coordinate system

1) Units of measurement 2) Projection (mathematical model) 3) Datum

3 parts of a coordinate system

1) units of measurement 2) mathematical model (projection) 3) datum

If a map has a scale of 1:20,000 an the distance between 2 spots is 4.5cm

1/20,000=4.5cm/Gd Gd=(4.5)*20,000 Gd=90,000 Gd=900m Therefore, 4.5cm on the map is equal to a ground distance of 900 meters.

Cylindrical

1:1 Scale factor at equator means no distortion. No distortion at any point of contact with standard lines. Mercator is cylindrical.

OBM Scales

1:10,000; 1:20,000; 1:2000

Small Scale(2)

1:250,000 1:12,000,000 1:100,000,000 (world map) 1:8,000,000 (map of ontario) 1:35,000,000 (national atlas of canada base map)

Large Scales

1:50,000 1:10,000 - OBM scale 1:200 - architecture map

Medium Scale

1:50,000 1:75,000 1:100,000 1:250,000 (N.Canada)

NTS Scales

1:50,000; 1:250,000

Ellipsoid

A sphere slightly flattened at the poles that is completely smooth. It's a theoretical mathematical surface for geodesists.

Mercator

Accurate compass bearing for sea travel. Straight lines drawn represent actual compass bearing. Route of constant direction between two locations of always a straight lines

Scale Problem of GIS

All features are stored with precise coordinates regardless of the precision of the original source data - output of mixing data of differing scale can lead to erroneous or inaccurate conclusions. Point A: 125.875,500,379 Point B: 126.000,500.00 Depending on the sale they may look like a single point or two seperate points (e.g., if decimals are ignored they will be identical)

Parallels of Latitude

Angle between point and equator a long meridian. 0 degrees at equator. Range from -90 degrees (South Pole) to +90 degrees (North Pole)

Projection

Any transformation between a curved reference surface of the Earth and a flat plane on a map

Equal Area

Areas on map = areas on globe. Preserve map areas by distorting shape, angle and scale.

Direction of projection planes orientation with respect to globe

Aspect

NAD27

Associate geographic coordinate system with Clarke 1866 ellipsoid. Involved adjustment of latitude and longitude coordinates of 25,000 geodetic control points across the USA from inital point of Meades Ranch Kansas. Geology maps often presented in NAD27 Until recently most survey computations and mapping in ontario (OBM) used NAD27

NAD83

Associates with GRS80. Is a single datum or control network covering North America consistently. Datum origin: Earths center of mass. Standard for Ontario government datasets (LIO,OGDE,OLID,OLIW) Almost all control stations stored in COSINE database have NAD83 coordinates.

Azimuthal

Based on a flat piece of paper touching the Earth at a point.

Babylonians

Believed Earth was a flat disc in an endless ocean.

NAD27 and NAD83

Both align coordinate system grids with ellipsoids, but different ones. NAD27 = Clarke 1866 ellipsoid NAD83 = GRS 80 ellipsoid Since ellipsoids different in shape and centre point there is a shift in Geographic coordinate grid when moving from NAD27 to NAD83. Approx. 200m difference between NAD27 and NAD83 in OBM map of Lindsay area. NTV2 - Canadian standard for conversion between NAD27 and NAD83 NADCON - US standard for NAD27 to NAD83 conversions

Biruni (Persian)

Calculated radius of Earth to be 6339.6km (modern is 6356.7km)

Arab & Persians

Caliph al-Mamun: his astronomers calculated Earths circumfrence to be 40,008km

Parallels of Latitude

Called phi. measures angle between point and equator along meridian. Is 0 degrees at equator and ranges from -90 (S.Pole) to +90 (N.Pole). Small circles are lines connecting all points of the same latitude (also called parallels)

Perspective Projections

Caused by changing position of the light source. a) Gnomonic b) Stereographic c) Orthographic

Polar Radius

Center of Earth to either pole. Semi-minor axis.

Van der Grinten

Compromise - not equal area or conformal. NatoGeo 1922-1988

Dymaxion

Compromise polyhedral - neither equal area or conformal. Heavily interrupted to preserve size and shape (intended for use on entire globe). Made by Buckminster Fuller.

Winkel-Tripel

Compromise pseudoazimuthal. Aims to reduce area, direction, distance distortions. NatGeo 1998 replacing Robinson

Robinson

Compromise psuedocylindrical - not equal area or conformal.

Distortion/Preservation Types

Conformal: Angles on map = angles between original lines on globe. Shapes of small areas are shown correctly. e.g., Mercator and Lambert Conformal Conic Equal Area: Areas on map = areas on globe. Preserves map area by distorting shape, angle and scale. e.g., Gall, Mollweide, Sinusodial Equidistant: Length of particular lines on map = length of original lines on globe. Preserves distance between certain points. Sinusodial, Werner, Azimuthal

COSINE

Control Survey Information Exchange Database - contains horizontal and vertical geodetic control survey data for the province of Ontario. Includes sketch image files giving details on finding monumented stations.

Plate Caree

Cylindrical compromise. Meridians are straight lines equally spaced. Parallels are horizontal straight lines equally spaced.

Gall-Peters

Cylindrical equal-area. Area of equal size on globe are equally sized on the map. Controversial in 70s and 80s.

Mercator Projection

Cylindrical projection - line of constant are straight segments. Linear scale is equal in all directions around any points. Size and shape severely distorted as you moved away from the equator.

Epochs

Datum revision

Lambert and Albers

Decent for Equal-area thematic maps

Aspect

Direction of the projection plane's orientation with respect to the globe. a) Normal b) Transverse c) Oblique

Arcs of Great Circles

Divide the Earth into 2 hemispheres

Universal Transverse Mercator(2)

Divided earth into 60 zones each of which is 6 degree of longitude (60 degrees * 6 = 360 degrees)

Graphic Scale / Scale Bar

Divided into segments showing the distance on the map labelled with the Earth distance it represents. Common practice for an RF to accompany the graphic scale bar. Subunits of basic interval are to the left of the zero. Remains accurate even through map enlargement or reduction.

Local ellipsoids

Dropping out of favor in use of global geocentric ellipsoids

Geoid

Earths mass is unevenly distributed - some areas have more gravitational pulls causing regions to buldge and dip above / below ellipsoid. Geoid is a 3D along which gravity is a specified constant OR Surface to which oceans would conform over Entire Earth if free to adjust to combined effect of Earths gravitation and centrifugal force of Earths rotation. Surface of Geoid extends across Earth at MSL across oceans and continues under continents at a level set by gravity. Surface is always at right angles to direction of local gravity and the surface is a reference against which heights are measured.

Hobo-Dyer

Equal-area cylindrical map comissioned by Bob Abramms and Howard Bronstein and drafted by Mike Dyer. Great pole compression but less latitude vertical stretching.

Only great circle

Equator

Earth radius

Equatorial radius / semi-major axis

UTM Zone

Extend from 80 degrees S to 84 degrees N and are numbered 1 through 60, starting at the IDL (longitude 180) and proceeding east. Zone 1 extends from 180 W to 174 W and is centered on 177 W (180+174)/2. Each zone is divided into horizontal bands spanning 8 degrees of latitude.

Aristotle

First person to try and calculate size of the Earth. Estimated 400,000 stades (73,225km around equator)

Prolate vs. Oblate.

French believed Earth is prolate (egg-shaped) based on Paris measurements English believed Earth is oblate (flattened at poles) based on Newons theory of gravity and centrifugal force. 2 expeditions (Peru and Sweden/Finland) determined Newton was right.

Developable Surface

Geometric shape such as a cone, cylinder or plane that can be flattened without distortion

Developable Surface

Geometric shape such as a cone, plane, cylinder that can be flattened without distortion.

GRS 80 Ellipsoid

Global reference ellipsoid and a gravity field model. Approved by Int.Ass.of.Geodesy in 1979. It's a gloval ellipsoid centered upon Earth's center of mass.

Light source at centre of globe

Gnomonic

Useful for defining navigation routes for sea and air travel because great circles are shown as straight lines

Gnomonic

Gnomonic

Good for air and sea navigation because great circles (shortest routes between points on a sphere) are shown as straight lines

Shortest distance on a sphere

Great Circle

Universal Transverse Mercator

Grid system of parallel lines running vertically and horizontally intersecting at 90 degrees; use plane coordinates. NTS 31D7 and OBM 10 17 6800 48100 both use the UTM grid system.

Ontario

Has 4 UTM zones.

Ellipsodial Height

Height above ellipsoid

Orthometric Height

Height above geoid

Tofers Radical Law

How many features can be retained when working from larger to smaller scale with a high degree of probability?

IGS

International Global Navigation Satellite Systems. An active control point for GPS and conducts international collaboration projects to observe pulsars and has a hydrogen master to participate in VLBI. Since 1960s.

Secant

Intersect horizontal surface along one closed line (plane) or two closed lines (cone or cylinder)

Equal-area thematic maps

Lambert, Albers equal-area conic

Effects of Scale Variation

Large Scale: Features look large - smaller ground area per cm/inch of map. More diversity of features included. Less need for generalization. Small Scale: Features look small, larger ground area per square cm/inch of map. Less diversity of features. More need to generalization.

Conventional Scales

Large: 1:75,000 or larger Medium: 1,75,000 to 1:100,000 Small: 1:1,000,000 or smaller

Equidistant

Length of particular lines on map = length of original lines on globe (accounting for map scale). Preserve distance between certain points.

Orthographic

Light source an infinite distance away from the point of tangency resulting in parallel rays

Stereographic

Light source at antipode of point of tangency

Gnmonic

Light source at centre of the globe

Small Circle

Line connecting all points of the same latitude, also called parallels

Loxodrome / Rhumb Line

Line of constant compass direction

Direction

Line of constant compass direction = loxodrome or rhumb line

Normal

Main orientation of the projection surface is parallel to the Earth's axis

Going from 3D to 2D

Map projection is a mathematical model that transforms locations of features on Earth's three-dimensional surface to locations on a two-dimensional surface.

Aryabhatiya

Mathematical astronomer esimated circumfrence of Earth within 1%.

Scale Change

May enlarge a map to show more detail or reduce physical printer size to fit in a report or file folder. 50% = 1/2 original size 200% = 2x original size Cs = Pr/Or * 100 Scale Change = New Product / Original Scale * 100

Posidonius

Measured angles from local plumb lines to stars near horizon. Measured at same time from 2 locations the difference could be used to calculate the circumfrence of Earth. Calculated 38,600km and widely accepted until 1500s (Mercator)

Eratosthenes

Measured circumfrence of Earth using suns rays at Syene located on Tropic of Cancer on summer solstice. At noon the sun shone directly to the bottom of the well with no shadow. At the same time in Alexandria the sun cast a shadow equivalent to 1/50th of a circle at the base of a column. Distance from Syene to Alexandria was 805km. 50*805 = 40,250km (only 4% off)

Northings

Measured relative to the equator. For locations in the northern hemisphere, Equator assigned a northing value of 0mN. For locations South of the equator, equator is assigned with a value of 10,000,000mN to avoid negatives. 7000m North of equator = 7000mN. 2,000,000 South of equator = 8,000,000mN.

Meridians of Longitude

Measures angle on equatorial plane between meridian of point and central meridian. From -180(west) to +180(east). Is 0 at Prime Meridian and 180 at IDL. Arcs of great circles divide the Earth into 2 hemispheres

Meridians of Longitude

Measures angle on equatorial plane between meridian of point and central meridian. Ranges from -180 (west) to +180 (east). 0 degrees is at the the Prime Meridian while 180 is at the International Dateline.

Displays accurate compass bearings for sea travel. Straight lines drawn represent actual compass bearings and route of constant direction between locations is always a straight lines.

Mercator

Transverse Mercator

Mercator where cylinder is rotated 90 degrees. CM can be chosen anywhere. Can be used to construct highly accurate maps of narrow width anywhere on the globe.

Clarke 1866 Ellipsoid

Minimizes deviations in North America with origin at Meades Ranch, Kansas. Geodial height at Meades ranch assumed to be zero.

Conical

Minimum distortion east-west Commonly used for Northern Latitudes such as Canada

Conical

Minimum distortion east-west direction. Common for northern latitudes such as Canada

Common North American Datums

NAD27 NAD83

Base Maps

NTS and OBM. Show positional relationship of a variety of topographic and geographic data and cultural features. They are deisgned with no specific user or use in mind.

Figure of Earth

Nearly spherical - equatorial radius of 6,378km. Because Earth has a very irregular surface we use a theoretical mathematical model called the ellipsoid.

Graticule

Network of lines of latitude and longitude or northings and eastings upon which a map is drawn

Oblique

Non-parallel, non-perpindicular orientations.

Main orientation of projection is parallel to Earths axis

Normal

Non-parallel; non-perpindicular

Oblique

RF

One unit of measurement on the map equal to number of same units on the Earth. Is unitless when expressed as an RF, no particular units of measurement are used. Most useful when doing scale calculations. 1:500 could mean 1cm equals 500 meters oR 1cm equals 500 yards.

Light source an infinite distance from the point of tangency resulting in parallel rays.

Orthographic

Transverse

Perpindicular to Earth's axis for N-S alignment

Waterman Butterfly

Polyhedral compromise. Unfolded globe treated as an octahedron.

Piece Quincuncial

Present sphere as a square.

Conformal Projection

Preserves angles.

Projection Light Source

Projecting ellipsoid onto a flat surface. Comes from notion of placing a light source inside a transparent globe, and projecting shadows of meridians onto a sheet of paper placed tangent to the globe.

Transformation between a curved reference surface of the Earth and a flat plane of the map.

Projection

Azimuthal

Projection based on a flat piece of paper touching the Earth at a point.

Projection Light Source

Projection ellipsoid onto a flat surface - comes from notion of placing a light source inside a transparent globe, and projecting shadow or meridians onto a sheet of paper placed tangent to the globe.

Goode Homolosine

Pseudocylindrical equal-area. Hybrid of mollweide and sinusodial projections. Good for thematic world maps.

Relative Product Area

Ra=(CS)^2. Perception of area is affected in 2 dimensions when scale changes. A 1:10,000,000 Canada map reduced to 1:15,000,000 is a change of scale of 66.66% 10m/15m*100 = 66.66 This means the perception of geographic areas will be 44.44% of the original image.

Pythagoreas and Aristotle

Reasoned Earth must be a sphere (observed ships disappering over the horizon, that the moon appeared spherical, and that constellations shift when viewed from opposite ends of the Mediterranean Sea). By 500 B.C most scholars knew Earth was a sphere.

Eastings

Referenced to the centre line of the zone (CM). CM of each zone is assigned an easting of 500,000mE. Vertical grid lines within each zone measure the meters east or eastings as more or less east than the central meridian of 500,000mE.

Cylindrical

Scale factor of 1:1 at equator means no distortion. No distortion at any point of contact with standard lines. Mercator is cylindrical.

Geodesy

Science of measuring and monitoring the size and shape of Earth (including gravity). Involves creation of a spatial references system and understanding of physical processes

Intersect horizontal surface along one closed line(plane) or two closed lines (cone or cylinder)

Secant

Horizontal Datums

Set of parameters defining specifications of ellipsodial reference surface (e.g., shape of the Earth). Define geometric relationship between a coordinate system grid and the Earth's surface. Local datums can be more accurate than WGS84.

Conformal

Shapes of small areas shown correctly on the map. Angles on map = angles between original lines on the globe.

Distortion Properties

Shapes, angles, areas, directions, distances become distorted when transforming a curved surface to a plane.

SAADD

Shapes, area, directions, angles, distances become distorted when transformed from a curved surface to a plane.

Great circle

Shortest distance on a sphere

Generalization

Smaller scale = more generalization needed, because amount of space available to show any given feature decreases as scale decrease (e.g., when a map "zooms out" there is more real-life phenomena but less ability to show it all)

NTS and OBM Grid Lines

Spaced 1000 meters (1km apart). Each grid is 1 square kilometer.

Central Meridian

Square grid superimposed on each and every zone and aligned so that vertical grid lines are parallel to the centre of the zone (the CM)

WGS84

Standard for cartography and geodesy consisting of: a) Standard coordinate frame b) Standard spherodial reference surface (ellipsoid) It originally used the GRS80 reference ellipsoid but now adjusted 0.105mm in polar axis. Uses Earth Gravitational Model EGM96 equipotential surface (geoid) Revised in 2004: Uses EPSG:4326. Longitudes were shifted 100m east from Greenwich, IERS reference meridian used as zero. WGS84 equatorial axis is 22lm longer than polar axis. Is used by NAVSTAR GPS system

Light source at antipode of point of tangency

Stereographic

Vertical Datum

Surface of 0 elevation to which heights of various points are referred. The datum is the entire system of zero elevation surface and methods of determing the heights relative to that surface. CGVD2013 (Canadian Geodetic Vertical Datum of 2013) is now availiable and is the new reference standard for Canadian heights. CGVD28 is no longer current stadaard. NAVD88 is US Standard (North American Vertical Datum of 1988)

Gravitational Influence of Moon and Sun

Surface of Earth rises and falls 30cm every day

Geodetic Suveying

Survey in which curvature of the Earth is taken into account and a higher degree of accuracy in linear and angular observations is achieved. Measurements are made on topographic surface of Earth, and computations are performed on the ellipsoid, and in relation to the geoid. Coordinates are calculated on the reference ellipsoid relevant to the local area.

Surface touches horizontal reference surface at only one point (plane) or along a closed line (cylinder,cone)

Tangent

Only great circle

The equator

Conformality and equidistance important

Topo and large-scale maps

Tangent

Touch the horizontal reference surface at only one point (plane) along a closed line (cone or cylinder).

Perpindicular to Earths axis (for n-s alignment)

Transverse)

Metric System

UTM grid coordinates are expressed as a distance in meters to the east, referred to as "easting" and a distance in meters to the north, "northing"

Wide mid-latitude countries (e.g., China)

Use Conic

Tall narrow countries (Argentina, Chile)

Use transverse cylinder

Triangulation

Used in 18th and 19th century. Determing fixed point by measuring angles to it from two other fixed points of a known distance apart. End of 19th century - major triangulation networks covered US, India, GB, Europe.

Lambert Conic Conformal

Used on aeronautical charts, and MNR uses this when showing entire province on a map. Pilots like it because a straight line drawn approximate a great-circle route between endpoints.

Lambert Conformal Conic

Used on aeronautical charts; MNR uses when showing map of entire province. Pilots like it because a straight line drawn approximates a great-circle route between endpoints.

MRS

Used to measure distances directly from maps and air photos. Six different scales: 1:500 1:1000 1:1250 1:1500 1:2000 1:2500

Scale (Word) Statement

Verbal scale statement stating in words the relationship between the map distance and earth distance using two units of measurement. 1cm = 4km OR 1 inch = 2000 feet There are two DIFFERENT units of measurement used. One would convert the word statement into an RF to do calculations. It's an older less used cumbersome method.

VLBI

Very Long Baseline Interferometry - collecting data from a single radio source via worldwide array of radio telescopes. Relative time-of-arrival signals from that source to reach each telescope is analyzed to provide ultra-precise measurements of Earth and its orientation in space.

Coordinate System

Way of representing the location of a spatial feature

Military Grid

Zone 17T 6[49,3]28mE, 4,9[33,0]88mN = 17T PK 493330

How projections are classified

a) Class b) Secancy c) Aspect d) Distortion property

Distortion/Preservation Types

a) Conformal b) Equal Area c) Equidistant

Choosing a Projection

a) Consider shape, location, and purpose. b) Thematic maps should use euqal-area so pheneomena per area are shown in correct projection (e.g., statistics like pop'n density) c) Maps of large areas usually use a conformal projection

Classes

a) Cylinder b) Conical c) Azimuthal

Types of Distortion

a) Distance - lat/long b) Direciton - angle c) Scale/shape - area

Distortion Property

a) Equivalent b) Equidistant c) Conformal

Disadvantages of UTM

a) Full global georeference requires the zone number, easting and northing. b) rectangular grid superimposed on zones defined by meridians cause axes on adjacent zones to be skewed with respect to each other. c) Problems arise in working across zone boundaries - no simple mathematical relationship exists between coordinates of one zone and the adjacent zone.

Three Pillars of Modern Geodesy

a) Geokinematics b) Earth rotation c) Gravity Field

NAD83 Epochs

a) NAD83 (1986) b) NAD83 (1992) c) NAD83 (2002) c) NAD83(CSRS) (1998 Canadian update) Original NAD83 - WGS84 - now a 1.3m shift between NAD83 and WGS84. NAD83(HARN) and NAD83(CORS96) are American regional updates of 6-8cm using GPS.

Aspect

a) Normal b) Transverse c) Oblique

Earth's Graticule

a) Parallels of latitude are parallel b) Parallels are equally spaced along meridians c) Meridians are equally spaced along parallels d) Meridians of longitude are half great circles that converge at the poles e) Meridians and parallels intersect at right angles f) Quadrilaterals formed by same two parallels have same longitudinal dimensions g) Area and distance scale is uniform

Scale Calculation Variables

a) Scale b) Map Distance c) Ground Distance

Generalization Methods

a) Selection - retention of the more important features of an area and elimination of less important ones b) Simplification of shapes of features retained c) Combination of two or more similar features into a larger feature d) Locational Shift and Size Exaggeration - 'cartographic license', exaggerate size of important feature or shift to get more space for exaggerated features.

Criteria for choosing a map projection

a) Shape of the area b) Location of the area c) Purpose of the map

Elements of the Earth System

a) Space b) Solar Wind c) Atmosphere c) Hydrosphere d) Ocean e) Cryosphere f) Land g) Earth Interior

Advantages of UTM

a) Square grid provides a constant distance relationship anywhere on the map. b) No negative numbers of east-west designators. Grid values increase from left-right and top to bottom. c) Coordinates are decimal based. No mins/secs to convert d) All UTM coordinates measured in meters.

Points of Secancy

a) Tangent b) Secant

Map Scale

a) direct ratio between real world distances and corresponding distances on a map. b) relationship of measured distance between two points on a map and the measured distance between the same two points on the ground c) expression of the relationship between the size of an image on a map and corresponding size of the image on the ground (real world)

Country near equator (kenya)

cylindrical (least distortion along equator)

Geodial Height / Geodial Seperation

difference between ellipsodial and orthometric height

small circle

imaginary circle made on Earth's surface by a plane that does not pass through the centre of Earth

Great Circle

imaginary circle made on earths surface by a plane passing through centre of Earth

GCS

most commonly used coordinate system. Is 3D, spherical, has latitude and longitude.