Geodesy and Georeferencing Flashcards
Geodesy
Branch of mathematics dealing with the shape and area of the earth or large portions of it.
Datum
Refers to a reference or foundation surface against which accurate position measurements are made.
Defines how a coordinate system is seathed over the ellipsoid
Datum
Refers to a reference or foundation surface against which accurate position measurements are made.
Defines how a coordinate system is seathed over the ellipsoid
A “connected” unified network of measurements,
North American Datum 1927 (NAD27) vs new North American Datum, 1983 (NAD28)
The origin of the new NAD28 system is the centre of mass of the Earth.
Issue with Earth’s shape and mapping….
- The earth is irregularly shaped and difficult to model
- Accurate x,y and z position measurements are needed for mapping, nautical charting flood risk, transportation, etc……..
The Earth’s Shape
Oblate Ellipsoid (Spheroid)
Slightly flattened at the North and South poles
The Earth’s Shape
“Lumpy” Geoid
Imperfect Oblate Ellipsoid (Spheroid)
Slightly flattened at the North and South poles
Ellipsoid Examples
Australian Nation 1966
Clarke 1866
International 1924
Horizontal Datum
A collection of points on the Earth that have been identified according to their precise northerly or southerly location (latitude) and easterly or westerly location (longitude)
How are horizontal datums created?
Surveyors mark each of the positions identified on the Earth with a brass, bronze or aluminum disk monument.
Datum Types
Horizontal
Vertical
Vertical Datum
A collection of spatially distributed points on the Earth with known heights either above or below mean sea level.
How is mean sea level calculated?
Near coastal areas: determined with a tide gauge
Areas far away from the coast: mean sea level is determined by the shape of the geoid
Elevation of a geographic location
Height above a fixed reference point (most commonly a reference geoid, a mathematical model of the Earth’s sea level.)
Digital elevation model (DEM)
Generic term used to describe a continuous digital elevation surface above sea level.
Coordinate System types
Cartesian
Latitude and Longitude
Digital surface model (DSM)
Includes the elevation of all the features in the terrain above seal level such as bare ground, buildings, trees, powerlines
Digital terrain model (DTM)
Contains only elevations of the bare ground above sea level without any buildings, trees, etc
Geographic Coordinate Systems vs Projected Coordinate Systems
are Latitude ?????????????????????????????????????????????
Graticules
??Only apply to geographic coordinate systems.
Laitude and Longitude Coordinates
Measured from a theoretical point at the center of the Earth
Latitude
The angular distance measured North or South of the equator from a point at the centre of Earth.
A line connecting all points of the same latitudinal angle is a parallel. (Compare Longitude.)
Graticules
A graticule is usually superimposed on the globe and consists of the spherical coordinate system based on lines of latitude and longitude.
Only apply to geographic coordinate systems.
Distance in curvature of a degree of latitude is always equal to about ____km
111
Distance in curvature of a degree of longitude is ________
Not constant.
Longitude converges at the poles.
Longitude Curvature equation
1 degree of longitude = 111 degrees cos(latitude)
Longitude Curvature equation
1 degree of longitude = 111 degrees cos(latitude)
i.e. at 60 degrees north latitude, the distance of 1 degree of longitude equals 55.5km
Great Circle
Any circle drawn on the globe with its center coinciding with the center of the globe, bisecting the earth into two equal halves.
The equator is a great circle.
The arc of a great circle can be used to measure the shortest distance between any two points on the surface of the Earth.
Map Projection
A systematic transformation of the 3-dimensional Earth into a 2-dimensional flat map
Secant to
Touching the sphere at two points, creating two standard parallels.
All map projections involve…
The transfer of distinctive global patterns of parallels of latitude and meridians of longitude onto a developable surface (e.g. a plane, cylinder, or cone)
In all maps, there is some form of _____
distortion
Characteristics normally considered in choosing a map projection are as follows:
Area
Shape
Scale
Direction
Special Characteristics
Area
Many map projections are designed to be equal area.
Area (Notes on Maps)
Many map projections are designed to be equal area.
Equal-Area
The idea is that a coin of any size on one part of the map covers exactly the same area of the actual Earth as the same coin on any other part of the map
Shape (Notes on Maps)
Many of the most common and most important projects are conformal. An important result of conformality is that the local scale in every direction around any one point is constant.
Conformal
Relating to the mapping of a surface or region onto another surface so that all angles between intersecting curves remain unchanged.
Meridians intersect parallels at 90 degrees.
Scale
No map projection shows scale correctly throughout the map, but there are usually one or more lines on the map along which the scale remains true.
By choosing the locations of these lines properly, the scale errors elsewhere may be minimized.
Scale (Notes on Maps)
No map projection shows scale correctly throughout the map, but there are usually one or more lines on the map along which the scale remains true.
By choosing the locations of these lines properly, the scale errors elsewhere may be minimized.
Projection preserving Area
Lambert cylindrical equal area projection
Projection preserving Direction
Two point equidistant projection
Projection preserving Scale
Azimuthal equidistant projection
Special characteristics
Several map projections provide special charaction provides.
Special characteristics (Notes on Maps)
Several map projections provide special charaction provides.
Mercator projection
All rhumb lines or lines of constant direction, are shown as straight lines.
Mercator projection (special characteristics?)
All rhumb lines or lines of constant direction, are shown as straight lines.
Gnomic projection (special characteristics?)
All great circle paths-the shortest routes between points on a sphere are shown as straight lines.
Direction (Notes on Maps)
While conformal maps give the relative local directions correctly at any given point, there is one frequently used group of map projections, called azimuthal, on which the directions or azimuths of all points on the map are shown correctly with respect to the center.
Conformal Map projections
Ensure that at any point on the map, the scale is the same in every direction
- meridians and parallels intersect at right angles
- shapes of small areas + angles with very short sides are preserved.
Equidistant map projections
Show true distances only from the center of the projection or along a special set of lines.
No flat map can be both equal area and _____ at the same time
conformal
Types of projections (4)
Conformal
Equidistant
Equal-Area
Azimuthal
Equal-Area Map Projections (Equvalent)
Show every part on the map, as well as the whole
Has same area as the corresponding part on the Eart, at the same reduced scale.
No flat map can be both equidistant and ____ at the same time
equal area
Azimuthal map projections
Projections to a plane placed tangent to (just touching) the global at a point. Correctly represent angular relationships.
Conformal Map Projection Example
World Mercator
Equidistant Map Projection Examples
-Plate Carree
Rhumb Line
A line of constant angular direction.
Central meridian
an arbitrary vaolue that exists in the middle of a meridian.
