Georeferencing
GIS 5210
Jake K. Carr
Week 3
Georeferencing Jake K. Carr Georeferencing
Recall from last time that the most primitive structure of geographic data is an atom which links a place, often a time, and some descriptive property (attribute) to that place
Time is an optional element in geographic information, but location is essential!!
There are many terms used to describe the act of assigning locations to geographic data, including: georeference, geo-locate, geocode, and/or geotag
Georeferences must be unique so each location has its own georeference and its meaning must be shared among users
Georeferencing Jake K. Carr Systems of Georeferencing
Georeferencing Jake K. Carr Placenames
An early, simple form of georeferencing
Some are more universally (globally) accepted, and others are accepted by locals New York = New York City? New York State? Horseshoe = Ohio Stadium
Different scales there are names for continents, small villages, neighborhoods
Almost 20 states have a city named Columbus
Georeferencing Jake K. Carr Places called “Santa Barbara”
Is “Santa Barbara” a valid georeference?
Georeferencing Jake K. Carr Postal Addresses and Postal Codes
Every dwelling and office is a potential destination for mail
Dwellings and offices are arrayed along streets, and numbered accordingly
Streets have names that are unique within local areas
Local areas have names that are unique within larger regions (hopefully)
If these assumptions are true, then a postal address is a useful georeference
Georeferencing Jake K. Carr Postal Codes
Georeferencing Jake K. Carr Postal Addresses
Points identifying the residential unit (Inward) postcode have been used to plot the locations of a doctor’s patients
The Outward Code areas have been shaded according to the density of patients per square kilometer
Georeferencing Jake K. Carr Linear Referencing Systems
Linear referencing-an incident’s position is determined by measuring its distance along a road from a well-defined point (an intersection with another street)
Georeferencing Jake K. Carr Cadasters and the U.S. Public Land Survey System
A map of land ownership in an area, maintained for the purposes of taxing land, creating a public record of ownership, or military draft
Widely used in property record (deed) to record land parcels
The Public Land Survey System (PLSS) is used to explicitly locate a cadastral unit for many states where cadasters are organized as townships and sections townships are laid out in 6 mile squares on either side of an accurately surveyed principal meridian
Georeferencing Jake K. Carr Cadasters and the U.S. Public Land Survey System
Georeferencing Jake K. Carr Ontario, CA
Google Earth view looking east along Baseline Road in Ontario, California
The road that follows the original survey baseline for Southern California laid out by Colonel Henry Washington in 1852
The monument marking the intersection between the baseline and the principal meridian is atop Mount San Bernardino, which appears on the horizon
Georeferencing Jake K. Carr Address Matching
The purpose of address matching is to: find the location (x, y) of an event which has been recorded at a street address
This process is also called geocoding1!!
Common Types of Errors: incorrect street numbers Ninth Street or 9th St.? street name errors “Route 123” or “US HWY 123”?
1A more in depth discussion next time? Georeferencing Jake K. Carr Address Table
Georeferencing Jake K. Carr Geocoded Addresses
Georeferencing Jake K. Carr Georeferencing and Coordinate Systems
A coordinate system is a reference framework that uses points, lines, and planes to determine positions in 2 or 3-dimensional space
Requires a model of the earth!!
The earth is ‘round’, but we know that it is not a perfect sphere the distance along the equator is longer than from pole to pole
Also, there are significant variations in elevation highest at Mount Everest (29,029 feet) lowest at the Marianas Trench (-35,827 feet)
Georeferencing Jake K. Carr Sheriods/Ellipsoids
Models of the earth are called spheriods/ellipsoids a mathematical model approximating the shape of the earth. averages the irregularities
Based on estimates of the equator, distance from pole to pole, as well as curvature
Spheriods/Ellipsoids are defined by the length of the major and minor axes
Halves of the major/minor axes are referred to as semi-major/semi-minor axes
Georeferencing Jake K. Carr Sheriods/Ellipsoids
The definition of the ellipsoid is formed by rotating the ellipse about its minor axis
Georeferencing Jake K. Carr Datums/Ellipsoids
A datum is constructed on a particular spheriod/ellipsoid to model the surface of the earth for a specific area the selected datum & spheriod/ellipsoid “fit” the particular area really well we call the estimate of the model surface the geoid
Along with the datum, there usually is a set of ground control points and associated triangulation lines
Georeferencing Jake K. Carr Ground Control Points
Actually on the ground!!
Precisely surveyed points are called bench marks
In the U.S., these points are maintained by the National Geodetic Survey (NGS)
Some bench marks are controlled through astronomic observations
And many more points are obtained via surface surveys
Georeferencing Jake K. Carr Datums (& Sheriods/Ellipsoids)
North American Datum of 1927 (NAD27) Spheriod: Clarke 1866 Semi-major axis: 6378206.4 meters Semi-minor axis: 6356583.7999 meters
North American Datum of 1983 (NAD83) Spheriod: Geodetic Reference System 1980 (GRS80) Semi-major axis: 6378137.0 meters Semi-minor axis: 6356752.314140 meters
World Geodetic System of 1984 (WGS84) Spheriod: World Geodetic System 1984 (WGS84) Semi-major axis: 6378137.0 meters Semi-minor axis: 6356752.314245 meters
Georeferencing Jake K. Carr NAD27 vs NAD83 (and WGS84)
The North American Datum of 1927 is based on Clark 1866 ellipsoid a point near Meades Ranch, Kansas, was used as the geodetic base point for all land survey has about 26,000 control points
The North American Datum of 1983 (NAD83) is based on the GRS80 ellipsoid earth-centered reference! uses the center of the earth to locate points
Shift from NAD27 to NAD83 can be up to 100 m NAD83 has been adjusted using new data
Georeferencing Jake K. Carr Geographic Coordinate Systems
A Geographic Coordinate System (GCS) uses a datum & spheroid to describe locations on the curved surface of the earth
GCS uses angular units of measure ⇒ most often in degrees
The “x-coordinate,” measured as the angle from a prime meridian, is called Longitude (λ)
Georeferencing Jake K. Carr Geographic Coordinate Systems
The “y-coordinate,” the angle between the equator and a line drawn perpendicular to the ellipsoid, is called Latitude (φ)
Georeferencing Jake K. Carr Lats and Lons
Latitudes (φ) are called parallels, Longitudes (λ) are called meridians
The earth is divided into 360◦ (D) around the equator one degree is 60 minutes (M or ’) one minute is 60 seconds (S or ”)
Lats and Lons are angles ⇒ values are often quoted in: degrees-minutes-seconds (DMS) decimal degress (DD)
M S Conversion: DD = D + 60 + 3600
Georeferencing Jake K. Carr Derby Hall!
Derby Hall is located at 154 N. Oval Mall Columbus, OH 43210:
Degree Minutes Seconds Direction Latitude 40 00 02.49 N Longitude 83 00 44.99 W
In decimal degrees (DD): 00 2.49 ◦ Latitude = 40 + 60 + 3600 = 40.000069 N 00 44.99 ◦ Latitude = 83 + 60 + 3600 = 83.012497 W
Georeferencing Jake K. Carr Distance Calculations Straight-line distance is given by: q 2 2 dij = (x1 − x2) + (y1 − y2)
Only works if locations are found on a flat plane
The shortest distance between two points on a sphere is an arc of a great circle, defined by slicing the sphere through the two points and the center of mass
Georeferencing Jake K. Carr Distances from Degrees (Lats/Lons)
Given an estimate for the radius of the earth (R), the distance on a sphere between two locations (φ1,λ1) and (φ2,λ2) is:
R × arccos[sin(φ1) sin(φ2) + cos(φ1) cos(φ1) cos(λ1 − λ1)]
Nicest aspect of this: distances measured have the units of the radius!
Suppose WGS geoid, then the R estimates are: 6378137 meters or 6378 kilometers 20925646.33 feet or 3963.19 miles
Georeferencing Jake K. Carr Projections and coordinates
Map projections are mathematical formulas applied to a GCS, defined by a datum & spheroid, to convert lat/lon (φ/λ) to a plane surface representing a grid
Georeferencing Jake K. Carr Why?
Projections are needed because many technologies for working with geographic data are flat, including paper and printing processes
The problem of accurately measuring directions, distances, lengths, or areas on the earth’s surface led to the need to define locations in linear units while we saw that we can measure distance with degrees, no nice formulas exist for similar calculations of area or direction
Degrees just can’t do it all!
Georeferencing Jake K. Carr Projections and coordinates
The Cartesian coordinate system assigns two coordinates to every point on a flat surface, by measuring distances from an origin parallel to two axes drawn at right angles we often talk of the two axes as x and y, and of the associated coordinates as the x and y coordinate, respectively
Because it is common to align the y axis with North in geographic applications, the coordinates of a projection on a flat sheet are often termed easting and northing
Two geographic datasets can differ in both the projection and the datum, so it is important to know both for every dataset
Georeferencing Jake K. Carr Projection Classes
Three basic classes based on developable surfaces – cylindrical, planar, and conic
Georeferencing Jake K. Carr Cylindrical Projections
Cylindricals are true “along the middle”, often at the equator and distortion increases outwards, toward the poles if wrapped around the Equator
Georeferencing Jake K. Carr Conical Projections
Conics are true along some parallel somewhere between the equator and a pole and distortion increases away from this standard line
Georeferencing Jake K. Carr Planar/Azimuthal Projections
Azimuthals are true at some point and distortion increases away from this mid-point
Georeferencing Jake K. Carr Distortions
In each case a sheet of paper is wrapped around the Earth, and positions of objects on the Earth’s surface are projected onto the paper ⇒ distortions abound!
The different types of projection are intended to preserve some specific property of geographic data: shape ⇒ called conformal projections area ⇒ called equal-area projections distance ⇒ called equidistant projections direction ⇒ called true-direction projections
While able to preserve one of the above properties, all projections distort the other properties!
Georeferencing Jake K. Carr Mercator Projection
Mercator projection is a tangent cylindrical class of conformal type
Georeferencing Jake K. Carr Lambert Projection
Lambert projection is a secant conic class of conformal type
Here, the cone onto which the surface is projected intersects the Earth along two lines of latitude: 20 N & 60 N.
Georeferencing Jake K. Carr Comparison of Projections
Georeferencing Jake K. Carr Robinson Projection
Specifically created in an attempt to find a good compromise to the problem of readily showing the whole globe as a flat image
Georeferencing Jake K. Carr Transverse Mercator Projection
A cylindrical projection where the developable surface is a horizontal cylinder
Georeferencing Jake K. Carr Universal Transverse Mercator Projection
The system of zones of the Universal Transverse Mercator (UTM) system
The zones are identified at the top. Each zone is six degrees of longitude in width
Georeferencing Jake K. Carr UTM Zones
Major features of UTM Zone 14 (from 102 W to 96 W)
The central meridian is at 99 W
Scale factors vary from 0.9996 at the central meridian to 1.0004 at the zone boundaries
Georeferencing Jake K. Carr State Plane Systems
The entire U.S. is divided into small zones (states) and each zone has its own projection small areas may have small errors
Two projections are used Lambert Conic Conformal Transverse Mercator exception: panhandle of Alaska
The projection for each state is defined by its Standard lines, central meridian, origin of the coordinates, and other parameters
Georeferencing Jake K. Carr State Plane Systems
Georeferencing Jake K. Carr State Plane System of TX
Note that the five zone boundaries are defined by counties, rather than parallels, for administrative simplicity
Georeferencing Jake K. Carr Georegistration
Georeferencing Jake K. Carr Measuring Latitude, Longitude, and Elevation: GPS
Positioning in three dimensions (latitude, longitude, and elevation) requires that at least four satellites are above the horizon
If elevation is not required then only three are needed
Simple GPS can get horizontal accuracies within 10m, differential GPS can improve accuracy to 1m or better
A variety of vertical datums are used, even within single countries
Georeferencing Jake K. Carr For Next Time!
Read Chapter 5 from Longley et al.2
Finish Lab 2
Bring Lab book with you on Tuesday!
Exam next week!
2Lecture slides adapted from Longley et al. Georeferencing Jake K. Carr