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Intro to GIS

Lesson 4: Coordinate Systems

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Objectives

Explain the basic properties and uses of coordinate systems
Describe the difference between geographic and projected coordinate systems
Recognize different projections and the distortions they cause
Choose appropriate projections for a map or geodatabase
Manage and troubleshoot coordinate systems of feature classes

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Coordinate Systems

Every G I S data set uses x, y, and sometimes z values to locate geographic data
The choice of values is the coordinate system
The data set is said to be georeferenced

Source: USGS

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Coordinate space

The coordinate space is the selected x,y values and units
An arbitrary or local coordinate space, like this building site, may be selected for convenience
G I S data usually use a standard coordinate space so that different data sets can be aligned

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Imagine that a surveyor, Carlos, is mapping an industrial site using typical surveying instruments that measure angles, directions, and distances. He may begin at a fence corner at the lower right of the complex and assign that point the coordinates (0, 0). This is the origin of the coordinate space (Fig. 4.1). Carlos then determines that the southwest corner of building A is 175 meters east and 200 meters north of the origin, and he assigns that corner the coordinates (175, 200). He uses meters to record the distances and to determine the coordinates, thereby establishing meters as the map units. The extent is the range of x-y values stored (in Fig. 4.1, about 0–800 for x and 0–700 for y.) The combination of origin and map units becomes the coordinate space of this map. In this case the coordinate space is arbitrary and chosen for convenience

Now imagine that the surveyor’s colleague Jasmin is surveying another site across town. She also chose the corner of her site as the origin, but she is measuring distances in feet. Carlos and Jasmin take their data back to the office and decide to create a map showing the location of both sites, each transferring the coordinates into a GIS. When they plot the sites, however, the two different sites show up in exactly the same spot, even though in real life they are several miles apart. This problem occurs because both surveyors used an arbitrary (0, 0) origin unrelated to the other site. Moreover Jasmin’s buildings appear about three times as large as Carlos’s buildings because she is measuring in feet instead of meters. To plot these together, the two surveyors would need to define a single common origin and convert both sites to the same map units. To avoid problems such as this, geographers and map creators usually employ a standard coordinate system (CS), a coordinate space whose characteristics are defined and established according to cartographic standards and tied to a specific location on the earth’s surface. The surveyors could have used a global positioning system (GPS) instrument to establish the x-y coordinates of their origins in a common coordinate system, such as Universal Transverse Mercator (UTM), and then entered their surveyed points relative to that base. Then their maps would have been located correctly with respect to each other.

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Standard coordinate systems

Source: Esri

Standard coordinate systems are found everywhere
A U S G S topo map has three standard coordinate systems: latitude-longitude, U T M, and State Plane
This Doty School location has different x-y values in each coordinate system

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Standard coordinate systems Both raster and vector data rely on x-y values to locate data to a particular spot on the earth’s surface. The x-y values of the coordinate pairs can vary, however. The choice of values and units to store a data set is called its coordinate system. Consider a standard topographic map, which actually has three different coordinate systems marked on it. The corners are marked with degrees of latitude and longitude, which is termed a geographic coordinate system (GCS). Another set of markings indicates a scale in meters representing the UTM, or Universal Transverse Mercator, coordinate system. A third set of markings shows a scale in feet, corresponding to a State Plane coordinate system. Any location on the map can be represented by three different x-y pairs corresponding to one of the three coordinate systems (Fig. 4.2).

When creating a vector or raster data set, one must choose a coordinate system and units for storing the x-y values. It is also important to label the data so that the user knows which coordinate system has been selected and what units were chosen for the x-y values. Thus, every GIS data set should have a label that records the type of coordinate system and units used to store the x-y data inside it. Coordinate systems fall into two categories, geographic coordinate

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Types of coordinate systems

Unprojected (geographic)

Based on spherical coordinates.
Measured in degrees of latitude and longitude.

Projected

Converts spherical coordinates to planar coordinates.
Uses a set of mathematical equations.
Projects 3D coordinates to a 2D map.

Source: Esri

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Coordinate systems for data

Every feature class stores x-y values based on a specific C S.
This STATES data set is projected and stores coordinates in meters
This ROADS data set is unprojected and stores coordinates in degrees.

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Geographic coordinate system

A geographic coordinate system, or G C S, stores locations in longitude-latitude values

Longitude measures east-west angles from the Prime Meridian.
Latitude measures north-south angles above the equator.

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G C S precision

Unprojected data in a G C S are stored in degrees

For accurate locations, keep at least 5 to 6 decimal places when recording degrees

A degree at the equator is about 110 km.
0.001 degrees ≈ 110 meters.
0.000001 degrees ≈ 0.1 meter.

Degrees, minutes and seconds are often used for better accuracy, but they must be converted to decimal degrees to store locations in a G I S

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The Earth is Infinitely Complex

Build Models to Simplify

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The shape of the earth

The irregular shape of the earth must be approximated for mapping
A spheroid (or ellipsoid) is a smooth shape with a slightly smaller north-south axis
A geoid is a surface modeled from gravity differences and is closest to the true shape, but is too complicated for mapping

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Because of the combined effects of gravitation and rotation, the Earth’s shape is roughly that of a sphere slightly flattened in the direction of its axis. For that reason, in cartography the Earth is approximated by an oblate spheroid instead of a sphere. The current World Geodetic System (WGS) model uses a spheroid whose radius is 6,378.137 km at the equator and 6,356.752 km at the poles. I'm

The word spheroid originally meant an approximately spherical body and that is how it is used in some older papers on geodesy. In order to avoid confusion, spheroid should be defined as an ellipsoid of revolution (if that is the intended meaning).

The surface of the geoid is higher than the reference ellipsoid wherever there is a positive gravity anomaly (mass excess) and lower than the reference ellipsoid wherever there is a negative gravity anomaly (mass deficit). The differences in gravity arise from the uneven distribution of mass in the Earth.

The geoid model is the basis for the new vertical or geopotential datum. This new datum will combine the ellipsoid height and the geoid height at the same point to calculate its elevation. To help improve accuracy of the new vertical datum, NGS is completing a major project called Gravity for the Redefinition of the American Vertical Datum, or GRAV-D.

NGS is flying over the entire US and collecting a unique, continuous gravity data set that will help us build a better geoid model, which will improve the accuracy of elevations measured using GPS technology. When the new datums are adopted, positioning information for existing structures and marks will change. The scale of the change will vary depending on your location, ranging from 0.5 to 1.5 meters in a horizontal direction, and 0 to 1.3 meters in elevation. These changes, based on our newest positioning technology and scientific knowledge, will provide more accurate positioning information. They will have an impacts in areas ranging from transportation, construction, flood plain mapping, agriculture and more.

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The Datum

An ellipsoid gives the base elevation for mapping, called a datum.
The geoid is a figure that adjusts the best ellipsoid and the variation of gravity locally.
It is the most accurate method, and is used more in geodesy than GIS and cartography.

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Datums

A datum is an approximation for the earth’s shape used for mapping. It shifts the ellipsoid relative to the geoid to achieve a best fit between the two.
A local datum optimizes the shift for the best fit at a particular location. It may also survey data to make further adjustments.
A geocentric or world-centered datum optimizes the fit for the entire earth.

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Datums used in North America

North American Datum 1927 (N A D 1927 or N A D27)

Based on Clarke 1866 spheroid, common until the 1980’s and still used for some data sets.

North American Datum 1983 (N A D 1983 or N A D83)

Current popular datum for most mapping. GRS80 spheroid.
First choice if you must assume an unknown datum for a set of undocumented data.

North American Datum 1983 H A R N (N A D 1983 H A R N)

Updates N A D83 with a High Accuracy Regional Network of fitted points.

World Geodetic Survey 1984 (W G S84)

Geocentric datum.
Seems to be default datum for many G P S units.

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Choosing a datum

Source: Esri

Sometimes you need to assign a datum to a data set.
Usually the common N A D 1983 choice is best.
The specialized versions are less commonly used and may cause data alignment issues.

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Datum transformations

Projections are exact mathematical formulas, but converting one datum to another often requires specialized fitting

Not exact; errors up to several meters may occur.
Errors accumulate with repeated transformations.
Several methods often available.

Some better than others for particular areas.
Not all methods work for all transformations.

Conversion should only be done when necessary, and care must be taken to choose the best method

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Transformation warning

Source: Esri

This warning alerts you when data sets in the same map have different datums
It’s OK to ignore it unless you are working with very large-scale or precise data
The warning is off by default
It is a good practice to turn it on in the Project options

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Note for G P S Users

G P S units may be set to collect points in more than one datum and projection

Often U T M or lon-lat units may be specified.

U T M N A D 1983.
U T M N A D 1927.
Lat-Lon N A D 1983… etc.

You MUST know and record the datum in order to use the data correctly later!!!!!!

Be careful—the default datum setting might not be the one you want.

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Mapping: �Projections and Coordinates

There are many reasons for wanting to project the Earth’s surface onto a flat plane. Primarily (and perhaps obviously):

The Earth has to be projected to see all of it at once.
It’s much easier to measure distance on a flat plane rather than a sphere.

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thetruesize.com

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Projections

A projection is a mathematical conversion of points on the earth’s surface to a flat plane (map)
The earth shape is defined by the datum or G C S
The choice of datum or G C S slightly affects the locations and coordinates on the map.

Source: Esri

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Projections and datums

Every projection has an underlying G C S

Projections based on different datums will be offset from one another

Both data sets shown are in the U T M coordinate system, but the photo is in N A D 1927 and the road features are in N A D 1983.

Source: Esri

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Types of projections

Source: Esri

Projections are classified by the shape of the projection surface

a) Cylindrical

b) Conic

c) Azimuthal ( or planar)

Each type has different properties

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Projection parameters

A projection is customized to work for the map region by setting parameters

Central meridian.
Standard parallels.
Latitude of origin.
False easting.
False northing.

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Standard parallels

Source: Esri

Standard parallels occur where the projection surface touches the ellipsoid

A tangent projection has one standard parallel.
A secant projection has two standard parallels.

Parallels are lines of no distortion

They are usually placed in the center of tangent projections, or at the upper and lower sixth of the map extent for secant projections, as in this map of Turkey.

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The coordinate origin

The central meridian is the line of longitude in the center of the map, where the x coordinates equal 0
The latitude of origin, or reference latitude, is the latitude at which the y coordinates equal 0
The origin is where both x and y equal 0
The extent indicates the range of x−y values present in the data

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Distortion

Source: Esri

All map projections distort one or more properties of

direction.
shape.
area.
distance.

The distortion varies by projection type

a) Cylindrical projections usually preserve direction and shape

b) Conic projections usually preserve area and/or distance

c) Azimuthal projections usually preserve area and/or distance

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Selecting a projection

Source: Esri

Maps shown in a geographic coordinate system (G C S) appear distorted, especially at high latitudes
Always choose the most appropriate projection for the region being mapped
Consider which properties need to be preserved: area, distance, shape, direction

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Projections for small scale maps

Source: Esri

Are used for continents and countries

Distortion is inevitable, so the map purpose drives the choice

Cylindrical projections when preserving direction and shape are important.
Conic or azimuthal equidistant projections when distances must be correct.
Conic or azimuthal equal area projections when areas must be correct.
Conformal or compromise projections for general purpose maps.

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Large scale maps: U T M

Universal Transverse Mercator has 60 N-S oriented zones around the world

Ideal for local, county, or small state maps in a single zone.
No distortion along the central meridian.
Preserves all four map properties well.

Source: Esri

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Large scale maps: State Plane 1

Source: Esri

The State Plane system has small zones designed for each state

N-S zones used Transverse Mercator.
E-W zones use Lambert Conformal Conic.
Alaska uses Oblique Mercator.

Minimal distortion for areas that fit in a single map zone

Other countries have similar systems

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Large scale maps: State Plane 2

Source: Esri

Custom projections are used when a standard projection is poorly suited for a region

Oregon spans two U T M zones and two State Plane zones.

Users can define a custom projection, but it can be difficult for a novice to choose good parameters

It is easier to adapt a standard projection by slightly modifying its properties

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Creating a custom projection

Source: Esri

Turkey is east-west oriented, so a conic projection like Lambert Conformal Conic is best
Use the same datum as the rest of the data in your collection
Set the central meridian to 35 degrees in the center of Turkey
Set the standard parallels to the upper and lower sixths of the extent of Turkey (41 and 37)
Choose a reference latitude
Use a false easting or northing if all positive x-y values are desired

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Adapt U T M for Oregon

Source: Esri

Start with U T M Zone 10
Change the coordinate system name to keep it distinct
Shift the central meridian (blue) to the center of Oregon (brown)
Leave all the other parameters the same

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Adapt State Plane for Kansas

Source: Esri

Start with the Kansas State Plane South projection
Shift the standard parallels (blue) to the upper and lower sixths of the state (brown)
Leave the other parameters the same

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Caution

Custom solutions will give better accuracy for maps, but there are some considerations.

You will need to take care to convert all data to your chosen coordinate system.
G P S units may not be able to collect data directly in your coordinate system.
When using non-standard projections you must be extra careful with your metadata so that users understand the differences.

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Impact on mapping

Source: Esri

They projection choice may affect the message of a map

A Mercator projection emphasizes the size and perceived importance of the northern hemisphere.

Projections should be chosen with the map objective in mind

Are equal distance or areas required?
Should north always be up for easy navigation?

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Impact on analysis

Source: Esri

The coordinate system used to store the data can impact the results of an analysis

Areas or distances may be incorrectly calculated.
In this distance analysis, the ‘closest’ stars are incorrectly assigned to Hotel C when the data are stored in a G C S
When the data are in U T M the starts are correctly assigned to Hotel B

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On the fly projection

Source: Esri

Data stored in any C S will be automatically converted to the map C S
The conversion does not affect the stored coordinates, only the display
It makes it easy to view data sets with different coordinate systems in the same map
It does not fix analysis issues, however

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Coordinate systems in a map

Source: Esri

Open the map properties to examine all of the coordinate systems being used in a map
It’s a good way to ensure that your coordinate systems match when compiling data for a geodatabase

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Coordinate system units

Source: Esri

Stored units are the x-y values stored in the file
Map units are determined by the coordinate system chosen for the map
Display units default to the map units but may be changed by the user

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Labeling coordinate systems

Proper alignment of data sets requires that each one have a label that records the complete coordinate system parameters
This label is called the Spatial Reference

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Spatial reference

Source: Esri

The projection name and coordinate system parameters are stored for projected data

All data sets have a geographic coordinate system (G C S) and datum

The spatial reference also includes

Storage units.
Domain, or maximum allowable x-y values.
Resolution, or the x-y precision.

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Projecting data

Source: Esri

The Project tool is used to permanently convert a data set from one coordinate system to another
It creates a new data set in the new coordinate system
A transformation must be specified if the new C S has different datum than the original C S

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Coordinate problems

Source: Esri

Coordinate problems occur when two data sets should align, but don’t

It often happens because the label on the data set is missing or incorrect

Large discrepancies (100’s to 1000’s of kilometers) typically occur when the projection is mislabeled.
Small discrepancies (10’s to 100’s of meters) typically occur when the datum is mislabeled.
Very small discrepancies (1’s to 10’s of meters) are usually accuracy issues related to data quality.

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Fixing missing labels

Source: Esri

Examine the layer properties

Determine the true coordinate system

Review the source of the data for information.
Examine the units in the map extent to determine whether the data are projected.
Guess and test if you have to.

Create the missing label with the Define Projection tool

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Fixing incorrect labels

Source: Esri

Examine the data set to determine the problem

The extent in the layer properties shows the x-y values.
If the units don’t match, the label is incorrect.

Determine the true coordinate system, if possible

Correct the label with the Define Projection tool

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Caution!�Do not confuse these two tools!

Define Projection tool

Creates or changes only the C S label.
Does not change the coordinates in the file.
Keeps the original data set.
Use only when C S is missing or incorrect.
Most C S problems are caused by misuse of this tool.

Project tool

Changes the coordinates in the file.
Changes the label.
Creates new data set.
Use when changing a C S permanently.
Use to assemble collections of data with the same stored C S.

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