Geographic data is commonly described by pairs of X-Y coordinates on the surface of the Earth, such as longitude and latitude. This is the type of spatial information that underlies the shapefiles used in the previous two sections, but it may also show up in simple tables. GPS receivers also describe your location using X-Y coordinates.
Since this tutorial will be using specific maps and data, the first step is to make your own copy of the tutorial data.
Set Up: Getting the Tutorial Data
The folder MappingCoordinates contains the following data layers:
Set Up: Initializing ArcMap and Adding Data
Move the cursor across the map, and notice the two changing numbers in the lower right corner of the window (here 95°20'"W 57°49'52.523"S). This pair of X-Y coordinates are the longitude and latitude of the tip of the cursor, to be described next.
Geographic coordinate systems, describing positions on the surface of the Earth in latitude and longitude, are the most common representation of spatial data.
Since the time of the Ancient Greeks it has been known that the Earth was a spherical object rather than a flat surface.
Though it was suggested millennia ago that the Earth rotates once a day, this fact was not widely accepted until the 17th century, and was not firmly established until the 19th century.
The Earth’s rotation defines certain reference points and circles that we can use to determine our position on its surface.
The Earth’s rotation axis is a line that passes through the the North Pole, the South Pole, and the center of the Earth.
The Equator is a circle on the Earth’s surface that’s perpendicular to its axis and equidistant from its poles:
The reference points described above establish the four Cardinal Directions.
The direction toward the North Pole is North, and South is in the opposite direction, toward the South Pole.
The direction parallel to the Equator and toward the Earth’s rotation is East, while the direction opposite to the Earth’s rotation is West.
By definition, North and South will always be at right angles to East and West, at any point on the surface of the Earth.
In addition, the direction toward or away from the Earth’s Center are, of course, down and up, respectively.
It is useful and important to be able to precisely specify positions on the Earth’s surface: to compare positions, calculate distances, and in general navigate from one point to another.
So, a pair of numbers or geographic coordinates are used that are similar to the x and y Cartesian coordinates in a plane, but designed for a sphere.
These two numbers, latitude and longitude, are angles measuring south-to-north and west-to-east, respectively.
Any circle parallel to the Equator is called a parallel of latitude.
The angle (with vertex at the center of the Earth) between a given parallel of latitude and the Equator describes that parallel and any point on it, and is called the latitude.
So, the North Pole is at 90° north latitude, the Equator itself is 0° latitude, and the South Pole is 90° south latitude.
Amherst is located at 42.37° north latitude.
Southern latitudes are often expressed as negative values, particularly in computer applications such as GIS.
One degree of latitude corresponds to a distance of 111 Km (69 miles) across the Earth’s surface.
Any semicircle passing through the poles is called a meridian of longitude.
One of these is designated as the Prime Meridian, usually the one passing through the Royal Observatory in Greenwich, England (just outside London).
The angle (with vertex at the center of the Earth) along the Equator between a given meridian and the Prime Meridian describes that meridian and any point on it.
So Amherst is located at 72.52° west longitude.
Western longitudes are often expressed as negative values, particularly in computer applications such as GIS.
Note that the antimeridian can be described by either 180° west longitude or 180° east longitude.
One degree of longitude at the Equator also corresponds to 111 Km; but this gets progressively smaller as one moves towards the poles, eventually shrinking to zero (varying as the cosine of latitude).
Because a degree of latitude or longitude is relatively large, a common practice is to break them down into smaller units.
A minute of arc is defined to be 1/60 of a degree, often abbreviated as a single prime (').
A minute of arc corresponds to 1.86 Km = 1.15 miles (called a "nautical mile").
A second of arc is defined to be 1/60 of a minute of arc, often abbreviated as a double prime ('').
A second of arc corresponds to 31.0 m = 101 feet.
The location of Amherst Center is, in fact, very accurately known.
In the seventeenth century, Isaac Newton suggested that, because the Earth is rotating and not perfectly rigid, it will bulge slightly at its equator.
So, the Earth is not precisely spherical, but instead is an oblate ellipsoid, like a squashed beach ball.
Precise measurements put the equatorial and polar diameters of the Earth at 12,756 Km and 12,713 Km, respectively, a difference of only 43 Km (0.34%).
This small oblateness can still effect the positioning of maps, so it must be taken into account.
In addition, the Earth has substantial variations in the elevation of its surface from point to point:
Because gravity depends on the mass of the Earth, there are small variations in gravitational force across its surface, which are reflected by local sea level (because fluids will move in response). The geoid is an equal-gravity surface that includes local sea level but also continues into continental areas, as shown in the image above. The GOCE satellite has provided detailed measurements of the geoid, whose variations are displayed in exaggerated form in this mp4 movie:
A datum is a choice of ellipsoid to model the Earth’s surface, viz. the location of its center, its size, and its orientation.
With the expansion of international travel and commerce, worldwide standards have been adopted, such as the World Geodetic System of 1984 (WGS84), which is based on the geoid.
Note that this means that a measurement of latitude and longitude will depend on which datum you use!
The map at the right comparing NAD27 and NAD83 demonstrates how much measured positions can shift when switching between datums.
You should therefore always ascertain the datum when you’ve been given geographic data (e.g. NAD83 for Amherst, above).
The datum is the foundation of a geographic data set’s spatial reference; let’s look at an example:
To view the Earth on a flat piece of paper or a computer screen, its curved surface must be projected.
Once a datum has been chosen as a model of the Earth, it is straightforward to reproduce its features on a globe.
For many purposes it’s much more useful to represent the Earth on a flat surface, such as paper or a computer screen.
Such a flattened representation of the Earth is called a map.
The flattening process is known as a projection.
Map projections are similar to other projections you may be familiar with, such as projecting a slide or transparency onto a screen.
There are three common, general ways to "flatten" the Earth: Planar, Conic, and Cylindrical:
There are also many other, more complicated, projections that are used for certain purposes.
Projection surfaces can be tangent to the Earth’s surface (touching it along one standard point or standard curve), as in all of the images above, or secant to it (intersecting at one or two standard curves), as in the following images:
For each of these surfaces, there are a number of different ways to project the Earth’s features onto them.
Any projection will necessarily distort some aspect of geography:
Warning: No projection can be both conformal and equal-area.
The Mercator projection (right) is a famous example of a conformal map, in this case a coaxial cylindrical projection that makes navigation easier by preserving directions, but severely distorts area near the poles. Because it also maintains shapes over small regions, it is used by Google Maps.
The Gall-Peters projection (below left) is an example of an equal-area map, also coaxial cylindrical, sometimes used to avoid the exaggerated area of the global north seen in the Mercator projection, but at the expense of shape accuracy away from 45° latitude.
The Plate Carrée projection (below right) is a specific case of the equirectangular projection, again a coaxial cylindrical projection that preserves (longitude, latitude) by simply mapping it to (x, y); however, it is neither conformal nor equal-area (though it is equidistant north-south and approximately along the equator).
Question: When bringing in data defined only in terms of geographic coordinates, ArcMap uses a default projection. Can you tell what it is?
Any distortion introduced by a projection will be smallest near the standard points or curves where the projection surface touches the Earth’s surface.
Non-global maps will therefore generally use a projection that minimizes distortion in the region of interest.
Regions that are elongated east-west are commonly represented by coaxial conic projections (touching along parallels).
Regions that are elongated north-south are commonly represented by transverse cylindrical projections (touching along meridians).
Regions that are not elongated one way or the other may be represented by concentric planar projections.
If the map will cover a relatively wide area, secant projections are generally used, as in the image above, since they even out the distortion around the multiple standard curves.
For example, here are two different coaxial conic projections:
Question: In this gallery of projections centered on Latin America, which do you think is the best choice?
It can be very important to make a good choice of projection; consider this discussion in a fictional White House.
GIS makes it easy to display your data with different projections.
The spatial reference of the map displayed by ArcMap is determined by the data frame, which is indicated by the stack-of-layers icon and the default name Layers(click-pause-click on the name to change it).
All layers in a data frame will be projected in the same way; essentially, it’s "the map".
A data frame’s spatial reference is initially determined by
the first layer added to it; in the Setup this was the layer countries.shp.
Experiment: A number of additional projections are available to display the entire world in what are sometimes more usable formats, e.g. including Mollweide, Eckert IV, and Polar. Try them!
Extra Absurdum: What does your favorite map projection say about you?
Once the Earth is flattened, its often easiest to use planar coordinates to describe it.
A map projection, being flat, will often be given its own set of Cartesian map coordinates.
The origin is generally chosen to be far west and south of the region of interest.
Both coordinates (x, y) then increase towards the east and north, and are therefore always positive numbers.
(x, y) are known as the easting and northing, respectively.
The origin is typically defined by the false easting and false northing, which are the map coordinates of the standard points or curves that define the projection.
Map coordinates are generally measured in linear units such as feet or meters.
State Plane Coordinates are defined by each individual state to provide a highly accurate (< 0.01%) system of mapping for surveying, etc.
Most data coming from government institutions at the scale of a state or less will be in state plane coordinates.
The low distortion requires state plane maps to be no more than 158 mi across, so most states use more than one projection to cover their area, breaking at county boundaries.
Massachusetts State Plane Coordinates are based on two Lambert Conic projections, one for the Mainland Zone (most of the state) and the other for the Island Zone (Dukes and Nantucket Counties the Elizabeth Islands and Martha’s Vineyard, and Nantucket Island):
The Universal Transverse Mercator system provides a uniform way to describe any non-polar location on the Earth with good accuracy (< 0.08%).
Most maps coming from the US Geological Survey will be in UTM.
The Earth is divided into sixty narrow north-south strips, each six degrees of longitude wide and extending from 80° S. Latitude to 84° N. Latitude:
The zones are numbered from west to east, starting with 1 from 180° W. Longitude, and are individually mapped with a transverse mercator projection centered on the zone.
The central meridian of each zone is assigned a false easting of 500,000 meters, and the Equator is assigned a false northing of zero meters in the northern hemisphere, and 10,000,000 meters in the southern hemisphere.
Massachusetts is covered by Zones 18N and 19N (3).
As a world-oriented coordinate system, UTM is usually used with the WGS84 datum (though not always).
UTM is also the basis of the new U.S.
National Grid system being used by
the Department of Homeland Security.
Let’s change the world map’s spatial reference to UTM 14N/WGS 84:
GIS lets you combine maps with different datums/projections/coordinate systems, and display them with any other one you prefer.
To accurately represent mapped data on a computer screen, and to ensure that it can successfully be used with other data, it must have a spatial reference defined for it, which includes a datum, possibly a projection, and a coordinate system.
The spatial reference determines how the map’s positions should be interpreted for display on the screen.
The spatial reference is described in a standard format that is provided with the data in a file with the extension .prj, and is said to be a part of its metadata (data about data).
Sometimes the .prj file will be missing, and the spatial reference must be manually assigned.
Combining Data with Different Spatial References
In order to simultaneously display two or more sets of GIS data with different spatial references, some of them must be recast to a common spatial reference.
Because each spatial reference is based on a particular datum and possibly also a projection, switching spatial references can involve a complicated mathematical process:
Switching datums is generally more complicated than simply unprojecting and reprojecting, so approximations are usually made that can introduce small errors.
ArcGIS has full support for multiple spatial references, and will automatically reproject data sets so that they are all displayed with the same reference.
However, because of the complexity of datum transformations, ArcGIS (usually) will not automatically transform one datum to another.
Instead, when data is added to a map that has a different datum, ArcGIS puts up a dialog warning of potential issues and giving you the option to pick a transformation.
The one exception is NAD 1927 to NAD 1983, for which there is an accepted standard.
If you are adding a layer to an existing map that has a different datum, e.g. the states layer we worked with in the previous class and the world map in UTM coordinates previously selected, you will be warned about transformation issues.
If a layer’s coordinate system isn’t self-described, ArcMap assumes it is the same as that of the data frame.
Let’s see what happens when you add a layer that doesn’t have a spatial reference defined for it to the current map:
Quite often a layer will lack a .prj file, and you’ll need to manually assign it a coordinate system. Ideally the source will provide this information in another format (typically just a text description).
To assign or alter the coordinate system of a layer, you must use the Catalog , which is designed for the management of individual layers, in particular their metadata.
Below the home folder is a list of your connected folders, followed by other resources such as database and GIS servers.
Navigate to the layer of interest, e.g. masscounties.shp. If necessary, make a new connection first by going to the toolbar Standard and clicking on the button Connect to Folder.
The selected coordinate system will then appear as the Current coordinate system.
Feature: You can add any layer in the Catalog to the map by dragging it into the map pane; if you apply the above procedure to masscounties.shp and then drag it into the map, the Massachusetts counties should be in their correct location.
To locate features and make measurements on a map, you can display both the geographic and projected coordinates.
As noted above, the location of the cursor on the map in the current map coordinates is displayed in the lower right corner of the map window, and they will change as you move the cursor over the map.
Questions: In what units are the current coordinates? Where on the map are they near zero?
It’s sometimes useful to change the displayed units; as with the map itself, this is controlled by the data frame that holds your layers.
Note that the displayed units will always be referenced to the origin of the coordinate system.
ArcGIS also lets you measure the distances between locations and the areas of regions.
Warning: Remember that distances and areas are usually distorted by map projections, and can therefore have different values in different projections (often by huge amounts)!
Map distortion is also important when displaying scale bars on a layout; they will usually only be perfectly accurate along standard parallels and meridians, and are best avoided if the map covers a much larger area.
Coordinate grids are common features on maps, helping to describe the locations of their features.
ArcMap can also superimpose a grid on the layout view of a map, corresponding to:
Many geographic features are described by data structures that include either geographic or projected coordinates.
Geographic data is commonly in the form of simple text tables describing points on the surface of the Earth. The tables consist of a pair of spatial coordinates (e.g. latitude and longitude) in each row, and possibly a feature label and other data. Such data is common in books and journals in all areas of research, whether archaeology or biology. This is also the simplest format of data downloaded from GPS receivers.
Tables can be in a number of different file formats but all sharing the same simple layout, as described in the document Mapping Place Name Data in the section Place Name Data and also in the section Formatting Tables for Joins. For example, a collection of Massachusetts lighthouses downloaded from the US Geological Survey can be expressed as comma-separated values (CSV):
Like place-name data, however, if tabular data needs to be cleaned up or processed in some other way, it is often easiest to bring it into Excel to work on it.
Important: When you compile tabular coordinate data, make certain you note its spatial reference! After some searching, the source for the data above says “All coordinates in the database are in NAD 83. They were converted from NAD 27 in September 2005.”
For the following procedures, it will be useful to start with a new map.
This will establish the spacial reference of the map as NAD 1983 StatePlane Massachusetts Mainland FIPS 2001 (meters).
The United States Geological Survey’s Geographic Name Information Service is a useful source of coordinate-based data, providing an extensive list of domestic features and their coordinates, including many historic sites that no longer exist. Another is the National Geospatial-Intelligence Agency’s Geonet Names Server, which provides a similar service for foreign names. These sites don’t provide their data in an easy-to-use, downloadable format, however, which is also true of many other web sites.
Many web pages include embedded geographic data, commonly street addresses and coordinates. Microsoft Excel can help extract this information.
For example, if Feature Name is in cell A1, Middlefield School will be in cell A2, its latitude and longitude would be in cells F2 and G2, respectively, and the variables lat and lon should be changed to F2 and G2.
= IF(OR(dir = "W", dir = "S"), -1, 1)*(deg + min/60 + sec/3600)
For example, the data provided by the Geonet International Names Server includes both DMS as well as decimal degree data (though the latter is hidden until one clicks on the cell or loads it into Excel). All four values are stored in one cell, and when it’s imported into Excel what was one row turns into four.
There are a few ways to fix this problem, one of which is to first edit the html file with a text editor to remove these tags. An Excel-oriented approach follows:
Then in the dialog Format Cells, click on the tab Alignment, uncheck the boxes Merge Cells and Wrap Text, and click on the button OK.
Then in the dialog Sort, make sure the item My data has headers is selected, and in the menu Sort by, choose the latitude column, e.g. (Column F), and click on the button OK.
You will sometimes find other data formats on the Internet, such as Keyhole Markup Language (KML) files and GPX files, which are also often produced by iPhone and Android apps.
You might also come across KMZ files, which are KML files compressed in the ZIP format — change their file extension from .kmz to .zip and you can open them and see their contents.
KML and GPX are both text formats, but rather than being tables they are structured in a hierarchical format called eXtensible Markup Language (XML).
For example, the CSV formatted file above, with NAD83 coordinates:
would be expressed in KML as:
<?xml version="1.0" encoding="UTF-8"?>
KML expects coordinates to be WGS84, hence there are slight differences from the values in the CSV data.
Recent versions of ArcGIS can add KML/KMZ files directly to your map the same as SHP files. To export, you can use the toolbox procedure described in Constructing and Sharing Maps.
Here the coordinate reference system used must be expressed in the
KML, GeoJSON, and many other formats can be read and written with the Data Interoperability Extension.