Basics of coordinate systems and projections
Understanding these fundamental concepts is essential for anyone working with geographic information systems. Accurate mapping and spatial data analysis depend on a solid grasp of how we represent the Earth's surface in a manageable and meaningful way.
Why does it matter?
- GIS programs MUST know what projection was used for data creation and where the Coordinate System’s point of origin is.
- Map data or satellite images in different projections, coordinate systems, or referenced to different datums may not overlay properly.
- For a spatial database to be useful, all parts must be registered to a common coordinate system.
Practical Applications in GIS
• Assigning Coordinate Systems: Ensuring spatial data has a defined coordinate system is crucial for maintaining accuracy.
• Reprojecting Data: Converting data from one coordinate system to another as needed for analysis or visualization.
• Choosing the Right Projection: Selecting an appropriate projection based on the spatial extent and purpose of the map (e.g., local vs. global scale, thematic emphasis).
1 - What is a Coordinate System?
A coordinate system is a reference system used to determine the precise location of points in space. In GIS, coordinate systems allow us to map and analyze geographic data accurately.
Coordinates tell you how far away from the origin of the axes you are (referenced as x,y pairs).
In cartography and surveying, the X axis coordinates are known as Eastings, and the Y axis coordinates as Northings. False eastings and northings are typically added to coordinate values to keep coordinates in the upper right quadrant of the graph (positive values).
2 - Components of a Coordinate System: Ellipsoid, Geoid, Datum.
- Ellipsoid
The earth is not a perfect sphere. There is a slight bulging at the equator and flattening at the poles due to the centrifugal force generated by Earth’s rotation. Mapping a point onto an ellipsoid better represents its position on the earth’s surface. Cartography defines the ellipsoid using a major and minor axis representing the longer and shorter radii of the ellipsoid.
- Geoid
The earth is not a perfect ellipsoid either. It has a topographic surface defined as the change in elevation from…what? From the geoid. It is not a mathematical model, but a model of mean sea level based on survey measurements taken across the planet. It is too complex and irregular to map with, so the ellipsoid is used.
But the discrepancy between the geoid and ellipsoid produces another source of error to locations.
- Datum
To minimize the discrepancy between the geoid and ellipsoid, a datum is defined. A datum is a mathematical model of the Earth that serves as a reference point for measuring locations. It defines the size and shape of the Earth and provides a base for coordinates. A datum 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 use a surveyed network of points to make further adjustments.
A geocentric or world-centered datum optimizes the fit for the entire earth.
A datum definition includes
- The particular ellipsoid (major and minor axis) chosen
- The adjustment or fit
Together they define the Geographic Coordinate System (GCS).
Datum used in North America
- North American Datum 1927 (NAD 1927or NAD27)
- North American Datum 1983 (NAD 1983or NAD83)
- North American Datum 1983 HARN (NAD1983 HARN)
- World Geodetic Survey 1984 (WGS84)
3 - Types of Coordinate Systems
- Geographic Coordinate Systems (GCS)
A geographic coordinate system uses a three-dimensional spherical surface to define locations on the Earth. It is based on a datum and a set of latitude and longitude lines.
Key Concepts
• Latitude: Measures the north-south position on the Earth's surface. It is the angle between the equator and a point on the Earth's surface, ranging from 0° at the Equator to ±90° at the poles.
• Longitude: Measures the east-west position. It is the angle between the Prime Meridian (0° longitude) and a point on the Earth's surface, ranging from 0° to ±180°.
Each degree is divided into 60 minutes and each minute into 60 seconds.
Properties
Measured in angular degrees:
Commonly portrayed as a planar coordinate system in GIS using decimal degrees, which introduces distortion.
- Primary use is for data distribution.
- User obtains data and then projects it into the desired coordinate system for the application.
- Not desirable for maps or analysis because of distortion.
Examples of Geographic Coordinate Systems
• WGS84 or WGS 1984 (World Geodetic System 1984): The standard coordinate system used for GPS and many global mapping applications. It uses the Earth’s center mass as the coordinate origin.
• NAD83 or NAD 1983 (North American Datum 1983): Commonly used in North America for mapping and surveying.
For the NAD83, State-by-state adjustments were completed in the 1990s, an effort referred to as the High Accuracy Reference Network (HARN).
Since then, the increasing accuracy and availability of GPS has required two adjustments of the entire network. These adjustments produced new realizations that are still on the same datum: NAD83(NSRS2007), and NAD83(2011).
What realization of NAD 83 should I use? Current surveys should use NAD 83 (2011) Epoch 2010.00 for the conterminous U.S., Alaska and Puerto Rico. Surveys in Hawaii or on the Pacific Plate should use NAD 83(PA11), Epoch 2010.00. Territories on the Marianas Plate should use NAD 83(MA11) Epoch 2010.00.
- Projected Coordinate Systems (PCS)
A projected coordinate system represents the Earth's curved surface on a flat plane. This involves mathematical transformations known as map projections. In projected coordinate systems, numerical values are expressed as x and y coordinates (also known as easting and northing).
Do I need to measure anything? If you say yes to this question, then you need to project your dataset. Projecting a dataset that has a GCS will convert its degrees of latitude and longitude into a measurable unit (meter, foot).
Key Concepts
• Map projection: A method by which the three-dimensional surface of the Earth is projected onto a two-dimensional plane. This process inevitably introduces some distortion.
• Coordinate grid: The resulting x and y (easting and northing) values that define locations on the flat map.
The Earth is a three-dimensional object, but to create usable maps, we need to project this 3D surface onto a 2D plane. Different projections serve different purposes and aim to minimize various types of distortion, such as shape, area, distance, and direction.
Types of Map Projections
- Cylindrical Projections
- Tend to be Conformal – Preserve local shapes and angles.
- Globe is projected onto a cylinder tangent at equator (typically).
- Low distortion at equator. Distances are true only along the Equator.
- Higher distortion approaching poles. Areas are greatly distorted increasing size at poles.
- A good choice for use in equatorial and tropical regions, e.g., Ecuador, Kenya, Malaysia.
Examples: Mercator projection and Transverse Mercator projection.
The Transverse version is widely used in national and international mapping (UTM = Universal Transverse Mercator) and is popular in scientific research.
- Works great for mapping large scale datasets that are mainly north-south in extent. Distances are true only along the central meridian, but all distances, directions, shapes, and areas are reasonably accurate within 15º of the central meridian.
- Convenience of a plane rectangular grid on a global level.
- Divides the Earth into 60 zones.
- Low distortion along the tangent central meridian, increasing E & W.
- Conic Projections
- Tend to be Equal Area. Preserve area, ensuring that the size of features is accurately represented.
- Surface of globe projected onto cone tangent at standard parallel.
- Distorts N & S of standard parallel(s).
- Normally shows just one semi-hemisphere in middle latitudes.
Examples: Albers Equal-Area projection, Lambert Conformal Conic.
The Albers Equal Area Conic projection is a conic, equal-area projection commonly used for displaying large countries that require equal-area representation (USA, Canada, Russia...).
The projection is particularly useful for regions with a larger east-west extent, such as the conterminous US (48 states), since it minimizes distortion in area. As it preserves the area it is very useful for statistical and thematic maps where area representation is critical.
Not suitable for world maps due to distortion far from the standard parallels.
Shapes and distance can be distorted, especially near the poles and the equator.
| Distortion | Description |
| Distance | True only on both standard parallels. |
| Scale | Distortion increases away from the standard parallels. |
| Direction | True direction is preserved along the standard parallels. Distortion in direction increases away from standard parallels. |
| Area | Accurate for areas near the standard parallels. Equal to the same areas on Earth, though it’s not conformal, perspective, or equidistant. Suitable for comparing different regions by size. |
The Lambert Conformal Conic is one of the many creations by Lambert in 1772 still widely used in the United States today (such as in the State Plane Coordinate System (SPCS)). It looks similar to the Albers Equal Area Conic, but graticule spacings differ so that it’s conformal rather than equal area. This projection is widely used for aeronautical charts and maps of large mid-latitude regions.
It uses a conic developable surface secant at two standard parallels, usually at 33° and 45° to minimize distortion. However, standard parallels vary depending on location. For example, Canada’s standard parallels are usually 49ºN. and 77ºN.
It is frequently used for mapping areas that extend in an east-west direction, such as the US, Europe, and other mid-latitude regions.
It preserves local shapes and angles, making it suitable for aeronautical charts and navigational charts.
Distortion of shapes is minimal near the standard parallels.
Does not preserve area, so it is not ideal for thematic maps where area comparison is crucial.
Distortion of scale and area increases away from the standard parallels.
| Distortion | Description |
| Distance | Distances are reasonably accurate and retained along standard parallels |
| Scale | Scale is constant along any given parallel. |
| Direction | True direction is preserved along standard parallels with distortion increasing away from standard parallels. |
| Area | It isn’t equal area as distortion increases away from standard parallels, especially near the poles. Suitable for mapping continental and regional areas. |
Conic Projection Advantages and Disadvantages
Both projections are conic and use standard parallels to minimize distortion, but they serve different purposes.
The Albers Equal Area projection is best for thematic maps where area accuracy is crucial, while the Lambert Conformal Conic projection is ideal for navigational purposes where preserving shape and angles is important. The choice between these projections depends on the map's purpose and the region being mapped.
- Azimuthal Projections (planar projections)
Azimuthal projections tend to be Conformal - Preserve directions from specific points. They are ideal for specific use cases, especially where a central point is of primary importance. For example, the azimuthal equidistant projection is excellent for distance calculations from a central point, while the stereographic projection is useful for preserving angles and shapes in polar maps.
- They project the surface of the earth onto a plane tangent at a single point, usually a pole or the equator.
- Distortion patterns radiate outward from the central point, with minimal distortion at the center and increasing distortion toward the edges.
- Usually only one hemisphere shown (often centered on N pole or S pole)
- Works well to highlight an area.
- Sometimes used by airports.
Examples: azimuthal equidistant. stereographic, and orthographic projections, each preserving different properties like distance, angle or area.
The Azimuthal Equidistant Projection
Maintains accurate distances from the center point of the map to any other point. It projects the surface of the Earth onto a flat plane, with the central point typically being a pole or specific location of interest. It is valuable for specific applications where distance accuracy from a central point is essential.
Displays the Earth in a way that distances and directions from the center point are preserved.
Distortion is minimized at the center point and increases towards the edges,
Significant distortion occurs near the edges of the map. Limits its use for large-scale mapping.
While distances are accurate from the center, area and shape distortion increase as one moves away from the center.
Widely used for air-route maps and seismic maps where accurate distance measurements are essential.
The United Nations Emblem uses an azimuthal equidistant projection centered on the North Pole.
The orthographic Projection
Simulates a view from space, preserving the appearance of the globe as seen from a great distance. Used for perspective views of the Earth, such as globes and planetary maps. The Orthographic projection geometrically projects the globe onto a plane with the point of projection as infinity. All the projection lines are orthogonal to the projection plane.
- The orthographic projection distorts shape and area near edges due to perspective.
- Directions are true from the point of projection, with scale defeating away from its radiating lines.
- The orthographic projection isn’t conformal nor equal area.
The Stereographic Projection
This map projection is commonly used for polar aspects and navigation maps because of how it preserves shapes (conformal).
- The stereographic projection is conformal, preserving angles and shapes around the central point. This ensures that small features appear in their true shapes.
- Often used for mapping polar regions and in meteorology.
- Distortion is minimal at the central point and increases as you move away from it.
- Used for mapping polar regions since it accurately represents the shape of features near the poles.
- Used in star charts and celestial maps due to its conformal nature, preserving the angles between constellations.
- Useful in applications where accurate bearings and angular relationships are crucial.
- Used to display the directional properties of seismic waves.
Azimuthal Projection Advantages and Disadvantages
- Useful for specific applications like air travel, seismic activity, and polar region mapping.
- Minimal distortion at the central point.
- Distortion increases significantly away from the center.
- Not suitable for large-scale maps due to extreme distortion at the edges.
Common Coordinate Systems and Projections
UTM (Universal Transverse Mercator)
UTM is a global map projection that divides the world into 60 N-S zones each spanning six degrees of longitude (0.5 degrees overlap each side). It uses the transverse Mercator projection for each zone.
- Projects the globe onto a cylinder tangent to a central meridian.
- Distortion is minimal within each zone.
- Provides high accuracy for small areas.
- Each zone has an origin, central meridian, and false origin, just as with State Plan Coordinate System
- Coordinates read similar to State Plane but in meters.
- Commonly used for topographic maps, engineering projects, and GPS.
Advantages
- High accuracy within each zone.
- Suitable for large-scale mapping.
Disadvantage
Not suitable for regions spanning multiple zones.
State Plane Coordinate System (SPCS)
SPCS is a set of map projections tailored for specific states or regions in the United States, using either transverse Mercator (N-S zones), Lambert conformal conic (E-W zones), or oblique Mercator (Alaska) projections.
- Used primarily in the United States.
- Each state is divided into one or more zones to minimize distortion. Each state is identified by a unique Federal Information Processing Standard (FIPS) number.
- Uses different projections based on the shape of the region.
- Used for land surveying, engineering, and local government mapping.
Advantages
- High accuracy for local areas.
- Tailored to minimize distortion for specific regions.
Disadvantage
Not suitable for national or global mapping.
Web Mercator
It is a variant of the Mercator projection, optimized for web mapping applications.
- Projects the globe onto a cylinder.
- Simplify calculations for online maps (web-friendly).
- Used by most online mapping applications (e.g., ArcGIS Basemaps, Google Maps...).
- A variant of the Mercator projection, useful for web mapping but not for accurate distance and area calculations.
Advantages
- Conformal, preserving shapes and angles.
- Simple for web tile rendering.
Disadvantages
- Significant area distortion near the poles.
- Not suitable for accurate distance and area measurements.
Understanding coordinate systems and projections is fundamental to effective GIS work. By mastering these concepts, you will be able to accurately map and analyze spatial data, making informed decisions based on reliable geographic information. Remember to consider the purpose and scale of your map when choosing coordinate systems and projections to ensure the best representation of your data.
- Geographic coordinate system / datum (point of origin used as a reference)
- Projection (if one is used)
- Storage units used to store the x-y values (degrees, feet, etc.)
- Domain, or maximum allowable x-y values
- Resolution, or the x-y precision
The following links allow you to compare the size of different countries, providing a great perspective on how map distortions and scales can be misleading.
Tips and Tricks for Understanding Coordinate Systems in ArcGIS Pro
Understanding CSs in ArcGIS Pro is crucial for accurate mapping and spatial analysis. Here are some tips and tricks to help you navigate and manage coordinate systems effectively:
1. Check Layer Properties Regularly
- Access Layer Properties: Right-click on a layer in the Contents pane and select "Properties." Go to the "Source" tab to view the coordinate system.
- Verify Coordinate Systems: Ensure that each layer in your map has the correct coordinate system to prevent misalignment and projection issues.
2. Understand the Dual Labels for Projected Layers
- GCS and PCS: Recognize that a PCS includes both the GCS and the PCS. The GCS defines the shape of the Earth, while the PCS transforms this shape onto a flat plane.
- Two Labels: Pay attention to both labels in the layer properties to understand how data is projected and displayed.
3. Use the Project and Define Projection Tools Appropriately
- Define Projection Tool: Use this tool to assign or correct the coordinate system metadata without changing the data’s coordinates. Ideal for datasets with undefined or incorrect projections.
- Project Tool: Use this tool to convert data from one coordinate system to another, recalculating the coordinates. This is essential for standardizing datasets to a common coordinate system for analysis.
4. Leverage the Search Function
- Search Coordinate Systems: Use the search function in the coordinate system selection dialog to quickly find and apply the appropriate coordinate system based on name, WKID, or keywords.
- Favorites and Recent: Utilize the "Favorites" and "Recent" tabs to quickly access commonly used coordinate systems.
5. Understand WKID (Well-Known ID)
- Identify Coordinate Systems: Each coordinate system has a unique WKID that simplifies identification and use. Familiarize yourself with common WKIDs, such as 4326 for WGS 1984 (GCS), 3857 for Web Mercator (PCS), 4269 for NAD 1983 (GCS)...
- Previous WKID: Be aware of the previous WKID for legacy data compatibility. This helps when working with older datasets or transitioning between different versions of coordinate systems.
6. Inspect the Extent
- View Extent Coordinates: Check the extent values (xmin, ymin, xmax, ymax) in the Layer Properties under the Source tab to understand the geographic coverage of your data.
- Units Matter: For GCS, extents are in degrees (longitude and latitude), while for PCS, they are in linear units like meters or feet.
7. Handle Geographic Transformations
- Transformation Options: When projecting between coordinate systems with different datums, ArcGIS Pro may prompt you to select a geographic transformation. Choose the appropriate transformation based on the geographic area and accuracy requirements.
- Transformation Library: Familiarize yourself with common transformations for your region and add them to your favorites for quick access.
8. Use Basemaps for Visual Verification
- Overlay with Basemaps: Add a basemap to your project to visually verify the alignment and projection of your data layers. This helps identify any misalignment issues early.
- Match Coordinate Systems: Ensure your basemap and data layers share the same coordinate system or use on-the-fly projection to align them.
9. Documentation and Resources
- ArcGIS Pro Help: Utilize the extensive documentation and resources available in ArcGIS Pro’s help system to understand coordinate systems and their parameters.
- NTGISC Support: Reach out to NTGISC support for assistance with complex coordinate system issues.
10. Practice with Real Data
- Experiment: Practice defining and projecting coordinate systems with sample datasets to build confidence and proficiency.
- Analyze Results: Analyze the results of your projections and transformations to understand the effects on your data’s accuracy and alignment.
By following these tips and tricks, you can effectively manage and understand coordinate system labels in ArcGIS Pro, ensuring accurate spatial data representation and analysis.
We hope that this article has been helpful! If you have any feedback or questions, please feel free to send us an email or connect with us for a chat. The NTGISC team is here to assist you further!
Resource(s)
https://www.ngs.noaa.gov/datums/horizontal/north-american-datum-1983.shtml
https://gistbok.ucgis.org/bok-topics/2017-quarter-03/map-projections
https://www.visualcapitalist.com/wp-content/uploads/2022/10/true-size-of-land-masses-full.html