Difference between projection and datum?

  • What's the difference between a projection and a datum?

    This is going to be one of the highly viewed questions on this stackexchange.

    the answer using text from the Manifold docs is rated higher because one doesn't have to click through to get the meat. Personally I don't find the projection page that illuminating, the datum one one the other hand I like, especially for the graphic: http://help.arcgis.com/en/arcgisdesktop/10.0/help/003r/GUID-E94B3A5F-D997-4E6F-B400-BC15C4B0DCDC-web.gif

    I wonder if this would be best as a community wiki, where we could collectively roll all of the answers up into a single, combined best answer. I'm personally not especially fond of broad questions where the answers are easily found on wikipedia, etc.

    Good idea, wikifying now - should help us develop a good, canonical answer :)

    I think someone should mention the distinction between the two possible interpretations of "Map Projection" - namely "Projected CRS", which includes the datum and is what wwnick seems to be describing (http://gis.stackexchange.com/questions/664/whats-the-difference-between-a-projection-and-a-datum/722#722) and "Projection Method", which is what is described in dev's answer (http://gis.stackexchange.com/questions/664/whats-the-difference-between-a-projection-and-a-datum/665#665).

    Great question for beginners! Here is another great explanation of the differences between datums, projections, coordinate systems, etc. with some illustrations (This is linked to in the PostGIS documentation): http://www.sharpgis.net/post/2007/05/Spatial-references2c-coordinate-systems2c-projections2c-datums2c-ellipsoids-e28093-confusing.aspx

    There won't be a single answer for this as "datum" in GIS can be one of at least three different things e.g. geodetic datum (a reference from which measurements are made), a single reference point (often sea level as in "Ordnance Survey datum" = mean sea level at Newlyn in Cornwall, UK) and a reference ellipsoid (which is probably how most GIS people use the term. Finally here's a fourth meaning for the sake of pedantic completeness - datum = singular of data (so any single piece of information is a datum) :)

    I have rolled back the revision of the title, since a datum doesn't always mean a Geographic Coordinate system, nor does a projection always mean projected coordinate system.

    I wrote an in-depth article on this on my blog here: http://www.sharpgis.net/post/2007/05/05/Spatial-references2c-coordinate-systems2c-projections2c-datums2c-ellipsoids-e28093-confusing It covers all these concepts in a hopefully easy to understand manner.

  • wwnick

    wwnick Correct answer

    10 years ago

    Geographic coordinate systems (lat/long) are based on a spheroidal (either truly spherical or ellipsoidal) surface that approximates the surface of the earth. A datum typically defines the surface (ex radius for a sphere, major axis and minor axis or inverse flattening for an ellipsoid) and the position of the surface relative to the center of the earth. An example of a datum is NAD 1927, described below

    Ellipsoid        Semimajor axis†          Semiminor axis†   Inverse flattening††
    Clarke 1866     6378206.4 m              6356583.8 m             294.978698214
    

    All coordinates are referenced to a datum (even if it is unknown). If you see data in a geographic coordinate system, such as GCS_North_American_1927, it is unprojected and is in Lat/Long, and in this case, referenced to the NAD 1927 datum.

    A Projection is a series of transformations which convert the location of points on a curved surface(the reference surface or datum) to locations on flat plane (ie transforms coordinates from one coordinate reference system to another).

    The datum is a integral part of the projection, as projected coordinated systems are based on geographic coordinates, which are in turn referenced to a datum. It is possible, and even common for datasets to be in the same projection, but be referenced to different datums, and therefore have different coordinate values. For example, the State Plane coordinate systems can be referenced to either NAD83 and NAD27 datums. The transformations from geographic to projected coordinates are the same, but as the geographic coordinates are different depending on the datum, the resulting projected coordinates will also be different.

    Also, projecting data may result in a datum conversion as well, for example, projecting NAD_1927 data to Web Mercator will require a datum shift to WGS 84. Similarly, it is possible to convert data from one datum to another without projecting it, as with the NGS's NADCON utility, which can shift coordinates from NAD27 to NAD83.

    Example of a point's coordinates referenced to different datums

    Coordinates referenced to NAD_1927_CGQ77

    19.048667  26.666038 Decimal Degrees
    Spheroid: Clarke_1866
    Semimajor Axis: 6378206.4000000004
    Semiminor Axis: 6356583.7999989809
    

    Same point referenced to NAD_1983_CSRS

    19.048248  26.666876 Decimal Degrees
    Spheroid: GRS_1980
    Semimajor Axis: 6378137.0000000000
    Semiminor Axis: 6356752.3141403561
    

    Could this be community wikied, so we can make it canonical?

    good idea, done.

    This answer seems somewhat misleading to me. It suggests that datum's are GCSs. "Datum's i.e. Geographic coordinate systems..." A datum is used to reference coordinates (both geographic and projected) in space. See my explanation below.

    Just a small comment on the first line "Datums, i.e. Geographic coordinate systems". It sounds like a Datum is a geographic coordinate system. That's not the case. Datums are part of a simple ellipsoidal earth model. Geographic coordinate systems uses a datum as part of it's definition. But so does geocentric and projected coordinate systems.

    dotMorten, you are correct. this answer is now a community wiki and has seen a few edits, will fix.

  • You will obviously get better answers from textbooks, but here is an simple explanation:

    Map Projection: It is a method for representing a spherical or curved surface on a flat plane.

    Datum: It is the reference or origin based on which measurements are made.

    I just reverted this answer to the original. A proposed and accpeted edit said that these definitions are quoted from wikipedia entries. They are not.

    @mkennedy Thank you. And even if they were exactly the same, given that more than three years have elapsed since this was posted we would need to double-check whether the Wikipedia entries were not actually quotations from *here*!

    @mkennedy: Thanks for reverting the edit. The same user had earlier in the day suggested the same thing, & I too had rejected it, since this isn't from the wikipedia.

  • After struggling with this question ten years ago, and finding many confusing things written about the topic, I published a brief article in Directions Magazine that presented an answer as simply, plainly, and accurately as I could make it. The following is excerpted from that article.

    Reprojecting geographic features

    Two things must happen when you draw a map: features in the real world must be "georeferenced" to a spheroid and the spheroid must be projected onto the paper.

    enter image description here

    The spheroid models the shape of the earth's surface. It is an idealization that does not account for local changes in topography.

    Georeferencing assigns locations (in three dimensions!) to points on a spheroid.

    Projecting is an operation that mathematically distorts and shrinks a portion of the spheroid onto flat paper. Projecting can be undone ("inverted"). "Unprojection" expands a feature on a map and plasters it back onto the spheroid.It, too, is a mathematical operation.

    Georeferencing is done with a datum. A datum is usually given by a starting point and direction: it specifies where a clearly identifiable point on earth (the base point) should appear on the spheroid and it shows where a base direction, such as north, points on the spheroid at the base point. The base point and direction allow surveyors to determine the distance and angle of any other point on the earth. Moving in the corresponding direction on the spheroid for the same distance determines where the new point should go on the spheroid.

    Spheroids have coordinates. They are latitude and longitude. (Geodetic) latitude is the angle made by a vertical line to the horizontal. It is not necessarily the same angle made by "straight up," because the latter is distorted by gravitational variation over the earth. It is not necessarily the angle made by a line to the center of the earth, because most spheroids have an elliptical cross-section, not a circular one.

    Therefore, georeferencing endows points near the earth with latitude, longitude, and height coordinates.

    (Subsequent sections discuss Change of datum, How to relate two maps, The wrong way to do it, and North America is a special case.)

    Thank you Bill. It's a joy to see this difficult subject *illustrated* as well as explained. (It's wonderful to see you here too, welcome aboard!)

    Thanks, Matt. It's always interesting to find a new GIS community.

    Seconded, thanks for the article, and thanks for joining the party!

    It would be nice if you had an excerpt or summary in your answer in case the article becomes unavailable from Directions Magazine.

    @Alex B That's a fair request. But Directionsmag has been around much longer than Wikipedia; that particular article has been up for over ten years now. I wrote it so tersely that it would be difficult to summarize without completely reproducing it and its illustrations. We can expect that the Wayback Machine will continue to store a copy for a long time, too: http://web.archive.org/web/20001202230300/www.directionsmag.com/article.asp?ArticleID=75

    @Alex After gaining more experience with this site I realize that you were quite right. I added an excerpt. Thank you for the suggestion.

    Very nice visualisation.

    Another link where this article is still present https://cals.arizona.edu/art/kb/reproj/huber.html

    Very fine article, i wish that you also visualize the datum explanation.

  • wwnick's answer is correct, but it is a bit misleading in the sense that it emphasizes ellipsoid parameters and IMO understates the importance of 'the position of the surface relative to the center of the earth' - the NAD 1927 example needs to mention that the geodetic "center" of NAD27 is a base station at Meades Ranch in Kansas.

    One could have (and often that's the case, especially with the increasing popularity of WGS84/GRS80 ellipsoid) several different datums based on the exact same ellipsoid parameters. The reason for this is that while the WGS 84 datum is OK globally since its surface is set to provide minimal average shifts due to tectonic movements across the globe, there's room for improvement on the local scale, where the reference can be fixed to some local reference point or at least to the local tectonic plate (e.g. ETRS, which is fixed to continental Europe)

    One could explain datum simply as "an agreement on the coordinate system type, shape and its absolute position and orientation relative to some well-known or well-defined real-world reference". The coordinate system doesn't even have to be ellipsoidal (e.g. Vertical datum, which is usually defined by saying that the height of some fixed point is such, and all other heights will be measured relative to this point).

    +1 These points need to be merged into the main answer? This is the info I was looking for, and good to see Google pointed me here when looking for a good datum definition.

  • Geographic projections are a way of showing the curved surface of the Earth on a flat surface like a piece of paper...

    From the Manifold user documentation:

    Earth is not an exact ellipsoid. In fact, because the Earth is such a "lumpy" ellipsoid no single smooth ellipsoid will provide a perfect reference surface for the entire Earth. The practical solution to this is to measure the Earth's shape in different areas and to then create different reference ellipsoids used for mapping different regions on Earth. A datum is a reference ellipsoid together with an offset from the center of the Earth. By specifying different offsets, you can use the same standard ellipsoids in many different regions of the Earth. Different countries will often use the same ellipsoid but with different offsets for standard government maps in those countries.

    Re: "A datum is a reference ellipsoid together with an offset from the center of the Earth." Just to be complete, it may also include a tilt of the axis of the ellipsoid and a scale factor. Geographic coordinates (latitude and longitude) can be off by hundreds of meters if you use the wrong datum. I have an ArcGIS-oriented overview of projections and datums here: http://www.ats.amherst.edu/software/gis/mapping_coordinate_data/

  • Think of projection as seeing your location on X/Y plane. Datum defines the reference point from where all measurements were made. Say you are located somewhere and need to tell your location to someone. You would say, i am X lat and Y long. This X and Y are deterministic because they are being referred from the Datum. The other person now knows that you are X-lat and Y-Long away from Datum. If you are a newbie, dont concentrate too much on Datum characteristics. Just remember that its the location from where all measurements are made.

  • I wrote an in-depth article on this on my blog here: http://www.sharpgis.net/post/2007/05/05/Spatial-references2c-coordinate-systems2c-projections2c-datums2c-ellipsoids-e28093-confusing

    It covers all these concepts in a hopefully easy to understand manner, and has been peer-reviewed by several.

    To sum it up: A datum is a definition of the size, orientation and position of an ellipsoid used as an approximation of the earths shape. It uses reference points on the surface to define it's placement and orientation, based on a date (which is why a number is in there for the year it was defined to account for tectonic plate movements). Datums are used in both spherical long/lat and projected coordinate systems. Consider it a reference point for your coordinates and ellipsoidal heights (ie where's the primemeridian, equator, and what's the height relative to the ellipsoid which isn't the mean sea level). Different datums are used different places because some fit some areas better than others.

    A projection is a formula used to convert long/lat coordinates into a flat coordinate system that you can use on paper or a computer screen. It's usually done from a geographic coordinate system, which in turn uses a datum as it's base definition. So the datum affects all of it. Projecting data creates a lot of distortion of the real world, so it really should only be done when putting your map data on a flat map, or you want to work in a "simpler" coordinate system and can live with the distortions.

    Using the wrong datum could result in your data being offset up to about a mile, so it's quite important to know the datum if you're mixing data together.

  • This won't compete with wwnicks answer and not rigorous, but the visualization I present to people, when asked, is the relationship between a string connected to a ball. Changing the projection is often like moving the 'loose' end of the string around, but still connected to the same point on the ball. Changing the datum is like changing the location of the ball. This might help those visual types.

  • We should remember the earth is not a simple sphere, if it was, we need one datum "= One calculation system to find a point on earth", earth is more ellipsoid, but not exactly. Earth is an astronomic geoid without a regular shape, so we may have many ways to calculate coordination of a point in this irregular 3D object, with many opinions and concepts, each one is a datum.

    ICSM's Fundamentals of Mapping page on Datums 1 – The Basics can be visited for more information.

  • In short, a projection is used to 'flatten' the ellipsoidal shape of the earth to rectangular coordinate system (e.g., a map). A datum is a specific, known point on or in the Earth that is used for reference. A projection uses the datum as a point of reference, it's location on Earth.

    In GIS, there are two types of "coordinate systems": Geographic Coordinate System (latitude and longitude) and Projected Coordinate System (X and Y). Both geographic coordinate system's and projected coordinate systems use a datum for reference.

    • A geographic coordinate system is not projected (not flat), they are in latitude and longitude. Think of a round globe, not a flat map.

    • Projected coordinate systems on the other hand are "flat" - but still need a point of reference (datum) to define locations in space.

    In other words, the datum is used to determine the point of origin on Earth by referencing a central point inside a 'model' of Earth.

License under CC-BY-SA with attribution


Content dated before 6/26/2020 9:53 AM