For this month’s Geospatial Frequently Asked Question (G-FAQ), I turn my attention to the topic of projections in ArcGIS with a focus on geographic transformations. Geographic transformations are those options that appear at the bottom of the Project Toolbox interface for both features and rasters. While the transformation will auto-populate (in Arc 10.1 at least), there is reason to be mindful of the option that is chosen.

With this in mind, the November and December G-FAQ’s will address this core set of questions:

*What exactly is a geographic transformation? How do the various Projections and Transformations toolbox functions differ? What advice can you offer when working with shapefiles, rasters and geographic transformations?*

In order to address the first core question, we need to start with a lesson on the basics of projections. I will focus on datums and coordinate systems as these are the two items you need to understand to use ArcGIS’ Projections-Transformations toolbox functions. Before we delve into this G-FAQ, let me be up front and mention that this discussion is not meant to be a complete lesson on projections; rather, it is a primer to give you a working understanding of the topic so as to avoid common errors in ArcGIS.

## The Basics of Horizontal Datums

The building block of a projection is the datum. In ArcGIS, we are typically working with surfaces that are defined in the XY directions only, hence many of us are only aware of horizontal datums; and this GFAQ will focus on horizontal datums only. As a side note, all geospatial datasets are also defined by a vertical datum which is similar in nature to a horizontal datum.

A horizontal datum is a representation of the shape of the planet upon which a XY coordinate system is based – such as decimal degree latitude and longitude values that many of us are familiar with (e.g. 85 degrees North, 40 degrees West). Horizontal datums measure positions on the surface of our planet (vis-á-vis vertical datums which measure land elevations). A datum is defined by a mathematical model, and over time multiple models have been created and then revised. Some datums are meant to be accurate for a specific region – such as the North American Datum 1983 (or NAD83); while others are created for global datasets – such as World Geodetic System 1984 (or WGS84).

In the world of physics, a datum is described as the theoretical shape of the planet whereby there is equal gravitational potential (or zero potential energy) on every point of the surface. The reason I say a theoretical shape is that a datum will not match the actual shape of our planet’s surface as we have features, such as mountain ranges and deep valleys, where potential energy is stored. When you calculate the gravitational center of our planet and create a datum from this, the shape is ellipsoidal with flatter poles and a bulge at the center. Depending on where you place this center, the shape of the ellipsoid will change, and hence the shape differences in NAD83 and WGS84 for instance. To further complicate things, as our calculation of the earth’s gravitational center improves, so too do the mathematical models that define WGS84 and NAD83. As such, we really should define a datum with its full name to include the revision number, something that is rarely done in our industry – for example, NAD83 (CORS93) and NAD83 (CORS96).

## The Basics of Coordinate Systems

A coordinate system is the other building block of projections in ArcGIS. A coordinate system is a way to define a point in space by a regularly spaced grid that is based on an origin or starting location. There are two basic types of coordinate systems: geographic and projected. We may be more familiar with geographic coordinate systems, such as latitude and longitude, given how commonly they are used in school environments and online mapping. Geographic coordinates systems are based on angular positions from the center of the planet, for instance Boulder, Colorado’s position which is 40.015 degrees North of the Equator (or the defined north-south centerline of the planet) and 105.27 degrees West of the Prime Meridian (or the defined east-west centerline). Geographic coordinate systems typically work globally or at least on the continental scale.

A projected coordinate system is meant to move three dimensional geographic coordinates to a flat, two dimensional surface or a planar surface, such as a piece of paper. Therefore, all projected systems are simply mathematical transformations of three-dimensional geographic coordinates to planar coordinates (i.e. X and Y values). To create a projected coordinate system, you need to define an arbitrary origin where the plane you are projecting on to intersects a 3D globe. Your mathematical model then transforms all of the coordinates that land in this zone from angular geographic values to a distance from the arbitrary origin in the X and Y axes. As you move farther from this origin, distortion will increase. Hence, most projected coordinate systems have multiple zones that define smaller geographies to minimize this distortion. Unlike geographic coordinate systems, projected systems are typically used for more local, fine-scale geospatial analyses. One of the most common projected coordinate systems is Universal Transverse Mercator (UTM) which was created by the US Army and divides the globe into 60 zones approximately six degrees wide. In this system, coordinates are defined as False Eastings and Northings in meters from the origin of the zone.

## What Then is a Geographic Transformation?

Now that we have an understanding of the components of a projection in ArcGIS – i.e. the datum and type of coordinate system – it is time to move on to an explanation of geographic transformations. Geographic transformations come into play when moving your geospatial data from one projection to another, which is also called re-projecting your data. The geographic transformation is the often ignored third step of a re-projection as it is typically filled in with a default value – which may or may not be the correct option to chose (we will address this topic more fully in Part II of this G-FAQ).

A geographic transformation is a mathematical formula that converts coordinates in the source geospatial dataset to the output coordinate system of choice. As was discussed above, all coordinate systems are based on a datum. So ultimately, a geographic transformation converts coordinates based on one datum, for instance WGS84, to coordinates based on a different datum, for instance NAD83. Geographic transformations are used for both projected and geographic coordinate systems.

Now, let’s layer a final consideration on this topic before moving on. Most (perhaps all) datums have undergone revisions over time as the mathematical models which describe them are improved along with our improved estimation of the location of the Earth’s gravitational center. Therefore, in some instances, a geographic transformation is not as simple as moving from NAD83 to WGS84, you might really be moving from NAD83 (CORS93) to WGS84 (EGM96) with may or may not require a selection other than the ArcGIS default. Stay tuned for more details on the implication of this…

## How Do I Determine if my Geospatial Data is Projected?

In this final part of the November G-FAQ, here is a short ArcGIS lesson on determining if your geospatial data is projected or not. There are three methods you can use to determine this; and in the short video that follows, I show you each of them:

– if your data is not projected, you will get a warning message.**When you load geospatial data**– you can access this by right-clicking on your data layer, selecting Properties and then opening the Source tab. This tab shows you info on the layer’s datum, coordinate system and more.**By looking at the Source tab in the Layer Properties menu**- By looking at file structure – in order for a shapefile to be projected, it must have a projection file (.PRJ) associated with it. For raster files, however, there is not a reliable way to determine if the data is projected by looking at its file structure.

*Click the image above to see a short video showing you how to determine if your geospatial data is projected or not.*

Until our next edition of G-FAQ, happy GIS-ing!

*Do you have an idea for a future G-FAQ? If so, let me know by email at brock@apollomapping.com.
*

**Find Out More About This Topic Here:**

- Esri ArcGIS Resources – About Geographic Transformations
- Esri ArcGIS Resources – Map Projection Animations
- Esri Knowledge Database – How To Article 24159
- National Park Service – Datums & Coordinate Systems
- University of Washington Course Notes – ESRM 250

*Brock Adam McCarty*

Map Wizard

(720) 470-7988

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