# Vertical coordinate systems

A vertical coordinate system defines the origin for height or depth values. As with a horizontal coordinate system, a vertical coordinate system ensures that data is spatially located accurately in relation to other data. This is especially important if you will edit the data, create data, or perform analysis.

A vertical coordinate system includes a unit of measure. This is always a linear unit, usually feet or meters (for example, international feet or meters). A vertical coordinate system also includes a direction. This specifies whether values are positive up, representing heights above a surface, or positive down, indicating that values are depths below a surface. The following diagram shows two vertical coordinate systems: mean sea level and mean low water. Mean sea level is used as the zero level for height values. Mean low water is a depth-based vertical coordinate system.

One z-value is shown for the height-based mean sea level system. Any point that falls below the mean sea level line but is referenced to it has a negative z-value. The mean low water system has two z-values associated with it. Because the mean low water system is depth-based, the z-values are positive. Any point that falls above the mean low water line but is referenced to it has a negative z-value.

##### Note:

When you work with gravity-based heights (elevations), the data will be drawn relative to the ellipsoidal coordinate system of the map.

A vertical coordinate system can be referenced to one of two types of surfaces: gravity related (geoidal) or spheroidal (ellipsoidal).

##### Note:

When processing begins, 100 random images are picked to evaluate vertical accuracy. For projects containing less than 100 images, all images are evaluated. If the image altitude for those images is below the expected threshold based on the coordinate systems in use, a warning appears recommending the use of ground control points or the adjust image altitude tool to apply a correction. The threshold is determined by comparing the relative altitude from the images (if available) to an adjusted relative altitude that is calculated automatically.

The following is an example:

An image has an absolute altitude of 192.09 meters, a relative altitude of 62.74 meters, and the ground elevation at that point is 142.84 meters.

An adjusted relative altitude is calculated (absolute altitude minus ground elevation): 192.09 meters - 142.84 meters = 49.25 meters.

If the difference between the original relative altitude and the adjusted relative altitude is greater than 10 percent, the image is flagged for adjustment.

Difference: ABS(62.74 meters - 49.25 meters) = 13.49 meters

10 percent of 62.74 meters = 6.274 meters

13.49 meters > 6.274 meters, so the image is flagged.

## Gravity-related (geoidal) vertical coordinate system

Most vertical coordinate systems are gravity related. A gravity-related vertical coordinate system is often only loosely connected to a particular geographic coordinate system. Any vertical coordinate system can be used with various horizontal coordinate systems. A gravity-related vertical coordinate system may set its zero point through a local mean sea level or a benchmark. Mean sea level will vary at different places due to topography, atmospheric effects, and so on.

A gravity-related vertical coordinate system includes a vertical datum as part of its definition. An example is shown below.

``VERTCS["EGM96_Geoid",VDATUM["EGM96_Geoid"],PARAMETER["Vertical_Shift",0.0],PARAMETER["Direction",1.0],UNIT["Meter",1.0],AUTHORITY["EPSG",5773]]``

## Spheroidal (ellipsoidal) vertical coordinate system

A spheroidal vertical coordinate system defines heights that are referenced to a spheroid of a geographic coordinate system. A global positioning system (GPS) unit natively reports heights relative to the World Geodetic System of 1984 (WGS84) ellipsoid. An onboard geoid model in the GPS unit converts the ellipsoidal heights to gravity-related elevations. A spheroidal height is a geometry quantity and does not have a physical sense, as a geographic coordinate systemâ€™s spheroid may fall above or below the actual earth surface. Spheroidal heights for an area may not reflect movement due to gravity; that is, the flow of water. Water can appear to run in an uphill direction when working with spheroidal heights.

A vertical coordinate system with heights or depths that are referenced to the spheroid will include a datum, rather than a vertical datum, definition. An example is shown below.

``VERTCS["WGS_1984",DATUM["D_WGS_1984",SPHEROID["WGS_1984",6378137.0,298.257223563]],PARAMETER["Vertical_Shift",0.0],PARAMETER["Direction",1.0],UNIT["Meter",1.0]]``

## Specify a vertical coordinate system on a 2D or 3D map

To specify a vertical coordinate system on a 2D or 3D map, complete the following steps:

1. In the Contents pane, right-click the 2D or 3D map and choose Properties.
2. On the Map Properties dialog box, click the Coordinate Systems tab.

The Current Z box shows the current vertical coordinate system of the map. There may be no vertical coordinate system defined. If one is defined, click Details above the Current Z box to see how it is defined.

3. Click the Current Z box to highlight it, and choose an appropriate coordinate system from the corresponding Z Coordinate Systems Available list to set or change the vertical coordinate system.

You can enter a search term in the Search box to help locate a specific coordinate system. Vertical coordinate systems in a global scene must be ellipsoidal or they can be gravity-based only if they cover a full world extent. EGM2008 Geoid and EGM96 Geoid are examples of global gravity-based vertical coordinate systems.

When the vertical coordinate system is ellipsoidal, it must share the same datum as the horizontal coordinate system. The datum name, the spheroid name, and all of the spheroid properties of the two coordinate systems must match exactly.

4. To remove a vertical coordinate system definition from a map or a scene, click Current Z, choose , and choose <None> from the Z Coordinate Systems Available list.