A vertical coordinate system can be referenced to one of two types of surfaces: gravity related (geoidal) or spheroidal (ellipsoidal).
Gravity-related (geoidal) vertical coordinate systems
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 particular vertical coordinate system may be used with different 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 forth.
A gravity-related vertical coordinate system includes a vertical datum as part of its definition. An example is shown below.
When you create a gravity-related vertical coordinate system, you can specify a custom vertical datum.
Spheroidal (ellipsoidal) vertical coordinate systems
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 system’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.