**FIGURE 1.2** Schematic showing the approximate relationship between the geoid, based on the Earth’s gravity field (and coinciding with the mean sea level), and the surface of the Earth (topography). Surveys using spirit leveling measure height differences along the geoid. Water flows downhill as defined by the orthometric heights (H). On the other hand, geometric heights (h) are reckoned relative to a conventional ellipsoid and are calculated from coordinates relative to the center of the Earth. In order to use such heights for flood modeling, an independent knowledge of the orthometric height relative to the ellipsoid (N) is required, known as the geoid height. This calls for densely sampled maps of the gravity field, which can be greatly improved nowadays by airborne surveys using GPS/GNSS navigation. Source: Committee on the National Requirements for Precision Geodetic Infrastructure.

important for a wide range of applications, including floodplain mapping and storm surge modeling. Vertical positions determined from GNSS/GPS are not connected to the geoid but represent an absolute height—called the *geometric height (or ellipsoid height)* (h)—calculated from coordinates whose origin is at the center of the Earth. The vertical distance from the ellipsoid and the geoid at any location on Earth is called the *geoid height* (N). Independent knowledge of the geoid allows geodesists to relate geometric to orthometric heights and, for example, to infer land surface elevations from GNSS/GPS measurements.

**Time and the Earth’s Rotation**

The Earth spins and wobbles in complex ways, causing the positions of the poles to shift by millimeters over the course of a day and by meters over the course of a year. Day-to-day variations in the length of day (which measures the Earth’s rate of spin) are typically on the order of fractions of milliseconds per day. The length of day also gradually lengthens as energy is dissipated—primarily through tidal friction—requiring the occasional “leap second” that is applied by international convention.^{4}

One of the primary roles of the global geodetic infrastructure is to determine the length of day and Earth orientation parameters and how they change with time relative to the Earth’s interior, as well as how they change relative to distant, “fixed” objects such as quasars. This requires the ability to synchronize distant clocks accurately, an operation commonly referred to as “time transfer.” Time synchronization is less stringent for such everyday functions such as bank transfers, transportation, television broadcasting, and power grid regulation (i.e., on the order of milliseconds or less). Even higher accuracy is needed for modern high-bandwidth digital networks. GNSS/GPS signals are the