it defines “zero” on the measurement scale. Horizontal datums are used to describe a location in latitude and longitude; vertical datums are used to describe heights above or depths below the earth’s surface.

To develop horizontal and vertical datums, the shape of the earth must first be defined. The science of geodesy is dedicated to “measurement and representation of the earth, including its gravity field, in a three-dimensional time varying space” (Vanicek and Krakiwsky, 1986), and some basic concepts of geodesy are explained before delving into the applications of remote sensing technology to floodplain mapping.

The mathematical model that is most often used to approximate the earth’s shape is an oblate ellipsoid, a spheroid that has been slightly flattened at the north and south poles. The Geodetic Reference System of 1980 (GRS80) is the widely accepted geodetic reference system adopted by the General Assembly of the International Union of Geodesy and Geophysics in 1979 (Moritz, 1980). GRS80 is a global reference ellipsoid for navigation and mapping; the center of mass of the earth is defined as its origin. The World Geodetic System of 1984 (WGS84) was developed by the U.S. Defense Mapping Agency (DMA; now the National Geospatial-Intelligence Agency, NGA) and officially published in 1987; WGS84 is the ellipsoidal reference used by the Global Positioning System (GPS). The difference between GRS80 and WGS84 is very small and can be considered negligible for most surveying and mapping purposes (NIMA, 1987).

In practice, one needs physical marks, or monuments, on the earth’s surface that have known coordinates of latitude and longitude on the reference ellipsoid. The National Geodetic Survey (NGS) maintains a system of monuments and published coordinates known as the North American Datum of 1983 (NAD83). NAD83 is a horizontal control datum that represents the best fit to GRS80 for the North American continent; it is the current standard (as defined by a Federal Register notice of June 13, 1989) used by the U.S. Geological Survey (USGS), FEMA, and others for national, state, and local mapping programs. A significant number of USGS topographic maps were created using an earlier horizontal control datum, the North American Datum of 1927 (NAD27), which is based on the Clarke spheroid of 1866. NGS has discontinued use of this datum in favor of NAD83.

The earth’s shape and gravity field are complex and vary over time; however, the gravity field is based on the variability of mass not on shape. Water flows downhill toward the sea following the forces of gravity, not following the shape of an imaginary ellipsoid. Therefore, we need a vertical reference system defined by gravity; the gravity surface that coincides on average with global sea level is called the geoid, as shown in Figure 4.1. In some places on the earth, zero elevation with respect to the geoid is many meters above zero with respect to the ellipsoid; in other locations the geoid may be many meters below the ellipsoid. The difference is known as the geoid separation.

Like NAD83 for horizontal, there is also a vertical control datum for elevation called the North American Vertical Datum of 1988 (NAVD88), which was established by a minimally

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