SALTWATER INTRUSION
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Purpose and Scope of Saltwater Intrusion Web Page
This is a nontechnical webpage on coastal saltwater intrusion (aka seawater intrusion). It is intended to introduce the layman to characteristics of coastal saltwater intrusion that are illustrated in the paper on this website titled "Three-Dimensional Analysis of Saltwater Intrusion, City of Pompano Beach, Broward County, Florida." Coastal saltwater intrusion is the movement of seawater into freshwater aquifers. It can lead to contamination of drinking water sources.
Ghyben-Herzberg Relation for Saltwater Intrusion
Some background information may be helpful in understanding saltwater intrusion. Buoyancy is important. An example of buoyancy in seawater is icebergs. It is well known that most of an iceberg is below the surface of the ocean. This effect is due to Archimedes' Principle which holds that the buoyant or lifting force on an object is equal to the weight of the fluid displaced by that object. This principle was discovered by Archimedes sometime prior to his death in 212 B.C. If the weight per unit volume (weight density, for example pounds per cubic foot, lb/ft3) of the object is less than the weight density of the fluid, the object will float. The weight of the fluid displaced by the floating object will equal the weight of the floating object. In the case of an iceberg with a weight density of 56 lb/ft3 floating in seawater with a weight density of 64 lb/ft3, the proportion of the iceberg submerged would be 56/64 or 0.875 (87.5 percent).
A similar concept applies to coastal groundwater systems. Freshwater is less dense than saltwater. So if a static lens of fresh groundwater were floating on saltwater in porous material beneath the surface of an island in the ocean, the weight of the freshwater lens would equal the weight of the saltwater it displaces. Such a freshwater lens is shown in Figure 1, which is a cross-section through a hypothetical oceanic island where the water table rises to 20 feet above sea level at the center of the island. In this case the weight of the freshwater displaces a volume of saltwater of equivalent weight. Furthermore, the scientists W. Badon-Ghyben of Holland (1888) and A. Herzberg of Germany (1901) independently recognized that any vertical column of water in a static freshwater lens extending from the water table to the interface is balanced by the weight of an equivalent column of saltwater extending from sea level to the same location on the interface. This concept is similar to Archimedes' Principal, but the weight of a column of saltwater displaced by a column of freshwater will equal the weight of the column of freshwater. If the weight density of the freshwater is 62.4 lb/ft3 and the weight density of the saltwater is 64 lb/ft3, the proportion of the freshwater column below sea level would be 62.4/64 or 0.975 (97.5 percent). So if the freshwater column were 43 feet high the proportion below sea level would be 0.975 X 43, which is 41.925 feet. This result is sometimes approximated as 40 feet, which is easy to remember and use. More generally, the depth to a sharp freshwater-saltwater interface below sea level is about 40 times the height of the water table above sea level. This relation is referred to as the Ghyben-Herzberg relation. It reveals why a significant fresh groundwater resource may exist near an ocean coast, as illustrated by Figure 1, where the freshwater-saltwater interface is at 800 feet below sea level at the center of the island. The concept of a freshwater column within the freshwater lens mentioned above is also illustrated in Figure 1.
Rather than use a freshwater column to explain the Ghyben-Herzberg relation, one could note that the pressure in the saltwater and the freshwater at any point on the sharp interface must be the same (since they are not separated), and the pressure in the freshwater is produced by depth below the water table while the pressure in the saltwater is produced by depth below sea level.