In geology

Geology

Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...

 a sag, or trough

Trough (geology)

In geology, a trough generally refers to a linear structural depression that extends laterally over a distance, while being less steep than a trench.A trough can be a narrow basin or a geologic rift....

, is a depressed, persistent, low area; the opposite of an arch, or ridge

Ridge

A ridge is a geological feature consisting of a chain of mountains or hills that form a continuous elevated crest for some distance. Ridges are usually termed hills or mountains as well, depending on size. There are several main types of ridges:...

, a raised, persistent, high area. The terms sag and arch were used historically to describe very large features, for example, characterizing North America as two arches with a sag between them.

Also, a sag is a former river bed which has been partially filled with debris from glaciation

Glacier

A glacier is a large persistent body of ice that forms where the accumulation of snow exceeds its ablation over many years, often centuries. At least 0.1 km² in area and 50 m thick, but often much larger, a glacier slowly deforms and flows due to stresses induced by its weight...

 or other natural processes but which is still visible in the surface terrain. Sags formed by the former river beds of large rivers often become the valleys of smaller streams after a change of course by the main river.

Examples of sags include the former continuations of the Grand

Grand River (South Dakota)

The Grand River is a tributary of the Missouri River in North Dakota and South Dakota in the United States. The length of the combined branch is 110 mi...

, Moreau

Moreau River

The Moreau River is a tributary of the Missouri River, approximately 200 mi long, in South Dakota in the United States.It rises in two forks in northwestern South Dakota, in the Badlands of Harding County. The North Fork rises approximately 10 mi northeast of Crow Buttes...

 and White

White River (South Dakota)

The White River is a Missouri River tributary that flows through the U.S. states of Nebraska and South Dakota. The name stems from the water's white-gray color, a function of eroded sand, clay, and volcanic ash carried by the river...

 rivers in South Dakota

South Dakota

South Dakota is a state located in the Midwestern region of the United States. It is named after the Lakota and Dakota Sioux American Indian tribes. Once a part of Dakota Territory, South Dakota became a state on November 2, 1889. The state has an area of and an estimated population of just over...

 in the United States

United States

The United States of America is a federal constitutional republic comprising fifty states and a federal district...

. Before the last ice age

Ice age

An ice age or, more precisely, glacial age, is a generic geological period of long-term reduction in the temperature of the Earth's surface and atmosphere, resulting in the presence or expansion of continental ice sheets, polar ice sheets and alpine glaciers...

 these rivers continued eastward past their current confluences with the present course of Missouri River

Missouri River

The Missouri River flows through the central United States, and is a tributary of the Mississippi River. It is the longest river in North America and drains the third largest area, though only the thirteenth largest by discharge. The Missouri's watershed encompasses most of the American Great...

. The sags are prominently visible on the plateau

Plateau

In geology and earth science, a plateau , also called a high plain or tableland, is an area of highland, usually consisting of relatively flat terrain. A highly eroded plateau is called a dissected plateau...

 of the Coteau du Missouri

Coteau du Missouri

The Coteau du Missouri, or Missouri Plateau, is a large plateau that stretches along the eastern side of the valley of the Missouri River in central North Dakota and north-central South Dakota in the United States...

, allowing small streams to drain into the Missouri from its eastern side.