What are a property owner's water rights called when their land is located along a river?

When a property owner has land that is adjacent to a river, their water rights are referred to as riparian rights. These rights are associated with the ownership of land that is directly next to a flowing body of water, such as a river or stream. Riparian rights afford the landowner the ability to use the water for various purposes, such as irrigation, consumption, and recreation, while also emphasizing that the use should not adversely affect the water quality or quantity for others downstream.

This concept stems from the understanding that water is a shared resource, and while landowners can utilize the water, they must do so in a manner that respects the rights of other users and the ecosystem.

The other options do not apply in this context. Littoral rights pertain to landowners whose property borders non-flowing bodies of water, like lakes or oceans. Prior appropriation rights are based on a "first in time, first in right" principle typically used in arid regions, allowing water rights to be granted to those who put the water to beneficial use. Hereditaments refer to all types of property that can be inherited, not specifically water rights. Thus, riparian rights are the appropriate term for property owners near rivers.