What system applies when water rights are based on the concept of priority, determined by usage duration?

The correct answer is the system known as "prior appropriation." This system is foundational to water rights, particularly in the western United States, where water is often scarce. Under prior appropriation, water rights are granted based on the principle of "first in time, first in right." This means that the first user to divert water for beneficial use has the first claim to that water, and this right is maintained as long as the water is used beneficially over time. It's a usage-duration concept, focusing on the actual diversion and use of water rather than ownership of land adjacent to a water source.

This approach is critical in areas where water scarcity necessitates clear rules about allocation to prevent overuse and conflict among users. The rights can be transferred or sold, but the priority remains with the first user. This contrasts with riparian rights, which are typically based on land ownership adjacent to a water source, where landowners have rights to use water without the need to establish a priority based on usage duration. Therefore, while the answer provided refers to the "appropriation-permit systems," it does not precisely capture the essence of priority based on usage duration as effectively as prior appropriation does.