Final answer:
The correct answer to the question is 'C. Appropriation', which is a method of water rights that allows a nonriparian property owner to use water from a source such as a lake, even without owning land adjacent to it.
Step-by-step explanation:
When a nonriparian owner of a ranch has received permission from the government to use a nearby lake, the legal mechanism is most likely appropriation. In law, appropriation is a water resource management method that allows an individual or corporation to use water from a source, such as a lake or river, without owning land adjacent to the water (nonriparian). It is particularly prevalent in western states of the US where water is scarcer, and differs from riparian water rights, which are common in the eastern states and allow only landowners adjacent to the water source to use it.
Other options listed, such as eminent domain, refer to the power of the government to take private property for public use, with the requirement that just compensation is provided to the property owner. Prescription would refer to the acquisition of rights through long-term use, and percolation is related to the movement of water through the soil, which is not directly relevant to legal water rights.