Final answer:
The Hawaiian island flooded by over 51 inches of rain from Hurricane Lane is Kauai. This is attributed to the island's topography and the rain shadow effect by Mount Waialeale. Kauai exemplifies the climatic diversity within the Hawaiian archipelago, shaped by its volcanic origins.
Step-by-step explanation:
The Hawaiian island that was flooded in some places by more than 51 inches of rain from Hurricane Lane is Kauai. Kauai is known for its high level of precipitation, with parts of the island receiving more than 460 inches of rain per year. This is largely due to the rain shadow effect created by Mount Waialeale. The same geographical phenomenon leads to semi-desert conditions on the leeward side of the mountains, resulting in significant differences in precipitation across the island.
These extraordinary weather patterns are consequences of Kauai's topography and climatic factors. Kauai, being the oldest island in the Hawaiian archipelago, has well-developed mountainous regions that facilitate such dramatic variations in weather. Additionally, the entirety of the Hawaiian Islands is formed from volcanic activity, with a stationary hotspot beneath the Pacific Plate being responsible for creating new volcanoes and thus new islands like Kauai over millions of years.