IGUAZÚ NATIONAL PARK, Argentina — Few times in my life have I felt the enormity and power of nature. Standing at the edge of Iguazú Falls, on the Brazil-Argentina border, was one of them.

Iguazú isn't just one imposing fall, but a complex of cascades spanning more than a mile across both countries. A rain-soaked October in Brazil has sent near-record volumes of water surging over its towering cliffs. Scientists link the relentless rains to this year's Super El Niño , causing extreme weather events across the globe.

But what a spectacular force of nature for the lower-than-average number of tourists who braved the deluge this month. The roar of the rushing Iguazú river under your feet penetrates your body; your eyes strain to keep up as the rusty swells disappear over the steep precipice.

One day during my recent visit, officials registered nearly 12 million liters (more than 3 million gallons) of water per second tumbling over the falls. That's 10 times the normal flow.…