New Delhi, Nov. 15 -- Hwang Seong-yeol stood at the edge of a golden field, watching nervously as a combine harvester crawled through his rice, churning up mud and stalks. Its steady hum filled the damp autumn air as grain poured into a truck waiting at the other end of the muddy paddy.

It was the final day of what Hwang said was one of his toughest seasons in three decades of farming. He and other farmers feel helpless against increasingly erratic weather that they link to climate change and damage to their crops. It has complicated their work and cast uncertainty over their futures.

Hwang is one of five South Korean farmers who recently sued the state utility Korea Electric Power Corporation and its power-generating subsidiaries, alle...