URING THE LAST WEEKEND of summer, the streets of Green River, Utah were filled with melons. Farmers rapidly chopped slices of peach-colored crenshaws and classic red crimson sweets to hand out in the town’s park. The fruit gave off a sugary, earthy aroma, and friends and family embraced each other with hands sticky from its juice. Pictures of melons dotted everything from bikini tops to bucket hats. A parade led by the town’s major melon-growing families featured a John Deere tractor pulling a 20-foot-long, 10-foot-tall wooden watermelon slice, originally constructed back in 1960.