Most mighty rivers enjoy a spectacular finale: a fertile delta, a mouth agape to the sea, a bay of plenty. But it had taken me almost a week to find where the Amu Darya comes to die.

Decades ago the river fed the Aral Sea, the world’s fourth largest lake, straddling the borders of modern-day Kazakhstan and Uzbekistan. Then Soviet planners engineered the waters to produce cotton. For a thousand miles, from the foot of the Pamirs and Hindu Kush, iron sluices line the Amu Darya, each suckling a maze of canals watering interminable cotton fields.

It is no secret that this thirst for cotton emptied the Aral Sea. Yet decades later, Uzbekistan’s authorities are still digging new canals, drawing the river’s water further into virgin desert. “White gold,” as the government calls it, is the country’s top cash crop; growing it employs roughly 30 percent of the population, but yields are sagging, temperatures rising, and farmers lamenting that the river is lower every year.

As I searched for its end, over hundreds of miles I saw it shallowing and narrowing.

The World Bank estimates that millions of people in Central Asia will be climate refugees by 2050. Mismanagement of water resources has already led to deadly unrest in Kyrgyzstan and Tajikistan, and probably fueled a bout of bloodletting here in western Uzbekistan two years ago.

In the 1980s, recognizing that the retreating Aral was not coming back, workers built a few miles of embankments to wall off the Amy Darya’s terminus in a reservoir about 12 miles from the former seashore. Kok-Su (Green Water) was intended to be a carp farm. But the idea was doomed. Thank the cormorants. Or maybe the poisoned run-off from the fields, heaving with pesticides and fertilizer. The fish that survive are too small to sell.

That doesn’t stop people from trying to coax a livelihood from the captive waters.

On one shore, I jumped up and down waving to a pair of men in a wooden dory. I wanted to hire them to take me upstream, around a bend, beyond the reeds, where I could see the Amu Darya enter Kok-Su to confirm for myself that this was its unmarked grave.

They stopped on the opposite shore. Through my telephoto lens, I could see them unload nets before one of them crossed to me.

He denied he had been fishing, despite the silvery scales sloshing over the floorboards. Anxieties about nosy foreigners here are common; the law is interpreted and enforced arbitrarily. He didn’t like questions or eye contact, preferring to row wordlessly as the oarlock clicked a steady rhythm.

Around the bend, winds rippled the sand bars. The source of water was unmistakable: There lay the Amu Darya, weak and piddly, trickling to its final resting place.