The dam, completed in 1963, was erected as a compromise.

In 1956 the Colorado River Storage Project Act paved the way for the construction of four large power-generating dams in the upper basin of the Colorado River — a project meant to match the dam development that the southern half of the river had already seen. The Bureau of Reclamation had zeroed in on a dam site on a tributary in northwestern Colorado called the Green River, where the resulting reservoir would have submerged a tract of treasured, fossil-laden parkland called Dinosaur National Monument. Environmentalists, led by David Brower, executive director of the Sierra Club, fought passionately to preserve the monument in one of the nation’s epic conservation battles.

As a compromise, all sides agreed instead to build a dam at a remote spot in southern Utah called Glen Canyon, in a region far from highways, about 200 miles northeast of Las Vegas. Glen Canyon Dam would help normalize the erratic flows of the Colorado and flood a land of barren sandstone domes and inaccessible dendritic canyons — transforming them into a surreal oasis called Lake Powell.

The result was an elegant, sweeping structure engineered in an arch bowing against the pressure of the water, enabling a relatively thin sheet of concrete to withstand unfathomable forces. The reservoir behind the dam would be so deep that the sheer height of the water promised to generate enormous currents of power. By all measures, its completion was a feat.

It took 17 years for the reservoir to fill; 19 years later, a steady decline began. Thanks to the steady overuse of the Colorado River system — which provides water to one in eight Americans and supports one-seventh of the nation’s crops — Lake Powell has been drained to less than half of its capacity as less water flows into it than is taken out.

That relative puddle is no longer capable of generating the amount of power the dam’s builders originally planned, and so the power has become more expensive for the government to deliver, with the burden increasingly falling on the nation’s taxpayers. In 2014 the agency managing power at the dam spent $62 million buying extra power on the open market to make up for shortfalls. The dam’s power sales are relied on to pay for the operations of other, smaller, dams and reservoirs used for irrigation in the West, and as Glen Canyon crumbles financially, so might the system that depends on it.

But it is not just the reservoir’s overuse that is causing it to shrink. More than 160 billion gallons of water evaporate off Lake Powell’s surface every year, enough to lower the reservoir by four inches each month. Another 120 billion gallons are believed to leak out of the bottom of the canyon each year into fissures in the earth — a loss that if tallied up over the life of the dam amounts to more than a year’s flow of the entire Colorado River.