MEXICO CITY — On bad days, you can detect the stench from a mile away, drifting over a nowhere sprawl of highways and office parks.

When the Grand Canal was completed, at the end of the 1800s, it was Mexico City’s Brooklyn Bridge, a major feat of engineering and a symbol of civic pride: 29 miles long, with the ability to move tens of thousands of gallons of wastewater per second.

It promised to solve the flooding and sewage problems that had plagued the city for centuries. Only it didn’t.

The canal was based on gravity. And Mexico City, a mile and a half above sea level, was sinking, collapsing in on itself. It still is, faster and faster, and the canal is just one victim of what has become a vicious cycle.

Always short of water, Mexico City keeps drilling deeper for more, weakening the ancient clay lake beds on which the Aztecs first built much of the city, causing it to crumble further.

It is a cycle made worse by climate change. More heat and drought mean more evaporation and yet more demand for water, adding pressure to tap distant reservoirs at staggering costs or further drain underground aquifers and hasten the city’s collapse.

Much is being written about climate change and the impact of rising seas on waterfront populations. But coasts are not the only places affected. Mexico City — high in the mountains, in the center of the country — is a glaring example.

The world has a lot invested in crowded capitals like this one, with vast numbers of people, huge economies, and the stability of a hemisphere at risk.

One study predicts that 10 percent of Mexicans ages 15 to 65 could eventually try to emigrate north as a result of rising temperatures, drought, and floods, potentially scattering millions of people and heightening already extreme political tensions over immigration.

The effects of climate change are varied and opportunistic, but one thing is consistent: They are like sparks in the tinder. They expose cities’ biggest vulnerabilities, inflaming troubles that politicians and city planners often ignore or try to paper over. And they spread outward, defying borders.

Around the world, extreme weather and water scarcity are accelerating repression, regional conflicts, and violence. A Columbia University report found that where rainfall declines, “The risk of a low-level conflict escalating to a full-scale civil war approximately doubles the following year.’’

The Pentagon’s term for climate change is “threat multiplier.’’

And nowhere does this apply more obviously than in cities.

This is the first urban century in human history, the first time more people live in cities than don’t, with predictions that three-quarters of the global population will be urban by 2050. By that time, according to another study, there may be more than 700 million climate refugees on the move.

Mexico City occupies what was once a network of lakes. In 1325, the Aztecs established their capital, Tenochtitlán, on an island. Over time, they expanded the city with landfill and planted crops on floating gardens called chinampas, plots of arable soil created from wattle and sediment. The lakes provided the Aztecs with a line of defense, the chinampas with sustenance.

Then the conquering Spaniards waged war against water, determined to subdue it. They replaced the dikes and canals with streets and squares. They drained the lakes and cleared forestland, suffering flood after flood, including one that drowned the city for five straight years.

Mexico City today is an agglomeration of neighborhoods that are really many big cities cheek by jowl.

Overseeing the city’s water supply is Ramón Aguirre Díaz, director of the Water System of Mexico City, who is unusually frank about the perils ahead.

“Climate change is expected to have two effects,’’ he said. “We expect heavier, more intense rains, which means more floods, but also more and longer droughts.’’

The problem is not simply that the aquifers are being depleted. Mexico City rests on a mix of clay lake beds and volcanic soil. Areas like downtown sit on clay. Other districts were built on volcanic fields.

Volcanic soil absorbs water and delivers it to the aquifers. It’s stable and porous. Picture a bucket filled with marbles. You can pour water into the bucket, and the marbles will hardly move.

Stick a straw into the bucket to extract the water, and the marbles still won’t move. For centuries, before the population exploded, volcanic soil guaranteed that the city had water underground.