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WASHINGTON — When almost a month’s worth of rain deluged this city on Monday morning, turning streets into rivers and basements into wading pools, it showed just how vulnerable cities with aging water systems can be in the era of climate change.

The rainfall overwhelmed the capital’s storm-water system, much of it built almost a century ago to handle a smaller population, far less pavement and not nearly as much water.

“We’re still approaching this 21st-century problem with 20th-century infrastructure, and it’s completely inadequate,” said Constantine Samaras, a professor of civil and environmental engineering at Carnegie Mellon University. “And it’s only going to get worse.”

Updating that infrastructure will be enormously expensive, experts warn, not just in Washington but around the country. That’s not only because upgrades are required. In many cases, cities are facing huge backlogs in general maintenance.