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The world's great cities could hold the key to the prosperity of the human race. Yet a comprehensive new study points to a worrying trend: The water they need to grow is getting more expensive, because they're failing to protect the nature that purifies it.

Cities are amazing engines of productivity. As the hubs of our modern societies, they mix together people with a diversity of skills and create fertile ground for learning and invention. In many respects, bigger tends to be better. Larger cities have more patents and inventions per person, and achieve better energy and resource efficiency thanks to economies of scale. For example, they require less conducting cable per person to carry electrical power where needed.

Concentrating people in cities also leaves more space for nature. It's one reason that Paul Romer, recently appointed as chief economist of the World Bank, has been championing the idea of charter cities — brand new cities that we could build and use to experiment with large-scale innovations in technology or government. Dozens of such cities could help us explore more sustainable ways of living, and also help meet the need to house many of the additional 3.4 billion people expected to be living by 2050.

It turns out, though, that protecting the surrounding nature is also crucial for cities to work. Any city draws its clean water from a natural watershed area — some close by, others farther away. The rainfall that drains into the area is filtered and purified by natural land cover — forests, marshes and grasslands — before entering as the "raw water" of treatment facilities. The water for New York City, for example, comes from large reservoirs located an average of 100 miles away in upstate New York.

As cities have grown, the land in their watersheds has been cleared to make way for housing, factories and agriculture. As a result, water quality has declined. Agricultural runoff, for example, boosts concentrations of nitrogen, phosphorous and sediment. Treatment centers must then remove these impurities, requiring the use of increasingly complex and costly technologies.

A new study, led by ecologist Robert McDonald of the Washington-based Nature Conservancy, suggests that the cost of water treatment is becoming a very large burden on a global scale. Looking at changes from 1900 to 2005 in the watersheds of 309 large cities, all with populations larger than 750,000, it finds that more than 90 percent have suffered degradation, and that nearly one third experienced a significant rise in treatment costs — many by more than 50 percent.

The study confirms what environmental economists previously only suspected: The loss of natural water purification capacity is systematically increasing the cost of treatment around the globe. The best estimate puts the added expense at more than $5 billion per year. And it's set to get worse: Watershed degradation is expected to become more severe in the next decade or so, as cropland continues to expand. By 2030, global fertilizer use is projected to rise by nearly 60 percent.

The lesson is that our cities will require concerted investment in watershed preservation. The good news is that it need not be terribly expensive: Targeted projects can make a big difference. Since 1997, for example, the New York City Department of Environmental Protection has moved to protect more than 130,000 acres of valuable watershed, and the city now has very low water treatment costs relative to other U.S. cities.

New York's forward thinking can and should be replicated globally. McDonald and others estimate that roughly one in four cities — home to about 800 million people — could reap a positive return on investment aimed at conserving watersheds. In other words, it's worth doing, and it would be an important step toward securing the kind of environment we need to survive.

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Mark Buchanan, a physicist and science writer, is the author of the book "Forecast: What Physics, Meteorology and the Natural Sciences Can Teach Us About Economics."