NEW YORK—Former President Bill Clinton and New York City Mayor Michael Bloomberg announced a new climate initiative Monday to help cities measure their risk for severe weather and natural disasters. The hope is to help curb the impact of deadly storms like Superstorm Sandy, which devastated parts of New York City last October. The project will be run through C40, a coalition of major cities around the world that united to study the impact of climate change on their municipalities. The group, chaired by Bloomberg, merged two years ago with the Clinton Climate Initiative—an offshoot of Clinton’s philanthropic foundation. Known...