BEIJING — The Obama administration's push to help clean up China is emerging as a bright spot in a relationship rife with economic and strategic tensions. The failure of the world's two largest economies to agree on tough carbon emissions limits four years ago doomed substantial progress on climate change and left each side blaming the other. Since the Copenhagen talks, however, the U.S. and China have ramped up their environmental cooperation as repeated outbreaks of thick, acrid smog have virtually shut down major Chinese cities and cost the country hundreds of billions of dollars a year. “For a period...