Here is a link to Climate Feedback, a worldwide network of scientists sorting fact from fiction in climate change media coverage. Their goal is to help readers know which news to trust.
Here is a link to Media Matters, a news watchdog site whose political biases, and Democratic party loyalties, are clear. But they offer solid research and frequently rapid-response analysis of media treatment of climate change.
Two academic outposts cover polling data and the receptiveness of audiences for climate news and information. The Yale Program on Climate Change Communication and the Center for Climate Change Communication often partner on projects.
At the University of Colorado, the Media and Climate Change Observatory does monthly content counts on how heavily (or not) climate issues are being covered internationally.