Even if you haven't been keeping up with mainstream news, you probably still already know that former Vice President Al Gore, along with the IPCC (Intergovernmental Panel on Climate Change) won the 2007 Nobel Peace Prize "for their efforts to build up and disseminate greater knowledge about man-made climate change, and to lay the foundations for the measures that are needed to counteract such change".
The point I'll make is that a good (should I say predominant?) amount of what we know about global warming, climate change, and Earth Science in general comes from data gathered from satellites. This data is stored in places like the National Snow and Ice Data Center, which Al Gore visited a few days ago.
Any approach to seriously understand the Earth on a global level, or to monitor changes to the environment and any attempts to adjust such change, is going to need the global view that would have to come from a lot of satellite hardware. It would also be very useful to have a better understanding of the Sun and how it affects the Earth, as well as the environments of other planets and moons so we can scientifically compare them to the Earth's environment.
That's going to take advances in cheap, reliable access to space, and cheap, reliable space infrastructure. We haven't been doing so well in these areas, so one hopes that innovative approaches like space prizes will help.
If we can get to this point, space also has a lot more to offer. A near-term possibility that could be helped with the prize approach is suborbital Earth monitoring, space hardware testing, and satellite instrument calibration platforms. Of course there are many more ambitious space goals - I'm sure you've heard of at least a dozen of them - that would help the Earth's environment. These tend to not be just science-oriented, but business-oriented (i.e., clean energy utilities, moving industry out of the biosphere, etc). Unfortunately they are all out of reach until we at least solve the access and LEO infrastructure problems.