Q. When people talk of the rising temperature of the earth, are they
talking about air temperature or surface temperature (skin or
meteorological)?
A. The discussion is about both skin temperature and lower tropospheric
temperature.
The data are spread amongst many instruments. There are ocean buoy,
ground station, radiosonde and satellite measurements. The devil is
in the details, for various researchers have had to institute strong
quality control to detect subtle trends within the much larger
seasonal and inter annual (El Nino, La Nina, Pacific and Atlantic
decadal oscillations) as well as instrumental effects. There is no
one agreed-upon compendium of measurements to which I can refer you.
Recently, a new set of observations has been added to the mix - sea
level and mass measurements. We can now measure mid-oceanic sea
levels to a faction of an inch from satellites and the mass of ice in
the polar regions from gravity anomalies.
I can only suggest that you look through the peer-reviewed literature
(Google Scholar is a good resource) and the various web sites
supported by NASA, NOAA and the Geological Survey. The scientific
publications are technical and filled with caveats that are very
important.
Bottom line is that yes, there is climate change. There appears to be
a warming. The fraction that is a long term trend, what is due to
solar, and what is due to human activity, and what the future course
will be are all areas requiring additional research.