I am looking for a detailed online source of maps of desert areas in North America produced annually since 1979, freely available (ideally). Could anyone point me in the right direction please?
To my knowledge, that does not exist. However, if you are very dedicated to this concept, you could make them using climate definitions and the PRISM datasets (prism.oregonstate.edu/recent) that could be supplemented/validated by satellite observations in more recent years (earthexplorer.usgs.gov or Google earth engine).
Multi-Resolution Land Characteristics (MRLC) Consortium https://www.mrlc.gov/ might get you part way there. 1979 is ambitious, since Landsat 1 was launch launched in July 1972 ( https://landsat.gsfc.nasa.gov/wp-content/uploads/2023/09/Landsat_Timeline_20230908-scaled.jpg ). Landsat 1,2, and 3 were still working out the technology, so there are generational differences which add to normalizing classification of the data across four decades until now. Worth a read, just to get an idea how complex your question is:
Homer, C., et al. "Completion of the 2011 National Land Cover Database for the Conterminous United States—Representing a Decade of Land Cover Change Information." Photogrammetric Engineering and Remote Sensing (2017). https://www.asprs.org/a/publications/pers/2015journals/PERS_May_2015/HTML/files/assets/common/downloads/PE&RS%20May%202015.pdf