I'm doing a temporal analysis of NDVI and temperature over 17 years, necessitating data from Landsat 5,7, & 8. I'm interested in using level-2 Landsat data available from https://espa.cr.usgs.gov/ordering/new/. I would be able to directly download NDVI as well as brightness temperature, which would save me a lot of time. However, the USGS is explicit that the algorithm used to calculate surface reflectance for Landsat 8 is not the same as the algorithm used for previous satellites.
My question is: are the level-2 products from Landsat-8 comparable on an apples-to-apples basis with Landsat 5 or 7 level-2 products, or does this kind of comparison require some sort of adjustment to the data? I haven't been able to find an answer to this question online.