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I am working on NDWI and MNDWI indices using Landsat 5,7 and 8 to identify permanent water bodies in two images by mosaicing them. When using Landsat collection 1 data I have performed atmospheric and radiometric correction on all of them. But recently I want to download Landsat Collection 2 Level 1 data because I only need to work with a few bands.

Do I need to do atmospheric and radiometric corrections for Landsat collection 2 level 1 data?

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The radiometric quality seems to be higher than in collection 1, so I do not think a radiometric correction is necessary. With regard to the atmospheric correction, Level-1 data are delivered at Top of Atmosphere Radiance (after scaling), and it is always better working at Bottom of atmosphere for reliable spatial and temporal comparison. However, it is not always a requisite when working with normalized indices.

To sum up, I suggest you should correct them atmospherically only.

Reference: https://www.usgs.gov/core-science-systems/nli/landsat/landsat-collection-2-level-1-data?qt-science_support_page_related_con=1#qt-science_support_page_related_con

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