I would like to know the definition of Level2 ground surface reflectance. For example, up to how many kilometers above the ground is it defined as surface reflectance? It is possible that I am mistaken in my perception of surface reflectance in the first place.

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Surface reflectance is defined as the "fraction of incoming solar radiation that is reflected from the Earth's surface to the Landsat sensor" (USGS Landsat Missions, link). To clarify, surface reflectance is not measured "above the ground" but at the ground. For more information on surface reflectance, the Science Direct resource is a good place to go, especially looking at the "Definition of Reflectance Quantities" in Earth's Energy Budget by Y. QU that is referenced on the page. Here's the link to the Science Direct page.

The L2 product, specifically, is the surface reflectance product corrected for atmospheric effects. It also includes more data products than L1. Some additional documentation for you on the L2 product can be found at this link.

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