Hi,
I see this thread being read and quoted quite often, and I am a bit surprised.
For me, andfor wikipedia, surface albedo is defined as “the ratio of irradiance reflected to the irradiance received by a surface”.
This means you have to integrate reflectance over all bands (accounting for solar irradiance, as explained in the paper), but you also need to integrate over all directions of observations (and there is a cosine in the formula). Doing so you get a black sky albedo. If you integrate again over all illumination directions, you get a white sky albedo.
The formula provided in the paper is not a broadband albedo, but a broadband reflectance. Depending on the directional signature of the observed surface (how the reflectance changes as a function of observation and illumination geometry), the broadband reflectance and broadband albedo may differ a lot. For a desert, whose directional signature is flat, it may be valid, but probably not for vegetation (even if I do not have the values of errors in mind).
It is not easy to compute albedo from Sentinel-2. Because Sentinel-2 observes very close to nadir, it does not provide the directional signature. You have to get it from another sensor, but sensors which provide directional signatures provide them at a coarse resolution. Computing an accurate albedo is therefore a matter of research.
As I said, I am not an albedo specialist, and don’t have the values in mind, but if you need an accurate albedo, use the formula from the reference above with caution.
For further reading :
Bsaibes, A., Courault, D., Baret, F., Weiss, M., Olioso, A., Jacob, F., … & Kzemipour, F. (2009). Albedo and LAI estimates from FORMOSAT-2 data for crop monitoring. Remote sensing of environment , 113 (4), 716-729.
Franch B, Vermote E, Skakun S, Roger J-C, Santamaria-Artigas A, Villaescusa-Nadal JL and Masek J (2018) Toward Landsat and Sentinel-2 BRDF Normalization and Albedo Estimation: A Case Study in the Peruvian Amazon Forest. Front. Earth Sci. 6:185.
Franch, B., Vermote, E. F., & Claverie, M. (2014). Intercomparison of Landsat albedo retrieval techniques and evaluation against in situ measurements across the US SURFRAD network. Remote sensing of environment , 152 , 627-637.