# Albedo equation for Sentinel-2 data

[I hope I’ve got the right category]

are there any hints/links (e.g. to scientific papers) about the albedo equation appropriate for sentinel-2 data around here?

thanks

1 Like

I think you can have a look at this paper (for albedo look at formula 1 and Table 3):

Federico

Hi Federico,

I just tried to calculate surface albedo with the equation but I’m not really happy with the results.
So I tried to update the weighting coefficients according to equation 2 in the paper but I could’t solve the problem properly.
May you have any hint what exactly `dλ` is?

All the best
Martin

Dear Martin,

dλ refers to the spectral width of the band. It represent the spectral range that is measured by each band, according to the Spectral Response Function of the MSI sensor. For more details see the updated Sentinel-2 Spectral Response Functions at this link:

https://earth.esa.int/web/sentinel/user-guides/sentinel-2-msi/document-library/-/asset_publisher/Wk0TKajiISaR/content/sentinel-2a-spectral-responses

The parameter dλ generally corresponds to the Full width at half maximum (FWHM) of the response curve:

Federico

Dear Federico,

thanks a lot for your instant reply! One more question related to the second variable: Rsλ? Does it refer to the extra terrestrial irradiance? Is it related to the third column in table 3 of the paper which is the Esun parameter [ W m -²]? and where do i get Rsλ for wavelength .4 and 2.4 nm form?

Martin

Dear Martin,

yes, the term ‘Rsλ’ should refer to the ‘Esun’ value for a specific wavelength.
You can use the ‘Esun’ values in the table, they are computed from the solar constant (with light incident angle equal to zero and earth at the mean distance from sun).
If you need to compute instantaneous surface albedo (for a specific location and instant), you can compute the extra-terrestrial radiation as function of a specific sun zenith angle (which is function of latitude, day of year and time). However, I am not sure that ‘ωbi’ weighting coefficients could change that much.

For further information you can have a look at this presentation, specifically slides 30 to 35:

Federico

Thanks so much Federico for your help!
I also found the slides before and had the same idea but for now it okay to take the default values for lights incident angle and earth distance from sun. Because I’m still struggling to solve the equation although it shouldn’t be so complicated. Which value do I have to plug into the bottom part of the formula for Rsλ?
Is it the extraterrestrial solar irradiance for wavelength 2000μm?

Martin

Hi Martin,

the denominator in the formula for Rsλ should be the integration of the the extraterrestrial spectrum between 0.4 and 2.4 µm.

Federico

Hi Federico,

thanks again. I finally got it now and calculated the weights for the albedo:)

Martin

Dear Martin,

good new!
It would be nice if you could share you results, so that other users can have a background for their analysis.

Federico

Hi Federico,
Am trying to calculate the weighting coefficients as described in the paper but I seem not to get the values right. For a quick check, I divided the ESUN with the corresponding weighing coefficient for each band and the value for the denominator is approximately 14, 550. However, I get a totally different value when I sum the WRC’s spectral irradiance spectrum between 0.4 and 2.4 micrometers. How did you do the calculations?

Dear Sammy,

I did not perform the calculation myself, since I do not have a portable radiometer or sunphotometer to validate the results.

Federico

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.

3 Likes

Hi Guys,

I am new to all this remote sensing utilities and i have spent some time reading through the docs and installing snappy and all py libraries on windows (wich is nooo joke ahah)

I alm interested in computing surface albado maps, but I don’t understand how you are doing this ?
Are you using band math ? or python?

Could you give me some help on this ?

Thanks

Hi all,
as OHagolle correctly pointed out, the albedo described in Vanino et al 2018 (https://www.sciencedirect.com/science/article/pii/S0034425718303134) must assume the land surface being a Lambertian reflector. This formulation of albedo is defined as “broadband hemispherical-directional reflectance factor (HDRF)”

There is a typo in Table 3 of the same paper and the correct weighting coefficients for the calculation of the HDRF for Sentinel-2 are:

Band Number Center λ (μm) Spectral width Δλ (μm) Esun (W m-2) ωbi
1 0.443 0.020
2 0.490 0.065 1927 0.1836
3 0.560 0.035 1846 0.1759
4 0.665 0.030 1528 0.1456
5 0.705 0.015 1413 0.1347
6 0.740 0.015 1294 0.1233
7 0.783 0.020 1190 0.1134
8 0.842 0.115 1050 0.1001
8a 0.865 0.020
9 0.945 0.020
10 1.375 0.030
11 1.610 0.090 242 0.0231
12 2.190 0.180 3 0.0003

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@MNEUW Can you please share the method, how you get the value of the weighting coefficient for the albedo.

Thank You

Hello Sir, @FedericoF

I am trying to calculate the weighting coefficient, but not getting the exact result as I am using - UPbi = 0.535 and LObi = 0.439, Rsλ = 1927, dλ= 0.065
What values I am taking wrong, please suggest the right values. It would be very helpful to me.

Thank You

Dear @Dimple,

I would suggest to contact the authors of the cited publications in order to received a comprehensive answer to your question.
Regards,

Federico