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There are many spectral indices in literature. However, the formulas mostly refer to landsat imagery, and thus the corresponding spectral bands.

Question: How can a formula that was originally designed for Landsat be converted into a Sentinel formula?

Problem: Not all Landsat and Sentinel bands seem to correlate well, as Sentinel has a higher number of bands that often also differ in the spread of wavelengths covered. These differences have to have some influence on the results when adjusting the formula from Landsat to Sentinel. I'm especially confused in Landsat8 Band 5, which is covered by Sentinel Band 8 and 8a. Furthermore, Sentinel data has Bands 5,6 and 7, which are not covered in Landsat8 data. Older Indices are missing these spectral bands completely.

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In some bands they also strongly differ reflectance.

Spectral responses of Landsat 7 ETM+, Landsat 8 OLI and Sentinel 2 MSI in the visible and near infrared. Data from ASTER Spectral library, Landsat Program and ESA Copernicus Sentinel Program. https://scientiaplusconscientia.wordpress.com/2017/03/04/remote-sensing-comparison-landsat-sentinel-visible-infrared-spectrum/

Example: Let's take the Enhanced Built-Up and Bareness Index (EBBI) formula as an example for discussion (As-syakur 2012). Band 4 and 6 are easy to pick (Sentinel 4 and 11, respectively)

Next, the formula states to take the Landsat 5 Band. When converting it to Sentinel, the question arises whether to take Band 8 or Band 8a.

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    I don't think there is a right or wrong choice, I would test both and see which suits me best. However, most indices translate Landsat-8 band 5 to Sentinel-2 band 8. It has a better spatial resolution than band 8a and it has more resemblance to other sensors NIR bands (L7, ASTER, L4, L5...), even though in L8 NIR is narrower. – Albert Mar 23 '18 at 10:29
  • You are right that most translate it with band 8 instead of Band 8a, and I think the spatial resolution is the main reason, as you stated. There is an interesting page with an overview of some Sentinel Indices, and none of these actually uses the band 8a. sentinel-hub.com/eotaxonomy/indices – loloj0 Mar 23 '18 at 11:35
  • I recommend you check Index Database (indexdatabase.de), which has a nice database of indices for both sensors. – Grega M. Mar 23 '18 at 13:15
  • That's a nice overview for many sensors, but I find it strange that they used Band 9 for NIR and Band 5 for Red for Sentinel-2. All other sources I know use 8 and 4. I tested their MSAVI formula and it produces way to small values – loloj0 Mar 23 '18 at 14:52
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In short, I'd recommend to use Sentinel-2's band 8a as the closest equivalent to Landsat 8's band 5, otherwise the band matching should be straightforward.

The reason for this lies in the spectral sensitivity of the bands, expressed by the spectral response functions of the two sensors. Sentinel-2's band 8a is narrow, and so is Landsat 8's band 5. These bands were designed to avoid a small water vapor absorption feature in the near-infrared region, and thus "break" with tradition of the Landsat TM series to some extent. Overall, the corresponding bands of Sentinel-2 and Landsat 8 seem to agree quite well despite some differences in their spectral response functions. See https://doi.org/10.4236/ars.2017.62011 for more on this, including an empirical comparison.

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