## Potential issue in 6S ground reflectance equation

### Description

A user reported a potential bug in OTB implementation of Vermote’s 1997 6S paper. Here is the full text of their message:

Greetings,

I see a discrepancy between the ground reflectance equation 12.10 and Vermote’s 1997 6S paper equation 1. Should the t(g)allgass term be the total gaseous transmission and not the spherical albedo of the atmosphere? Should your variable Sx be the spherical albedo of the atmosphere.

Also, Vermote’s equations appears to have Tg (gaseous transmission) multiplied by the atmospheric reflectance term. This appears to be missing in your equation. Below are both equations solved for the ground reflectance.

OTB (12.10): rho(s) = rho(TOA) - rho(ATM) / (Tup*Tdown*Tg + Sx*rho(TOA) – Sx*rho(ATM)) Vermote (1): rho(s) = rho(TOA) - Tg*rho(R+A) / (Tup*Tdown*Tg + S*rho(TOA) – S*Tg*rho(R+A) ) http://6s.ltdri.org/files/publication/Vermote_et_al_1997.pdf

rho(ATM) = Tg*rho(R+A)? Or did something change with 6S between Vermote’s paper and OTB’s implementation. Sx = S?

Thanks,

### Steps to reproduce

To be confirmed.

### Configuration information

NA