I am getting very low reflectance values (mostly < 0.1) in Landsat 8 bands 2-7 on different scenes after rescaling from Digital Numbers (DN) to Reflectance. All scenes are in a tropical landscape with a lot of vegetation, secondary and old grown forests, agriculture (rice paddy) and urban areas & infrastructure. I see no reason that the majority of reflectance values should be that low.
I am using the formula for TOA planetary reflectance with correction for solar angle (provided on http://landsat.usgs.gov/Landsat8_Using_Product.php).
The mean DN value in Band 4 (red band) of my scene is 6937. Putting that into the formula for planetary reflectance
ρλ = ρλ'/cos(solar_zenith_angle)
ρλ' = Mρ * Qcal + Aρ
Mp = 2.0000E-05 (REFLECTANCE_MULT_BAND_4) Qcal = 6937 (DN) Ap = -0.100000 (REFLECTANCE_ADD_BAND_4)
(0.00002×6937-0.1)/cos(90-41.71087310) = 0.058
Is it possible, that the Ap value (-0.1) has to be "positive" (0.1) in the formula? If it was positive, my reflectance values would become more reasonable:
(0.00002×6937+0.1)/cos(90-41.71087310) = 0.36
For a comparison I also tried to use i.landsat.toar in GRASS 7 but I also get very low reflectance values (TOA, uncorrected) there. Here the mean reflectance values for each band after i.landsat.toar:
B2: 0.0898574 B3: 0.0747076 B4: 0.0582399 B5: 0.252395 B6: 0.160692 B7: 0.0808918
I am having this problem regularly also with other scenes from different locations.