Can surface reflectance be negative ?

Olivier Hagolle, 6 avril 2021

Here is a frequently asked question :

I noticed, in such L2A product processed by MAJA, that some pixels had negative reflectances, is it normal ?

No, it should not happen, but the fact it happens is not entirely surprising, I will explain it below. Unlike negative reflectances, reflectances greater than one can exist, this is explained here.

Reflectance should be positive, as it corresponds, with a normalization factor, to the ratio of the radiance reflected by the earth’s surface (positive or zero) and the illumination received by this surface (positive or zero). This said, the surface reflectances observed in nature can be very low, of the order of 0.01 to 0.03 for example, in the following cases:

in cloud or topographic shadows
on slopes facing away from the sun
over water or lava flows
over dense vegetation in the visible

Atmospheric corrections are not without error. Our estimates of MAJA performance have shown that the standard deviation of atmospheric correction errors on locally uniform scenes is about 0.01. These errors are probably mainly due to errors in estimating the optical thickness of aerosols or to errors in the choice of the aerosol type. MAJA is however one of the software that provides the best atmospheric correction performances, as shown by the ACIX-I experiment.

RMS errors for surface reflectances obtained by different atmospheric correction methods, compared to reflectances obtained using in-situ optical properties from the Aeronet network, using the 6SV radiative transfer code. These results are from the ACIX-I experiment. As the LaSRC chain also uses 6SV, this criterion gives a significant advantage to this atmospheric correction method. These performances do not take into account the adjacency effects and the quality of their correction. For each wavelength, the best performances are written in red, and the second best performances in blue.

A standard deviation of 0.01 means that in about 1% of the cases, the errors can be greater than 0.03. In this case, the reflectances of the few cases described above can become negative. They occur in general when the optical thickness of aerosols is overestimated. The errors of the surface reflectances can also be larger than the estimate provided above, due to adjacency effects and residuals of their correction. We are currently working on improving the adjacency effects correction, especially using the ROSAS station located in Lamasquère.

So how do we deal with the unavoidable negative reflectances in MAJA? We provide two types of output products from MAJA: reflectances before correction of topographic effects (coded SRE for Surface REflectances), and reflectances after this correction (coded FRE for Flat surface REflectances)

SRE : we leave the negative reflectances in the product, because we see no point in hiding these errors, which are also present on all the pixels
FRE : as the correction of the effects of the relief can lead to multiply by 5 the reflectances, and thus to make them even more negative, we put these reflectances at zero.

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