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Most Earth observation satellites consider large Solar Zenith Angle as undesirable are therefore do not process them. There are indeed several known image quality issues, such as low signal (inducing low signal-to-noise ratio) and the so called "chromatic artefact" (inducing distorted spectral signatures).

Low signal is due to the cosine relationship between the energy per square meter and the incidence angle.

As far as I understand at this stage, chromatic artefacts are due to the different behaviour of the light going through the atmosphere depending on its wavelength. This includes absorption and diffraction. However, it is not clear to me why it is so difficult to manage by atmospheric correction experts and why this has so much impact on the satellite images (considering that the satellite viewing angle is close to nadir).

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As you mention yourself, different wavelengths behave differently through the atmosphere. In theory, this can be counteracted through atmospheric correction, however, modelling the atmosphere accurately is a complicated matter, especially for medium and high resolution satellites where the required information is not acquired along with the images (due to spectral constraints).

Performing an atmospheric correction requires modelling the path and interactions that the light will take through the atmosphere. When that path is long, as it is when either the sun and/or the sensor zenith angle is high, the light will be scattered more and the artifacts start appearing. To counteract this, a set of correction factors are calculated. Some satellites (usually coarse resolution satellites) carry sensors to acquire the information required to calculate these corrections factors.
However, when working with medium and high resolution imagery, you'll usually be looking at retrieving atmospheric parameters from coarse resolution imagery (usually only available in situations with "normal"/"low" solar zenith angles) or modeled data. This works well for low zenith angles, but when working with high zenith angles, the light will have passed through multiple "pixels" worth of atmospheric parameters required for determining the correction parameters - atmospheric parameters that usually aren't provided with enough variability as a function of elevation.

All in all, while the imagery can be corrected sufficiently with full information, getting that information without a significant field campaign coinciding with the imagery acquisition is not feasible. As such, it is more palatable to reduce the amount of trouble that you're facing, by limiting the solar zenith angle. Due to the sun-synchronous orbits of the majority of EO-satellites, the limit on solar zenith angle only means that acquisitions in the regions far from equator are rejected during the local winter, which in general is of little concern, due to the high snow cover in those areas that those times.

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    thanks for this answer. I am looking at the snow, so discarding winter images is not the best option. If I understand well, the main obstacles for a good atmospheric correction with high SZA is the fact that most algorithm consider the total optical thickness of a vertical column of atmosphere, but oblique light rays get accross different layers of atmosphere depending on the elevation ?
    – radouxju
    Commented Jul 27, 2016 at 10:58
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    also, you mention that coarse resolution satellites retrieve atmospheric parameters from own spectral bands, but then why does it seem not to work with large SZA ? Do you think that it would be possible ?
    – radouxju
    Commented Jul 27, 2016 at 11:04
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    @radouxju, which systems are you referring to? For example, MODIS acquires its own atmospheric parameters, which are used for correction, but few other systems actually do this. Commented Jul 27, 2016 at 11:09
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    MODIS does and so does Sentinel-3. But both are limiting their acquisitions with a maximum SZA (86.5 and 80° respectively). I would like to understand better why there are no standard correction at those latitudes as I guess that this is the main reason for the cut off.
    – radouxju
    Commented Jul 27, 2016 at 11:17
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    The combination of a very long path through the atmosphere, a complex set of equations and very few uses for the data makes it a unlikely area of focus. Perhaps you could look at passive microwave or SAR methods for your snow mapping? Commented Jul 27, 2016 at 11:32
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In addition to the complexity of the atmospheric correction due to the slant path penetrating the atmosphere, large solar zenith angle portion of the image can also introduce sun glint effect when viewed by large zenith angle. These sun glint effect are also different for different wavelengths, thus the colors are distorted.

In general, this is caused by the coupling of surface and the atmosphere, and this coupling effect is also dependent of wavelengths.

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