Caution ! This post contains formulas !
Aerosols play a great role in the atmospheric effects. Aerosols are particles suspended in the atmosphere, which can be of several types: sand or dust, soot from combustion, sulfates or sea salt, surrounded by water... Their size ranges between 0.1 micron and a few microns, depending on the type of aerosol or on the air moisture. Their quantity is also extremely variable : rain can suddenly reduce their abundance (known as "aerosol optical thickness"). The abundance variations result in great variations of observable reflectances from one day to the next, and it is therefore necessary to know the quantity and type of aerosols, in order to correct their effects.
Unfortunately, to correct the effects of aerosols, there is no global aerosol observation network, and the only available data are local observations from the few hundred points of Aeronet network. Therefore, this network can not be used operationally to correct the satellite images over large areas.
Weather forecast models just start predicting the amounts of aerosols, based on satellite observations and modeling of sources and sinks and of the transport of aerosols by the winds, but these data do not seem to have sufficient accuracy yet to be used for the atmospheric correction of images.
Our atmospheric correction method, named MACCS, is therefore based on an estimate of aerosol optical depth from the images themselves. To understand how this method works, one must already understand the effects of aerosols on radiation. We have seen in this post, that the effects of diffusion can be modelled as follows (assuming the corrected gas absorption):
ρTOA = ρatm +Td ρsurf
The reflectance at the top of the atmosphere ρTOA (Top of Atmosphere) is the sum of the atmospheric reflectance ρatm and of the surface reflectance ρsurf transmitted by the atmosphere. We seek to know the surface reflectance, but for each measurement made at the top of the atmosphere, there are three unknowns to be determined. To separate the effects of the atmosphere and surface effects, we must use other information.
Dark pixel method
When the image includes a surface whose surface reflectance is nearly zero, the reflectance observed at the top of the atmosphere becomes ρTOA = ρatm. We can therefore deduce the atmospheric reflectance and using a radiative transfer model, the aerosols optical thickness (AOT). Finally, knowing the AOT, we can compute the diffuse transmission, and finally calculate ρsurf. An even simpler and more approximate version of this method consists in subtracting directly the reflectance of the dark pixel (or ρatm) to the entire image (neglecting the transmission) [Chavez, 1988].
However, this method assumes that there is a very dark area in the image (which is not always the case), and that the reflectance of the dark surface is known. The method also assumes that the amount of aerosols is constant over the image and it neglects the effect of terrain. The results obtained by this method can be quite inaccurate. In our method (MACCS), however, we use the method of black pixel determine the maximum value of the optical thickness in the area.
Multi Spectral Method, called "DDV"
If you know the type of aerosols in the atmosphere, it is possible to deduce the properties of aerosols in a spectral band from the optical properties in another spectral band.
If there are two spectral bands, there are two measures ρsurf and three unknowns (both surface reflectance in these bands, and the amount of aerosols). An additional equation can be obtained if we know the relationship between the surface reflectance of the two bands.
The method named "Dark Dense Vegetation" (DDV) is based on assumptions about relationships between surface reflectances of the dense vegetation exploiting the fact that the spectrum of dense green vegetation is quite constant. The most famous version of this method is that used by NASA for MODIS project [Remer 2005]. It connects the surface reflectance in the blue and red with those in the SWIR. This provides two equations for estimating the type of aerosol optical thickness. This method works well in temperate and boreal zones, but not in arid areas where it is difficult to find the dense vegetation. Early versions used the following equations:
ρBlue = 0.5 ∗ ρSWIR
ρRed = 0.25 ∗ ρSWIR
The following versions of the MODIS DDV algorithm are a bit more complicated but follow the same principle. Our work has shown that using the equation below allows a more accurate determination of the optical thickness, for less dense vegetation cover (NDVI to a 0.2) because bare soil brown also respect this relationship.
ρBlue = 0.5 * ρRed
(the exact value of the coefficient is adjusted according to the spectral bands of the instrument)
This version of the method, however, does not allow to determine the aerosol model. In the case of SPOT4 (Take5), the absence of a blue band does not allow us to use this equation, resulting in a slight loss in accuracy.
Multi Temporal Method
In most cases, the reflectance of the land surface changes slowly over time, while the aerosol optical properties vary rapidly from one day to another. We can therefore consider what changes from one image to another (apart from special cases often linked to human intervention) is associated with aerosols, and deduce the properties of aerosols and then correct for atmospheric effects. This method is too complex to be explained in detail here, interested readers can refer to [Hagolle 2008].
So that surface reflectance be nearly constant from one image to another, however, it is required that images be acquired at a constant angle. Indeed, the reflectance depend on the viewing angles : this is what we call directional effects. This method therefore applies only to satellite observations obtained with constant angle. It does not apply to standard SPOT data, but this condition is true for SPOT4 (Take5) data. It will also apply to Landsat Venμs and Sentinel-2.
Remer, L. A., and Coauthors, 2005: The modis aerosol algorithm, products, and validation. J. Atmos. Sci., 62, 947–973.
Hagolle, O and co-authors, 2008. « Correction of aerosol effects on multi-temporal images acquired with constant viewing angles: Application to Formosat-2 images ». Remote sensing of environment 112 (4)
Hagolle, O.; Huc, M.; Villa Pascual, D.; Dedieu, G. A Multi-Temporal and Multi-Spectral Method to Estimate Aerosol Optical Thickness over Land, for the Atmospheric Correction of FormoSat-2, LandSat, VENμS and Sentinel-2 Images. Remote Sens. 2015, 7, 2668-2691.