Atmospheric Error and Correction
what is that process atmospheric correction is the process of removing the effects of the atmosphere on the reflectance values of images taken by satellite or airborne sensors. Here it has been mentioning the reflectance value these values can be also an emittance value. So the atmosphere correction is the process of removing, the facts of the atmosphere as I have already said that this is because of complications within the atmosphere about the radiation this is really challenging. So large amounts of images as we know are being collected by satellites and have already been collected by various satellites of various countries. And these are largely contaminated or affected by the atmosphere or the particles which are present and gases. And almost all images are suffering from either absorption scattering of the radiation of the earth's surface.
So you see an image that will be having some effects on the atmosphere, I will let me give you one example. Like during monsoon time in India or especially in the winter monsoon time just after the rain when sunlight is there even our visibility alone the horizon increases very significantly. So think if at that time satellite is over passing it will acquire very clear image why. Because the rain will reduce you know this absorptions thing, absorption phenomena of absorption materials from the atmosphere. Because there might be dust particles, there might be aerosols and some other things which are present. And all these because of rain they will come on the ground and therefore the atmosphere becomes very clean.
So sometimes just after the rain if one is lucky and a satellite is overpassing get a very clear image. And clear image means it is suffering from fewer atmospheric effects, less because absorption means scattering. Once these particles are only a little are present then obviously the scattering and absorption would be less image would be clear. So this can be seen even on the ground just after the rain if sunlight comes there.
So basically the main purpose of atmospheric correction is to retrieve the surface reflectance basically minus distortions induced by an earth's atmosphere. And this characterizes that basically these surface reflectance which characterizes the surface properties from remote sensing images by removing atmospheric effects. Now there are different approaches some are implemented easily and some are very difficult to implement because a lot of input data is required. So correction approaches are sophisticated approaches as computational depending and have only been validated for a few small scale studies. If I want to do it regularly on all the images it is not possible. So that is why I have been using the word challenging for removing 100% removal of atmospheric distortions. Though there are algorithms, a lot of algorithms are there, models are there through remove these atmospheric distortions, 2 major steps which are done through these algorithms.
The first one is the optical characteristics of the atmosphere are estimated and how these are estimated using special features of the ground surface or by direct measurements of atmospheric constituents or by using theoretical models. Now we will spend some time on this particular sentence here. If there are special features on the ground that means if you are having an object which is having very high reflectance, very high (()). Then you can take that one as one of the references how to suppose you are having a patch that you expect that it should be having in 8-bit image scenario, it should be having the highest reflection close to saying 255. Suppose it register reflection in the pixel is 2 250, so after seeing the image of that pixel I know that because of absorption the remaining 5 value has not come. So that means to say if I adjust by 5 then probably I have got rid of atmospheric distortions. So using special features, now every image cannot have special features because images are being acquired regularly. And whenever there is a revisit or satellite and various satellites are involved. So it is very hard in practical terms that get a special feature present within the image, so this possibility is very rare.
However this is one way of getting rid of atmospheric correction, the second one is by direct measurement of atmospheric constituents. So if you are having some other method of metrological stations or profiling or other things. By which you know what is the concentration of aerosols, what is the concentration of different gases which are creating distortions in different parts of EM spectrum absorption in scattering. And if that information of that particular time when satellite image was acquired, if that is available then this technique can work very well. Again it is very difficult because all the time satellites are over passing and too many inputs are required about atmospheric constituents. For that particular time when the image was acquired, so this itself is also very challenging. Now the third the most popular one is using theoretical models and if you go through the demerits about this that everything is fixed but same time we know the atmosphere is very dynamic. So theoretical models may also bring some level of atmospheric distortions corrections but not fully. So the problem lies here because of all these complications which are present within the atmosphere. So various quantities that mean the atmospheric constituents to the atmosphere correction can then be computed by radiative transfer algorithm given the atmospheric optical properties. And another one that the first approach was the like this the second approach can be that corrected by
inversion procedures that drive the surface reflectance. So again when we go for inversion again a lot of things will be assumed there. Anyway, this is one way of a very quick way of getting rid of atmospheric distortions without
bringing any more data or many more inputs about atmospheric constituents assuming that within this image I should have the full dynamic range pixel values occupied the full dynamic range. In 8 width scenario that is 0 to 255, so like when I see this image and the corresponding is 2 grams. What I see is that this also recalls I also discuss the LUT lookup table. So now the lookup table is been used here.
So on the y axis, this is the input histogram as you can see it is restricted to the very beginning values only up to the maximum value is up to 100 and the minimum value is around 40. And therefore the image which is seen here this image is completely black because it is not occupying the full dynamic range which is available between 0 to 255. Assuming that this image is having some high reflex because these clouds are taking that part of the histogram or other absorptions phenomena are creating or you know taking this beginning part of my histogram means lower
values. And this reflection by the cloud is being occupied by the higher value. So we assume that this is the situation that means I can if I stretch it linearly stretch it then I what I am going to do it I will you know occupy the full dynamic range that is in 8 width scenario between 0 to 255 and my image may become something like this. So also it is shown in the look-up table that as soon as it touches here then it is just going to the top that is 255 value. So 2 things are here, one is atmospheric correction by a short of simple linear stretch or contrast stretch and the second thing also use of lookup table. So this is an example of Landsat TM 3 band on the left side and this is of the Sudan-Eritrea border. And you can realize how quickly one can get rid of atmospheric correction by applying simple linear contrast stretch.
But these will also this method is short of a brute force method if there is no information or input from the atmosphere. So whatever the atmospheric conditions we have not bothered and just got rid of these corrections. So this is again this cannot be extended for atmospheric correction but when we do not have much input data available neither a specific feature of the ground surface nor we do not have or atmospheric constituents or theoretical models. Then this is the quickest way of doing atmospheric correction, now so atmospheric correction consists basically of 2 parts. One is the estimation of atmospheric parameters, so this is again estimation, a lot of assumptions would be there and retrieval of surface reflectance. And if the surface is Lambertian and all the atmospheric parameters are known then remote sensing images can be calculated to directly retrieve the surface reflectance.
So these are the conditions, so based on radiative transfer theory and assuming that the target is on a uniform Lambertian surface. And then the radiance can be received by a sensor or can be estimated assuming that sensor is getting like this and that is the top of the atmosphere TOA. And which can be expressed as an L, L0 + rho 1 - s rho and multiplied by TF d by pi. So where L0 is the atmospheric radiation path in case of a no surface reflection and T is the transmittance from the surface to the sensor and s is the atmospheric spherical reflectance, rho is the surface target reflectance, F d is the downward radiation flux reaching the surface. And according to this equation, the radiative received by sensors is given by L, L0, s, TF, and rho can be calculated by the radiative transfer model and used to calculate surface reflectance. So s at this stage you can realize that so many parameters are required and which are that parameter that is dynamic and that creates some problems.
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