It is a good question and quite complicated to answer. There are several algorithms to obtain surface reflectance from satellite-derive images, from the simplest as DOS to the most complex that include the atmospheric modelling with MODTRAN or 6S which require several inputs that are difficult to measure or estimated. By another hand, some types of scattering are wavelength dependent, this means that for some bands the effects are different. In a study published by Moran and Jackson (1992) where compared the surface reflectance calculated from satellite and aircraft-based data, they found positive and negative differences between them, this suggest that it is possible to get higher values in TOA.

https://pubag.nal.usda.gov/download/37763/PDF

Dear Muhammad,

It may be added or reduced by scattering.

Shorter wavelengths are more readily scattered that longer wavelengths. Light at shorter wavelengths (blue and violet) are scattered by small particles that include NO2 and O2. Since blue light is at the short wavelength end of the visible spectrum, it is more strongly scattered in the atmosphere than long wavelength red light. This results in the blue color of the sky. Rayleigh scatter is also responsible for haze in images.

Source: Principles of Remote Sensing (Tempfli et al.)

Dear Lizardo Reyna

Thanks for your valuable input and sharing an interesting article. I have checked the article and noticed that the authors have discussed the mean reflectance difference (Fig. 3) between surface reflectance estimates based on satellite and aircraft data. However, the asked question is related to the mean difference between TOA reflectance and surface reflectance. I have revised the question for better understanding.

Dear Mostafa Khosravirad

Thanks for your input - I have revised the question for better understanding. Please check it.

Dear Muhammad,

I think when is being spoken about satellite-derived. It means every calculation on satellite sensor bands data.so with correction or without it.

If it is correct. The surface reflectance(BOA) usually is greater than the top of atmosphere reflectance(TOA) due to the elimination of the effects of vapour and aerosol via atmospheric correction algorithm.

If the atmospheric correction is done well. Every band BOA is greater than TOA. But It usually is not correct for Vegetation indices. Because in the vegetation indices calculation, is use more than one band.

It may be one grow more than the that one.

Dear Mostafa ,

Thanks for your answer. According to my understanding, the attached equation i.e. TOA = Atmospheric path reflectance + surface function (SR, Total transmission and atmospheric back scattering ratio) indicates that TOA is a sum of two parts and atmospheric correction algorithms remove the 1st part (atmospheric path reflectance) from TOA to derive surface reflectance which should be less than TOA. May be I am wrong.

Could you please provide any reference to support this statement " The surface reflectance(BOA) usually is greater than the top of atmosphere reflectance(TOA) due to the elimination of the effects of vapour and aerosol via atmospheric correction algorithm" - I do not agree with you on this statement based on my understanding, I am sorry.

Interesting question. If you mean average reflectance of a band of a satellite image, I think it is possible for specific wavelengths. There are factors, which rise the apparent above atmosphere (TOA) reflectance to level higher than BOA reflectance - mostly downwelling radiation backscattering in the atmosphere. Such radiation is added to the radiation coming up from the surface. But there are also factors, which lower it, like absorption of upwelling radiance.

The net result of these and all the other effects of atmosphere on an image converted into TOA radiance pixel values can be theoretically both positive and negative. I think, that generally in bands in the visible region of electromagnetic spectrum the effect should always be positive, i.e. the average image band TOA reflectance > BOA reflectance. But in regions of spectra, where backscattering is relatively low, while absorption is strong, the TOA might be less than BOA (with clear atmosphere with low aerosol content). Based on that, I suppose such situation may happen especially for bands in spectral regions with strong absorption of atmospheric components, in the infrared part of the spectrum, where the scattering is not so strong, but you can still get image of the surface, if the atmosphere is clear - like for example Sentinel-2 band 9.

Based on the above I tried to look practically on clear image I use as a reference in relative radiometric correction: T33UWR tile of Sentinel-2A image from 2015-07-11, path R122, bands 04, 08 and 09, all at 60m resolution (04 and 08 are resampled to that resolution). Band 04 is red band in visible spectrum, 08 is narrow NIR band and 09 is in region with relatively strong atmopheric absorption, designed to show water vapour, but still showing the surface image fine and able to be atmospherically corrected. Both bands 08 and 09 have similar bandwidth and are relatively close to each other in the spectrum (865 and 945 nm). In advance I am sure 04 will have average TOA>BOA, 08 I suppose still TOA>BOA, but not sure about 09, it might be TOA

Dear Muhammad,

I attached a good pdf document.

at image attached, you can see transmission effects.

%=============individual Bands 1 and 2 of AVHR

in p1(min)=-4.2-0.7+0.02+0.05=-4.83%

in p1(max)=-12-4.4+0.06+0.12=-16.26%

in p2(min)=-7.7+0.006+0.003=-7.691

in p2(max)=-25+0.02+0.083=-24.897

%=================NDVI on bare and soil

in NDVI(min)=0.02-0.011-0.036-0.006=-0.033

in NDVI(max)=0.06-0.12-0.094-0.085=-0.239

%=================NDVI on forest

in NDVI(min)=0.006-0.036-0.086-0.022=-0.138

in NDVI(max)=0.017-0.038-0.23-.035=-0.601

https://modis.gsfc.nasa.gov/data/atbd/atbd_mod08.pdf

Dear Tomáš Brunclík

Thanks for your valuable inputs. As you mentioned that BOA > TOA is possible for spectral regions with relatively strong absorption of atmospheric components , i.e. red to infrared channels. Actually, I also found similar results for Landsat but I am looking for a reference to support these results. Do you have any reference?

I have further two questions:

1. How about if BOA > TOA at green wavelength as it does not have strong absorption of atmospheric components?

2. In comparison of two BOA methods, one has BOA > TOA for red to infrared channels, whereas, the other has BOA < TOA, so which one can be considered more accurate?

Dear Mostafa Khosravirad

Thanks for the PDF document. I will check it.

Dear Lizardo Reyna Mostafa Khosravirad Tomáš Brunclík

Many thanks for providing valuable and useful information. But I am looking for an answer in context of the attached equation. According to my understanding, TOA has two parts: Atmospheric path reflectance and surface function, so theoretically, SR cannot be greater than TOA reflectance for any spectral region? What do you think?

Dear Muhammad Bilal [Ph.D] , looking at the equation, observe that both atmospheric path reflectance and surface reflectance are within a function, so you do not simply add the two together.

Let's forget about particulars of the formula for a while and simplify the situation to that the resulting reflectance is just sum of apparent reflectance of the atmosphere and apparent reflectance of the surface as seen from space. Now consider only upwelling radiation absorption in the atmosphere, let''s suppose it is 90% for example - now if the BOA reflectance was 0.5 measured at surface, the addition of it to the TOA would be only 0.05 above the atmosphere. Then if the addition of atmosphere would equal 0.1 for example, you get TOA reflectance 0.15 for surface of BOA reflectance 0.5. So BOA>TOA.

Of course in the simplification I neglected other factors as for example absorption of down-welling radiance to get the idea - and that one would play to make the difference BOA>TOA even more profound.

dear sir,

1. in EMR spectrum; Gama, x-rays and UV absorbed by atmosphere and scattering (Rayleigh and mie and non selective scattering ) is predominant so reflection is commonly less in all spectral bands (visible, infrared, (micro and radio-wave not interact with atmosphere)) and it depends atmospheric composition.

it is possible that satellite-derived surface reflectance can be greater than the top of atmosphere reflectance.

2. in Ideal remote sensing principle no atmospheric interaction so here no atmospheric relectance

3. if increasing pollution or other components in the atmosphere which commonly cause scattering not reflection

Dear Tomáš Brunclík

Once again, thanks for your answer. If I follow your statement "simplify the situation to that the resulting reflectance is just sum of apparent reflectance of the atmosphere and apparent reflectance of the surface as seen from space ", i.e.

TOA = Atmospheric reflectance + surface reflectance (BOA), right?

If BOA reflectance is 0.5 and TOA reflectance is 0.05, as you said, then atmospheric reflectance should be -0.45, not 0.1.

Atmospheric reflectance = TOA - BOA = 0.05 - 0.5 = -0.45

OR

If BOA = 0.5 and atmospheric reflectance = 0.1, as you said, then TOA should be

TOA = 0.1 + 0.5 = 0.6 > BOA, which make a sense. What do you think?

I apologize for my poor understanding.

Hello Muhammand,

I thought I would add some comments to those already given by others.

The equation you are using is more detailed and complicated than what I have used in my work from many years ago (as you know from our previous discussions). In my view if you consider atmospheric corrections in very general terms (as has been suggested) you can think of needing an additive and a multiplicative correction as stated in my 1996 paper that you are familiar with.

The additive term (atm in your equation) makes the TOA value smaller, however, depending on the atmospheric conditions the multiplicative term can make the value larger. In some cases the multiplicative correction can be larger than the additive correction, therefore, making the BOA value larger than the TOA value. If you isolate the additive term (atm) and the multiplicative terms in your equation you will be able to see under what conditions this occurs. There actually could be a pivot point where the TOA value is equal to the BOA value because the two corrections ‘cancel’ each other out.

I don’t know if this is helpful for what you are looking for but hopefully it will give you some ideas to think about.

Pat

Just a quick additional note:

In my first comment 'The additive term (atm in your equation) makes the TOA value smaller, however .......' kind of implies that these terms make the TAO value smaller and larger. I left out the important word 'correction'. That is, the additive correction makes the BOA value smaller and the multiplicative correction can make the BOA value larger. Sorry for the confusion.

Pat

Dear Prof. Pat S. Chavez, Jr.

Many thanks for your valuable comments. Your comments make sense to me. By combining our previous discussion via email and these comments, now I have a clear idea when BOA can be smaller or larger than TOA.

Many thanks.

Kind regards,

Bilal

Bilal,

I am glad the comments were helpful. I did not mention that another thing that can make the computed BOA values equal to or larger than the TOA values is that the additive and/or multiplicative values used to convert from TOA to BOA are incorrect. For example, if the additive (scattering) value used is to high the correction will over correct and make the BOA values to small; if the multiplicative (absorption) value is to small it will under correct and make the BOA values to large. In the DOS and COST methods that I have developed that use only image data to get the correction values the additive term can be to high if a valid dark object does not exist in the image being used. The multiplicative value can be to small when the sun elevation is lower than 35 degrees (solar zenith angle higher than 55 degrees).

Pat

Dear Prof. Pat S. Chavez, Jr.

Once again thanks for the explanation - I have found that Sentinel-2A data have used the low additive ( scattering ) value for green band which make the BOA values greater than TOA over bright surfaces.

Kind regards,

Bilal

Dear All,

I am pleased to share my new method “A Simplified and Robust Surface Reflectance Estimation Method (SREM) for Use over Diverse Land Surfaces Using Multi-Sensor Data” published in MDPI #Remote Sensing Journal.

Abstract: https://www.mdpi.com/2072-4292/11/11/1344

PDF Version: https://www.mdpi.com/2072-4292/11/11/1344/pdf

https://www.researchgate.net/project/Simplified-and-Robust-Surface-Reflectance-Estimation-Method-SREM