LAB 2: Radiometric and Atmospheric Correction

Goal
The main goal of this lab is to gain practical experience on correcting remotely sensed images for atmospheric correction. This lab will provide the knowledge to perform multiple methods for absolute atmospheric correction, and additionally relative atmospheric corrections will be performed. The two absolute atmospheric correcting methods that were used are Empirical Line Calibration (ELC) and Dark Object Subtraction (DOS). Additionally the Relative Atmospheric correction process requires using a multidate image normalization process.

 Methods
Part 1: Absolute atmospheric correcting using empirical line calibration 
In the first part of this lab atmospheric correction was performed on an Eau_Claire2011.img. This is a Landsat 5 TM image, that was collected on August 3rd 2011 at 10:41 am CST. In order to remove the atmospheric interference from this imaghe, spectral libraries are necessary for providing in situ data to help understand spectral profiles of surfaace features. 

To perform an ELC the equation; CRk = DNk * Mk + Lk,  Is used to remove the atmospheric interference.

CRk  = corrected digital output pixel values for a band.
DNk = the image band to be corrected. 
Mk  = is a multiplicative term affecting the brightness values on the image. (gain)
Lk = is an additive term. (offset)     

The values for this equation come from a regression analysis between a specific surface feature, and that same feature from a spectral library. This process shows the difference in the pixel values between bands and allows for adjustments to be made on values that should be higher or lower based on the spectral library information. Once the Regression analysis was performed by collecting multiple surface feature points and there library spectral signature in the Spectral Analysis Workshop. then this tool runs a model with the equation above, and produces a corrected image.

Part 2: Absolute atmospheric correction using enhanced image based Dark object subtraction
In the second part of the lab, enhanced image based dark object subtraction is utilized to correct for atmospheric interference. This process utilizes a number of parameters to make corrections: sensor gain, offset, solar irradiance, solar zenith angle, atmospheric scattering and absorption, and path radiance. The process has two steps, the first converts the satellite image to at-satellite spectral radiance image, next that is converted into true surface reflectance.

This first portion converting satellite images to at satellite spectral radiance is executed through the equation: Lλ = ( LMAXλ−LMINλ) (Qcal −Qcal min)+LMINλ                                                                                         Qcal max−Qcal min
Lλ    =  At-sensor spectral radiance        
Qcal =  Landsat image (digital number DN)
Qcalmin = Minimum quantized calibrated pixel value corresponding to LMINλ        
Qcalmax = Maximum quantized calibrated pixel value corresponding to LMAXλ
LMINλ  = Spectral at-sensor radiance that is scaled to Qcalmin
LMAXλ   = Spectral at-sensor radiance that is scaled to Qcalmax          
This was done in the lab through the use of Model maker (Figure 1), the image eau_claire2011.img was utilized with all its bands, to convert each band to an at-satellite image. To execute the model, each band was entered into the input for each model (Bands 1-5 & 7). In each Function, the equation above was entered, by placing data found in the META data about each band. Once this occured, we came up with 6 radiance outputs for each of the 6 bands utilized. 
Figure 1: this image shows the model that is utilized to convert satellite imagery into at-satellite spectral radiance images.


The second portion converting the at-satellite to true surface reflectance is performed through the equation: Rλ  = ∏ * D² * (Lλ  -  Lλhaze)/ (TAUv * Esunλ   * COS θs   * TAUz)                                         Rλ = True surface reflectance.
∏= 3.14159
D= Distance between Earth and sun      
Lλ= At-sensor spectral radiance image.
Lλhaze= path radiance.
TAUv= Atmospheric transmittance from ground to sensor.         Esunλ= Mean atmospheric spectral irradiance   
θs= sun zenith angle
TAUz= Atmospheric transmittance from sun to ground.            

This portion is also performed through the use of a model (Figure 2). All portions of the equation shown above were found through Meta data, the labs appendix, and through calculating the sun zenith angle in DEGREES. In the input of the model, each incividual bands radiance image is now the input, and the equation above is the function input.
 Figure 2: This image shows the model utilized to convert at-satellite spectral radiance images, to true surface reflectance.

 Finally a layer stack is performed on the 6 output band images, to produce a false color atmospherically corrected image. (Eau_Claire_2011_DOS)

Part 3: Relative atmospheric correction using multidate image normalization
In this Final portion of the lab, atmospheric interference is corrected using multidate image normalization. this portion of the lab require in situ data to perform a regression analysis between two images, to remove the atmosphere interference so that it reflects the older image in this case 2009 image reflecting the 2000 image. The first portion require taking sample points from the base image and the subsequent image. In this lab 15 were collected from water bodies urban areas, airport hanger roofs, and other features. These sample points provide the ability to create scatter plots that allow for the extraction of data to be used to convert the image into a corrected image. the scatter plots that were produced are shown in figure 3.
Figure 3: These scatter plots are used to gather the gain and bias from the equation.

After gathering and creating thes plots, the normalization model is produced, this model utilizes the equation: Lλsensor = Gainλ * DN + Biasλ
Lλsensor = At satellite radiance image.
Gainλ = a multiplicative component (the regression coefficient)  
DN  = Subsequent image band 
Biasλ  = the regression equation intercept.  
the gain comes from what would normally be the slope in a normal linear equation y=ax+b with a being the slope, and b the constant, or in thiss case a being gain, and b offset, and x is the DN or Subsequent image band. The model looks as follows, in Figure 4. The input is the subsequent image individual bands, and the function is the equation above.
Figure 4:This model shows the process for normalizing imagery to correct for atmospheric interference. 
Results

Part 1: Absolute atmospheric correcting using empirical line calibration 
The results from runing the Spectral Analysis Workshop  to perform an ELC produced a slightly better image than the original (Figure 5). I see it as only a slightly better image, because there is multiple areas for error in performing this process. To begin one error could come from choosing the wrong surface feature in the original non corrected image, and comparing it to a spectral library that may not be the same surface feature. Errors can also arise from not taking into consideration the sun and its elevation in relation to the earth. with not taking this into consideration, some features may have an incorrect pixel value when adjusted. This correction is very minimal to the naked eye. the only way to see a difference in the image without using a spectral profile is to stack the images and turn the top one on and off, the naked eye can barely see the ELC image is slightly darkker, but it is. There fore to see the correction Figure 6 shows the spectral profiles of an aluminum roof at the Eau Claire airport.
Figure 5: This shows the entire extent of the ELC corrected image, with the original 2011 image on the left, and the 2011 ELC image on the right. as seen in this figure, they look the exact same.

Figure 6: This figure shows a zoomed in version of  Figure ? and it also shows two spectral profile plots of an aluminum roof, both taken from a hanger at the Eau Claire Airport. Looking at spectral profiles is the only way to see a difference from an ELC corrected image.
Part 2: Absolute atmospheric correction using enhanced image based Dark object subtraction 
The results after performing an enhanced image dark based subtraction Produces an atmospherically correct image (Figure 7 right) , this is noticed more through the spectrol profiles being closer to accurate, to the naked eye it is very difficult to see, but the DOS image is slightly darker than the original image. This is because the pixel values are brought to there correct value based on the removing of the atmosphere. 
Figure 7: The image on the left is the original image, and the one on the right shows an atmospherically correct image through the use of DOS.
Part 3: Relative atmospheric correction using multidate image normalization
The results for this Relative atmospheric process are shown in Figure 8. This process produces a darker colored image, with reflective image colors appearing more accurate, and also it is a sharper image. 
Figure 8: This image shows a zoomed in portion of the Chicago area, 2000 un normalized image on the left, and the 2009 normalized image on the right. 

Sources

Landsat satellite image is from Earth Resources Observation and Science Center, United States Geological Survey. 
Spectral signatures are from the respective spectral libraries consulted. 

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