Lab 3 Atmospheric Correction

Goal and Background

                The purpose of this lab was the introduction and beginning experience with different forms of correction of remotely sensed imagery. Remotely sensed images can become skewed and visually displeasing and that is where the use of correction comes in handy. By having corrected images there is a more comprehensible output and view. Multiple methods were used for this lab. These methods were empirical line calibration, dark object subtraction, and multidate image normalization. Empirical line calibration is the method of correcting remotely sensed images using spectral information from spectral libraries. Dark object subtraction being another method of correction uses a number of variables to correct an image. These variables are sensor gain, offset, solar irradiance, solar zenith angle, atmospheric scattering and absorption, and path radiance. The last correction, multidate image normalization, is used when no in situ data can be found. Multidate image normalization uses two different dated images to correct an image. An image can be corrected by finding the same object in the two different images and using the spectral reflectance from the object for correction.

Methods

                In the first part of this lab the correction method that was used was the empirical line calibration method. The image that was corrected was an image titled eau_claire2011. To correct this image ERDAS Imagine was used specifically the Spectral Analysis option. To get the Spectral Analysis Workstation click on the Raster tab, next Hyperspectral, then Spectral Analysis Workstation. This will open up the Spectral Analysis Workstation. Here the image of Eau Claire was added. At first the image is in the wrong color band combination. This is changed to false color infrared. The main procedure here is to select the Edit Atmospheric Correction option. This is signified as a certain icon. Once here the method that is chosen is Empirical Line. With this chosen a spectral plot will appear. This is to show a spectral sample. Numerous spectral signatures were taken using the Create a point selector tool. This tool is designated as a crosshair. This crosshair takes the spectral signature and plots it.  The goal is to get very similar spectral signatures for comparison and correction. Once all signatures are collected the image was ready to be corrected. To allow for calculations the information was saved as an aad. file. To get a temporary product the procedure of selecting View, Preprocess, and then Atmospheric Adjustment was done. The final image was saved as a preprocessed image. Once all was saved checking the spectral signature was the final step to view the product. The spectral signature of the first and final images are different and can be viewed in the Spectral Profile.

Figure 1: Spectral Analysis Workstation with Edit Atmospheric Correction Icon

                The second part of the lab was atmospheric correction using enhanced image based Dark object subtraction. Like the first correction method this uses an equation to correct the image, but the variables of the equation need to be entered manually. This equation Lλ = (LMAXλ-LMINλ/Q_{cal max} – Q_{cal min})(Q_cal – Q_{cal min})+ LMIN_λ is put into model maker in ERDAS Imagine. The variables of this equation are as follows. These variables can be found in the metadata file.

 Lλ = At-sensor spectral radiance in [W/(m² sr µm)]

 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 [W/(m² sr µm)]

 LMAXλ = Spectral –at sensor radiance that is scaled to Qcalmax [W/(m² sr µm)]

To get the newly corrected image a model was built in model maker. Three objects were placed in the model those being a raster object, a function, and an output raster. 6 models were built for each band (1-5,7). Each original band was put into the raster object. The equation above with the proper variables was the function, and an at-satellite spectral radiance image was the output raster. The image that was created above is not void of all atmospheric interference. To do this another equation was needed. This equation is Rλ = ∏ * D² * (Lλ - Lλhaze)/ (TAUv * Esunλ * COS θs * TAUz). The variables are as follows

Rλ = True surface reflectance.

 ∏ = Mathematical constant equal to 3.14159 [unitless].

 D = Distance between Earth and sun [astronomical units].

 Lλ = At-sensor spectral radiance image.

 Lλhaze = path radiance.

 TAUv = Atmospheric transmittance from ground to sensor.

 Esunλ = Mean atmospheric spectral irradiance [W/(m² µm)]

θs = sun zenith angle (or 90- sun elevation angle).

 TAUz = Atmospheric transmittance from sun to ground. (TAUz values are different for TM bands, seen below)

TM Band TAUz

Band 1 0.70

Band 2 0.78

Band 3 0.85

Band 4 0.91

Again a model was built this time with the original output raster images as the raster image, the above equation with proper variables becomes the function, and the output raster images will be the final corrected images. Before the image can be viewed in the proper way the bands needed to be layer stacked. Once all were stacked the final image was created.

Figure 2: A model similar to the ones used in this lab

The third and final part of this lab was to use multidate image normalization. Again, an equation was used to correct an image. Images of Chicago in 2000 and 2009 are both being used for correction. The 2000 image is the image being used for correction and the 2009 image is the image that needs correcting. For this correction sample points of same objects on the images were taken. 6 from Lake Michigan, 5 from ubran areas, and 4 from waterways. The signatures are viewed in a Spectral Profile Viewer. The pixel values were needed for the lab. To view the pixel values the procedure of going to View, then Tabular Data. These pixel values’ means are entered into Microsoft Excel. These are the means of all the layers and the 15 selected spectral values. These means were needed for a regression analysis which the variables were created using a scatter plot. After the variables were found they were input in an equation for atmospheric correction. The variables were R² and the slope equation. This equation was Lλsensor = Gainλ * DN + Bias. The variables are represented as

Lλsensor = At satellite radiance image.

Gainλ = a multiplicative component (the regression coefficient)

DN = Subsequent image band (chicago2009.img image band(s)).

Biasλ = the regression equation intercept

The slope equation Y=mx+b is used where m is the Gain and b is the bias. As before a model was needed for each band. The raster is the 2009 image, the function is the equation above, and the output raster is the new image.

Figure 3: Scatter plots essential for completion of Multidate Image Normalization

Results

Below are the image results from the lab

Here are the results of atmospheric correction. The first image is the Multidate Normalization, the second is Dark Object Subtraction with  an error in the equation which skewed the results (if this image comes out incorrectly some editing is needed in the equation), the third image is Empirical Line Calibration. 

Sources

All formulas and original images were provided by Dr. Cyril Wilson from the University of Wisconsin-Eau Claire. All models and image operations were done in ERDAS Imagine 2013