Radiometric and Atmospheric Correction

- Introduction -

Remotely sensed images often will contain radiometric errors caused by atmospheric attenuation, atmospheric scattering and absorption, and path radiance, determined by atmospheric attenuation and the topography of the landscape. Removal of error, or noise, from remotely sensed imagery is referred to as atmospheric correction. There are four factors that determine if this noise needs to be removed: (1) the nature of the project, (2) the type of remote sensing data, (3) the amount of in situ data available, and (4) the amount of accuracy needed from biophysical information.  In general, single data land use or land cover characterization and multi-date land use or land cover change detection do not require atmospheric correction. If the objective of the study is focused on water properties, vegetation characteristics, or soil properties or entail image mosaic, band ratio techniques, or multi-sensor data integration, atmospheric correction is required.

Atmospheric correction is divided into two methods: absolute and relative. Absolute atmospheric correction models the atmospheric conditions at the time the image was captured to reduce noise by use of Radiative Transfer Codes (RTC) and large amounts of in situ data. The need for extensive in situ data often limits the use of RTC and absolute atmospheric correction, although, spectral libraries can be used to simulate the in situ data needed. Relative atmospheric correction uses information within the image to reduce noise by either normalizing the pixel brightness values between the different bands for single date imagery or normalizing the pixel brightness values between similar bands in multi-date imagery. In this lab, both absolute (ELC and DOS) and relative (multi-date image normalization) atmospheric correction will be preformed on the same study area and the results will be compared.

- Methods -

Absolute Atmospheric Correction - Empirical Line Calibration (ELC)



Figure 1: Screenshot of the Landsat TM imagery used for
atmospheric correction by ELC

Landsat TM imagery of Eau Claire, WI and its surrounding area captured on 10/3/2014 at 10:41am CST (Figure 1) will be atmospherically corrected using the ELC method with spectral library data to replace nonexistent in situ data.

ELC is preformed through this equation:





Where,
the subscript k indicates band number
DN = the image band to be corrected
M = gain (obtained through regression equation)
L = offset (obtained through regression equation)



Figure 2: The Spectral Analysis Workstation

In ERDAS IMAGINE 2013, the Spectral Analysis Workstation (Figure 2) was opened by navigating to Raster > Hyperspectral > Spectral Analysis Workstation. The desired imagery was loaded into the workstation by navigating to File > Open Analysis Image in the workstation. Landsat 5 TM - 6 bands was chosen in the popup window and the color composite was changed by navigating to View > Preset RGB Combinations - TM False Color.







Figure 3: The Atmospheric Adjustment Tool.
A spectral sample of water has been taken and is then compared
to tap water, the only fresh water reference sample
available in the ASTER library.

Next, the Atmospheric Adjustment Tool (Figure 3) was opened by selecting the Edit Atmospheric Correction icon. The method was then changed to Empirical Line via dropdown menu located at the top of the Atmospheric Adjustment Tool window. Spectral samples of features in the imagery were collected in three steps: (1) visually interpreting features, (2) zooming in until individual pixels can be distinguished, and (3) using the Create a Point Selector tool. After a spectral sample had been collected, an appropriate reference sample from the ASTER spectral library was dragged onto the Spectral Plot. The spectral plot now has two spectral signatures (Figure 3). This process was then repeated for a total of 5 spectral plots: water (ref. Tap Water), forested vegetation (ref. Pine Wood), agricultural land (ref. Grass), metal rooftop (ref. Alunite AL706 NA), and asphalt (ref. Asphaltic Concrete). The regression coefficients needed for ELC have been automatically calculated by the Atmospheric Adjustment Tool. The regression information was saved and the model was run by navigating to View > Preprocess > Atmospheric Adjustment in the Spectral Analysis Workstation. The resulting image then needed to be saved by navigating to File > Save preprocessed image. This image was then compared to the original.

Absolute Atmospheric Correction - Enhanced image based Dark Object Subtraction (DOS)

The same imagery of Eau Claire, WI and its surrounding area that was used for the ELC method was used for the DOS method. DOS is preformed in two steps: (1) conversion of the satellite image to at-satellite spectral radiance and (2) conversion of the at-satellite reflectance to true surface reflectance.

Step one is carried out through this equation:

Where,

Qcal = the band to be corrected

All other variables found in image metadata.





Figure 4: The 6 models to create the at-satellite
spectral radiance images.



To apply the equation, six models (Figure 4) were made in ERDAS IMAGINE 2013 by navigating to Toolbox > Model Maker. Each model applies the above equation to a different reflective band from the original image and outputs an at-satellite spectral radiance image. Each at-satellite spectral radiance image's histogram was opened and path radiance was estimated by visually identifying the distance between the start of the x-axis and the beginning of the histogram. This path radiance number is used in step two.




 Step two is carried out through this equation:

Where,
D = distance between earth and sun (found in an ancillary table)
L(lambda) = the at-satellite spectral radiance image created in step one
L(lambda haze) = path radiance (estimated from the at-satellite spectral radiance image's histogram)
TAU(v) = atmospheric transmittance from ground to sensor (obtained through use of a sun photometer, this data was not available so a value of 1 was used)
Esun(lambda) = mean atmospheric spectral irradiance (found in an ancillary table)
Theta(s) = sun zenith angle (calculated by [90 - sun elevation angle], sun elevation angle found in image metadata)
TAU(z) = atmospheric transmittance from sun to ground (found in an ancillary table)

The true surface reflectance images were created by a similar process to the at-satellite spectral radiance images. Six models were made in model maker where the above equation was applied to the at-satellite spectral radiance images and true surface reflectance images were generated. These true surface reflectance images were then stacked to create a color composite image that was then compared to the original image and the image produced through the ELC method.


 Relative Atmospheric Correction - Multi-date Image Normalization


Figure 6: A screenshot of the two images used for multidate
 image normalization. The base image (2000) is on the left
and the image to be corrected (2009) is on the right.

Multi-date image normalization was preformed on Landsat TM imagery of Chicago and the surrounding area captured on May 3rd, 2000 and May 20th, 2009 (figure 6). The image from 2000 was chosen as the base image. Fifteen Pseudo-invariant features (PIFs) were selected from the base image and corresponding PIFs were collected from the 2009 image. The mean values of these PIF pairs were then used to build linear regression equations to calculate gain and bias needed for atmospheric correction.



Figure 7: Screenshot of each image, their associated PIFs, and
spectral profiles

To collect PIFs, the images were opened in ERDAS IMAGINE 2013 and a spectral profile window was opened for each image by navigating to Multispectral > Spectral Profile. PIFs were collected in equal proportions from Lake Michigan, urban features, and rivers/lakes. Once all 15 PIFs were collected (figure 7), the mean pixel values for each band were found by navigating to View > Tabular data... in both spectral profile windows. The mean pixel values for each separate band were paired between the images and plotted in Microsoft Excel with the 2000 values on the Y axis and the 2009 values on the X axis. A linear trend line was added. The equation of this line contained the gain(slope) and bias(y-intercept) values needed for atmospheric correction.

Six models were arranged in model maker, the same as in figure 4.

However this time, the equation,


, is applied to each band of the 2009 image to normalize it's radiometric properties to that of the 2000 image. This equation is the same as the linear regression equations developed in Excel with L(lambdasensor) replacing Y and DN replacing X. After the model had run, the images were stacked into a color composite image and compared to the 2000 image to assess the quality of the correction.


- Results -

Absolute Atmospheric Correction


Figure 8(a): Comparison of the spectral profiles for water between the original image (left) and
the ELC corrected image (right). Compare to Figure 8(b) below.

Figure 8(b): Comparison of the spectral profiles for water between the original image (left) and
the DOS corrected image (right).

Relative Atmospheric Correction




Figure 9(a): Comparison of the spectral profiles for the same feature between the original 2000 image (left) and the original 2009 image (right). Compare to Figure 9(b) below.

Figure 9(b): Comparison of the spectral profiles for the same feature between the original 2000 image (left) and the normalized 2009 image (right)

- Discussion -

In evaluating the effectiveness of the ELC and DOS methods, the spectral profiles of five different land surface features were compared to the original (water is given as an example in Figures 8(a) and 8(b)). Overall, the ELC method did a good job at correcting errors for forested areas and agricultural land but a poor job at correcting errors for water. The DOS method did a better job at correcting errors for all features compared to the ELC method. Spectral libraries were used in the ELC method because of a lack of in situ data. This limited the correction ability of the ELC method to how well the samples would compare to the available reference samples. Also, the DOS method took more into account than the ELC method such as distance from the sun, solar zenith angle, and path radiance.

Just like in the evaluation of the ELC and DOS methods, the spectral profiles of five land surface features were compared between the original and normalized images to determine the effectiveness in the multi-date image normalization (an urban rooftop is given as an example in Figures 9(a) and 9(b)). This method resulted in noticeable correction for all features in bands 2, 3, and 4 while little change took place in bands 1, 5, and 6. Overall, the normalization seemed to do what was intended because the spectral profiles of the normalized 2009 image better reflected the spectral profiles of the original 2000 image.


- Conclusion -

In most cases, atmospheric interference will be present in remotely sensed images and will need to be removed by preforming atmospheric correction. Absolute atmospheric correction relies on large amounts of in situ data and RTCs. Because of this, absolute atmospheric correction has high effectiveness but it's applications are limited. Relative atmospheric correction uses data present in the metadata and in ancillary tables making it more practical for use on most current and historical images, although it is not as effective as absolute. The DOS method did a better job at correcting errors than the ELC method because it took more variables into account. The multi-date image normalization did what was expected and transformed the radiometric properties of an image captured in 2009 to that of an image captured in 2000, though the spectral profiles of features were only similar, not the same.


- Sources -

Earth Resources Observation and Science Center, United States Geological Survey. (2000) (2009)(2011). Landsat TM