## Principal Component Image (PCI) transformation of GOES imager bands

Principal component analysis (or eigenvector/eigenvalue analysis) is a technique that can be used to help interpret the information content of multi-spectral satellite imagery. This technique determines which part of the multi-spectral signal is common to all the bands (or bands) and separates that information from other image information which is sensed by smaller numbers of bands or by individual bands only. Whereas the original images may (and often do) contain redundant information, the component images contain independent information separated out of the original images. This allows the image analyst to see the independent components in multi-spectral imagery.

The number of component images resulting from a PCI transformation is equal to the number of band images input, and those component images contain the same information as the original imagery. The components also have the same explained variance as the original data, but in a new order. Another way to look at the transformation is to consider the new components as a new coordinate system, where each component is a linear combination of the inputs so that the maximum amount of variance can be explained by the first component image, then the second component image, etc., down to the last component image. In the simplest case of two image bands, the new component images are a transformation of the original non-perpendicular axes (bands) into: a first component image (a band combination) which explains most of the variance in the two bands; and a second component image (another band combination) which explains the remaining variance that is not common to the two bands. In that two-dimensional case the component images are the average and difference images. In a three-band case the problem can be visualized as a transformation of axes in three-dimensional space. But for increasing numbers of bands the problem is increasingly harder to visualize. The concept is easiest to explain when simplified to a small number of bands or dimensions.

In the case of GOES, the Principal Component Image (PCI) transformation of all 5 GOES bands yields a set of 5 component images (combination of original images) that helps explain what is seen in the original bands. Below is a typical example of a set of daytime GOES imagery transformed into GOES PCIs along with an interpretation of the individual component images.

### GOES imager bands - day case

The following five images are typical of daytime imagery in all 5 GOES bands. The scene contains a variety of surfaces (land and water) and clouds at multiple levels. References to these images will be made when discussing the resulting component images to follow. Band-1 is a visible image (containing reflected solar radiation), band-2 is a shortwave infrared image (containing both emitted terrestrial radiation and reflected solar radiation), band-3 is an infrared water vapor image (with significant atmospheric absorption and emission), and bands 4 and 5 are longwave infrared images (containing emitted terrestrial radiation). Some of the bands use enhanced gray scales to bring out features in the imagery.

### GOES PCI transform - day case

The following plot contains the transformation vectors used to convert the 5 GOES bands above into 5 Principal Component Images. These transformations were generated for this data set and in the strictest sense are unique to the data set. However, the resulting transformation is typical of that for daytime imagery when performed on all 5 bands. The image bands contributing to each component image (1-5 on the vertical axis) is read across the graph. Each component image contains a contribution from each band (lines 1-5), although that contribution may be positive, negative, or zero. The magnitude of each band's contribution is indicated by the horizontal axis, with positive contributions on the right, negative contributions on the left, and smaller, near-zero contributions are in the middle. Each band is represented by a colored line and the contribution of each band to each component image is connected merely to help the user see where the original bands contribute their information. Bands contributing a significant amount to a particular component image are those bands with either large positive or negative values.

The right-hand vertical axis gives the explained variance in the original images that is associated with each of the component images. Together these variances add up to 100%, with the first component explaining the majority, 86.6%, of the variance in the original images. Successive component images explain smaller amounts of variance until the last component image explains only 0.1% of the total variance. Generally all component images, even though the explained variance in some is quite small, contain important information that may be hidden in the original imagery. Some of the details are revealed in the individual component images as explained below.

### GOES Principal Component Images (PCIs) - day case

The following five images are the daytime Principal Component Image (PCI) transformation of the 5 GOES bands above. Near the bottom of each image, the bands contributing to that component image are designated as numbers over the gray bar. The positions of the band numbers is on a plus/minus scale similar to that in the transformation graph above, but the positions may be inverted left-to-right due to the fact that some of the component images are inverted to display cloudy areas as white. Positive contributions are on the right, negative contributions on the left, and smaller, near-zero contributions are in the middle. Little plus and minus signs are at each end of the gray bar, and a vertical line is the zero point at the center of the gray bar. Bands contributing a significant amount of information to a particular component image are those bands with their numbers at either a large positive or large negative position.

The first component (PCI-1) contains the signal which is most common among all the 5 GOES bands. This image looks similar to the two longwave infrared bands (bands 4 and 5). Emphasis in this PCI is on the coldest cloud tops and the warmest land surfaces, information typically available in infrared "window band" imagery. All infrared bands contribute negatively to this component image, while the visible band contributes positively for the same reason infrared imagery is typically inverted to display clouds as white. Clouds are typically the coldest but the brightest features in satellite imagery, whereas land areas are the darkest but the warmest features. The visible and infrared signals are generally negatively correlated. Bands 4 and 5 contribute the most negatively to this component, but the other infrared bands (bands 2 and 3) contribute negatively as well, but with a smaller magnitude. The visible band (band-1) contributes positively for the reason explained but with a much smaller magnitude than the contributions of bands 4 and 5.

The second component (PCI-2) looks similar to the visible band. It is composed of a large negative contribution from the GOES visible band (band-1) and a smaller negative contribution from band-2 due to the reflected component of radiation in this band during the daytime. The other three bands (3, 4, and 5) contribute much smaller amounts to this component image. In this component the higher, colder clouds in the northwestern part of the image are de-emphasized and surface features are emphasized. What is most apparent is the emphasis on snow-covered versus clear ground (when not obscured by high clouds) and other variations in the earth's surface. Surface variations are more easily seen in this component image since they are not intermingled with high clouds as they are in the visible band alone.

The third component (PCI-3) has by far its largest contribution from the GOES water vapor (WV) band (band-3) and looks similar to the enhanced WV band (band-3) above. Emphasis in this PCI is on upper-level water vapor features. The only other band contributing significantly to this component is band-2, resulting in land surface characteristics due to emissivity variations in the shortwave infrared.

The fourth component (PCI-4) has its largest contributions from GOES band-2 (negative) and band-4 and 5 (positive). This image combination is similar to the GOES fog product generated by subtracting band-4 from band-2. In this component image the different layers of cloud in the northeastern part of the image are distinguished. Higher, colder (ice) clouds are darker than lower, warmer (water) clouds.

The fifth component (PCI-5) has its largest contributions from GOES band-4 and 5, but with opposite signs. This component emphasizes thin cirrus clouds (shown as white in this image). These thin clouds show up in the band difference due to differential transmittance (different optical thickness) between the two bands. Also seen are slight variations in surface emissivity between these two bands. During the summer when the atmosphere contains more moisture, variations in the amount of water vapor absorption in the lower atmosphere can also be detected.

### Summary

The above set of component images shows the daytime transformation of all 5 GOES bands into 5 component images. This component analysis separates the redundant information in multi-spectral imagery to reveal differing cloud and surface features not as readily viewable in the original band images. The transformation plot and the numbers over the gray bar on the component images help explain the combination of bands contributing to each component image.

### References

• Hillger, D.W., 1996a: Meteorological features from principal component transformation of GOES-8/9 Imager and Sounder data. Eighth Conference on Satellite Meteorology and Oceanography, AMS, 28 January-2 February, Atlanta GA, 90-95.
• Hillger, D.W., 1996b: Meteorological features from principal component image transformation of GOES imagery. International Symposium on Optical Science, Engineering, and Instrumentation (GOES-8 and Beyond Conference), SPIE, 4-9 August, Denver CO, 111-121.
• Hillger, D.W., 1996c: Meteorological analysis using principal component image transformation of GOES imagery. International Radiation Symposium - IRS'96: Current Problems in Atmospheric Radiation, (W.L. Smith and K. Stamnes, Editors; A. Deepak Publishing), 19-24 August, Fairbanks AK, 480-483.
• Hillger, D.W., and G.P. Ellrod, 2000: Detection of unusual atmospheric and surface features by employing Principal Component Image transformation of GOES imagery, Tenth Conference on Satellite Meteorology and Oceanography, AMS, 9-14 January, Long Beach CA, 461-464.
• This Web page maintained by Don Hillger, PhD
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