The inability to accurately measure the geometrical effects or errors is a challenge when trying to determine the geometric effects in Landsat Thematic Mapper (TM) No-Payload Correction Data (PCD).
Because the Thematic Mapper instrument is a whiskbroom sensor (where the along-track distance of any one scan measures 16 pixels and the disturbances associated with the no-PCD data is contained within individual scans), measurements must be limited to individual scans. Due to some disturbances being uncorrelated between scans, each scan must be individually characterized to fully understand all the disturbances present. The time-varying dependencies of these changes, along with the small spatial extent of the affected areas, generally makes measuring these disturbances impossible.
This image demonstrates this issue from an image-to-image correlation perspective. Each image shows the same road. The images on the left represent a road imaged such that there is a high order disturbance present during imaging, beyond just a simple shift or rotation. The images on the right represent the pristine road that will be used as a reference to measure the disturbance in the imaged road. The dashed lines represent the image-to-image correlation window that will be used to measure differences between the imaged road and the pristine road.
The correlation window measures the mean offset in the line and sample direction between the two images, which for the correlation window size of the top left and right images will not fully take into account the rapidly changing state of the road.
To better account for this situation and determine how the road was imaged, smaller correlation windows are used to measure the differences between the imaged and pristine road (as seen in the bottom two images). However, when smaller windows are used, less image information can be detemined, which increases the chances of creating a correlation that lacks the strength and signal-to-noise ratio needed to provide an accurate measurement of the geometric differences between the two images. Due to the rapidly changing state of scan disturbance that is measured and stored within the PCD, the no-PCD data need to have a reference data set that each scan of the imagery could be independently measured to fully determine the state of all the scans within the image. These small correlation windows, presence of clouds in the imagery, and the temporal changes between the no-PCD imagery and any reference imagery makes this kind of assessment on a routine basis impractical.
PCD Geometric Disturbances
Several types of disturbances occur on board the Landsat 4 and Landsat 5 spacecraft during image acquisition. These disturbances can include, but are not limited to, items as the scanning mirror, reaction wheels, high gain antenna movement, solar array movement, and thermal pressure. The expected disturbances (with respect to frequency and magnitude according to the Landsat to Ground Station Interface Control Document (ICD) are listed below.
Hertz (Hz) (arc-second 1 sigma)
0.00 to 0.01 36 all axes
0.01 to 0.40 10 all axes
0.40 to 7.00 5 all axes
7.0 or greater 2 Roll
7.0 or greater 1 Pitch
7.0 or greater 2 Yaw
The ICD states that no significant error belonging to any geometric disturbance will occur above 77 Hertz (Hz). Considering that one arc-second is 4.8448x10-6 radians, the instantaneous field of view of a TM detector is 42.5x10-6 radians and a full image acquisition is approximately 24 seconds (0.042Hz) in length, this information demonstrates the concerns about the geometric errors that may be present with the TM no-PCD products.
Landsat geometric processing takes the multiple sources of attitude information available within the PCD and integrates that information into one set of time tagged roll, pitch, and yaw values that are used during Level-1 data generation.
A typical set of these data values for a TM scene is shown in this image. The Y axis is the displacement in pixels of each state of the attitude that is to be applied to the imagery while the X axis represents seconds of each attitude point from a reference time before the first scan within the image.
Since a typical Landsat scene’s acquisition time is approximately 24 seconds, the plot represents a time frame of a little over one acquisition.
There are a number of important aspects of the plots shown within this image, including: (1) the presence of low frequency disturbances, along with higher order harmonics as indicated above; (2) the maximum peak-to-peak change that occurs and is measured by the PCD is around a one-pixel disturbance. This change transpires over several scans. This dispersion of the one-pixel displacement across several scans creates what could still look like decent scan-to-scan geometry, but are in fact small sub-pixel scan misalignments spread evenly across several scans; and (3) some of the dominant changes appear to occur within the roll axis. This is expected as one the major disturbances during imaging is the scanning mechanism of the mirror and its interaction with the bumpers at the start and end of each scan.
This image shows Fast Fourier Transformation (FFT) of the Integrated Attitude of the image above. FFT points out the location of the harmonics that are noticeable in the image above, with the dominant approximately 7Hz, 14Hz and 21Hz harmonics in the roll axis due to the scan mirror which operates on a 7Hz scan cycle. The 2Hz harmonic is due to the reaction wheels that can be commanded at a rate of 0.512 seconds.
Although the scan mirror could be consistent within most scenes, and possibly its phase locked down, the lower frequency and what at times has shown to be the larger component of the disturbances are due to the reaction wheels or other less predictable low-to-mid frequencies disturbances. These disturbances are dependent on factors that are random with respect to one acquisition to the next making characterization not possible on a consistent basis across multiple scenes. The scan mirror and reaction wheel disturbances are of a higher order than what the precision correction process can remove from the Level-1 terrain corrected products.
Characterizing What no-PCD TM Data Means Geometrically
Due to the issues described earlier with measuring the no-PCD geometric distortions based upon comparing this data to a known reference, the absence of the attitude information and its effect on products was determined by looking at over 1000 TM-R data sets that did contain PCD information, but their PCD data was removed/zeroed to represent the no PCD data format. The correction associated with having PCD was then used to infer what effect the absence of this data would have on products.
Although this approach is reasonable and can provide better characterization metrics as the same imagery (with PCD) will be used for comparison, there are some limitations with this approach:
- There could be dependencies on either geographic location or acquisition time of the actual no-PCD scene which may affect the PCD that is not represented in the test data sets chosen.
Using the integrated attitude without taking into account what could be in the precision correction process using the ground control points would overestimate the error within the no-PCD precision-terrain products.
To alleviate the first limitation, the test scenes chosen from a wide geographic and temporal variety, covering the time frame from which the no-PCD data will be drawn.
The second limitation was mitigated by analyzing the errors with and without removing the linear trend (correlated with time) within the integrated attitude. For each test image, the start and stop times were found for each scan and a roll, pitch, yaw value was extracted from the integrated attitude at a set of points along the scan. These attitude values were then used to measure the change in line-of-sight (LOS) for the scan mirror and scaled from angular displacement to a nominal pixel size on the ground. These changes were considered as errors within what would be no-PCD data if the PCD was not used in product generation for these data sets. These errors per-scan were squared and summed across the entire image.
A plot of the results is shown here. The left image shows the maximum error calculated (Y axis) and the results with the linear trend removed, and not removed. The ability to remove the linear trend within the integrated attitude reduces the maximum error that would otherwise be present within the imagery by as much as 50 percent. The right image displays the accumulated error across the full image (Y axis) with the linear trend removed from the integrated attitude.
These results drove the decision to add a 0.3-pixel RMSE to the reported Geodetic Accuracy of the no-PCD data by determining the root sum of squares (RSS) of these two values. Although it may be considered an overly-conservative assessment of the quality of the imagery, it was deemed a good approach for Landsat Collection 1, but may need to be re-addressed for Landsat Collection 2, after all no-PCD data is received and can be better assessed.
As stated previously for the case of the missing ephemeris, there are two options available for supplying this information:
- The Landsat Flight Ops team has produced post-pass ephemeris using satellite tracking information.
- A method was developed by the USGS to calculate Two-Line Element (TLE) sets for the Landsat 4 and Landsat 5 missions.
- TLE generation is based on using precision corrected results for TM data that is not part of the no-PCD family but is acquired over the same time frame. The generated TLEs are not expected to be as accurate as the ephemeris associated with having the PCD available or that generated by the Landsat Flight Ops Team. These errors will be larger in the systematic products but should mostly be accounted for with the use of ground control and the precision correction process such that the precision-terrain products should not be adversely affected by the use of the TLEs.
An approach similar to the one used in characterizing the absence of the attitude for the no-PCD data was taken to assess the use of the TLEs within the product generation. This analysis of over 150 TM scenes with valid PCD was processed using the TLEs.
The results between using PCD ephemeris and TLEs for product generation are shown here, for both the pre-fit and post-fit Geodetic Accuracy standard deviation.
As seen in the pre-fit standard deviation (left image), the systematic image at times is adversely affected by the use of the TLE in product generation. The right image displays the post-fit standard deviations and shows a handful of times where the TLEs appear to produce an adverse effect also on the precision-terrain corrected product, however these results need to be viewed in a different light than those produced from the attitude related study, since: (1) These images were chosen randomly with respect to the known quality of the precision-corrected product and its corresponding Geodetic Accuracy results, therefore some of these datasets may have had poor precision results regardless of the ephemeris used in the correction process; and (2) Further inspection showed a number of the scenes used in the study contain a large amount of clouds adversely affecting the results. A limited number of GCPs and what more than likely is a poor quality of correlation between the systematic image and the ground control contributed to these poor results.
From this study involving the use of the USGS-generated TLEs, there may be a small degradation in the quality of the product when the TLEs are used, as compared to those that are present within the data due to the missing attitude information. This analysis did not study the combined effect of using TLE for the no PCD TM data which may further degrade the quality of the Level-1 products. Also, any interaction effect between TLE and loss of attitude information was not studied, but they are in general highly uncorrelated and their effect should be negligible.
Landsat no-PCD Geometric Example
As mentioned previously, the kind of geometric disturbances typically associated with a no-PCD product will not show up as a readily visible scan-to-scan displacement. With the help of the maximum displacement plot above, the larger displacements can be located and visually inspected until a vertically oriented feature can be found within the maximum displacement time frame.
This image represents a location found with this type of criteria - it shows the nominal image on the left and the no-PCD created image on the right with a factor of 4 times for the bottom two zoomed images.
A slight road misalignment can be seen in the images — following this road, slight misalignments can be seen when comparing the simulated no-PCD data to the nominal TM image. This type of scan misalignment is similar to that observed in real-time bumper mode processing for data from the Landsat 7 ETM+ and Landsat 5 TM instruments late in the life of those instruments.
Unlike the bumper mode calibration changes that cause this type of scan-to-scan misalignment, those associated with the no-PCD data is not a slowly varying trend that can be determined and corrected for over long-time frames (multiple days). Instead, they are short-term changes dependent on the current dynamics of the spacecraft and instrument for that given interval or even scene in some cases during that acquisition time frame.
Collection 1 no-PCD
At the time that this analysis was done, only a few hundred no-PCD datasets were available for inspection. The geographic distribution of this data, along with the possible time frame of acquisition, was thought to be fairly well known; however, the exact number of data sets was not.
Some of the early no-PCD data also had corresponding nominal TM-R data available. Since the lack of PCD was due to a ground processing issue, and since multiple ground stations downlink the same data acquired by the instrument, some TM-R data were available that could be used for comparison with the no-PCD data.
Since the duplicate data would alleviate many of the image-to-image correlation issues, the results and analysis were further verified by comparing the corresponding TM-R and no-PCD datasets.
A better estimate and assessment of the geometric errors for no-PCD data will only be possible after all of the no-PCD data is received, ingested and processed into Landsat Collection 1.
As mentioned in the first section, radiometrically, users may notice differences in radiance calcuations when using both no-PCD and standard PCD scenes. The absence of any attitude data from the TM PCD causes a measurable but unpredictable geometric distortion to be present in the output product. This distortion is scan-based in direction and its magnitude in the majority of the data that was analyzed was found to less than one pixel peak-to-peak.
The significant issue with this type of geometric distortion is that it is of high enough frequency within the data that ground control cannot correct for the problem, but low enough frequency that is not easily identifiable by visual inspection. There is also no reliable and repeatable way to quantify the errors present in the data, however it has been shown to be directly related to the amplitude of the integrated roll, pitch, and yaw corrections that are applied to nominal TM data during product generation. Therefore, an overall expectation of what this data will look like from a geometric perspective can be obtained by looking at the attitude information associated with nominal TM-R datasets. In the case of the use of TLEs, when neither the PCD nor Flight Ops post-pass ephemeris is available during product generation, the systematic imagery will show the largest loss of geometric accuracy, while the precision-terrain corrected imagery could have a small degradation when compared to other TM products.
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