2.1.

Geolocation Error Measurements

The nadir-equivalent circular (or radial) errors were calculated from outputs of the control-point matching (CPM) program. The CPM program has been developed previously by NASA to characterize MODIS geolocation errors, and it was later adapted for VIIRS.¹² For VIIRS, the geolocation errors are computed by cross correlation of VIIRS daytime data in band I1 (600 to 680 nm) with spatially aggregated data in the Landsat “red” band (630 to 690 nm). The 30-m ground sample distance of the Landsat data allows for finding the optimal shift of the aggregated Landsat data that provide the maximum correlation to the VIIRS data with the 375-m resolution (at nadir). The evaluation uses 800-by-800 pixel subsets of Landsat data that form ground control point (GCP) “chips.” Landsat geolocation data for each chip provide the ground “truth,” and VIIRS geolocation data with the best match to the shifted Landsat data are the GCP observations. Outputs of the CPM program include latitude, longitude, and height above the WGS84 ellipsoid for the ground-truth and observed GCPs. Spacecraft position and attitude at the time of the GCP observation are provided as well. VIIRS geolocation errors were measured by calculating the distance on the WGS84 ellipsoid between points with latitude and longitude of the ground-truth and observed GCPs.

Similar analyses of geolocation accuracy based on pre-selected set of GCP chips were previously conducted for MODIS,¹² AVHRR,¹⁴ and MERIS.¹⁵ Significant efforts were also dedicated to increase the number of the chips available for the matchups and to make the chips more consistent with the current ground surface.¹⁶ In a more recent approach, much larger sets of GCPs were dynamically created for selected Earth scenes and applied in the geolocation evaluation for the MERSI-II sensor.¹⁷ In another approach, a large set of GCPs was created from the terrain elevation data along coastlines and was applied for the geostationary imaging sensors from the GEOS and Himawari satellites.¹⁸

The number of globally distributed GCP chips that were selected for characterization of the N20 VIIRS geolocation errors was 1179. CPM results used in the evaluations of the VIIRS SDR data were produced at STAR with a step of 0.2 pixel-size before the optimization (“on-orbit calibration”) of the geolocation processing parameters and 0.05 pixel-size after the optimization. In addition to the geolocation errors, the CPM program also provides a value of image cross-correlation obtained for each matchup. The cross-correlation values measure the quality of the matchups. CPM results generated for the N20 VIIRS SDR both before and after the optimization contained clusters of matchups with high cross-correlation. This enabled the selection of a cross-correlation threshold that allows for using in analysis only the matchups with the highest quality. The threshold of 0.975 was selected for the evaluations of compliance with the geolocation requirements, but that needed accumulation of the GCP matchups over 12-month periods, resulting in about 3000 matchups for each year. Time dependence of the geolocation errors was studied with finer temporal resolution using 16-day periods and the threshold of 0.9, typically providing about 700 matchups for each period.

2.2.

Transformations to Angular and Nadir-Equivalent Errors

As described in the VIIRS geolocation ATBD,⁹ to produce geolocation data for VIIRS radiometric measurements, several transformations need to be applied to convert detector position on a focal plane to geodetic coordinates of a location observed on the Earth surface (Fig. 1). The first transformation to the instrument coordinate system is based on a model of the VIIRS optics that includes the rotating telescope and the half-angle mirror (HAM) that “de-rotates” the optical image.

Fig. 1

Coordinate systems used in the VIIRS pointing and geolocation algorithm.

The next transformation, from the instrument to spacecraft coordinates, is based on the instrument-to-spacecraft alignment information (the “mounting matrix”). Spacecraft attitude (the roll, pitch, and yaw angles) is used for transformation between spacecraft and orbital coordinates. Transformation between orbital and Earth-centered inertial (ECI) coordinates is derived from the spacecraft position and velocity vectors. ECI coordinates can be transformed into non-inertial Earth-centered Earth-fixed (ECEF) coordinates, and vice versa, using known astronomical parameters. These four transformations can be represented as a series of three-dimensional rotations, as shown in the following equation:

2.3.

Minimization of Geolocation Errors

Uncertainty of the N20 VIIRS geolocation products was reduced by minimizing the root-mean-square of the angular errors. The improvement was achieved by adjusting only the instrument-to-spacecraft rotation angles through multiplying the mounting matrix by a corrective rotation matrix. The three correction angles were optimized using the Nelder–Mead method that offers robust performance while requiring only a limited number of goal function evaluations by applying predefined transformations (“reflection,” “expansion,” “contraction,” and “shrink”) to the optimized parameters.¹⁹ The optimized mounting matrix is valid for the specific VIIRS optics model that is implemented in IDPS, and when that model was corrected, the matrix had to be re-optimized. The mounting matrix optimizations were based on all global GCP matchups collected over a 16-day JPSS orbit repeat period. Because shortly after launch of the N20 satellite the number of available cloud-free Earth observations was limited, the initial optimization of the mounting matrix was based on reprocessing a small set of VIIRS SDR from North Africa and the Middle East. The suitability of that approach was demonstrated previously.²⁰ Subsequent mounting matrix optimizations that further reduced the geolocation uncertainty were based on full 16-day datasets from the same area, but even that had to be extended to global matchups to achieve the desired accuracy while limiting the number of needed iterations. Although the geolocation errors are calculated for the terrain-corrected VIIRS SDR products, the mounting matrix optimization based on the angular errors omits the effects from terrain correction. The effects for rough terrain seem to be negligible on the global scale used in the optimization, but several iterations of the optimization followed by reprocessing of the used dataset were done to ensure that it is indeed the case. Reprocessing the VIIRS SDR data with the optimized geolocation parameters was conducted using the Algorithm Development Library (ADL) software that incorporates the computer code deployed in IDPS.

2.4.

DNB Adjustments

Although only band I1 is used to maintain VIIRS geolocation accuracy, band-to-band registration between band I1 and the other I-bands as well as the M-bands ensures that those bands have comparable geolocation uncertainty. However, DNB is not co-registered with the other bands. Although the DNB ground sampling distance is nearly constant along the cross-track scan, due to sub-pixel aggregation of detector arrays, it increases away from nadir for the I-bands and the M-bands. Because detector arrays for both the DNB and band I1 are on the same focal plane, DNB geolocation can be tied up with I1. Single, near-nadir point (a west Sahara river mouth) was initially used to achieve agreement between DNB and I1 geolocation by adjusting a processing parameter specific to the positions of the DNB detectors. DNB geolocation was later refined by optimizing that parameter to achieve maximum cross-correlation between a near-nadir subset of a DNB image (512 by 512 pixels) and an I1 image re-projected to the latitude and longitude of the DNB pixels. It is also possible to use cross-correlation for the entire VIIRS granule to align DNB and I1, but it was not applied for N20 because of the modification of the DNB aggregation scheme that was done to avoid the effects of radiometric response nonlinearity.³

2.5.

Evaluation of Geolocation Uncertainty

Although the uncertainty evaluation is based on global matchups collected over a 12-month period, even with more than 1000 of the GCPs, the applied CPM program collects over that time period only about 3000 GCP matchups that exceed the selected cross-correlation threshold. That seems barely sufficient to estimate the geolocation uncertainty just by counting the errors within the required range. Instead, the Burr Type XII distribution was used to approximate the probability distribution of the geolocation errors,²¹ to estimate its parameters, and to predict the 99.7% level of the cumulative distribution that provides the geolocation uncertainty. As the circular errors are never negative, their random distribution is described by Poisson statistics better than by Gaussian statistics, and the Burr distribution provides the best fit to it using two shape parameters and a scale parameter to express a wide range of distribution forms, such as gamma, log-normal, log-logistic, and bell-shaped.

3.1.

Initial Post-Launch Calibration

For the N20 VIIRS geolocation error evaluation before the optimization (on-orbit calibration) of the processing parameters, nine days without significant disturbances of the satellite orbit were selected: 21, 22, 24, 25, 27, 28 December 2017 and 1, 2, 4 January 2018. Although it was not possible to select for the initial evaluation all 16 days from the full orbit repeat period, Fig. 2 shows that a sufficient number of GCP matchups was collected, even with the applied cross-correlation threshold of 0.9. A cluster of matchups with high cross-correlation can be identified on the graph shown in Fig. 2 (top left). This enables using a cross-correlation threshold to select matchups with the highest quality. When only those matchups are applied in the evaluation, the determined N20 VIIRS geolocation errors prior to the on-orbit calibration are around 2 km, as shown in Fig. 2 (bottom left). Such large geolocation errors can also be seen on VIIRS images when re-projected to geographic coordinates and compared with known geolocation of coastlines and other recognizable objects. Figure 2 also shows that many of these selected GCP matchups are located in North Africa and the Middle East.

Fig. 2

Nadir-equivalent geolocation errors (left) and global maps of the GCP matchups (right) analyzed with (bottom) and without (top) applying the cross-correlation threshold of 0.9.

To evaluate geolocation errors after the first mounting matrix optimization and deployment of the updated processing parameters in IDPS on January 5, 2018, VIIRS SDR products from 16 consecutive days (January 7 to 22, 2018) without significant orbit disturbances were analyzed. Figure 3 shows the nadir-equivalent geolocation errors determined from the CPM program outputs with and without applying the cross-correlation threshold of 0.9. The errors were clearly reduced by the mounting matrix optimization from about 2 km to typically $<200\mathrm{m}$.

Fig. 3

N20 VIIRS nadir-equivalent geolocation errors after the initial on-orbit calibration analyzed with (b) and without (a) applying the cross-correlation threshold of 0.9.

Figure 4 shows the angular errors, decomposed into the roll, pitch, and yaw directions, before and after the first optimization of the mounting matrix. Despite scatter of the measured points, biases of approximately $400\mathrm{arcsec}$ in the roll direction and $-200\mathrm{arcsec}$ in the pitch direction can be seen before the optimization. These biases clearly diminished after the optimization.

Fig. 4

Roll, pitch, and yaw components of the angular errors before (a) and after (b) the initial on-orbit calibration of the N20 VIIRS geolocation processing parameters.

3.2.

Further Geolocation Improvements

Subsequent to the initial post-launch update of the mounting matrix in early January 2018, five updates of the VIIRS geolocation processing parameters were made during the first 5 years of the N20 operations on orbit. The first of these updates was made in February 2018 after a full set of 16-day data became available, allowing for re-optimization of the mounting matrix. The second update was in May 2018 when updated parameters for VIIRS optical model became available and thermal conditions stabilized after the “mid-mission” outgassing conducted in March 2018. The third update (in October 2019) added parameters for seamless switching between two “sides” of the scan controller electronics in case it needs to be done on orbit, but it did not change the existing geolocation calculations. In addition to the correction of the VIIRS optical model,¹³ the fourth update (in February 2021) included optical model parameter values derived from the pre-launch measurements conducted for N20 VIIRS by the manufacturer. The updated values replaced the SNPP VIIRS ones used previously. The optimization of the mounting matrix for that update was not fully successful, adding small biases to the geolocation errors, and the fifth update (a re-optimized mounting matrix) was deployed in July 2021. The improvement was achieved by analyzing global GCP matchups instead of those located in North Africa and the Middle East only. Values of the parameters from the latter update are listed in Table 1. Although the instrument-to-spacecraft roll/pitch/yaw angles were obtained by the mounting matrix optimization, the HAM alpha/beta/gamma angles, defined in ATBD,⁹ are from the measurements acquired during VIIRS pre-launch testing. The table also shows corresponding values obtained at NASA by optimizing all six parameters for processing NASA level 1b products.¹³

Table 1

Major geolocation parameter values for NOAA-20 VIIRS.

In addition to being applied to improve the accuracy of the geolocation products, the angular corrections derived for the 16-day periods were also used to monitor the geolocation errors over timeline of the N20 mission. Figure 5 shows that, following the adjustments of the geolocation processing parameters in 2018, the angular errors display annual oscillations that periodically increase the geolocation errors by up to about 50 m on the ground. These oscillations are most likely a thermal effect, and a correction was developed based on the day of year. This correction has not been implemented yet in the operational processing due to software engineering concerns. Additionally, an increase of a few arcseconds in the pitch and yaw biases can be seen in Fig. 5 between February and July 2021 because a limited geographic area was initially used in the mounting matrix optimization, as described in the previous paragraph.

Fig. 5

Time series of the roll, pitch, and yaw components of the angular error corrections for the N20 VIIRS SDR geolocation products. The breaks in the plotted lines indicate updates of the geolocation processing parameters.

3.3.

DNB Adjustments

The image cross-correlation technique was used to refine the accuracy of the DNB geolocation after the initial adjustment of the mounting matrix. Figure 6 shows a composite image with the different color layers displaying subsets of a DNB image and a re-projected band I1 image that were used to adjust the DNB “detector position” parameters. The “grid points” for the re-projection are the DNB pixels to which the I1 pixels are re-projected based on the two geolocation datasets, but these points are not on a grid, and linear interpolation combined with a Delaunay triangulation is used to perform the non-gridded re-projection. The subset images are very similar despite DNB having a broader spectral response than I1, and the composite image appears grayscale. The presented image was generated after the parameter adjustment, and there is almost no shift between the DNB and I1 images in the horizontal direction (along scan). That shift is controlled by the DNB detector position parameter for the scan direction. Cross-correlation between the DNB and I1 images also changes accordingly to allow for the determination of the detector position value that provides the maximum cross-correlation, as shown in Fig. 7. The determined optimal parameter value agrees well with that obtained by Lin et al.¹³ based on an independent analysis of cross-correlation between VIIRS DNB and Landsat images.

Fig. 6

Composite RGB image showing a DNB image and a re-projected I1 image overlaid in different color layers: such image subsets were used to adjust the N20 VIIRS DNB geolocation processing parameter (“detector position”). Gray regions in the composite image show where the two images have nearly the same intensities, and the magenta and green regions show where the intensities are different (not visible for the optimal detector shift).

Fig. 7

Cross-correlation between DNB and re-projected I1 images (filled circles) produced with different values of the DNB detector position parameter. The dotted line shows quadratic interpolation of the measured points that supports the determination of the maximum’s position.

3.4.

Geolocation Uncertainty

To evaluate the uncertainty of the VIIRS SDR geolocation products while using a sufficient number of GCP matchups to limit outlier fluctuations, the time span to collect the data was extended from 16 days to 12 months to allow for increasing the cross-correlation threshold from 0.9 to 0.975. That also allows for accounting for the annual oscillations observed in the geolocation errors. Two examples of histograms and distribution functions generated for the VIIRS SDR geolocation errors observed over 12-month periods are shown in Fig. 8. The graphs are for the geolocation products generated before and after the VIIRS optical model correction. Estimates of the 3-sigma uncertainty of the geolocation products are also shown on the graphs by the vertical dashed lines. Although the uncertainty appears to be lower before the optical model correction, the distribution of the errors is clearly more complex. Nevertheless, in both cases the estimated uncertainty is well within the product requirements. One may actually notice that most of the VIIRS SDR geolocation errors are in the 200 m range.

Fig. 8

Two examples of histograms and distribution functions generated for the N20 VIIRS SDR geolocation errors observed over 12-month periods before (a) and after (b) the VIIRS optical model correction in February 2021.

Geolocation uncertainty estimates for all 12-month periods since the N20 launch are shown in Fig. 9. Except for the first estimate that includes data from a few days before the initial correction of the mounting matrix in January 2018, the uncertainty remains within the required range. There is even a substantial margin from the requirement after the processing parameter optimizations conducted in 2018.

Fig. 9

N20 VIIRS geolocation uncertainty evaluated for the successive 12-month periods since the initial on-orbit calibration. The red line shows the geolocation uncertainty requirement for the N20 mission.