John R. Weirich 29 Sep 2023 Product Description for "Phoebe SPC Shape Model and Assessment Products” ======================================================== This package contains topography and albedo data generated by the Gaskell Stereophotoclinometry (SPC) software suite, as well as quality assessment data, for the Saturnian moon Phoebe. The Digital Terrain Model (DTM) of Phoebe in this bundle is similar to the previous PDS model (Gaskell 2020). The images and the SPICE kernels are the same between the two models, but there are some differences. Minor processing was performed to ensure model stability, which may have changed the heights, especially in regions with poor imagery, such as the poles that are less constrained. In addition, the coordinate system of the model was shifted 1.03 km so the center of the coordinate system used by SPC was the same as the Center of Figure of the model. The images used to generate the model are from the PDS Cartography and Imaging Sciences Node, and the kernels are from the Navigation and Ancillary Information Facility (NAIF). Images and kernels used to build the model can be found in document/phoebeimglist.txt and document/phoebekernellist.txt, respectively. The phoebeshapeassessment.pdf in the document directory contains plots of the assessment data, and some of the figures are annotated to indicate the portions of the model we think are reliable and suspect. The native SPC format for a global model is the implicitly connected quadrilateral (ICQ). We provide two ICQ models in this bundle. One with a Q of 512, which means it has 1,579,014 vertices, and one with a Q of 128, which has 99,846 vertices. The Q of 512 is the preferred model, though we provide a Q of 128 model since some programs cannot handle a large number of vertices. For an individual model the distance between vertices is approximately the same over the whole global model, and we refer to this distance as the Ground Sample Distance (GSD). We also provide the model in other formats, which are discussed below. Object Name ICQ Spacing for Q=512 / Q=128 Mean Radius (km) Phoebe 0.300 / 1.195 km GSD 106.5 Topography and Albedo Data ------------------------------------ We generated the global Digital Terrain Models (DTM) using Cassini images for Phoebe. The topography data is provided in various formats. These formats include the native SPC format of Implicitly Connected Quadrilateral (ICQ), plate vector (PLT), Object Vector (OBJ) readable by programs like the Small Body Mapping Tool (SBMT), cubes readable by the USGS ISIS program, and geoTiff which can only be read by GIS programs such as ArcGIS. The albedo data is provided in cube and geoTiff formats. Estimates of the topographic error of SPC DTMs come from testing for the OSIRIS-REx mission. Weirich et al. (2022) used a synthetic, but realistic, digital asteroid with known heights to produce a simulated mission image suite. Note that this test was performed with an early version of the mission image suite, which had less stereo than the flown mission. With only these images, and no access to the synthetic asteroid, we generated an SPC global DTM. This SPC DTM was then compared to the original synthetic DTM to characterize the actual errors. Weirich et al. (2022) showed that a sufficient, but not ideal, image set produced DTMs that were typically accurate to one image pixel of the finest-resolution image. See Weirich et al. (2022) for definitions of a sufficient and ideal image set, which are difficult to explain succinctly. The worst vertex in the test DTM was accurate to about three image pixels of the finest-resolution image. Note that these errors are for both the vertical (i.e. radial) and horizontal directions. We use the above values as an estimate for the DTM errors in this package. What are the uncertainties of the Phoebe shape model? Providing the uncertainty of each vertex is a difficult task, and we cannot give a definitive value. We have many internal consistency checks we perform, but they do not always translate well to uncertainty. The image set of this package is globally comparable to the sufficient, but not ideal, image set of the OSIRIS-REx tests. However, imagery over some locations is better than others, so the assessment data is provided to give a more complete picture of the quality of the model. Unlike the OSIRIS-REx testing, we did not always build the DTMs with a GSD of the finest-resolution image. So for some locations on the model, instead of the typical vertex being accurate to one image pixel of the finest-resolution image, it is accurate to one DTM GSD. Likewise, for these locations the worst DTM vertex is likely to be accurate to three DTM GSD. Overall, a good rule of thumb for the uncertainty is to base it off the best maplet GSD or the shape model GSD, whichever gives the poorer GSD (i.e larger GSD). The uncertainty is then one to two times this poorer GSD. This means that the Q=512 model, with a 300 m GSD, will have a minimum uncertainty of 300 to 600 m. Portions of the Q=512 model will have a larger uncertainty, depending on the best maplet GSD (see document/phoebeshapeassessment.pdf). The Q=128 model, with a 1.195 km GSD, will have most of the surface with an uncertainty of 1.195 to 2.390 km GSD, with the Northern region having a slightly larger uncertainty. The above discussion, considering the details found in the shape assessment PDF, provides the best description of the topographic error. However a single number is often useful when assessing a model, or when comparing against another model. For this value we use the Formal Uncertainty (FormU) defined in Weirich et al. (2022). The FormU is often given for only the highest-resolution maplets, but that will not be sufficient for the Phoebe model because the highest-resolution maplets have such small coverage. Instead we, give the FormU for the maplets with the best global coverage, that of the 500 m maplets. These maplets have a FormU of 0.270 km. Since Phoebe has sporadic maplet coverage, we also give the FormU of all maplets, which is slightly better at 0.255 km. Although FormU is a measure of internal consistency, and not accuracy, Weirich et al. (2022) found the FormU to be within a factor of 2 of the actual error for the OSIRIS-REx testing models. The FormU of Phoebe is an indicator that the error is likely 1 to 2 GSD for the 500 m maplets, which corresponds to 0.5 to 1.0 km. When determining the uncertainty for a specific region of the shape model, the finest-resolution image, best maplet resolution, and ICQ GSD need to be considered as described above. Formats: ICQ: The native SPC format for a global model is the implicitly connected quadrilateral (ICQ), and the models in this bundle have a Q of 512 or 128. The file format is ASCII text with three columns (if topography only) or four columns (if topography and albedo). The ICQ files in this bundle are all four columns. The first three columns are the X (column 1), Y (column 2), and Z (column 3) of the radius vector with units of kilometers, set in the body fixed frame. The +X axis defines 0 degrees longitude, while the +Z axis defines the positive pole (i.e. North Pole for prograde rotation). The fourth column is relative albedo, though we nonetheless still refer to it as simply "albedo". The albedo is a number that varies between 0 (darkest) and 2 (brightest) with the average being 1. Photometric modeling is needed to convert these "albedo" values to an albedo with physical meaning, such as geometric albedo. Further details of the ICQ format and SPC in general, as well as Fortran code to read in the ICQ format, can be found in Gaskell et al. (2008) and Gaskell (2020), respectively. All ICQ files end with an "i" to distinguish them from other files. PLT and OBJ: As previously stated, PLT is a plate model, while OBJ is an object vector readable by the SBMT. These files were generated using the Applied Physics Lab tools generated for the OSIRIS-REx mission. The programs used are ICQ2PLT and PLT2OBJ. The OBJ files generated by PLT2OBJ have been modified to reduce the number of significant figures and the columns have been padded with white spaces to align all columns. Both formats are in units of kilometers. All PLT files end with a "p" to distinguish them from other files. All OBJ files end with a "o" to distinguish them from other files. Cubes: The topography and albedo of the Q=512 model are provided as separate cubes, both with global equirectangular projection and square pixels. They are resampled values from the ICQ generated by SPC. The SPC data was converted to a cube using the Generic Mapping Tool (GMT) programs blockmean and sphinterpolate, followed by the Geospatial Data Abstraction Library (GDAL) program gdal_translate. The cube geometry block was then set using ISIS maptemplate and maplab. The topography is given as radius in meters. The horizontal spacing is kept close to that of the ICQ GSD. All Cube files end with a "c" to distinguish them from other files. GeoTiff: The topography and albedo of the Q=512 model are provided as separate geoTiffs with global equirectangular projection and with square pixels. They were generated from the cubes using the GDAL program gdal_translate. As such, they are also resampled values from the ICQ generated by SPC, and are in units of meters. These files are 32-bit, which is required to obtain the spatial resolutions needed for some solar system bodies. To provide data product similarity across all bodies, we always generate 32-bit geoTiffs even when high spatial resolution is not needed. 32-bit geoTiff files cannot be read by simple programs, and require programs such as ArcGIS to be accessed. All GeoTiff files end with a "g" to distinguish them from other files. Quality Assessment Data ------------------------------ We provide metadata to understand the quality of the topography and albedo data. This metadata is in the form of sigma values of the topography, best maplet resolution, number of images, and best image resolution. All quality assessment data is provided in USGS ISIS cube format. We provide images of these products, along with our assessment of each, in document/phoebeshapeassessment.pdf. To better understand the sigma values and best maplet resolution, a brief description of an SPC maplet is given here. Further details can be found in Palmer et al. (2022). A maplet is a DTM that is usually 99 x 99 vertices and represents a portion of the surface. Maplets can have any vertex spacing, also called Ground Sample Distance (GSD), and are placed to overlap with other maplets. Initial stages of the global DTM are made with large maplets, and as the global DTM develops, smaller and smaller maplets are used. If imagery allows, the result is every portion of the surface has multiple maplets with many different GSD values. Like the radius and albedo, all data uses an equirectangular projection with square pixels. All assessment products are in 1 degree bins, and have 360 by 180 pixels. Best Maplet Resolution: The best maplet resolution is given in units of meters in cube format. The best maplet resolution could be the same everywhere, but for many objects, such as Phoebe, the maplet resolution is better where there are higher resolution images. Note that the maplet resolution can be any value, and this value can be better or worse than the GSD of the global DTM, and better or worse than the best image resolution. When the maplets have a worse GSD than the global DTM, the accuracy of the DTM vertices are closer to that of the maplet's GSD, and not the GSD of the global DTM. Portions with no maplet coverage are listed as 9999 m/vertex (i.e. NoData=9999). Sigma Values: The sigma value is a measure of how well all the maplets agree at a particular vertex on the global DTM, with smaller values indicating better agreement. Note that the sigma is not a measure of the error of the radius at that vertex, rather it is a measure of internal consistency. Nonetheless, the more the maplets differ in their height, the less likely the final radius will be close to the truth. SPC returns the sigma value in meters for each vertex of the global DTM. We downsample these sigma values into 1 degree bins using GMT. Portions of the surface that have one or zero maplets will have an undefined sigma. These undefined portions have a value of 9999, which should be taken as NoData. Note that the data has been resampled and averaged, so sigma values near pixels with a NoData value of 9999 are artificially inflated because of the averaging technique performed by GMT. This artificial inflation cannot be seen in the provided PDF, but will be noticeable when using the digital sigma file. Maximum Image Resolution: Maximum image resolution refers to the best or finest-resolution image. The maximum image resolution is given as meters. Pixels with maximum image resolution of 999999 m/px are actually NoData. Number of Images: Typically more images indicate more accurate heights. SPC has a theoretical lower limit of three images, though in practice four or five images are the lower limit. Areas with fewer than five images should be treated with caution. In general, the number of images is the least useful quality assessment since it does not capture the uniqueness of the viewing conditions. An example is five images taken one second apart. The sun vector has not changed and the spacecraft vector has not changed appreciably, so those five images are effectively one unique image. Another example is a single spacecraft flyby with ten images of the same region on the surface, versus ten spacecraft flybys from different angles, each with a single image of the same surface. The latter is far better than the former even though they each have ten images. This is because it will have a larger variety of emission and incidence angles (see Palmer et al. 2022 and Barnouin et al. 2020 for details, and a description of good and poor imagery). Another example of the limitation of the number of images is that low resolution images are counted, even if they do not contribute to the solution. An example is five good images at 300 m/px, and fifty images at 3,000 m/px. The number of images will be 55, even though effectively there are only five images. Nonetheless, we feel it is still a good qualitative measure of quality, and can highlight low quality areas of the surface that would otherwise appear to be high quality. An example is a portion of the surface with high image resolution, but only three images. Formats Cubes: All assessment data is provided in USGS ISIS cubes, as well as thumbnails in document/phoebeshapeassessment.pdf. As stated above, all products are given in 1 degree bins with an equirectangular projection. All Cube files end with a "c" to distinguish them from other files. ................................................................................ References: ========= Barnouin, O., Daly, M., Palmer, E., and 20 colleagues, Digital terrain mapping by the OSIRIS-REx mission, Planetary and Space Science, Vol. 180, id 104764, 2020. https://doi.org/10.1016/j.pss.2019.104764 Gaskell, R.W., O. Barnouin-Jha, D.J. Scheeres, A.S. Konopliv, T. Mukai, S. Abe, J. Saito, M. Ishiguro, T. Kubota, T. Hashimoto, J. Kawaguchi, M. Yoshikawa, K. Shirakawa, T. Kominato, N. Hirata, and H. Demura, Characterizing and navigating small bodies with imaging data, Meteoritics and Planetary Science, 43, Nr 6, 1049-1061, 2008. https://doi.org/10.1111/j.1945-5100.2008.tb00692.x Gaskell, R.W. Gaskell Phoebe Shape Model V1.0. urn:nasa:pds:gaskell.phoebe.shape-model::1.0. NASA Planetary Data System, 2020. https://doi.org/10.26033/ehkj-xj95 Palmer, E.E., Gaskell, R., Daly, M.G., Barnouin, O.S., Adam, C.D. and Lauretta, D.S., Practical Stereophotoclinometry for Modeling Shape and Topography on Planetary Missions. Planetary Science Journal, Vol. 3, No. 5, id 102, 16 pp., 2022. https://doi.org/10.3847/PSJ/ac460f Weirich, J.R., Palmer, E.E, Daly, M.G., Barnouin, O.S., Getzandanner, K., Kidd, J.N., Adam, C.D., Gaskell, R., Lauretta, D.S., Quality Assessment of Stereophotoclinometry as a Shape Modeling Method Using a Synthetic Asteroid. Planetary Science Journal, Vol. 3, No. 5, id 103, 12 pp., 2022. https://doi.org/10.3847/PSJ/ac46d2