DOI: 10.7291/d16h3s
title: Pluto and Charon limb profile topography

description: We derived updated and expanded topography datasets for Pluto and Charon.
 This is done through finding the body edge (i.e. the limb) in images, and
 with those body edge locations we can apply simple geographical techniques
 to produce limb profiles. The process involves some human intervention,
 but is primarily automation based. Our limb profile topography is useful
 for geologic and geophysical studies of Pluto and Charon. Additionally, we
 provide processed data of how we used the limb profile data in our study.
 The first set of additional data is the result of the processing required
 to determine the Fourier transformation that breaks down the data into its
 wavelength based components. This is done by interpolating the raw data
 onto a evenly spaced grid, then detrending the data by setting the
 end-points to equal elevations. Our second addition has the base 10
 logarithm of our variance spectra results for Pluto and Charon, which is
 the primary result of the scientific portion of the study. We found that
 Charon has a statistically significant break in slope, while Pluto does
 not. This is likely a signal of their crust's structures.
description: We achieve this by determining the edge of the planetary body
 from images (“limb picks”). Using map projections and the known observing
 geometry, we can transform the pixel locations of the limb picks into a
 list of elevations at specific latitude and longitude locations. While our
 methodology mostly matches that of Nimmo et al. (2017), we will reiterate
 some aspects of their methods to detail updates and changes.
 We began our process with a survey of <i>New Horizons
 </i>images from the Long-Range Reconnaissance Imager (LORRI; Cheng
 et al., 2008) and the Ralph instrument’s Multispectral Visible Imaging
 Camera (MVIC; Reuter et al., 2008) sub-instrument. Data from both
 instruments have been used extensively to study Pluto, Charon, and most
 recently Arrokoth (Spencer et al., 2020). Starting with the Planetary Data
 System, we surveyed the images to create a list of images containing body
 edges starting when Pluto was ~100 pixels in diameter. In addition, we
 removed redundant images from the list. This list contained both day-side
 and night-side images from both LORRI and MVIC as the starting point for
 further analysis. While we initially performed limb
 picks and fits for both LORRI and MVIC images, we found large-amplitude,
 long-wavelength undulations for MVIC limb profiles. This occurs in MVIC
 images due to the line-scan exposure method combined with spacecraft
 motion (Weaver et al., 2009). Due to the relatively small number of MVIC
 images, we instead focus on the LORRI images in this analysis.
 For limb picks of day-side (i.e. front-lit) images, we use Method
 A as presented in Nimmo et al. (2017). This method scans each row and
 column in the image, using a threshold approach similar to the method
 described in Dermott and Thomas (1988). We generally use the same
 brightness threshold (50%) and calculate the average brightness over the
 same distance range (0.5<i>d</i> to 0.9<i>d</i>,
 where <i>d</i> is the on-body profile length from center to
 body edge) as used in Nimmo et al. (2017). Once the
 list of limb pixel locations is determined, we visually verify the
 algorithmically chosen limb picks and manually remove picks that are
 obviously not on the limb. These false limb points are often the result of
 either albedo variations or the terminator. Large albedo variations are
 only an issue with Pluto images that contain Cthulhu Regio (CR), a region
 south-west of Sputnik Planitia (SP). Limb picks of images that contain
 areas of CR that border regions of high albedo (e.g. SP) tend to place the
 limb location in CR inward of the actual limb. This happens because the
 average disk brightness is incorporated into the algorithm, and if the
 brightest area of Pluto is near the middle while the darkest is at the
 edge, the 50% cutoff will occur before the actual limb location. However,
 we note that the local albedo at the limb does not show a systematic
 correlation with topography (see section 3.1), suggesting that this effect
 is minor. The algorithm also does not discriminate between the limb and
 terminator of the body, and we only use locations where the edge of the
 lighted hemisphere is caused by the edge of the body (limb) rather than
 the edge of the illuminated hemisphere (terminator). While some terminator
 picks can be accidentally incorporated into a set of limb picks, we apply
 additional geometric checks in the fitting method described below to
 remove points not located on the illuminated limb. 
 After determining the limb location in terms of pixels (x,y), we
 project these points onto a spherical body to convert to an equivalent
 latitude, longitude position (<i>φ, θ</i>) on a spherical body
 given the image coordinates of the body’s center
 (x<sub>0</sub>, y<sub>0</sub>), the latitude and
 longitude of the sub-spacecraft location
 (<i>φ<sub>0</sub>, θ<sub>0</sub></i>),
 the body’s radius <i>R</i> and the orientation of the rotation
 pole relative to the image (<i>ϕ</i>). The spacecraft
 parameters are calculated using the most consistent SPICE information
 based on the smithed kernels from Schenk et al. (2018a&b). We
 report these values for all used images in supplementary Tables 1 and 2 of
 the study, and the results of the pixel locations for
 <i>x<sub>0</sub>, y<sub>0</sub></i>
 and <i>R</i> (in pixels) in supplementary Tables 3 and 4. We
 utilize a general vertical perspective (GVP) projection for determining
 the latitude, longitude positions (<i>φ, θ</i>) of limb pick
 locations (Snyder, 1987). Near closest approach, we account for the effect
 that can lead to a shifting of the limb to an angle less than
 90<sup>0</sup> away from the sub-spacecraft point. At
 distances <i>d</i> far from the body center (<i>d
 &gt;&gt; R</i>), the GVP projection reduces to the
 orthographic projection, which is commonly used in limb profile fitting
 studies (Nimmo et al., 2017). In our projections we assume that both Pluto
 and Charon are spherical, based on the results of Nimmo et al. (2017).
 This simplifies the map projection calculations and determination of the
 radii from the (x,y) pixel locations. Elevation is reported as relative to
 the mean radius of Pluto (1188.3 km) and Charon (606 km) also determined
 in Nimmo et al. (2017). After we obtain raw limb
 profile topography, the data are processed to remove a few different
 possible problems as described below. Generally, we use the raw data for
 most of our analysis, while the processed data is used with presentation
 of limb profiles and some aspects of our analysis. When we apply the
 line-scan method, the algorithm scans both vertically and horizontally.
 This can introduce noise when the scan brightness curves to pick the limb
 near the same coordinate are different in the horizontal and vertical, and
 usually occurs in areas of varying brightness around the limb. To remove
 the shorter wavelength noise, as well as prepare our limb profiles for
 further analysis, we interpolate the limb topography onto a grid with
 constant spacing at a slightly worse ground sampling distance (half the
 total number of original data points). We use a gaussian weighted
 interpolation technique (equation 1 in the study). We then detrend the
 profiles by removing the linear trend through the end-points of the
 profile. Topography generated from limb profiles can be
 used to analyze the long-wavelength properties of worlds. Limb topography
 variance spectra are a useful way of quantifying roughness as a function
 of wavelength (Araki et al., 2009; Shepard et al., 2001; Nimmo et al.,
 2011; Ermakov et al., 2018). To obtain the average variance spectrum, we
 calculate the discrete Fourier transform for each limb profile and then
 find the mean variance in a sequence of bins (Press, 1992; see equation 2
 in the study).
description: The data is contained within comma separated values files with
 the .llk extension, treat them as text files with loading them into your
 mapping software or programs. A read me file is
 contained within the zip file, but the information contained is repeated
 here: This data repository contains Limb
 profile topography data of Pluto and Charon from New Horizons images of
 the two worlds, this in addition to 2 derivative products. The first is
 the processed data from the initial processing we do in order to perform
 Fourier transformations on the data. Second is the binned Variance Spectra
 results. -- Limb profile topography
 files are in a comma separated values format with the file type llk.
 "llk" refers to latitude, longitude, radius
 (kilometers). Each line of values includes:<br>
 latitude, longitude, radius (kilometers), x pixel, y pixel, radius
 (pixels) Latitude is between +/- 90 degrees.<br>
 Longitude is sometimes above 360 degrees if the limb profile wraps around
 the "prime" meridian.<br> Radius is from the body center.
 The Nimmo et al. (2017) mean values for Pluto and Charon are 1188.6 km and
 606.0 km respectively.<br> x pixel/y pixel are based on the source
 image. -- Processed limb profile
 topography files are in a comma separated values format with the file type
 dlle. "dlle" refers to distance, latitude, longitude, elevation
 (kilometers, with mean body radius removed). The limb profiles were
 processes by interpolating onto an even grid spacing and detrended by
 setting the end points to equal elevations. Each line
 of values includes:<br> distance, latitude, longitude,
 elevation Latitude is between +/- 90 degrees.<br>
 Longitude is sometimes above 360 degrees if the limb profile wraps around
 the "prime" meridian. --
 Variance spectra files are in a comma separated values format
 with the standard file type .csv. There are column
 headers with labels of the contained information.<br> Each line
 contains the base 10 logarithm of the Wavenumber (km**-1), Variance
 (km**2), and Standard Deviation