Early Icesat-2 On-Orbit Geolocation Validation Using Ground-Based Corner Cube Retro-Reﬂectors

Article Early ICESat-2 on-orbit Geolocation Validation Using Ground-Based Corner Cube Retro-Reﬂectors

Lori A. Magruder 1,* , Kelly M. Brunt 2,3 and Michael Alonzo 1

1 Applied Research Laboratories, University of Texas at Austin, Austin, TX 78712, USA; [email protected] 2 National Aeronautics and Space Administration, Goddard Space Flight Center, Greenbelt, MD 20771, USA; kelly.m.brunt@nasa.gov 3 University of Maryland, College Park, MD 20742, USA * Correspondence: [email protected]; Tel.: +1-512-835-3068

Received: 1 October 2020; Accepted: 5 November 2020; Published: 7 November 2020

Abstract: The Ice, Cloud and Land Elevation Satellite-2 (ICESat-2), an Earth-observing laser altimetry mission, is currently providing global elevation measurements. Geolocation validation confirms the altimeter’s ability to accurately position the measurement on the surface of the Earth and provides insight into the fidelity of the geolocation determination process. Surfaces well characterized by independent methods are well suited to provide a measure of the ICESat-2 geolocation accuracy through statistical comparison. This study compares airborne lidar data with the ICESat-2 along-track geolocated photon data product to determine the horizontal geolocation accuracy by minimizing the vertical residuals between datasets. At the same location arrays of corner cube retro-reflectors (CCRs) provide unique signal signatures back to the satellite from their known positions to give a deterministic solution of the laser footprint diameter and the geolocation accuracy for those cases where two or more CCRs were illuminated within one ICESat-2 transect. This passive method for diameter recovery and geolocation accuracy assessment is implemented at two locations: White Sands Missile Range (WSMR) in New Mexico and along the 88◦S latitude line in Antarctica. This early on-orbit study provides results as a proof of concept for this passive validation technique. For the cases studied the diameter value ranged from 10.6 to 12 m. The variability is attributed to the statistical nature of photon-counting lidar technology and potentially, variations in the atmospheric conditions that impact signal transmission. The geolocation accuracy results from the CCR technique and airborne lidar comparisons are within the mission requirement of 6.5 m.

Keywords: ICESat-2; ATLAS; geolocation; laser altimetry

1. Introduction The Ice, Cloud and land Elevation Satellite-2 (ICESat-2) launched in September 2018 and was placed in near polar orbit to measure global heights. Similar to its predecessor, ICESat (2003–2009), the primary scientiﬁc goal of ICESat-2 is to collect the critical measurements needed to better understand climate and climate processes [1,2]. These critical measurements are focused on the Polar Regions as they create the ability to derive ice sheet mass balance [3], and sea ice thickness [4]—aspects that indicate controlling mechanisms in climate dynamics [5]. Additionally, ICESat-2 provides heights for vegetation and land surfaces that indicate carbon stock and biomass while atmospheric and ocean measurements contribute to a comprehensive understanding of climate system interactions [6]. ICESat-2 carries a photon counting laser altimeter, ATLAS (Advanced Topographic Laser Altimeter System), to provide range measurements from space. These range measurements in concert with the satellite precision pointing and positioning information produce a geolocation and elevation for photon

Remote Sens. 2020, 12, 3653; doi:10.3390/rs12213653 www.mdpi.com/journal/remotesensing Remote Sens. 2020, 12, 3653 2 of 21 events detected by ATLAS. As indicated by the “photon counting” description of ATLAS, the signal detection sensitivity is at a single photon level which provides an operational advantage for lower power laser requirements and high repetition rates [7]. ATLAS produces a 532 nm laser pulse at 10 kHz. The single pulse is parsed into 6 separate beams, configured into three beam pairs, each containing a tandem of low and high relative energies. The beam pairs are separated by ~3.3 km in the across-track direction on the surface and 90 m between the pair components. This configuration is specifically designed to disentangle elevation change from surface slope (local and regional) while the energy variation increases the dynamic range of the instrument’s detection response to surface reflectance. The spacecraft’s mean orbital altitude is 496 km ( 6 km) which creates the scenario of illuminating ± the surface of the Earth every 0.7 m along track (a pulse every 0.1 msec at ~7 km/sec) with expected footprint diameter of less than 17 m based on the pre-launch design specification. The diameter of the footprint is defined as the spatial extent of the laser energy illumination on the surface of the Earth. ATLAS records the arrival time of photons to less than a billionth of a second. These photon arrival times are aligned with the appropriate time of the transmitted laser pulse to assign each photon to a particular laser footprint on the Earth. Although the photon counting technology is producing aggregates of along-track measurements instead of elevations for individual laser pulses, the diameter does contribute significantly to horizontal and vertical resolution of the features within the footprint on the surface [8]. The scientific goals of the mission governed not only the attributes of the instrumentation relative to footprint diameter, data rates, measurement resolution and spatial coverage but also the operational implementation plans and the methodologies for computing the geophysical data products [9]. Each of the geophysical products are designated with the prefix “ATL” and a unique number. The geolocated photons are a Level 2a product-designated as ATL03. The surface specific products are Level 3a and include ATL06-ATL13 for land ice, sea ice, land/vegetation, ocean, atmosphere and inland water. The mission requirement for ATL03 geolocation accuracy is 6.5 m [2] representing the capability to resolve a measured geodetic position among the contribution of errors from the precision orbit and pointing determination processes. Since ATL03 is the input data for all of the higher-level data products, any errors in the geolocation will propagate forward to these surface specific Level 3a surface interpretations (static and dynamic). Here, we present a method for validating the horizontal position accuracy of ICESat-2 using corner cube retro-reflector (CCR) arrays and high-resolution reference data. The strategy of using passive ground-based methods for geolocation validation was investigated for the original ICESat mission [10,11] and recently studied for the application to the contemporary mission [12]. These CCRs provide an independent measure of footprint level positioning, the laser footprint diameter on the surface, insight into the pointing control of the observatory and overall instrument performance. The comparison to reference data such as airborne lidar gives another independent assessment of the satellite horizontal geolocation accuracy and also provides confirmation of the deterministic solutions derived from the CCR concept presented here. Ultimately, the goal of this work is to provide a proof of concept for small diameter ground-based optics as a means for space-based lidar geolocation validation while also proving that the satellite is meeting the 45 m ± mission requirement for pointing control. The next section of the paper will provide the details of the CCR selection process specific to ICESat-2 characteristics, the approach for analyzing the signatures and the implementation of the technique at two test sites. The following section will present the results of the three satellite overpasses and provide discussion on the variability between each case. Finally, the paper will provide conclusions on how this technique should move forward with respect to geolocation validation and footprint diameter assessment. Remote Sens. 2020, 12, 3653 3 of 21

2. Materials and Methods

2.1. Corner Cube Retro-Reflectors CCR analysis started in the early 1970s with the expectation that they would prove useful for both lunar laser ranging and satellite laser ranging given their specific reflective capabilities [13–15]. The CCR is a unique component that provides a reflection along the initial energy angle of incidence, somewhat mimicking a specular reflection as opposed to a diffuse return. Chang et al. [16] studied the far-field diffraction pattern for corner cubes, using methods presented by Fraunhofer years earlier for circular apertures. This theoretical analysis was used to determine the appropriate size CCR for both ICESat and ICESat-2 mission use cases, with the implementation of putting CCR arrays on the Earth’s surface for independent space-based lidar geolocation validation [12]. The CCR diameter selection is a function of the wavelength, distance from the aperture (e.g., altitude of the satellite), and energy level of the laser. The derived strength of the signal return is proportional to the radius of the CCR, which means larger corner cubes reflect larger signal levels back to the satellite receiver. However, as the CCR diameter increases, the central diffraction disk of returned energy becomes smaller (e.g., diameter of disk is inversely proportional to diameter of the CCR). The Fraunhofer diffraction disk diameter is important in satellite applications as it requires consideration in context of spacecraft velocity aberration. If the velocity aberration value does not converge with the reflected disk diameter, the signal will fall outside of the receiver telescope field of view. In this situation, there is a chance to receive signal from the outer lobes of the Fraunhofer diffraction pattern but it is much less than the signal in the central disk that may or may not be an adequate return given atmospheric scattering and other optical losses [14]. The theoretical CCR size selection for ICESat-2 (wavelength and energy levels) was determined as a range of 6 to 8 mm diameters. This diameter range mitigates the issues with velocity aberration and yet provides an acceptable signal level given the estimated 60% atmospheric transmission each way, a 20% quantum efficiency and 50% detector efficiency [9]. In contrast, the ICESat mission successfully used a 12 mm diameter CCRs to supply both a geolocation accuracy assessment [11] as well as a signature tag for timing accuracy validation [10]. In preparation for ICESat-2 CCR validation, studies using the ATLAS airborne engineering testbed, MABEL (Multiple Altimeter Beam Experimental Lidar) [12] were conducted. The studies revealed that the CCR approach could provide an independent validation of geolocation despite the operational and technical differences between the ICESat’s full-waveform, high-energy lidar technology and the photon-counting technology of MABEL and ICESat-2. However, the analysis of the return signatures required a new approach to accommodate the transition from a single large footprint illumination of multiple corner cubes (ICESat) to the ICESat-2/MABEL illumination of one CCR with multiple laser shots. Understanding multiple laser illuminations of a single CCR for geolocation validation requires a geometric analysis of relative positioning of the CCR and footprint centerline (diameter) and knowledge of the ICESat-2 geolocation determination process. A theoretical scenario for a CCR position exactly aligned with the centerline of the laser footprint would nominally provide a signal every 0.7 m with a timestamp step of 0.1 msec (10 kHz) through the entire length of the ICESat-2 footprint diameter. If the diameter is equal to 17 m (pre-launch best estimate) then in an ideal case this would provide at least one CCR reflected photon from 24 individual laser shots over 2.4 msec. These points appear to be successive single, or multiple, photon detections along-track (at 0.1 msec delta timestamps) with an elevation representative of the height of the CCR above the surface. A conceptual view from a horizontal perspective of the CCR signal and associated ground return elevations is shown in Figure1a, each point representing a geolocated photon, black specific to terrain or ground photons and green from the CCR. The red X represents the actual position of the CCR. The top view of the CCR returns, in Figure1b, show the alignment, horizontally, of the CCR and ground returns despite the difference in elevation. This alignment brings an interesting challenge to the CCR signature analysis in that any detected photon associated with a specific laser shot will be geolocated at the geometric centroid or “bounce point” regardless of spatial separation Remote Sens. 2020, 12, 3653 4 of 21

between that reﬂection point source and the footprint centroid. As such, if the position of the CCR is coincident to the footprint centerline, then the CCR signature requires no additional interpretation Remotewith respectSens. 2020 to, 11 comparing, x FOR PEER the REVIEW ATL03 geolocation to the known position of the CCR. 4 of 21

FigureFigure 1. 1. A Aconceptual conceptual view view of the of thealong-track along-track relative relative elevations elevations of ground of ground and corner and cornercube retro- cube reflectorretro-reflector (CCR)-detected (CCR)-detected photons photons from from a side a side (a) (anda) and top top (b) ( bviewpoint.) viewpoint. The The (a) (a diagram) diagram shows shows the the observedobserved separation separation of of elevation elevation between between the the terrain terrain and and the the CCR CCR but but (b) (b) reveals reveals that that the the geolocation geolocation processprocess positions all detectionsdetections atat thethe centerline centerline of of the the laser laser footprint footprint despite despite the the relative relative position position of theof theCCR CCR within within the the laser laser spot. spot. Keeping the focus on the scenario of the CCR and along-track ATL03 alignment in Figure1, Figure2 Keeping the focus on the scenario of the CCR and along-track ATL03 alignment in Figure 1, presents a time lapse representation of multiple footprint illuminations for one optical component Figure 2 presents a time lapse representation of multiple footprint illuminations for one optical and the expected detected photons. The dotted green circles are the individual laser footprints based component and the expected detected photons. The dotted green circles are the individual laser on the ATL03 geolocated centroids and the blue circles are associated with statistical determination footprints based on the ATL03 geolocated centroids and the blue circles are associated with statistical of the footprint location relative to the CCR position. Although not to scale, the diagram illustrates determination of the footprint location relative to the CCR position. Although not to scale, the the collection of CCR detected signals as they initiate with the leading edge of the first relevant laser diagram illustrates the collection of CCR detected signals as they initiate with the leading edge of the shot (Figure2b) and ends with the trailing edge of the final spot (Figure2f), in this case, the third first relevant laser shot (Figure 2(b)) and ends with the trailing edge of the final spot (Figure 2(f)), in footprint. Figure2f highlights the recovered chord length (along-track distance of the CCR photons) this case, the third footprint. Figure 2(f) highlights the recovered chord length (along-track distance as equivalent to the diameter of the laser footprint. The mid-point of the CCR signature is directly of the CCR photons) as equivalent to the diameter of the laser footprint. The mid-point of the CCR compared to the known CCR position to assess the ATL03 geolocation accuracy in both along-track signature is directly compared to the known CCR position to assess the ATL03 geolocation accuracy (∆Y) and across track (∆X) directions. In the case of Figure2, the geolocation has no error ( ∆X = ∆Y = in both along-track (ΔY) and across track (ΔX) directions. In the case of Figure 2, the geolocation has 0) as the predicted mid-point of the CCR signature matches exactly with the known CCR coordinates. no error (ΔX = ΔY = 0) as the predicted mid-point of the CCR signature matches exactly with the Figure3 illustrates the case where the CCR is still aligned with the centerline but there is geolocation known CCR coordinates. Figure 3 illustrates the case where the CCR is still aligned with the centerline error in the data. In this example, the predicted CCR position (blue square) using the mid-point of the but there is geolocation error in the data. In this example, the predicted CCR position (blue square) CCR signature is not equal to the actual CCR position (red X) such that ∆X and ∆Y are the horizontal using the mid-point of the CCR signature is not equal to the actual CCR position (red X) such that ΔX offsets and indicate the ATL03 geolocation accuracy. and ΔY are the horizontal offsets and indicate the ATL03 geolocation accuracy. More complexity occurs when the CCR position and footprint centerline are not aligned. For those More complexity occurs when the CCR position and footprint centerline are not aligned. For cases, the apparent along-track chord length of the CCR signature will decrease. This length will be those cases, the apparent along-track chord length of the CCR signature will decrease. This length inversely proportional to the across-track distance from the centroid of the footprint based on the will be inversely proportional to the across-track distance from the centroid of the footprint based on geometry of a circle. Figure4 provides the relative chord length (c) of the CCR signature when its the geometry of a circle. Figure 4 provides the relative chord length (c) of the CCR signature when its position (black dot) is a distance (x) from the footprint center (C1). To determine the geolocation position (black dot) is a distance (x) from the footprint center (C1). To determine the geolocation accuracy of the data, the horizontal offset between the CCR position and the footprint centroid must be accuracy of the data, the horizontal offset between the CCR position and the footprint centroid must calculated using simple geometry for a given footprint diameter and measured chord length. be calculated using simple geometry for a given footprint diameter and measured chord length.

Remote Sens. 2020, 12, 3653 5 of 21 RemoteRemote Sens. Sens. 2020 2020, ,11 11, ,x x FOR FOR PEER PEER REVIEW REVIEW 55 of of 21 21

Figure 2. Time lapse scenario of multiple laser footprints illuminating a single CCR when its position FigureFigureFigure 2. 2.2. Time Time lapse lapse scenario scenario of of multiple multiple laser laser footprints footprints illuminating illuminating a aa single singlesingle CCR CCRCCR when whenwhen its itsits position positionposition is aligned with the along-track centerline. Each panel ((a) – (f)) represents a theoretical time step isisis aligned aligned with withwith the thethe along-track along-trackalong-track centerline. cecenterline.nterline. Each EachEach panel panelpanel (a–f) ((a)((a) represents –– (f))(f)) representsrepresents a theoretical aa theoreticaltheoretical time step associatedtimetime stepstep associated with successive CCR illuminations. associatedwithassociated successive with with successive CCRsuccessive illuminations. CCR CCR illuminations. illuminations.

Figure 3. (a) Scenario when the CCR is aligned with the footprint centerline and there are errors in FigureFigureFigure 3. 3.3. (a) ((a)a) Scenario ScenarioScenario when whenwhen the thethe CCR CCRCCR is isis a alignedalignedligned with withwith the thethe footprint footprintfootprint centerline centerlinecenterline and andand there therethere are areare errors errorserrors in inin the ATL03 geolocations. (b) Geolocation accuracy method for using the along (ΔY) and across (ΔX) thethethe ATL03 ATL03ATL03 geolocations. geolocations.geolocations. (b) ((b)b )Geolocation Geolocation accuracy accuracy method method for for using using the the along along ( (ΔΔ∆Y)Y) and and across across ( (Δ∆ΔX)X) tracktracktrack distances distancesdistances between betweenbetween the thethe known knownknown CCR CCR position position an andandd the the mid-point mid-point of of the the CCR CCR signature signature (blue (blue box). box). (c)((c)c) Final FinalFinal corrected correctedcorrected ATL03 ATL03ATL03 track track based based on on theoretical theoretical results. results.

FigureFigureFigure 4. 4.4. Geometric Geometric representation representation of of the the relative relative position positionposition of of a a CCR CCR (black (black dot) dot) to toto the thethe laser laserlaser footprint footprintfootprint along-track centerline (C ) and its corresponding chord length (c), which is less than the full diameter along-trackalong-track centerline centerline (C (C111)) and and its its corresponding corresponding chord chord length length (c), (c), which which is is less less than than the the full full diameter diameter ofofof the thethe spot. spot.spot. The The horizontal horizontal offset ooffsetﬀset (x) (x) of ofof the thethe CCR CCRCCR po positionpositionsition and andand the thethe center centercenter point pointpoint can cancan be bebe calculated calculatedcalculated using usingusing simple geometry with the diameter/radius of the footprint and measured chord length to determine the simplesimple geometry geometry with with the the diameter diameter/radius/radius of of the the footprint footprint and and meas measuredured chord chord length length to to determine determine horizontal geolocation accuracy. thethe horizontal horizontal geolocation geolocation accuracy. accuracy.

Remote Sens. 2020, 12, 3653 6 of 21

Remote Sens. 2020, 11, x FOR PEER REVIEW 6 of 21 Figure5 depicts the scenario where the CCR and centerline are not aligned and there is a geolocationFigure error.5 depicts Similar the toscenario the other where ﬁgures, the theCCR panel and atcenterline the end ofare the not time aligned lapse and of laser there shots is a providesgeolocation the resultserror. forSimilar the along-track to the other (∆ Y)figures, and across-track the panel at oﬀ setthe (∆endX) betweenof the time the predictedlapse of laser footprint shots centroidprovides and the the results CCR for position. the along-track This is the (Δ applicableY) and across-track approach usedoffset for(ΔX) the between ICESat-2 the CCR predicted based geolocationfootprint centroid validation and moving the CCR forward. position. This is the applicable approach used for the ICESat-2 CCR based geolocation validation moving forward.

FigureFigure 5. 5.( a(a)) Scenario Scenario when when the the CCR CCR is is not not aligned aligned with with the the footprint footprint centerline centerline and and there there are are errors errors in thein the ATL03 ATL03 geolocations. geolocations. (b) (b) Geolocation Geolocatio accuracyn accuracy method method for for using using the the along along (∆ (ΔY)Y) and and across across ( ∆(ΔX)X) tracktrack distances distances between between the the known known CCR CCR position position and and the the mid-point mid-point of of the the CCR CCR signature signature (blue (blue box) box) forfor the the ( c ) (c) Final Final corrected corrected ATL03 ATL03 track track based based on on theoretical theoretical results. results. An important detail in the geometric analysis for ATL03 geolocation validation using CCR arrays An important detail in the geometric analysis for ATL03 geolocation validation using CCR is the approach for systematic chord length extraction from ATL03 data to ensure statistical consistency arrays is the approach for systematic chord length extraction from ATL03 data to ensure statistical for multiple overpasses and different ICESat-2 beams. Although the diagrams presented in Figures1–5 consistency for multiple overpasses and different ICESat-2 beams. Although the diagrams presented clearly show a very stark beginning and end of the CCR signature length in theory, the reality is in Figures 1–5 clearly show a very stark beginning and end of the CCR signature length in theory, the much different given the variability with radiometric (signal strength) influences such as atmospheric reality is much different given the variability with radiometric (signal strength) influences such as attenuation, surface reflectance, solar background noise and beam energy. Figure6 shows example atmospheric attenuation, surface reflectance, solar background noise and beam energy. Figure 6 CCR data from an ICESat-2 overpass collected at White Sands Missile Range (WSMR). The figure is a shows example CCR data from an ICESat-2 overpass collected at White Sands Missile Range side view of the ATL03 geolocated point cloud, showing detected ground photons in black and CCR (WSMR). The figure is a side view of the ATL03 geolocated point cloud, showing detected ground detected photons in green. Although not the case in this example, when heavy solar background noise photons in black and CCR detected photons in green. Although not the case in this example, when is present, signal finding can be more difficult. heavy solar background noise is present, signal finding can be more difficult. Typically, laser diameters are the equivalent to the 1/e2 Gaussian beam diameter; representative Typically, laser diameters are the equivalent to the 1/e2 Gaussian beam diameter; representative of 86.6% of the total energy spatial profile. It is entirely possible to detect CCR returns from outside of 86.6% of the total energy spatial profile. It is entirely possible to detect CCR returns from outside of the 1/e2 boundary based on theoretical calculations, but those are more susceptible to radiometric of the 1/e2 boundary based on theoretical calculations, but those are more susceptible to radiometric losses. As such, the 1/e2 assumption provides standardization with the fact that the 1/e2 diameter is losses. As such, the 1/e2 assumption provides standardization with the fact that the 1/e2 diameter is associated with a 2σ value of a Gaussian energy profile so the chord length extracted from the signature associated with a 2σ value of a Gaussian energy profile so the chord length extracted from the would mimic this estimation. Figure7 provides the statistical histogram representation of the CCR signature would mimic this estimation. Figure 7 provides the statistical histogram representation of signature shown in Figure6 and the corresponding Gaussian profile. Although the along-track distance the CCR signature shown in Figure 6 and the corresponding Gaussian profile. Although the along- for those data in Figure6 is 10.1 m the 2 σ value is 10.7 m. Pre-launch ATLAS laser measurements track distance for those data in Figure 6 is 10.1 m the 2σ value is 10.7 m. Pre-launch ATLAS laser confirmed a Gaussian beam profile [17] but certainly the CCR distribution profiles are not a perfect measurements confirmed a Gaussian beam profile [17] but certainly the CCR distribution profiles are Gaussian representation, particularly when the sample size of photons is relatively small. More not a perfect Gaussian representation, particularly when the sample size of photons is relatively appropriate distribution statistics can be explored as more satellite overpasses are captured. However, small. More appropriate distribution statistics can be explored as more satellite overpasses are as a preliminary effort the Gaussian fits provide the means for exploring the efficacy of the technique captured. However, as a preliminary effort the Gaussian fits provide the means for exploring the and have skew values that are still considered approximately symmetric. efficacy of the technique and have skew values that are still considered approximately symmetric. The CCR return photon chord length geometrically constrains the geolocation solution but only if the diameter is known to determine the distance of the CCR position relative to the centerline. Although pre-launch estimates of diameter exist there is no on-orbit method capable of confirming the true operational value. Furthermore, even if the diameter is known if there is only one CCR illuminated, the symmetry of the spot creates ambiguity as to if the CCR position is east or west of the centroid. The mitigation for these uncertainties is the collection of multiple CCR returns within

Remote Sens. 2020, 11, x FOR PEER REVIEW 7 of 21 Remote Sens. 2020, 11, x FOR PEER REVIEW 7 of 21 one overpass. The analysis of the signals in concert create a unique scenario purely based on the one overpass. The analysis of the signals in concert create a unique scenario purely based on the relative geometry of the CCR positions in the array and chord lengths of the signal signatures. This relative geometry of the CCR positions in the array and chord lengths of the signal signatures. This creates a deterministic method for finding the effective diameter of the laser footprint and the Remotecreates Sens. 2020a deterministic, 12, 3653 method for finding the effective diameter of the laser footprint and7 of 21the geolocation simultaneously. geolocation simultaneously.

Figure 6. Corner cube signature for a strong beam CCR illumination. The black data are the signal FigureFigure 6. Corner6. Corner cube cube signature signature for for a stronga strong beam beam CCR CCR illumination. illumination. The The black black data data are are the the signal signal attributed to the ground surface and the green data are those presumed to be from a single CCR based attributedattributed to theto the ground ground surface surface and and the the green green data data are are those those presumed presumed to beto be from from a single a single CCR CCR based based on the location and height of signature. onon the the location location and and height height of signature.of signature.

FigureFigure 7. Along-trackAlong-track CCR signal distributiondistribution statisticalstatistical extraction extraction of of the the eff effectectiveive chord chord length length based based on Figureσ 7. Along-track CCR signal distribution statistical extraction of the effective chord length based onthe the 2 value2σ value for a Gaussianfor a Gaussian energy energy profile asprofile a preliminary as a preliminary assessment assessment of the optimal of the signal optimal distribution. signal on the 2σ value for a Gaussian energy profile as a preliminary assessment of the optimal signal distribution. Thedistribution CCR return. photon chord length geometrically constrains the geolocation solution but only if the diameter is known to determine the distance of the CCR position relative to the centerline. The comprehensive (diameter and geolocation accuracy) CCR analysis approach calculates both AlthoughThe pre-launch comprehensive estimates (diameter of diameter and geolocation exist there isaccuracy) no on-orbit CCR method analysis capable approach of confirming calculates the both through an iterative process, varying the diameter and finding the best fit to the geometric truethrough operational an iterative value. Furthermore, process, varying even if the diameterdiameter is and known finding if there the is onlybest one fit CCRto the illuminated, geometric constraints. Figure 8 shows one iteration for diameter recovery for which the laser ground track theconstraints. symmetry Figure of the spot8 shows creates one ambiguity iteration asfor to diameter if the CCR recovery position for is which east or the west laser of the ground centroid. track passes to the east of two CCRs (panel 1). Starting with an initial estimate of footprint diameter, the Thepasses mitigation to the foreast these of two uncertainties CCRs (panel is the1). Starting collection with of multiplean initial CCR estimate returns of footprint within one diameter, overpass. the algorithm determines the geolocation offsets (ΔX, ΔY) for each CCR signature. Since the goal is to Thealgorithm analysis ofdetermines the signals the in concertgeolocation create offsets a unique (ΔX, scenario ΔY) for purely each CCR based signature. on the relative Since geometrythe goal is of to determine one final geolocation offset for the track, the mean of the offset contributions from the thedetermine CCR positions one final in the geolocation array and chordoffset lengthsfor the oftrack, the signalthe mean signatures. of the offset This creates contributions a deterministic from the method for finding the effective diameter of the laser footprint and the geolocation simultaneously.

The comprehensive (diameter and geolocation accuracy) CCR analysis approach calculates both through an iterative process, varying the diameter and ﬁnding the best ﬁt to the geometric constraints. Remote Sens. 2020, 12, 3653 8 of 21

Figure8 shows one iteration for diameter recovery for which the laser ground track passes to the east of two CCRs (panel 1). Starting with an initial estimate of footprint diameter, the algorithm determines Remotethe geolocation Sens. 2020, 11, o xff FORsets PEER (∆X, REVIEW∆Y) for each CCR signature. Since the goal is to determine one8 finalof 21 Remotegeolocation Sens. 2020 off, 11set, x for FOR the PEER track, REVIEW the mean of the offset contributions from the individual CCRs is8 used, of 21 individualdenoted as CCRs∆Xµ andis used,∆Yµ denotedin Panel as 3 Δ ofX Figureμ and Δ8.Y Toμ in assess Panel the3 of geolocation Figure 8. To solution, assess the the geolocation root mean individualsolution,squared errorthe CCRs root (RMSE) ismean used, between squared denoted all error centroidas Δ(RMSE)Xμ and predictions betwΔYμ eenin Panel andall centroid CCR 3 of positionsFigure predictions 8. isTo calculated assess and CCR the with geolocationpositions the idea is calculatedsolution,that the minimum the with root the mean RMSEidea squared that is representative the error minimum (RMSE) of RMSE thebetw best eenis representative fit all to centroid the geometry. predictions of the This best and process fit toCCR the is positions performedgeometry. is Thiscalculatedfor all process possible with is performed footprintthe idea diametersthat for allthe possible minimum at 10 cmfootprint incrementsRMSE diameters is representative from at 5 to10 20cm mof increments andthe repeatedbest fit from to for the 5 allto geometry. 20 footprint m and repeatedThisconfigurations, process for isall performed e.g.,footprint the relative configurations,for all possible track position footprinte.g., the to thediametersrelative CCR track positions. at 10 position cm increments The to number the CCR from of positions. configuration5 to 20 m andThe numberrepeatedcombinations of for configuration all is footprint 2N, where combinations configurations, N is the number is 2e.g.,N, ofwhere the CCRs re Nlative illuminatedis the track number position within of CCRs oneto the illuminated overpass. CCR positions. For within the caseTheone overpass.numberpresented of For inconfiguration Figure the case8, there presented combinations will be fourin Figure possibleis 2N , 8,where ther geometriese N will is the be evaluated numberfour possible of for CCRs mean geometries illuminated geolocation evaluated within o ffset oneandfor overpass.meanRMSE geolocation of theFor solution the offsetcase for presented and a given RMSE diameterin of Figure the solution (Figure 8, ther 9fore). will Thea given be lowest four diameter RMSEpossible (Figure scenario geometries 9). will The provide evaluatedlowest aRMSE final for scenariomeangeolocation geolocation will accuracy provide offset anda final and estimate geolocationRMSE ofof thethe accuracy lasersolution footprint and for aestimate given diameter. diameter of the laser (Figure footprint 9). The diameter. lowest RMSE scenario will provide a final geolocation accuracy and estimate of the laser footprint diameter.

Figure 8. Iterative process ((a) – (c)) of determining the geolocation offsets associated with the multiple Figure 8. Iterative process (a–c) of determining the geolocation oﬀsets associated with the multiple (2) Figure(2) CCR 8. signature Iterative processcharacteristics ((a) – (c)) and of determiningrelative geometry the ge forolocation a given offsets laser footprintassociated diameter. with the multiple (2)CCR CCR signature signature characteristics characteristics and and relative relative geometry geometry for for a given a given laser laser footprint footprint diameter. diameter.

FigureFigure 9. IterativeIterative process (((a)a–d )– for(d)) exploring for exploring the relative the relative positioning positioning of the laserof the ground laser ground track and track the Figureandlocations the 9. locations ofIterative the illuminated of process the illuminated ((a) CCRs. – (d)) The CCR for number s.exploring The number of combinations the reoflative combinations positioning is 2N, where is 2 Nof N, wherethe is the laser numberN isground the number of CCRstrack ofandconsidered CCRs the locations considered (e.g., 2of CCRs the(e.g., illuminated= 2 fourCCRs possible = fourCCR possible geometrics. The number geometric conﬁgurations). of combinations configurations) is 2. N, where N is the number of CCRs considered (e.g., 2 CCRs = four possible geometric configurations). 2.2. Ground-Based Validation Implementation: White Sands Missle Range (WSMR), New Mexico 2.2. Ground-Based Validation Implementation: White Sands Missle Range (WSMR), New Mexico The analysis to determine the precise location, configuration and orientation of the CCR arrays was Thebased analysis on the to pre-launch determine thedetails precise for location,ATLAS beamconfiguration spacing andon theorientation surface ofand the the CCR planned arrays referencewas based ground on the tracks. pre-launch The spacecraft details for orbit ATLAS is inclined beam at spacing 92º relative on theto the surface celestial and equator the planned which meansreference 2º groundfrom a truetracks. polar The orbit spacecraft [2]. The orbit inclination is inclined creates at 92º arelative 6.3º angle to the relative celestial to equatora north/south which means 2º from a true polar orbit [2]. The inclination creates a 6.3º angle relative to a north/south

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2.2. Ground-Based Validation Implementation: White Sands Missle Range (WSMR), New Mexico The analysis to determine the precise location, configuration and orientation of the CCR arrays was based on the pre-launch details for ATLAS beam spacing on the surface and the planned reference ground tracks. The spacecraft orbit is inclined at 92◦ relative to the celestial equator which means 2◦ Remote Sens. 2020, 11, x FOR PEER REVIEW 9 of 21 from a true polar orbit [2]. The inclination creates a 6.3◦ angle relative to a north/south orientation of the satellite ground tracks at the WSMR latitude. The ground track orientation is an important geometryorientation consideration of the satellite in theground physical tracks design at the of WSMR the CCR latitude. arrays inThe the ground hope to track capture orientation multiple is CCR an signaturesimportant forgeometry a beam consideration pair (weak and in strong) the physical during de a singlesign of overpass. the CCR Thearrays global in the design hope of to the capture arrays usesmultiple the diamondCCR signatures pattern (Figurefor a beam 10) created pair (weak by the an descendingd strong) during and ascending a single reference overpass. ground The global track intersectionsdesign of the inarrays nearest uses proximity the diamond of the pattern target location (Figure and 10) usescreated each by of the the descending four diamond and vertices ascending as a centerreference point ground position track for intersections a local array. in Thesenearest four proxim arrayity locations of the target coincide location with and the uses orange each squares of the infour Figure diamond 10. Sincevertices the as array a center design point goal position is to capture for a local one array. of the These three four beam array pairs locations during coincide a single overpass,with the orange it is important squares toin understandFigure 10. Since how thethe pairsarray are design identified. goal is For to capture the three one pairs, of the pair three 1 is onbeam the leftpairs side during of the a satellitesingle overpass, relative to it the is directionimportant of to motion. understand The individual how the pairs components are identified. within theFor pairthe arethree deemed pairs, pair Ground 1 is Trackon the 1 left left side (GT1l) of the and satellit Grounde relative track 1 rightto the (GT1r). direction The of nadir motion. beam The pair individual is pair 2 andcomponents the pair towithin the right the pair of the are satellite deemed direction Ground of Trac motionk 1 left is pair(GT1l) 3. Thoseand Ground individual track beams 1 right are (GT1r). GT2l, GT2r,The nadir GT3l, beam and GT3r,pair is respectively.pair 2 and the The pair array to the positions, right of in the Figure satellite 10, aredirection designed of motion to capture is pair GTxl 3. withThose the individual east and southbeams array are GT2l, and GTxrGT2r, with GT3l, the and north GT3r, and respectively. west arrays The for aarray descending positions, pass. in Figure For an ascending10, are designed pass the to same capture configuration GTxl with will the captureeast and GTxr south with array the eastand andGTxr north with arrays the north and GTxland west with thearrays south for anda descending west respectively. pass. For The an geographic ascending distancespass the same of the configuration arrays and the will selected capture spacing GTxr of with the CCRsthe east within and north the arrays arrays is providedand GTxl inwith Figure the sout11. h and west respectively. The geographic distances of the arrays and the selected spacing of the CCRs within the arrays is provided in Figure 11.

Figure 10. Ascending and descending ground track intersection pattern that informed the relative Figure 10. Ascending and descending ground track intersection pattern that informed the relative positioning of multiple CCR arrays designed to capture multiple CCR signatures for a beam pair (weak positioning of multiple CCR arrays designed to capture multiple CCR signatures for a beam pair and strong) during a single overpass. The GTl and GTr are the Ground Track Left/Right components of (weak and strong) during a single overpass. The GTl and GTr are the Ground Track Left/Right the pair. components of the pair. Although one ICESat-2 reference ground track (RGT) is planned to directly pass over the arrays, additionalAlthough ground one ICESat-2 tracks in reference near proximity ground willtrack require (RGT) theis planned observatory to directly to point pass o overﬀ-nadir the arrays, to this targetadditional of opportunity ground tracks (TOO). in near TOOs proximity can be implemented will require viathe uploaded observatory instrument to point commandoff-nadir to ﬁles this if target of opportunity (TOO). TOOs can be implemented via uploaded instrument command files if not in violation of the operational limit of 5º. These off-nadir instances are important for validation studies as they often magnify errors or biases in the position or pointing determination solutions not normally observed during typical near-nadir pointing [18–20]. The success of a TOO is indicative of the observatory pointing control capability and confirms that the instrument command process, and on-board attitude control systems are working appropriately. As previously discussed, the correlation of corner cube position and the resultant signal along- track chord length provides the opportunity to determine both the ground track’s positional offsets and the laser footprint diameter. However, there remains a need to appropriately identify which CCR

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not in violation of the operational limit of 5◦. These off-nadir instances are important for validation studies as they often magnify errors or biases in the position or pointing determination solutions not normally observed during typical near-nadir pointing [18–20]. The success of a TOO is indicative of the observatory pointing control capability and confirms that the instrument command process, and on-board attitude control systems are working appropriately. As previously discussed, the correlation of corner cube position and the resultant signal along-track chord length provides the opportunity to determine both the ground track’s positional offsets and Remotethe laser Sens. footprint 2020, 11, x FOR diameter. PEER REVIEW However, there remains a need to appropriately identify which10 CCR of 21 belongs to a specific signature. If that information is unknown, it will be impossible to determine the belongsappropriate to a specific geometric signature. constraint. If that That information said, if the is CCRunknown, mount it heightswill be impossible within an arrayto determine are varied, the appropriateany given linear geometric (along-track) constraint. signal That detection said, if the sequence CCR mount is unique heights with within respect an toarray the are vertical varied, off anysets givenwithin linear the array. (along-track) Figure 11 depictssignal detection the array contentsequence in is terms unique of individual with respect mount to heights,the vertical suffi offsetsciently withinpopulated the array. so as Figure to increase 11 depicts the likelihood the array content of ICESat-2 in terms ground of individual track intersections mount heights, and sufficiently to support populatedunambiguous so as determination to increase the of CCR likelihood ownership of ICESat-2 to those signaturesground track in theintersections ATL03 product. and to support unambiguous determination of CCR ownership to those signatures in the ATL03 product.

Figure 11. CCRCCR array array geometry geometry at White Sands Missile Range (WSMR). Each array contains 12 CCRs on varying height poles to ensure ensure the the correct correct CCR CCR lo locationcation is is identified identified from from the the CCR CCR signal signal signature. signature. The deployment of the CCR arrays was completed just prior to the satellite launch date to ensure The deployment of the CCR arrays was completed just prior to the satellite launch date to ensure they were assembled in time for early on-orbit validation but were not overly-exposed to environmental they were assembled in time for early on-orbit validation but were not overly-exposed to conditions that might degrade the optics unnecessarily. The CCRs were embedded in 0.4 m PVC environmental conditions that might degrade the optics unnecessarily. The CCRs were embedded in caps customized to hold the 8 mm diameter optical components. These caps were placed on PVC 0.4 m PVC caps customized to hold the 8 mm diameter optical components. These caps were placed pipes of variable length to adhere to the pattern shown in Figure 11: 0.75, 1.5, 2.3, and 3 m. These on PVC pipes of variable length to adhere to the pattern shown in Figure 11: 0.75, 1.5, 2.3, and 3 m. heights were chosen based on the vertical resolution within ATLAS, as they would provide distinct These heights were chosen based on the vertical resolution within ATLAS, as they would provide elevation separation from the surface as well from each other. Furthermore, none of these mount distinct elevation separation from the surface as well from each other. Furthermore, none of these heights created significant logistical challenges associated with securing in place as taller poles are at mount heights created significant logistical challenges associated with securing in place as taller poles risk of breaking or collapsing in the known environment experienced previously with the validation are at risk of breaking or collapsing in the known environment experienced previously with the efforts for ICESat. The pipes were secured to the surface with partially submerged metal rebar and validation efforts for ICESat. The pipes were secured to the surface with partially submerged metal support wires. The position of each CCR was surveyed with differential Global Navigation Satellite rebar and support wires. The position of each CCR was surveyed with differential Global Navigation System (GNSS) for a geolocation accuracy to within 1 m. Satellite System (GNSS) for a geolocation accuracy to within 1 m. Another method for independent ICESat-2 geolocation validation can be accomplished by Another method for independent ICESat-2 geolocation validation can be accomplished by comparing the satellite data to known, high-resolution datasets. These “reference” surfaces provide comparing the satellite data to known, high-resolution datasets. These “reference” surfaces provide accurate characterization of the region that can be directly compared to the ICESat-2 ATL03 elevations accurate characterization of the region that can be directly compared to the ICESat-2 ATL03 as well as the higher-level geophysical data products at variable length scales. The University of elevations as well as the higher-level geophysical data products at variable length scales. The Texas at Austin Bureau of Economic Geology performed an airborne lidar survey over the region of University of Texas at Austin Bureau of Economic Geology performed an airborne lidar survey over the region of WSMR within the broader range perimeter using a Leica Chiroptera lidar system and a high-resolution imager. The airborne collection acquired both near-infrared (NIR) and visible (green) data at ~10 pts/m2. Accuracy of the lidar dataset was enhanced using GNSS base-stations for data post processing. These receivers enabled differential solutions to produce the most accurate lidar measurement for surface characterization. Based on the effective post processing and the characteristics of the Leica system the airborne measurements provide, on average, better than 10 cm vertical accuracy and 1 m horizontal. The terrain is somewhat homogeneous at WSMR but there are distinct geophysical features within the scene that can be used as ground control, or reference points in the comparison to those relevant ICESat-2 transects across the region. This method provides an

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WSMR within the broader range perimeter using a Leica Chiroptera lidar system and a high-resolution imager. The airborne collection acquired both near-infrared (NIR) and visible (green) data at ~10 pts/m2. Accuracy of the lidar dataset was enhanced using GNSS base-stations for data post processing. These receivers enabled diﬀerential solutions to produce the most accurate lidar measurement for surface characterization. Based on the eﬀective post processing and the characteristics of the Leica system the airborne measurements provide, on average, better than 10 cm vertical accuracy and 1 m horizontal. The terrain is somewhat homogeneous at WSMR but there are distinct geophysical features within theRemote scene Sens. that2020,can 11, x be FOR used PEER as REVIEW ground control, or reference points in the comparison to those relevant11 of 21 ICESat-2 transects across the region. This method provides an independent assessment of both the horizontalindependent and assessment vertical accuracy of both ofthe the horizontal ATL03 product and vertical and was accuracy also planned of the ATL03 to validate product theresults and was of thealso CCR planned proof to of validate concept the for results geolocation of the validation.CCR proof of concept for geolocation validation.

2.3. Ground-Based Validation Implementation: 88S Traverse Since thethe validationvalidation eeffortsfforts at at WSMR WSMR provide provide assessment assessment of of the the satellite satellite measurement measurement accuracy accuracy at aat single a single northern-hemisphere northern-hemisphere point point within within the orbit, the CCRorbit, arrays CCR werearrays also were deployed also deployed along a portion along ofa theportion 88◦ South of the (88S) 88º South line of (88S) latitude line in of Antarctica, latitude in where Antarctica, a large-scale where ICESat-2 a large-scale validation ICESat-2 effort, validation referred toeffort, as the referred 88S Traverse, to as the is 88S underway Traverse, [21 ].is Givenunderway that ICESat-2[21]. Given has that an orbitalICESat-2 inclination has an orbital of 92◦ inclination, the orbits convergeof 92º, the alongorbits 88S,converge making along it a dense88S, making region it of a grounddense region tracks of and ground cross-over tracks points.and cross-over points. A total of 5 small arrays were deployed along th thee 88S Traverse during thethe two different different traverse seasons (2017–2018 and and 2018–2019). 2018–2019). The The geographical geographical location location of ofthe the traverse traverse and and the theCCR CCR arrays arrays are areprovided provided in Figure in Figure 12. 12The. The arrays arrays contained contained anywhere anywhere from from 4 4to to 9 9CCRs CCRs and and were were mounted on bamboo poles using PVC caps. The bamboo poles varied in height from ~0.5 m to just under 2 m, in patterns suchsuch that that a givena given CCR CCR was was distinguishable distinguishable from from the neighboring the neighboring CCRs, CCRs, similar similar to the concept to the ofconcept Figure of3. Figure The spacing 3. The between spacing the between bamboo the poles bamb wasoo ~30poles m, was such ~30 that m, the such spacing that the was spacing larger than was thelarger ICESat-2 than the expected ICESat-2 footprint expected diameter footprint ~17 diameter m, but much ~17 m, smaller but much than thesmaller across-track than the spacing across-track of the ICESat-2spacing of beams the ICESat-2 (~90 m) beams and the (~90 mission m) and requirement the mission of requirement spacecraft pointing of spacecraft control pointing (45 m). control (45 m).

Figure 12. Geographical locations of the CCR arrays along 88S (left), with a representative array also shown (right).

The positions of the bamboo poles were measuredmeasured using kinematic GNSS methods and Precise Point PositioningPositioning post-processing post-processing techniques techniques in in a commerciala commercial software software package package [22]. [22]. Metal Metal poles poles were alsowere deployed also deployed in the centerin the ofcenter each of array each to array allow to for allow easy for resurveying easy resurveying of a single of positiona single ofposition the array of tothe assess array horizontalto assess horizontal movement movement of the arrays of the due arra toys ice-sheet due to ice-sheet flow; the flow; positions the positions of the metalof the metal poles markingpoles marking the centers the centers of the arraysof the that arrays were that deployed were deployed during the during first field the seasonfirst field were season resurveyed were duringresurveyed the second duringseason. the second season. Revisiting and resurveying the arrays in the second season provided insight into the stability of this surface with respect to validation of both satellite ranging and the horizontal movement of the ice sheet (~0.3 m/year). The snow surface in this region is extremely flat on large length scales, varying by only 100 m over 300 km, but is relatively rough on short length scales. This roughness is associated with sastrugi, or fields of wind-driven ridges that are ~1 m high on ~10 m length scales. The position of sastrugi in the vicinity of our CCR arrays changed between seasons 1 and 2, as expected [23]; thus, during the second survey of the arrays, the relative heights of the bamboo poles changed non- uniformly. Most poles were still within the height range of ~0.5 m to just under 2 m; one bamboo pole was 0.48 m while another bamboo pole was anomalously low at 0.06 m. The horizontal displacements due to ice flow of five of the metal poles marking the centers of the arrays were extremely small, with a mean value 0.35 m. Thus, CCR arrays along the 88S Traverse are an excellent means of validation

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Revisiting and resurveying the arrays in the second season provided insight into the stability of this surface with respect to validation of both satellite ranging and the horizontal movement of the ice sheet (~0.3 m/year). The snow surface in this region is extremely flat on large length scales, varying by only 100 m over 300 km, but is relatively rough on short length scales. This roughness is associated with sastrugi, or fields of wind-driven ridges that are ~1 m high on ~10 m length scales. The position of sastrugi in the vicinity of our CCR arrays changed between seasons 1 and 2, as expected [23]; thus, during the second survey of the arrays, the relative heights of the bamboo poles changed non-uniformly. Most poles were still within the height range of ~0.5 m to just under 2 m; one bamboo pole was 0.48 m while another bamboo pole was anomalously low at 0.06 m. The horizontal displacements due to ice flow of five of the metal poles marking the centers of the arrays were extremely small, with a mean value 0.35 m. Thus, CCR arrays along the 88S Traverse are an excellent means of validation of horizontal accuracy and to assess the size of the ICESat-2 footprint, but these arrays are not ideal for the validation of satellite ranging as the pole heights are relative to the changing surface.

3. Results

3.1. White Sands Missile Range Airborne Lidar Comparison The overpass on 2 November 2018 provided one of the first cases to investigate the ICESat-2 pointing control and geolocation accuracy. The TOO was implemented on reference ground track (RGT) #531, a descending pass that falls west of the validation site. For this pass the TOO command required a 3.41◦ off-nadir angle (31 km) which was performed through a roll maneuver to point left (east) of the sub-satellite point. The TOO targeted beam GT2r which is the middle pair’s right component, the strong spot for the +x spacecraft yaw orientation [3] at the time of the overpass. Although the beam did not illuminate a CCR array, analysis for ATL03 quality utilized positional offsets using the best fit to the airborne lidar reference surface. The results of the comparison initially were well outside the mission requirements but further calibration analysis on-orbit helped eliminate many of the errors and remove the biases. Comparison to the reference surface (1 m raster) at WSMR indicates 3 m along-track − and 1 m across-track error in the geolocation reported in this test case. The thematic output of the automated comparison algorithm is shown in Figure 13 and the vertical error over the full transect at WSMR is provided in Figure 14. The thematic contours in Figure 13 show the optimization process as the ATL03 elevations are shifted in along-track and across-track directions to determine the best fit to the reference. The red dot, in Figure 13, indicates this best fit. The geolocation offset, or geolocation error, is the translational distance during the optimization.

3.2. Corner Cube Signatures at White Sands Missile Range An overpass on 31 March 2019 provided the first successful CCR signal collection at WSMR with RGT #28, a descending pass to the east of the array location. The TOO required an observatory maneuver 2.4◦ off-nadir (21 km) from the sub-satellite point and placed the right beam (weak) in the middle pair (GT2r) on one CCR in the east array and two CCRs in the south array. The nadir view of the relative geometry for the ICESat-2 #28 RGT ATL03 along-track data and the four CCR arrays are shown in Figure 15. The ATL03 signal photons are green and the ATL03 signal photons attributed to the CCR reflections are blue. Remote Sens. 2020, 11, x FOR PEER REVIEW 12 of 21 of horizontal accuracy and to assess the size of the ICESat-2 footprint, but these arrays are not ideal for the validation of satellite ranging as the pole heights are relative to the changing surface.

3. Results

3.1. White Sands Missile Range Airborne Lidar Comparison The overpass on 2 November 2018 provided one of the first cases to investigate the ICESat-2 pointing control and geolocation accuracy. The TOO was implemented on reference ground track (RGT) #531, a descending pass that falls west of the validation site. For this pass the TOO command required a 3.41º off-nadir angle (31 km) which was performed through a roll maneuver to point left (east) of the sub-satellite point. The TOO targeted beam GT2r which is the middle pair’s right component, the strong spot for the +x spacecraft yaw orientation [3] at the time of the overpass. Although the beam did not illuminate a CCR array, analysis for ATL03 quality utilized positional offsets using the best fit to the airborne lidar reference surface. The results of the comparison initially were well outside the mission requirements but further calibration analysis on-orbit helped eliminate many of the errors and remove the biases. Comparison to the reference surface (1 m raster) at WSMR indicates −3 m along-track and 1 m across-track error in the geolocation reported in this test case. The thematic output of the automated comparison algorithm is shown in Figure 13 and the vertical error over the full transect at WSMR is provided in Figure 14. The thematic contours in Figure 13 show the optimization process as the ATL03 elevations are shifted in along-track and across-track directions to determineRemote Sens. the2020 best, 12, 3653 fit to the reference. The red dot, in Figure 13, indicates this best fit. The geolocation13 of 21 offset, or geolocation error, is the translational distance during the optimization.

Figure 13. Thematic output for optimized ﬁt between the airborne lidar reference surface (1 m Figure 13. Thematic output for optimized fit between the airborne lidar reference surface (1 m resolution raster surface) and the ICESat-2 ATL03 elevations for the 2 November, 2018 overpass of resolution raster surface) and the ICESat-2 ATL03 elevations for the 2 November, 2018 overpass of RemoteWSMR. Sens. The 2020 solution, 11, x FOR indicates PEER REVIEW the geolocation corrections for ATL03. 13 of 21 WSMR. The solution indicates the geolocation corrections for ATL03.

FigureFigure 14. 14.Elevation Elevation comparison comparison between between the the reference reference surface surface derived derived from from airborne airborne lidar lidar measurementsmeasurements and and ATL03 ATL03 (a) and(a) and the the error erro statisticsr statistics along along the the transect transect (b). (b).

3.2.Analysis Corner Cube of these Signatures signatures at White individually Sands Missile and collectively Range provides information on signal strength, laser spatial proﬁle, and certainly, geolocation accuracy. Figure 16 shows the sequence of CCR An overpass on 31 March 2019 provided the first successful CCR signal collection at WSMR with signatures within the transect (elevation versus UTM northing). As observed in Figure 16, the heights RGT #28, a descending pass to the east of the array location. The TOO required an observatory of the illuminated CCRs moving south to north (left to right) are 1.01, 1.68, and 0.79 m. Coordinating maneuver 2.4º off-nadir (21 km) from the sub-satellite point and placed the right beam (weak) in the these CCR heights in ATL03 with those approximated heights in the arrays conﬁrms the CCR positions middle pair (GT2r) on one CCR in the east array and two CCRs in the south array. The nadir view of of those required for the geolocation and diameter retrieval process. the relative geometry for the ICESat-2 #28 RGT ATL03 along-track data and the four CCR arrays are shown in Figure 15. The ATL03 signal photons are green and the ATL03 signal photons attributed to the CCR reflections are blue.

Figure 15. Overview of the 31 Mar 2019 overpass of WSMR CCR arrays. The ground tracks shown here have been adjusted using the airborne lidar survey comparison technique to correct for horizontal offsets. The red points are locations of the CCRs and the black box indicates which arrays contain illuminated CCR for this transect.

Analysis of these signatures individually and collectively provides information on signal strength, laser spatial profile, and certainly, geolocation accuracy. Figure 16 shows the sequence of CCR signatures within the transect (elevation versus UTM northing). As observed in Figure 16, the heights of the illuminated CCRs moving south to north (left to right) are 1.01, 1.68, and 0.79 m. Coordinating these CCR heights in ATL03 with those approximated heights in the arrays confirms the CCR positions of those required for the geolocation and diameter retrieval process.

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Figure 14. Elevation comparison between the reference surface derived from airborne lidar measurements and ATL03 (a) and the error statistics along the transect (b).

3.2. Corner Cube Signatures at White Sands Missile Range An overpass on 31 March 2019 provided the first successful CCR signal collection at WSMR with RGT #28, a descending pass to the east of the array location. The TOO required an observatory maneuver 2.4º off-nadir (21 km) from the sub-satellite point and placed the right beam (weak) in the middle pair (GT2r) on one CCR in the east array and two CCRs in the south array. The nadir view of the relative geometry for the ICESat-2 #28 RGT ATL03 along-track data and the four CCR arrays are Remote Sens. 2020, 12, 3653 14 of 21 shown in Figure 15. The ATL03 signal photons are green and the ATL03 signal photons attributed to the CCR reflections are blue.

Figure 15. Overview of of the 31 Mar 2019 overpass of WSMRWSMR CCR arrays. The ground tracks shown here havehave beenbeen adjusted adjusted using using the airbornethe airborne lidar surveylidar survey comparison comparison technique technique to correct to for correct horizontal for Remote Sens. 2020, 11, x FOR PEER REVIEW 14 of 21 horizontaloﬀsets. The offsets. red points The red are points locations are locations of the CCRs of the and CCRs the blackand the box black indicates box indicates which arrays which contain arrays containilluminated illuminated CCR for CCR this transect.for this transect.

Figure 16. Sequence of three CCR signal signatures at WSMR on 31 March 2019. Each group of detected Figure 16. Sequence of three CCR signal signatures at WSMR on 31 March 2019. Each group of photons represent multiple laser shots on one CCR on a specific height pole. detected photons represent multiple laser shots on one CCR on a specific height pole. The 31 March WSMR data were analyzed using the methods described previously. The signal The 31 March WSMR data were analyzed using the methods described previously. The signal distribution and Gaussian function for one of the CCRs illuminated are shown in Figure 17, with distribution and Gaussian function for one of the CCRs illuminated are shown in Figure 17, with a a noticeable attenuation at the footprint boundaries where the energy levels are significantly lower. noticeable attenuation at the footprint boundaries where the energy levels are significantly lower. Using the chord lengths and iterative analysis with the geometric constraints the results it a footprint Using the chord lengths and iterative analysis with the geometric constraints the results it a footprint diameter of 10.6 m for this particular beam and environmental scenario. The centroid of the true diameter of 10.6 m for this particular beam and environmental scenario. The centroid of the true geolocation is calculated based on the now known diameter and the chord length horizontal distance geolocation is calculated based on the now known diameter and the chord length horizontal distance from the centerline of the footprint. The horizontal geolocation offsets were determined to be 1.8 m from the centerline of the footprint. The horizontal geolocation offsets were determined to be− −1.8 m for both the along and across-track directions to produce a total horizontal geolocation accuracy to for both the along and across-track directions to produce a total horizontal geolocation accuracy to within 2.5 m (0.34 RMSE). Figure 18 illustrates the ATL03 data (black dots), the predicted location of within 2.5 m (0.34 RMSE). Figure 18 illustrates the ATL03 data (black dots), the predicted location of the CCR relative to the footprint centroid based on the chord length (blue squares) and the ATL03 the CCR relative to the footprint centroid based on the chord length (blue squares) and the ATL03 track correction based on the recovered geolocation offsets (green dots). Independent from the CCR track correction based on the recovered geolocation offsets (green dots). Independent from the CCR approach for ICESat-2 geolocation error assessment is the error evaluation using the ATL03 data approach for ICESat-2 geolocation error assessment is the error evaluation using the ATL03 data comparison to the WSMR airborne lidar survey. Comparison of the lidar reference data for the March comparison to the WSMR airborne lidar survey. Comparison of the lidar reference data for the March overpass estimated a 2 m (RMSE 0.16 m) horizontal geolocation error. The comparison of the two overpass estimated a 2 m (RMSE 0.16 m) horizontal geolocation error. The comparison of the two results from the independent validation strategies confirms the fidelity of the CCR methodology for results from the independent validation strategies confirms the fidelity of the CCR methodology for geolocation retrievals at WSMR and other locations, like 88S, where the surface is changing and/or reference data are not available.

Remote Sens. 2020, 11, x FOR PEER REVIEW 14 of 21

Figure 16. Sequence of three CCR signal signatures at WSMR on 31 March 2019. Each group of detected photons represent multiple laser shots on one CCR on a specific height pole.

The 31 March WSMR data were analyzed using the methods described previously. The signal distribution and Gaussian function for one of the CCRs illuminated are shown in Figure 17, with a noticeable attenuation at the footprint boundaries where the energy levels are significantly lower. Using the chord lengths and iterative analysis with the geometric constraints the results it a footprint diameter of 10.6 m for this particular beam and environmental scenario. The centroid of the true geolocation is calculated based on the now known diameter and the chord length horizontal distance from the centerline of the footprint. The horizontal geolocation offsets were determined to be −1.8 m for both the along and across-track directions to produce a total horizontal geolocation accuracy to within 2.5 m (0.34 RMSE). Figure 18 illustrates the ATL03 data (black dots), the predicted location of the CCR relative to the footprint centroid based on the chord length (blue squares) and the ATL03 track correction based on the recovered geolocation offsets (green dots). Independent from the CCR approach for ICESat-2 geolocation error assessment is the error evaluation using the ATL03 data Remotecomparison Sens. 2020 to, 12 the, 3653 WSMR airborne lidar survey. Comparison of the lidar reference data for the15 March of 21 overpass estimated a 2 m (RMSE 0.16 m) horizontal geolocation error. The comparison of the two results from the independent validation strategies confirms the fidelity of the CCR methodology for geolocation retrievals at WSMR and other locations, like 88S, where the surface is changing and/or geolocation retrievals at WSMR and other locations, like 88S, where the surface is changing and/or reference data are not available. reference data are not available.

Remote Sens. 2020, 11, x FOR PEER REVIEW 15 of 21

Figure 17. Along-track CCR signal distribution statistical extraction of the effective chord length Figurebased on 17. theAlong-track 2σ value for CCR a Gaussian signal distributionenergy profile statistical as a preliminary extraction assessment of the eﬀ ectiveof the optimal chord length signal σ baseddistribution on the 2duringvalue the for March a Gaussian overpass energy of WSMR proﬁle for as aa preliminaryweak beam. assessment of the optimal signal distribution during the March overpass of WSMR for a weak beam.

Figure 18. Analysis results for CCR geolocation accuracy recovery from 31 March 2018. The black Figure 18. Analysis results for CCR geolocation accuracy recovery from 31 March 2018. The black points are the ATL03 reported photon geolocations and the green are the true locations using the CCR points are the ATL03 reported photon geolocations and the green are the true locations using the CCR positions and the signal signature chord lengths. positions and the signal signature chord lengths. Another overﬂight of WSMR on 28 September 2019 provided capture of the strong beam in the Another overflight of WSMR on 28 September 2019 provided capture of the strong beam in the middle pair on the same track previously analyzed (RGT #28, GT2r). Although the same spot location middle pair on the same track previously analyzed (RGT #28, GT2r). Although the same spot location (GT2r) as the previous overpass in March, the satellite had performed a yaw maneuver for the purpose (GT2r) as the previous overpass in March, the satellite had performed a yaw maneuver for the of solar panel orientation which repositioned the strong and weak beam placement within the pair purpose of solar panel orientation which repositioned the strong and weak beam placement within naming convention. The satellite was able to place the beam just 20 m from the intended TOO geodetic the pair naming convention. The satellite was able to place the beam just 20 m from the intended location requested. This particular pass was a daytime pass, and although the background noise level TOO geodetic location requested. This particular pass was a daytime pass, and although the background noise level increased, the stronger beam energy provided significantly more signal than the weak beam delivered in March. Figure 19 illustrates the geometry of the track relative to the CCRs arrays; three distinct CCR signatures were identified in the data transect, one from the north array and two from the east. The geometry of the array with the apparent chord lengths of the CCR signatures gave a deterministic assessment of the footprint diameter to be 12 m (RMSE of 1.8 m).

Remote Sens. 2020, 11, x FOR PEER REVIEW 15 of 21

Figure 17. Along-track CCR signal distribution statistical extraction of the effective chord length based on the 2σ value for a Gaussian energy profile as a preliminary assessment of the optimal signal distribution during the March overpass of WSMR for a weak beam.

Figure 18. Analysis results for CCR geolocation accuracy recovery from 31 March 2018. The black points are the ATL03 reported photon geolocations and the green are the true locations using the CCR positions and the signal signature chord lengths.

Another overflight of WSMR on 28 September 2019 provided capture of the strong beam in the middle pair on the same track previously analyzed (RGT #28, GT2r). Although the same spot location (GT2r) as the previous overpass in March, the satellite had performed a yaw maneuver for the Remote Sens. 2020, 12, 3653 16 of 21 purpose of solar panel orientation which repositioned the strong and weak beam placement within the pair naming convention. The satellite was able to place the beam just 20 m from the intended increased,TOO geodetic the stronger location beam requested. energy providedThis partic signiﬁcantlyular pass morewas signala daytime than thepass, weak and beam although delivered the inbackground March. Figure noise 19 level illustrates increased, the the geometry stronger of beam the track energy relative provided to the significantly CCRs arrays; more three signal distinct than CCRthe weak signatures beam delivered were identiﬁed in March. in the Figure data 19 transect, illustrates one the from geometry the north of the array track and relative two from to the the CCRs east. Thearrays; geometry three distinct of the array CCR with signatures the apparent were identifi chord lengthsed in the of thedata CCR transect, signatures one from gave the a deterministic north array assessmentand two from of the the footprint east. The diameter geometry to beof 12the m arra (RMSEy with of 1.8 the m). apparent chord lengths of the CCR signatures gave a deterministic assessment of the footprint diameter to be 12 m (RMSE of 1.8 m).

Figure 19. Overview of the 28 September 2019 overpass of WSMR CCR arrays. The ground tracks shown here have been adjusted using the airborne lidar survey comparison technique to correct for horizontal geolocation oﬀsets. The red points are locations of the CCRs and the black box indicates which arrays contain illuminated CCRs.

Figure 20 shows the actual ATL03 data (black) and the adjusted positions based on the 12 m effective diameter, known locations of the two CCRs and the resulting geolocation offsets. This analysis concluded that geolocation accuracy of ATL03 is better than 5 m horizontal ( 4 m across-track and − 3 m along-track). In comparison, using the airborne lidar survey for geolocation accuracy assessment resulted in the same conclusion ( 4 m across-track, 3 m along-track) which again confirms the fidelity − of the CCR methodology for diameter and geolocation retrievals. Remote Sens. 2020, 11, x FOR PEER REVIEW 16 of 21

Figure 19. Overview of the 28 September 2019 overpass of WSMR CCR arrays. The ground tracks shown here have been adjusted using the airborne lidar survey comparison technique to correct for horizontal geolocation offsets. The red points are locations of the CCRs and the black box indicates which arrays contain illuminated CCRs.

Figure 20 shows the actual ATL03 data (black) and the adjusted positions based on the 12 m effective diameter, known locations of the two CCRs and the resulting geolocation offsets. This analysis concluded that geolocation accuracy of ATL03 is better than 5 m horizontal (−4 m across- track and 3 m along-track). In comparison, using the airborne lidar survey for geolocation accuracy Remote Sens. 2020, 12, 3653 17 of 21 assessment resulted in the same conclusion (−4 m across-track, 3 m along-track) which again confirms the fidelity of the CCR methodology for diameter and geolocation retrievals.

Figure 20. Analysis results for CCR geolocation accuracy recovery from 28 September 2019. The black pointsFigure are 20. the Analysis ATL03 results reported for photon CCR geolocation geolocations accuracy and the recovery green are from the true28 September locations using2019. theTheCCR black positionspoints are and the the ATL03 signal reported signature photon chord geolocations lengths. and the green are the true locations using the CCR positions and the signal signature chord lengths. 3.3. Corner Cube Signatures at 88S 3.3. Corner Cube Signatures at 88S Compared to the number of possible TOOs at WSMR, the 88S CCR arrays have more opportunities for illuminationCompared based to the on thenumber spatial of convergence possible TOOs of the at reference WSMR, ground the 88S tracks CCR at thisarrays latitude. have Frommore manyopportunities successful for captures illumination of CCR based signatures, on the spatial 10 December convergence 2018 of wasthe reference one of special ground interest tracks at as this it illuminatedlatitude. From three many targets successful within the captures AR4 array of CCR (Figure signatures, 12) on one 10 RGT December track (#1111). 2018 was Figure one 21of showsspecial theinterest location as it of illuminated this particular three track targets and thewithin corresponding the AR4 array locations (Figure of 12) the on CCRs one responsible RGT track for(#1111). the signalFigure signature 21 shows in the the location transect. of This this overpassparticular captured track and the the same corresponding strong beam locations analyzed of at the WSMR. CCRs Usingresponsible the iterative for the approach signal signature and the in known the transect locations. This of theoverpass optical captured targets, the beamsame strong diameter beam is determinedanalyzed at to WSMR. be 11.6 mUsing and the geolocationiterative approach accuracy an isd 0.5the m known (80 m RMSE).locations Additional of the optical 88S overpassestargets, the ofbeam the CCRsdiameter will is provide determined a consistent to be 11.6 method m and for the horizontal geolocation geolocation accuracy evaluation is 0.5 m for(80 continualm RMSE). monitoringAdditionalRemote Sens. 2020 of 88S the, 11 overpasses,system x FOR PEER performance of REVIEW the CCRs over will the provide mission a lifetime.consistent method for horizontal geolocation17 of 21 evaluation for continual monitoring of the system performance over the mission lifetime.

Figure 21. ATL03 geolocation signal photons for track 1111 at 88S. The green points are signal, the blue Figure 21. ATL03 geolocation signal photons for track 1111 at 88S. The green points are signal, the circles are those signal determined to be from the CCRs and the red x’s are the actual CCR positions. blue circles are those signal determined to be from the CCRs and the red x’s are the actual CCR positions.

A summary of the results over the three ICESat-2 overpass opportunities at each of the validation test sites is presented in Table 1.

Table 1. Summary of CCR overpass results.

Footprint Location/Technique/Date Geolocation Accuracy Diameter 2.5 m WSMR/CCR 31 March, 2019 10.6 m (RMSE 0.34 m) 2.0 m WSMR/lidar 31 March, 2019 N/A (RMSE 0.16 m) 5 m WSMR/CCR 28 September, 2019 12.0 m ((RMSE 1.8 m) 5 m WSMR/lidar 28 September, 2019 N/A (RMSE 0.15 m) 0.5 m 88S/CCR 10 December, 2018 11.6 m (RMSE 0.8 m)

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A summary of the results over the three ICESat-2 overpass opportunities at each of the validation test sites is presented in Table1.

Table 1. Summary of CCR overpass results.

Location/Technique/Date Footprint Diameter Geolocation Accuracy 2.5 m WSMR/CCR 31 March, 2019 10.6 m (RMSE 0.34 m) 2.0 m WSMR/lidar 31 March, 2019 N/A (RMSE 0.16 m) 5 m WSMR/CCR 28 September, 2019 12.0 m ((RMSE 1.8 m) 5 m WSMR/lidar 28 September, 2019 N/A (RMSE 0.15 m) 0.5 m 88S/CCR 10 December, 2018 11.6 m (RMSE 0.8 m)

4. Discussion After launch, the satellite was inserted into orbit and began the initial protocols for system power-up and observatory check-out. Upon a successful post-launch assessment, the spacecraft began normal operations in October 2018. In the early phase of science data collection, the geolocation errors were predominantly related to the pointing determination uncertainties as significant thermal variability within the orbital cycle created the need to determine pointing calibrations relative to orbit angle. The orbit angle, in turn, created a latitude dependence on the pointing knowledge. Similarly, many biases in the pointing remain until there is opportunity to perform a full orbital cycle analysis for instrument alignment characterization to the satellite reference frame. These pointing uncertainties and biases affect both pointing control and pointing knowledge. The pointing control accuracy utilizes an on-board calibration table to effectively point the transceiver at a specific location on the surface. This process allows ICESat-2 to follow the prescribed reference ground tracks as well as perform maneuvers for TOOs. The calibration tables are routinely updated as the pointing biases are better characterized over time for improved pointing control. Pointing knowledge integrates these calibrations within the geolocation calculation during ground processing for improved positional accuracy in ATL03. On-orbit analysis of the pointing determination solution error is currently 2.3 µrad (1σ) or less than 0.5 arc sec. This contribution to uncertainties in horizontal geolocation is 1.1 m. This value is well within the mission requirement of 3.7 µrad for pointing knowledge and achieved despite moving operations from the primary star tracker to one positioned on the observatory as a back-up [24]. The precision orbit determination (total position) for the mission to date is 4.9 cm, also well within the (20 cm) requirement. With time (and orbit cycles) the pointing calibration can be resolved through dedicated on-orbit maneuvers that isolate the range residuals to determine corrections across the full orbital cycle [19]. Table2 provides the uncertainties associated with each of the aforementioned processes that contribute to the overall ICESat-2 geolocation. However, there is also an instrument performance dependency on the relative angle between the satellite orbital plane and the Sun causing thermal variation on the spacecraft. As such, a full calibration determination requires data from the full range of solar angles (~16 months) although the initial biases identified early on-orbit were able to eliminate the largest errors contributing to the geolocation error. The early overpasses of WSMR and 88S assisted with validation of the pointing biases and calibration effectiveness and will continue to provide independent assessment of the geolocation for specific orbit angles as a window into the overall fidelity of the overall error budget. Remote Sens. 2020, 12, 3653 19 of 21

Table 2. Geolocation sources of error.

Current Best on-orbit Accuracy Source Mission Requirement Estimate Precision Pointing Determination 3.7 µrad/0.7 arc sec 2.3 µrad/0.5 arc sec Precision Orbit Determination 20 cm total position 4.9 cm total position [25] µrad = micro-radians, arc sec = arc second. Values are all root mean squared values (RMS), 1σ.

Although the motivation behind the array implementation at WSMR was to capture a beam pair, these initial results are for single beams. Given the previous discussion on geolocation sources of error (Table2) there is a direct correlation on the pointing control capabilities as they are related to the ability to characterize the pointing biases from on-board calibration tables. As such, the uncertainties in the “targeting” of ICESat-2 often resulted in missing the TOO position completely or capturing the “non-targeted” beam since only one beam can be directed to a specific location and the errors early on-orbit were based on pre-launch assessments. Additionally, there is variation in the pair separation (nominally 90 m) along the track during TOOs as a result of spacecraft motion in the yaw axis. This effect can place one beam outside of the array geometry despite capturing the other. The agreement between the airborne lidar geolocation validation technique and the CCR technique at WSMR is important for using CCR arrays at other locations in the orbit where reference sources/data are not available. The geolocation accuracy will vary throughout the orbit but should maintain the 6.5 m mission requirement at the footprint scale regardless of latitude. The diameter deterministically determined using the CCRs should also stay consistent although the value will vary slightly throughout the orbit based on the stability of the laser optics during pre-launch studies [13]. The difference in diameters recovered for the overpasses is not surprising as variations in atmosphere attenuation, beam energy strength and background levels will surely have an impact on the potential detection of a photon for every shot relevant to a CCR location. In the case where the energy levels are low (e.g., leading edge of initial footprint or trailing edge of last footprint) there is a heightened chance of not detecting a return from the CCR. This is particularly relevant to the weak beams that bring only a fourth of the energy as the strong. When “edge” photons are missed the chord lengths will differ, producing 0.7 m variation in the deterministic diameter recovered based on the ± along-track measurement resolution of ATLAS. For the case when both “edge” photons are missed the diameters would differ by ~1.4 m, which is what is observed in the comparison between the 31 March 2019, and 28 September 2019, overpasses. Another consideration for diameter variations determined for independent overflights is laser beam divergence. Divergence increases the effective diameter with distance traveled. This is an interesting point for TOOs that require off-nadir pointing and increased slant ranges. However, using the diameters recovered from these two specific WSMR overpasses, the divergence calculated from diameter, known altitude and off-nadir angle for each case differs by less than a µradian which is equivalent to <10 cm variation on the ground. This small impact on the derived diameter implies the overall value is affected more by signal losses than range dependent laser spreading. The variability in both diameter retrieval and geolocation accuracy is not significant but warrants further analysis as additional opportunities occur to increase the sample size of the data. Future articles will use the aggregation of opportunities to determine a statistically justified assessment of single values.

5. Conclusions The goal of this work was to establish a passive method for using CCRs to measure the effective diameter of the ICESat-2 laser and provide an independent assessment of the geolocation accuracy. Although a similar approach was implemented previously with the original ICESat mission, the ICESat-2 altimeter technology required significant changes in the analysis technique of the unique signatures provided by the ground based optics. These CCR reflections back to the satellite are Remote Sens. 2020, 12, 3653 20 of 21 compared directly to the known location of the optical component. The CCR array configuration allows for unambiguous determination of which CCRs were illuminated for position comparison and also allows for a deterministic recovery of the footprint diameter based on the geometry of the scenario. Specific to ICESat-2, multiple CCRs were placed in strategic configurations in New Mexico and along the 88S Traverse in Antarctica. For one overpass of WSMR, the arrays captured multiple CCR returns with the GT2r beam. The weak beam diameter was determined to be 10.6 m with a corresponding geolocation accuracy of 2.5 m horizontally. The fidelity of the approach is confirmed through comparison with another independent method for determining the offsets of the ICESat-2 geolocation using high-resolution reference data, which determined nearly the same result for that overpass. A subsequent overflight of WSMR captured the strong beam of the central pair and determined its geolocation offset to be 5 m horizontal and a diameter of 12 m. The difference in diameter is expected given varying levels of atmospheric attenuation and potential beam differences. The comparison of the ATL03 transect to the airborne data concurred with similar geolocation offset. For the WSMR analysis both approaches, reference data and CCR, concluded that the current geolocation accuracy is better than 2 m. Studies at 88S for geolocation accuracy result in similar performance metrics which indicates consistent data quality for high latitude regions.

Author Contributions: Conceptualization, L.A.M.; methodology, L.A.M.; software, M.A.; validation and formal analysis, L.A.M.; investigation, L.A.M., K.M.B. and M.A.; resources, K.M.B. and L.A.M.; writing—original draft preparation, L.A.M. and K.M.B.; writing—review and editing, L.A.M. and K.M.B. funding acquisition, L.A.M. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by NASA grant NNX15AC68G (PI Magruder). Acknowledgments: The authors wish to thank the NASA ICESat-2 Science Team and Project Science Office for their hard work preparing the data used in this study. We would also like to acknowledge the UT-BEG team for the airborne lidar data collection, specifically Kutalmis Saylam. We thank the 88S Traverse teams (Tom Neumann, Chad Seay, Forrest McCarthy, Adam Greely, Matt Means, and Chris Simmons), the NSF, and the numerous personnel with the U.S. Antarctic Program for Antarctic CCR deployment. The UT team at WSMR includes Amy Neuenschwander, Brad Klotz, and Michael Wharton—we wish to thank them as well in addition to Christine Simurda for edits and Holly Leigh for the WSMR CCR configuration design. The ICESat-2 data are available through the National Snow & Ice Data Center (https://nsidc.org/data/icesat-2). Funding for L. Magruder and M. Alonzo was provided by NASA grant 80NSSC17K0410 and K. Brunt was supported through the NASA ICESat-2 Project Science Office at GSFC. Conflicts of Interest: The authors declare no conflict of interest.

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