Roll Calibration for Cryosat-2: a Comprehensive Approach

remote sensing

Technical Note Roll Calibration for CryoSat-2: A Comprehensive Approach

Albert Garcia-Mondéjar 1,* , Michele Scagliola 2 , Noel Gourmelen 3,4 , Jerome Bouffard 5 and Mònica Roca 1

1 isardSAT S.L., Barcelona Advanced Industry Park, 08042 Barcelona, Spain; [email protected] 2 Aresys SRL, 20132 Milano, Italy; [email protected] 3 School of GeoSciences, University of Edinburgh, Drummond Street, Edinburgh EH8 9XP, UK; [email protected] 4 IPGS UMR 7516, Université de Strasbourg, CNRS, 67000 Strasbourg, France 5 ESA ESRIN, 00044 Frascati, Italy; [email protected] * Correspondence: [email protected]

Abstract: CryoSat-2 is the ﬁrst satellite mission carrying a high pulse repetition frequency radar altimeter with interferometric capability on board. Across track interferometry allows the angle to the point of closest approach to be determined by combining echoes received by two antennas and knowledge of their orientation. Accurate information of the platform mispointing angles, in particular of the roll, is crucial to determine the angle of arrival in the across-track direction with sufﬁcient accuracy. As a consequence, different methods were designed in the CryoSat-2 calibration plan in order to estimate interferometer performance along with the mission and to assess the roll’s contribution to the accuracy of the angle of arrival. In this paper, we present the comprehensive approach used in the CryoSat-2 Mission to calibrate the roll mispointing angle, combining analysis from external calibration of both man-made targets, i.e., transponder and natural targets. The roll calibration approach for CryoSat-2 is proven to guarantee that the interferometric measurements are exceeding the expected performance.

Keywords: SARIn; interferometry; CryoSat-2; roll; mispointing; transponder; swath

Citation: Garcia-Mondéjar, A.; Scagliola, M.; Gourmelen, N.; Bouffard, J.; Roca, M. Roll Calibration 1. Introduction for CryoSat-2: A Comprehensive Approach. Remote Sens. 2021, 13, 302. The CryoSat-2 mission was designed to measure changes in the thickness of sea and https://doi.org/10.3390/rs13020302 land ice fields [1]. The requirements of the system were defined in terms of the uncertainty of the perennial ice thickness change measurement caused by all contributing elements, Received: 29 November 2020 including satellite performance and ground processing capabilities [2]. The altimeter Accepted: 5 January 2021 mounted on board the CryoSat-2 satellite, namely SAR/Interferometric Radar Altimeter Published: 16 January 2021 (SIRAL), was designed with synthetic aperture and interferometry capabilities in order to meet those requirements. It works in three operating modes: Synthetic Aperture mode Publisher’s Note: MDPI stays neutral (SAR), SAR Interferometric mode (SARIn) and Low-Resolution Mode (LRM). SARIn mode with regard to jurisdictional claims in enables aperture synthesis, as does SAR mode, but using two antennas for phase compari- published maps and institutional affil- son (interferometry) between the radar echoes sensed by them allows us to determine the iations. across-track direction of the return echo. Additionally, CryoSat-2 has three Star Trackers in charge of measuring satellite orientation. The quaternions computed from them have inherent biases of ~1µrad. According to [3], the worst case error on the angle of arrival for CryoSat-2 was expected to be 411µrad. Starting from the error budget for the angle of arrival Copyright: © 2021 by the authors. in [3], in the framework of the roll calibration, we can consider the requirement of the roll Licensee MDPI, Basel, Switzerland. bias accuracy to be given by the sum of the instrument internal calibration accuracy and of This article is an open access article the contribution from uncorrected thermal deformation of the star tracker-bench-antenna distributed under the terms and assembly, resulting in 176µrad. conditions of the Creative Commons However, different studies revealed that the mispointing angles in the early versions Attribution (CC BY) license (https:// of the CryoSat-2 Level1b were affected by static offsets [4–6], which are now compen- creativecommons.org/licenses/by/ sated [7]. Both the roll and pitch biases are related to inaccuracies in the rotations applied 4.0/).

Remote Sens. 2021, 13, 302. https://doi.org/10.3390/rs13020302 https://www.mdpi.com/journal/remotesensing Remote Sens. 2021, 13, 302 2 of 13

to the Star Tracker quaternions to translate them from their internal reference frame to the interferometer baseline one. A comprehensive approach has been exploited for the calibration of the roll mispointing due to its direct impact on the accuracy of the across-track angle of arrival (AoA) retrieved by interferometric processing. Three different activities within the CryoSat-2 QWG (Quality Working Group) have been able to analyze the CryoSat-2 roll bias with three different strategies: (i) calibration over the Svalbard transponder [8], (ii) ocean roll campaigns, and (iii) analysis of CryoSat-2 swath data over land ice. Transponder acquisitions have been used to monitor range, datation, and interferometric phase performances since the beginning of the CryoSat-2 mission. The transponder tracking is programmed twice a month, and the data is analyzed continuously providing a very useful way to detect not only drifts in the component of the instrument but also anomalies in the on-board and ground processors. Calibration campaigns have been periodically performed in order to monitor CryoSat-2 interferometer performances. The calibration strategy for the interferometer uses the open ocean as a well-known target. It is characterized by a rough uniform sloped surface. CryoSat-2 SARIn acquisitions are used to measure the slope of the surface in the across-track direction. They are compared with the a priori known slope of the ocean surface. Analysis of the interferometric measurements from the calibration campaigns revealed that (i) the roll angle measured by the Star Trackers has a bias with respect to the measured angle of arrival, (ii) this roll bias depends on the Star Tracker being used, and (iii) the accuracy of the roll can be improved by properly correcting the mispointing angles for the aberration of light [9]. The swath processing method was not foreseen to be used for calibration purposes. Although the method was initially used with the CryoSat-2 proof of concept airborne campaigns, it was applied to CryoSat-2 data for the ﬁrst time 5 years after it was launched. By analyzing the capabilities of the three methods, the following considerations can be drawn. With the ocean roll campaigns, better precision is achieved, and errors linked to the baseline orientation knowledge can be ignored. However, it has the drawback of requiring spacecraft maneuvers, causing the suspension of science acquisitions. On the other hand, transponder calibration has the great advantage of being very frequent and can perform absolute calibration measurements with just a single pass, which can be also used to detect anomalies. However, it requires a transponder site facility, with maintenance over time. Finally, the swath processing method has the advantage of using science acquisitions available over large areas for assessing the roll bias, but a large amount of data over different regions and seasons is required.

2. Methods 2.1. Transponder Calibration The transponder equipment used for the CryoSat-2 external calibration is located in the Svalbard archipelago. It was designed and installed in 1987, built for ERS-1 usage and refurbished for the CryoSat-2 mission. The input data for this calibration analysis are the stack breakpoint products over the transponder location that are produced on request by the on-ground Level1 processor. These products include the individual Doppler beams that have been steered exactly to the Transponder location, providing a very good alignment and signal-to-noise ratio. With these I&Q (in-phase and quadrature signal components) focused beams, the power and phase from both receiving chains can be extracted. The phase difference (Φ (t,r)) is a vector of 1024 range bins (after a zero padding of 2) with the difference between the phase of the signal received from both chains. The angle of arrival measured by the instrument is obtained from the retracked (ri) phase difference (a single value from the 1024 is selected) with λ · Φ (t, r ) Θ (t) = sin−1 i − χ(t), (1) meas 2π · B Remote Sens. 2021, 13, 302 3 of 13

휆⋅훷 (푡,푟 ) 훩 (푡) = 푠𝑖푛−1 ( 푖 ) − 휒(푡), (1) 푚푒푎푠 2휋⋅퐵 where 휆 is the wavelength of the radar signal, 22.084 mm; B is the distance between the Remote Sens. 2021, 13, 302 3 of 13 centres of two antennas, 1.1676 m; 휒 is the roll angle; and Φ (t,r) is the measured phase difference in radians, varying for every beam (t). The theoretical angle of arrival is computed by geometry (as shown in Figure 1) following:where λ is the wavelength of the radar signal, 22.084 mm; B is the distance between the centres of two antennas, 1.1676 m; χ is the roll angle; and Φ (t,r) is the measured phase −1 푑0 difference in radians, varying훩 for( every푡) = beam푠𝑖푛 (t).( ), (2) 푡ℎ푒표 푟(푡) The theoretical angle of arrival is computed by geometry (as shown in Figure1) wherefollowing: d0 is the distance from the closest point of the ground track to the transponder position, r(t) is the distance from the transponder location d0 to the satellite burst locations, Θ (t) = sin−1 , (2) and 훩 is the across track angle (angle betweentheo line fromr( tthe) satellite to the transponder position and the nadir direction). where d0 is the distance from the closest point of the ground track to the transponder Finally, the bias is computed as the difference between the measured and the theo- position, r(t) is the distance from the transponder location to the satellite burst locations, retical angle of arrivals. and Θ is the across track angle (angle between line from the satellite to the transponder position and the nadir direction).

Figure 1. Geometry of the angle of arrival with transponder (TRP) measurements. CryoSat-2 sends Figure 1. Geometry of the angle of arrival with transponder (TRP) measurements. CryoSat-2 sends and receives pulses to the transponder location along the overpass. Figure taken from [8]. and receives pulses to the transponder location along the overpass. Figure taken from [8].

2.2. Roll CampaignsFinally, the over bias Ocean is computed as the difference between the measured and the theoreti- Thecal angleoperational of arrivals. calibration plan for CryoSat-2 foresees that interferometer calibration campaigns are periodically performed for calibration purposes, complementing the acquisitions2.2. Roll over Campaigns transponder. over Ocean An interferometer calibration campaign consists of a sequence of TheSIRAL operational acquisitions calibration in SARIn plan mode for CryoSat-2 over the tropical foresees and that mid interferometer latitude oceans calibration whilecampaigns the spacecraft are periodicallyis rolling from performed side to side for calibrationat about ±0.4 purposes, degrees complementing. The range of com- the acqui- mandedsitions roll overangles transponder. was defined An to interferometer be representative calibration of the range campaign of slopes consists that of are a sequence ex- pectedof to SIRAL be experienced acquisitions while in SARIn acquiring mode over over ice the sheets. tropical and mid latitude oceans while the Duringspacecraft interferometer is rolling from calibration side to campaigns, side at about the± 0.4purpose degrees. of the The CryoSat range- of2 interfer- commanded ometerroll is anglesto estimate was definedthe across to-track be representative slope of the ocean of the surface range of [4 slopes], so that that the are end expected-to-end to be error experiencedon the angle whileof arrival acquiring is assessed over by ice comparison sheets. of the measured across-track slope with an a-prioriDuring known interferometer across-track calibration slope. The campaigns, acquisition the geometry purpose of is therepresented CryoSat-2 in interferom- Fig- ure 2.eter We isdenote to estimate the roll the angle across-track as 휒, the slope across of the-track ocean slope surface of the [4 ],ocean so that surface the end-to-end as β and error the angleon the made angle by of the arrival direction is assessed of first by arrival comparison (i.e., Point of the of measured Closest Approach, across-track POCA) slope with with antennasan a-priori′ boresight known across-track direction as slope. 휗. It is The worth acquisition recalling geometry that the interferometer is represented inbase- Figure2. line isWe defined denote as the the roll vector angle as followingχ, the across-track the direction slope between of the ocean antenna surface 1 (the as β transmit-and the angle 0 ting/receivingmade by theantenna, direction leftof one first in arrival Figure (i.e., 2) and Point antenna of Closest 2 phase Approach, centers POCA) (the receiving with antennas only antenna,boresight right direction one in as Figureϑ. It is 2). worth Since recalling the interferometer that the interferometer baseline is kept baseline in flight is defined or- as thogonalthe vectorto the ground following track, the directionthe orientation between of antennathe interferometer 1 (the transmitting/receiving baseline in the across antenna,- left one in Figure2) and antenna 2 phase centers (the receiving only antenna, right one in Figure2). Since the interferometer baseline is kept in flight orthogonal to the ground track, the orientation of the interferometer baseline in the across-track plane corresponds to the roll angle χ. According to the acquisition geometry in Figure2, the across-track slope of the ocean surface results in β = η(ϑ − χ), (3) Remote Sens. 2021, 13, 302 4 of 13

Remote Sens. 2021, 13, 302 track plane corresponds to the roll angle 휒. According to the acquisition geometry in Fig-4 of 13 ure 2, the across-track slope of the ocean surface results in 훽 = 휂(휗 − 휒), (3) wherewhere 휂 ηis isa geometric a geometric factor factor that that is given is given by by휂 =η1=+ ℎ1/+푅 hbeing/R being h, theh ,altitude the altitude of the of sat- the 0 ellitesatellite with with respect respect to the to ellipsoid the ellipsoid,, and andR is Rtheis Earth the Earth′s radius.s radius.

Figure 2. Roll campaigns: acquisition geometry in the across-track plane (angles exaggerated for Figure 2. Roll campaigns: acquisition geometry in the across-track plane (angles exaggerated for clarity).clarity). β representsβ represents the the ocean ocean across across the thetrack track slope slope and and 휒 theχ platformthe platform roll angle. roll angle. Figure Figure taken taken fromfrom [9 [].9 ].

RecallingRecalling that that the the angle angle of of first first arrival arrival 휗ϑ inin thethe across-trackacross-track plane plane can can be be computed computed by evaluating the interferometric phase difference at POCA, Φ , we found that the end-to-end by evaluating the interferometric phase difference at POCA,0 Φ0, we found that the end- error on the AoA resulted in to-end error on the AoA resulted in Φ β e = 0 − χ − , (4) e2e 훷 훽 k0B0 η 휖푒2푒 = − 휒 − , (4) 푘0퐵 휂 where k0 is the carrier wavenumber and B is the interferometer baseline length. According whereto the 푘0 definitionis the carrier above, wavenumber the end-to-end and 퐵is error the interferometer is composed baseline of three length. different According terms: (i) tothe the error definition contribution above, the from end the-to measured-end error angleis composed of arrival of ϑthree, which different includes terms: the (i SIRAL) the errorinstrument contribution noise from and inaccuraciesthe measured from angle the of Level1arrival ground휗, which processor includes andthe SIRAL interferometer instru- mentcalibration noise and tool; inaccuracies (ii) the knowledge from the error Level1 on roll groundχ, which processor is given and by the interferometer combination ofcali- the brationinternal tool; accuracy (ii) the of knowledge Star Trackers error and on ground roll 휒, processingwhich is given of downlinked by the comb quaternions;ination of the and internal(iii) the accuracy knowledge of Star error Trackers on the a-prioriand ground known processing ocean surface of downlinked slope β. quaternions; and (iii) theAccording knowledge to error the considerationson the a-priori known drawn ocean in [4], surface the knowledge slope 훽. error on the ocean surfaceAccording slope isto assumedthe considerations to be negligibly drawn in small, [4], the while knowledge the error error contribution on the ocean from su ther- facemeasured slope is angle assumed of arrival to beresults negligibly in unbiased small, while noise. the As error a consequence, contribution the from end-to-end the meas- error uredon theangle AoA of arrivalee2e can results be modeled in unbiased as a linear noise. function As a consequence, of the angle the of end arrival-to-end itself, error and on the thecalibration AoA 휖푒2푒 functioncan be modeled for the CryoSat-2as a linear interferometerfunction of the finally angle of results arrival in itself, and the calibration function for the CryoSat-2 interferometer finally results in F(ϑ) = a · ϑ + χ0, (5) 퐹(휗) = 푎 ⋅ 휗 + 휒0, (5) wherewhere the the linear linear coefficient coefficient 푎a corresponds toto thethe contributioncontribution from from the the phase phase departure departure [1 ], while the constant term χ0 is addressed to a static bias affecting the roll mispointing angle [1], while the constant term 휒0 is addressed to a static bias affecting the roll mispointing (i.e., a roll bias). angle (i.e., a roll bias). From an operative point of view, the inputs of the interferometer calibration tool are From an operative point of view, the inputs of the interferometer calibration tool are the Level 1b products for the acquisitions commanded during campaigns for the calibration the Level 1b products for the acquisitions commanded during campaigns for the calibra- of the CryoSat-2 interferometer. The 20 Hz power waveform is retracked to identify the tion of the CryoSat-2 interferometer. The 20 Hz power waveform is retracked to identify POCA, and the angle of arrival is computed. Then, according to Equation (5), the error in the POCA, and the angle of arrival is computed. Then, according to Equation (5), the error the angle of arrival e is obtained by knowledge of the roll mispointing angle and the in the angle of arrival 휖e2e is obtained by knowledge of the roll mispointing angle and the ocean surface slope from푒2푒 the geoid. Finally, the parameters for the calibration function ocean surface slope from the geoid. Finally, the parameters for the calibration function for for the CryoSat-2 interferometer are obtained by linear regression, as depicted in Figure3, the CryoSat-2 interferometer are obtained by linear regression, as depicted in Figure 3, where the end-to-end error in the angle of arrival for calibration campaign #3 as a function of the angle of arrival and the corresponding calibration function are depicted.

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Remote Sens. 2021, 13, 302 where the end-to-end error in the angle of arrival for calibration campaign #3 as a function5 of 13 of the angle of arrival and the corresponding calibration function are depicted.

FigureFigure 3.3. EndEnd-to-end-to-end error error i inn the the angle angle of of arrival arrival for for calibration calibration campaign campaign #3 #3 as as a function a function of ofthe the angleangle ofof arrivalarrival andand thethe correspondingcorresponding calibration calibration function. function. The The blue blue points points represent represent the the individual individual interferometric measurements and the red line the linear regression over them. Figure taken interferometric measurements and the red line the linear regression over them. Figure taken from [9]. from [9]. 2.3. Swath-Based Roll 2.3. Swath-Based Roll When in SARIn mode and in the presence of a suitable across-track angle, namely, typical conditionsWhen in overSARIn land mode ice, elevationand in the can presence be retrieved of a beyondsuitable the across point-of-closest-approach-track angle, namely, (POCA),typical conditions leading to aover swath land of elevationice, elevation in the can across-track be retrieved direction beyond [10 the–12 ].point This-of approach-closest- hasapproach been used (POCA) to improve, leading the to spatial a swath resolution of elevation of time-dependent in the across- elevationtrack direction change [10 across–12]. theThis two approach polar ice has sheets been [12used–15 to], asimprove well as the icecaps spatial and resolution glaciers worldwide of time-dependent [16–19]. elevation changeThe across-track across the position two polar and ice elevation sheets [12 are–15 directly], as well related as icecaps to the and roll glaciers angle and world- the lookwide angle [16–19 via]. (2). The existence of a roll bias will lead to an elevation bias between ascending andThe descending across-track passes; position a bias and that,elevation within are a directly given waveform, related to willthe roll increase angle with and thethe distancelook angle to via the (2). POCA. The Thisexistence elevation of a biasroll bias can thenwill lead be used to an to elevation invert the bias most-likely between roll as- biascending by adding and descending a roll bias passes term to; a Equationbias that, (5)within and a solving given waveform, for the roll will bias, increase minimizing with thethe differencedistance to in the elevation POCA. between This elevation ascending bias and can descending then be used passes to invert over athe common most-likely loca- tionroll bias [12,20 by]. adding The approach a roll bias has term so far to been Equation implemented (5) and solving by subtracting for the roll a reference bias, minimizing elevation (e.g.,the difference ground-based in elevation GPS, operation between iceascending bridge airborneand descending laser altimeter, passes over ASIRAS a common airborne lo- Ku-bandcation [12 radar,20]. The altimeter) approach from has the so CryoSat-2 far beendata implemented and analyzing by subtracting the ascending-descending a reference ele- elevationvation (e.g. bias, ground to compare-based the GPS, differences operation in ice elevation bridge residualsairborne laser[12,20 altimeter,]. This strategy ASIRAS limits air- theborne use Ku of- theband approach radar altimeter) to areas where from collocatedthe CryoSat elevation-2 data referenceand analy campaignszing the ascending have been- conducted.descending Anelevation alternative, bias to not compare used here, the differences would be to in compare elevation swath residuals crossovers, [12,20]. thusThis makingstrategy thelimits approach the use independent of the approach of the to useareas of where an accurate collocated reference elevation elevation. reference cam- paignsThe have experiment, been conducted. then, consists An alternative, of running thenot swathused here, processing would a numberbe to compare of times swath with differentcrossovers, values thus of making the roll the bias; appro in thisach instance, independent we run of the the experiment use of an withaccurate increments reference of ◦ rollelevation. bias of 0.01 , and the discrete record is then oversampled to improve the resolution of the rollThe angle experiment determination., then, consists The most of likely running roll biasthe swath is then processing determined a fromnumber the widthof times of thewith elevation different residual values distribution.of the roll bias; in this instance, we run the experiment with increments of roll bias of 0.01°, and the discrete record is then oversampled to improve the 3. Results and Discussion resolution of the roll angle determination. The most likely roll bias is then determined fromThe the resultswidth of in the the elevation following residual were obtained distribution. comparing CryoSat-2 Level1b products from different Baselines, i.e., versions of the products generated by different versions of3. Results the Level1 and processor Discussion and corresponding conﬁguration. Limiting to the mispointing angle computation and the roll bias applied by conﬁguration, the differences between The results in the following were obtained comparing CryoSat-2 Level1b products the Baselines are listed in the following: (i) in Baseline-B, the SARIn phase difference from different Baselines, i.e., versions of the products generated by different versions of was compensated for a 0.1054 degrees roll bias; (ii) in Baseline-C, a roll bias equal to 0.1062the Level1 degrees processor was compensated, and corresponding and the configuration. mispointing Limiting angles were to the computed mispointing from an thegle optimalcomputation Star Trackerand the accordingroll bias applied to an on-boardby configuration, selection; the and differences (iii) in Baseline-D, between the the Base- roll was compensated for a bias varying as a function of both the Mission lifetime and the Star Tracker in use, while the mispointing angles computation accounted for the aberration of light [7,9].

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3.1. Transponder Calibration Results for the Angle of Arrival for each Transponder pass are shown in Figure4. The overall 0.0071 degrees of bias is equivalent to a displacement in the geolocations across- track of about 87 m, and the standard deviation of 0.0040 degrees denotes an uncertainty of around 50 m. The results are slightly within the 0.0083 degrees of AoA requirement.

Figure 4. Angle of Arrival (AoA) calibration with transponder results. Each point represents the retrieval for a single transponder pass. Figure taken from [8].

By averaging all the different errors, the AoA bias is 0.0071 degrees, bearing in mind that for each pass, different Star Trackers (STRs) with different temperature conditions have been used. The AoA pass-to-pass results variations depend mainly on the error of the estimation of the roll and are different for each STR, even if they should measure the same. So, for a single transponder pass, different AoA results can be obtained depending on which STR is used to retrieve the attitude. In the Baseline-C processor, a specific module, called an STR processor, is in charge of estimating the attitude [9]. The STR selection method was improved from Baseline-B. The previous method just selected the first available STR, while in Baseline-C, the selected STR is the one used by the Attitude and Orbital Control Systems. Additionally, the STR processor performs smoothing on the roll, pitch and yaw before writing them on the product. Although these changes improve the attitude measurements, the STR selection on board sometimes does not use the STR with the smallest error. A comparison between the AoA results from both baselines is shown in Figure5. It can be seen that some Baseline-C results are worse than the ones available from Baseline-B. Further studies concluded with the need to implement an improved attitude solution in the Star Tracker processor (currently operational in Baseline-D products). The links between the AoA results have tried to be related to the temperature of the spacecraft, but the sparse number of transponder passes made analysis difficult. The bending of the antenna bench due to spacecraft interface temperature can cause mispointing from the STRs nominal positions and consequent bias in the attitude measurements. These biases can be corrected by averaging the attitude measured by two opposite STRs, but only in the case where bending is symmetric. However, different illuminations of the sun can increase the attitude noise, making the “hot” STRs less precise.

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Figure 5. BaselineBaseline-B-B and Baseline Baseline-C-C AoA results. Read, b bluelue and g greenreen points represent the individual AoA retrievals for Star Trackers (STRs)(STRs) 1, 2 and 3. Yellow dots represent the retrieval of the STR selected by the STR processor. Figure taken from [8]. from [8]. The links between the AoA results have tried to be related to the temperature of the 3.2. Roll Campaigns over Ocean spacecraft, but the sparse number of transponder passes made analysis difficult. The bendingThroughout of the antenna this section, bench due the resultsto spacecraft of the interface interferometer temperature calibration can cause analysis mispoint- of the ingCryoSat-2 from the SARIn STRs L1b nominal products positions from the and interferometer consequent calibrationbias in the campaignsattitude measurements. are presented. TheseTable1 biases includes can the be maincorrected information by averaging for each the interferometer attitude measured calibration by two campaign. opposite STRs, but only in the case where bending is symmetric. However, different illuminations of the Table 1. Interferometer calibration campaigns. sun can increase the attitude noise, making the ‘‘hot” STRs less precise. Campaign Dates L1b Products ST1 ST2 ST3 3.2. Roll Campaigns Over Ocean #1 27–28 July 2010 6 OFF ON ON #2 17–18 OctoberThroughout 2011 this section, 9 the results of the ON interferometer OFF calibration analysis ON of the #3 11–12CryoSat September-2 2012SARIn L1b products 8 from the interferometer OFF calibration ON campaigns ON are pre- #4 10–12sented. October Table 2013 1 includes the 8main information ON for each interferometer ON calibration OFF cam- #5 4–5paign. January 2014 8 ON ON ON #6 6 May 2015 8 ON ON ON #7 31 August–1 September 2016 8 ON ON ON Table 1. Interferometer calibration campaigns. #8 6 February 2018 8 ON ON ON Campaign#9 Dates 25 April 2019L1b Products 8ST1 ONST2 ONST3 ON #1 27–28 July 2010 6 OFF ON ON #2 17–18 October It2011 is worth recalling9 that the StarON Trackers were placedOFF on the spacecraftON to have a #3 11–12 Septemberdifferent 2012 orientation, 8 so that at any timeOFF at least one Star TrackerON was free fromON sun or moon #4 10–12 Octoberblinding 2013(tagged “OFF”8 on the Table)ON [2]. This can beON verified by inspectionOFF of Table1 , #5 4–5 Januarywhere, 2014 for each campaign,8 at least twoONStar Trackers wereON available (tagged “ON”ON on the Table). #6 6 May 2015 8 ON ON ON The SARIn L1b product only contains mispointing angles computed from the optimal 31 August–1 September #7 Star Tracker according8 to the rule definedON on board in theON attitude orbit controlON system. In 2016 order to include the roll mispointing angle from the Star Tracker available in the calibration #8 6 Februaryanalysis, 2018 we processed8 our own theON quaternions generatedON by the Star TrackersON using #9 25 Aprilexactly 2019 the same processing8 functionsON and configuration thatON are used in Level1ON operational processor. This way, a calibration function for each available Star Tracker was computed. It hasIt tois beworth remarked recalling that that in thethe followingStar Trackers we presentwere placed the results on the ofspacecraft the interferometer to have a differentcalibration orientation obtained, (i)so that by computing at any time the at mispointingleast one Star angles Tracker on-ground was free from by properly sun or mooncorrecting blinding for the (tagged aberration “OFF” of on light the [Table)1] and [2]. (ii) This by exploiting can be verified an improved by inspection version of ofTable the 1,interferometer where, for each calibration campaign tool,, at where least thetwo accuracy Star Trackers of the a-prioriwere available known across-track(tagged “ON” ocean on theslope Table). was increased. TheIn Figure SARI6n, L1b we plottedproduct the only calibration contains mispointing function parameters angles computed that were from obtained the opti- for malthe differentStar Tracker interferometer according to calibration the rule defined campaigns on board and in for the each attitude available orbit Starcontrol Tracker system. In order to include the roll mispointing angle from the Star Tracker available in the

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calibration analysis, we processed our own the quaternions generated by the Star Trackers using exactly the same processing functions and configuration that are used in Level1 operational processor. This way, a calibration function for each available Star Tracker was computed. It has to be remarked that in the following we present the results of the interferometer calibration obtained (i) by computing the mispointing angles on-ground by properly correcting for the aberration of light [1] and (ii) by exploiting an improved version of the interferometer calibration tool, where the accuracy of the a-priori known Remote Sens. 2021, 13, 302 across-track ocean slope was increased. 8 of 13 In Figure 6, we plotted the calibration function parameters that were obtained for the different interferometer calibration campaigns and for each available Star Tracker by processing Baseline-C L1b products. By inspection of Figure 6a, where the linear coefficient by processing Baseline-C L1b products. By inspection of Figure6a, where the linear for the interferometer calibration function is reported, it can be noticed that similar values coefﬁcient for the interferometer calibration function is reported, it can be noticed that are obtained from the available Star Trackers for each campaign. This behavior was ex- similar values are obtained from the available Star Trackers for each campaign. This pected since the parameter a is a function of sea surface roughness only. By inspection of behavior was expected since the parameter a is a function of sea surface roughness only. Figure 6b, where the estimated roll bias 휒0is reported, it can be noticed that 휒0 exhibits a By inspection of Figure6b, where the estimated roll bias χ0 is reported, it can be noticed dependence on the Star Tracker. This suggests that a different roll bias is present depend- that χ0 exhibits a dependence on the Star Tracker. This suggests that a different roll bias is presenting on depending the rotation on between the rotation each between Star Tracker each Starframe Tracker and the frame interferometer and the interferometer baseline. Ad- baseline.ditionally, Additionally, a decreasing a decreasing trend can trendbe observed, can be observed,at least up at to least 2018. up to 2018.

(a) (b) 휒 FigureFigure 6. Calibration6. Calibration function function parameters parameters from from Baseline-C Baseline- L1bC L1b products: products: (a) ( lineara) linear coefﬁcient coefficient a and a and (b) ( constantb) constant term termχ0 . 0.

It hasIt has to to be be remarked remarked that that in in Figure Figure6b the6b the total total uncorrected uncorrected roll roll bias biasχ0 휒is0is presented. presented. RecallingRecalling that that a roll a roll bias bias equal equal to 0.1062 to 0.1062 degrees degrees was was compensated compensated in Baseline-C, in Baseline an-C, average an aver- residualage residual roll bias roll of bias 0.0097 of 0.0097 degrees degrees with a with standard a standard deviation deviation of 0.0019 of 0.0019 degrees degrees is ﬁnally is fi- obtained.nally obtained. It is worth It is noticing worth noticing that the averagethat the residualaverage rollresidual bias in roll Baseline-C bias in Baseline was already-C was compliantalready compliant with the requirement with the requirement for the roll for bias the given roll bias in Section given1 in. Section 1. AsAs an an outcome outcome of of the the roll roll calibration calibration exploiting exploiting the the interferometer interferometer calibration calibration cam- cam- paignpaign over over ocean, ocean, we we decided decided to to apply apply a differenta different roll roll bias bias as as function function of of the the Star Star Tracker Tracker andand variable variable as as a functiona function of of the the mission mission lifetime lifetime for for the the reprocessed reprocessed products products in in Baseline- Baseline- D[D20 [20]. By]. By processing processing Baseline-D Baseline-D products products from from the the interferometer interferometer calibration calibration campaigns, campaigns, thethe residual residual roll roll bias bias for for each each Star Star Tracker Tracker shown shown in in Figure Figure7 was 7 was obtained. obtained. By By inspection inspection ofof Figure Figure7, it 7 can, it becan noticed be noticed that thethat residual the residual roll bias roll in bias Baseline-D in Baseline is steadily-D is steadily around zero,around Remote Sens. 2021, 13, 302 9 of 13 independentlyzero, independently of the Star of the Tracker Star andTracker of the and campaign, of the campaign, resulting resulting in an average in an roll average bias of roll 0.0006bias degreesof 0.0006 with degrees a standard with a deviationstandard deviation of 0.0009 degrees.of 0.0009 degrees.

FigureFigure 7. 7.ResidualResidual roll roll bias bias from from Baseline Baseline-C-C and and Baseline Baseline-D-D acquisitions. acquisitions.

In the framework of this analysis, the roll bias was subsequently addressed, and the existence of an antenna bench bending for SIRAL was investigated together with its impact on interferometric acquisitions. As detailed in [2], the rigid bench where antennas are mounted is expected to undergo convex or concave flexing when subject to a thermal gra- dient. To minimize the effect of this bending, antenna feeds are decoupled from the antenna bench while the Star Trackers are coupled with the antenna bench. As a consequence, a bending of the antenna bench can affect the roll measured by the Star Trackers so that the measured roll does not correspond to the real direction of the interferometer antenna baseline. Aiming to evaluate the in-flight flexing of the bench, the difference of the roll measured by each Star Tracker pair was computed. If a difference far from zero is observed for two Star Trackers on opposite sides of the bench, it can be due to its bending, under the assumption of the exact roll computed by Star Trackers and by on-ground processing. In Figure 8 shows the roll difference for each Star Tracker pair from the beginning of the mission up to 2017. It can be noticed that roll differences between Star Trackers on the same side of the antenna bench are nearly zero, as expected. On the other hand, the roll differences between Star Trackers on the opposite side of the antenna bench is larger than zero in absolute value and varies as a function of mission lifetime.

Figure 8. Roll difference for each Star Tracker pair. Blue represents differences between ST1 and ST3, yellow between ST2 and ST3, and red between ST1 and ST2.

Under the assumption that the roll difference of Star Tracker pairs at different sides of the antenna bench is due to bending and that the bending is symmetrical with respect

Remote Sens. 2021, 13, 302 9 of 13

Remote Sens. 2021, 13, 302 Figure 7. Residual roll bias from Baseline-C and Baseline-D acquisitions. 9 of 13

In the framework of this analysis, the roll bias was subsequently addressed, and the existence of an antenna bench bending for SIRAL was investigated together with its im- pactIn on the interferometric framework of acquisitions. this analysis, As the detailed roll bias in was[2], the subsequently rigid bench addressed, where antennas and the are existencemounted of is anexpected antenna to bench undergo bending convex for or SIRAL concave was flexing investigated when togethersubject to with a thermal its impact gra- ondient. interferometric To minimize acquisitions. the effect of Asthis detailed bending, in antenna [2], the feeds rigid benchare decoupled where antennas from the arean- mountedtenna bench is expected while theto undergo Star Trackers convex are or concave coupled flexing with the when antenna subject bench. to a thermal As a gradi- conse- ent.quence, To minimize a bending the of effect the antenna of this bending, bench can antenna affect feedsthe roll are measured decoupled by from the Star the antennaTrackers benchso that while the measured the Star Trackers roll does are not coupled correspond with to the the antenna real direction bench. Asof the a consequence, interferometer a bendingantenna ofbaseline. the antenna Aiming bench to evaluat can affecte the the in- rollflight measured flexing of by the the bench, Star Trackersthe difference so that of thethe measured roll measured roll does by each not Star correspond Tracker topair the was real computed. direction of If thea difference interferometer far from antenna zero is baseline.observed Aimingfor two toStar evaluate Tracker thes on in-flight opposite flexing sides of of the the bench, bench, it thecan differencebe due to its of bending, the roll measuredunder the by assumption each Star Tracker of the exact pair wasroll computed.computed by If aStar difference Trackers far and from by zero on-ground is observed pro- forcessing. two Star Trackers on opposite sides of the bench, it can be due to its bending, under the assumptionIn Figure of the8 show exacts the roll roll computed difference by Starfor each Trackers Star Tracker and by on-groundpair from the processing. beginning of the missionIn Figure up8 showsto 2017. the It can roll be difference noticed forthat each roll Stardifferences Tracker between pair from Star the Trackers beginning on ofthe thesame mission side of up the to 2017.antenna It can bench be noticedare nearly that zero, roll differencesas expected. between On the Star other Trackers hand, the on theroll samedifferences side of between the antenna Star benchTrackers are on nearly the opposite zero, as side expected. of the antenna On the other bench hand, is larger the than roll differenceszero in absolute between value Star and Trackers varies onas thea function opposite of sidemission of the lifetime. antenna bench is larger than zero in absolute value and varies as a function of mission lifetime.

FigureFigure 8. 8.Roll Roll difference difference for for each each Star Star Tracker Tracker pair. pair. Blue Blue represents represents differences differences between between ST1 ST1 and and ST3, ST3, yellow yellow between between ST2 ST2 andand ST3, ST3 and, and red red between between ST1 ST1 and and ST2. ST2.

UnderUnder the the assumption assumption that that the the roll roll difference difference of of Star Star Tracker Tracker pairs pair ats differentat different sides sides of theof the antenna antenna bench bench is due is due to bending to bending and and that that the the bending bending is symmetrical is symmetrical with with respect respect to the center of the antenna bench, the error in the angle of arrival due to bench bending can be modeled as equal to half the roll difference. Considering the whole mission, the average error in the angle on arrival due to bench bending at 1Hz is equal to 0.0020 degrees with a

standard deviation equal to 0.0112 degrees.

3.3. Swath-Based Roll This approach has been applied over the Greenland Ice Sheet, where OIB (Operation Ice Bridge) [21] surveys have been conducted yearly during the CryoSat-2 period (Figure9). To limit the chance of elevation difference occurring due to temporal change and surface slopes, each CryoSat-2 height record has been matched with the closest OIB elevation, setting a maximum spatial distance of 50 m and temporal separation of 10 days. The elevation difference between OIB and CryoSat-2 due to their different positions is further corrected using arcticDEM [22] as reference topography. Remote Sens. 2021, 13, 302 10 of 13

to the center of the antenna bench, the error in the angle of arrival due to bench bending can be modeled as equal to half the roll difference. Considering the whole mission, the average error in the angle on arrival due to bench bending at 1Hz is equal to 0.0020 degrees with a standard deviation equal to 0.0112 degrees.

3.3. Swath-Based Roll This approach has been applied over the Greenland Ice Sheet, where OIB (Operation Ice Bridge) [21] surveys have been conducted yearly during the CryoSat-2 period (Figure 9). To limit the chance of elevation difference occurring due to temporal change and surface slopes, each CryoSat-2 height record has been matched with the closest OIB elevation, setting a maximum spatial distance of 50 m and temporal separation of 10 days. The elevation difference between OIB and CryoSat-2 due to their different positions is further corrected using arcticDEM [22] as reference topography. From the CryoSat-2 and the OIB datasets covering the month of April 2011, we ob- Remote Sens. 2021, 13, 302 tained over 50,000 collocated measurements equally split between ascending and10 de- of 13 scending orbits.

FigureFigure 9. 9.LocationLocation of ofthe the collocated collocated swath swath-OIB-OIB (Operation (Operation Ice Ice Bridge) Bridge) measurements. measurements. EOLIS EOLIS (Ele- (Eleva- vationtion OverOver LandLand IceIce fromfrom Swath)Swath) DEM DEM along along the the west west coast coast of of the the Greenland Greenland Ice Ice Sheet Sheet overlaid overlaid over overthe the MEaSUREs MEaSUREs MODIS MODIS (Moderate (Moderate Resolution Resolution Imaging Imaging Spectroradiometer) Spectroradiometer) Mosaic Mosaic of Greenland of Green- [23]. landThe [23 inland]. The limit inland of thelimit DEM of the corresponds DEM corresponds to the CryoSat-2 to the CryoSat0s SARIn-2′s modeSARIn mask mode (dashed mask (das line);hed else- line)where; elsewhere the ice mask the ice is inmask accordance is in accord withance the with Greenland the Greenland Ice Mapping Ice Mapping Project (GIMP) Project dataset (GIMP [)24 ]. Ice datasetBridge [2 elevation4]. Ice Bridge acquired elevation in March, acquired April in and March, May April 2011 and (black). May Figure 2011 (black). taken from Figure [12 ].taken from [12]. From the CryoSat-2 and the OIB datasets covering the month of April 2011, we obtainedAnalysis over of 50,000the Baseline collocated-C dataset measurements reveals a clear equally minimum split between elevation ascending bias found and for de- a scendingroll bias of orbits. ~0.007°, a value in agreement with the alternative methods described alongside theAnalysis swath method of the Baseline-C, as seen in dataset Figure reveals 10. The a clearsameminimum analysis o elevationf Baseline bias-D data found again for a showsroll bias a clear of ~0.007 minimum◦, a value, but in this agreement time it is with cen thetered alternative on ~0°, an methods expected described outcome alongside since Baselinethe swath-D data method, incorporate as seen in the Figure improved 10. The attitude. same analysis We also of Baseline-Dnote that the data width again of shows the minima clearization minimum, is reduced but this for time Baseline it is centered-D case oncompared ~0◦, an expectedwith Baseline outcome-C, suggesting since Baseline-D that thedata attitude incorporate correction the improvedperformed attitude. on Baselin Wee- alsoD data note has that addressed the width some of the of minimizationthe variabil- ityis in reduced the roll forerror Baseline-D seen in Baseline case compared-C data. with Baseline-C, suggesting that the attitude correction performed on Baseline-D data has addressed some of the variability in the roll error seen in Baseline-C data. The chosen strategy of using a reference elevation, in this case, OIB airborne laser, limits the use of this approach to areas where collocated elevation reference campaigns have been conducted. An alternative approach would be to extract point-to-point elevation difference from ascending and descending passes. This latter approach would allow us to exploit more of the CryoSat-2 datasets and analyze the roll bias as a function of orbit

position and time to assess external forcings in the roll-bias variation. This approach could also lead to continuous platform attitude assessment and correction as no particular campaign needs to be programmed. This would potentially reduce some of the largest errors related to uncertainty in the Angle of Arrival and subsequent errors in geophysical variables extracted from Interferometric Radar Altimeters. Remote Sens. 2021, 13, 302 11 of 13 Remote Sens. 2021, 13, 302 11 of 13

FigureFigure 10.10. ElevationElevation biasbias betweenbetween ascendingascending andand descendingdescending CryoSat-2CryoSat-2 passespasses as a function of roll angleangle bias.bias. TheThe rollroll biasbias that that minimizes minimizes the the dispersion dispersion of of the the elevation elevation difference difference for for Baseline-C Baseline-C data data is found at 0.007°. The same exercise using Baseline-D data shows a minimum elevation dis- is found at 0.007◦. The same exercise using Baseline-D data shows a minimum elevation dispersion persion with no significant roll angle bias. Figure taken from [12]. with no signiﬁcant roll angle bias. Figure taken from [12].

4. ConclusionsThe chosen strategy of using a reference elevation, in this case, OIB airborne laser, limits the use of this approach to areas where collocated elevation reference campaigns Three different methods have been used to determine roll stability during the CryoSat- have been conducted. An alternative approach would be to extract point-to-point eleva- 2 mission. Analysis with transponder acquisitions provided a very accurate and uniform solutiontion difference thanks from to the ascending good knowledge and descending of the target passes. and Thi thes frequency latter approach of the would acquisitions allow (twiceus to exploit a month more uninterruptedly). of the CryoSat However,-2 datasets it and was analy difficultze the to measureroll bias as seasonal a function distortions of orbit relatedposition to and the benchtime to bending assess external and to disregard forcings in an the error roll due-bias to variation. phase difference from errors due toThis antenna approach baseline could orientation also lead knowledge.to continuous Analysis platform of attitude the roll campaignassessment data and over cor- oceanrection increased as no particular the number campaign of records needs analyzed to be programmed. compared with This single would target potentially measurements reduce oversome the of transponders.the largest errors However, related theto uncertainty complexity in of the the Angle roll campaign of Arrival only and allowed subsequent for 9error campaigns,s in geophysical compared variables with the extracted 87 transponder from Inter passes.ferometric The Radar swath Altimeters. method provided a very good approach, with the ability to use science data directly over a specific land ice4. Conclusions region, but it required the use of an additional instrument to measure the reference elevation,Three which different limited methods the use have of the been method used to to areas determine where collocatedroll stability elevation during reference the Cry- campaignsoSat-2 mission. had A beennalysis conducted. with transponder Alternatively, acquisitions swath crossoversprovided a couldvery accurate be used, and which uni- wouldform solution not rely thanks on such to reference the good elevation. knowledge A comparisonof the target of and the the roll frequency bias results of for the each acqui- of thesitions methods (twice is a listed month in Tableuninterruptedly).2 in the case ofHowever, Baseline-C. it was difficult to measure seasonal distortions related to the bench bending and to disregard an error due to phase difference Tablefrom 2.errorsComparison due to antenna of the roll baseline bias results orientation for Baseline-C. knowledge. Analysis of the roll campaign data over oceanMethod increased the number of Biasrecords analyzed compared Standard with Deviation single target measurements over the transponders. However, the complexity of the roll campaign only Transponder 0.0071 degrees 0.0040 degrees allowed for 9 campaigns, compared with the 87 transponder passes. The swath method Ocean Roll 0.0097 degrees 0.0019 degrees provided a verySwath good approach, with 0.0070the ability degrees to use science data directly - over a specific Aimingland ice at takingregion advantage, but it require of the capabilitiesd the use andof an advantages additional of each instrument of the methods, to measure the comprehensive the refer- approachence elevation, for roll calibration which thatlimit hased been the exploited use of inthe the method CryoSat-2 to Mission areas foresees where that collocated (i) absolute elevation roll bias is evaluatedreference using campaigns the campaign ha datad been over conducted. ocean; (ii) the stabilityAlternatively, of the roll swath mispointing crossovers is continuously could monitored, be used, exploiting the transponder acquisitions; and (iii) the performance from a user perspective is assessed using swath datawhich analysis. would Following not rely the approachon such above, reference it was possibleelevation. to refine A comparison the roll bias correction of the roll in Baseline-D, bias results and thisfor ineach turn of was the proven methods to reduce is listed the residual in Table roll 2 bias in withthe case a direct of impactBaseline on the-C. quality of interferometric measurements. Table 2. Comparison of the roll bias results for Baseline-C. Author Contributions: Method The contributions of thisBias reported work can beStandard listed as follows: Deviation writing- original draft preparation, A.G.-M.; writing—review and editing A.G.-M. Transponder analysis M.R., A.G.-M.; rollTransponder campaigns over ocean M.S.; Swath-based0.0071 degrees analysis N.G.; supervision0.0040 and degrees final revision M.R., J.B. AllOcean authors Roll have read and agreed0.0097 to the degrees published version of the manuscript.0.0019 degrees Swath 0.0070 degrees -

Remote Sens. 2021, 13, 302 12 of 13

Funding: This work has been developed in the framework of ESA/ESTEC (Contracts No. C18318/05/NL and 4200022114/08/NL/JA), ESA/ESRIN (Contracts No. 4000104810/11/I-NB and 4000111597/14/I- AM and 4000111474/14/I-NB and 4000107394/12/I-NB and 4000116874/16/I-NB). Data Availability Statement: The input data used in this manuscript can be freely downloaded from ESA portal. Transponder and Land Ice data from the CryoSat-2 Science Server (https://science-pds. cryosat.esa.int/) and the roll campaigns from its specific portal (https://earth.esa.int/web/guest/ missions/esa-eo-missions/cryosat/roll-campaigns). Acknowledgments: We would like to thank the participants of the ESA CryoSat-2 Quality Working Group for the interesting exchanges and discussions. Conflicts of Interest: The authors declare no conflict of interest.

References 1. Wingham, D.J.; Phalippou, L.; Mavrocordatos, C.; Wallis, D. The mean echo and echo cross product from a beamforming interferometric altimeter and their application to elevation measurement. IEEE Trans. Geosci. Rem. Sens. 2004, 42, 2305–2323. [CrossRef] 2. ESA Team. CryoSat Mission and Data Description; Report no. CS-RP-ESA-SY-0059; ESTEC: Noordwijk, The Netherlands, 2007; Available online: http://esamultimedia.esa.int/docs/Cryosat/Mission_and_Data_Descrip.pdf (accessed on 15 January 2021). 3. Wingham, D.J.; Francis, C.R.; Baker, S.; Bouzinac, C.; Brockley, D.; Cullen, R.; de Chateau-Thierry, P.; Laxon, S.W.; Mallow, U.; Mavrocordatos, C.; et al. CryoSat: A mission to determine the ﬂuctuations in Earth’s land and marine ice ﬁelds. Adv. Space Res. 2006, 37, 841–871. [CrossRef] 4. Galin, N.; Wingham, D.J.; Cullen, R.; Fornari, M.; Smith, W.H.F.; Abdalla, S. Calibration of the CryoSat-2 Interferometer and Measurement of Across-Track Ocean Slope. IEEE Trans. Geosci. Remote Sens. 2012, 51, 57–72. [CrossRef] 5. Galin, N.; Wingham, D.J.; Cullen, R.; Francis, R.; Lawrence, I. Measuring the Pitch of CryoSat-2 Using the SAR Mode of the SIRAL Altimeter. IEEE Geosci. Remote Sens. Lett. 2014, 11, 1399–1403. [CrossRef] 6. Scagliola, M.; Fornari, M.; Tagliani, N. Pitch Estimation for CryoSat by Analysis of Stacks of Single-Look Echoes. IEEE Geosci. Remote Sens. Lett. 2015, 12, 1561–1565. [CrossRef] 7. Meloni, M.; Bouffard, J.; Parrinello, T.; Dawson, G.; Garnier, F.; Helm, V.; Di Bella, A.; Hendricks, S.; Ricker, R.; Webb, E.; et al. CryoSat Ice Baseline-D validation and evolutions. Cryosphere 2020, 14, 1889–1907. [CrossRef] 8. Garcia-Mondéjar, A.; Fornari, M.; Bouffard, J.; Féménias, P.; Roca, M. CryoSat-2 range, datation and interferometer calibration with Svalbard transponder. Adv. Space Res. 2018, 62, 1589–1609. [CrossRef] 9. Scagliola, M.; Fornari, M.; Bouffard, J.; Parrinello, T. The CryoSat interferometer: End-to-end calibration and achievable performance. Adv. Space Res. 2018, 62, 1516–1525. [CrossRef] 10. Hawley, R.L.; Shepherd, A.; Cullen, R.; Helm, V.; Wingham, D.J. Ice-sheet elevations from across-track processing of airborne interferometric radar altimetry. Geophys. Res. Lett. 2009, 36, L22501. [CrossRef] 11. Gray, L.; Burgess, D.; Copland, L.; Cullen, R.; Galin, N.; Hawley, R.; Helm, V. Interferometric swath processing of Cryosat-2 data for glacial ice topography. Cryosphere Discuss. 2013, 7, 3133–3162. [CrossRef] 12. Gourmelen, N.; Escorihuela, M.J.; Shepherd, A.; Foresta, L.; Muir, A.; Garcia-Mondejar, A.; Drinkwater, M.R. CryoSat-2 swath interferometric altimetry for mapping ice elevation and elevation change. Adv. Space Res. 2018, 62, 1226–1242. [CrossRef] 13. Gourmelen, N.; Goldberg, D.; Snow, K.; Henley, S.; Bingham, R.; Kimura, S.; Hogg, A.; Shepherd, A.; Mouginot, J.; Lenearts, J.; et al. Channelized melting drives thinning under a rapidly melting Antarctic ice shelf. Geophys. Res. Lett. 2017, 44, 9796–9804. [CrossRef] 14. Gray, L.; Burgess, D.; Copland, L.; Langley, K.; Gogineni, P.; Paden, J.; Smith, B. Measuring height change around the periphery of the Greenland Ice Sheet with radar altimetry. Front. Earth Sci. 2019, 7, 146. [CrossRef] 15. Shepherd, A.; Ivins, E.; Rignot, E.; Smith, B.; van Den Broeke, M.; Velicogna, I.; Whitehouse, P.; Briggs, K.; Joughin, I.; Krinner, G.; et al. Mass balance of the Greenland Ice Sheet from 1992 to 2018. Nature 2020, 579, 233–239. 16. Gray, L.; Burgess, D.; Copland, L.; Demuth, M.N.; Dunse, T.; Langley, K.; Schuler, T.V. CryoSat-2 delivers monthly and inter-annual surface elevation change for Arctic ice caps. Cryosphere 2015, 9, 1895–1913. [CrossRef] 17. Foresta, L.; Gourmelen, N.; Pálsson, F.; Nienow, P.; Björnsson, H.; Shepherd, A. Surface elevation change and mass balance of Icelandic ice caps derived from swath mode CryoSat-2 altimetry. Geophys. Res. Lett. 2016, 43, 12138–12145. [CrossRef] 18. Foresta, L.; Gourmelen, N.; Weissgerber, F.; Nienow, P.; Williams, J.; Shepherd, A.; Drinkwater, M.R.; Plummer, S. Heterogeneous and rapid ice loss over the Patagonian Ice Fields revealed by CryoSat-2 swath radar altimetry. Remote Sens. Environ. 2018, 211, 441–455. [CrossRef] 19. Jakob, L.; Gourmelen, N.; Ewart, M.; Plummer, S. Ice loss in High Mountain Asia and the Gulf of Alaska observed by CryoSat-2 swath altimetry between 2010 and 2019. Cryosphere 2020.[CrossRef] 20. Gray, L.; Burgess, D.; Copland, L.; Dunse, T.; Langley, K.; Moholdt, G. A revised calibration of the interferometric mode of the CryoSat-2 radar altimeter improves ice height and height change measurements in western Greenland. Cryosphere 2017, 11, 1041–1058. [CrossRef] Remote Sens. 2021, 13, 302 13 of 13

21. Studinger, M.; Koenig, L.; Martin, S.; Sonntag, J. Operation icebridge: Using instrumented aircraft to bridge the observational gap between Icesat and Icesat-2. IEEE Inter. Geosci. Remote Sens. Symp. 2010.[CrossRef] 22. Morin, P.; Porter, C.; Cloutier, M.; Howat, I.; Noh, M.J.; Willis, M.; Bates, B.; Williamson, C.; Peterman, K. ArcticDEM; A publically available, high resolution elevation model of the Arctic. In Proceedings of the EGUGA 2016, Vienna, Austria, 17–22 April 2016. EPSC2016-8396. 23. Haran, T.; Bohlander, J.; Scambos, T.; Fahnestock, M. Modis Mosaic of Greenland (Mog) Image Map; NSIDC—National Snow and Ice Data Center: Boulder, CO, USA, 2013. 24. Howat, I.M.; Negrete, A.; Smith, B.E. The Greenland Ice Mapping Project (GIMP) land classiﬁcation and surface elevation data sets. Cryosphere 2014, 8, 1509–1518. [CrossRef]