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Article A Modiﬁed Empirical Retracker for Lake Level Estimation Using Cryosat-2 SARin Data

Hui Xue 1,2, Jingjuan Liao 1,* and Lifei Zhao 3

1 Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing 100094, China; [email protected] 2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Hebei Sales Branch of PetroChina Company Limited, Shijiazhuang 050000, China; [email protected] * Correspondence: [email protected]; Tel.: +86-010-8217-8160

Received: 29 September 2018; Accepted: 2 November 2018; Published: 5 November 2018

Abstract: Satellite radar altimetry is an important technology for monitoring water levels, but issues related to waveform contamination restrict its use for rivers, narrow reservoirs, and small lakes. In this study, a novel and improved empirical retracker (ImpMWaPP) is presented that can derive stable inland lake levels from Cryosat-2 synthetic aperture radar interferometer (SARin) waveforms. The retracker can extract a robust reference level for each track to handle multi-peak waveforms. To validate the lake levels derived by ImpMWaPP, the in situ gauge data of seven lakes in the Tibetan Plateau are used. Additionally, ﬁve existing retrackers are compared to evaluate the performance of the proposed ImpMWaPP retracker. The results reveal that ImpMWaPP can efﬁciently process the multi-peak waveforms of the Cryosat-2 SARin mode. The root-mean-squared errors (RMSEs) obtained by ImpMWaPP for Qinghai Lake, Nam Co, Zhari Namco, Ngoring Lake, Longyangxia Reservoir, Bamco, and Dawa Co are 0.085 m, 0.093 m, 0.109 m, 0.159 m, 0.573 m, 0.087 m, and 0.122 m, respectively. ImpMWaPP obtains the lowest mean RMSE (0.175 m) over the seven lakes, indicating that it extracts lake levels well during icing and no-ice periods, and is more suitable for lakes frozen in winter.

Keywords: Cryosat-2 SARin; multi-peak waveform; modiﬁed retracker; lake level

1. Introduction Satellite radar altimetry has been used successfully for more than two decades to measure water levels over inland waters [1–7]. Unfortunately, its use for rivers, narrow reservoirs, and small lakes has been restricted by waveform contamination caused by it’s relatively large footprint [8,9]. For conventional pulse-limited altimeters such as the TOPEX/Poseidon family of satellites, the footprint diameter is typically 5–10 km in mountainous areas [10], making it difficult to monitor small lakes. Cryosat-2 ushered in a new era in radar altimetry. It was launched by the European Space Agency (ESA) in April 2010 and is still operating. Because of its high along-track resolution and dense spatial sampling, the Cryosat-2 satellite is an important data source for monitoring lake levels, especially those of small lakes [11–15]. However, the footprint of Cryosat-2 in the cross-track direction is still sufﬁciently large to cause some waveforms to be polluted by signals from nearby terrain. Cryosat-2 carries on board a state-of-the-art synthetic aperture interferometric radar altimeter (SIRAL) that has three measurement modes, namely low resolution (LR), synthetic aperture radar (SAR), and SAR interferometer (SARin). These modes cover different regions, with the SARin mode being mainly activated over mountainous regions such as the Tibetan Plateau and the Andes [13]. The SARin mode includes an additional receiving antenna that allows the position of the reﬂecting surface to be determined [15], and it has a 300 m along-track resolution, but its footprint ranges up to

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15 km in the cross-track direction. Thus, the SARin waveforms can be contaminated by land signals by an amount that is closely related to lake shape and surrounding terrain. Additionally, the SARin waveform features a steep leading edge and a faster-decaying trailing edge [16] that allow polluted waveforms to contain multiple distinguishable surface heights [10]. Therefore, retracking the SARin waveforms is a challenging task [10]. Previous studies have paid little attention to retracking algorithms for the Cryosat-2 SARin waveforms, particularly the applications to lakes. Kleinherenbrink et al. proposed a retracking algorithm based on cross-correlation of simulated and observed Cryosat-2 SARin waveforms [10]. Villadsen et al. and Nielsen et al. explored the performance of various retrackers for Cryosat-2 SAR waveforms [17,18]. Göttl et al. focused on processing the Cryosat-2 SAR waveforms by waveform classification and an improved threshold retracker (ITR) [19]. Gommenginger et al. systematically described those retrackers that could handle different types of LR mode waveform [20]. Typically, the retrackers in those studies did not account fully for the complexity of terrain and interferometry in Cryosat-2 SARin observations, making them weak at handling complex multi-peak waveforms. Furthermore, some previous studies discarded complex data, an approach that could lead to significant data loss, especially for small lakes [21]. The present paper considers various shapes of along-track waveform and presents an improved algorithm that integrates the advantages of the error mixture model and the Multiple Waveform Persistent Peak (MWaPP) retracker [17,18]. This algorithm uses a novel method for identifying the water’s leading edge, thereby improving the processing performance for multi-peak waveforms. Furthermore, the capabilities of five existing algorithms for handling Cryosat-2 SARin waveforms are explored. In previous studies, examination of these retrackers was focused mainly on the Cryosat-2 SAR waveforms of low-elevation lakes, with mountainous lakes ignored. Compared with the waveforms of lakes surrounded by low topography, those of lakes with complex surrounding terrain are more susceptible to being polluted by land signals [7], especially near the shore. The present study focuses on developing an improved retracker for processing Cryosat-2 SARin waveforms to obtain high-precision water levels. The water levels for seven Tibetan Plateau lakes derived from the new retracker and five existing retrackers are compared with in situ gauge data.

2. Study Areas and Data

2.1. Study Areas Seven lakes in the Tibetan Plateau were chosen as study areas, each having in situ water levels and varying characteristics (e.g., extent, morphology, and surrounding landscape) (Figure1). Their names are Qinghai Lake, Nam Co, Zhari Namco, Ngoring Lake, Longyangxia Reservoir, Bamco, and Dawa Co. They have the following characteristics: (1) The topography surrounding these lakes features large ﬂuctuations, with the maximum change being up to several hundred meters. (2) The average altitude is more than 2500 m and ice formations are present in winter. The freezing time is generally from November of that year to April of the following year. (3) Longyangxia Reservoir is an artiﬁcial lake whose water levels are controlled by a management agency, but the other lakes have been rarely affected by human activities. The details of all the lakes are given in Table1. It should be noted that Longyangxia Reservoir and Qinghai Lake were observed by the Cryosat-2 SARin mode only after December 2015.

2.2. Data

2.2.1. Water Mask: The 2014 Sub-Dataset Water masks were used to extract the observations over all the lakes and were gathered from the 2014 sub-dataset for Tibetan Plateau lakes [22]. The latest status of each of 1171 lakes with an area greater than 1 km2 in the Tibetan Plateau is given in this dataset, including name, location, morphology, Water 2018, 10, x FOR PEER REVIEW 3 of 16

Table 1. Details of the seven lakes used in the present study.

Lake Name Coordinates Area [km2] Altitude 1 [m] Tracks 2 Date Mode Qinghai Lake 100.20, 36.89 4435 3194 49 01/2016–08/2017 Absolute Nam Co 90.60, 30.74 1920 4724 79 11/2010–12/2014 Relative Zhari Namco 85.61, 30.93 1023 4612 59 04/2010–12/2014 Relative Ngoring Lake 97.70, 34.90 610 4267 58 09/2010–12/2015 Absolute Water 2018Longyangxia, 10, 1584 100.73, 36.01 359 2569 5 12/2015–06/2017 Absolute3 of 17 Bamco 90.58, 31.27 180 4560 8 06/2013–12/2014 Relative Dawa Co 84.96, 31.24 118 4623 6 06/2013–12/2014 Relative and area.1 Altitudes This are dataset from the was Shuttle obtained Radar by Topography interpreting Mission 11 Landsat-8 (SRTM) Digital Operational Elevation Land Model Imager (DEM); (OLI) images2 Tracks acquired column in 2014 shows and number 136 Chinese of tracks Gaofen-1 for each lake. images with wide-ﬁeld-of-view cameras.

FigureFigure 1.1. LakesLakes and and corresponding corresponding Cryosat-2 Cryosat-2 SARin SARin tracks tracks.. Blue Blue and and gray gray solid solid lines lines represent represent the theobservations observations of icing of icing and and no-ice no-ice periods, periods, respectively. respectively. Red Red circles circles mark mark the the locations of ﬁxedfixed measuringmeasuring stations.stations.

Table 1. Details of the seven lakes used in the present study. 2.2. Data Lake Name Coordinates Area [km2] Altitude 1 [m] Tracks 2 Date Mode 2.2.1.Qinghai Water Lake Mask: 100.20, The 2014 36.89 Sub-Dataset 4435 3194 49 01/2016–08/2017 Absolute Nam Co 90.60, 30.74 1920 4724 79 11/2010–12/2014 Relative ZhariWater Namco masks 85.61,were 30.93used to extract 1023 the observatio 4612ns over 59all the lakes04/2010–12/2014 and were gatheredRelative from the Ngoring2014 sub-dataset Lake 97.70, for 34.90Tibetan Plateau 610 lakes [22]. 4267 The latest status 58 of each09/2010–12/2015 of 1171 lakes withAbsolute an area greaterLongyangxia than 1 km 100.73,2 in 36.01the Tibetan 359 Plateau is 2569 given in this 5 dataset,12/2015–06/2017 including name,Absolute location, Bamco 90.58, 31.27 180 4560 8 06/2013–12/2014 Relative morphology,Dawa Co and area. 84.96, 31.24This dataset 118 was obtained 4623 by interpreting 6 11 06/2013–12/2014Landsat-8 OperationalRelative Land Imager1 Altitudes (OLI) areimages from the acquired Shuttle Radar in Topography2014 and Mission136 Ch (SRTM)inese DigitalGaofen-1 Elevation images Model with (DEM); wide-field-of-view2 Tracks column cameras.shows number of tracks for each lake.

2.2.2.2.2.2. Cryosat-2Cryosat-2 SARinSARin DataData SIRALSIRAL carriedcarried byby Cryosat-2Cryosat-2 isis thethe world’sworld’s ﬁrstfirst space-bornespace-borne altimeteraltimeter featuringfeaturing delayeddelayed DopplerDoppler technologytechnology [16]. [16]. The The Cryosat-2 Cryosat-2 SARi SARinn Baseline Baseline C version C version of Level-1b of Level-1b and andLevel-2 Level-2 data dataproducts products were wereused usedin the inpresent the present study study(ftp://science-pds.cryosat.e (ftp://science-pds.cryosat.esa.intsa.int). Each 20-Hz). Each waveform 20-Hz waveform given by the given Level- by the Level-1b data consists of 1024 bins (Figure2) and includes some improvements compared to the Baseline B data product [23]. All observations were selected by the nadir positions given by the Level-1b data. Figure2a,b shows typical Cryosat-2 SARin waveforms from water and ice surfaces, respectively. Water 2018, 10, x FOR PEER REVIEW 4 of 16

1b data consists of 1024 bins (Figure 2) and includes some improvements compared to the Baseline B Waterdata 2018product, 10, 1584 [23]. All observations were selected by the nadir positions given by the Level-1b 4data. of 17 Figure 2a,b shows typical Cryosat-2 SARin waveforms from water and ice surfaces, respectively.

Figure 2. ((a)) WaterWater surfacesurface waveformwaveform andand ((bb)) iceice surfacesurface waveform.waveform. Green and red pointspoints mark the nominal tracking and retrackingretracking points,points, respectively.respectively.

In addition, the Level-2 data provides the retracked heights based on the Wingham–Wallis ﬁtting In addition, the Level-2 data provides the retracked heights based on the Wingham–Wallis algorithm (ESAL2) [13]. Because of interferometric processing, the observation position (Level-2 fitting algorithm (ESAL2) [13]. Because of interferometric processing, the observation position (Level- position)2 position) in in the the Level-2 Level-2 data data has has been been relocated, relocated, andand thethe Level-2Level-2 datadata containscontains manymany off-nadir observations with high noise [[10].10]. A track over Ngoring Lake and the correspondingcorresponding waveforms is observations with high noise [10]. A track over Ngoring Lake and the corresponding waveforms◦ is shown in Figure3 3 and and Appendix AppendixA A.. There There are are clearly clearly many many off-nadir off-nadir observations observations from from 34.82 34.82° to shown◦ in Figure 3 and Appendix A. There are clearly many off-nadir observations from 34.82° to 34.8534.85°,, such as spots 6 and 9,9, andand theirtheir waveformswaveforms areare veryvery complex.complex. These waveformswaveforms with high noise may affect the stabilitystability ofof thethe statisticalstatistical methodmethod inin SectionSection 3.33.3..

Figure 3. (a) Track overover NgoringNgoring LakeLake onon 55 JuneJune 2011 (black(black and red solid points represent nadir and corresponding Level-2 positions of all observations, respectively), and (b) corresponding waveforms. 2.2.3. In Situ Data 2.2.3. In Situ Data The in situ data for three lakes (Qinghai Lake, Ngoring Lake, and Longyangxia Reservoir) The in situ data for three lakes (Qinghai Lake, Ngoring Lake, and Longyangxia Reservoir) is is from (i) the Hydrology and Water Resources Survey Bureau in Qinghai Province, (ii) China’s from (i) the Hydrology and Water Resources Survey Bureau in Qinghai Province, (ii) China’s hydrological yearbooks, and (iii) the Yellow River Commission of the Ministry of Water Resources hydrological yearbooks, and (iii) the Yellow River Commission of the Ministry of Water Resources (http://www.yellowriver.gov.cn/), respectively. The data is referenced to China’s 1985 National (http://www.yellowriver.gov.cn/), respectively. The data is referenced to China’s 1985 National Height Datum. Height Datum. The in situ data for Nam Co, Zhari Namco, Bamco, and Dawa Co is from the Institute of Tibetan The in situ data for Nam Co, Zhari Namco, Bamco, and Dawa Co is from the Institute of Tibetan Plateau Research, Chinese Academy of Sciences. Table1 lists the measurement time and mode of the Plateau Research, Chinese Academy of Sciences. Table 1 lists the measurement time and mode of the in situ data of the seven lakes. All in situ water levels are daily measurements, and the relative in situ in situ data of the seven lakes. All in situ water levels are daily measurements, and the relative in situ data is measured by manually placed water-level gauges. data is measured by manually placed water-level gauges.

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3. MethodsWater 2018, 10, x FOR PEER REVIEW 5 of 16

3.1. Estimation3. Methods of Lake Level The water level H with respect to the 2008 Earth Gravitational Model (EGM2008) [24] geoid was 3.1. Estimation of Lake Level obtained using The water level H with respect to the 2008 Earth Gravitational Model (EGM2008) [24] geoid was H = Halt − Hrange − Ngeoid (1) obtained using where Halt is the satellite altitude and Ngeoid is the geoid height with respect to the ellipsoid. Hrange is = − − (1) the range and is computed as where Halt is the satellite altitude and Ngeoid isc the geoid height with respect to the ellipsoid. Hrange is the Hrange = WD + Rretrack + Hgeo (2) range and is computed as 2 where c is the speed of light, WD is the window delay in seconds relative to the central range bin, Rretrack = + + (2) is the retracking correction (Figure2), and Hgeo2 is the geophysical corrections, including ionosphere, dry troposphere,where c is the wet speed troposphere, of light, WD solid is the earth window tide, delay pole in tide, seconds and relative ocean loading to the central tide. Bothrange WDbin, and Hgeo areRretrack included is the inretracking the Level-1b correction data product.(Figure 2), and Hgeo is the geophysical corrections, including Inionosphere, addition, dry to validatetroposphere, the wet water troposphere, levels derived solid earth from tide, the pole different tide, and algorithms, ocean loading several tide. extra processingBoth WD steps and were Hgeo are required. included (1) in The the trackLevel-1b mean data level product. was calculated using the static error mixture In addition, to validate the water levels derived from the different algorithms, several extra model described in Reference [18], and the track standard deviation of the lake level was obtained processing steps were required. (1) The track mean level was calculated using the static error mixture after removing the outliers using one standard deviation from the track mean level. (2) After removing model described in Reference [18], and the track standard deviation of the lake level was obtained the abnormalafter removing track meanthe outliers levels using by visual one standard inspection, deviation the Cryosat-2 from the time track series mean was level. obtained (2) After using Gaussianremoving filtering the abnormal on theremaining track mean levels track by mean visual levels inspection, [25,26 the]. Cryosat-2 (3) For each time Cryosat-2series was obtained time series, a constantusing offsetGaussian with filtering respect on tothe the remaining in situ track data mean was computedlevels [25,26]. and (3) removed,For each Cryosat-2 so has thetime same series, mean valuea as constant the in situoffset data with [19 respect]. to the in situ data was computed and removed, so has the same mean value as the in situ data [19]. 3.2. Improved Multiple Waveform Persistent Peak Retracker (ImpMWaPP) 3.2. Improved Multiple Waveform Persistent Peak Retracker (ImpMWaPP) In this section the new ImpMWaPP retracker is presented, which is a modified algorithm based on the MWaPPIn this retrackersection thegiven new ImpMWaPP by Reference retracker [17]. Foris presented, this retracker, which is a a reliable modified reference algorithm water based level per trackon the was MWaPP obtained retracker and used given to by identify Reference the [17]. part For of thethis waveformretracker, a (subwaveform)reliable reference reflectedwater level by the per track was obtained and used to identify the part of the waveform (subwaveform) reflected by the water directly beneath the satellite. The steps of the new retracker are illustrated in Figure4. water directly beneath the satellite. The steps of the new retracker are illustrated in Figure 4.

FigureFigure 4. Flowchart4. Flowchart describing describing thethe ImprovedImproved Multiple Waveform Waveform Persistent Persistent Peak Peak Retracker Retracker (ImpMWaPP).(ImpMWaPP). Steps Steps with with yellow yellow background background are are different different fromfrom the MWaPP MWaPP retracker. retracker.

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First, for each Cryosat-2 SARin 20-Hz waveform, the heights corresponding to all bins were determined according to Equation (3). Thus, a bin height Hbin(i, j) was estimated for each i = 1, ... , p and j = 1, ... , k, where p is the number of the waveforms in the track and k is the number of the bins in each waveform. c H (i, j) = H (i) − WD + w (k − j) − H (i) − N (i), (3) bin alt 2 b o geo geoid where Halt is the satellite altitude, c is the speed of light, WD is the window delay, wb is the bin width (0.2342 m for Cryosat-2 SARin mode waveforms), ko is the nominal range bin number (512 for Cryosat-2 SARin), Hgeo is the sum of the applied geophysical corrections, and Ngeoid is the geoid correction. Second, the reference water level Hbase for each track was determined. The details are described in Section 3.3. Generally, because the height from a water surface is more stable than that from land, Hbase is determined by a robust statistical method. Compared to MWaPP, ImpMWaPP uses Hbase instead of the average waveform to identify the leading edge of water reﬂection, an approach that is better at avoiding noise effects. Third, for each Cryosat-2 SARin 20-Hz waveform, the peak where power exceeded 20% of the maximum power and the corresponding bin height was closest to Hbase was found. Thus, a subwaveform comprising the bin of the peak and its two previous and two subsequent bins was extracted. Finally, the off-center-of-gravity (OCOG) amplitude A [27] for each extracted subwaveform was calculated by v u Npp u ∑ P4(t) A = t L=1 L (4) Npp 2 ∑L=1 PL(t) where Npp is the number of bins in the subwaveform and PL(t) is the power for each L = 1, ... , Npp. The point at which the subwaveform exceeds 80% of A was marked as the retracking point.

3.3. Determination of Reference Water Level Hbase First, the observations used to calculate Hbase were selected. To reduce the effects of noise, the off-nadir observations were removed by a distance threshold D. For each observation in the track, if the distance between its nadir and corresponding Level-2 position was larger than D, then it was removed. Each track has a unique D, which can be determined by the following steps.

(1) Calculate the distance between the nadir and corresponding Level-2 position for each observation in the present track, and construct the cumulative distribution function (CDF) of these distances at 100 m intervals. After this, we can obtain the distance corresponding to the minimum second-order difference quotient of this CDF, which is considered as D1. (2) Repeat step 1 for all observations of all tracks over the lake and obtain another distance as D2. (3) The minimum of D1 and D2 is ﬁnally accepted as D for the present track. The reason for this is that the present track may be dominated by the off-nadir observations, thus it is difﬁcult to get a reasonable D if only this track is processed. Therefore, all observations of all tracks over the lake are considered.

For example, Figure5 shows the calculation of D for the track over Ngoring Lake in Figure3a. Because the D1 (200 m; Figure5a) from the present track is less than D2 (400 m; Figure5b) from all tracks, D of this track is determined as the minimum of D1 and D2 (200 m). From Figures3a and5c, it is seen that the off-nadir observations have been removed effectively. Water 2018, 10, 1584 7 of 17 Water 2018, 10, x FOR PEER REVIEW 7 of 16 Water 2018, 10, x FOR PEER REVIEW 7 of 16

Figure 5. ((aa)) Cumulative Cumulative distributi distributionon function function (CDF) (CDF) and and D1D1 fromfrom the the track track in Figure in Figure 3a.3 (a.b) (CDFb) CDF and andD2Figure fromD2 5.from all(a) tracksCumulative all tracks over over Ngoring distributi Ngoring Lake.on function Lake. Magenta Magenta (CDF) lines and linesrepresent D1 represent from the the locations thetrack locations in Figureof D1 of and3a.D1 ( bandD2) CDF. (D2c) .(Theandc) TheselectedD2 from selected results. all tracks results. over Ngoring Lake. Magenta lines represent the locations of D1 and D2. (c) The selected results. Second, Tbase corresponding to each threshold Thres was calculatedcalculated for eacheach track.track. Thres is a percentageSecond, of Tbase the maximum corresponding power to of each the waveform threshold andThres takes was a calculatedvalue of 0.20 for to each 0.80 track.in steps Thres of of 0.10. 0.10.is a Eachpercentage Tbase representsof the maximum aa stablestable power heightheight of andand the can canwaveform bebe expressedexpressed and takes asas a value of 0.20 to 0.80 in steps of 0.10.

Each Tbase represents a stable height and can be expressed as o f f =+ (5) H = Tbase + σ e , (5) q =+obs q, , (5) where is the peak height of the q-th selected observation, is a scaling parameter, is o f f where H is the peak height of the q-th selected observation, σ is a scaling parameter, σ e is the thewhere observation q is the noise peak term, height and of the qfollows-th selected a mixture observation, of Gaussian obs isand a scaling Cauchy parameter, distributionsobs q [18]. is observation noise term, and e follows a mixture of Gaussian and Cauchy distributions [18]. Tbase Tbasethe observation and were noise obtained term, and qby maximum-likelihood follows a mixture esti of mationGaussian for andall selected Cauchy observations. distributions Here, [18]. andtheTbase peakσ obsandwere height obtained were represents obtained by maximum-likelihood a binby maximum-likelihoodheight corresponding estimation esti tomation the for first all for selected peak all selected that observations. exceeds observations. Thres Here, of Here, the peakmaximumthe peak height height power. represents represents Figure a bin 6 shows heighta bin theheight corresponding peak corresponding heights to at the different ﬁrst to the peak Thres first that forpeak exceeds two that tracks.Thres exceeds of the Thres maximum of the power.maximum Figure power.6 shows Figure the 6 peak shows heights the peak at different heights atThres differentfor two Thres tracks. for two tracks.

Figure 6. Cont.

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Figure 6. ((aa)) All All peak peak heights heights for for the the track track over over Ngoring Ngoring Lake Lake on on 5 June 5 June 2011. 2011. (b) (Allb) All peak peak heights heights for forthe thetrack track over over Dawa Dawa Co Co on on 30 30 December December 2014. 2014. Bl Blueue and and red red symbols symbols represent represent the selected and removed observations,observations, respectively.respectively.

Third, Hbase was calculated. For each track, when the standard deviation of all Tbase is less than 0.10 m, the average of all Tbase isis takentaken asas Hbase.. In this case, all peak heights at different Thres were very closeclose (see(see FigureFigure6 6a),a), accounting accounting forfor 89%89% ofof all all processed processed tracks. tracks. However,However, whenwhen thethe standardstandard deviation of all Tbase is moremore thanthan 0.100.10 m,m, thethe peakpeak heightsheights at differentdifferent Thres may vary greatly (see Figure6 6b).b). BecauseBecause thethe noisenoise isis greatlygreatly reducedreduced byby thethe previousprevious steps,steps, thethe ﬁrstfirst stablestable signalsignal reﬂectedreflected by the selectedselected observations can represent the waterwater surface. In this case, the maximum of all Tbase waswas accepted asas HbaseHbase,, accountingaccounting forfor 11%11% ofof allall processedprocessed tracks.tracks. It should be noted that the optimal ThresThres reliesrelies onon thethe shapeshape ofof thethe along-trackalong-track waveformswaveforms ratherrather thanthan thethe lakelake area.area.

4. Results and Discussion 4.1. Comparison of Retracking Methods 4.1. Comparison of Retracking Methods 4.1.1. Multi-Peak Waveform Processing 4.1.1. Multi-Peak Waveform Processing The performance of ImpMWaPP was evaluated by comparing it to those of five existing The performance of ImpMWaPP was evaluated by comparing it to those of five existing algorithms: (i) The Narrow Primary Peak Threshold retracker (NPPTR) with a 50% threshold level algorithms: (i) The Narrow Primary Peak Threshold retracker (NPPTR) with a 50% threshold level (NPPTR[0.5]) [28], (ii) NPPTR with an 80% threshold level (NPPTR[0.8]) [28], (iii) the Narrow Primary (NPPTR[0.5]) [28], (ii) NPPTR with an 80% threshold level (NPPTR[0.8]) [28], (iii) the Narrow Primary Peak OCOG Retracker (NPPOR) [28], (iv) the MWaPP retracker [17], and (v) ESAL2 [29]. Peak OCOG Retracker (NPPOR) [28], (iv) the MWaPP retracker [17], and (v) ESAL2 [29]. Figure7 shows the retracked results for four waveforms corresponding to spots 1, 5, 8, and Figure 7 shows the retracked results for four waveforms corresponding to spots 1, 5, 8, and 9 in 9 in Figure3a. It is clear that ImpMWaPP handles all the waveforms successfully, showing it to Figure 3a. It is clear that ImpMWaPP handles all the waveforms successfully, showing it to be highly be highly adept at processing multi-peak waveforms. However, MWaPP, NPPTR[0.5], NPPTR[0.8], adept at processing multi-peak waveforms. However, MWaPP, NPPTR[0.5], NPPTR[0.8], and and NPPOR fail to determine the leading edge of the water reflection for the waveform of spot 9 NPPOR fail to determine the leading edge of the water reflection for the waveform of spot 9 (Figure (Figure7d), and ESAL2 fails to properly process the echo of spot 5 (Figure7b). Figure7d also shows 7d), and ESAL2 fails to properly process the echo of spot 5 (Figure 7b). Figure 7d also shows that that MWaPP is seriously influenced by a larger noise in front of the water signal in the waveform MWaPP is seriously influenced by a larger noise in front of the water signal in the waveform compared to ImpMWaPP. compared to ImpMWaPP. 4.1.2. Comparison of Along-Track Water Levels To illustrate the advantages of ImpMWaPP, the results for a track over Bamco are shown in Figure8. From Figure8a,b, this track includes many near-shore and off-nadir observations with complex echoes. From Figure8c, the water levels derived by ImpMWaPP are stable, whereas those derived by the other retrackers vary largely, especially in the near-shore and off-nadir spots. The standard deviations of the water levels derived by the different retrackers are 1.17 m (ESAL2), 0.62 m (MWaPP), 1.24 m (NPPTR[0.5]), 1.25 m (NPPTR[0.8]), 1.24 m (NPPOR), and 0.23 m (ImpMWaPP).

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Figure 7. Retracked results for four waveforms corresponding to spots (a) 1, (b) 5, (c) 8, and (d) 9 in Figure 3a. Magenta numbers represent the values of the in situ water levels.

4.1.2. Comparison of Along-Track Water Levels To illustrate the advantages of ImpMWaPP, the results for a track over Bamco are shown in Figure Figure8.Figure From 7. 7.Retracked FigureRetracked 8a,b, results results this for for fourtrack four waveforms waveforms includes corresponding correspondingmany near-shore toto spotsspots and (a(a)) 1, 1,off-nadir ( b(b)) 5, 5, (c ()c 8,) 8, andobservations and (d ()d 9) in9 in with complexFigure Figureechoes. 3a.3a. Magenta MagentaFrom Figure numbers numbers 8c, represent represent the water the valuesvalueslevels of ofderived the the in in situ situ by water water ImpMWaPP levels. levels. are stable, whereas those derived byIt shouldthe other be notedretrackers that thevary absence largely, of someespecially results in inthe Figure near-shore8c is because and off-nadir of the removal spots. The 4.1.2. Comparison of Along-Track Water Levels standardof abnormal deviations water of levelsthe water greater levels than derived 4575 m, by which the different occurred retrackers mainly for are MWaPP, 1.17 m NPPTR[0.5], (ESAL2), 0.62 m (MWaPP),NPPTR[0.8],To illustrate 1.24 and m the NPPOR.(NPPTR[0.5]), advantages However, of1.25 ImpMWaPP, ImpMWaPP m (NPPTR[0.8]), can the handle results 1.24 more mfor (NPPOR), observationsa track over and effectively.Bamco 0.23 m are (ImpMWaPP). shown in Figure 8. From Figure 8a,b, this track includes many near-shore and off-nadir observations with complex echoes. From Figure 8c, the water levels derived by ImpMWaPP are stable, whereas those derived by the other retrackers vary largely, especially in the near-shore and off-nadir spots. The standard deviations of the water levels derived by the different retrackers are 1.17 m (ESAL2), 0.62 m (MWaPP), 1.24 m (NPPTR[0.5]), 1.25 m (NPPTR[0.8]), 1.24 m (NPPOR), and 0.23 m (ImpMWaPP).

Figure 8. Cont.

Water 2018, 10, 1584 10 of 17 Water 2018, 10, x FOR PEER REVIEW 10 of 16

FigureFigure 8. (a 8.) (aTrack) Track over over BamcoBamco on on 4 May 4 May 2014 (black2014 and(black red solidand points red solid mark thepoints nadir mark and corresponding the nadir and correspondingLevel-2 positions, Level-2 respectively), positions, ( brespectively),) corresponding (b waveforms,) corresponding and (c) retrackedwaveforms, water and levels. (c) retracked water 4.2.levels. Time Series

It shouldTable2 be gives noted the root-mean-squaredthat the absence of errors some (RMSEs) results for in theFigure seven 8c lakes is because between of the the Cryosat-2 removal of time series and the in situ data. The abnormal track mean levels that have been removed, and the abnormal water levels greater than 4575 m, which occurred mainly for MWaPP, NPPTR[0.5], statistical results of the track mean levels used for the Cryosat-2 time series, are shown in AppendixA. NPPTR[0.8], and NPPOR. However, ImpMWaPP can handle more observations effectively. It can be seen that ImpMWaPP provides excellent results for all the lakes and has the best results for four lakes (Qinghai Lake, Nam Co, Ngoring Lake, and Longyangxia). Compared to the other retrackers, 4.2. Time Series ImpMWaPP also has the lowest mean RMSE (0.175 m) for all the lakes. In addition, for Qinghai Lake, theTable RMSE 2 gives from the ImpMWaPP root-mean-squa is betterred than errors the RMSE (RMSEs) of 0.093 for m the derived seven from lakes the between Cryosat-2 the LR Cryosat-2 mode time dataseries given and by the Reference in situ data. [25]; and The for abnormal Nam Co, track the RMSE mean from levels this that retracker have isbeen also betterremoved, than and the the statisticalRMSE results of 0.18 mof giventhe track by Reference mean levels [30]. used for the Cryosat-2 time series, are shown in Appendix

A. It can Tablebe seen 2. Root-mean-squared that ImpMWaPP errors provides (RMSEs) excellen for the sevent results lakes betweenfor all the the Cryosat-2lakes and time has series the andbest results for four lakesthe in situ(Qinghai data. Lake, Nam Co, Ngoring Lake, and Longyangxia). Compared to the other retrackers, ImpMWaPP also has the lowest mean RMSE (0.175 m) for all the lakes. In addition, for Lake Name ESAL2 MWaPP NPPTR[0.5] NPPTR[0.8] NPPOR ImpMWaPP Qinghai Lake, the RMSE from ImpMWaPP is better than the RMSE of 0.093 m derived from the 0.113 m 0.092 m 0.096 m 0.121 m 0.114 m 0.085 m Qinghai Lake Cryosat-2 LR mode data given[48,48] by Reference [49,49] [25]; [48,48] and for Nam [48,48] Co, the RMSE [46,46] from [49,49]this retracker is also better than the RMSE0.094 of 0.18 m m given 0.094 m by Reference 0.240 m [30]. 0.159 m 0.213 m 0.093 m Nam Co [78,36] [78,36] [78,36] [78,36] [78,36] [79,36] 0.120 m 0.106 m 0.254 m 0.192 m 0.257 m 0.109 m TableZhari 2. Root-mean-squared Namco errors (RMSEs) for the seven lakes between the Cryosat-2 time series [58,50] [59,51] [57,49] [58,50] [57,49] [59,51] and the in situ data. 0.314 m 0.289 m 0.241 m 0.164 m 0.189 m 0.159 m Ngoring Lake Lake Name ESAL2[58,58] MWaPP [58,58] NPPTR[0.5] [58,58] NPPTR[0.8] [58,58] NPPOR [58,58] ImpMWaPP [58,58] 3.701 m 0.871 m 0.930 m 0.951 m 0.921 m 0.573 m Longyangxia 0.113 m 0.092 m 0.096 m 0.121 m 0.114 m 0.085 m Qinghai Lake [5,5] [5,5] [5,5] [5,5] [5,5] [5,5] [48,48] [49,49] [48,48] [48,48] [46,46] [49,49] 0.397 m 0.079 m 0.251 m 0.156 m 0.210 m 0.087 m Bamco 0.094 m 0.094 m 0.240 m 0.159 m 0.213 m 0.093 m Nam Co [7,5] [7,5] [7,6] [8,6] [8,6] [8,6] [78,36] [78,36] [78,36] [78,36] [78,36] [79,36] 0.112 m 0.146 m 0.128 m 0.105 m 0.143 m 0.122 m Dawa Co 0.120[5,5] m 0.106 [6,5]m 0.254 [5,4]m 0.192 [6,5] m 0.257 [6,5] m 0.109 [6,5] m Zhari Namco The two values in each[58,50] pair of square[59,51] bracket are the [57,49] counts for the lake [58,50] levels retrieved [57,49] from the Cryosat-2 [59,51] time series data and the in0.314 situ water m levels, 0.289 respectively. m 0.241 Because m of the discontinuity 0.164 m of the 0.189 in situ m data in 0.159 some m lakes, Ngoringthese two countsLake are not always consistent. [58,58] [58,58] [58,58] [58,58] [58,58] [58,58] 3.701 m 0.871 m 0.930 m 0.951 m 0.921 m 0.573 m ExceptLongyangxia for Longyangxia and Ngoring Lake, the results derived by MWaPP for the other lakes are [5,5] [5,5] [5,5] [5,5] [5,5] [5,5] similar compared to those from ImpMWaPP. Generally, ImpMWaPP and MWaPP give better results 0.397 m 0.079 m 0.251 m 0.156 m 0.210 m 0.087 m Bamco [7,5] [7,5] [7,6] [8,6] [8,6] [8,6] 0.112 m 0.146 m 0.128 m 0.105 m 0.143 m 0.122 m Dawa Co [5,5] [6,5] [5,4] [6,5] [6,5] [6,5] The two values in each pair of square bracket are the counts for the lake levels retrieved from the Cryosat-2 time series data and the in situ water levels, respectively. Because of the discontinuity of the in situ data in some lakes, these two counts are not always consistent.

Water 2018, 10, 1584 11 of 17

than do the other retrackers. Additionally, compared to the other retrackers, the number of valid epochs in the Cryosat-2 time series obtained by ImpMWaPP is slightly higher, which is also beneﬁcial for monitoring the water level of lakes with sparse observations. The Cryosat-2 time series for four lakes and the in situ data is shown in Figure9. For all four lakes, the time series derived by ImpMWaPP agree well with the in situ data. MWaPP and ESAL2 also show good results for Qinghai Lake, Nam Co, and Zhari Namco; however, for Ngoring Lake, because many observations with weak water signals are not handled effectively, the deviations between the Cryosat-2 time series derived by these two retrackers and the in situ data are large in some epochs. In addition, because of the inability to effectively handle the waveforms with high land noise in front of the water signal, the results from NPPTR[0.5], NPPTR[0.8], and NPPOR for Zhari Namco are the worst. Figure 10 shows the spatial distribution of the deviations between the Cryosat-2 time series for Ngoring Lake and the in situ data. The results reveal that ImpMWaPP performs the best, with most of the deviations by this retracker being less than 0.30 m. However, in many ice-surface and narrow-water tracks, the results derived by MWaPP and ESAL2 all exceed 0.30 m. Compared to NPPTR[0.5] and NPPOR, NPPTR[0.8] gives signiﬁcantly better results, but still slightly worse than those from ImpMWaPP.

Water 20184.3., 10 Time, x FOR Series PEER of Icing REVIEW andNo-Ice Periods 11 of 16

ExceptA for retracker’s Longyangxia ability isand affected Ngoring by the Lake, freezing the of results lake water derived [7,31]. by Because MWaPP most for lakes the covered other lakes by the Cryosat-2 SARin data ice over during winter, the abilities of the different retrackers during are similar compared to those from ImpMWaPP. Generally, ImpMWaPP and MWaPP give better icing and no-ice periods were explored. The two periods are deﬁned by regular dates in Section 2.1. resultsTables than 3do and the4 give other the RMSEsretrackers. for four Additionally, lakes between compared the Cryosat-2 to timethe seriesother inretrackers, the icing and the no-ice number of valid epochsperiods, in respectively, the Cryosat-2 and the time in situseries data. obtained For MWaPP by andImpMWaPP ESAL2, most is slightly of the results higher, in the which no-ice is also beneficialperiod for are monitoring better than the those water in the level icing period,of lakes and with the resultssparse in observations. both periods derived by ImpMWaPP Theare Cryosat-2 all excellent. time Meanwhile, series for except four for lakes Ngoring and Lake, the NPPTR[0.5],in situ data NPPTR[0.8], is shown andin Figure NPPOR 9. achieve For all four lakes, thesigniﬁcantly time series worse derived results in by the ImpMWaPP no-ice period thanagree do well the other with retrackers. the in situ Therefore, data. MWaPP we suggest and that ESAL2 ImpMWaPP should be used to handle the Cryosat-2 SARin data for lakes that ice over in winter. also show good results for Qinghai Lake, Nam Co, and Zhari Namco; however, for Ngoring Lake, because4.4. many Along-Track observations Standard Deviations with weak water signals are not handled effectively, the deviations between the Cryosat-2 time series derived by these two retrackers and the in situ data are large in To further compare the different retrackers, Table5 lists the mean and median of all track standard some epochs.deviations In foraddition, each retracker because over ofeach the inability lake. It is seento effectively that ImpMWaPP handle has the the waveforms lowest results with over high all land noise inlakes, front showing of the that water the water signal, levels the derived results by from ImpMWaPP NPPTR[0.5], are the most NPPTR[0.8], stable. In general, and NPPOR NPPTR[0.5], for Zhari NamcoNPPTR[0.8], are the worst. and NPPOR give similar results, but are worse than the other retrackers.

Figure 9. Cont.

Water 2018, 10, x FOR PEER REVIEW 11 of 16

Except for Longyangxia and Ngoring Lake, the results derived by MWaPP for the other lakes are similar compared to those from ImpMWaPP. Generally, ImpMWaPP and MWaPP give better results than do the other retrackers. Additionally, compared to the other retrackers, the number of valid epochs in the Cryosat-2 time series obtained by ImpMWaPP is slightly higher, which is also beneficial for monitoring the water level of lakes with sparse observations. The Cryosat-2 time series for four lakes and the in situ data is shown in Figure 9. For all four lakes, the time series derived by ImpMWaPP agree well with the in situ data. MWaPP and ESAL2 also show good results for Qinghai Lake, Nam Co, and Zhari Namco; however, for Ngoring Lake, because many observations with weak water signals are not handled effectively, the deviations between the Cryosat-2 time series derived by these two retrackers and the in situ data are large in some epochs. In addition, because of the inability to effectively handle the waveforms with high land noise in front of the water signal, the results from NPPTR[0.5], NPPTR[0.8], and NPPOR for Zhari Namco are the worst.

Water 2018, 10, 1584 12 of 17

Water 2018, 10, x FOR PEER REVIEW 12 of 16

FigureFigure 9. Cryosat-2 9. Cryosat-2 time time series series for for four four lakes lakes obtainedobtained from from different different retrackers retrackers and compared and compared with the with in situ data: (a) Qinghai Lake; (b) Nam Co; (c) Zhari Namco; (d) Ngoring Lake. the in situ data: (a) Qinghai Lake; (b) Nam Co; (c) Zhari Namco; (d) Ngoring Lake.

Figure 10 shows the spatial distribution of the deviations between the Cryosat-2 time series for Ngoring Lake and the in situ data. The results reveal that ImpMWaPP performs the best, with most of the deviations by this retracker being less than 0.30 m. However, in many ice-surface and narrow- water tracks, the results derived by MWaPP and ESAL2 all exceed 0.30 m. Compared to NPPTR[0.5] and NPPOR, NPPTR[0.8] gives significantly better results, but still slightly worse than those from ImpMWaPP.

Figure 10. Spatial distribution of deviations between Cryosat-2 time series for Ngoring derived from different retrackers and in situ data: (a) ESAL2; (b) MWaPP; (c) NPPTR[0.5]; (d) NPPTR[0.8]; (e) NPPOR; (f) ImpMWaPP.

4.3. Time Series of Icing and No-Ice Periods A retracker’s ability is affected by the freezing of lake water [7,31]. Because most lakes covered by the Cryosat-2 SARin data ice over during winter, the abilities of the different retrackers during icing and no-ice periods were explored. The two periods are defined by regular dates in Section 2.1. Tables 3 and 4 give the RMSEs for four lakes between the Cryosat-2 time series in the icing and no- ice periods, respectively, and the in situ data. For MWaPP and ESAL2, most of the results in the no- ice period are better than those in the icing period, and the results in both periods derived by ImpMWaPP are all excellent. Meanwhile, except for Ngoring Lake, NPPTR[0.5], NPPTR[0.8], and NPPOR achieve significantly worse results in the no-ice period than do the other retrackers. Therefore, we suggest that ImpMWaPP should be used to handle the Cryosat-2 SARin data for lakes that ice over in winter.

Water 2018, 10, x FOR PEER REVIEW 12 of 16

Figure 9. Cryosat-2 time series for four lakes obtained from different retrackers and compared with the in situ data: (a) Qinghai Lake; (b) Nam Co; (c) Zhari Namco; (d) Ngoring Lake.

Waterand NPPOR,2018, 10, 1584 NPPTR[0.8] gives significantly better results, but still slightly worse than those13 from of 17 ImpMWaPP.

Figure 10. Spatial distribution of deviations between Cryosat-2 time series for Ngoring derived from Figure 10. Spatial distribution of deviations between Cryosat-2 time series for Ngoring derived from different retrackers and in situ data: (a) ESAL2; (b) MWaPP; (c) NPPTR[0.5]; (d) NPPTR[0.8]; (e) NPPOR; different retrackers and in situ data: (a) ESAL2; (b) MWaPP; (c) NPPTR[0.5]; (d) NPPTR[0.8]; (e) (f) ImpMWaPP. NPPOR; (f) ImpMWaPP. Table 3. RMSEs between Cryosat-2 time series and in situ data: icing period. 4.3. Time Series of Icing and No-Ice Periods Lake Name ESAL2 MWaPP NPPTR[0.5] NPPTR[0.8] NPPOR ImpMWaPP A retracker’s ability is affected by the freezing of lake water [7,31]. Because most lakes covered 0.138 m 0.073 m 0.078 m 0.075 m 0.094 m 0.079 m Qinghai Lake by the Cryosat-2 SARin[23] data ice over [23] during winter, [23] the abilities [23] of the different [22] retrackers [23] during icing and no-ice periods were explored. The two periods are defined by regular dates in Section 2.1. 0.133 m 0.136 m 0.276 m 0.170 m 0.217 m 0.131 m Nam Co Tables 3 and 4 give the [2]RMSEs for four [2] lakes between [2] the Cryosat-2 [2] time series [2] in the icing [2] and no- ice periods, respectively, and the in situ data. For MWaPP and ESAL2, most of the results in the no- 0.126 m 0.120 m 0.264 m 0.228 m 0.239 m 0.111 m Zhari Namco ice period are better than[14] those in [14] the icing period, [14] and the [14] results in both [14] periods derived [14] by ImpMWaPP are all excellent. Meanwhile, except for Ngoring Lake, NPPTR[0.5], NPPTR[0.8], and 0.402 m 0.370 m 0.182 m 0.168 m 0.168 m 0.156 m Ngoring Lake NPPOR achieve significantly[23] worse [23] results in [23] the no-ice period [23] than do [23] the other retrackers. [23] Therefore, we suggest that ImpMWaPP should be used to handle the Cryosat-2 SARin data for lakes Value in square brackets is the number of in situ water levels for that calculation. that ice over in winter. Table 4. RMSEs between Cryosat-2 time series and in situ data: no-ice period.

Lake Name ESAL2 MWaPP NPPTR[0.5] NPPTR[0.8] NPPOR ImpMWaPP 0.083 m 0.107 m 0.111 m 0.152 m 0.130 m 0.089 m Qinghai Lake [25] [26] [25] [25] [24] [26] 0.091 m 0.091 m 0.237 m 0.159 m 0.213 m 0.091 m Nam Co [34] [34] [34] [34] [34] [34] 0.118 m 0.096 m 0.251 m 0.175 m 0.263 m 0.104 m Zhari Namco [36] [37] [35] [36] [35] [37] 0.239 m 0.219 m 0.273 m 0.161 m 0.201 m 0.161 m Ngoring Lake [35] [35] [35] [35] [35] [35] Value in square brackets is the number of in situ water levels for that calculation. Water 2018, 10, 1584 14 of 17

Table 5. Means and medians of track standard deviations derived by the different retrackers over the seven lakes.

Lake Name ESAL2 MWaPP NPPTR[0.5] NPPTR[0.8] NPPOR ImpMWaPP 0.170 m 0.145 m 0.413 m 0.394 m 0.396 m 0.098 m Qinghai Lake [0.116 m] [0.092 m] [0.401 m] [0.366 m] [0.379 m] [0.084 m] 0.251 m 0.246 m 0.490 m 0.479 m 0.472 m 0.208 m Nam Co [0.137 m] [0.156 m] [0.457 m] [0.422 m] [0.446 m] [0.102 m] 0.213 m 0.241 m 0.674 m 0.636 m 0.618 m 0.108 m Zhari Namco [0.158 m] [0.157 m] [0.502 m] [0.463 m] [0.475 m] [0.105 m] 0.256 m 0.239 m 0.267 m 0.254 m 0.254 m 0.129 m Ngoring Lake [0.122 m] [0.105 m] [0.216 m] [0.229 m] [0.217 m] [0.097 m] 0.668 m 0.295 m 0.532 m 0.464 m 0.519 m 0.126 m Longyangxia [0.442 m] [0.098 m] [0.622 m] [0.350 m] [0.608 m] [0.089 m] 0.389 m 0.461 m 0.626 m 0.594 m 0.581 m 0.178 m Bamco [0.190 m] [0.182 m] [0.697 m] [0.651 m] [0.662 m] [0.127 m] 0.320 m 0.224 m 0.478 m 0.461 m 0.523 m 0.128 m Dawa Co [0.239 m] [0.163 m] [0.480 m] [0.487 m] [0.492 m] [0.110 m] Medians are written in square brackets.

5. Conclusions In this study, a modiﬁed retracker (ImpMWaPP) for Cryosat-2 SARin waveforms was proposed that can effectively process multi-peak waveforms over inland water. ImpMWaPP is not a pure single-waveform retracker, and it’s core function is to obtain a reference water level using a robust statistical method and to identify the water-surface signal of the waveform based on this reference water level. We tested the retracking performance of six algorithms for Cryosat-2 SARin waveforms in comparison to the in situ data of seven Tibetan Plateau lakes with different characteristics. The six algorithms used in this study were ImpMWaPP, ESAL2, MWaPP, NPPTR[0.5], NPPTR[0.8], and NPPOR. The results reveal that ImpMWaPP outperforms the other algorithms in handling multi-peak waveforms from the Cryosat-2 SARin mode. As a result, the Cryosat-2 time series obtained by ImpMWaPP has good precision and slightly more epochs, which is positive for monitoring lakes with sparse data. Additionally, ImpMWaPP has good performance for lakes during icing and no-ice periods, and is more suitable for lakes that ice over in winter. However, the disadvantage of this algorithm is that the observation position must be relocated, and the relocated position can be obtained from Cryosat-2 SARin Level-2 data. In addition, the other algorithms also have their own advantages. First, for less affected observations, high-precision lake levels can be obtained directly from the Cryosat-2 Level-2 Baseline C data products with no additional computation. Second, MWaPP can give quite accurate water levels using observations from the no-ice period. Finally, it remains necessary to rely on the superior performance of space-borne altimeters (e.g., spatial and temporal resolution) to fundamentally overcome the difﬁculty in monitoring the water levels of small lakes. Such altimeters include the three-dimensional imaging microwave altimeter carried by the Tiangong-2 space laboratory and the altimeter carried by the Surface Water Ocean Topography (SWOT) satellite [32,33]. In future, they can help to better monitor lake levels.

Author Contributions: H.X. processed Cryosat-2 data, built the model, and wrote the manuscript. J.L. contributed with discussions and manuscript writing. L.Z. processed Cryosat-2 data. Funding: This research was supported by the National Key Research and Development Program of China (2016YFB0501501), and the National Natural Science Foundation of China (41871256). Acknowledgments: We thank the ESA for providing the Cryosat-2 SARin data, and the Hydrology and Water Resources Survey Bureau in Qinghai Province, the Yellow River Commission of the Ministry of Water Resources, and the Institute of Tibetan Plateau Research, Chinese Academy of Sciences for providing the in situ data. Water 2018, 10, x FOR PEER REVIEW 14 of 16 statistical method and to identify the water-surface signal of the waveform based on this reference water level. We tested the retracking performance of six algorithms for Cryosat-2 SARin waveforms in comparison to the in situ data of seven Tibetan Plateau lakes with different characteristics. The six algorithms used in this study were ImpMWaPP, ESAL2, MWaPP, NPPTR[0.5], NPPTR[0.8], and NPPOR. The results reveal that ImpMWaPP outperforms the other algorithms in handling multi-peak waveforms from the Cryosat-2 SARin mode. As a result, the Cryosat-2 time series obtained by ImpMWaPP has good precision and slightly more epochs, which is positive for monitoring lakes with sparse data. Additionally, ImpMWaPP has good performance for lakes during icing and no-ice periods, and is more suitable for lakes that ice over in winter. However, the disadvantage of this algorithm is that the observation position must be relocated, and the relocated position can be obtained from Cryosat-2 SARin Level-2 data. In addition, the other algorithms also have their own advantages. First, for less affected observations, high-precision lake levels can be obtained directly from the Cryosat-2 Level-2 Baseline C data products with no additional computation. Second, MWaPP can give quite accurate water levels using observations from the no-ice period. Finally, it remains necessary to rely on the superior performance of space-borne altimeters (e.g., spatial and temporal resolution) to fundamentally overcome the difficulty in monitoring the water levels of small lakes. Such altimeters include the three-dimensional imaging microwave altimeter carried by the Tiangong-2 space laboratory and the altimeter carried by the Surface Water Ocean Topography (SWOT) satellite [32,33]. In future, they can help to better monitor lake levels.

Author Contributions: H.X. processed Cryosat-2 data, built the model, and wrote the manuscript. J.L. contributed with discussions and manuscript writing. L.Z. processed Cryosat-2 data.

Funding: This research was supported by the National Key Research and Development Program of China (2016YFB0501501), and the National Natural Science Foundation of China (41871256).

Acknowledgments: We thank the ESA for providing the Cryosat-2 SARin data, and the Hydrology and Water Resources Survey Bureau in Qinghai Province, the Yellow River Commission of the Ministry of Water Resources, and the InstituteWater 2018 of, 10Tibetan, 1584 Plateau Research, Chinese Academy of Sciences for providing15 the of 17 in situ data. Moreover, the authors are grateful to the anonymous reviewers for their constructive suggestions to improve this manuscript.Moreover, the authors are grateful to the anonymous reviewers for their constructive suggestions to improve this manuscript. Conflicts of Interest:Conﬂicts of The Interest: authorsThe authors declare declare no noconflicts conﬂicts of interest.interest.

Appendix AAppendix A

Figure A1.Figure Waveforms A1. Waveforms at atspots spots 1–12 corresponding corresponding to Figure to 3Figurea. 3a. Table A1. Abnormal track mean levels. Lake Name ESAL2 MWaPP NPPTR[0.5] NPPTR[0.8] NPPOR ImpMWaPP 3194.727 m Qinghai Lake 3196.316 m - 3197.114 m 3196.246 m 3196.446 m - 3196.617 m Nam Co 5069.691 m 5087.456 m 5087.989 m 5087.395 m 5087.663 m - 4617.650 m 4617.647 m Zhari Namco 4949.409 m - 4982.618 m - 4982.154 m 4980.273 m Ngoring Lake ------Longyangxia ------Bamco 4646.898 m 4706.849 m 4569.472 m - - - Dawa Co 4626.380 m - 4629.480 m - - - Water 2018, 10, 1584 16 of 17

Table A2. Mean and standard deviation of track mean levels used for the Cryosat-2 time series derived by each retracker over each lake.

Lake Name ESAL2 MWaPP NPPTR[0.5] NPPTR[0.8] NPPOR ImpMWaPP 3195.919 m 3195.552 m 3195.903 m 3195.695 m 3195.657 m 3195.539 m Qinghai Lake [0.24 m] [0.22 m] [0.22 m] [0.22 m] [0.23 m] [0.22 m] 4726.067 m 4725.733 m 4726.235 m 4725.955 m 4725.968 m 4725.715 m NamCo [0.30 m] [0.33 m] [0.46 m] [0.36 m] [0.43 m] [0.32 m] 4615.237 m 4614.912 m 4615.467 m 4615.149 m 4615.185 m 4614.892 m Zhari Namco [0.17 m] [0.18 m] [0.49 m] [0.35 m] [0.49 m] [0.17 m] 4272.831 m 4272.532 m 4273.130 m 4272.834 m 4272.625 m 4272.837 m Ngoring Lake [0.53 m] [0.51 m] [0.42 m] [0.36 m] [0.38 m] [0.32 m] 2576.587 m 2573.791 m 2574.390 m 2574.180 m 2574.122 m 2573.583 m Longyangxia [1.76 m] [4.12 m] [4.43 m] [4.38 m] [4.44 m] [3.99 m] 4567.314 m 4567.085 m 4567.479 m 4567.296 m 4567.190 m 4567.094 m Bamco [0.36 m] [0.11 m] [0.24 m] [0.17 m] [0.21 m] [0.15 m] 4627.790 4627.543 m 4627.723 m 4627.640 m 4627.582 m 4627.429 m Dawa Co [0.21 m] [0.41 m] [0.22 m] [0.290 m] [0.31 m] [0.28 m] Standard deviations are written in square brackets.

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