Coastal Waveform Retracking for Jason-2 Altimeter Data Based on Along-Track Echograms Around the Tsushima Islands in Japan

remote sensing

Article Coastal Waveform Retracking for Jason-2 Altimeter Data Based on Along-Track Echograms around the Tsushima Islands in Japan

Xifeng Wang 1,2,* and Kaoru Ichikawa 3

1 School of Marine Science and Environment Engineering, Dalian Ocean University, Dalian 116023, China 2 Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, Fukuoka 8168580, Japan 3 Research Institute for Applied Mechanics, Kyushu University, Fukuoka 8168580, Japan; [email protected] * Correspondence: [email protected]; Tel.: +86-0411-84763561

Received: 27 March 2017; Accepted: 21 July 2017; Published: 24 July 2017

Abstract: Although the Brown mathematical model is the standard model for waveform retracking over open oceans, due to heterogeneous surface reflections within altimeter footprints, coastal waveforms usually deviate from open ocean waveform shapes and thus cannot be directly interpreted by the Brown model. Generally, the two primary sources of heterogeneous surface reflections are land surfaces and bright targets such as calm surface water. The former reduces echo power, while the latter often produces particularly strong echoes. In previous studies, sub-waveform retrackers, which use waveform samples collected from around leading edges in order to avoid trailing edge noise, have been recommended for coastal waveform retracking. In the present study, the peaky-type noise caused by fixed-point bright targets is explicitly detected and masked using the parabolic signature in the sequential along-track waveforms (or, azimuth-range echograms). Moreover, the power deficit of waveform trailing edges caused by weak land reflections is compensated for by estimating the ratio of sea surface area within each annular footprint in order to produce pseudo-homogeneous reflected waveforms suitable for the Brown model. Using this method, altimeter waveforms measured over the Tsushima Islands in Japan by the Ocean Surface Topography Mission (OSTM)/Jason-2 satellite are retracked. Our results show that both the correlation coefficient and root mean square difference between the derived sea surface height anomalies and tide gauge records retain similar values at the open ocean (0.9 and 20 cm) level, even in areas approaching 3 km from coastlines, which is considerably improved from the 10 km correlation coefficient limit of the conventional MLE4 retracker and the 7 km sub-waveform ALES retracker limit. These values, however, depend on the topography of the study areas because the approach distance limit increases (decreases) in areas with complicated (straight) coastlines.

Keywords: radar altimeter; coastal waveform retracking; echogram; tide gauge

1. Introduction Radar altimeters transmit modulated chirp pulses towards the sea at nadir, and then record the echoes reflected from the sea surface in an altimeter footprint [1]. The time series of the power of the echoes received by altimeters is commonly referred to as a “waveform”. Waveforms are sampled with a specific time resolution, which is 3.125 ns for the Ocean Surface Topography Mission (OSTM)/Jason-2 satellite, and each cell within a waveform is called a “gate”. Geophysical parameters are retrieved by a process called “waveform retracking”, which consists of fitting a theoretical model to the measured waveforms. Over the open ocean, the so-called Brown mathematical model [2,3] is the standard model used for this process.

Remote Sens. 2017, 9, 762; doi:10.3390/rs9070762 www.mdpi.com/journal/remotesensing Remote Sens. 2017, 9, 762 2 of 13 Remote Sens. 2017, 9, 762 2 of 13

AsAs shown shown in in Figure Figure 11,, aa typicaltypical Brown Brown waveform waveform which which is controlledis controlled by by the the altimeter altimeter antenna antenna gain gainpattern, pattern, has has a well-defined a well-defined shape shape consisting consisting of three of three parts, parts, thermal thermal noise, noise, a fast-rising a fast-rising leading leading edge, edge,and aand decaying a decaying trailing trailing edge. The edge. fundamental The fundam parametersental parameters obtained through obtained waveform through retracking waveform are retrackingthe satellite are height the satellite above the height sea surface above (range),the sea su therface significant (range), wave the heightsignificant (SWH), wave and height the backscatter (SWH), andcoefficient the backscatter (sigma0, σcoefficient0), which is(sigma0, related to sea), which surface is wind. related Moreover, to sea surface an antenna wind. mispointing Moreover, angle an antenna(ξ) parameter, mispointing which isangle linked (ξ) to parameter, the slope of which the trailing is linked edge, to has the a strongslope of impact the trailing on sigma0 edge, estimation has a strongbecause impact it reduces on sigma0 the apparent estimation backscatter because coefficient it reduces for the the apparent radar antenna backscatter (i.e., anycoefficient deviation for of the the radarradar antenna aiming (i.e., point any from deviation nadir). of the radar aiming point from nadir).

FigureFigure 1.1. CharacteristicsCharacteristics of of a atypical typical Brown Brown waveform waveform over over the the open open ocean. ocean.

InIn contrast contrast to to the the open open ocean, ocean, waveforms waveforms collect collecteded when when the the altimeters altimeters operate operate in in proximity proximity to to coastlinescoastlines are are often often corrupted corrupted due due to to the the heteroge heterogeneousneous surfaces. surfaces. Figure Figure 2a2a shows shows the the along-track along-track waveformswaveforms (or (or azimuth-range azimuth-range radar-gram; radar-gram; hereafter hereafter referred referred to to as as an an echogram) echogram) measured measured by by the the Jason-2Jason-2 altimeter altimeter over over the the southern southern Tsushima Tsushima Islands Islands in in Ja Japanpan (pass (pass 36, 36, cycle cycle 22). 22). Each Each column column of of the the echogramechogram represents represents an an individual individual waveform waveform at at a agiven given latitude. latitude. Waveforms Waveforms in in the the echogram echogram have have beenbeen realigned realigned based based on on the the tracker tracker movements movements and and rescaled rescaled by the by theautomatic automatic gain gain control control (AGC) (AGC) of theof antenna the antenna [4]. [Waveforms4]. Waveforms measured measured over over land land areas areas are are masked masked in inthe the echogram echogram because because they they cannotcannot be be properly properly realigne realigned.d. As As can can be be seen seen in in Figure Figure 2a,2a, land land reflections reflections are are generally generally significantly significantly weakerweaker than than reflections reflections from from the the sea sea surface surface [5]. [5]. Th Thisis is is why why the the trailing trailing edge edge of of a awaveform waveform will will decaydecay rapidly rapidly when when an an altimeter altimeter approaches approaches land, land, thereby thereby resulting resulting in in a apower power deficit deficit area area in in the the echogramechogram [6]. [6]. Moreover, Moreover, several brightbright parabolicparabolic traces traces can can be be seen seen at at the the waveform waveform trailing trailing edge edge area, area,which which indicate indicate that that bright bright targets targets exist exist within within the altimeterthe altimeter footprint. footprint. FigureFigure 2b2b shows shows an an example example of of a a corrupted corrupted waveform waveform measured measured at at the the location location indicated indicated by by thethe red red point point in in Figure Figure 2a2a (34.20°N). (34.20 ◦N). The The black black line line represents represents the the actual actual waveform waveform and and the the red red line line representsrepresents the the fitted fitted waveform waveform using using the the four-parameter four-parameter Brown Brown theoretical theoretical model. model. An An unweighted unweighted least-squaresleast-squares estimator estimator whosewhose convergence convergence is obtainedis obtained through through the Nelder-Meadthe Nelder-Mead algorithm algorithm is adopted is adoptedin the present in the study.present It isstudy. obvious It is that obvious the estimated that the Brownestimated waveform Brown deviateswaveform seriously deviates from seriously an ideal fromundistorted an ideal waveformundistorted without waveform redundant without peaks redundant around peaks gates around 60–80. gates 60–80. InIn the the last last couple couple of years,years, aa significantsignificant amount amount of of research research has has been been aimed aimed at overcoming at overcoming the effectthe effectof waveform of waveform corruption corruption on retracking on retracking over coastal over zones.coastal Aszones. a result, As severala result, dedicated several dedicated parametric parametricand non-parametric and non-parametric models have models been have proposed, been aproposed, detailed reviewa detailed of whichreview can of bewhich found can in be [7 ]. foundIn some in previous[7]. In some studies, previous sub-waveform studies, retrackerssub-waveform [8–11 ],retrackers which use [8–11], only thewhich waveform use only samples the waveformaround the samples leading edgearound rather the than leading the full waveforms,edge rather have than been the recommended full waveforms, for coastal have waveform been recommendedretracking. These for coastal retrackers waveform successfully retracking. suppress Thes trailinge retrackers edge noise, successfully and hence suppress extend thetrailing capabilities edge noise,of waveform and hence retracking extend inthe coastal capabilities zones closerof wavefo to therm shorelines. retracking However, in coastal loss zones of the closer trailing to edgethe shorelines.during the However, retracking loss process of the will trailing also reduceedge du thering precision the retracking of estimated process geophysical will also reduce parameters, the precisionespecially of for estimated sigma0 estimationgeophysical [10 parameters,]. Moreover, es althoughpecially sub-waveformfor sigma0 estimation retrackers [10]. depend Moreover, on the althoughdetection sub-waveform accuracy of the retrackers leading edge depend in a waveform,on the detection practically accuracy speaking, of the it is leading difficult edge to separate in a waveform,the leading practically edge from individualspeaking, multi-peakit is difficult waveforms to separate when the numerous leading speckles edge from are present. individual multi-peak waveforms when numerous speckles are present.

Remote Sens. 2017, 9, 762 3 of 13 Remote Sens. 2017, 9, 762 3 of 13

(a) (b)

Figure 2. (a) Rescaled and realigned along-track waveforms (echogram) measured by the Jason-2 Figure 2. (a) Rescaled and realigned along-track waveforms (echogram) measured by the Jason-2 altimeter over the southern Tsushima Islands (pass 36, cycle 22). The shaded area (black patch) altimeter over the southern Tsushima Islands (pass 36, cycle 22). The shaded area (black patch) corresponds to land. Each column of the echogram represents an individual waveform at a given correspondslatitude toand land. the rescaled Each column power is of indicated the echogram by the color represents scale; (b an) Example individual of corrupted waveform waveform at a given latitudemeasured and the at rescaledthe location power indicated is indicated by the red by poin thet colorin Figure scale; 2a ((34.20°N).b) Example The ofblack corrupted line represents waveform ◦ measuredthe actual at the waveform location and indicated red line by represents the red point the fitted in Figure waveform2a (34.20 using N).the Thefour blackparameter line Brown represents the actualtheoretical waveform model. and red line represents the fitted waveform using the four parameter Brown theoretical model. The previous concept regarding individual waveform noise detection was based on the Theon-board previous processing concept strategy regarding of individualradar altimeters. waveform However, noise more detection reliable was detection based on is thepossible on-board processingthrough strategy post-processing of radar using altimeters. along-track However, waveformsmore because reliable waveform detection noise at is a given possible location through post-processingcan be expected using to along-track be geographically waveforms related because to such waveform noise in adjacent noise at locations. a given location Thus, trailing can be edge expected noise can be explicitly determined based on its spatial relationship in the echogram. Sub-waveform to be geographically related to such noise in adjacent locations. Thus, trailing edge noise can be explicitly retrackers limit the analysis of waveform samples around the leading edge to avoid trailing edge determined based on its spatial relationship in the echogram. Sub-waveform retrackers limit the analysis of noise. This is equivalent to limiting the altimeter footprint size near the nadir points where waveformhomogeneous samples aroundsea surface the conditions leading edge could to avoidbe expect trailinged, even edge though noise. the This number is equivalent of samples to limitingwithin the altimeterthe footprintfootprint sizeis decreased. near the nadirIn contrast, points in where the pr homogeneousesent study, significant sea surface noise conditions in the couldtrailing be edge expected, even thoughcaused by the bright number targets of samplesis remove withind or modified the footprint by using is decreased.echograms. InThis contrast, approach in will the also present assist study, significantin obtaining noise in homogeneous the trailing edge sea surface caused conditions, by bright targets which isis removednecessary orin modifiedorder to adopt by using the echograms.Brown This approachmodel, by will keeping also assist the number in obtaining of samples homogeneous within the sea footprints surface conditions, constant. A which similar is necessaryapproach, in in order to adoptwhich the bright Brown peaks model, were by removed keeping by the comparing number ofthem samples with waveforms within the in footprints the adjacent constant. open water, A similar approach,was examined in which brightin a recent peaks study were [12]. removed In the present by comparing study, however, them with bright waveforms targets are in more the adjacentexplicitly open detected and removed by using spatial restriction conditions in the along-track waveforms. water, was examined in a recent study [12]. In the present study, however, bright targets are more explicitly The remainder of this paper is organized as follows. The dataset used in the present study is detected and removed by using spatial restriction conditions in the along-track waveforms. presented in Section 2. Here, we selected Japan’s Tsushima Islands as our test site because it is an Thearea remainderwhere waveform of this corruption, paper is such organized as that asshown follows. in Figure The 2, dataset is often usedobserved. in the The present detection study of is presentednoise incaused Section by bright2. Here, targets we selectedthrough their Japan’s parabolic Tsushima signatures Islands within as ouran echogram test site is because introduced it is an area wherein Section waveform 3.1. In Section corruption, 3.2, compensating such as that for shown the waveform in Figure trailing2, is oftenedge power observed. deficit The due detection to weak of noiseland caused reflection by bright is considered. targets through The derived their parabolic along-track signatures sea surface within height an echogramanomalies (SSHAs) is introduced are in Sectionvalidated 3.1. In Sectionby tide gauge3.2, compensating measurements for and the compared waveform with trailing sensor edge geophysical power deficit data record due to (SGDR) weak land reflectionand adaptive is considered. leading-edge The derived sub-waveform along-track (ALES) sea produc surfacets in heightSection 4. anomalies Finally, a (SSHAs)brief discussion are validated and by tidesummary, gauge measurements focusing specifically and on compared the geographical with sensor dependency geophysical of the results, data record is presented (SGDR) in Section and adaptive 5. leading-edge sub-waveform (ALES) products in Section4. Finally, a brief discussion and summary, 2. Dataset focusing specifically on the geographical dependency of the results, is presented in Section5. The 20 Hz ALES coastal altimetry product of Jason-2 around the Tsushima Islands (pass 36, as 2. Datasetshown in Figure 3) are used in this study. This is an experimental product from the ALES processor that is included in SGDR-type files alongside the standard products and corrections. The specific Thedescription 20 Hz ALES can be coastal found altimetry at http://www.coastalt.eu product of Jason-2/community. around the The Tsushima dataset covers Islands the (pass period 36, asfrom shown in FigureJuly3 2008) are to used April in 2015. this The study. coastal This features is an experimentalof the Tsushima product Islands fromalong thethe ALESJason-2 processor ground track that is includedare characterized in SGDR-type by files semi-closed alongside bays the standardwithin the products altimeter andfootprints. corrections. Because The semi-closed specific description bays can beoften found appear at http://www.coastalt.eu/community as bright targets in radar echograms,. The waveforms dataset covers measured the period in the fromcomplicated July 2008 to April 2015. The coastal features of the Tsushima Islands along the Jason-2 ground track are characterized by semi-closed bays within the altimeter footprints. Because semi-closed bays often appear as bright targets in radar echograms, waveforms measured in the complicated coastlines of the study area are Remote Sens. 2017 9 Remote Sens. 2017, , 762, 9, 762 4 of 13 4 of 13

coastlines of the study area are seriously corrupted. For comparison purposes, another track (pass 164) seriouslycrossing corrupted. the relatively For comparisonsmooth coastlines purposes, of southern another Taiwan track is also (pass processed, 164) crossing as described the relatively in Section smooth 5 coastlines(Figure of 13). southern Taiwan is also processed, as described in Section5 (Figure 13). TheThe Global Global Self-Consistent, Self-Consistent, Hierarchical, Hierarchical, High-R High-Resolutionesolution Geography Geography database database (GSHHS) (GSHHS) [13] is [ 13] is usedused at full at resolutionfull resolution to determine to determine the coastlinethe coastline and and estimate estimate the oceanthe ocean area area located located within within altimeter annularaltimeter footprints. annular footprints. HourlyHourly tide tide gauge gauge data data obtained obtained fromfrom the Japan Japan Oceanographic Oceanographic Data Data Center Center (JODC) (JODC) are used are to used to validatevalidate the the quality quality of of derived derived along-track along-track sea su surfacerface heights heights (SSHs). (SSHs). A te Amporal temporal interpolation interpolation was was performed before validation to match the JODC data with the altimeter measurements. The shortest performed before validation to match the JODC data with the altimeter measurements. The shortest distance distance between tide gauge and Jason-2 ground track is about 6 km. Since tide gauge stations are betweenlocated tide within gauge port and waters, Jason-2 the ground tidal amplitudes track is about registered 6 km. are Since not tide the gaugesame as stations those for are the located waters within portoutside waters, the the harbors. tidal amplitudes Such discrepancies registered result are not in the considerable same as those height for differences, the waters outsidealthough the their harbors. Suchspatial discrepancies scale would result be inlarge. considerable height differences, although their spatial scale would be large.

(a) (b)

Figure 3. (a) Ground track (blue line) and footprint (blue circles draw for every 1 s, radius is 10 km) Figure 3. (a) Ground track (blue line) and footprint (blue circles draw for every 1 s, radius is 10 km) of of the Jason-2 altimeter over the Tsushima Islands (pass 36). The shortest distance between the tide the Jason-2 altimeter over the Tsushima Islands (pass 36). The shortest distance between the tide gauge gauge (red point) and altimeter ground track is about 6 km; (b) Enlarged local map for the southern (redsection point) andof the altimeter pass. The ground vertices track in Figure is about 2a indica 6 km;te ( bthat) Enlarged the reflection local points mapfor are the located southern 3 km sectionand of the pass.5 km apart The vertices from the innadir Figure track2a at indicate 34.23°N thatand 34.21° the reflectionN, respectively. points These are located locations, 3 km which and include 5 km apart ◦ ◦ fromsemi-closed the nadir trackbays, atare 34.23 markedN by and circles. 34.21 N, respectively. These locations, which include semi-closed bays, are marked by circles. 3. Waveform Retracking Strategy 3. Waveform Retracking Strategy 3.1. Detection of the Noise Caused by Bright Targets 3.1. DetectionGenerally, of the the Noise backscatter Caused by coeffi Brightcient Targets sigma0 for radar altimeters is inversely proportional to the sea surface roughness. In particular, sigma0 will sharply increase when centimeter-scale Generally, the backscatter coefficient sigma0 for radar altimeters is inversely proportional to the wavelets are absent from the sea surface. Over the open ocean, occurrences of unrealistically high sea surface roughness. In particular, sigma0 will sharply increase when centimeter-scale wavelets values of are usually referred to as “sigma-0 blooms”. These occur during low wind and calm are absentsea conditions, from the or sea can surface. be caused Over by theslick open sea surfaces, ocean, occurrences for example. of Previous unrealistically studies highhave valuesshown of σ0 are usuallythat the referredoccurrence to asof “sigma-0unrealistically blooms”. high values These of occur sigma0 during affect low almost wind 5% and of calmthe open sea conditions,ocean or canmeasurements be caused by [14]. slick sea surfaces, for example. Previous studies have shown that the occurrence of unrealisticallyUnlike the high open values ocean, of reflection sigma0 affectfrom bright almost targets 5% of is theone open of the ocean primary measurements reasons for coastal [14]. waveformUnlike the distortion. open ocean, Parabolic reflection signatures from caused bright by targets bright istargets one ofwere the found primary in almost reasons all of for the coastal waveform252 cycles distortion. of the Jason-2 Parabolic echogram signaturess around caused the Tsushima by bright Islands. targets The werebright found targets in are almost related all toof the 252 cyclesthe vertexes of the Jason-2of the parabolic echograms traces around in the the echo Tsushimagram, namely, Islands. the The latitude bright and targets distance are related to the to the vertexes of the parabolic traces in the echogram, namely, the latitude and distance to the midpoint of the leading edges [6]. Using a local map (Figure3b), the bright parabolic traces in Figure2a are found to be reflections from semi-closed bays (circles). Remote Sens. 2017, 9, 762 5 of 13

AsRemote shown Sens. 2017 in, 9 Figure, 762 2b, the redundant peaks in the waveform trailing edge significantly5 of 13 depart from the expected Brown waveform shape. However, since coastal waveforms are generally midpoint of the leading edges [6]. Using a local map (Figure 3b), the bright parabolic traces in complicated by the presence of several redundant peaks, it is difficult to identify such corruption in Figure 2a are found to be reflections from semi-closed bays (circles). an individualAs shown waveform. in Figure In 2b, this the section, redundant it is peaks shown in howthe waveform echoes that trailing are corruptededge significantly by bright depart targets are detectedfrom the and expected masked Brown utilizing waveform their parabolic shape. Ho signatureswever, since within coastal an echogram. waveforms are generally Acomplicated point target by ofthe height presenceδ above of several sea levelredundant located peak ats,distance it is difficultd from to identify the satellite such corruption nadir will in give an echoan witheindividual a round-trip waveform. delay In this time section,t defined it is shown by [5 how]: echoes that are corrupted by bright targets are detected and masked utilizing their parabolic signatures within an echogram. ct 1 Re + H A point target of height above= sea− δ level+ located atd2 distance+ H from the satellite nadir will (1) give an echo withe a round-trip delay2 time defined2 Re Hby [5]:

1 + where c is the speed of light, H is the satellite=−+ height and Re +is the Earth’s radius. (1) 2 2 As shown in Figure4a, y0 represents the location at the nearest approach to a high reﬂector where is the speed of light, is the satellite height and is the Earth’s radius. on the sea surface, while t0 and d0 represent the round-trip delay time and geographical distance, As shown in Figure 4a, represents the location at the nearest approach to a high reflector on respectively. yi is a point located at a distance ∆y from y0, while ti and di represent the corresponding the sea surface, while and represent the round-trip delay time and geographical distance, round-trip delay time and geographical distance, respectively. Considering the geometric relationship, respectively. is a point located at a distance ∆ from , while and represent the ∆y2 = d 2 − d 2, Equation (1) can be expressed as: correspondingi 0 round-trip delay time and geographical distance, respectively. Considering the geometric relationship, ∆ = − , EquationR +(1)H can be expressed as: c∆t = e ∆y2 (2) R +H ∆ = e ∆ (2) where ∆t represents the round-trip delay time difference, ∆t = ti − t0 and ∆y is the geographical where ∆t represents the round-trip delay time difference, ∆t = − and ∆ is the geographical distance between a measurement point yi and the nearest measurement point y0. distance between a measurement point and the nearest measurement point . The parabolicThe parabolic shape shape determined determined by Equation Equation (2) (2) in an in echogram an echogram is shown isshown in Figure in 4b. Figure The 4b. The horizontalhorizontal axis represents the the latitude latitude of of the the sa satellitetellite nadir. nadir. The The vertical vertical axis axis represents represents the the round-tripround-trip delay delay time time for for the the gate, gate, and and the the sampling sampling resolutionresolution is is 3.125 3.125 ns ns for for Jason-2. Jason-2. The The vertex vertex of of the parabolathe parabola is related is related to the to location the location of the of brightthe brig target,ht target, as seenas seen in Figurein Figure3b, 3b, and and the the parabola parabola shape is solelyshape determined is solely determined by the altimeter’s by the altimeter’s orbital andorbital sampling and sampling parameters. parameters.

(a) (b)

Figure 4. (a) Schematic showing the geometrical relationship between an altimeter and a strong Figure 4. (a) Schematic showing the geometrical relationship between an altimeter and a strong reflector (bright patch) on the sea surface. The altimeter is closest to the reflector at point with a reﬂector (bright patch) on the sea surface. The altimeter is closest to the reﬂector at point y0 with distance ; (b) Parabolic shape in the echogram. The value ∆ corresponds to the geographical a distance d0;(b) Parabolic shape in the echogram. The value ∆y corresponds to the geographical distance between point of the altimeter with (nearest approach), and ∆ represents the distance between point y of the altimeter with y (nearest approach), and ∆t represents the round-trip round-trip time difference,i ∆ = −. 0 time difference, ∆t = t1 − t0. In the present study, an iterative method is used to detect the parabolic trajectories in the Inechogram. the present It consists study, of an thre iterativee steps methodas follows is (Figure used to 5): detect the parabolic trajectories in the echogram. It consistsStep 1: of three Mark steps all pixels as follows in the (Figureechogram5): with the 2% largest echoes, but reset those that do not exceed 10 dB. The 2% threshold is determined empirically based on the size of the study area Step 1: Markand is all approximately pixels in the two echogram times the with standard the 2% deviation. largest echoes, The 10 butdB sigma0 reset those is used that as dothe not lower exceed 10limit dB. of The the 2% obvious threshold noise iscaused determined by bright empirically targets. based on the size of the study area and is approximately two times the standard deviation. The 10 dB sigma0 is used as the lower limit of the obvious noise caused by bright targets. Remote Sens. 2017, 9, 762 6 of 13 RemoteRemote Sens. Sens. 2017 2017, 9, ,9 762, 762 6 6of of 13 13

StepStepStep 2: 2: 2:Shift Shift Shift the ﬁxedthe the fixed fixed parabolic parabolic parabolic shape shape shape in thein in the echogramthe echogram echogram in bothin in both both the the the latitude latitude latitude and and and gate gate gate directions, directions, directions, and then count the number N of marked pixels along the given parabolic line. andand then then count count the the number number mark of of marked marked pixels pixels along along the the given given parabolic parabolic line. line. StepStepStep 3: 3: 3:Find Find Find the parabolic thethe parabolicparabolic shape shapeshape that that providesthat providesprovides the largest thethe largestlargest along-line along-linealong-line number number numberNmax . Mask. . MaskMask all pixels allall pixelspixels(with (with (with and withoutand and without without marks) marks) marks) along along along the the parabolicthe parabolic parabolic shape shape shape if Nif if max is larger is is larger larger than than than 10 10 or10 or exceedsor exceeds exceeds 50% 50%50%of theof of the numberthe number number of pixels of of pixels pixelsNp along along along the parabolicthe the parabolic parabolic line line withinline within within the studythe the study study area. area. area. Repeat Repeat Repeat from from from Step 1, StepStepuntil 1, 1, Nuntil untilmax is smaller isis smaller smaller than 10than than and 10 10 the and and ratio the the ratio Nratiomax /Np /becomes/ bbecomesecomes less less thanless than than 50%. 50%. 50%.

FigureFigure 5. 5. Purple Purple points points represent represent the the marked marked pixels pixels in in the the echogram echogram for for the the 2% 2% threshold threshold criterion. criterion. Figure 5. Purple points represent the marked pixels in the echogram for the 2% threshold criterion. Cyan CyanCyan points points represent represent the the parabolic parabolic shape shape described described by by Equation Equation (2). (2). The The red red point point is is the the vertex vertex of of points represent the parabolic shape described by Equation (2). The red point is the vertex of the parabola. thethe parabola. parabola. Figure6a depicts the masked echogram for pass 36 cycle 22 of the Jason-2 data over the southern FigureFigure 6a6a depictsdepicts thethe maskedmasked echogramechogram forfor papassss 3636 cyclecycle 2222 ofof thethe Jason-2Jason-2 datadata overover thethe Tsushima Islands (the same as Figure2a). Although some echoes located at the parabola tail, as shown southernsouthern Tsushima Tsushima Islands Islands (the (the sa sameme as as Figure Figure 2a). 2a). Although Although some some echoes echoes located located at at the the parabola parabola intail, Figuretail, as as 2shown a,shown are notin in Figure particularlyFigure 2a, 2a, are arestrong not not particularly particularly (weaker than strong strong 10 (weaker dB)(weaker due than tothan antenna 10 10 dB) dB) gaindue due powerto to antenna antenna decay, gain gain it is reasonablepowerpower decay,decay, to remove itit isis all reasonablereasonable of the echoes toto remove alongremove the allall same ofof thethe parabola echoesechoes that alongalong are contaminatedthethe samesame parabolaparabola by a strong thatthat are pointare source.contaminatedcontaminated Here, four by by parabolic a a strong strong point trajectories point source. source. are Here, Here, detected four four andparabolic parabolic masked. trajectories trajectories These echoes are are detected detected will be and removedand masked. masked. in the processTheseThese ofechoes echoes waveform will will be be retracking. removed removed in in the the process process of of waveform waveform retracking. retracking.

(a(a) ) (b(b) ) Figure 6. (a) Masked echogram for pass 36 cycle 22 of Jason-2 data south of the Tsushima Islands. All FigureFigure 6. 6.( a()a) Masked Masked echogram for for pass pass 36 36 cycle cycle 22 22of Jason-2 of Jason-2 data data south south of the of Tsushima the Tsushima Islands. Islands. All pixelpixel traces traces along along the the parabolic parabolic shape shape are are mask masked.ed. The The shaded shaded area area represents represents the the land; land; ( b(b) )Bright Bright All pixel traces along the parabolic shape are masked. The shaded area represents the land; (b) Bright targetstargets masked masked waveform waveform (dash (dash line) line) and and fitted fitted Br Brownown waveform waveform (solid (solid line) line) measured measured at at 34.2°N 34.2°N targets masked waveform (dash line) and fitted Brown waveform (solid line) measured at 34.2◦N (the(the same same waveform waveform as as shown shown in in Figure Figure 2b). 2b). (the same waveform as shown in Figure2b). TheThe masked masked waveform waveform and and the the fitted fitted Brown Brown waveform waveform measured measured at at 34.2°N 34.2°N are are shown shown in in Figure Figure The masked waveform and the fitted Brown waveform measured at 34.2◦N are shown in Figure6b. 6b.6b. Compared Compared to to Figure Figure 2b, 2b, the the masked masked waveform waveform shows shows strong strong agreement agreement with with the the fitted fitted Brown Brown Compared to Figure2b, the masked waveform shows strong agreement with the fitted Brown waveform.waveform. However, However, an an unrealistic unrealistic antenna antenna mispointing mispointing angle angle is is obtained, obtained, which which will will have have a a strong strong waveform. However, an unrealistic antenna mispointing angle is obtained, which will have a strong2 influenceinfluence on on the the sigma0 sigma0 estimation. estimation. Since Since the the estimated estimated mispointing mispointing angle angle is is smaller smaller than than − −0.20.2 deg deg2, , − 2 influenceaccordingaccording on to theto the the sigma0 data-editing data-editing estimation. criterion criterion Since in in thethe the estimatedstanda standardrd Jason-2 Jason-2 mispointing product, product, angle it it sh sh isouldould smaller be be flagged flagged than as 0.2as bad bad deg , accordingdata.data. In In fact, tofact, the the the data-editing negative negative mispointing mispointing criterion angle in angle the repres standardrepresentsents Jason-2a a steepening steepening product, of of the the it trailing shouldtrailing edge beedge flagged and and cannot cannot as bad data.bebe interpreted Ininterpreted fact, the as negativeas an an actual actual mispointing physical physical mispointing anglemispointing represents of of the thea instrument. steepeninginstrument. In ofIn this thethis trailingcase, case, the the edge trailing trailing and edge cannotedge besteepening interpretedsteepening is is ascaused caused an actual by by the the physical extra extra power power mispointing deficit deficit du du ofee to theto the the instrument. weak weak land land reflection. Inreflection. this case, Our Our the power power trailing deficit deficit edge steepeningcompensationcompensation is caused method method by is theis discussed discussed extra power in in the the deficitnext next section. section. due to the weak land reflection. Our power deficit compensation method is discussed in the next section.

Remote Sens. 2017, 9, 762 7 of 13

Remote Sens. 2017, 9, 762 7 of 13 3.2. Compensating for the Waveform Trailing Edge Power Deficit 3.2. Compensating for the Waveform Trailing Edge Power Deficit The power of an echo in a waveform is proportional to the area of the corresponding annular footprintThe and power is controlled of an echo by in the a waveform antenna beamis proporti pattern.onal to In the areas area where of the corresponding land is located annular within the footprint and is controlled by the antenna beam pattern. In areas where land is located within the altimeter footprint, since the land reflection is very weak, the power is approximately proportionate altimeter footprint, since the land reflection is very weak, the power is approximately proportionate to theto oceanthe ocean area area within within the the annular annular footprint. footprint. As shown shown in in Figure Figure 7a,7 a,the the power power of the of thewaveform waveform trailingtrailing edge edge decays decays rapidly rapidly with with decreasing decreasing sea sea surface surface area area in annularin annular footprints. footprints. Therefore, Therefore, a powera deficitpower area deficit can be area seen can in be the seen echogram, in the echogram, as shown as shown in Figure in Figure2a. 2a.

(a) (b)

Figure 7. (a) Annular altimeter footprint (drawn for every five gates) for the waveform measured at Figure 7. (a) Annular altimeter footprint (drawn for every five gates) for the waveform measured at 34.2°N (corresponding to the red point shown in Figure 2a); (b) Compensated waveform (dashed 34.2◦N (corresponding to the red point shown in Figure2a); ( b) Compensated waveform (dashed line) line) and the fitted Brown waveform (solid line) measured at the location shown in (a). and the fitted Brown waveform (solid line) measured at the location shown in (a). The “illumination hole” in the annular footprint that forms behind the trailing edge of the pulse isThe a circle “illumination with a radius hole” and in area the that annular expand footprint at the same that formsrates. The behind area of the each trailing annular edge footprint, of thepulse is a circle, remain with a unchanged radius and and area can that be expressed expand at as the[15]: same rates. The area of each annular footprint, Aann, remain unchanged and can be expressed as [15τ]: = (3) (1 + ⁄ ) πcτH where is the width of the pulse, isA annthe =speed of light, is the satellite height and is the (3) (1 + H/Re) Earth’s radius. The sea surface area within two consecutive annular footprints, , is actually a polygon where τ is the width of the pulse, c is the speed of light, H is the satellite height and Re is the Earth’s radius. and can be estimated using the method described by Thibaut et al. [13]. In the present study, the The sea surface area within two consecutive annular footprints, Aocean, is actually a polygon and power of each waveform trailing edge echo is roughly compensated for by dividing by the ratio, can be estimated using the method described by Thibaut et al. [13]. In the present study, the power of ⁄. each waveform trailing edge echo is roughly compensated for by dividing by the ratio, A /A . Figure 7a shows the annular footprints for the waveform measured at 34.20°N (red point in Figureocean 2a). ann ◦ TheFigure compensated7a shows waveform the annular and footprintsthe corresponding for the fitted waveform Brown waveform measured are at shown 34.20 inN Figure (red point7b. in FigureCompared2a). The compensatedwith Figure 6b, waveform a positive and mispoint the correspondinging angle is fittedobtained. Brown The waveform improved arepositive shown in Figuremispointing7b. Compared angle withis found Figure all along6b, a positivethe track, mispointing as shown in Figure angle is8d. obtained. Additionally, The sigma0 improved shows positive a mispointingdrop near angle the coast is found before all the along land compensation the track, as shown(Figure 8c), in Figure indicating8d. Additionally,stronger wind speeds, sigma0 but shows a dropthe near SWH the remains coast before almost the the land same compensation as that for (Figurethe open8c), ocean indicating (Figure stronger 8b). After wind the speeds, land but the SWHcompensation, remains almostit can be the seen same that as this that sigma0 for the drop open inconsistency ocean (Figure near8 theb). coast After has the been land modified. compensation, it can be seenIn order that to this quantitatively sigma0 drop assess inconsistency the effect of near land the compensation coast has been on waveform modified. retracking, the root mean squared difference (RMSD) for the range, SWH, sigma0 and mispointing angle before In order to quantitatively assess the effect of land compensation on waveform retracking, the root and after land compensation are calculated (Figure 9). The results show that the power deficits due meanto squared weak land difference reflection (RMSD) seriously for theinfluence range, SWH,the simultaneous sigma0 and estimati mispointingon of anglesigma0 before and andthe after landmispointing compensation angle. are Although calculated the (Figurewaveform9). trailing The results edge showis not directly that the used power to estimate deficits the due range to weak landand reflection SWH, seriouslythe latter influencevalues are thealso simultaneous slightly affected estimation by the compensation of sigma0 and for the the mispointing land deficit. angle. AlthoughTherefore, the waveformin addition trailingto of the edgeeffect is of not bright directly targets, used the topower estimate deficit the for range the waveform and SWH, trailing the latter valuesedge are should also slightly also be carefully affected considered by the compensation for waveform for retracking the land around deficit. coastal Therefore, areas. in addition to of the effect of bright targets, the power deficit for the waveform trailing edge should also be carefully considered for waveform retracking around coastal areas. Remote Sens. 2017, 9, 762 8 of 13 Remote Sens. 2017, 9, 762 8 of 13 Remote Sens. 2017, 9, 762 8 of 13

(a) (b) (a) (b)

(c) (d) (c) (d) Figure 8. SSH (a); SWH (b); sigma0 (c) and mispointing angle (d) before (green) and after (red) land Figure 8. SSH (a); SWH (b); sigma0 (c) and mispointing angle (d) before (green) and after (red) land compensationFigure 8. SSH south(a); SWH of the (b );Tsushima sigma0 ( cIsland) and smispointing for cycle 22 angleof the (Jason-2d) before altimeter. (green) and after (red) land compensation south of the Tsushima Islands for cycle 22 of the Jason-2 altimeter. compensation south of the Tsushima Islands for cycle 22 of the Jason-2 altimeter.

(a)(b) (a)(b)

(c)(d) (c)(d) Figure 9. RMSD between the results with and without land compensation south of the Tsushima IslandsFigure for 9. sevenRMSD years between of Jason-2 the altimeterresults with data; andfor range without (a); SWH land ( bcompensation); sigma0 (c) and south mispointing of the Tsushimaangle (d). Figure 9. RMSD between the results with and without land compensation south of the Tsushima Islands Islands for seven years of Jason-2 altimeter data; for range (a); SWH (b); sigma0 (c) and mispointing angle (d). for seven years of Jason-2 altimeter data; for range (a); SWH (b); sigma0 (c) and mispointing angle (d).

Remote Sens. 2017, 9, 762 9 of 13

4. Validation and Comparisons with Other Retrackers Remote Sens. 2017, 9, 762 9 of 13 In addition to the coastal zone, waveform corruption can also appear in open ocean areas where small-scale4. Validation sigma0-bloom and Comparisons events and rainwith cells Other occur. Retrackers A threshold of sigma0 is always adopted as the bloom detection criterion,In addition e.g., to the the 15 dBcoastal and 18zone, dB criteriawaveform for thecorruption Environmental can also Satellite appear (Envisat)in open Radarocean Altimeterareas 2 (RA2)where data discussedsmall-scale insigma0-bloom [14]. Considering events the and sigma0 rain differencescells occur. betweenA threshold various of sigma0 altimeters, is always this study uses aadopted relative largeas the threshold bloom detection of 18 dB criterion, for Jason-2 e.g., sigma0-bloom the 15 dB and event 18 dB detection. criteria for The the sigma0-bloom Environmental events are foundSatellite in 18 (Envisat) of 252 cycles Radar at theAltimeter study area.2 (RA2) More data specifically, discussed about in [14]. 7% ofConsidering the Jason-2 the measurements sigma0 are corrupteddifferences by thebetween sigma0-bloom various altimeters, events. This this rate stud isy consistentuses a relative with thelarge study threshold on Jason-1 of 18 data dB (6%)for as discussedJason-2 in [sigma0-bloom14]. Note that event the sigma0-bloomdetection. The sigma0-bloom effect on waveform events are retracking found in is18 out of 252 of thecycles scope at the of the presentstudy study, area. and More the 18 specifically, cycles of data about have 7% been of directly the Jason-2 removed measurements from waveform are corrupted retracking. by the sigma0-bloom events. This rate is consistent with the study on Jason-1 data (6%) as discussed in [14]. In order to validate the quality of the range estimation, the along-track SSHA is calculated as follows: Note that the sigma0-bloom effect on waveform retracking is out of the scope of the present study, and the 18 cycles of data have been directly removed from waveform retracking. SSHA = SSH – SSH (4) In order to validate the quality of the range estimation, the along-track SSHA is calculated as follows: where SSH is the mean SSH from cycle 1 toSSHA cycle = 252. SSH – In SSH the present study, SSH values larger(4) than 100 mwhere or smaller SSH isthan the −mean130 mSSH are from treated cycleas 1 to outliers cycle 252. (see In the the Jason-2 present productstudy, SSH handbook). values larger In than order to make100 a comparison m or smaller with than tide −130 gauge m are measurements,treated as outliers the (see tidal the componentsJason-2 product and handbook). the inverse In order barometric to componentsmake a arecomparison not removed with tide from gauge either measurements, the altimeter the measurements tidal components or and the tidethe inverse gauge barometric records. Twocomponents statistics, are thenot correlationremoved from coefficient either the alti (CC)meter and measurements the RMSD or between the tide gauge the time records. series of SSHA derived fromTwo altimeter statistics, and the tidecorrelation gauge measurements,coefficient (CC) and are usedthe RMSD to validate between the the data time quality series asof discussedSSHA in [16].derived Figure from 10a altimeter shows the and CC tide variation gauge measurements, along the track are over used the to Tsushimavalidate the Islands data quality for the as three discussed in [16]. Figure 10a shows the CC variation along the track over the Tsushima Islands for different methods. Figure 10b is the RMSD in centimeters. These results show that the conventional the three different methods. Figure 10b is the RMSD in centimeters. These results show that the ocean retracker in the SGDR product cannot provide a correct estimation within 10 km from the conventional ocean retracker in the SGDR product cannot provide a correct estimation within 10 coastline,km whichfrom the corresponds coastline, which approximately corresponds to theapprox radiusimately of the to Jason-2 the radius altimeter of the footprint. Jason-2 altimeter Meanwhile, since thefootprint. ALES Meanwhile, retracker only since uses the ALES the sub-waveform retracker only arounduses the thesub-waveform leading edge, around the noisethe leading that first appearsedge, in thethe waveformnoise that trailingfirst appears edge in has the no waveform influence trailing on the rangeedge has estimation. no influence As a on result, the therange ALES rangeestimation. estimation As can a result, be extended the ALES to range about estimation 7 km from can be the extended coastline. to about 7 km from the coastline. However,However, once once the echoesthe echoes used used in in the the ALES ALES estimation estimation windows become become corrupted, corrupted, they they will will seriouslyseriously influence influence the accuracythe accuracy of of range range estimation estimation duedue to reduced ALES ALES retracker retracker echo echo numbers, numbers, as shownas shown in Figure in Figure 11. 11. Note Note that that all all echoes echoes withinwithin thethe estimation windows windows whose whose widths widths are are determined by the SWH are used in the ALES, regardless of reliability. In the present study, determined by the SWH are used in the ALES, regardless of reliability. In the present study, however, however, the range is estimated based on the modified waveforms from which the effects of the two the range is estimated based on the modified waveforms from which the effects of the two primary primary sources of heterogeneous surface reflections, i.e., land and bright targets, are removed. sourcesFigure of heterogeneous 10a shows that the surface CC remains reflections, larger i.e.,than land 0.9 (99.9% and brightconfidence targets, level) are even removed. at locations Figure only 10a showsabout that the3 km CC away remains from larger the coast. than 0.9Overall, (99.9% both confidence the CC and level) RMSD even comparison at locations show only that about this 3 km awaymethod from the is coast.more effective Overall, for both examining the CC areas and RMSDvery close comparison to land than show the thatocean this retracker method and/or is more effectiveALES for retracker. examining areas very close to land than the ocean retracker and/or ALES retracker.

(a) (b)

Figure 10. Correlation coefficient (CC) (a) and RMSD (b) for the SSHA derived from tide gauge and Figure 10. Correlation coefﬁcient (CC) (a) and RMSD (b) for the SSHA derived from tide gauge and altimeter measurements for three different methods. Black is the result for the SGDR product, blue is altimeter measurements for three different methods. Black is the result for the SGDR product, blue is the result for the ALES product, and red is the result for this study. the result for the ALES product, and red is the result for this study.

Remote Sens. 2017, 9, 762 10 of 13 Remote Sens. 2017, 9, 762 10 of 13

FigureFigure 11. 11.Comparison Comparison of of SSHA SSHA time time series series derived derived from from ALES ALES retracker retracker (blue) (blue) and and this this study study(red) (red) at 34.21at ◦34.21°NN with with tide gaugetide gauge measurements measurements (green). (green).

5. Discussion and Summary 5. Discussion and Summary Generally speaking, geophysical parameters can be correctly estimated over open ocean areas Generally speaking, geophysical parameters can be correctly estimated over open ocean areas using the theoretical Brown model, which is based on the assumption of a homogeneous sea surface. using the theoretical Brown model, which is based on the assumption of a homogeneous sea surface. However, altimeter waveforms are often corrupted at coastal zones due to heterogeneous surface However, altimeter waveforms are often corrupted at coastal zones due to heterogeneous surface reflections within the altimeter footprint. In particular, bright targets such as calm water in reflectionssemi-closed within bays the and altimeter the vicinity footprint. of land In particular,have distin brightctly different targets scattering such as calm characteristics water in semi-closed at nadir. baysSub-waveform and the vicinity retrackers of land havesuch distinctlyas ALES differentuse only scatteringwaveform characteristics samples selected at nadir. from Sub-waveform around the retrackersleading suchedge as in ALES order use to onlyavoid waveform trailing edge samples noise. selected This method from around is equivalent the leading to reducing edge in orderthe to avoidaltimeter trailing footprint. edge noise.Because This homo methodgeneous is equivalentsea surface toconditions reducing ar thee more altimeter easily footprint. anticipated Because for homogeneoussmaller footprints, sea surface such conditionsretrackers can are moreextend easily their anticipatedwaveform retracking for smaller abilities footprints, closer such to the retrackers coast. canIn extend contrast, their this waveform study considered retracking a method abilities of closermodifying to the waveforms coast. In contrast,in order to this make study them considered suitable a methodfor use ofin modifyingthe Brown model. waveforms in order to make them suitable for use in the Brown model. ReflectionsReflections from from bright bright targets targets often often appear appear as as redundant redundant peakspeaks in coastal waveforms, waveforms, which which havehave sharp sharp power power variations variations similar similar to waveform to waveform leading leading edges (Figureedges 2(Figureb). When 2b). multiple When redundantmultiple peaksredundant appear inpeaks a waveform appear trailingin a waveform edge, it istrailing difficult edge, to identify it is difficult this noise to inidentify an individual this noise waveform. in an Onindividual the other hand,waveform. reflections On the from other a hand, fixed-point reflections target from trace a fixed-point a parabola target in the trace sequential a parabola along-track in the waveformssequential (or, along-track azimuth-range waveforms echogram). (or, Therefore,azimuth-range by utilizing echogram). the parabolic Therefore, signature by utilizing in the radarthe echogram,parabolic noise signature caused in the by radar bright echogram, targets can noise be caus explicitlyed by bright detected targets and can masked, be explicitly as discussed detected in Sectionand masked,3.1. When as compared discussed within Section an actual 3.1. waveform,When compared the masked with an waveform actual waveform, shows good the agreement masked waveform shows good agreement with the fitted Brown waveform (Figure 6b), even though the with the fitted Brown waveform (Figure6b), even though the unrealistic mispointing angle indicates unrealistic mispointing angle indicates an extra power deficit for waveform trailing edge due to an extra power deficit for waveform trailing edge due to weak land reflection. Thus, it is necessary weak land reflection. Thus, it is necessary to compensate for the power deficit by estimating the to compensate for the power deficit by estimating the ratio of the sea surface area and each annular ratio of the sea surface area and each annular footprint, as discussed in Section 3.2. footprint, as discussed in Section 3.2. In Section 4, waveforms measured south of the Tsushima Islands (pass 36) were retracked. BothIn Sectionsignificantly4, waveforms bright targets measured from south calm ofwater the Tsushimasurfaces in Islands semi-closed (pass bays 36) were and retracked.power deficits Both significantlydue to land bright were targetsmodified from in the calm echograms water surfaces in order in semi-closedto obtain pseudo-homogeneous bays and power deficits sea surface due to landconditions. were modified Our validations in the echograms of altimeter-derived in order to obtain SSHA pseudo-homogeneous with tide gauge records sea surfaceshowed conditions. that the Ourresults validations of the present of altimeter-derived method agree SSHAbetter withthan both tide gaugethe conventional records showed ocean retracker that the resultsused in of the the presentSGDR method product agree and betterthe ALES than retracker. both the The conventional CC and RMSD ocean remain retracker similar used to in the the open SGDR ocean product values and the(0.9 ALES and retracker. 20 cm), even The CCin the and coastal RMSD sea remain about similar 3 km away to the from open land. ocean The values above (0.9 results and 20reveal cm), that even in thethe coastalpresent method sea about can 3 retrieve km away SSHA from as close land. as The 3 km above from resultsthe southeast reveal coast that of the the present Tsushima method Islands. can retrieveHowever, SSHA as closethe approach as 3 km distance from the strongly southeast depend coasts ofon the the Tsushima area geography. Islands. Figure 12 shows the resultsHowever, around the the approach northwest distance coast stronglyof the Tsushima depends Islands. on the area As can geography. be seen Figurein Figure 12 shows12a, the the resultsnorthwest around coastline the northwest is very coast complex of the due Tsushima to the Islands.numerous As cansmall be bays. seen inIn Figureaddition, 12a, a the small northwest cape coastline(Karasaki) is very around complex 34.36°N due toseparates the numerous Asou smallBay fr bays.om the In addition,open ocean. a small As capeshown (Karasaki) in Figure around 12b 34.36echogram◦N separates example, Asou the Bay section from theof pass open 36 ocean. in Asou As Bay shown (purple in Figure line in12 bFigure echogram 12a) includes example, an the sectionexcessive of pass number 36 in Asou of bright Bay targets. (purple Since line in the Figure pres ent12a) method includes identifies an excessive and removes number isolated of bright bright targets. Sincetargets the present in the trailing method edge, identifies it cannot and removesbe applied isolated to that bright area targetsof Asou in Bay. the trailingFor the edge, north it of cannot Cape be

Remote Sens. 2017, 9, 762 11 of 13

Remote Sens. 2017, 9, 762 11 of 13 applied to that area of Asou Bay. For the north of Cape Karasaki (from 34.36 to 34.6◦N), however, the methodKarasaki described (from 34.36 in Section to 34.6°N),3 is successfully however, the applied. method Atdescribed each latitude, in Section the 3 root is successfully mean squared applied. (RMS) variationAt each for latitude, the SSHA the isroot calculated mean squared with three (RMS) different variation retrackers for the (Figure SSHA 12 c).is calculated When approaching with three from ◦ thedifferent open ocean retrackers (34.6 N), (Figure the RMS 12c). gradually When approaching increases, but from that the of the open SGDR ocean SSHA (34.6°N), suddenly the increasesRMS aboutgradually 13 km increases, from the Capebut that Karasaki of the coastline. SGDR SSHA The othersuddenly two productsincreases maintainabout 13 akm gradual from the growth Cape rate untilKarasaki 7 km fromcoastline. the coastline, The other but two the products approach mainta distancesin a aregradual larger growth than that rate in until Section 7 4km. from the coastline,For comparison but the approach purposes, distances retracking are larger for than another that in pass Section over 4. a relatively smooth coastline is examined.For comparison Figure 13a showspurposes, pass retracking 164 over thefor southeastanother pass of Taiwan.over a relatively An example smooth of the coastline along-track is echogramexamined. (Figure Figure 13 13ab) shows includes pass no 164 obvious over the bright southeast targets. of Taiwan. As shown An inexample Figure of 13 thec, thealong-track difference amongechogram the three (Figure retrackers 13b) includes is almost no negligible,obvious bright although targets. the As ALES shown retracker in Figure shows 13c, a the relatively difference larger RMSamong within the 5three km from retrackers the coast. is almost negligible, although the ALES retracker shows a relatively largerOverall, RMS thewithin present 5 kmmethod from the enables coast. proper SSHA retrieval even in areas within 10 km from land. AlthoughOverall, the approach the present distance method towards enables the proper land variesSSHAwith retrieval the geography even in areas of the within study 10 area, km from a closer land. Although the approach distance towards the land varies with the geography of the study area, approach is expected using the present method than using the other retrackers. The present method a closer approach is expected using the present method than using the other retrackers. The present works especially well for removing isolated bright targets, but other factors causing inhomogeneous method works especially well for removing isolated bright targets, but other factors causing sea surface reﬂection, such as internal waves, sigma0 bloom events, and rain cells [17], are currently not inhomogeneous sea surface reflection, such as internal waves, sigma0 bloom events, and rain cells [17], considered. Hence, further studies in other coastal zones will be necessary to generalize the efﬁciency are currently not considered. Hence, further studies in other coastal zones will be necessary to ofgeneralize the present the method. efficiency of the present method.

(a) (b)

(c)

Figure 12. (a) Ground track (blue line) of Jason-2 altimeter pass 36 over northwestern coast of the Figure 12. (a) Ground track (blue line) of Jason-2 altimeter pass 36 over northwestern coast of the Tsushima Islands. Points are plotted every 5 km from the coast of Cape Karasaki together with Tsushima Islands. Points are plotted every 5 km from the coast of Cape Karasaki together with corresponding footprints with a 10 km radius. The section of the pass over Asou Bay is identified by corresponding footprints with a 10 km radius. The section of the pass over Asou Bay is identiﬁed by the purple line; (b) Rescaled and realigned along-track waveforms (echogram) measured by the the purple line; (b) Rescaled and realigned along-track waveforms (echogram) measured by the Jason-2 Jason-2 altimeter over the northwestern coast of the Tsushima Islands (pass 36, cycle 22); (c) RMS c altimetervariation over for theSSHA northwestern derived from coast altimeter of the Tsushimameasurements Islands for (pass three 36, different cycle 22); method ( ) RMSs. Black variation is the for SSHAresult derived of SGDR from product, altimeter blue measurementsis the result of A forLES three product, different and red methods. is the result Black of is this the study. result of SGDR product, blue is the result of ALES product, and red is the result of this study.

Remote Sens. 2017, 9, 762 12 of 13

(a) (b)

(c)

Figure 13. (a) Ground track (blue line) of Jason-2 altimeter pass 164 over southeast coast of Taiwan. Figure 13. (a) Ground track (blue line) of Jason-2 altimeter pass 164 over southeast coast of Taiwan. Points are plotted for every 5 km from the coast together with corresponding footprints with 10 km Points are plotted for every 5 km from the coast together with corresponding footprints with 10 km radius; (b) Rescaled and realigned along-track waveforms (echogram) measured by Jason-2 altimeter radius; (b) Rescaled and realigned along-track waveforms (echogram) measured by Jason-2 altimeter over Taiwan (pass 164, cycle 47); (c) RMS variation for SSHA derived from altimeter measurements over Taiwan (pass 164, cycle 47); (c) RMS variation for SSHA derived from altimeter measurements for three different methods. Black is the result for the SGDR product, blue is the result for the ALES for three different methods. Black is the result for the SGDR product, blue is the result for the ALES product, and red is the result for this study. product, and red is the result for this study. Acknowledgments: The present study was supported in part by a project called “Monitoring and prediction of Acknowledgments:marine and atmosphericThe present environmental study was changes supported in inthe part East by Asia” a project of calledthe Research “Monitoring Institute and of prediction Applied of marineMechanics and atmospheric (RIAM), Kyushu environmental Universi changesty, and inby the The East Japan Asia” Society of the Researchfor the Promotion Institute of of Applied Science Mechanics (JSPS) (RIAM),KAKENHI Kyushu Grant University, Number JP15H05821. and by The Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Number JP15H05821. Author Contributions: Xifeng Wang contributed to the conception of the study, performed the data analyses, Author Contributions: Xifeng Wang contributed to the conception of the study, performed the data analyses, and wroteand thewrote manuscript the manuscript under under Kaoru Kaoru Ichikawa’s Ichikawa’s guidance. guidan Thisce. workThis work was completedwas completed in Kyushu in Kyushu University, University, Japan, whenJapan, Xifeng when Wang Xifeng was Wang a Ph.D. was student.a Ph.D. student. ConﬂictsConflicts of of Interest: Interest:The The authors authors declare declare no noconﬂict conflict ofof interest.interest.

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