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International Journal of Remote Sensing

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Improving mesoscale observations from satellitealtimetry using bottom pressure and tide gaugemeasurements in the Japan Sea

Hongjie Li & Yongsheng Xu

To cite this article: Hongjie Li & Yongsheng Xu (2017) Improving mesoscale observationsfrom satellite altimetry using bottom pressure and tide gauge measurements in the Japan Sea,International Journal of Remote Sensing, 38:22, 6247-6267

To link to this article: http://dx.doi.org/10.1080/01431161.2017.1350307

Published online: 24 Jul 2017.

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Improving mesoscale observations from satellite altimetryusing bottom pressure and tide gauge measurements in theJapan SeaHongjie Lia,b,c and Yongsheng Xua,b

aKey Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences,Qingdao, China; bLaboratory for Ocean and Climate Dynamics, Qingdao National Laboratory for MarineScience and Technology, Qingdao, China; cEarth Science Institute, University of Chinese Academy ofSciences, Beijing, China

ABSTRACTIn the Japan/East Sea (Sea of Japan), the basin-scale barotropichigh-frequency signals cause aliasing error in the gridded sea levelanomaly (SLA) product of the satellite altimeters. The aliasingerrors can produce false mesoscale eddies and alter the dynamicalexplanation of ocean circulation. In this article, we corrected non-tidal aliasing errors in gridded SLA product using bottom pressure(BP) data and tide gauge (TG) data. The root mean square (RMS) ofthe aliasing induced SLA is about 3 cm in the Sea of Japan, whichaccounts for about 20% of the total energy. We found that, afterBP correction, the percentage of error variance (PEV) is reducedfrom 43% to 34% for satellite-derived velocity, and from 22%to14% for 70-day low-pass filtered gridded SLA product.However, the improvement for TG correction is not notable. Thebasin-scale barotropic high-frequency signals are likely to befound in other nearly enclosed marginal seas. We suggested thatmore BP measurements should be conducted in the marginal seasfor aliasing correction. The work in this article offers a usefulreference for suppressing non-tidal alias errors in other marginalseas.

ARTICLE HISTORYReceived 18 January 2017Accepted 27 June 2017

1. Introduction

With global coverage and high accuracy, satellite altimetry can periodically detect thesea level changes and has an incomparable advantage in the study of ocean mesoscaleobservation (Fu and Cazenave 2001; Chelton, Schlax, and Samelson 2011). So far, a seriesof satellite altimetry, such as Topex/Poseidon (T/P), ERS-1/2, Envisat, Jason-1/2, etc., havebeen launched. Although the orbit error and environmental corrections have beengreatly improved owe to the advance of new technologies, an intrinsic systematicerror, known as aliasing, may seriously corrupt satellite altimetry measurements(Fukumori, Raghunath, and Fu 1998; Chen and Ezraty 1996). Aliasing is an effect thatcauses different signals to become indistinguishable (or aliases of one another) when

CONTACT Yongsheng Xu yongsheng.xu@qdio.ac.cn Key Laboratory of Ocean Circulation and Waves, Instituteof Oceanology, Chinese Academy of Sciences, 7 Nanhai Road, Qingdao, 266071, P. R. China

INTERNATIONAL JOURNAL OF REMOTE SENSING, 2017VOL. 38, NO. 22, 6247–6267https://doi.org/10.1080/01431161.2017.1350307

© 2017 Informa UK Limited, trading as Taylor & Francis Group

sampled (Chen and Ezraty 1996) as shown in Figure 1. According to the NyquistFrequency Laws, satellite altimeter can only reveal ocean phenomenon whose timescaleis at least two times longer than cycle period of satellite altimetry. If the timescale of sealevel changes is less than two times of cycle period of satellite altimetry, high-frequencysignals will fold into the low-frequency signals and lead to aliasing in the altimeterobservation (Schlax and Chelton 1994). The alias-free periods for altimeters, such as ERS-1.2 and T/P, are between 70 and 19.8 days. The high-frequency barotropic motions thathave periods shorter than twice of satellite altimetry period are potential candidates foraltimetric aliasing. Except for tide, high-frequency energetic sea level movement hasbeen found in the open ocean, particularly outside the tropics (Fukumori, Raghunath,and Fu 1998; Stammer, Wunsch, and Ponte 2000; Tierney et al. 2000). For example,Fukumori, Raghunath, and Fu (1998) pointed out that, in most of the ocean poleward of30°, over half of the spectral energy for sea level variance in the intraseasonal band(<180 days) occurs at periods longer than 20 days and will be aliased by the 10-daysampling of sea surface height provided by the T/P satellite and its successors, Jason-1/2.Moreover, the barotropic large-scale motions in marginal seas are likely to producealiasing errors in satellite altimetry observations (Fukumori, Menemenlis, and Lee 2007;Xu et al. 2007). Aliasing error in a single satellite altimetry can be brought into multi-mission gridded products through merging processes (Xu, Randolph Watts, and Park2008). How to remove the non-tidal aliasing error has become a serious challenge tofurther improve the quality of the altimeter observations.

In this article, we focus on the aliasing due to the basin-wide barotropic fluctuationsin the Sea of Japan. We selected the Sea of Japan as the study domain because the high-frequency barotropic motions are significant in the Sea of Japan due to its semi-enclosed feature (Lyu and Kim 2005; Park and Watts 2005), and these high-frequencymotions can produce serious aliasing errors in the altimetric measurements. The basin-

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Figure 1. An example of aliasing due to low-frequency sampling from a high-frequency signal. Thered stars mean the sampling points and the black line is a false single arising from insufficientsampling.

6248 H. LI AND Y. XU

wide barotropic motions in the Sea of Japan are called ‘common mode’ here in order todistinguish it from mesoscale or smaller scale variability. The common mode containsenergetic high-frequency signals with periods ranging from several days to a month (Lyuand Kim 2005), which means that aliasing errors may arise in altimetry observations. Xu,Randolph Watts, and Park (2008) illustrated an example of spatio-temporal aliasingcaused by common mode in the ERS-2 observations. However, the influence ofcommon-mode aliasing in gridded products from multi-altimeter missions is still unclear.In this article, we explore aliasing errors presented in the gridded sea level anomaly(SLA) from multiple altimeter satellites and evaluate different methods to suppress thealiasing error.

This article was organized as follows: Section 2 describes data used in this article.Section 3 illustrates the existence of common mode in the Sea of Japan. Section 4introduces the methodology of suppressing the aliasing of the common mode in thegridded SLA data merged from multiple satellite altimeters. Section 5 presents results forthe corrected SLA map by bottom pressure (BP) and tide gauge (TG) data, respectively,analyses key changes in the mesoscale signals, and gives the comparisons between thecorrected SLA and in situ measurements including drifter data and TG data. A summaryand perspectives are given in Section 6.

2. Data and processing

2.1. Satellite altimeter data

Along-track SLA products from ERS-2 and T/P from 1999 to 2001 were used in this study. Theorbital altimeter data products are supplied by the French Space Agency, Archiving,Validation, and Interpretation of Satellite Oceanographic Data (AVISO). A description of thedata can be found in the SSALTO/DUACS (2015). We use their ‘calibrated’ SLA data products,on which not only ‘standard’ corrections had been applied for tides, inverse barometer (IB),radiometer, and electromagnetic bias, but also longwave corrections. To remove the residualnoise and small-scale signals, a 65-km low-pass Lanczos filter was applied to the SLA data set.Finally the along-track data were sub-sampled at every 14-km interval.

2.2. BP data

The BP measurements came from pressure-recording inverted echo sounders (PIES)which were deployed in the southwestern Sea of Japan and covered all of the UlleungBasin (UB) from June 1999 to July 2001. (Mitchell et al. 2004; Xu et al. 2007). Figure 2(a)gives the situation of 23 PIES which were used in this study. The hourly BP records wereconverted into sea level signals η using the hydrostatic approximation

η ¼ Pρg

; (1)

where P is the pressure at each PIE site, g (9.8 ms�2) is gravitational acceleration, ρ is thesea water density at 500 dbar from the historical hydrology data. The tidal componentsof the BP were removed using tidal response analysis techniques (Munk and Cartwright

INTERNATIONAL JOURNAL OF REMOTE SENSING 6249

1966). In order to suppress the aliasing caused by high-frequency signals (higher than 48day−1) such as waves, the hourly sampled BP signals were averaged every day. So thatthe impact of the crests and valleys on the BP will be largely offset. The BP measure-ments require no inverted barometer corrections because they respond to non-isostaticbarotropic variations. The detided BP measurements were averaged at all positions torepresent the barotropic oscillation of the common mode in the Sea of Japan. Theremight be aliasing errors in BP data arising from even higher frequency signals. Thesealiasing errors should be small due to high-frequency sampling of BP measurements.The averaged BP contains less local high-frequency signals, so it becomes a better proxyfor the common mode. We assume that the average of BP data can reduce these localhigh-frequency signals significantly.

2.3. TG data

Thirteen TGs from the Japan Oceanographic Data Center and the Korean NationalFisheries Research and Development Institute were used; their positions are shown inFigure 2(a). Hourly TG sea level data from 1999–2001 at sites in the Sea of Japan werecollected from TG records. The processing of TG data includes filtering tides and the

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Figure 2. (a) Location of the Sea of Japan and the distribution of Pies and TG (Square: Pies; Circular:TG). (b)Time series of BP at P1-1, P1-6, P3-2, P5-1, P5-5. (c) Variance-preserving PSD of average BP(blue line) and its 95% confidence interval (black lines).

6250 H. LI AND Y. XU

application of the IB correction. The method of IB correction is based on the simpleempirical relationship between the sea surface and its surface atmospheric pressure. Theair pressure data were derived from the National Centers for Environmental Predictionand have in space 2:5� � 2:5� and in 6 h time resolution. They were spatio-temporallyinterpolated to obtain Pa time series corresponding to sea level time series at each TGsite. The IB response ζ was obtained by the following formula:

ζ ¼ 1ρ0g

ðPa � PaÞ; (2)

where Pa is the global average sea surface atmospheric pressure at a given time, ρ0 isthe surface density of the sea. In order to obtain the SLA of TG, the average of 2-year TGdata was subtracted from TG data, respectively.

2.4. Lagrangian drifter data

In situ Lagrangian drifter data from the Global Drifter Program (GDP) were used tovalidate the corrected SLA maps in the Sea of Japan. The drifter data provide zonal andmeridional near-surface current velocity by the satellite-tracked drifters (Lumpkin. andPazos 2007). In this article, undrogued data have been removed and only drogueddrifters were used. We collected 28 floating buoys in total and used 14,459 profilesfrom these data sets between 21 June 1999 and 12 June 2001 in the Sea of Japan. Thedrifter locations were shown in Figure 3. Because drifter observations are not in grids,

Figure 3. Trajectories of the GDP Lagrangian drifters in the JES between June 1999 and July 2001.

INTERNATIONAL JOURNAL OF REMOTE SENSING 6251

they were interpolated via Kriging method (Hansen and Poulain 1996) to form the meshproducts, and the horizontal resolution is 0:25� � 0:25�.

3. Common mode

The Sea of Japan is a semi-enclosed marginal sea connected to the Pacific Ocean and theSea of Okhotsk through four shallow straits: The Korea (Tsushima), Tsugaru, Soya, andTartarsky straits. This is shown in Figure 2(a). The Tsushima Current flows into the Sea ofJapan through the Korea Strait and flows out mainly through the Tsugaru and Soya straits(Lee et al. 2001; Cho and Kim 2000). Since the inflow and outflow of seawater throughdifferent straits do not match in time, the mass of the Sea of Japan is constantly changing;this leads to a rise or fall of the Sea of Japan as a whole. To demonstrate the common-mode signal, we examined the changes of the BPs at five different PIES locations in theSea of Japan. From Figure 2(b) we can see that the five BP time series show nearlyconsistent variations through 2 years, even though the mooring sites span as large as 350km between P1-1 and P5-5. This indicates BP signals are nearly uniform throughout theUB. Furthermore, by the spectral analysis of the average BP data as was shown in Figure 2(c), we find that the variance-preserving power spectrum density (PSD) of BP has highvalues at timescales between 3.5–14 days, and the spectrum peak occurs at 0.2 cycles perday or 5 days. This shows that the BP signals reveal the high-frequency variations of thecommon-mode signal, and this result has also been confirmed by Park and Watts (2005).

In order to illustrate that the common mode is a basin-wide uniform signal in the Sea ofJapan, we calculated the spatial correlation from satellite altimetry and PIES measurements.First, somepoints in the Seaof Japanwere selected fromalong-track SLAdata of T/P and ERS-2.The rules were set for the selection of these points whose distances are smaller than 1000 kmaway from the PIES and far from the coast. The locations of the selected points were shown in

129 oE 131 oE 133 oE 135 oE 137 oE 139 oE 34 oN

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Figure 4. The chosen points to calculate the spatial scale from the along-track ERS-2 (green points)and T/P (red points), the black points are the PIES points.

6252 H. LI AND Y. XU

Figure 4. The time and space windows of the sampled points were 734 days and 900 km,respectively. Second, the time series of sea level changes for each PIES site were sampled atintervals of T/P and ERS-2, respectively. The correlation between the time series at all selectedpoints and the time series of a fixed PIE point was then calculated and expressed as a functionof the radial distance between these points and the PIES site. Finally, the correlation functionwas smoothed by a 15-km low-pass filter. In order to reveal the mesoscale effect, wesubtracted the BP common-mode signal. The results were shown as the black circles andblue circles in Figure 5. It canbe seen that the spatial correlation coefficient is usually close to orabove the constant 0.5 due to the presence of large-scale signals. However, when large-scalesignals were removed, the spatial correlations reveal an approximately Gaussian form for themesoscale variability. In short, we can conclude that the common mode is a nearly uniformhigh-frequency basin-scale barotropic signal in the Sea of Japan. Figure 6 shows the common-mode SLA hourly time series from June 1999 to June 2001 and the sub-sampled commonmode by the T/P with 10-day cycle and by ERS-2 with 35-day cycle at nearby 137:5�E; 37:5�N.This figure clearly illustrates the aliasing effects, especially by the ERS-2 sub-sampling.

4. Methodology

4.1. Correcting method

In this article we attempt to produce corrected SLA products that suppress the aliasing of thecommon mode in the Sea of Japan. To achieve this goal, we removed the common-modealiasing fromeachof the along-track ERS-2 and T/P in the Sea of Japan. To correct ERS-2, the BPwas high-pass filtered with a cut-off frequency of 1/70 day−1. This cut-off frequency waschosen because the alias-free period of ERS-2 is 70 days. Then the filtered BPwas sub-sampledalong tracks according to the sampling time of ERS-2. Finally, the sub-sampled BP was

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Figure 5. The spatial correlations of all SLA from PIES and satellite altimetric measurements as afunction of the distance to site (131.2° E,37.6° N) black circles suggesting the correlation of the totalSLA; blue circles suggesting the correlation of the mesoscale SLA.

INTERNATIONAL JOURNAL OF REMOTE SENSING 6253

subtracted fromalong-track SLA of ERS-2. To correct T/P, the processingmethod is the same asERS-2, except that BP needs to be high-pass filteredwith a cut-off frequency of 1/20 day−1. Thecorrected along-track data of ERS-2 and T/P were finally used to produce gridded product.

Although the sampling precision of BP measurements is high, the duration time of BPmeasurement is short (that is only 2 years); whereas the TGs provide much longermeasurements of SLA. So we also tried to use TG to remove aliasing instead of BP. Toreduce the effects of wind setup and coastal trapped waves on the TG, all TGs werespatially averaged to present the mean sea level of Sea of Japan. In order to removelarge-scale seasonal sea level change, the average TG sea level was filtered with a 70-dayhigh-pass filter and used to serve as a proxy of the common mode of Sea of Japan. Theaveraged sea level from TG data captures about 78% of the sea level variance from theBP (Xu, Randolph Watts, and Park 2008). Just like the way of correcting altimeter with BP,the along-track SLA of satellite altimetry can be corrected by subtracting common modeestimated from the TG along-track SLA.

4.2. Mapping method

To determine the gridded SLA products from different satellite altimeter, we used aspace/time suboptimal interpolation method to merge multiple satellite altimeter data(Bretherton, Davis, and Fandry 1976). The value of a field � (� is here the SLA) at a gridpoint x is determined by the following formula:

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Figure 6. Hourly common-mode anomaly estimated from the BP measurements (blue curve). Greentriangles and red stars are sampling time points at 137:5�E; 37:5�N by T/P (10-day period) and ERS-2(35-day period), respectively. Green and red curves are significantly aliased by the high-frequencysignals in BP measurements.

6254 H. LI AND Y. XU

�estðxÞ ¼Xn

j¼1

Xn

l¼1

A�1j;l Cx;lϕ

jobs; (3)

with ϕjobs ¼ ϕj þ εj, j ¼ 1; 2; . . . ; n, where ϕj is the true value and εj is the measure error.

Here A is the covariance matrix for the observations, and C the covariance vector for theobservations and the field to be estimated. The following space–time correlation func-tion Cðr; tÞ of the SLA field (Le Traon et al. 1995) was used:

Cðr; tÞ ¼ ½1þ ar þ 16ðarÞ2 � 1

6ðarÞ3� expð�arÞ expð� t2

T2Þ (4)

where r is the distance, t time, a = 3.34/L, L is the space correlation radius (first zerocrossing of C), and T the temporal correlation radius. We set L 58 km according to e�1

falling scale of correlation of mesoscale variability in Figure 5 (blue curve). The temporalcorrelation scale is set 30 days, which is a typical timescale of mesoscale variability (Xu,Li, and Dong 2009). Using this time–space optimal interpolation method, the along-trackSLA of different altimeters can be merged and produce meshed products. Finally, wemade 106 pairs of gridded SLA products consisting of the SLA uncorrected and thecorrected by BP. To verify the effectiveness of the gridded SLA products, we made acomparison between the uncorrected SLA produced from the ERS-2 and T/P with theMaps of Sea Level Anomalies (MSLA) provided by the AVISO (2016). From Figure 7, wefound that these two mapping mean values are very similar, and the root mean square(RMS) of difference between them is smaller than 2 cm in most of positions. Thepercentage of produced SLA variance explained by the MSLA is less than 5% exceptthe edge of the Sea of Japan. This proved that the uncorrected SLA products were verynear to the MSLA provided by the AVISO.

4.3. Validation by drifter data

To assess and verify the quality of the modified SLA product, ocean surface current iscompared with drift velocity. Ocean surface current includes geostrophic flow andEkman velocity, which is derived by wind stress. To acquire the geostrophic current, amean dynamic Topography (MDT) is added to the gridded SLA to obtain ocean dynamictopography. Note we have two meshed SLA products before and after aliasing correc-tions in hand. Here the MDT is obtained from the difference between the MADT and theMSLA provided by AVISO (2016). It has a 0:25� � 0:25� spatial resolution and one-dayinterval. The geostrophic currents Ug ¼ ðug; vgÞ were computed by geostrophicrelationship:

ug ¼ � gf@η

@y; vg ¼ g

f@η

@x; (5)

where η is the sum of the mapping SLA and MDT, and f is the Coriolis parameter. As forEkman currents Ue, we adapted a two-parameter regression model which was proposedby both Van Meurs and Niiler (1997) and Lagerloef et al. (1999). This model was definedas follows:

INTERNATIONAL JOURNAL OF REMOTE SENSING 6255

Ue ¼ Beiθðτx þ iτyÞ; (6)

where B is the amplitude coefficient, and θ is the turning angle relative to the winddirection. Here i is a complex number which satisfies the formula: i2 ¼ �1: In additionτ ¼ τx þ iτy is the surface wind stress, and x, y represents the zonal and meridional

direction, respectively. In the region away from 25� S to 25� N, B ¼ 0:3ms�1Pa�1, θ ¼55� (Sudre and Morrow 2008; Hui and Xu 2016). The wind stress data were fromQuikSCAT, which was launched by the National Aeronautics and Space Administration.According to Lagerloef et al. (1999), ocean surface current Uc can be expressed as

Uc ¼ Ug þ Ue: (7)

Thus we obtained two different surface currents derived from SLAs before and after BPcorrection. To assess their consistence with drifter velocities, we computed the percen-tage of error variance (PEV) of satellite-derived velocity defined by

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Figure 7. (a) The average uncorrected SLA produced from ERS-2 and T/P along-track SLA between1999 and 2001. (b) The average MSLA from AVISO during the same time. (c) The RMS of thedifference between the produced SLA and the MSLA. (d) The percentage of produced SLA varianceexplained by the MSLA.

6256 H. LI AND Y. XU

PEV ¼ varðUc � UdÞvarðUdÞ (8)

where Uc;Ud stands for the time series of surface currents and drifter velocity at a pointin the Sea of Japan, respectively, and var means calculating the variance of time series. Ifthe corrected product has a smaller PEV, it indicates that the aliasing of the altimeterwas effectively suppressed.

4.4. Validation by TG

Aliasing can make high-frequency signals fold into low-frequency signals (see Figure 1).If the aliasing is effectively suppressed by corrections, false low-frequency signals will beremoved from the satellite observations, and SLA meshed product will be improvedafter the correction. We compared the low-frequency variability of SLA products with theTG data by interpolating the gridded SLA products to positions of TGs. Both TG data andSLA products were filtered with a 70-day low-pass filter to retain only low-frequencysignals. We calculated the RMS of the difference between the satellite altimeter SLA andTG, and the percentage of error variance of 70-day low-pass filtered altimeter SLAproduct (PEL) is defined by

PEL ¼ varðSLA� TGÞvarðTGÞ : (9)

The less the RMS and PEL are, the better the SLA product is.

5. Results and discussion

In this section, we examine the improvement of the corrected SLA products. Afterconfirming the improvement, we investigated the deference on the description of themesoscale sea level variability before and after the correction while recognizing that thecorrection may not be a perfect one.

5.1. Correction of the gridded SLA with BP

5.1.1. Drifter comparison resultWe first compared ocean surface currents derived from the altimeter SLA products (seesection 4.3) with the drift velocities on the special day (7 March 2000). From Figure 8 wecan see that the zonal velocities derived from both SLA products have similar structurewith the drifter velocities in the southern part of the Sea of Japan, but in the region from38° N to 41° N, the zonal velocities from the corrected SLA were more agreement withdrifter velocities. For example, in the region of 134�E � 135�E; 39�N� 40�N; there was awarm vortex in both corrected velocity map (Figure 8(b), white rectangle) and driftervelocity map (Figure 8(c), white rectangle), but it did not appear in the uncorrectedvelocity map (Figure 8(a), white rectangle). In addition to that, a few anomaly highvelocities in the southern and eastern Sea of Japan were in Figure 8(d) but not inFigure 8(e,f). In general, velocities from the corrected SLA are more realistic than theuncorrected one.

INTERNATIONAL JOURNAL OF REMOTE SENSING 6257

To quantify the effect of long-term corrections, we compared the correlation betweenthe drift velocity and the velocity derived from the satellite altimeter in the Sea of Japan.From Figure 9 we can see that the correlations in the southwest of the Sea of Japanwere higher than other region of the Sea of Japan, because the drifter mainly distributedin this region. It can be found that both the zonal correlation and the meridional

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Velocity (cm s -1)

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Figure 8. Velocity comparisons between altimetry data and drifter data on 7 March 2000. (a) Zonalcomponent from uncorrected altimetry SLA map. (b) Zonal component from BP-corrected altimetrySLA map. (c) Zonal component from drifter data. (d) Meridional component from drifter data. (e)Meridional component from uncorrected altimetry SLA map. (f) Meridional component from BP-corrected altimetry SLA map. White rectangle denotes the region: 134�E� 135�E; 39�N� 40�N.

6258 H. LI AND Y. XU

correlation have been improved after BP correction. In the region of 129�E �136�E; 36�N� 41�N (Figure 9, white rectangle), after BP correction, the average zonalcorrelation between the drift velocities and the altimetry velocities increased from 73%to 77%, and the mean correction of meridional velocities increased from 67% to 72%. Inaddition, the averaged velocities of drifter and altimetry in about 2 years were also givenin Figure 10. It showed that the average velocities with and without BP correction werevery similar, and they were both consistent with the drifter velocities. So the average

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Correlation

0.2 0.4 0.6 0.8

Figure 9. Spatial distributions of the correlations between satellite-derived velocities and driftervelocities. (a) Zonal correlations from uncorrected altimetry SLA map. (b) Zonal correlation from BPcorrection. (c) Meridional correlations from uncorrected altimetry SLA map. (d) Meridional correla-tions from BP correction. White rectangle denotes the region: 129�E� 136�E; 36�N� 41�N.

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velocity does not show that the corrected SLA is better than the uncorrected SLA. Inorder to further demonstrate the advantages of BP-corrected product, we calculate thePEV of ocean surface currents relative to the drifter velocities at each point in the Sea ofJapan during 2000–2001 based on formula (8). Figure 11 shows the PEV of the uncor-rected and corrected velocities. It can be easily seen that after correcting with BP boththe zonal PEV and the meridional PEV decreased. Especially, the meridional PEVdecreased more in most of the Sea of Japan. The PEV in the middle and southwestern

129oE 133oE 137oE 141oE

36oN

39oN

42oN

45oN

48oN

(a) Zonal mean without correction

129oE 133oE 137oE 141oE

36oN

39oN

42oN

45oN

48oN

(b) Zonal mean by BP correction

129oE 133oE 137oE 141oE

36oN

39oN

42oN

45oN

48oN

(c) Zonal drifter mean

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36oN

39oN

42oN

45oN

48oN

(d) Meridional drifter mean

129oE 133oE 137oE 141oE

36oN

39oN

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45oN

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(e) Meridional mean without correction

129oE 133oE 137oE 141oE

36oN

39oN

42oN

45oN

48oN

(f) Meridional mean by BP correction

Velocity (cm s-1)

-20 -10 0 10 20 30 40

Figure 10. (a) Zonal average velocities between January 2000 to July 2001 from uncorrectedaltimetry SLA map. (b) Same as (a) but from the BP correction. (c) Same as (a) but from drifterdata. (d) Same as (c) but for Meridional component. (e) Same as (a) but for Meridional component.(f) Same as (b) but for Meridional component.

6260 H. LI AND Y. XU

Sea of Japan is less than that of other area, because there are more drifter data there. Tocompare the difference between the corrected and uncorrected SLA, we chosen fivepoints in the Sea of Japan. These five stations are distributed in the northern, central,and southern parts of the Sea of Japan, as shown in the Figure 11(c). They representdifferent regions of the Sea of Japan. Table 1 summarizes the velocity differencesbetween ocean surface currents (derived from uncorrected and corrected SLA) and

129oE 133oE 137oE 141oE

36oN

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(a) Zonal PEV without correction

129oE 133oE 137oE 141oE

36oN

39oN

42oN

45oN

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(b) Meridional PEV without correction

129oE 133oE 137oE 141oE

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(c) Zonal PEV by BP correction

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36oN

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(d) Meridional PEV by BP correction

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36oN

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(e) Zonal PEV by TG correction

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(f) Meridional PEV by TG correction

PEV

0.2 0.4 0.6 0.8

Figure 11. The PEV for (a) zonal velocities without correction; (b) meridional velocities without correction;(c) zonal velocities with BP correction; (d) meridional velocities with BP correction; (e) zonal velocities withTG correction; (f) meridional velocities with TG correction. The red asterisks in (c) are the compared pointsappearing in the Table 1, and the red points in (e) are the chosen TG appearing in the Table 2.

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drifter velocities in five different locations which were shown in Figure 11(c), and thedifferences are given in RMS and PEV. It can be seen that the PEV from the corrected SLAare generally smaller than that from the uncorrected SLA. The results may change withdifferent chosen points, but on the whole the variances by BP correction are smallerthan that of uncorrected, as seen from Figure 11(a–d). The mean is reduced from 41% to33% for zonal velocities, and from 45% to 35% for meridional velocities. This means thatthe products of corrected SLA are better adapted to in situ currents.

5.1.2. TG comparison resultAs discussed in Section 4.4, the TG also provided valuable information to examine theimprovement of the aliasing corrections. For comparison, the uncorrected and BP-corrected SLAs were interpolated to the position of TGs, and both altimetry and TGdata were filtered through a 70-day low-pass filter. Figure 12 shows the results at two TGsites. It can be seen that BP-corrected SLA is more coherent with TG than the uncor-rected one in the two TGs. To quantify the improvement, we calculated the RMS and PELbased on formula (9). Table 2 summarizes results for six tidal stations which were shownin Figure 11(e). For all tidal stations, the RMS of the difference between TG and correctedSLA is less than that between TG and uncorrected SLA. After BP correction, the averagedRMS of the difference between the meshed SLA and TG data in the six TGs is reducedfrom 4.03 to 3.32 cm, and the mean PEL is reduced from 22% to 14%. The resultsindicate that the low-frequency signal of BP-corrected SLA is more accurate than that ofthe uncorrected product in the Sea of Japan.

Table 1. The PEV and RMS of the difference between satellite-derived velocities (before and after BPcorrection) and drifter velocities at five locations.

Location PEV (%)/RMS (cm s−1)

Zonal velocity Meridional velocity

Without correction Correction with BP Without correction Correction with BP

139�E; 45

�N PEV 24 21 43 38

RMS 2.9 2.5 3.2 2.4137�E; 42�N PEV 47 37 45 42

RMS 3.3 2.7 4.8 3.0132�E; 40�N PEV 30 27 41 36

RMS 3.9 3.2 4.2 3.5135�E; 40�N PEV 48 44 42 38

RMS 5.6 5.3 4.8 4.2130�E; 35�N PEV 25 24 51.0 38

RMS 4.5 4.2 6.5 5.2

Table 2. The PEL and RMS of the difference between 70-day low-pass filtered satellite altimeter SLAsand TG at six TG stations.TG station Location PEL (%)/RMS (cm) Uncorrected SLA SLA with BP correction SLA with TG correction

Awashima 139:2�E; 38:5�N PEL 16 10 28RMS 4.09 3.23 5.48

Toyama 137:2�E; 36:7�N PEL 21 16 35RMS 5.39 4.76 6.94

Pusan 129:0�E; 35:1�N PEL 21 12 35RMS 3.06 2.33 3.94

Ulsan 129:3�E; 35:5�N PEL 18 12 14RMS 2.65 2.20 2.41

Pohang 129:4�E; 36:0�N PEL 35 17 41RMS 3.92 2.75 4.24

Sado 138:5�E; 38:3�N PEL 21 17 28RMS 5.10 4.66 6.01

6262 H. LI AND Y. XU

5.1.3. Difference in mapped mesoscale variabilityFigure 13 gives an example of gridded SLA merged from ERS-2 and T/P before and aftercorrections. Figure 13(a) is the uncorrected product on 7 March 2000, Figure 13(b) is theBP-corrected product on the same day. Comparing these two maps, significant changescan be seen in mesoscale sea level variability. Mesoscale anomalies are not clearly seenin the northern Sea of Japan before correction. After correction, obvious mesoscalevariability can be seen in the north of the Sea of Japan; moreover, cold mesoscale eddiesin the southern Sea of Japan are more in Figure 13(b) than Figure 13(a). To compare thesea level variability during the periods from June 1999 to June 2001, we calculated theRMS of the difference of the mapped SLAs before and after BP correction. The result isshown in Figure 13(c). It can be seen that the high RMS appears along the track ofsatellite altimetry. For example, the highlighted region coincides with ERS-2 tracks 492and 34 in the Sea of Japan, suggesting that this is the consequence of the common-mode sampling. The averaged RMS is about 3 cm which represents common-modealiasing induced SLA in the mapped SLA product. We computed the differences aspercentage of uncorrected SLA variance and found that the aliasing induced sea levelvariability accounts for about 20% of the total variance in the Sea of Japan.

0 200 400 600 800 1000-20

-15

-10

-5

0

5

10

15

20

25

Time (days from 1 January 1999)

SLA

(cm

)

Pohang:129°E,36°NPohang:129°E,36°N

0 200 400 600 800 1000-20

-15

-10

-5

0

5

10

15

20

25

Saigo:133.3°E,36.2°N

(b)(a)

Time (days from 1 January 1999)

SLA

(cm

)

Saigo:133.3°E,36.2°N

TGWithout correctionBP correctionTG correction

Figure 12. (a) Comparison of TG and altimetry products at station Pohang. (b) Same as (a), but atSaigo. The blue lines are 70-day filtered TG time series, and the black lines and red lines are 70-dayfiltered SLA time series with and without BP correction, respectively. The green lines represent SLAtime series with TG correction.

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5.2. Correction of the gridded SLA with TG

To evaluate the effect of the TG-corrected SLA product, we also calculated the PEV forTG correction. The results were shown in Figure 11(e,f). Obviously, the PEV of TGcorrection is greater than that of the BP correction, and the PEV of the zonal andmeridional velocities are 42% and 44%, respectively, slightly larger than the mean PEVbefore correction. This indicates that the velocities obtained by the TG correction havelarge deviation from the drifter velocities. On the other hand, we also compared the low-frequency signals between TG with that of SLA products before and after TG correction.The TG-corrected SLA was interpolated to the TG positions and was then filteredthrough a 70-day low-pass filter. The results are reflected in the green curve inFigure 12 and the last column in Table 2. Figure 12 shows that the TG-correctedaltimeter SLA sequence has approximately the same shape as the SLA sequence ofthe TG itself, but the correlation between the two is not very high especially in Figure 12(a). From the last column of Table 2, we can see that the PEL of the SLA with TGcorrection is slightly larger than the uncorrected one. So we conclude that the high-frequency common mode may not be effectively removed by TG correction.

6. Conclusions

The ocean supports fluctuations on all time and space scales. Altimetry missions weredesigned under the assumption that, after removing tidal signals, the energy of non-tidal high-frequency motions are small and it would not interfere the description of low-frequency motions in gridded altimeter SLA products. In this work, we found thatenergetic non-tidal high-frequency motions lead to significant aliasing errors in thegridded map merged from multiple satellite altimeters in the Sea of Japan. We foundthat the aliasing induced sea level variability accounts for about 20% of the total

129oE 133oE 137oE 141oE

36oN

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SLA (cm)

-10 0 10

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36oN

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SLA (cm)

-10 0 10

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RMS (cm)

0 5

Figure 13. Gridded SLA by merging ERS-2 and T/P on 7 March 2000. (a) The uncorrected SLA. (b)The corrected SLA from BP. (c) The RMS of the difference between the uncorrected SLA andcorrected SLA in the same period.

6264 H. LI AND Y. XU

variance in the Sea of Japan. It indicates that aliasing error in one satellite altimeter canenter into the gridded map in the merging process. This challenges the traditionalassumption for altimetry missions. Non-tidal aliasing may become a major challengeto further improve the accuracy of altimeter observations.

We evaluated methods to suppress high-frequency aliasing error that appears in thegridded SLA of satellite altimetry. The BP correction is an effective way to de-aliasing thecommon-mode signals in the Sea of Japan. The PEV between the altimetry velocity anddrifter velocity was reduced from 8% to 10%, and the PEL between the SLA from thealtimetry and the six TGs were averagely reduced by 8%. However, the TG correctiondoes not improve the gridded SLA, suggesting that the local effect on TG were notcancelled out by averaging different TGs. The local effect includes local harbour setupand coastal-trapped waves which are especially strong near the coast. So long-term BPmeasurements may be necessary for high-frequency common-mode de-aliasing.

Acknowledgements

The author acknowledge the AVISO for providing the sea surface height (SSH) data, and also thankJapan Oceanographic Data Center for their coastal tide gauge data. In situ Lagrangian drifter datawere provided by the Global Drifter Program.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This work was supported by the National Key R&D Program of China (grant 2016YFC1401004;grant 2016YFC1401008), the National Natural Science Foundation of China (grant 41676168; grant41376028), the National Basic Research Program of China (grant 2013CB956202), the NSFCInnovation Group Grant (grant 41421005), the NSFC-Shandong Joint Fund for Marine ScienceResearch Centers (grant U1406401), and the open Foundation of State Key Laboratory of RemoteSensing Science (grant OFSLRSS201504), the Leadership in Entrepreneurship and InnovationAwarded by Qingdao Municipal Government (grant 13-CX-26), and the Natural ScienceFoundation of Shandong Province, China (grant ZR2014DQ027).

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