Improving mesoscale observations from satellite altimetry using bottom pressure and tide gauge measurements in the Japan Sea

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1 International Journal of Remote Sensing ISSN: (Print) (Online) Journal homepage: Improving mesoscale observations from satellite altimetry using bottom pressure and tide gauge measurements in the Japan Sea Hongjie Li & Yongsheng Xu To cite this article: Hongjie Li & Yongsheng Xu (2017) Improving mesoscale observations from satellite altimetry using bottom pressure and tide gauge measurements in the Japan Sea, International Journal of Remote Sensing, 38:22, To link to this article: Published online: 24 Jul Submit your article to this journal View related articles View Crossmark data Full Terms & Conditions of access and use can be found at Download by: [ ] Date: 24 July 2017, At: 05:44

2 INTERNATIONAL JOURNAL OF REMOTE SENSING, 2017 VOL. 38, NO. 22, Improving mesoscale observations from satellite altimetry using bottom pressure and tide gauge measurements in the Japan Sea Hongjie Li a,b,c and Yongsheng Xu a,b a Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, Qingdao, China; b Laboratory for Ocean and Climate Dynamics, Qingdao National Laboratory for Marine Science and Technology, Qingdao, China; c Earth Science Institute, University of Chinese Academy of Sciences, Beijing, China ABSTRACT In the Japan/East Sea (Sea of Japan), the basin-scale barotropic high-frequency signals cause aliasing error in the gridded sea level anomaly (SLA) product of the satellite altimeters. The aliasing errors can produce false mesoscale eddies and alter the dynamical explanation of ocean circulation. In this article, we corrected nontidal aliasing errors in gridded SLA product using bottom pressure (BP) data and tide gauge (TG) data. The root mean square (RMS) of the aliasing induced SLA is about 3 cm in the Sea of Japan, which accounts for about 20% of the total energy. We found that, after BP correction, the percentage of error variance (PEV) is reduced from 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. The basin-scale barotropic high-frequency signals are likely to be found in other nearly enclosed marginal seas. We suggested that more BP measurements should be conducted in the marginal seas for aliasing correction. The work in this article offers a useful reference for suppressing non-tidal alias errors in other marginal seas. ARTICLE HISTORY Received 18 January 2017 Accepted 27 June Introduction With global coverage and high accuracy, satellite altimetry can periodically detect the sea level changes and has an incomparable advantage in the study of ocean mesoscale observation (Fu and Cazenave 2001; Chelton, Schlax, and Samelson 2011). So far, a series of satellite altimetry, such as Topex/Poseidon (T/P), ERS-1/2, Envisat, Jason-1/2, etc., have been launched. Although the orbit error and environmental corrections have been greatly improved owe to the advance of new technologies, an intrinsic systematic error, known as aliasing, may seriously corrupt satellite altimetry measurements (Fukumori, Raghunath, and Fu 1998; Chen and Ezraty 1996). Aliasing is an effect that causes 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, Institute of Oceanology, Chinese Academy of Sciences, 7 Nanhai Road, Qingdao, , P. R. China 2017 Informa UK Limited, trading as Taylor & Francis Group

3 6248 H. LI AND Y. XU Height (m) Time (day) Figure 1. An example of aliasing due to low-frequency sampling from a high-frequency signal. The red stars mean the sampling points and the black line is a false single arising from insufficient sampling. sampled (Chen and Ezraty 1996) as shown in Figure 1. According to the Nyquist Frequency Laws, satellite altimeter can only reveal ocean phenomenon whose timescale is at least two times longer than cycle period of satellite altimetry. If the timescale of sea level changes is less than two times of cycle period of satellite altimetry, high-frequency signals will fold into the low-frequency signals and lead to aliasing in the altimeter observation (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 that have periods shorter than twice of satellite altimetry period are potential candidates for altimetric aliasing. Except for tide, high-frequency energetic sea level movement has been 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 of 30, 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-day sampling 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 produce aliasing 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 multimission gridded products through merging processes (Xu, Randolph Watts, and Park 2008). How to remove the non-tidal aliasing error has become a serious challenge to further improve the quality of the altimeter observations. In this article, we focus on the aliasing due to the basin-wide barotropic fluctuations in the Sea of Japan. We selected the Sea of Japan as the study domain because the highfrequency barotropic motions are significant in the Sea of Japan due to its semienclosed feature (Lyu and Kim 2005; Park and Watts 2005), and these high-frequency motions can produce serious aliasing errors in the altimetric measurements. The basin-

4 INTERNATIONAL JOURNAL OF REMOTE SENSING 6249 wide barotropic motions in the Sea of Japan are called common mode here in order to distinguish it from mesoscale or smaller scale variability. The common mode contains energetic high-frequency signals with periods ranging from several days to a month (Lyu and Kim 2005), which means that aliasing errors may arise in altimetry observations. Xu, Randolph Watts, and Park (2008) illustrated an example of spatio-temporal aliasing caused by common mode in the ERS-2 observations. However, the influence of common-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 the aliasing 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 4 introduces the methodology of suppressing the aliasing of the common mode in the gridded SLA data merged from multiple satellite altimeters. Section 5 presents results for the 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 the corrected SLA and in situ measurements including drifter data and TG data. A summary and perspectives are given in Section 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. The orbital altimeter data products are supplied by the French Space Agency, Archiving, Validation, and Interpretation of Satellite Oceanographic Data(AVISO). A description of the data 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 residual noise 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 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 Ulleung Basin (UB) from June 1999 to July (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 were converted into sea level signals η using the hydrostatic approximation η ¼ P ρg ; (1) where P is the pressure at each PIE site, g (9.8 ms 2 ) is gravitational acceleration, ρ is the sea water density at 500 dbar from the historical hydrology data. The tidal components of the BP were removed using tidal response analysis techniques (Munk and Cartwright

5 6250 H. LI AND Y. XU 48 N 45 N 42 N 39 N 36 N (a) Japan Sea P1-1 P1-6 P3-2 P5-1 P5-5 Korea Strait Soya Strait Tsugaru Strait 33 N 127 E 132 E 137 E 142 E Pressure (dbar) PSD (10-3 db 2 ) (b) P P P P P Jul Oct Jan Apr Jul Oct Jan Apr Time (days from 1 January 1999) (c) Frequency (cycles day -1 ) 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). 1966). In order to suppress the aliasing caused by high-frequency signals (higher than 48 day 1 ) such as waves, the hourly sampled BP signals were averaged every day. So that the impact of the crests and valleys on the BP will be largely offset. The BP measurements require no inverted barometer corrections because they respond to non-isostatic barotropic variations. The detided BP measurements were averaged at all positions to represent the barotropic oscillation of the common mode in the Sea of Japan. There might be aliasing errors in BP data arising from even higher frequency signals. These aliasing 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 proxy for the common mode. We assume that the average of BP data can reduce these local high-frequency signals significantly TG data Thirteen TGs from the Japan Oceanographic Data Center and the Korean National Fisheries Research and Development Institute were used; their positions are shown in Figure 2(a). Hourly TG sea level data from at sites in the Sea of Japan were collected from TG records. The processing of TG data includes filtering tides and the

6 INTERNATIONAL JOURNAL OF REMOTE SENSING 6251 application of the IB correction. The method of IB correction is based on the simple empirical relationship between the sea surface and its surface atmospheric pressure. The air pressure data were derived from the National Centers for Environmental Prediction and have in space 2:5 2:5 and in 6 h time resolution. They were spatio-temporally interpolated to obtain P a time series corresponding to sea level time series at each TG site. The IB response ζ was obtained by the following formula: ζ ¼ 1 ρ 0 g ðp a P a Þ; (2) where P a is the global average sea surface atmospheric pressure at a given time, ρ 0 is the surface density of the sea. In order to obtain the SLA of TG, the average of 2-year TG data was subtracted from TG data, respectively Lagrangian drifter data In situ Lagrangian drifter data from the Global Drifter Program (GDP) were used to validate the corrected SLA maps in the Sea of Japan. The drifter data provide zonal and meridional near-surface current velocity by the satellite-tracked drifters (Lumpkin. and Pazos 2007). In this article, undrogued data have been removed and only drogued drifters were used. We collected 28 floating buoys in total and used 14,459 profiles from these data sets between 21 June 1999 and 12 June 2001 in the Sea of Japan. The drifter 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.

7 6252 H. LI AND Y. XU they were interpolated via Kriging method (Hansen and Poulain 1996) to form the mesh products, and the horizontal resolution is 0:25 0: Common mode The Sea of Japan is a semi-enclosed marginal sea connected to the Pacific Ocean and the Sea of Okhotsk through four shallow straits: The Korea (Tsushima), Tsugaru, Soya, and Tartarsky straits. This is shown in Figure 2(a). The Tsushima Current flows into the Sea of Japan 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 through different 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 commonmode signal, we examined the changes of the BPs at five different PIES locations in the Sea of Japan. From Figure 2(b) we can see that the five BP time series show nearly consistent variations through 2 years, even though the mooring sites span as large as 350 km between P1-1 and P5-5. This indicates BP signals are nearly uniform throughout the UB. 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 high values at timescales between days, and the spectrum peak occurs at 0.2 cycles per day or 5 days. This shows that the BP signals reveal the high-frequency variations of the common-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 of Japan, we calculated the spatial correlation from satellite altimetry and PIES measurements. First, some points in the Sea of Japan were selected from along-track SLA data of T/P and ERS-2. The rules were set for the selection of these points whose distances are smaller than 1000 km away from the PIES and far from the coast. The locations of the selected points were shown in 40 o N 38 o N 37 o N 35 o N 34 o N 129 o E 131 o E 133 o E 135 o E 137 o E 139 o E 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.

8 INTERNATIONAL JOURNAL OF REMOTE SENSING Correlation for the total SLA Correlation for the mesoscale SLA 0.75 Correlation Spatial lag (km) Figure 5. The spatial correlations of all SLA from PIES and satellite altimetric measurements as a function of the distance to site (131.2 E,37.6 N) black circles suggesting the correlation of the total SLA; blue circles suggesting the correlation of the mesoscale SLA. 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 at intervals of T/P and ERS-2, respectively. The correlation between the time series at all selected points and the time series of a fixed PIE point was then calculated and expressed as a function of the radial distance between these points and the PIES site. Finally, the correlation function was smoothed by a 15-km low-pass filter. In order to reveal the mesoscale effect, we subtracted the BP common-mode signal. The results were shown as the black circles and blue circles in Figure 5. It can be seen that the spatial correlation coefficient is usually close to or above the constant 0.5 due to the presence of large-scale signals. However, when large-scale signals were removed, the spatial correlations reveal an approximately Gaussian form for the mesoscale variability. In short, we can conclude that the common mode is a nearly uniform high-frequency basin-scale barotropic signal in the Sea of Japan. Figure 6 shows the commonmode SLA hourly time series from June 1999 to June 2001 and the sub-sampled common mode 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 the common mode in the Sea of Japan. To achieve this goal, we removed the common-mode aliasing from each of the along-track ERS-2 and T/P in the Sea of Japan. To correct ERS-2, the BP was high-pass filtered with a cut-off frequency of 1/70 day 1.Thiscut-off frequency was chosen because the alias-free period of ERS-2 is 70 days. Then the filtered BP was sub-sampled along tracks according to the sampling time of ERS-2. Finally, the sub-sampled BP was

9 6254 H. LI AND Y. XU Common mode signal TP sub-sampled ERS-2 sub-sampled 15 Height (cm) Time (days since 1 January 1999) Figure 6. Hourly common-mode anomaly estimated from the BP measurements (blue curve). Green triangles 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-frequency signals in BP measurements. subtracted from along-track SLA of ERS-2. To correct T/P, the processing method is the same as ERS-2, except that BP needs to be high-pass filtered with a cut-off frequency of 1/20 day 1.The corrected 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 BP measurement is short (that is only 2 years); whereas the TGs provide much longer measurements of SLA. So we also tried to use TG to remove aliasing instead of BP. To reduce the effects of wind setup and coastal trapped waves on the TG, all TGs were spatially averaged to present the mean sea level of Sea of Japan. In order to remove large-scale seasonal sea level change, the average TG sea level was filtered with a 70-day high-pass filter and used to serve as a proxy of the common mode of Sea of Japan. The averaged sea level from TG data captures about 78% of the sea level variance from the BP (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 mode estimated from the TG along-track SLA Mapping method To determine the gridded SLA products from different satellite altimeter, we used a space/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 grid point x is determined by the following formula:

10 INTERNATIONAL JOURNAL OF REMOTE SENSING 6255 est ðxþ ¼ Xn j¼1 X n l¼1 A 1 j;l C x;l ϕ j obs ; (3) with ϕ j obs ¼ ϕ j þ ε j, j ¼ 1; 2;...; n, where ϕ j is the true value and ε j is the measure error. Here A is the covariance matrix for the observations, and C the covariance vector for the observations and the field to be estimated. The following space time correlation function Cðr; tþ of the SLA field (Le Traon et al. 1995) was used: Cðr; tþ ¼½1þar þ 1 6 ðarþ2 1 6 ðarþ3 Š expð arþ expð t2 T2Þ (4) where r is the distance, t time, a=3.34/l, L is the space correlation radius (first zero crossing 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 temporal correlation 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-track SLA of different altimeters can be merged and produce meshed products. Finally, we made 106 pairs of gridded SLA products consisting of the SLA uncorrected and the corrected by BP. To verify the effectiveness of the gridded SLA products, we made a comparison between the uncorrected SLA produced from the ERS-2 and T/P with the Maps of Sea Level Anomalies (MSLA) provided by the AVISO (2016). From Figure 7, we found 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. The percentage of produced SLA variance explained by the MSLA is less than 5% except the edge of the Sea of Japan. This proved that the uncorrected SLA products were very near to the MSLA provided by the AVISO Validation by drifter data To assess and verify the quality of the modified SLA product, ocean surface current is compared with drift velocity. Ocean surface current includes geostrophic flow and Ekman velocity, which is derived by wind stress. To acquire the geostrophic current, a mean dynamic Topography (MDT) is added to the gridded SLA to obtain ocean dynamic topography. Note we have two meshed SLA products before and after aliasing corrections in hand. Here the MDT is obtained from the difference between the MADT and the MSLA provided by AVISO (2016). It has a 0:25 0:25 spatial resolution and one-day interval. The geostrophic currents U g ¼ðu g ; v g Þ were computed by geostrophic relationship: u g ¼ ; v g ¼ ; (5) where η is the sum of the mapping SLA and MDT, and f is the Coriolis parameter. As for Ekman currents U e, we adapted a two-parameter regression model which was proposed by both Van Meurs and Niiler (1997) and Lagerloef et al. (1999). This model was defined as follows:

11 6256 H. LI AND Y. XU (a) SLA (cm) 15 (b) SLA (cm) o E 133 o E 137 o E 141 o -15 E (c) RMS (cm) 48 o 5 N (d) % Figure 7. (a) The average uncorrected SLA produced from ERS-2 and T/P along-track SLA between 1999 and (b) The average MSLA from AVISO during the same time. (c) The RMS of the difference between the produced SLA and the MSLA. (d) The percentage of produced SLA variance explained by the MSLA. U e ¼ Be iθ ðτ x þ iτ y Þ; (6) where B is the amplitude coefficient, and θ is the turning angle relative to the wind direction. Here i is a complex number which satisfies the formula: i 2 ¼ 1: In addition τ ¼ τ x þ iτ y is the surface wind stress, and x, y represents the zonal and meridional direction, respectively. In the region away from 25 Sto25 N, B ¼ 0:3 ms 1 P 1 a, θ ¼ 55 (Sudre and Morrow 2008; Hui and Xu 2016). The wind stress data were from QuikSCAT, which was launched by the National Aeronautics and Space Administration. According to Lagerloef et al. (1999), ocean surface current U c can be expressed as U c ¼ U g þ U e : (7) Thus we obtained two different surface currents derived from SLAs before and after BP correction. To assess their consistence with drifter velocities, we computed the percentage of error variance (PEV) of satellite-derived velocity defined by

12 INTERNATIONAL JOURNAL OF REMOTE SENSING 6257 PEV ¼ varðu c U d Þ varðu d Þ (8) where U c ; U d stands for the time series of surface currents and drifter velocity at a point in the Sea of Japan, respectively, and var means calculating the variance of time series. If the corrected product has a smaller PEV, it indicates that the aliasing of the altimeter was effectively suppressed 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 be removed from the satellite observations, and SLA meshed product will be improved after the correction. We compared the low-frequency variability of SLA products with the TG data by interpolating the gridded SLA products to positions of TGs. Both TG data and SLA products were filtered with a 70-day low-pass filter to retain only low-frequency signals. We calculated the RMS of the difference between the satellite altimeter SLA and TG, and the percentage of error variance of 70-day low-pass filtered altimeter SLA product (PEL) is defined by PEL ¼ The less the RMS and PEL are, the better the SLA product is. varðsla TGÞ : (9) varðtgþ 5. Results and discussion In this section, we examine the improvement of the corrected SLA products. After confirming the improvement, we investigated the deference on the description of the mesoscale sea level variability before and after the correction while recognizing that the correction may not be a perfect one Correction of the gridded SLA with BP Drifter comparison result We first compared ocean surface currents derived from the altimeter SLA products (see section 4.3) with the drift velocities on the special day (7 March 2000). From Figure 8 we can see that the zonal velocities derived from both SLA products have similar structure with the drifter velocities in the southern part of the Sea of Japan, but in the region from 38 N to 41 N, the zonal velocities from the corrected SLA were more agreement with drifter velocities. For example, in the region of 134 E 135 E; 39 N 40 N; there was a warm vortex in both corrected velocity map (Figure 8(b), white rectangle) and drifter velocity map (Figure 8(c), white rectangle), but it did not appear in the uncorrected velocity map (Figure 8(a), white rectangle). In addition to that, a few anomaly high velocities in the southern and eastern Sea of Japan were in Figure 8(d) but not in Figure 8(e,f). In general, velocities from the corrected SLA are more realistic than the uncorrected one.

13 6258 H. LI AND Y. XU (a) Zonal velocity without correction (b) Zonal velocity by BP correction (c) Zonal drifter velocity (d) Meridional drifter velocity (e) Meridional velocity without correction (f) Meridional velocity by BP correction Velocity (cm s -1 ) Figure 8. Velocity comparisons between altimetry data and drifter data on 7 March (a) Zonal component from uncorrected altimetry SLA map. (b) Zonal component from BP-corrected altimetry SLA 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 BPcorrected altimetry SLA map. White rectangle denotes the region: 134 E 135 E; 39 N 40 N. To quantify the effect of long-term corrections, we compared the correlation between the 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 Japan were higher than other region of the Sea of Japan, because the drifter mainly distributed in this region. It can be found that both the zonal correlation and the meridional

14 INTERNATIONAL JOURNAL OF REMOTE SENSING 6259 (a) Zonal correlation without correction (b) Zonal correlation by BP correction (c) Meridional correlation without correction (d) Meridional correlation by BP correction Correlation Figure 9. Spatial distributions of the correlations between satellite-derived velocities and drifter velocities. (a) Zonal correlations from uncorrected altimetry SLA map. (b) Zonal correlation from BP correction. (c) Meridional correlations from uncorrected altimetry SLA map. (d) Meridional correlations from BP correction. White rectangle denotes the region: 129 E 136 E; 36 N 41 N. 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 zonal correlation 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%. In addition, the averaged velocities of drifter and altimetry in about 2 years were also given in Figure 10. It showed that the average velocities with and without BP correction were very similar, and they were both consistent with the drifter velocities. So the average

15 6260 H. LI AND Y. XU (a) Zonal mean without correction (b) Zonal mean by BP correction (c) Zonal drifter mean (d) Meridional drifter mean (e) Meridional mean without correction (f) Meridional mean by BP correction Velocity (cm s -1 ) Figure 10. (a) Zonal average velocities between January 2000 to July 2001 from uncorrected altimetry SLA map. (b) Same as (a) but from the BP correction. (c) Same as (a) but from drifter data. (d) Same as (c) but for Meridional component. (e) Same as (a) but for Meridional component. (f) Same as (b) but for Meridional component. velocity does not show that the corrected SLA is better than the uncorrected SLA. In order to further demonstrate the advantages of BP-corrected product, we calculate the PEV of ocean surface currents relative to the drifter velocities at each point in the Sea of Japan during based on formula (8). Figure 11 shows the PEV of the uncorrected and corrected velocities. It can be easily seen that after correcting with BP both the zonal PEV and the meridional PEV decreased. Especially, the meridional PEV decreased more in most of the Sea of Japan. The PEV in the middle and southwestern

16 INTERNATIONAL JOURNAL OF REMOTE SENSING 6261 (a) Zonal PEV without correction (b) Meridional PEV without correction (c) Zonal PEV by BP correction (d) Meridional PEV by BP correction (e) Zonal PEV by TG correction (f) Meridional PEV by TG correction PEV 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 with TG correction; (f) meridional velocities with TG correction. The red asterisks in (c) are the compared points appearing in the Table 1, and the red points in (e) are the chosen TG appearing in the Table 2. Sea of Japan is less than that of other area, because there are more drifter data there. To compare the difference between the corrected and uncorrected SLA, we chosen five points 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 represent different regions of the Sea of Japan. Table 1 summarizes the velocity differences between ocean surface currents (derived from uncorrected and corrected SLA) and

17 6262 H. LI AND Y. XU Table 1. The PEV and RMS of the difference between satellite-derived velocities (before and after BP correction) and drifter velocities at five locations. Zonal velocity Meridional velocity Location PEV (%)/RMS (cm s 1 ) Without correction Correction with BP Without correction Correction with BP 139 E; 45 N PEV RMS E; 42 N PEV RMS E; 40 N PEV RMS E; 40 N PEV RMS E; 35 N PEV RMS drifter velocities in five different locations which were shown in Figure 11(c), and the differences are given in RMS and PEV. It can be seen that the PEV from the corrected SLA are generally smaller than that from the uncorrected SLA. The results may change with different chosen points, but on the whole the variances by BP correction are smaller than that of uncorrected, as seen from Figure 11(a d). The mean is reduced from 41% to 33% for zonal velocities, and from 45% to 35% for meridional velocities. This means that the products of corrected SLA are better adapted to in situ currents TG comparison result As discussed in Section 4.4, the TG also provided valuable information to examine the improvement of the aliasing corrections. For comparison, the uncorrected and BPcorrected SLAs were interpolated to the position of TGs, and both altimetry and TG data were filtered through a 70-day low-pass filter. Figure 12 shows the results at two TG sites. It can be seen that BP-corrected SLA is more coherent with TG than the uncorrected one in the two TGs. To quantify the improvement, we calculated the RMS and PEL based on formula (9). Table 2 summarizes results for six tidal stations which were shown in Figure 11(e). For all tidal stations, the RMS of the difference between TG and corrected SLA is less than that between TG and uncorrected SLA. After BP correction, the averaged RMS of the difference between the meshed SLA and TG data in the six TGs is reduced from 4.03 to 3.32 cm, and the mean PEL is reduced from 22% to 14%. The results indicate that the low-frequency signal of BP-corrected SLA is more accurate than that of the uncorrected product in the Sea of Japan. Table 2. The PEL and RMS of the difference between 70-day low-pass filtered satellite altimeter SLAs and 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 RMS Toyama 137:2 E; 36:7 N PEL RMS Pusan 129:0 E; 35:1 N PEL RMS Ulsan 129:3 E; 35:5 N PEL RMS Pohang 129:4 E; 36:0 N PEL RMS Sado 138:5 E; 38:3 N PEL RMS

18 INTERNATIONAL JOURNAL OF REMOTE SENSING 6263 (a) (b) 25 TG Without correction BP correction 20 TG correction SLA (cm) 5 0 SLA (cm) Pohang:129 E,36 N Saigo:133.3 E,36.2 N Time (days from 1 January 1999) Time (days from 1 January 1999) Figure 12. (a) Comparison of TG and altimetry products at station Pohang. (b) Same as (a), but at Saigo. The blue lines are 70-day filtered TG time series, and the black lines and red lines are 70-day filtered SLA time series with and without BP correction, respectively. The green lines represent SLA time series with TG correction Difference in mapped mesoscale variability Figure 13 gives an example of gridded SLA merged from ERS-2 and T/P before and after corrections. Figure 13(a) is the uncorrected product on 7 March 2000, Figure 13(b) is the BP-corrected product on the same day. Comparing these two maps, significant changes can be seen in mesoscale sea level variability. Mesoscale anomalies are not clearly seen in the northern Sea of Japan before correction. After correction, obvious mesoscale variability can be seen in the north of the Sea of Japan; moreover, cold mesoscale eddies in the southern Sea of Japan are more in Figure 13(b) than Figure 13(a). To compare the sea level variability during the periods from June 1999 to June 2001, we calculated the RMS of the difference of the mapped SLAs before and after BP correction. The result is shown in Figure 13(c). It can be seen that the high RMS appears along the track of satellite altimetry. For example, the highlighted region coincides with ERS-2 tracks 492 and 34 in the Sea of Japan, suggesting that this is the consequence of the commonmode sampling. The averaged RMS is about 3 cm which represents common-mode aliasing induced SLA in the mapped SLA product. We computed the differences as percentage of uncorrected SLA variance and found that the aliasing induced sea level variability accounts for about 20% of the total variance in the Sea of Japan.

19 6264 H. LI AND Y. XU (a) (b) (c) SLA (cm) SLA (cm) RMS (cm) Figure 13. Gridded SLA by merging ERS-2 and T/P on 7 March (a) The uncorrected SLA. (b) The corrected SLA from BP. (c) The RMS of the difference between the uncorrected SLA and corrected SLA in the same period Correction of the gridded SLA with TG To evaluate the effect of the TG-corrected SLA product, we also calculated the PEV for TG correction. The results were shown in Figure 11(e,f). Obviously, the PEV of TG correction is greater than that of the BP correction, and the PEV of the zonal and meridional velocities are 42% and 44%, respectively, slightly larger than the mean PEV before correction. This indicates that the velocities obtained by the TG correction have large deviation from the drifter velocities. On the other hand, we also compared the lowfrequency 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 filtered through a 70-day low-pass filter. The results are reflected in the green curve in Figure 12 and the last column in Table 2. Figure 12 shows that the TG-corrected altimeter SLA sequence has approximately the same shape as the SLA sequence of the 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 TG correction is slightly larger than the uncorrected one. So we conclude that the highfrequency common mode may not be effectively removed by TG correction. 6. Conclusions The ocean supports fluctuations on all time and space scales. Altimetry missions were designed under the assumption that, after removing tidal signals, the energy of nontidal high-frequency motions are small and it would not interfere the description of lowfrequency motions in gridded altimeter SLA products. In this work, we found that energetic non-tidal high-frequency motions lead to significant aliasing errors in the gridded map merged from multiple satellite altimeters in the Sea of Japan. We found that the aliasing induced sea level variability accounts for about 20% of the total

20 INTERNATIONAL JOURNAL OF REMOTE SENSING 6265 variance in the Sea of Japan. It indicates that aliasing error in one satellite altimeter can enter into the gridded map in the merging process. This challenges the traditional assumption for altimetry missions. Non-tidal aliasing may become a major challenge to further improve the accuracy of altimeter observations. We evaluated methods to suppress high-frequency aliasing error that appears in the gridded SLA of satellite altimetry. The BP correction is an effective way to de-aliasing the common-mode signals in the Sea of Japan. The PEV between the altimetry velocity and drifter velocity was reduced from 8% to 10%, and the PEL between the SLA from the altimetry and the six TGs were averagely reduced by 8%. However, the TG correction does not improve the gridded SLA, suggesting that the local effect on TG were not cancelled out by averaging different TGs. The local effect includes local harbour setup and coastal-trapped waves which are especially strong near the coast. So long-term BP measurements 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 thank Japan Oceanographic Data Center for their coastal tide gauge data. In situ Lagrangian drifter data were 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 2016YFC ; grant 2016YFC ), the National Natural Science Foundation of China (grant ; grant ), the National Basic Research Program of China (grant 2013CB956202), the NSFC Innovation Group Grant (grant ), the NSFC-Shandong Joint Fund for Marine Science Research Centers (grant U ), and the open Foundation of State Key Laboratory of Remote Sensing Science (grant OFSLRSS201504), the Leadership in Entrepreneurship and Innovation Awarded by Qingdao Municipal Government (grant 13-CX-26), and the Natural Science Foundation of Shandong Province, China (grant ZR2014DQ027). References Bretherton, F., R. Davis, and C. Fandry A Technique For Objective Analysis and Design of Oceanographic Experiments Applied to MODE-73. Deep Sea Research and Oceanographic Abstracts 23 (7): doi: / (76) Chelton, D. B., M. G. Schlax, and R. M. Samelson Global Observations of Nonlinear Mesoscale Eddies. Progress Oceanogr 91 (2): doi: /j.pocean Chen, G., and R. Ezraty Alias Impacts on the Recovery of Sea-Level Amplitude and Energy from Altimeter Measurements. International Journal Romote Sensing 17: doi: / Cho, Y., and K. K. Kim Branching Mechanism of the Tsushima Current in the Korea Strait. Journal of Physical Oceanography 30: doi: / (2000)030<2788: BMOTTC>2.0.CO;2.

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