The Impact of the Mesoscale Ocean Variability on the Estimation of Tidal Harmonic Constants Based on Satellite Altimeter Data in the South China Sea

: The estimation accuracy of tidal harmonic constants is of great signiﬁcance to maritime trafﬁc and port construction. However, due to the long sampling period of satellite altimeters, tidal signals alias the mesoscale ocean frequencies. As a result, the harmonic analysis is affected by mesoscale environmental noise. In this study, the inﬂuence of the mesoscale ocean variability (MOV) on the estimation of tidal harmonic constants was quantiﬁed by analyzing 25 years of altimeter data from the Topex/Poseidon (T/P) and Jason satellites in the South China Sea (SCS). The results indicated that the absolute amplitude differences (AADs) of the eight major tidal constituents before and after the mesoscale variability correction (MVC) were generally within 10 mm, and most were within 6 mm. For the relative impact, M 2 , O 1 , and K 1 were not obviously affected by the MOV because of their large amplitudes, and the AADs generally accounted for less than ± 10% of the amplitudes. As a tidal constituent with amplitude less than 2 cm in the SCS, the amplitude of K 2 was signiﬁcantly affected by the MOV, with the ratios of the AADs to its own amplitudes ranging from − 64.79% to 95.99% in space. In terms of phase, the K 2 tide was most affected by the MOV: 63% of the data points before and after correction were over ± 5 ◦ , and the maximum and minimum values were 86.46 ◦ and − 176.27 ◦ , respectively. The absolute phase differences of other tidal constituents before and after the MVC were generally concentrated within ± 5 ◦ . The impact of the MOV on the evolution of tidal amplitudes in the SCS was also explored. It was found that the MOV can cause pseudo-rapid temporal variations of tidal amplitudes in some regions of the SCS.


Introduction
Tides, one of the most prevalent ocean motions, are the periodic movements of sea water induced by the celestial tide-generating force from the sun and the moon. Previous studies have shown that ocean tides have important effects on earth rotation, ocean circulation, deep ocean mixing, etc. [1,2]. The accuracy of ocean tides estimation plays an important role in numerous fields, such as coastal engineering, maritime traffic, and aquaculture [3].
Until the 1990s, ocean tidal data were obtained mainly from tide gauges around the world. Due to the limitation of location and quantity, water level records were mainly observed in coastal areas, and few tidal gauges were located in the deep sea. The advent and wide use of satellite altimetry have revolutionized the ocean observation scale in space. However, there are also limitations to this technique. Because the tidal signals of the Topex/Poseidon and Jason (T/P-Jason) satellites are sampled over a period of 9.915642 days, the semidiurnal and diurnal tides are aliased into low-frequency fluctuations with periods of several months. Desai et al. (1997) and Tierney et al. (1998) found that mesoscale energy in the ocean reduced the accuracy of tidal estimation due to the long sampling interval, which can be alleviated by increasing the time series of satellite altimeters [4,5]. At present, although the satellite data have a long time span, the nontidal background noise still affects the accuracy of tidal harmonic constants to some extent, especially in the regions with strong mesoscale ocean variability (MOV). Ray and Byrne (2010) analyzed tidal features in the southeast Atlantic Ocean using bottom pressure records collected at 11 stations aligned on a single ground track of the T/P-Jason satellites. By comparing the estimated tidal constants, they found that high MOV clearly corrupted the altimeter-based tidal estimations even with data spanning a 17 year period. They further used a multi-satellite mapped sea level anomalies (SLA) product as a "correction" for tide estimation, thus improving the accuracy of the altimeter-based harmonic constants [6].
MOV mainly exists in the form of mesoscale eddies, which are the horizontal rotating water in the ocean with a horizontal diameter of 100~500 km and a duration of several days to several months. Mesoscale eddies are an important component of dynamical oceanography across the range of scales. They can transport heat, mass momentum, and biogeochemical properties from one area to other, remote areas [7].
As the largest semi-enclosed marginal sea in the western Pacific, the South China Sea (SCS) has attracted oceanographers because of its significant monsoon climate, special geographical location, and rich natural resources. Since 1956, mesoscale eddies have been discovered in the South China Sea [8]. Previous studies have shown that the SCS is a region with one of the strongest MOVs in the world and the upper layer of the SCS has complex structural characteristics [9,10]. Since the launch of the Topex/Poseidon satellite in 1992, numerous studies on tidal characteristics in the SCS have been performed [11][12][13][14].
However, it appears that no studies have discussed in detail the potential influence of MOV on tidal estimation in the SCS. One of the purposes of this paper is to fill this gap.
In this study, the mesoscale variability correction (MVC) method proposed by Ray and Byrne (2010) was applied to the SCS, and the newest harmonic tidal analysis package S_TIDE [15] (add see the Supplementary Materials) was used to conduct tidal analysis on the T/P-Jason data. The paper is organized as follows. Section 2 describes the satellite altimeter data for tidal harmonic analysis and the multi-satellite mapped sea level anomaly (SLA) fields for MVC. The influence of MOV on the extraction of tidal amplitudes and phases is analyzed in Section 3. An improved understanding of tidal evolution from satellite altimeter data using the MVC method is discussed in Section 4. Section 5 presents the conclusion and summary.

Altimetric Data
The sea level observations for tidal harmonic analysis were taken from four satellite altimeters: Topex/Poseidon (T/P) and three Jason satellites (Jason-1, Jason-2, and Jason-3). The orbital period of these satellites is 112.0 min, and the repetition period is 9.915642 days. To ensure consistency, the system bias caused by different terrestrial reference frames was removed and the four altimeter datasets were combined. In this study, the observations with a total length of 25 years from October 1992 to September 2017 were analyzed. To ensure the accuracy and the reliability of this research, we selected 1600 observation points with a time span longer than 18.61 years and missing values less than 20%. It can be seen that the selected points are mainly concentrated in the central deep-sea basin of the SCS (Figure 1).  Similar to the approach of Ray and Byrne (2010) [6], multi-satellite gridded daily SLA fields provided by the Copernicus Marine and Environment Monitoring Service (CMEMS) were used for MVC. This SLA product merges all available altimeter missions (T/P-Jason, ENVISAT, Geosat Follow-On (GFO), AltiKa, Haiyang-2A, etc.) [16]. The filter method introduced by Zaron and Ray (2018) was used to eliminate the residual tidal signals in this mapped SLA product, and the remaining information was identified as the mesoscale variability. By subtracting the filtered SLA fields from the T/P-Jason data, the influence of the MOV on satellite-based tidal estimation was removed and the MOV operation was completed [17].

Tidal Aliasing in Altimetric Data
As mentioned above, tidal aliasing refers to a phenomenon during the sampling process in which, due to the long sampling interval, the component with a frequency higher than the folding frequency in the original time series folds towards that with a low frequency, thus, forming false spectral lines (peaks) in the frequency spectrum and causing confusion between the high and low frequency components [18]. According to the sampling theory, when the sampling interval is determined, the highest frequency that can be resolved is the folding frequency. Because the sampling period of T/P-Jason satellites is 9.915642 days, the oscillation period that can be identified is about 20 days. Because tides are mainly composed of diurnal and semidiurnal tides, the tidal signals with high frequency are folded into signals with low frequency. The minimum period corresponding to the folding frequency is the aliasing period (Table 1).
It should be noted that the mesoscale eddies (with periods ranging from ten days to half a year) are common in the SCS. Chen et al. (2011) conducted a statistical analysis of the mesoscale eddies in the SCS using 17 years of satellite data from October 1992 to October 2009, in which a total of 393 cyclonic eddies and 434 anticyclonic eddies were extracted, and the average lifetime of these eddies was 8.8 weeks (61.6 days) [10]. The own periods and aliasing periods of major tidal constituents under the T/P-Jason sampling interval are shown in Table 1 [19]. It can be seen that the aliasing period of main tidal constituents is close to the mean period of mesoscale eddies. Thus, the results of harmonic analysis of satellite altimeter data include two parts: ocean tide (barotropic tide and the surface manifestation of internal tide) and MOV. In the SCS, due to the high mesoscale eddy activities, the tidal harmonic constants are disturbed by MOV, and the accuracy of tidal estimation is partly limited. Similar to the approach of Ray and Byrne (2010) [6], multi-satellite gridded daily SLA fields provided by the Copernicus Marine and Environment Monitoring Service (CMEMS) were used for MVC. This SLA product merges all available altimeter missions (T/P-Jason, ENVISAT, Geosat Follow-On (GFO), AltiKa, Haiyang-2A, etc.) [16]. The filter method introduced by Zaron and Ray (2018) was used to eliminate the residual tidal signals in this mapped SLA product, and the remaining information was identified as the mesoscale variability. By subtracting the filtered SLA fields from the T/P-Jason data, the influence of the MOV on satellite-based tidal estimation was removed and the MOV operation was completed [17].

Tidal Aliasing in Altimetric Data
As mentioned above, tidal aliasing refers to a phenomenon during the sampling process in which, due to the long sampling interval, the component with a frequency higher than the folding frequency in the original time series folds towards that with a low frequency, thus, forming false spectral lines (peaks) in the frequency spectrum and causing confusion between the high and low frequency components [18]. According to the sampling theory, when the sampling interval is determined, the highest frequency that can be resolved is the folding frequency. Because the sampling period of T/P-Jason satellites is 9.915642 days, the oscillation period that can be identified is about 20 days. Because tides are mainly composed of diurnal and semidiurnal tides, the tidal signals with high frequency are folded into signals with low frequency. The minimum period corresponding to the folding frequency is the aliasing period (Table 1). It should be noted that the mesoscale eddies (with periods ranging from ten days to half a year) are common in the SCS. extracted, and the average lifetime of these eddies was 8.8 weeks (61.6 days) [10]. The own periods and aliasing periods of major tidal constituents under the T/P-Jason sampling interval are shown in Table 1 [19]. It can be seen that the aliasing period of main tidal constituents is close to the mean period of mesoscale eddies. Thus, the results of harmonic analysis of satellite altimeter data include two parts: ocean tide (barotropic tide and the surface manifestation of internal tide) and MOV. In the SCS, due to the high mesoscale eddy activities, the tidal harmonic constants are disturbed by MOV, and the accuracy of tidal estimation is partly limited.
According to the Rayleigh criterion, the length of record (LOR) required to separate the two different tidal constituents should satisfy the following: Thus, the LOR required to separate the eight main tidal constituents in T/P-Jason observations can be obtained ( Table 2). The LOR to fully separate P 1 and K 2 is 9.18 years, which is the longest compared to other pairs of constituents. The period of 9.18 years is significantly less than the 25 years of altimeter data recorded in this paper. Therefore, the eight major constituents can be guaranteed to be fully resolved.

Tidal Harmonic Analysis
The observed sea level h can be regarded as the superposition of n tidal constituents. Equation (3) is the linearized version of Equation (2).
where H i and g i are the amplitude and the phase of the tidal constituents, respectively, which are collectively called harmonic constants. h 0 is the mean sea level. ω i , f i , and u i are the frequency, the nodal factor, and the nodal angle of i-th constituent, respectively. U i and V i are transformed by: When conducting linear regression, Equation (3) is converted to the following matrix form: where H, A, and X are the matrix of observed sea levels, the matrix of known coefficients, and the matrix of the parameters that need to be solved, respectively. When there are m sea level observations, the matrices are expressed as follows: F(1, 2) · · · F(n, 2) G(1, 2) · · · G(n, 2) · · · · · · · · · · · · · · · · · · · · · 1 F(1, m) · · · F(n, m) G(1, m) · · · G(n, m) Unknown tidal parameters can be estimated using Equation (9): To eliminate the effects of some outliers in tidal signals, iteratively reweighed least squares (IRLS) regression, which is the extension of the ordinary least squares (OLS), was performed in this study. Previous study [20,21] showed that the IRLS algorithm can reduce the influence of broad-spectrum noise and thus improve the reliability of the regression results. The newest harmonic tidal analysis package, S_TIDE, was used in this study to realize the IRLS algorithm [22].
Before evaluating the results of the tidal harmonic analysis, we first verify the reliability of the regression results using the signal-to-noise ratio (SNR), which can be described by: where H is the estimated amplitude of a tidal constituent and H e is the estimated error [23].
In general, the SNR can analyze the characteristics and influence of nontidal components on tidal estimation in the course of harmonic analysis. A higher SNR indicates a lower noise level in the tidal signal and, thus, the harmonic constants will be more reliable [24]. Table 3 shows the space-averaged changes of SNR for the eight major tidal constituents before and after the MVC. We find that the errors of tidal amplitudes can be obviously reduced and the corresponding SNRs are significantly increased after the MVC, which represents a significant improvement in the accuracy and reliability of the estimated tidal constants. Among all the SNRs of the eight main constituents, that of K 2 constituent is the smallest. The amplitudes of K 2 are the smallest among the eight main tides in the SCS, which means that K 2 tides are more vulnerable to the influence of MOV. On the contrary, the SNRs of M 2 , O 1 , and K 1 constituents are larger than the others, indicating that the amplitudes of these constituents are less affected by the nontidal components. These three tidal constituents are the most important constituents in the SCS, and their large amplitudes weaken the influence of background noises.
Previous statistical analyses have shown that the mesoscale eddies are concentrated in the west of the Luzon Strait and the western boundary of the deep-sea basin. They are also distributed in the south of the north slope of the SCS and the middle of the deep-sea basin [25][26][27][28]. The errors of M 2 and S 2 error in the western Luzon Strait and the western boundary of the deep-sea basin (framed areas in Figure 2a) are larger than those in other regions, which is consistent with the significant area of mesoscale eddies in the SCS. Lower SNRs are also found in these regions ( Figure 3). The phenomenon is clearly mitigated, although did not disappear completely after MOV. Other tides also conform to this distribution. Previous statistical analyses have shown that the mesoscale eddies are concentrated in the west of the Luzon Strait and the western boundary of the deep-sea basin. They are also distributed in the south of the north slope of the SCS and the middle of the deep-sea basin [25][26][27][28]. The errors of M2 and S2 error in the western Luzon Strait and the western boundary of the deep-sea basin (framed areas in Figure 2a) are larger than those in other regions, which is consistent with the significant area of mesoscale eddies in the SCS. Lower SNRs are also found in these regions ( Figure 3). The phenomenon is clearly mitigated, although did not disappear completely after MOV. Other tides also conform to this distribution.   Figure 4 shows the results of the amplitude difference (ΔH) before and after MVC (detailed distribution statistics are displayed in Table A1 in Appendix A). The distributions of the amplitude differences of eight major constituents conforms to a Gaussian distribution whose mathematical expectation is nearly zero, which indicates that, for most data points, the MOV has negligible effects on the results of the tidal harmonic analysis. The potential effects of the MOV should only be considered at a small number of points at which the MOV is strong. It was found that the influence of MOV has different effects on the estimation of the amplitudes of the eight main tides, although they are all mainly distributed within ±10 mm and most of them are concentrated within ±6 mm. The amplitude differences of N2 tides are small: the maximum and minimum amplitude differences are 8.4 and −8.3 mm, respectively. At about 64.81% of the total data points, the amplitude differences of N2 tides are between ±2 mm. The amplitude differences of K1 and M2 are the largest among the eight main constituents: at about only 35.56% (46.38%) of the data points, the amplitude differences of K1 (M2) are between ±2 mm, and at 22.31% (9.44%) of the data points, the amplitude differences of K1 (M2) are beyond ±6 mm, with a maximum value of 16.2 (15.2) mm and a minimum value of −16.8 (−17.9) mm.  Figure 4 shows the results of the amplitude difference (∆H) before and after MVC (detailed distribution statistics are displayed in Table A1 in Appendix A). The distributions of the amplitude differences of eight major constituents conforms to a Gaussian distribution whose mathematical expectation is nearly zero, which indicates that, for most data points, the MOV has negligible effects on the results of the tidal harmonic analysis. The potential effects of the MOV should only be considered at a small number of points at which the MOV is strong. It was found that the influence of MOV has different effects on the estimation of the amplitudes of the eight main tides, although they are all mainly distributed within ±10 mm and most of them are concentrated within ±6 mm. The amplitude differences of N 2 tides are small: the maximum and minimum amplitude differences are 8.4 and −8.3 mm, respectively. At about 64.81% of the total data points, the amplitude differences of N 2 tides are between ±2 mm. The amplitude differences of K 1 and M 2 are the largest among the eight main constituents: at about only 35.56% (46.38%) of the data points, the amplitude differences of K 1 (M 2 ) are between ±2 mm, and at 22.31% (9.44%) of the data points, the amplitude differences of K 1 (M 2 ) are beyond ±6 mm, with a maximum value of 16  Considering the fact that the eight major constituents have different magnitudes in amplitudes, the ratio (ΔH/H) of amplitude differences before and after MVC (ΔH) to the amplitude after correction (H) were derived, and this ratio was defined as the relative influence of the MOV on tidal estimation. Table 4 shows the maximum and minimum values of the relative influence acting on each tidal constituent. As the most important tidal constituents in the SCS, M2, O1, and K1 tides have average amplitudes of tens of centimeters, which can help to weaken the relative impact of the MOVs on themselves in the case of the same magnitude of amplitude difference. For example, in the case of the O1 tide, which benefits from a large amplitude, the relative influence of the MOV ranges from −3.12% to 5.59%, which is the least among all the tidal constituents. The extreme values of relative influence on the M2 (K1) tide are 12.97% (9.13%) and −7.43% (13.36%), respectively. The amplitude estimates of these three tidal constituents are least affected by the MOV in terms of the relative influence. As the tide with amplitudes of a few centimeters, the K2 tide has the maximum (95.99%) and minimum (−64.79%) ratio of amplitude difference to the average amplitude, indicating that the amplitude estimation of K2 tide is the most relatively affected by the MOV.  Considering the fact that the eight major constituents have different magnitudes in amplitudes, the ratio (∆H/H) of amplitude differences before and after MVC (∆H) to the amplitude after correction (H) were derived, and this ratio was defined as the relative influence of the MOV on tidal estimation. Table 4 shows the maximum and minimum values of the relative influence acting on each tidal constituent. As the most important tidal constituents in the SCS, M 2 , O 1 , and K 1 tides have average amplitudes of tens of centimeters, which can help to weaken the relative impact of the MOVs on themselves in the case of the same magnitude of amplitude difference. For example, in the case of the O 1 tide, which benefits from a large amplitude, the relative influence of the MOV ranges from −3.12% to 5.59%, which is the least among all the tidal constituents. The extreme values of relative influence on the M 2 (K 1 ) tide are 12.97% (9.13%) and −7.43% (13.36%), respectively. The amplitude estimates of these three tidal constituents are least affected by the MOV in terms of the relative influence. As the tide with amplitudes of a few centimeters, the K 2 tide has the maximum (95.99%) and minimum (−64.79%) ratio of amplitude difference to the average amplitude, indicating that the amplitude estimation of K 2 tide is the most relatively affected by the MOV. To further demonstrate the effect of MVC, we introduced the global ocean tidal model TPXO9 and FES2014 [29]. The TPXO9 tidal model was developed based on the Oregon State University Tidal Inversion Software (OTIS) and assimilates a large number of satellite altimetry data and tidal gauge observations. It is generally believed that, although the tidal constants provided by the TPXO9 model still have some room for improvement in coastal areas with complex topography and coastlines, the prediction of this model is extremely close to the actual values in the deep ocean [30]. The FES2014 is the newest global ocean tidal atlas, and aims to provide altimetry data with tidal de-aliasing correction. Due to the unstructured grid flexible resolution, recent progress in hydrodynamic tidal solutions, and use of the ensemble data assimilation technique, the FES2014 atlas shows extremely significant improvements in all ocean compartments, and particularly in shelf and coastal seas [31]. The effect of MVC can be evaluated by comparing the results of TPXO9 and the FES2014 with those of harmonic analysis of T/P-Jason data.

The Effect of MVC on the Estimation of Tidal Amplitude
The estimated tidal amplitudes on selected points at which the altimeter-based tidal estimates are most seriously affected by MOV are compared with those based on TPXO9 and FES2014 (Tables 5 and 6), and the locations of the selected points are shown in Figure 5. At most selected data points, altimeter-based tidal estimates are closer to the TPXO9 (FES2014) model after MVC. For example, the error rate of Q 1 tidal amplitude at 20.45 • N, 119.00 • E sharply decreases from 20.8% (18.6%) to 3.73% (1.1%). At 109.99 • E and 12.08 • N, the error rate of N 2 tidal amplitude sharply decreases from −30.93% (−26.0%) to −6.01% (−2.0%).
In general, the minor tidal constituents can be deduced by major constituents, which are called tidal inference. Inference is also used in satellite altimeter analyses when a constituent cannot be well determined due to either noise or aliasing problems [32]. The standard ratio routinely used in tidal inference calculations for P 1 to K 1 is 0.3309 and for K 2 to M 2 is 0.1270 according to the equilibrium tidal theory [33][34][35]. After accounting for the nearby diurnal free wobble (NDFW) resonance, P 1 /K 1 is expected to be approximately 0.3180 [36]. Figure 6 is a histogram of P 1 /K 1 and K 2 /M 2 in the SCS. Obviously, both before and after correction, the peaks are all close to their standard ratio, but in the corrected histograms, the results cluster more closely to the standard ratio. To further demonstrate the effect of MVC, we introduced the global ocean tidal model TPXO9 and FES2014 [29]. The TPXO9 tidal model was developed based on the Oregon State University Tidal Inversion Software (OTIS) and assimilates a large number of satellite altimetry data and tidal gauge observations. It is generally believed that, although the tidal constants provided by the TPXO9 model still have some room for improvement in coastal areas with complex topography and coastlines, the prediction of this model is extremely close to the actual values in the deep ocean [30]. The FES2014 is the newest global ocean tidal atlas, and aims to provide altimetry data with tidal de-aliasing correction. Due to the unstructured grid flexible resolution, recent progress in hydrodynamic tidal solutions, and use of the ensemble data assimilation technique, the FES2014 atlas shows extremely significant improvements in all ocean compartments, and particularly in shelf and coastal seas [31]. The effect of MVC can be evaluated by comparing the results of TPXO9 and the FES2014 with those of harmonic analysis of T/P-Jason data.
The estimated tidal amplitudes on selected points at which the altimeter-based tidal estimates are most seriously affected by MOV are compared with those based on TPXO9 and FES2014 (Tables 5 and 6  Through the above verifications, after MVC, the influence of MOV on altimeter-based tidal estimates is thought to have been successfully removed, and thus, the results are extremely close to the actual values.   Table 7 show the results of tidal phase difference (∆g) before and after MVC; detailed distribution statistics are displayed in Table A2 in Appendix A. The MOV has a distinct influence on the estimation of tidal phases of distinct constituents. The phases of M2 and O1 are the least affected by MOV, whose phase differences are mainly distributed within ±3°. The M2 (O1) tide has a maximum phase difference of 8.56° (2.95°) and the minimum is −3.51° (−2.36°). The distribution of the phase differences of the K2 tide is relatively dispersed, ranging from −176.27° to 86.46°, and most of these values are negative. Similar to the amplitude, the influence of MOV on the phase of K2 tides in the SCS is also much greater than that of other major constituents. Through the above verifications, after MVC, the influence of MOV on altimeter-based tidal estimates is thought to have been successfully removed, and thus, the results are extremely close to the actual values.  Table 7 show the results of tidal phase difference (∆g) before and after MVC; detailed distribution statistics are displayed in Table A2 in Appendix A. The MOV has a distinct influence on the estimation of tidal phases of distinct constituents. The phases of M 2 and O 1 are the least affected by MOV, whose phase differences are mainly distributed within ±3 • . The M 2 (O 1 ) tide has a maximum phase difference of 8.56 • (2.95 • ) and the minimum is −3.51 • (−2.36 • ). The distribution of the phase differences of the K 2 tide is relatively dispersed, ranging from −176.27 • to 86.46 • , and most of these values are negative. Similar to the amplitude, the influence of MOV on the phase of K 2 tides in the SCS is also much greater than that of other major constituents. Remote Sens. 2021, 13, x FOR PEER REVIEW 12 of 20   Figure 8 shows the spatial distribution of amplitude differences and phase differences before and after MVC of M2 and O1 tides in the SCS, respectively. The influence of MOV on altimeter-based tidal estimation is distinct in space. For these two tidal constituents, the common point is that the amplitude and phase differences increase significantly in the west of Luzon Strait (the extreme value appears at 20.68° N, 119.03° E). In addition, at the western boundary of the deep-ocean basin, the amplitude difference of M2 clearly increases, whereas the amplitude difference of O1 significantly decreases (the extreme value appears at 11.46° N and 111.36° E). Compared with the areas with high mesoscale eddy activities in the SCS mentioned above, we find that there is a certain overlap, which indicates that the altimeter-based tidal estimation is more vulnerable to the background noise when the mesoscale variability is strong.   Figure 8 shows the spatial distribution of amplitude differences and phase differences before and after MVC of M 2 and O 1 tides in the SCS, respectively. The influence of MOV on altimeter-based tidal estimation is distinct in space. For these two tidal constituents, the common point is that the amplitude and phase differences increase significantly in the west of Luzon Strait (the extreme value appears at 20.68 • N, 119.03 • E). In addition, at the western boundary of the deep-ocean basin, the amplitude difference of M 2 clearly increases, whereas the amplitude difference of O 1 significantly decreases (the extreme value appears at 11.46 • N and 111.36 • E). Compared with the areas with high mesoscale eddy activities in the SCS mentioned above, we find that there is a certain overlap, which indicates that the altimeter-based tidal estimation is more vulnerable to the background noise when the mesoscale variability is strong. Remote Sens. 2021, 13, x FOR PEER REVIEW 13 of 20

Influence of Mesoscale Variability on the Estimation of Tidal Evolution
In recent years, sea level rise related to global warming and human activities such as land reclamation have significantly altered the water depth and coastline, which further influences the propagation of tidal waves [37][38][39]. Numerous studies have shown that tidal amplitudes are not stationary in many regions around the world [40][41][42]. Flick et al. (2003) found that the tidal range in San Francisco increased by 64 mm from 1900 to 1998, whereas in Wilmington, N.C., tidal range was found to have increased by 542 mm per century from 1935 to 1999 using the National Oceanic and Atmospheric Administration (NOAA) long-term tide gauge data [43]. In 1990, Woodworth noted that the tidal range of 13 ports in the British Isles had trends ranging from −1.8 to 1.3 mm [44]. In 2010, he further noted that long-term tidal changes are common around the world based on quasi-global tide gauge observations [45]. In the past few decades, the research of tidal evolution has been conducted by analyzing tide gauge data, and few studies have been conducted using satellite altimeter data. Although sea level observations at tide gauges are long, they are limited to coastal areas. By contrast, satellite altimeter observations are wider in space, and have been accumulated for more than 20 years. Although it is feasible to study tidal evolution using satellite data, but the interference of MOV remains uncertain.
To explore the tidal evolution, we divided the T/P-Jason observations into two periods, which were bounded on 1 January 2005. Tidal harmonic analysis during the two periods was carried out on the T/P-Jason data before and after the correction (

Influence of Mesoscale Variability on the Estimation of Tidal Evolution
In recent years, sea level rise related to global warming and human activities such as land reclamation have significantly altered the water depth and coastline, which further influences the propagation of tidal waves [37][38][39]. Numerous studies have shown that tidal amplitudes are not stationary in many regions around the world [40][41][42]. Flick et al. (2003) found that the tidal range in San Francisco increased by 64 mm from 1900 to 1998, whereas in Wilmington, N.C., tidal range was found to have increased by 542 mm per century from 1935 to 1999 using the National Oceanic and Atmospheric Administration (NOAA) long-term tide gauge data [43]. In 1990, Woodworth noted that the tidal range of 13 ports in the British Isles had trends ranging from −1.8 to 1.3 mm [44]. In 2010, he further noted that long-term tidal changes are common around the world based on quasi-global tide gauge observations [45]. In the past few decades, the research of tidal evolution has been conducted by analyzing tide gauge data, and few studies have been conducted using satellite altimeter data. Although sea level observations at tide gauges are long, they are limited to coastal areas. By contrast, satellite altimeter observations are wider in space, and have been accumulated for more than 20 years. Although it is feasible to study tidal evolution using satellite data, but the interference of MOV remains uncertain.
To explore the tidal evolution, we divided the T/P-Jason observations into two periods, which were bounded on 1 January 2005. Tidal harmonic analysis during the two periods was carried out on the T/P-Jason data before and after the correction (H 1992∼2005 and H 2005∼2017 are the amplitudes before correction, H 1992∼2005 and H 2005∼2017 are the amplitudes after correction), and the amplitude differences between the two periods were Comparing the tidal ampli-tude changes before and after the MVC offers a glimpse of the effect of mesoscale variability on altimeter-based tidal evolution. Here, only the results of the four major tides, namely, M 2 , S 2 , K 1 , and O 1 are shown in Figures 9 and 10. It can be seen that the evolution of tidal amplitudes of the four constituents in some areas is abnormally significant before MVC. These abnormally large values are eliminated after MAC, which indicates that they are not real but induced by MOV.
By comparing the tidal evolution before and after the MVC, we conclude that there are a large number of artificial changes in the tidal evolution caused by MOV (Figure 11). Mesoscale variability significantly increases the number of spatial points with large temporal changes of tidal amplitude. In addition, the extreme values of the tidal changes in the SCS increase. For example, in the case of the K 1 tide, when the MOV is uncorrected, the maximum amplitude change of K 1 is 52.7 mm, and the minimum is −32.3 mm. After the MVC, the maximum and minimum amplitudes change sharply, decreasing to 23.2 and −11.0 mm, respectively ( Table 8). The mesoscale variability has a significant influence on the tidal evolution results. In some specific areas, the influence is large and the results without MVC cannot be trusted. . Comparing the tidal amplitude changes before and after the MVC offers a glimpse of the effect of mesoscale variability on altimeter-based tidal evolution. Here, only the results of the four major tides, namely, M2, S2, K1, and O1 are shown in Figures 9 and 10. It can be seen that the evolution of tidal amplitudes of the four constituents in some areas is abnormally significant before MVC. These abnormally large values are eliminated after MAC, which indicates that they are not real but induced by MOV.  By comparing the tidal evolution before and after the MVC, we conclude that there are a large number of artificial changes in the tidal evolution caused by MOV. Mesoscale variability significantly increases the number of spatial points with large temporal changes of tidal amplitude. Meanwhile the extreme values of the tidal changes in the SCS increase. Take K1 tide for example. When the MOV is uncorrected, the maximum amplitude change of K1 is 52.7mm, and the minimum is −32.3mm. After the MVC, the maximum and minimum amplitude change sharply decrease to 23.2mm and −11.0mm, respectively. The mesoscale variability has a significant influence on the tidal evolution results. In some specific areas, the influence is huge and the results without MVC cannot be trusted.  Figure 11. Histogram of amplitude change before and after the MVC based on T/P-Jason data.   Figure 11. Histogram of amplitude change before and after the MVC based on T/P-Jason data.

Tidal Evolution in the South China Sea
The selected data points are distant from the coast and mainly located in the deep-sea basin in the central part of the SCS; the water depth in the central deep-sea basin of the SCS is more than 2000 m, with the maximum depth reaching 5500 m. Therefore, the change of water depth caused by sea level rise has a limited impact on the tidal changes in this region. Located in the tropical monsoon climate zone, the sea water in the SCS has strong stratification [46]. It should also be noted that the SCS is one of the most active regions of internal tides in the world [47][48][49]. The points at which the temporal changes of K 1 (O 1 ) tidal amplitude exceed 25 (18) mm are marked in Figure 12. It is clear that these points are mainly located in the areas where the bottom topography is complex and the water depth changes sharply in space, which is conducive to the generation of the internal tides. Baroclinic energy conversion is highly related to the ocean stratification, which has an obvious long-term trend in the SCS due to global warming. Therefore, we think it is likely that the evolution of surface tides in this region is induced by the changing ocean stratification under global warming via baroclinic generation. A similar phenomenon occurs at Hawaii, where internal tides are also strong. Colosi and Munk (2004) noted that the long-term trend of M 2 tidal amplitude in this area was related to the response of internal tidal phase to ocean warming by analyzing the observations of multi-year tide gauge data [50]. likely that the evolution of surface tides in this region is induced by the changing ocean stratification under global warming via baroclinic generation. A similar phenomenon occurs at Hawaii, where internal tides are also strong. Colosi and Munk (2004) noted that the long-term trend of M2 tidal amplitude in this area was related to the response of internal tidal phase to ocean warming by analyzing the observations of multi-year tide gauge data [50].

Summary and Conclusions
The accurate extraction of tidal characteristics could be used to provide reliable predictions for future tides, which is important for coastal construction and shipping transportation. In addition, the demands for tidal information in the scientific community have

Summary and Conclusions
The accurate extraction of tidal characteristics could be used to provide reliable predictions for future tides, which is important for coastal construction and shipping transportation. In addition, the demands for tidal information in the scientific community have become more exacting in recent years. This paper provides a reference for experiments that need high-quality tidal constants.
The harmonic constants based on T/P-Jason satellite observations are usually mixed with the contributions of non-tidal components, and particularly the MOV. This paper quantifies the influence of the MOV on the satellite-based results of tidal harmonic analysis in the SCS for the first time, using the SLA product to extract pure tidal field. The results show that the effects of the MOV on different tidal constituents are distinct. In terms of the absolute influence, the N 2 tide is less affected, and the absolute amplitude differences (AADs) of 64.81% of data points before and after the MVC are within ±2 mm. In terms of the relative influence, the K 2 tide is the most affected by the MOV, mainly because the amplitude of the K 2 tide is less than 2 cm. The maximum and minimum AADs before and after the MVC account for 60.38% and −74.15% of the K 2 amplitude. As the largest tidal constituents in the SCS, the estimation of M2, K1, and O1 tides is not significantly influenced by the MOV.
For some areas with intense MOV in the SCS, particularly in the western part of the Luzon Strait, the south of the northern continental slope and the western boundary of the deep-sea basin, the tides are significantly disturbed by the MOV. It was also found that, in some regions, the rapid changes of tidal amplitudes are not genuine and are caused by the MOV. Therefore, the MVC must be performed in advance to obtain the real satellite-based tidal evolution.