The tide gauges used in this study are provided by three data agencies in Taiwan, namely, the Central Weather Bureau, the Water Resources Agency, and the Harbor and Marine Technology Center. Figure 1 and Table 1 display these 18 stations along the coast of Taiwan and one station at the Penghu offshore islet. The gauges have unsynchronized sampling intervals of 6 min, 10 min, or hourly. Although the start dates of the records used in this study vary, most of these tide gauges remained operational in 2015 (Table 1). To avoid the reduced accuracy of sea-level estimates, all gauges had at least 15 years of data [19,20]. Moreover, pre-processing of the raw observations was required to ensure that the data was free of external influences. The quality control included visual and statistical checks of the tide gauge time series. The daily values were calculated with a simple average of all available raw values in a day if <30% records in that day were missing. Likewise, the monthly values were calculated from the daily data with a simple average of all the available daily values in a month if <30% values in that month were missing (following the rule of quality control from the University of Hawaii Sea Level Center (UHSLC)). In addition, tide gauge stations were excluded if their valid records were less than 70% in a >15-year time span or included nonlinear vertical motion as compared with neighboring tide gauges and altimetric measurements.

Satellite altimetry has provided high-quality and global observations of sea surface heights since the early 1990s. It has been widely agreed that satellite altimetry provides a synoptic view of global ocean circulation and mesoscale variabilities. The along-track, time-delayed sea-level anomaly data used in this study were obtained from the Archiving, Validation, and Interpretation of Satellite Oceanographic (AVISO) data center, including TOPEX/Poseidon and Jason-1/2 (http://www.aviso.altimetry.fr/en/home.html). The AVISO data were processed with instrument, medium (ionospheric, wet, and dry tropospheric), and geophysical corrections (solid earth, polar, ocean and load tides, sea state bias, and inverted barometer correction). In order to combine it with tide gauge data to determine the vertical crustal motion at the tide gauges and the sea-level rise, the along-track altimetric data within 2° of each tide gauge location was utilized to generate monthly average time series using the weight from the square of the reciprocal of the distance. Given that sea-level trends are non-uniform around Taiwan [7], the along-track altimetric data were divided into the east coast (Pacific Ocean) and the west coast (Taiwan Strait) of Taiwan along the line of longitude 121° E, and we used altimetric data from the east or west part of Taiwan to compute the sea-level variations in combination with the tide gauges located along the east or west coasts.

To investigate the rate of sea-level change around Taiwan and how it is affected by low-frequency climate variability, two climate indices were used in this study. The Southern Oscillation Index (SOI) was selected to represent ENSO variability [21,22], which is based on the observed sea-level pressure differences between Tahiti and Darwin, Australia. Prolonged periods of negative SOI values indicate El Niño episodes, and positive values are associated with La Niña events. The other index is PDO, which is highly correlated with ENSO episodes but for a longer period. The PDO index is defined as the leading principal component of monthly sea surface temperature anomalies in the North Pacific basin (poleward of 20° N in 1900–1993), and the PDO index covering the period from 1948 to 2015 can be downloaded from the Joint Institute for the Study of the Atmosphere and Ocean, University of Washington (http://research.jisao.washington.edu/pdo/PDO.latest) [23,24]. We applied an eleven-month and five-year moving average for the SOI and PDO indices, respectively, to clearly describe the interannual characteristics of these two indicators.

Ocean tides, or astronomical tides, are caused by the changing positions of celestial bodies and result in the tidal periodicity phenomenon. Theoretically, ocean tides are composed of an infinite number of tidal constituents, but the main tidal constituents are usually applied to analyze local ocean tides. A number of studies have utilized the moving average method or harmonic analysis [25] to correct the tide gauge records for ocean tides. In this study, to avoid the influence of datum shift errors on the section of tide gauge records through the moving average method, harmonic analysis was applied to correct the effect of ocean tides in the tide gauge records. The original tide gauge records, TG, can be expressed as (1) T G ( t ) = a 0 + ∑ i = 1 m a i H ( t - t a i ) + b t + ∑ j = 1 n [ A j sin ( ω j t ) + B j cos ( ω j t ) ] , H ( t - t a i ) = { 1 , t ≥ t a i 0 , t < t a i where a₀ and b are the bias and the rate of relative sea-level change, respectively. a_j is the ith datum shift in the tide gauge records, and H is a step function. The amplitudes, C_i, for a particular tidal constituent frequency, ω_j, can be derived from the combination of sine and cosine amplitudes, A_j and B_j ( C i = ( A j 2 + B j 2 ) 1 / 2 ). ω_j represent the major tidal constituent frequency (n = 37), including eighth-diurnal constituents (M8), sixth-diurnal constituents (M6 and S6), quarter-diurnal constituents (MN4, S4, M4, and MS4), third-diurnal constituents (M3, MK3, and 2MK3), semi-diurnal tides (M2, S2, N2, K2, L2, T2, R2, MU2, NU2, 2N2, LAM2, and 2SM2), diurnal tides (K1, O1, P1, Q1, OO1, S1, M1, J1, RHO1, and 2Q1), the long-term tides (Mm, MSf, and Mf), and the annual term Sa and semi-annual term Ssa [26]. In this study, the unknown coefficients in Equation (1) were estimated by the least squares method. Then, we removed the fitted ocean tides, excluding the annual and semi-annual signals, from the tide gauge records.

The effect of atmospheric pressure loading is evident in the global ocean, except for in the tropics and the western boundary current extension regions [27]. Therefore, we aimed to correct the IB effect on tide gauge records in this study. The IB effect can be expressed as IB = −9.948 × (P_atm − P)(2) where 9.948 is a scale factor derived from the theoretical value at mid-latitudes [28,29], P_atm is the sea surface pressure, and P is the monthly average sea-level pressure obtained over the global ocean. To correct the IB effect on tide gauge records, we used the global monthly mean sea-surface pressure field during the period from 1979–2015 with a spatial resolution of 0.75° × 0.75° from the European Centre for Medium-Range Weather Forecasts (ECMWF) [30] (downloaded from http://www.ecmwf.int/). Considering the discrepancy of temporal sampling—6 min, 10 min, or hourly for the tide gauge data and six-hourly for the sea-level pressure field—from the ECMWF, the daily means of the sea-level changes and the sea surface pressures were computed from the tide gauges and the ECMWF data, respectively, to correct the IB effect on tide gauge records. Several studies indicate that IB effect has to be corrected in tide gauge records [27,29,31], and it mainly influences seasonal sea-level variations (annual and semi-annual cycles) [31,32]. Therefore, daily data is dense enough to capture IB influences. In addition, the ECMWF sea-surface pressure data used in this study have been compared with the in-situ observed pressure data from the Central Weather Bureau of Taiwan, and both agree well (not shown here).

The tide gauge stations measure sea-level heights accurately relative to a nearby geodetic benchmark (local datum), but the tide gauge records could contain uncorrected datum shifts that will affect sea-level trend determination because of natural disasters, human errors, or poor maintenance. However, the agency responsible for managing tide gauge stations does not provide the supporting documentation showing the maintenance dates for instrument repair or replacement. Therefore, all tide gauge records have to be carefully checked for possible datum shifts.

The data used for datum shift detection are the differences between two records in two consecutive time periods (from one month to the previous in each of the tide gauge time series) [33]. However, multiple jumps could appear in the differences because of strong seasonal variations (annual and semi-annual) in the sea-level induced by monsoons and thermal expansion or sporadic storm surges (e.g., typhoons). Therefore, a two-step process was applied to the tide gauge records. The first step was to remove the seasonal signals in the monthly tide gauge time series through a six-parameter regression analysis (bias, trend, annual, and semi-annual terms) as depicted in Figure 2a (purple curve). The second step was to analyze the non-seasonal variations of the tide gauge data through the multiresolution analysis method [34,35]. Multiresolution analysis based on wavelet theory aims to remove high-frequency signals from the monthly tide gauge data. The multiresolution analysis method includes two important parameters, namely, wavelet functions, ψ , and scaling functions, ϕ which are used to find the signal details and approximations, respectively. We represent the tide gauge records, f, as an orthogonal series with ψ and ϕ (3) f ( t ) = ∑ k c j 0 ( k ) 2 j 0 / 2 ϕ ( 2 j 0 t − k ) + ∑ k ∑ j = j 0 ∞ d j ( k ) 2 j / 2 ψ ( 2 j t − k ) where t is the time, and c and d are the coefficients of low- and high-pass filters, respectively, which are computed using the discrete wavelet transformation [34,35]. j and k are the dilation and translation parameters. j = j₀, j₀ + 1,…, J − 1 and j₀ and J are the coarsest and finest levels, respectively.

Multiresolution analysis is used to numerically decompose and reconstruct a signal. We applied the Haar wavelet to decompose the tide gauge data down to the third (j = J − 3) or fourth (j = J − 4) level depending on the length of the tide gauge data and then to reconstruct the denoised, nonseasonal tide gauge data (red curve in Figure 2b).

The reconstructed low-pass data were then used to calculate the differences between the two adjacent times (one month to the previous in each of the time series). A difference larger than 50 mm was automatically considered a suspected datum shift (green stars in Figure 2c). To discover the actual datum shifts from the suspected datum shifts derived from the previous step, we averaged the two-year records before and after the epoch of the suspected shift using the deseasonal data (purple curve in Figure 2a) and calculated the difference of these two means. If the difference was significantly larger than 100 mm (the threshold), then the jump was considered a datum shift (star in Figure 2d). If the difference approximated 100 mm, then the data were compared with the neighboring tide gauges and altimetric data for a double check. To get the two threshold values mentioned above, we analyzed sea-level variations around Taiwan derived from the along-track altimetric data by using the same procedure of datum shift detection applied to the tide gauges.

The vertical land motion at the tide gauge stations was determined by a classic approach using the differences of altimetric and tide gauge data [19,36,37], which is expressed as: (4) u ( λ , φ , t ) = a l t ( λ , φ , t ) − T G ( λ , φ , t ) where u is the vertical land motion; alt is the altimetric data; TG is the tide gauge records; λ and ϕ are the latitude and longitude, respectively; and t is time.

The vertical motion and datum shifts are then estimated by fitting a linear regression as follows: (5) u ( t ) = a 0 + ∑ i = 1 m a i H ( t - t a i ) + b ′ t H ( t - t a i ) = { 1 , t ≥ t a i 0 , t < t a i where a_o and b ′ are the bias and the rate of vertical motion, respectively; a_i is the ith datum shift (m: the number of datum shifts); and H is the step function.

On the southwestern coast of Taiwan, vertical ground motions could be significantly larger than neighboring sea-level variations because of a number of geophysical processes and human activities, such as groundwater pumping [12,13]. Vertical land motions have to be corrected in tide gauge records to obtain the absolute sea-level changes. In previous studies, e.g., [12,38], glacial isostatic adjustment (GIA) models, leveling, and GPS observations were used for vertical motion correction. However, leveling and GPS measurements are unavailable at all tide gauges in Taiwan, and the magnitude of the GIA effect around Taiwan is about 0.1 mm/yr and is negligible [39], because the effect is much smaller than the realistic motions due to other geophysical processes [40]. Tide gauge records contain vertical land motions and absolute sea-levels, whereas satellite altimeters observe geocentric sea-level changes only. Therefore, the vertical land motions at the tide gauge stations can be estimated by the classic approach as expressed previously in Equations (4) and (5) using a combination of the altimetric and tide gauge data [19,36]. Then, we used the estimated land motion rates to correct tide gauge records to determine the absolute sea-level rise.

A total of 199 continuous GPS observations covering 2002–2012 were used to validate our estimates of vertical land motion (updated from Ching et al. [13]). The GPS stations were selected as closely as possible to the tide gauge sites, and the threshold of the distance between the tide gauge and the continuous GPS station was set at 1 km (Table 1).

Our processed Keelung and Kaohsiung tide gauge records were compared with those from the UHSLC data to evaluate our data processing. The Kaohsiung tide gauge records agree well, but the Keelung data show a discrepancy from 1999–2001 and 2003–2005 because of large data gaps. The sea-level trends determined using tide gauges with different geophysical and datum corrections in 1993–2015 are displayed in Table 2. The sea-level trends derived from the original data with or without ocean tides and IB corrections have no significant trend differences, which are in the ranges of −0.9–0.8 and −0.6–0.4 mm/yr, respectively, and are nearly smaller than or equal to the average standard deviation of the trend of 0.8 mm/yr. The average trends changed from 5.9 to 8.7 mm/yr when the datum shift was applied to the tide gauge data and from 8.7 to 2.2 mm/yr when the land motion was corrected. The standard deviation of the trends reduced to approximately 0.5 mm/yr. This result implies the significant contributions of datum shift and vertical land motion corrections to sea-level change around Taiwan. The relative sea-level trends corrected for datum shifts are geographically nonuniform. Higher rates of relative sea-level trends (>20 mm/yr) appear in southwest Taiwan (Table 2), which may be associated with land subsidence (discussed later). After all the corrections were applied (including ocean tides, IB, datum, and vertical land motions), the absolute sea-level trends around Taiwan using the tide gauge data covering 1993–2015 show a range from −0.5 to 3.7 mm/yr (Table 2).

To illustrate the contributions of each geophysical and datum correction to sea-level variations around Taiwan, the absolute value of trend differences after the different corrections was calculated and is presented in Figure 3. The ocean tides change the sea-level trends in the range of 0–0.9 mm/yr, with a mean of 0.2 mm/yr, and the effect of the IB change ranges from 0.1 to 0.6 mm/yr, with a mean of 0.3 mm/yr. The results indicate that ocean tides and IB have a slight impact on sea-level trends around Taiwan, as determined by the tide gauges, constituting approximately 9% and 14% of the observed trend, respectively. The datum shift has a significant impact on sea-level trends as derived from the tide gauges at 0.4–39.5 mm/yr, with an average trend of 7.3 mm/yr; the vertical land motions contribute to the regional sea-level trends in the study area with a range of 0.4–31.0 mm/yr, with an average trend of 8.0 mm/yr (Figure 3). These values are significantly larger than the global mean sea-level rise of 3.2 ± 0.1 mm/yr [1] derived from satellite altimetry for 1993–2012, thereby indicating that they have to be considered when calculating absolute sea-level trends around Taiwan from tide gauge data.

Vertical motion correction is crucial in the Taiwan region because vertical motions along the southwestern and northeastern coasts of Taiwan are larger than sea-level trends [13]. The results of the estimated vertical motions for each station are illustrated in Figure 4. The results are geographically nonuniform. In the eastern area of Taiwan, the estimated vertical land motion trends indicate a range of −6.2–4.2 mm/yr; the maximum subsidence trend of 6.2 mm/yr is from the Hualien tide gauge data, where subsidence was observed at 10 mm/yr relative to Hualien City, using the space-borne synthetic aperture radar interferometry method for 2004–2008 [41]. The discrepancy between our result and the result from a previous study [41] may be caused by the observations covering different time periods. Significant subsidence was observed at the tide gauges in the western area of Taiwan, especially in the southwestern area of the Boziliao, Dongshi, and Wengang tide gauge sites, with rates of 23.5–31.0 mm/yr (Figure 4; see Supplementary Material for details about the Dongshi tide gauge records). This strong subsidence was also confirmed by GPS observations around Taiwan [13]. The southwestern plains of Taiwan are highly developed agricultural and fishery areas. Thus, land surface elevation falls gradually because of groundwater pumping in the southwestern plains [13,42].

In Figure 4, the GPS and altimeter–tide gauge derived results agree well, and both results indicate land subsidence. The mean of the trend differences between the GPS and the altimeter-gauge derived vertical motion trends is 1.3 ± 2.8 mm/yr. The large standard deviations may be caused by the rare validation of GPS data. In Figure 4, the estimated vertical motion trend in Houbihu has a large discrepancy compared with the GPS velocity, which may be caused by the distance between the two stations at 0.23 km, and such an area could produce locally significant rates of vertical deformation [13].

The rates of absolute sea-levels around Taiwan from the tide gauge and satellite altimeter data for 1993–2015 are presented in Table 1. All tide gauge rates presented in this study agree well with the satellite altimeter. In 1993–2015, the average of the absolute sea-level trends around Taiwan derived from all coastal tide gauge data is 2.2 mm/yr, which is identical to the rate of 2.2 ± 0.3 mm/yr from the altimeter data covering the same time span within the latitude of 21–26° N and longitude of 119–123° E (Table 1). These regional rates are significantly lower than those estimated from the altimeter data (5.0 mm/yr from Tseng et al. [8]) for 1993–2007 and also slightly lower than the observed global mean of 3.2 ± 0.1 mm/yr during the period from 1993 to 2012 [1]. In Figure 5, it can be seen that the mean sea-level around Taiwan decreased significantly in 2014–2015. Thus, this discrepancy might have resulted from the different time periods for calculating the rates. In addition, comparing our estimates with the results of Feng and Tsimplis [10] indicates the trends derived from the tide gauges are 2.0–14.1 mm/yr with an average trend of 6.0 mm/yr from 1954 to 2012, the large discrepancy might have resulted from the uncorrected vertical land motion in tide gauge records and the data used covering different time spans.

Interannual sea-level variability is related to ENSO and PDO around Taiwan [43,44]. Figure 5 shows the interannual sea-level variability around Taiwan, derived from altimeter data that has been smoothed with an 11-month running mean, and overlaid with the low-pass filtered SOI and PDO (smoothed with the 11-month and five-year running mean, respectively). The sea-level anomalies around Taiwan present an increasing trend from 1993 to 2013, but an obvious decreasing trend after 2013, occurring when the PDO (SOI) index exhibits a negative (positive) trend. The comparison between the sea-level change and the SOI and PDO indexes implies that the interannual sea-level variability around Taiwan is highly correlated with the SOI and PDO (with a correlation coefficient of 0.55/−0.58). Both the SOI and PDO are associated with changes of sea-level pressure, trade winds, and ocean temperature. The IB effect has only a minor impact on sea-level trends around Taiwan, whereas the sea-level changes in the Western Pacific Ocean are mainly driven by trade wind and seawater density variations caused by ocean temperature and salinity changes, which increase when the SOI or PDO index manifests a positive or negative trend, respectively, and vice versa [45,46,47]. The absolute sea-level trend derived from the altimeter data covering 1993–2013 is 2.8 ± 0.4 mm/yr, while the rates decrease to 2.2 ± 0.3 mm/yr for 1993–2015. The difference between the regional rates of the sea-level rise during the two periods is 0.6 mm/yr, which is tested to be statistically significant at 90% confidence level. This result means that low-frequency variability strongly influences the regional sea-level around Taiwan, and the trend is mainly influenced by the PDO phenomenon, because the 10–30 study data span is longer than the data span of the altimeter [23]. The PDO shows a negative trend for 1993–2012, but a significantly positive trend after 2012 (Figure 5). Therefore, the PDO may undergo a phase shift as shown in Figure 5 [48], leading to lower sea-level trends around Taiwan in the next few decades. In addition, the 18.6-year nodal tide is not included in the harmonic analysis in this study, because it is not corrected in the AVISO altimetric data that was used and it would be small, especially in middle-latitude areas [49,50]. Cherniawsky et al. [49] indicated that the observed amplitudes of the 18.6-year nodal tide are about 1.5–3.5 cm, but theoretical amplitudes are less than 1 cm everywhere, suggesting that the difference results from part of the broad-band decadal ocean variability. In Taiwan, the amplitude of the 18.6-year nodal tidal cycle is about 3 mm [50]. We simulated the influence of the 18.6-year nodal tide with an amplitude of 3 mm on trend analysis when the time series cover 15 years and 19 years. Results show trend changes of 0.5 mm/yr for a 15-year time series and 0.2 mm/yr for a 19-year time series, showing that this effect would be small when the records span a couple of decades [50]. In this study, 74% of the gauges we used cover a time span longer than 19 years.