The altimetry satellite Jason-2 was launched on June 20, 2008. The main objective of Jason-2 is to measure ocean surface ensuring the continuity of the TOPEX/Poseidon and Jason-1 missions. Due to the improvements in the echo acquisition and tracking modes, the Poseidon-3 altimeter onboard Jason-2 maintained significantly higher data availability over land or mixed land-sea terrain in comparison with its predecessor Poseidon-2 onboard Jason-1 (Desjonquères et al., 2010). It guaranteed an additional goal of Jason-2, which is to provide measurements over coastal areas and inland waters.

For retracking, SGDR product should be used. The Jason-2 SGDR products (version d) are downloaded from Archiving, Validation, and Interpretation of Satellite Oceanography (AVISO, https://www.aviso.altimetry.fr). The dataset provides 1 and 20Hz sampling values. Waveforms contained in the dataset allow customized retracking for refining measurements. The dataset provides four kinds of ranges derived using different retracking strategies. One is the onboard operating tracker (hereafter referred to as “Raw”). The other three retrackers are MLE4 (4-parameter Maximum Likelihood Estimator), MLE3 (3-parameter), and ICE, respectively (Dumont et al., 2017).

The PISTACH products were developed by Collecte Localization Satellites (CLS) with support from CNES. PISTACH is dedicated to refining Jason-2 data over coastal regions and inland waters for coastal and hydrological applications. For this purpose, several new retracking algorithms were developed. A set of four alternative retracked ranges are provided in the PISTACH products. The four retrackers are ICE1, ICE3, RED3, and OCE3, respectively. Furthermore, the PISTACH products include several state-of-the-art geophysical corrections, e.g., wet tropospheric corrections and sea state bias corrections. More details about these retrackers are available in the PISTACH handbook (Mercier et al., 2010). These products can be accessed via AVISO ftp (ftp://ftp-access.aviso.altimetry.fr/pub/oceano/pistach).

The ALES Jason-2 dataset was produced by DGFI-TUM (Deutsches Geodätisches Forschungsinstitut Technische Universität München) and distributed via Open Altimeter Database (OpenADB, https://www.openadb.dgfi.tum.de). This dataset was a reprocessed product using the ALES retracker. This retracker selects part of each waveform by adapting its width according to the significant wave height and models the subwaveform with the classic Brown model by means of least square estimation (Passaro et al., 2014). A number of studied have validated that ALES has good performance over coastal areas (Passaro et al., 2014; Xu et al., 2018; Gómez-Enri et al., 2019; Birol et al., 2021). As well as PISTACH, the ALES product is used as a reference to evaluate the performance of the new retracking scheme proposed in this work.

Sea level measured by tide gauge is usually used to validate the altimeter-derived sea surface heights (SSHs). Tide gauge data used in this study are the Research Quality Data (RQD) at hourly resolution, achieved by UHSLC (University of Hawaii Sea Level Center) (Caldwell et al., 2015). The RQD is a final science-ready dataset with quality control, which can be downloaded from the ftp sever of UHSLC (ftp://ftp.soest.hawaii.edu/uhslc/rqds). Four stations equipped with float gauge were used for validation. The four stations are located at Los Angeles (United States), Cape May (United States), Funchal (Madeira Island), and Ko Lak (Thailand), respectively. The float gauge has an accuracy of several millimeters. Thus, the tide gauge data are preferred for validating altimeter-derived SSHs. However, each tide station has a unique local datum, and datum information of some stations are not given. Therefore, relative validation is frequently conducted by removing their mean values.

Figure 1 shows four test areas chosen to validate the upgraded strategy, which are same as those in Huang et al. (2017). One Jason-2 pass (red line) accompanied by a tide gauge station (white pentacle) nearby is used for each case. Cycle 1-252 altimeter data were used in this study. In each area, the coastal topography and ocean floor are very different from each other, representing different sea state and surface reflectivity. General information of these regions are tabulated in Table 1. In Los Angeles, the coastal topography is a 500 m high mountain. The along-track bathymetry within 10 km offshore varies from 0 to 600 m, which has a sharp slope within 4–6 km. The terrain in Cape May is very flat and low altitude and ocean water is very shallow. While the third case is near Madeira Island, where the coast is very steep and the bathymetry sharply drops by 2000 m within 4 km. In the last case, the coast terrain is smooth and water depth is shallow. However, the satellite track is very close to the coastline, which induces a great amount of noise in altimeter waveforms. According to the classification of waveforms in PISTACH, percentages of each waveform class within 20 km offshore are listed in Table 1. It clearly shows that serious waveform contamination occurred in each case, especially in the Ko Lak region.

SSH is the height of sea surface with respect to the reference ellipsoid. By altimetry, SSH can be determined by subtracting altimeter range from the altitude of the satellite. Ranges measured by the altimeter must be corrected for instrument effects, path delay in the atmosphere, and the nature of the reflecting sea surface. The resultant SSH is given by h = A l t − ( R + Δ R instr + Δ R atmos + Δ R ssb + Δ R dyn + Δ R retrack ) , (1) where h is the altimetry-derived SSH, Alt is the orbit altitude of the satellite, R is the altimeter range, and ΔR represents corrections for the range. The subscripts “instr,” “atmos,” and “ssb” indicate instrumental corrections, atmospheric corrections, and sea state bias (SSB) corrections, respectively. ΔRdyn is the correction for the dynamic response to atmospheric pressure. The last item ΔRretrack is an optional correction, which is applied only when retracking is implemented.

In general, instrumental corrections consist of the distance offset between antenna and center of gravity, USO (Ultra Stable Oscillator) frequency drift correction, internal path correction, Doppler correction, modeled instrumental errors correction, and system bias. For the Jason-2 SGDR products, all retracked ranges have been corrected for all instrumental corrections. It is noteworthy that the last three corrections are not included in raw ranges. They should be additionally counted if one makes use of the raw ranges or implements customized retracking processing. Atmospheric corrections consist of wet troposphere correction, dry troposphere correction, and ionosphere correction. Model-derived atmospheric corrections in SGDR are used in this study. The SSB and dynamic atmosphere corrections used in the study are retrieved from the PISTACH product, which is suggested in the previous study (Huang et al., 2017).

The main idea of waveform decontamination is identifying and amending anomalous samples in the waveform according to some preset criteria. The criteria have to be determined based on each echogram as no other a priori information can be available. The reference waveform, which is determined by averaging whole waveforms in the echogram, plays an important role in this procedure. It is shown that the migration of the leading edge of along-track waveforms will lead to misjudgment of contaminated gates due to improper selection of the reference waveform (Huang et al., 2017). In order to reduce the effect caused by the shift of the leading edge, a method is proposed to realign waveforms in the echogram (see Realignment of Waveforms). In addition, new algorithms are adopted for the detection and remedy of outliers (see Outlier Detection).

The internal variability in each cycle of the along-track SSHs with respect to the geoid can reflect the performance of various retrackers. Standard deviations (SD) of the differences between the retracked SSHs and the geoid are frequently employed to evaluate the variability (Hwang et al., 2006; Lee et al., 2010). Meanwhile, data availability is an important consideration. Generally, a good retracker should be capable to retrieve more valid data with the smaller SD. We hence introduced the ratio of the percentage of valid measurements to SD as an evaluation index (Wang et al., 2019), which is expressed as P S R i = p i σ i , (11) where p i is the percentage of valid measurements after retracking and the calibration procedure (a 3 σ de-outlier process), σ i is the SD (in meter) of the differences between the retracked SSHs and the geoid, and P S R i is the ratio for each cycle. Statistical results of the tests in four regions are presented graphically in Figure 3. The left panels show the SDs in all cycles for each retracker in 0–10 km zone. Corresponding PSRs are illustrated in the right panels. Table 2 summarizes the mean values of these evaluation indices. The best performing retracker in each case is highlighted in bold.

Obviously, the nonretracked (SGDR-RAW) SSHs are of poor quality, which is a common sense in coastal altimetry community. The Brown model-based retrackers, such as MLE4 and MLE3, do not perform well because they are developed for “clean” ocean waveforms. As observed in Figure 3, the SDs of ICE retracker are much smaller than those of other retrackers in SGDR, and its corresponding PSRs are relatively high indicating good data availability in the coastal area. These results are consistent with those reported previous studies (Kuo et al., 2012; Tseng et al., 2014; Huang et al., 2017). Validation at Ko Lak tide gauge station performed by Idris et al. (2020) also indicated that the ICE retracker is the best in the SGDR data. Compared with SGDR-ICE, PISTACH retrackers do not seem to bring significant improvement as expected. Although OCE3 achieves good accuracy, its percentage of valid measurements is very low. ICE3 and RED3 are also not as good as ICE1 in the four test areas. On average, ALES outperforms SGDR and PISTACH.

Threshold retrackers with different threshold levels are applied to RWs, MWs, and DWs separately. TR20 achieved much better results than TR50, implying that 20% threshold level is more suitable for retrieval of coastal data. It is reasonable because peaky noise extensively appearing in coastal waveforms may lead TR50 to overestimate the epoch. On the other hand, it can be seen in Figure 3 and Table 2 that the performance of the same retrackers when applying to DWs is apparently superior to that when applying to RWs and MWs. Among 16 retrackers, furthermore, DW-TR20 and DW-ICE1 got the largest PSR values, as well as the smallest SDs in all cases. The results show a strike effect of our upgraded decontamination algorithm on refining the coastal SSHs.

To explore how close to the shore valid SSH data retrieved by each retracker can reach to, we plotted along-track SSHs along with the EGM2008 geoid for all tracks used in this study and made a movie for each region for easy scanning. Figure 4 presents a plot as an example. Only the SSHs by seven retrackers with relatively high accuracy were illustrated in the plot, and arbitrary constants were added to each result for visual clarity. It shows that the DW-TR20 and DW_ICE1 retrackers can stably retrieve valid SSHs in the last 1 km stripe, while the other retrackers become unstable in 0–4 km zone. It is notable that some biased values appear in the SSHs by MW-TR20 at about 6–9 km. It might be attributable to null values in waveforms set by the old version of the decontamination algorithm (Huang et al., 2017).

Tide gauge provides independent sea level observations to validate altimeter-derived SSHs. In order to compare with in situ sea level, tidal corrections were excluded from the SSHs. Since tide gauge stations do not locate on the satellite track, geoid gradient corrections were applied to the SSHs. To avoid possible datum bias between altimeter measurements and gauge data, the mean value of each time series was subtracted. The RMSE value was calculated to show the mean error of retracked results compared with gauge data. Correlation coefficients (CCs) between altimeter-derived SSHs and gauge data were also computed. Statistical results within 0–20 km zone offshore for each retracker in the four test regions are demonstrated in Figure 5. In each panel, bars at the bottom represent RMSE values and CCs are illustrated as waterfalls on the top. The color denotes along-track distance to the coastline, changing from red to blue corresponding to the increase in distance from 0 to 20 km.

Figure 5 visually depicts that the accuracy of the altimeter-derived SSHs decreases when approaching to the coast. In 10–20 km coastal zone, most retrackers perform well keeping the RMSE value below 20 cm and CC higher than 0.9. However, within 10 km, the RMSE increases rapidly and the correlation decreases correspondingly. Remarkably, two retrackers (DW-TR20 and DW-ICE1) developed in this study show very robust performance. The two retrackers can consistently yield small RMSEs in 0–20 km coastal zone. Overall, the performance of various retrackers revealed in Figure 5 agrees well with the evaluation results in Evaluating the Variability of Along-Track SSHs.

Figure 6 presents an example of SSH time series within 20 km offshore near Ko Lak gauge station by several selected retrackers, which have relatively good performance in the coastal area. It is obvious that the results based on retracking denoised waveforms are better than those based on retracking raw waveforms. Comparing results of MW-ICE1 and DW-ICE1, we can conclude that the upgraded decontamination strategy made a great improvement. In this case, ALES achieved the smallest RMSE. The reason is due to the good efficacy of ALES in the zone beyond 7-8 km offshore. Enough high accuracy measurements in the farther zone can help to reject crude measurements in the very near coastal area by the de-outlier process during constructing the SSH time series. However, the efficiency of ALES dramatically declines within 8 km (Huang et al., 2017; Wang and Ichikawa, 2017), which can also be verified by results in Figure 5 and Table 2.

Focusing on the last several kilometers, we compared the performance of various retrackers within 4 km. The improvement percentage (IMP) was computed to assess the improvement over the nonretracked SSHs (Hwang et al., 2006). Statistical results are given in Table 3. We can observe that most retrackers yield large RMSE and small CC except DW-TR20 and DW-ICE1. On rare occasion, ALES has the minimum RMSE of 7 cm in the third case (Pass 61), where the percentage of Brown and Brown-like waveforms is more than 95% (see Table 1). However, its performance is much poorer than that of DW-TR20 or DW-ICE1 in other cases. It implies that the ALES retracker has a good ability to handle with the Brown-like waveforms, but it is not good at processing the more complicated coastal waveforms. It makes sense because the ALES retracker is based on the Brown model (Passaro et al., 2014). Evidently, the DW-TR20 and DW-ICE1 retrackers achieve the biggest improvement in accuracy in 0–4 km zone. Their IMP values are larger than 80% in all cases. It is indicated that our technique works well not only for the Brown-like waveforms but also for the extremely distorted waveforms.

It is ideal to minimize noise interference during waveform retracking. Traditional subwaveform technique works well in many situations by extracting the clean leading edge according to partitioning waveforms (Guo et al., 2006; Guo, et al., 2010; Idris and Deng, 2012; Yang, et al., 2012a; Passaro et al., 2014). However, this passive approach gets into trouble in near coast zone where waveforms are seriously distorted. The results in Table 2 and Table 3 illustrate that subwaveform-based retrackers such as ALES, RED3, and ICE3 are poor performing for the complicated waveforms. It can be attributed to the difficulty for determining the noise-free leading edge in this situation.

In another way, the decontamination technique which is developed to actively reduce noise in waveform has proved to be very effective for processing complex coastal waveforms (Tseng et al., 2014; Huang et al., 2017; Wang and Ichikawa, 2017). The core of this technique is how to locate polluted sampling gates and how to fix them. The strategy proposed in the current study is easy to implement and not time-consuming. By considering the issue of shifting of the leading edge and adopting gate-wise judging criteria, the new strategy improves the outlier detection procedure. This can be verified by comparing MW- and DW-retrackers. However, there is still no other sophisticated method for amending outliers except interpolation from neighbors. Furthermore, rounding off the offset derived by Eq. 2 during realignment might induce alignment error in individual cases, which may influence subsequent denoising. Small jaggies might appear in the along-track SSHs in this case, e.g., at 18 km in Figure 4. This effect can be eliminated by smoothing or downsampling into 1 Hz data.