*4.2. Validations*

The MSSH model (shown in Figure 6) was called Model 1. The retracked SSHs by the 50% threshold retracker for the raw waveforms was also used to establish an MSSH model called Model 2. The fundament for both Model 1 and Model 2 was a seven-year (from 2002 to 2009) mean profile of Jason-1. The main difference between Model 1 and Model 2 was whether the SSA algorithm was used for noise reduction during data processing.

In order to validate the accuracy and reliability of the MSSH model established in the present study and whether SSA can effectively improve the accuracy of the MSSH model, Model 1 and Model 2 were compared in terms of SSHs with the CLS15 [26] and DTU18 [27] models in the South China Sea, respectively. CLS15 was published by the Collecte Localisation Satellites (CLS) and the French Centre National d'Etudes Spatiales (CNES), and DTU18 was released by the Technical University of Denmark (DTU). The fundament for CLS15 and DTU18 with a grid of 1 × 1 was a 20-year (from 1993 to 2012) mean profiles of T/P, Jason-1, and Jason-2. The difference between the MSS models depends on the dataset used for calculation and the data processing method [25].

**Figure 6.** Mean sea surface height (MSSH) model over the South China Sea from the SSHs of the SSA-denoised waveform retracking of Jason-1.

Model 1 (represented by M1), Model 2 (represented by M2), CLS15 (represented by C), and DTU18 (represented by D) were compared in terms of SSHs with each other, as listed in Table 4. The table shows that means of Model 1 and Model 2 compared with CLS15 and DTU18 were obviously systematic biases. These systematic biases were mainly caused by two reasons: The differences between the SSHs measured by different altimetry satellites, and the impact of the oceanic variability. Both CLS15 and DTU18 were established from multi-satellite altimeter data, and these data were adjusted to have the same reference ellipsoid and frame as T/P. However, there was a systematic bias between the SSHs measured by T/P and those measured by Jason-1 of about 10.86 cm in the South China Sea [28]. These four models have different reference time periods: The reference periods of Model 1 and Model 2 span from 2002 to 2009, while the reference periods of CLS15 and DTU18 span from 1993 to 2012. Moreover, the sea level in the South China Sea showed an upward trend, with an increase rate of about 4.25 mm/yr [28,29].

**Table 4.** Statistics on the differences between different MSS models (Model 1 and Model 2 were established using the retracked sea surface heights (SSHs) from the SSA + 50% threshold and 50% threshold retracker, respectively; M1 for Model 1; M2 for Model 2; C for CLS15; D for DTU18) (in m).


The STDs of Model 1 and Model 2 compared with CLS15 were much smaller than those compared with DTU18, and the differences of STDs among CLS15, Model 1, and Model 2 were within 1 cm of DTU18. This indicates the high-degree consistency among Model 1, Model 2, and CLS15, and the obvious differences from DTU18. The STDs of Model 1 were smaller than those of Model 2, compared with CLS15 and DTU18.

These four models were compared in terms of SSH in the open ocean and coastal region (i.e., ~10 km from land), respectively, and the results are listed in Table 5. The table shows that the STDs of Model 1 and Model 2 compared with CLS15 and DTU18 were 5~7 cm in the open ocean, whereas they rose up to the several decimeters in coastal region. Moreover, the STDs of Model 1 and Model 2 compared with DTU18 were almost twice of those compared with CLS15 in the coastal region. This indicates that DTU18 mainly di ffered from Model 1, Model 2, and CLS15 in coastal region, and it is assumed that this was mainly caused by the di fferences in the preprocessing of altimeter data. The STDs of the discrepancy between Model 1 and Model 2 were less than 2 cm in the open ocean and 3 cm in the coastal region. This indicates that these two models displayed more di fference in the coastal region. In addition, the STDs of Model 1 compared with the two models CLS15 and DTU18 were lower than those of Model 2 compared with the two, indicating that the accuracy of Model 1 was superior to that of Model 2.

**Table 5.** Statistics on the di fferences between di fferent MSS models (Model 1 and Model 2 were established using the retracked sea surface heights (SSHs) from the SSA + 50% threshold and 50% threshold retracker, respectively; M1 for Model 1; M2 for Model 2; C for CLS15; D for DTU18) in the open ocean and coastal region (in m).

