**1. Introduction**

Satellite radar altimeters provide information on the Earth's surface by transmitting a series of radio-frequency pulses and recording their echo waveforms [1]. Satellite altimetry has been widely used in geodesy, geophysics, and oceanography [2]. Some satellite altimetry products have been obtained using satellite altimeter data, e.g., ocean tide models, gravity field models, and mean sea surface height (MSSH) models. Among them, the MSSH model is the time-averaged physical height of the ocean's surface [3] and is an essential and important parameter to support oceanographic and geophysical studies [4]. The accuracy of the MSSH model is affected by the quality of satellite altimeter data, as well as the theory and methods of data processing. With the improvement of satellite altimetry error correction theory and data processing methods [5], using waveform retracking to improve the quality of altimeter data has gradually become the key to improving the accuracy and application of altimeter data, especially in coastal regions [6].

Altimeter waveforms are usually contaminated due to land, island, sea reef, sea ice, seabed terrain, etc. If the extracted ranges from these corrupted waveforms are used, sea levels calculated from these ranges will be incorrect as well. Waveform retracking is a method to find the right tracking gate, cutting the midpoint of the leading edge from these corrupted waveforms to extract the actual ranges [7]. So far, the waveform retracking technique has developed a variety of retracking methods, which are mainly divided into two categories: One based on the empirical statistical properties of the waveform data, and the other based on fitting functional model [2,8]. These retracking methods can improve the quality of altimeter data, but the accuracy of the data still cannot meet the actual needs [9–11]. Besides, the noise information contained in altimeter waveforms is not considered during the process of waveform retracking.

Several altimeter waveforms are connected end-to-end to form a waveform series, which oscillates periodically with the number of the waveform samples (e.g., the waveform samples of Jason-1 are 104). The altimeter waveform can be regarded as composed of two parts: The main waveform information and the noise information. The main waveform information includes the thermal noise area, leading edge, and trailing edge of the altimeter waveform, while the noise information is caused by reflective surfaces such as land, sea, glaciers, etc. By performing singular spectrum analysis (SSA) on the waveform series, the noise information contained in altimeter waveforms can be reduced, so that useful waveform information is extracted.

SSA is a nonparametric method of time series analysis [12,13]. It can reduce noise information from time series containing noise and extract as much reliable information as possible [14,15]. This method has been widely used in meteorology, climatology, geophysics, and other fields [13]. Therefore, SSA can be used to decompose and reconstruct the waveform series, reduce the noise level in altimeter waveforms, and obtain SSA-denoised waveforms. Then, these SSA-denoised waveforms are reprocessed by the waveform retracking technique to improve the accuracy and application of altimeter data.

The goal of this work was to reduce the noise level in Jason-1 altimeter waveforms with SSA to improve the accuracy of Jason-1 altimeter data, and to validate whether SSA can effectively improve the accuracy of MSSH model over the South China Sea established from SSA-denoised waveforms retracking of Jason-1 data. The structure of the thesis is as follows: Section 2 mainly introduces the study area, the data used, and data processing methods; Section 3 involves the results; Section 4 presents MSSH model over the South China Sea established from SSA-denoised waveforms retracking of Jason-1 data and validates whether SSA can effectively improve the accuracy of MSSH model; and the main conclusions and perspectives are given in Section 5.

#### **2. Study Area, Data, and Data Processing Methods**

#### *2.1. Study Area and Data*

The area around the South China Sea, covering 0◦–25◦ N, 105◦–125◦ E, was selected as the study area. The South China Sea belongs to the western Pacific Ocean and is one of the three marginal seas in Asia. It is located at the intersection of the Eurasian plate, Indo-Australian plate, and Pacific plate. Covering an area of about 3.5 million square kilometers, it is the third largest sea in the world, following the Coral Sea in the South Pacific and the Arabian Sea of the Indian Ocean. With an average depth of 1212 m and the deepest point of 5377 m, the South China Sea is virtually surrounded by land, peninsulas, and islands. The South China Sea is linked in the northeast to the East China Sea and the Pacific Ocean through the Taiwan Strait; in the south to the Java Sea, the Andaman Sea, and the Indian Ocean through the Malacca Strait; and in the east to the Sulu Sea through the Bashi Strait. Located in the low-latitude region, the South China Sea has the warmest climate of all tropical deep seas of China, with a high surface water temperature (25 ◦C–28 ◦C), small annual temperature variation (3 ◦C–4 ◦C), year-round high temperature and humidity, and long summer without winter. It has a maximal salinity of 35‰ and tidal difference below 2 m.

Jason-1 was launched on 7 December 2001 and decommissioned on 1 July 2013, obtaining about 11.5 years of altimeter waveforms data [16]. These data were used in our study as listed in Table 1. The data, spanning from 2002 to 2013, are version E of sensor geophysical data records (SGDR) products (including the so-called measured 20-Hz waveforms) provided by Archiving, Validation, and Interpretation of Satellite Oceanographic Data (AVISO). The orbit of Jason-1 had three different phrases. From its launch, its orbit had the same ground tracks as TOPEX/Poseidon (T/P), which was

the first phrase. In mid-February, 2009 (cycle 262), Jason-1 assumed a new orbit midway between its original ground tracks, which was the second phrase. At the end of February and in early March 2012, it began a series of maneuvers to reduce the orbit on a geodetic orbit, which was the third phrase. In the former two phrases, Jason-1 performed exactly repeated mission (ERM) (the mission of the first phrase hereafter called ERM1 and the second phrase ERM2) with a cycle of 9.9 days. In the third phrase, Jason-1 performed the geodetic mission (GM), and its orbit was a drifting orbit with a cycle of 406 days and some sub-cycles of 3.9–10.9–47.5–179.5 days.


**Table 1.** Altimeter waveforms data of Jason-1 missions.

Figure 1 is the ground tracks map of Jason-1 in South China Sea. Figure 1a is the ground tracks map of ERM1 and ERM2, and Figure 1b is that of GM.

**Figure 1.** The ground tracks map of Jason-1 in South China Sea. (**a**) The ground tracks map of ERM1 and ERM2. The number 153 is the pass number, the green lines are the ERM1 ground tracks, and the blue lines are the ERM2 ground tracks; (**b**) the ground tracks map of the geodetic mission (GM).

#### *2.2. Data Processing Methods*

Jason-1 waveforms were connected end-to-end to form the waveform series (one pass corresponded to one waveform series), and the waveform series was denoised with SSA to obtain the SSA-denoised waveforms. Then, these SSA-denoised waveforms were retracked by a 50% threshold retracker to obtain the retracked sea surface heights (SSHs). The process of Jason-1 waveforms processing is shown in Figure 2.

**Figure 2.** Processing flowchart of Jason-1 waveforms.

#### 2.2.1. Singular Spectrum Analysis (SSA) Applied to Altimeter Waveforms

SSA constructs a multidimensional trajectory matrix for a waveform series and decomposes and reconstructs the trajectory matrix to extract signals that represent the main waveform information and noise information.

Assume that a waveform series consisting of *i* waveforms is *<sup>X</sup>*(*t*){*xt* : 1 < *t* < *N*}, *N* = *i* × 104 (104 is the number of waveform samples of Jason-1). SSA was used to denoise this waveform series, and the process was mainly divided into four steps [14,15]:
