## 4 Retrieval of Sea Surface Height
### Retrieval of Sea Surface Height Using Carrier-Phase Measurement  
Carrier-phase delay altimetry, referred to as carrier-phase altimetry (CaPA), measures the phase delay of signals by analyzing the reflection of satellite signals on the sea surface. This technology has been widely used in positioning systems such as GPS and has been implemented on ice sheets [105], sea ice [23; 105], and lakes [24]. A change in sea surface height can cause a change in the phase of signal reflection, thus inferring the height information of the sea surface. Unlike code delay height measurement, using spaceborne GNSS-R carrier-phase delay to measure sea surface height can achieve a high-precision measurement of sea surface height (up to the centimeter level). However, there is currently little research on using spaceborne GNSS-R raw IF signals for carrier-phase height measurements of sea surface. The main limitation is that carrier-phase height measurement is limited by the coherence of reflected signals, and the sea surface follows a scattering mechanism. Therefore, this method can only be applied to nearshore and calm sea surface areas, except for observations made under very tilted geometric shapes, as previous studies have shown that very high incident angles can effectively reduce the actual roughness of the sea surface [43; 105]. [PERSON] et al. [106] used carrier waves to observe GNSS signals and established a linear relationship between the Doppler residual values, thereby deriving the deviation of sea surface height and promoting the accuracy of sea surface height retrieval. It has been proposed that observation under very tilted geometric conditions can effectively reduce actual roughness. [PERSON] et al. [100] obtained GNSS data from a flight at an altitude of 3500 m in the open sea, indicating that in the height measurement results, the elevation angles with centimeter precision for the eight orbits are between 11\({}^{\circ}\) and 33\({}^{\circ}\). However, these studies were conducted at low speeds and low altitudes. In order to evaluate the feasibility of sea surface carrier-phase altimetry for spaceborne GNSS-R, [PERSON] et al. [43] first achieved grazing angle carrier-phase sea surface altimetry with a centimeter-level altimetry accuracy. This study used the raw dataset collected by CYGNSS to investigate the accuracy of the system at different frequencies of sampling, achieved through GPS and Galileo signal transmission, and found that the accuracy of the measurement results at 20 Hz downsampling could be compared to professional radar altimeters. But this technology can only be applied under certain relatively calm water surface conditions to obtain sufficient coherence signals for CaPA measurement. Recently, the literature [46] reviewed the BuFeng-1 GNSS-R mission, which used a 20 Hz carrier-phase measurement of sea surface height from BF-1 raw IF samples. The results showed that, compared with DTU MSS products, its evaluation accuracy was in the order of 5 cm. However, elevation angle and sea surface roughness can greatly affect the carrier-phase height measurement of GNSS-R. Studies have shown that carrier-phase height measurement with this accuracy can only be achieved under water surface conditions with wind speeds of less than 6 m/s and waves of less than 1.5 m [43; 107]. In addition to using carrier-phase height measurement on the sea surface, recently, spaceborne GNSS-R raw IF data has also been utilized for river slope carrier-phase measurement. River slope is the gradient of river water surface elevation with respect to the geoid. [PERSON] et al. [108] focused on introducing river widths greater than 500 m using CYGNSS and Spire grating-angle GNSS-R raw IF data. Their experimental results showed that on an ideal 5 km river section at a 30\({}^{\circ}\) elevation angle, the total uncertainty was approximately 0.38 cm/km. This study demonstrates the potential application of carrier-phase height measurement. Figure 7 shows the flow chart of coherent GNSS-R signal carrier-phase-based altimetry retrieval.