# Performance Analysis of Ocean Surface Topography
## 1 Introduction  
Under the influence of ocean tides, eddies and bathymetry variety, ocean surface topography (OST) changes at a global level [1; 2]. Satellite radar altimetry has been utilized for over three decades since the first spaceborne radar altimeter on geodetic satellite (GEOAT)to acquire high precision OST. Now the latest Poseidon-3B on Jason-3 can achieve a 2-cm precision [3]. The altimeter sends special shaped pulse to the nadir point and times the round trip delay to measure the ocean surface height. The pulse size projected on the ocean surface, also referred to as a footprint, decides the swath width and resolution of the altimeter, which is usually on the order of 2-10 km [4], as shown in Figure 1. An altimeter is none-imaging radar, it only measures one-dimensional OST along the satellite track. It is difficult for an altimeter to map mesoscale or sub-mesoscale (15-300 km) oceanic processes, since a 200-300 km gap usually exists between two successive tracks. Therefore, an altimeter is normally used to study large-scale (>300 km) oceanic processes [5]. In recent years, there has been a growing demand for scientific research on mesoscale and sub-mesoscale oceanic processes, such as eddies and currents [6; 7]. Interferometric synthetic aperture radar (InSAR), which is capable of measuring OST with high precision and a wide swath, is expected to be the next generation of satellite altimeter. InSAR has been successfully used to map terrain elevation, and the Shuttle Radar Topography Mission (SRTM) is one of the most typical examples [8]. InSAR altimetry is performed by acquiring two synthetic aperture radar (SAR) complex images of the same region during the single pass or repeat pass of the satellite [9]. Topography change is then recorded by the interferometric phase, which is the phase difference between two SAR complex images [10]. Different from terrain elevation measurement, ocean surface height changes randomly, hence two SAR antennas should be borne on satellites to acquire the images simultaneously. Moreover, OST altimetry demands centimeter-level precision, which is far beyond the capability of current InSAR systems. Therefore, several key parameters of InSAR need to be adjusted to fulfill the stringent requirements, which include near-nadir incidence, long physical baseline and short radar wavelength, and near-nadir incidence is the most distinctive characteristic from any other existing InSAR systems. Near-nadir InSAR is imaging radar; by using a pulse compressing technique, the image resolution is about a few meters, which is much smaller than its swath, as shown in Figure 1. Therefore, near-nadir InSAR can be used to measure surface water (lakes, rivers, wetlands, etc.) as well [11]. The wide-swath ocean altimeter (WSOA) is the first near-nadir InSAR proposed by National Aeronautics and Space Administration (NASA), and its two antennas work at Ku-band and form a baseline of 6.4 m. The incidence ranges from 0.6\({}^{\circ}\) to 4\({}^{\circ}\), and a 5-cm precision is expected on a 15 km grid [12; 13]. However, due to the technical limitations at that time, WSOA was finally canceled. The Surface Water and Ocean Topography (SWOT) mission, a collaboration between NASA and Centre National d'Etudes Spatiales (CNES), draws from the heritage of WSOA. KaRIN, as its main instrument, is a Ka-band near-nadir InSAR. A 10-m boom links its antennas to guarantee that the baseline is long enough to achieve a 3-cm precision on a 1-km grid. SWOT is planned to be launched in 2021 [5]. CNES carried out a series of airborne near-nadir InSAR experiments on surface water measurement to imitate SWOT performance [14; 15]. [PERSON] [16] reported that the surface water was severely influenced by layover effect from its surrounding landscape because of the near-nadir incidence. Nevertheless, due to high land/water contrast, which was about 10-20 dB, the layover could be mitigated to some extent. [PERSON] et al.