# Sea Level Estimation Based on GNSS Dual-Frequency Carrier Phase Linear Combinations and SNR
## 1 Introduction  
As of 1997, about 37% of the global population was living within 100 km of a coastline [1] and that number is still increasing. Coastal areas also contain a significant concentration of the world's economic activities and urbanization. Climate change and related global warming are expected to cause sea levels to rise, forcing people to abandon certain coastal areas that may become submerged. Thus, accurate and effective monitoring of sea level change and its impact on social development is of vital importance. Since the nineteenth century, tide gauges (TG) have been used to measure global sea level changes by providing a relative measure with respect to land [2], but land motions around a land-based TG can result in inaccuracies in sea level measurements. Globally, there is also a decreasing number of TGs, thus limiting extensive sea level measurements. There is therefore a need for additional sea level monitoring techniques. Satellite radar altimetry is a powerful technique used for monitoring sea level changes [3] and studying circulation [4] in the open ocean. Radar altimetry provides high-precision sea surface topography data, but it often has poor precision in near-shore regions because of the complex and fast changing dynamics of the ocean in these areas [5; 6]. Moreover, it is unable to provideinformation on mesoscale phenomena, such as swell and waves, which need better spatiotemporal sampling [7]. Global navigation satellite system reflectometry (GNSS-R) was first proposed for use in ocean altimetry by [PERSON] in 1993 [8]. Over the last twenty years, this technique has been used to retrieve accurate sea surface heights from various ground-based and airborne platforms using an upward Right-Handed Circular Polarization (RHCP) antenna, a downward Left-Handed Circular Polarization (LHCP) antenna and a specialized receiver [9; 10; 11; 12; 13; 14]. Space-borne GNSS-R altimetry has been used to retrieve sea surface height (SSH) data with an accuracy of ~7.0 m using data from the British TechDemoSat-1 (TDS-1) satellite [15]. Both of these studies were conducted using a specialized setup, and most needed a customized GNSS-R receiver, which requires significant computing power and vast amounts of data for analysis. Another ground-based GNSS-R altimetry setup consists of only one upward antenna and one geodetic receiver, which is the same as the GNSS positioning application. It is known as the Interference Pattern Technique (IPT) and measures the power and phase fluctuations of the interference of direct and reflected electric fields as the GNSS satellite moves [16; 17]. Analysis of the multipath effect in GNSS observables allows the properties of the reflector surface to be inferred. [PERSON] et al. [18; 19] first proposed the positive use of multipath effects for retrieval of soil moisture data without modifying existing geodetic global positioning system (GPS) stations. Later, the same authors and [PERSON] et al. [20; 21] expanded the application to estimate snow depth and vegetation by analyzing the signal-to-noise (SNR) data from the geodetic receiver. Some other studies using GPS L5, L2P, and L2C signals with a dipole antenna have also been tested [22; 23; 24]. [PERSON] and [PERSON] [25] first used GPS to measure snow depth by using geometry-linear combinations of carrier phases, and then [PERSON] and [PERSON] [26] extended the combinations of carrier phases to GLONASS (Global Navigation Satellite System) signals for snow depth retrieval. [PERSON] et al. [27] proposed a new snow depth estimation approach using a linear combination of phase measurements of triple-frequency (L1, L2 and L5) GPS signals, because the inter-frequency ionospheric delay was contained in the dual-frequency phase combination. Monitoring of sea level change is another application of this GPS multipath method. Several researchers have concentrated on the SSH retrieval technique using SNR data [23; 24; 25; 26]. [PERSON] et al.