Sea level monitoring is vital for applications such as urban planning and climate studies. Traditional tide gauges, which often use radar measurements, remain the most common method but require placing sensors near the water surface, exposing them to potential damage in hostile maritime environments.
The demand for precise and high-frequency sea level monitoring has led to the development of innovative techniques, including Global Navigation Satellite System Reflectometry (GNSS-R). This promising method enables continuous, global sea level measurements (e.g., Larson et al., 2013) without the limitations of traditional sensors such as underwater (pressure gauges), in contact (float gauges), or above-surface (acoustic and radar). Furthermore, it takes advantage of the high availability of existing GNSS installations around the globe, potentially expanding the scope of tide gauge measurements on a global scale.
GNSS-R measurement methods are typically based on the analyze of the Signal-to-Noise Ratio (SNR) and most of the applied methods are using spectral analysis, such as Lomb-Scargle periodograms, to achieve centimeter-level accuracy in average sea level estimation (Larson, Ray and Williams, 2017). However, these methods require long SNR time series, limiting their ability to capture high-frequency sea level variations. This as the effect to restricted spectral methods to observing slow sea level variations, such as tides. Recent advancements have demonstrated that Kalman filtering can achieve sub-5 cm accuracy while increasing data sampling rates (e.g., Santamaría-Gómez and Watson, 2017; Strandberg, Hobiger and Haas, 2019; Liu et al., 2023).
We present a novel approach to enhance the accuracy and temporal resolution of sea level observations from SNR analysis, using an Extended Kalman Filter (EKF) to estimate SNR oscillation frequency and amplitude. The main advantage it to abble to ofer a flexibility to select the sampling rate of the resulting time series, allowing sea level estimates at rates up to the original SNR measurement frequency.
Our approach integrates data from all available GNSS constellations and carriers, improving data redundancy and robustness, particularly during signal loss or satellite transitions. Additionally, we apply a correction for phase center offset (PCO) variations, specific to each carrier and antenna model. This ensures that the resulting water height time series is referenced to a precise physical point, the Antenna Reference Point (ARP).
We validated our method by reconstructing a year-long sea level time series at Brest, France, with a 10-second sampling interval. We finally achieved a root-mean-square-error (RMSE) of 2.6 cm compared to the data of a co-located radar tide gauge. Similar performance was observed at other sites, with sampling rates as high as 1 second. Furthermore, the algorithm's ability to track irregular and unpredictable sea level variations beyond tidal models was evaluated during 10 days of observation at Cedar Key (Florida, USA) during Hurricane Milton. The resulting water height time series showed an RMSE of 1.9 cm compared to the data of a co-located tide gauge, demonstrating the method's efficiency under complex hydrodynamic conditions.