Sea level time series and ocean tide analysis from multipath signals at five GPS sites in different parts of the world

Abstract

We present sea level observations derived from the analysis of Signal-to-Noise Ratio (SNR) data recorded at five coastal GPS sites. These sites are located in different regions around the world, both in the northern and the southern hemisphere, in different multipath environments, from rural coastal areas to busy harbors, and experience different tidal ranges. The recorded SNR data show periodic variations that originate from multipath, i.e. the interference of direct and reflected signals. The general assumption is that for satellite arcs facing the open sea, the SNR variations are due to reflections off the sea surface. The SNR data recorded from these azimuth intervals were analyzed by spectral analysis with two approaches, a simple analysis approach assuming static sea level during a satellite arc, and an extended analysis approach that involves a time dependent sea level during a satellite arc. The GPS-derived sea level results were compared to sea level records from co-located traditional tide gauges, both in the time and frequency domain. The sea level time series are highly correlated with correlation coefficients on the order of 0.89 − 0.99. The root-mean-square (RMS) differences are on the order of 6.2 cm for stations with low tidal range (up to 165 cm) and 43 cm for stations with high tidal range (up to 772 cm). The relative accuracy, defined as the ratio of RMS and tidal range, is between 2.4 % and 10.2 % for all stations. The results based on the extended SNR-analysis approach agree better with the tide gauge results, than the results of the simple approach, for the stations with high tidal range. For the station with the highest tidal range (772 cm), the RMS is reduced by 47 % when using the extended approach. Furthermore, the results also indicate that the simple approach assuming a static sea level can be used for stations with a tidal range of up to about 270 cm, without performing significantly worse than the extended analysis approach. Tidal amplitudes and phases were derived by harmonic analyses of the sea level records. Again, a high level of agreement is observed between the tide gauge and GPS-results. The results based on the extended SNR-analysis approach show a higher degree of agreement with the tide gauge results, than the results of the simple approach for stations with large tidal range. Spectral analysis of the residuals after the harmonic analysis reveals remaining signal power at multiples of the draconitic day. This indicates that the observed SNR data are to some level disturbed by additional multipath signals, in particular for GPS sites that are located in harbors.

Derivation of the Cramér-Rao Bound in the GNSS-Reflectometry Context for Static, Ground-Based Receivers in Scenarios with Coherent Reflection

“…In the case of long observation intervals, the CRB computed confirms the link between the variation of the satellite elevation and the achievable precision. Moreover, the CRB evaluation presented confirms the cm level precision that has been reported by many works, e.g., [29,32,38,41,77,78,79], among others, some of them using standard GNSS geodetic stations [80]. Reasonable accuracy was obtained in the estimation (joint) of ${\epsilon }_r$ and σ over observation times covering satellite elevation variations above 10°.…”

Sea level measurements using multi-frequency GPS and GLONASS observations

“…Both the SNR and the phase delay analysis have been described before, e.g., the SNR analysis in [14,16] and the phase delay analysis in [22,24]. However, for the sake of completeness, both analysis methods are summarized below.…”

“…This effect, known as multipath, is one of the major error sources in high-accuracy positioning, and there are several studies on how to mitigate the effect, e.g., [9,10,25]. In addition, there are studies on how to use the reflected signals to measure properties of the reflecting surface, e.g., sea level [13,14,16], soil moisture [26], and snow depth [27].…”

“…It is also possible to model a reflector height that is changing during a satellite arc [15]. However, this is not necessary for stations with a sub-diurnal tidal range of less than about 2.7 m [16]. By spectral analysis of the δSNR data as a function of sine of elevation angle, it is possible to derive the dominant multipath frequency.…”

“…The one-antenna configuration builds upon using the signal interference pattern, originating from the otherwise unwanted multipath signals interfering with the direct GNSS signals (see, e.g., [9,10]), and was proposed by [11][12][13]. In later studies, GPS stations with zenith-looking antennas, installed primarily for geodetic measurements, have been used to measure the sea level of the nearby ocean (see [14][15][16]). For these types of studies, the interference pattern of the signal-to-noise ratio (SNR) is usually recorded with a geodetic receiver and analyzed with an interferometric approach.…”