Coastal sea level measurements using a single geodetic GPS receiver

This paper presents a method to derive local sea level variations using data from a single geodetic-quality Global Navigation Satellite System (GNSS) receiver using GPS (Global Positioning System) signals. This method is based on multipath theory for specular reflections and the use of Signal-to-Noise Ratio (SNR) data. The technique could be valuable for altimeter calibration and validation. Data from two test sites, a dedicated GPS tide gauge at the Onsala Space Observatory (OSO) in Sweden and the Friday Harbor GPS site of the EarthScope Plate Boundary Observatory (PBO) in USA, are analyzed. The sea level results are compared to independently observed sea level data from nearby and in situ tide gauges. For OSO, the Root-Mean-Square (RMS) agreement is better than 5 cm, while it is in the order of 10 cm for Friday Harbor. The correlation coefficients are better than 0.97 for both sites. For OSO, the SNR-based results are also compared with results from a geodetic analysis of GPS data of a two receivers/antennae tide gauge installation. The SNR-based analysis results in a slightly worse RMS agreement with respect to the independent tide gauge data than the geodetic analysis (4.8 cm and 4.0 cm, respectively). However, it provides results even for rough sea surface conditions when the two receivers/antennae installation no longer records the necessary data for a geodetic analysis.     

Coherent superposition of multi-GNSS wavelet analysis periodogram for sea-level retrieval in GNSS multipath reflectometry

The multipath signals of GNSS can act as a tide gauge via a technology called Global Navigation Satellite Systems multipath reflectometry (GNSS-MR), which is based on the relationship between multipath frequency and height to sea surface. In addition to the traditional frequency extraction method of Lomb–Scargle periodogram (LSP), wavelet analysis can be applied to extract instantaneous multipath frequencies of GPS L1, thus improving data utilization. However, because of the sensitivity of instantaneous frequency to noise and the introduction of more signals, multi-constellation retrievals exhibit many outliers and errors. The aim of this study is to apply wavelet analysis to multi-constellation multi-frequency signals and most importantly to find a method to avoid noise. We used coherent superposition to overlap the intra-track inter-signal instantaneous frequency spectrograms to enhance effective information and to weaken noise. This coherent superposition method can achieve intra-track inter-signal combination. The multi-GNSS data from two Multi-GNSS Experiment (MGEX) stations were used. The results showed that the coherent superposition spectrogram has a clear energy concentration, and the frequencies calculated from it depict sea-level changes. To compare the method with the LSP method and to combine inter-track retrievals, a robust regression method was used to combine retrievals and to produce equally spaced retrieval series. The results show that the combined retrievals from the coherent superposition method have a slightly higher accuracy than those from the classical LSP method. Because this method can be used to retrieve sea-level data from instantaneous frequency, it increases data utilization and provides a way to obtain details of SNR arcs, which is a potential method to benefit GNSS-MR, especially for sites with narrow reflecting sensing zones in a small sea azimuth range.     

Estimates of vertical land motion along the southwestern coasts of Turkey from coastal altimetry and tide gauge data

The differences between coastal altimetry and sea level time series of tide gauges in between March 1993 and December 2009 are used to estimate the rates of vertical land motion at three tide gauge locations along the southwestern coasts of Turkey. The CTOH/LEGOS along-track coastal altimetry retrieves altimetric sea level anomalies closer to the coast than the standard along-track altimetry products. However, the use of altimetry very close to the coast is not found to improve the results. On the contrary, the gridded and interpolated AVISO merged product exhibits the best agreement with tide gauge data as it provides the smoothest variability both in space and time compared with along track altimetry data. The Antalya gauge to the south (in the Mediterranean Sea) and the Mentes/Izmir gauge to the west (in the Aegean Sea) both show subsidence while the Bodrum tide gauge to the south (in the Aegean Sea) shows no significant vertical land motion. The results are compared and assessed with three independent geophysical vertical land motion estimates like from GPS. The GIA effect in the region is negligible. The VLM estimates from altimetry and tide gauge data are in good agreement both with GPS derived vertical velocity estimates and those inferred from geological and archaeological investigations.     

基于TechDemoSat-1卫星的GPS反射信号海面高度反演

针对星载GPS反射信号（GPS-R）海面测高的误差问题，基于星载GPS-R实测数据进行星载海面测高模型和误差修正模型的研究，并验证其有效性。利用TechDemoSat-1（TDS-1）数据，使用时延多普勒图（DDM）海面高度反演技术，着重分析了星载GPS-R海面高度反演中的各类误差，并建立了相应的误差模型。对星载GPS-R海面高度反演模型进行优化，采用DTU15全球平均海面模型、DTU全球海潮模型验证反演精度。结果证明:优化后反演模型得到的全球海面高度反演结果的平均绝对误差（MAD）为6.05 m，精度提高了约29%，有效提高了海面高度反演的精度。研究成果对于推广星载GNSS反射信号（GNSS-R）的海面测高应用具有一定的意义。      

Monitoring coastal sea level using reflected GNSS signals

A continuous monitoring of coastal sea level changes is important for human society since it is predicted that up to 332 million people in coastal and low-lying areas will be directly affected by flooding from sea level rise by the end of the 21st century. The traditional way to observe sea level is using tide gauges that give measurements relative to the Earth’s crust. However, in order to improve the understanding of the sea level change processes it is necessary to separate the measurements into land surface height changes and sea surface height changes. These measurements should then be relative to a global reference frame. This can be done with satellite techniques, and thus a GNSS-based tide gauge is proposed. The GNSS-based tide gauge makes use of both GNSS signals that are directly received and GNSS signals that are reflected from the sea surface. An experimental installation at the Onsala Space Observatory (OSO) shows that the reflected GNSS signals have only about 3 dB less signal-to-noise-ratio than the directly received GNSS signals. Furthermore, a comparison of local sea level observations from the GNSS-based tide gauge with two stilling well gauges, located approximately 18 and 33 km away from OSO, gives a pairwise root-mean-square agreement on the order of 4 cm. This indicates that the GNSS-based tide gauge gives valuable results for sea level monitoring.     

An improved sea level retrieval method using the differential evolution of GNSS SNR data

This paper presents an improved new method with differential evolution and the cubic spline approach is proposed to retrieve sea level height based on GNSS SNR observations from a single geodetic receiver. Considering the B-spline function is unstable at the beginning or end, and the feature that B-spline functions do not pass through nodes may introduce errors. Thus, the cubic spline is applied to the retrieval process and accounts for a continuous and smooth in sea level retrieval time series. Besides, the biases caused by tropospheric delay and dynamic sea level are considered and corrected. Testing data from two stations with different tidal range and the final solution agrees well with measurements from co-located tide gauges, reaching the RMSE of 3.67 cm at Friday Harbor, Washington, and 1.36 cm at Onsala, Sweden. Comparison of the nonlinear least squares, this method leads to a clear increase in precision of the sea level retrievals within 50%. Additionally, referring to the result of Purnell et al. (2020) and the IAG inter-comparison campaign, the results of this paper show more potential.     

GPS-based sea level measurements to help the characterization of land contamination in coastal areas

The Corsica site has been established in 1996 to perform altimeter calibration on TOPEX/Poseidon and then on its successors Jason-1 and Jason-2. The first chosen location was under the #85 ground track that overflight the Senetosa Cape. In 2005, it was decided to develop another location close to Ajaccio, to be able to perform the calibration of Envisat and in a next future of SARAL/AltiKa that will flight over the same ground tracks. Equipped with various instruments (tide gauges, permanent GPS, GPS buoy, weather station…) the Corsica calibration site is able to quantify the altimeter Sea Surface Height bias but also to give an input on the origin of this bias (range, corrections, orbits, …). Due to the size of Corsica (not a tiny island), the altimeter measurement system (range and corrections) can be contaminated by land. The aim of this paper is to evaluate this land contamination by using GPS measurements from a fixed receiver on land and from another receiver onboard a life buoy. Concerning the altimeter land contamination, we have quantify that this effect can reach 8 mm/km and then affects the Sea Surface Height bias values already published in the framework of the Corsica calibration site by 5–8 mm for TOPEX and Jason missions. On the other hand, the radiometer measurements (wet troposphere correction) are also sensitive to land and we have been able to quantify the level of improvement of a dedicated coastal algorithm that reconciles our results with those coming from other calibration sites. Finally, we have also shown that the standard deviation of the GPS buoy sea level measurements is highly correlated (∼87%) with the Significant Wave Height derived from the altimeters and can be used to validate such parameter.     

Sensing snow height and surface temperature variations in Greenland from GPS reflected signals

The in situ measurements of snow surface temperature (SST) and snow height (SH) are very difficult with high costs, particularly in Greenland Ice Sheet (GrIS). Since the snow depth variations coupling with surface temperature are related to GPS multipath, it is possible to estimate the snow depth and surface air temperature variations by incorporating GPS-Reflectometry (GPS-R). In this paper, the reflected signals from ground GPS receivers are used to sense the SST and SH variations based on the thermophysical behavior and variations of snow layer from April to June 2010 at SMM1 site and from March to December 2010 at MARG site in Greenland. The results show that the mean daily changes in the ionospheric geometrical-free linear combination (GPS-L4) of dual-frequency GPS signals are related to daily SST and SH variations. The nonparametric bootstrapping model in direct (forward) and inverse models are developed and applied to estimate the SST and SH variations. The mean biases of SST and SH estimates are 0.18 °C and 0.23 m at SMM1 site, respectively, and 3.8 °C and 0.13 m at MARG site, respectively.     

The challenges in long-term altimetry calibration for addressing the problem of global sea level change

Long-term change of the global sea level resulting from climate change has become an issue of great societal interest. The advent of the technology of satellite altimetry has modernized the study of sea level on both global and regional scales. In combination with in situ observations of the ocean density and space observations of Earth’s gravity variations, satellite altimetry has become an essential component of a global observing system for monitoring and understanding sea level change. The challenge of making sea level measurements with sufficient accuracy to discern long-term trends and allow the patterns of natural variability to be distinguished from those linked to anthropogenic forcing rests largely on the long-term efforts of altimeter calibration and validation. The issues of long-term calibration for the various components of the altimeter measurement system are reviewed in the paper. The topics include radar altimetry, the effects of tropospheric water vapor, orbit determination, gravity field, tide gauges, and the terrestrial reference frame. The necessity for maintaining a complete calibration effort and the challenges of sustaining it into the future are discussed.     

The use of ionospheric tomography and elevation masks to reduce the overall error in single-frequency GPS timing applications

Signals from Global Positioning System (GPS) satellites at the horizon or at low elevations are often excluded from a GPS solution because they experience considerable ionospheric delays and multipath effects. Their exclusion can degrade the overall satellite geometry for the calculations, resulting in greater errors; an effect known as the Dilution of Precision (DOP). In contrast, signals from high elevation satellites experience less ionospheric delays and multipath effects. The aim is to find a balance in the choice of elevation mask, to reduce the propagation delays and multipath whilst maintaining good satellite geometry, and to use tomography to correct for the ionosphere and thus improve single-frequency GPS timing accuracy. GPS data, collected from a global network of dual-frequency GPS receivers, have been used to produce four GPS timing solutions, each with a different ionospheric compensation technique. One solution uses a 4D tomographic algorithm, Multi-Instrument Data Analysis System (MIDAS), to compensate for the ionospheric delay. Maps of ionospheric electron density are produced and used to correct the single-frequency pseudorange observations. This method is compared to a dual-frequency solution and two other single-frequency solutions: one does not include any ionospheric compensation and the other uses the broadcast Klobuchar model. Data from the solar maximum year 2002 and October 2003 have been investigated to display results when the ionospheric delays are large and variable. The study focuses on Europe and results are produced for the chosen test site, VILL (Villafranca, Spain). The effects of excluding all of the GPS satellites below various elevation masks, ranging from 5° to 40°, on timing solutions for fixed (static) and mobile (moving) situations are presented. The greatest timing accuracies when using the fixed GPS receiver technique are obtained by using a 40° mask, rather than a 5° mask. The mobile GPS timing solutions are most accurate when satellites at lower elevations continue to be included: using a mask between 10° and 20°. MIDAS offers the most accurate and least variable single-frequency timing solution and accuracies to within 10 ns are achieved for fixed GPS receiver situations. Future improvements are anticipated by combining both GPS and Galileo data towards computing a timing solution.     

Using altimetry and seafloor pressure data to estimate vertical deformation offshore: Vanuatu case study

Measuring ground deformation underwater is essential for understanding Earth processes at many scales. One important example is subduction zones, which can generate devastating earthquakes and tsunamis, and where the most important deformation signal related to plate locking is usually offshore. We present an improved method for making offshore vertical deformation measurements, that involve combining tide gauge and altimetry data. We present data from two offshore sites located on either side of the plate interface at the New Hebrides subduction zone, where the Australian plate subducts beneath the North Fiji basin. These two sites have been equipped with pressure gauges since 1999, to extend an on-land GPS network across the plate interface. The pressure series measured at both sites show that Wusi Bank, located on the over-riding plate, subsides by 11 ± 4 mm/yr with respect to Sabine Bank, which is located on the down-going plate. By combining water depths derived from the on-bottom pressure data with sea surface heights derived from altimetry data, we determine variations of seafloor heights in a global reference frame. Using altimetry data from TOPEX/Poseidon, Jason-1, Jason-2 and Envisat missions, we find that the vertical motion at Sabine Bank is close to zero and that Wusi Bank subsides by at least 3 mm/yr and probably at most 11 mm/yr.     

Vertical crustal motion derived from satellite altimetry and tide gauges,and comparisons with DORIS measurements

A somewhat unorthodox method for determining vertical crustal motion at a tide-gauge location is to difference the sea level time series with an equivalent time series determined from satellite altimetry. To the extent that both instruments measure an identical ocean signal, the difference will be dominated by vertical land motion at the gauge. We revisit this technique by analyzing sea level signals at 28 tide gauges that are colocated with DORIS geodetic stations. Comparisons of altimeter-gauge vertical rates with DORIS rates yield a median difference of 1.8 mm yr⁻¹ and a weighted root-mean-square difference of 2.7 mm yr⁻¹. The latter suggests that our uncertainty estimates, which are primarily based on an assumed AR(1) noise process in all time series, underestimates the true errors. Several sources of additional error are discussed, including possible scale errors in the terrestrial reference frame to which altimeter-gauge rates are mostly insensitive. One of our stations, Malè, Maldives, which has been the subject of some uninformed arguments about sea-level rise, is found to have almost no vertical motion, and thus is vulnerable to rising sea levels.     

Integrating Non-Tidal Sea Level data from altimetry and tide gauges for coastal sea level prediction

The main objective of this paper is to integrate Non-Tidal Sea Level (NSL) from the joint TOPEX, Jason-1 and Jason-2 satellite altimetry with tide gauge data at the west and north coast of the United Kingdom for coastal sea level prediction. The temporal correlation coefficient between altimetric NSLs and tide gauge data reaches a maximum higher than 90% for each gauge. The results show that the multivariate regression approach can efficiently integrate the two types of data in the coastal waters of the area. The Multivariate Regression Model is established by integrating the along-track NSL from the joint TOPEX/Jason-1/Jason-2 altimeters with that from eleven tide gauges. The model results give a maximum hindcast skill of 0.95, which means maximum 95% of NSL variance can be explained by the model. The minimum Root Mean Square Error (RMSe) between altimetric observations and model predictions is 4.99 cm in the area. The validation of the model using Envisat satellite altimetric data gives a maximum temporal correlation coefficient of 0.96 and a minimum RMSe of 4.39 cm between altimetric observations and model predictions, respectively. The model is furthermore used to predict high frequency NSL variation (i.e., every 15 min) during a storm surge event at an independent tide gauge station at the Northeast of the UK (Aberdeen).     

A comparison of seasonal variations of sea level in the southern Baltic Sea from altimetry and tide gauge data

In this paper, seasonal sea level variations have been determined at five locations in the Baltic Sea from satellite altimetry for the period 1993–2015. The results were compared to tide gauge water level data. Annual and semi-annual amplitudes have been investigated for both sea level anomalies and tide gauge water level. It was found that the two independent observations of sea level variations along the Polish coast are in good agreement both in terms of their annual and semi-annual amplitudes and their annual and semi-annual phases. The annual cycles in the sea level variations measured by altimetry and tide gauge reach maximum values at approximately the same month (November/December).Moreover, this article shows the differences between the annual and semi-annual amplitudes and phases in the sea level anomalies and water level data within the same time frame. The difference in the annual amplitudes between the satellite altimetry and the tide gauge results is between 0.33?cm and 1.53?cm. The maximum differences in the annual cycle of the sea level changes were found at the Swinoujscie station. The correlations between the original series and the calculated curves were determined, and the relationship between the amplitudes and the phases were investigated. The correlation between the annual variations observed from the two independent observation techniques is 0.92.To analyse the dynamics of the change in sea level, the linear trend was estimated from the satellite altimetry and tide gauge time series both in the original time series of the data and in the time series in which seasonal variations were removed. In addition, we calculated the estimated errors of regression and how many years’ worth of data are needed to obtain an accuracy of 0.1?mm per year. The estimated errors of regression showed that to get an accuracy of 0.1?mm per year, we need 100?years of data.     

Estimating sea level rise around Australia using a new approach to account for low frequency climate signals

Regional sea level studies help to identify the vulnerable areas to the sea level rise. This study investigates the impact of climate modes on sea level variations and trends around Australia using altimetry data, climate indices, and sea level records from tide gauge stations. Here, we show that the sea level variations are negatively correlated with climate indices to the north and west of Australia. The spectral analyses of the climate indices and tide gauge data suggest that a low frequency signal with a period of 11 years emerges during the mid 1980s. Since the 25-year length of the satellite altimetry record is yet too short to detect low frequency signals, their effect on the estimation of regional sea level trend is unknown. Therefore, we estimate the sea level trend with consideration of this signal and using a two-step method. All signals with periods shorter than 7.5 years are first removed from sea level time series and then the trend is estimated using the parametric model that includes the 11-year signal. The skill of the parametric model in explaining the variations in sea level anomaly validates the presence of the 11-year signal detected in the spectrograms of the tide gauge data and climate indices. The average sea level trend for the study area is estimated as 3.85 ± 0.15 mm/year.     

Analysis of coastal altimetry in the Mexican Caribbean

A reprocessing of sea-level anomalies (SLA) resulting from X-TRACK coastal altimetry was carried out for the ENVISAT (2002–2010) and TOPEX/POSEIDON-Jason (1992–2019) satellite missions in the coastal area of the Mexican Caribbean. This consisted of applying a tidal correction to coastal altimetry sea level observations. Harmonic analysis of five coastal tide gauge records was performed to estimate the most important tidal components of the area, resulting on M2, N2, O1, S2, K1, MF, and MM. The tidal signal was reconstructed with the seven tidal components using the TPXO9 model. The SLA signals corrected with the seven tidal components were validated with in situ data from coastal tide gauges. The validation showed that the TPXO9 tidal barotropic model (1/30° grid) used to reconstruct the tidal signal with the seven representative tidal components performed better than the FES2012 global model (1/16° grid) that uses 33 tidal components. The reprocessed SLAs showed clear seasonality with significant signals at 4, 6, and 12 months, with the annual signal being the dominant one. In the Mexican Caribbean coastal zone, oceanographic processes with different scales (from coastal to mesoscale) converge, showing their complexity in the different SLA signals observed. The aim of this work is to contribute to the analysis of coastal altimetry data and understanding the sea level variations in the Mexican Caribbean. This work is the first step in the implementation of methodologies that take advantage of coastal satellite altimetry in the Caribbean Sea.     

主动雷达导引头多路径效应的数字仿真

对于平整和起伏的地面或海面,分别给出了一种基于多反射点复杂目标的多路径回波的时域复包络波形数字仿真模型.采用随机分形插值算法利用地形实测数据对复杂的起伏地面和海面进行三维地形建模.对不同粗糙度地面上的低空目标的多路径回波进行了仿真计算,并使用主动雷达导引头数字仿真模型进行了多路径干扰环境下对低空目标的跟踪实验.仿真实验表明,多路径效应对雷达跟踪低空目标会产生较大的误差.     

Evaluation and improvement of coastal GNSS reflectometry sea level variations from existing GNSS stations in Taiwan

Global sea level rise due to an increasingly warmer climate has begun to induce hazards, adversely affecting the lives and properties of people residing in low-lying coastal regions and islands. Therefore, it is important to monitor and understand variations in coastal sea level covering offshore regions. Signal-to-noise ratio (SNR) data of Global Navigation Satellite System (GNSS) have been successfully used to robustly derive sea level heights (SLHs). In Taiwan, there are a number of continuously operating GNSS stations, not originally installed for sea level monitoring. They were established in harbors or near coastal regions for monitoring land motion. This study utilizes existing SNR data from three GNSS stations (Kaohsiung, Suao, and TaiCOAST) in Taiwan to compute SLHs with two methods, namely, Lomb–Scargle Periodogram (LSP)-only, and LSP aided with tidal harmonic analysis developed in this study. The results of both methods are compared with co-located or nearby tide gauge records. Due to the poor quality of SNR data, the worst accuracy of SLHs derived from traditional LSP-only method exceeds 1?m at the TaiCOAST station. With our procedure, the standard deviations (STDs) of difference between GNSS-derived SLHs and tide gauge records in Kaohsiung and Suao stations decreased to 10?cm and the results show excellent agreement with tide gauge derived relative sea level records, with STD of differences of 7?cm and correlation coefficient of 0.96. In addition, the absolute GNSS-R sea level trend in Kaohsiung during 2006–2011 agrees well with that derived from satellite altimetry. We conclude that the coastal GNSS stations in Taiwan have the potential of monitoring absolute coastal sea level change accurately when our proposed methodology is used.     

An Integer Precise Point Positioning technique for sea surface observations using a GPS buoy

GPS data dedicated to sea surface observation are usually processed using differential techniques. Unfortunately, the precision of resulting kinematic positions is baseline-length dependent. So, high precision sea surface observations using differential GPS techniques are limited to coasts, lakes, and rivers. Recent improvements in GPS satellite products (orbits, clocks, and phase biases) make phase ambiguity fixing at the zero difference level achievable and opens up the observation of the sea surface without geographical constraints. This paper recalls the concept of the Integer Precise Point Positioning technique and discusses the precision of GPS buoy positioning. A sequential version of the GINS software has been implemented to achieve single epoch GPS positioning. We used 1 Hz data from a two week GPS campaign conducted in the Kerguelen Islands. A GPS buoy has been moored close to a radar gauge and 90 m away from a permanent GPS station. This infrastructure offers the opportunity to compare both kinematic Integer Precise Point Positioning and classical differential GPS positioning techniques to in situ radar gauge data. We found that Precise Point Positioning results are not significantly biased with respect to radar gauge data and that horizontal time series are consistent with differential processing at the sub-centimetre precision level. Nevertheless, standard deviations of height time series with respect to radar gauge data are typically [4–5] cm. The dominant driver for noise at this level is attributed to errors in tropospheric estimates which propagate into position solutions.     

DORIS and GPS monitoring of the Gavdos calibration site in Crete

Due to its specific geographical location as well as its geodetic equipment (DORIS, GNSS, microwave transponder and tide gauges), the Gavdos station in Crete, Greece is one of the very few sites around the world used for satellite altimetry calibration. To investigate the quality of the Gavdos geodetic coordinates and velocities, we analyzed and compared here DORIS and GPS-derived results obtained during several years of observations. The DORIS solution is the latest ignwd11 solution at IGN, expressed in ITRF2008, while the GPS solution was obtained using the GAMIT software package. Current results show that 1–2 mm/yr agreement can be obtained for 3-D velocity, showing a good agreement with current geophysical models. In particular, the agreement obtained for the vertical velocity is around 0.3–0.4 mm/yr, depending on the terrestrial reference frame. As a by-product of these geodetic GPS and DORIS results, Zenith Tropospheric Delays (ZTDs) estimations were also compared in 2010 between these two techniques, and compared to ECMWF values, showing a 6.6 mm agreement in dispersion without any significant difference between GPS and DORIS (with a 97.6% correlation), but with a 13–14 mm agreement in dispersion when comparing to ECMWF model (with only about 90% correlation for both techniques). These tropospheric delay estimations could also provide an external calibration of the tropospheric correction used for the geophysical data of satellite altimetry missions.