Sea-level Estimates Research Articles

Datum Alignment Between GNSS-IR Sea Level Estimations and Tide Gauges in Türkiye: A Vertical Local Tie Approach

Connecting Asia and Europe, Türkiye is vital for maritime transit, which requires continuous and precise sea level monitoring. Traditional tide gauges (TGs), while valuable, often have data gaps. GNSS-IR provides an alternative, though aligning it with TG measurements is challenging. This study introduces a method to estimate Vertical Local Tie (VLT) between the TG zero and the GNSS antenna phase centre, allowing GNSS-IR sea level estimates to be aligned with TG measurements. In disruptions, GNSS-IR can consistently supplement TG data. We validated this approach by evaluating a 1-year data from four GNSS stations namely, ARSZ, GADA, TRBZ, and YLVA involving in the Türkiye National Sea Level Monitoring System (TUDES) network. These stations are located on the coasts of the Mediterranean, Aegean, Black, and Marmara Seas, respectively. Compared with the TG measurements, ARSZ achieved the highest epoch-based correlation as 87.00%. For daily averages, the GADA and TRBZ showed a correlation of over 96% with TG data. Notably, TRBZ recorded the lowest daily average RMSE at 2.2 cm using the VLT-median approach. The results demonstrate that when VLT is utilized, well-configured GNSS stations, ensuring uninterrupted transmissions and appropriate data intervals, provide a reliable alternative or complement to TGs for sea level monitoring.

Estimates of Baroclinic Tidal Sea Level and Currents from Lagrangian Drifters and Satellite Altimetry

Abstract Internal waves generated by the interaction of the surface tides with topography are known to propagate long distances and lead to observable effects such as sea level variability, ocean currents, and mixing. In an effort to describe and predict these waves, the present work is concerned with using geographically distributed data from satellite altimeters and drifting buoys to estimate and map the baroclinic sea level associated with the M2, S2, N2, K1, and O1 tides. A new mapping methodology is developed, based on a mixed L1/L2-norm optimization, and compared with previously developed methods for tidal estimation from altimeter data. The altimeter and drifter data are considered separately in their roles for estimating tides and for cross-validating estimates obtained with independent data. Estimates obtained from altimetry and drifter data are found to agree remarkably well in regions where the drifter trajectories are spatially dense; however, heterogeneity of the drifter trajectories is a disadvantage when they are considered alone for tidal estimation. When the different data types are combined by using geodetic mission altimetry to cross validate estimates obtained with either exact-repeat altimetry or drifter data, and subsequently averaging the latter estimates, the estimates significantly improve on the previously published HRET8.1 model, as measured by their utility for predicting sea level and surface currents in the open ocean. The methodology has been applied to estimate the annual modulations of M2, which are found to have much smaller amplitudes compared to those reported in HRET8.1, and suggest that the latter estimates of these tides were not reliable. Significance Statement The mechanical and thermodynamic forcing of the ocean occurs primarily at very large scales associated with the gravitational perturbations of the sun and moon (tides), atmospheric wind stress, and solar insolation, but the frictional forces within the ocean act on very small scales. This research addresses the question of how the large-scale tidal forcing is transformed into the smaller-scale motion capable of being influenced by friction. The results show where internal waves are generated and how they transport energy across ocean basins to eventually be dissipated by friction. The results are useful to scientists interested in mapping the flows of mechanical energy in the ocean and predicting their influences on marine life, ocean temperature, and ocean currents.

Global assessment of linear trend and seasonal variations of GNSS-IR sea level retrievals with nearby tide gauges

Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) sea level retrievals and tide gauges at 40 globally distributed stations spanning from about 4.5 to 18 years are compared on a site-by-site basis, in terms of noise background, rate and seasonal variations by using the weighted least squares estimation (LSE) along with the Maximum likelihood estimation (MLE). The result shows that monthly GNSS-IR data agree well with tide gauges for most stations except the site Tuktoyaktuk, Canada. The mean correlation is 0.95 and the mean root mean square difference is 2.9 cm, respectively. The discrepancies of rate and seasonal amplitude estimates are within ± 1 cm for most stations. We confirm both the two sea level data exhibit temporal correlation, which has a great effect on the rate uncertainty estimates. Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC) favor Matérn and first-order autoregressive (AR1) the preferred stochastic model for the daily and monthly mean sea level time series, respectively. Owing to the data span dependence for the rate uncertainty estimates, to get an accuracy of sub-mm/yr in linear rate using the weighted LSE, at least 30 years of data (depends on data quality) is required. We recommend using long time series and a proper stochastic model for the rate estimation of sea level.

Machine learning models applied to altimetry era tide gauge and grid altimetry data for comparative long-term trend estimation: A study from Shikoku Island, Japan

Estimation of sea level trends is essential for understanding sea level rise dynamics. In this study, the performance of traditional Ordinary Least Squares (OLS) linear trend forecasting is compared with modern machine learning techniques, specifically Random Forests (RF) and Least Squares Support Vector Machines (LS-SVM).These methods are applied to 50 years of long-term tide gauge (TG) data from six tide gauge stations off the coast of Shikoku Island, Japan, and CMEMS Grid Altimetry data from 1993 to the present. The analysis uses OLS, RF, and LS-SVM to estimate trends from both data sets and compares the results. The objective is to determine the consistency and accuracy of RF and LS-SVM methods compared to the OLS method. The results indicate that machine learning algorithms (LS-SVM) effectively estimate sea level trends, offering potential improvements in precision for both long-term and medium-term analyses. Shikoku Island's coastal sea level trend is determined as 2.91±1.44 mm/yr using TG data and 3.00±1.52 mm/yr using CMEMS Grid Altimeter data with the OLS approach. Using the LS-SVM approach, the trend is found as 2.96±1.58 mm/yr with TG data and 3.02±1.60 mm/yr with CMEMS Grid Altimetry data. The novelty of this study lies in its thorough comparison of traditional and machine learning approaches for sea level trend estimation, providing valuable insights for future predictions of the sea level rise.

Re-evaluating Marine Isotope Stage 5a paleo-sea-level trends from across the Florida Keys reef tract

Unraveling how Global Mean Sea Level (GMSL) fluctuated during past warm periods can improve our understanding of linkages between sea-level fluctuations, orbital forcing, and ice-sheet dynamics. Current estimates of GMSL for Marine Isotope Stages (MIS) 5a and 5c — two warm intervals following the relatively well-documented MIS 5e — contain meters of uncertainty and fewer data due to several challenges. These challenges include concealment of datable in-situ coral facies by MIS 1 deposits and inaccessibility due to submergence by modern sea level. We present a comprehensive dataset based on U–Th dating and stratigraphic correlation of 23 cores totaling over 170 m of recovered coral-reef deposits across the tectonically stable Florida Keys Reef Tract (FKRT). Following detailed facies descriptions, 34 in-situ, minimally altered aragonitic coral samples (≤2.7% calcite) below the Holocene-Pleistocene boundary were targeted for U–Th geochronology. Fourteen closed-system coral U–Th ages from MIS 5a include the commonly used sea-level indicator Acropora palmata, but also the massive coral taxa Pseudodiploria strigosa, Siderastrea siderea, Orbicella spp., and Porites astreoides. Dating yielded ages in the range of 88–81 ka (average 2σ uncertainty of less than 200 years). These ages suggest MIS 5a reef initiation at ∼88 ka BP, a peak near 83 ka with minimum elevations between −6.0 ± 0.5 and −5.6 ± 0.5 m MSL (2σ uncertainty and subsidence-corrected), and reef termination and sea-level fall by ∼81 ka BP. Notably, the range of peak MIS 5a relative sea-level estimates of −6.5 to −5.1 m MSL are more than 2 m shallower (higher) than previous estimates of −11 to −9 m. Our higher resolution regional sea-level reconstruction across four subregions of the Florida Keys reef tract aligns with changes in July insolation at 65° N: a trend that most other records, such as deep-sea sediments, do not have the accuracy and precision to resolve. Three massive coral samples from MIS 5c, consisting of Pseudodiploria clivosa, and Orbicella spp., yielded ages in the range of 104 to 99 ka (average 2σ uncertainty less than 200 years); however, because only one sample met the closed-system criteria, our ability to estimate MIS 5c sea level is relatively limited. More empirical estimates of sea-level from the MIS 5a and MIS 5c intervals based on numerical dating of reliable local sea-level constraints are critical for GMSL calculations and relating changes in sea-level amplitude and timing to global ice volume modeling and glacio-isostatic effects, all of which can improve predictions of future sea-level changes in coastal regions.

Evolution of Coastal Environments under Inundation Scenarios Using an Oceanographic Model and Remote Sensing Data

A new methodology to map Italian coastal areas at risk of flooding is presented. This approach relies on detailed projections of the future sea level from a high-resolution, three-dimensional model of the Mediterranean Sea circulation, on the best available digital terrain model of the Italian coasts, and on the most advanced satellite-derived data of ground motion, provided by the European Ground Motion Service of Copernicus. To obtain a reliable understanding of coastal evolution, future sea level projections and estimates of the future vertical ground motion based on the currently available data were combined and spread over the digital terrain model, using a GIS-based approach specifically developed for this work. The coastal plains of Piombino-Follonica and Marina di Campo (Tuscany Region), Alghero-Fertilia (Sardinia), and Rome and Latina-Sabaudia (Lazio Region) were selected as test cases for the new approach. These coastal stretches are important for the ecosystems and the economic activities they host and are relatively stable areas from a geological point of view. Flood maps were constructed for these areas, for the reference periods 2010–2040, 2040–2070, and 2040–2099. Where possible, the new maps were compared with previous results, highlighting differences that are mainly due to the more refined and resolved sea-level projection and to the detailed Copernicus ground motion data. Coastal flooding was simulated by using the “bathtub” approach without considering the morphodynamic processes induced by waves and currents during the inundation process. The inundation zone was represented by the water level raised on a coastal DTM, selecting all vulnerable areas that were below the predicted new water level. Consequent risk was related to the exposed asset.

The Significance of Interseismic Vertical Land Movement at Convergent Plate Boundaries in Probabilistic Sea‐Level Projections for AR6 Scenarios: The New Zealand Case

AbstractAnticipating and managing the impacts of sea‐level rise for nations astride active tectonic margins requires understanding of rates of sea surface elevation change in relation to coastal land elevation. Vertical land motion (VLM) can either exacerbate or reduce sea‐level changes with impacts varying significantly along a coastline. Determining rate, pattern, and variability of VLM near coasts leads to a direct improvement of location‐specific relative sea level (RSL) estimates for coastal hazard risk assessment. Here, we utilize vertical velocity field from interferometric synthetic aperture radar (InSAR) data, calibrated with campaign and continuous Global Navigation Satellite System data, to determine the VLM for the entire coastline of New Zealand. Guided by available knowledge of the seismic cycle, the VLM data infer secular, interseismic rates of land surface deformation. Using the Framework for Assessing Changes to Sea‐level (FACTS), we build probabilistic RSL projections using the same emissions scenarios employed in IPCC Assessment Report 6 and local VLM data at 8,179 sites, thereby enhancing spatial coverage that was previously limited to four tide gauges. We present ensembles of probability distributions of RSL for each scenario to 2150, and for low confidence sea‐level processes to 2300. Where land subsidence is occurring at rates >2 mm/y VLM makes a significant contribution to RSL projections for all scenarios out to 2150. Our approach can be applied to similar locations across the world and has significant implications for adaptation planning, as timing of threshold exceedance for coastal inundation can be brought forward (or delayed) by decades.

Advancing Accuracy in Sea Level Estimation with GNSS-R: A Fusion of LSTM-DNN-Based Deep Learning and SNR Residual Sequences

The global navigation satellite system reflectometry (GNSS-R) technique has shown promise in retrieving sea levels using signal-to-noise ratio (SNR) data. However, its accuracy and performance are often limited compared to conventional tide gauges, particularly due to constraints in satellite elevation angles. To address these limitations, we propose a methodology integrating Long Short-Term Memory Deep Neural Networks (LSTM-DNN) models, utilising SNR residual sequences as key feature inputs. Our study focuses on the SC02 station, examining elevation angles ranging from 5° to 10°, 5° to 15°, and 5° to 20°. Results reveal notable reductions in root mean square errors (RMSE) of 2.855%, 17.519%, and 15.756%, respectively, showcasing improvements in accuracy across varying elevation angles. Of particular significance is the enhancement in precision observed at higher elevation angles. This underscores the valuable contribution of our approach to nearshore sea level wave height retrieval, promising advancements in the GNSS-R technique.

Uncovering sea level patterns in Caspian Sea altimetry data

ABSTRACT This study introduces a technique to uncover concealed patterns in satellite altimetry data, reflecting sea level variations in inland water bodies. We applied the methodology to the Caspian Sea, using altimetry data from four satellite missions over 27 years (1993–2020): TOPEX/Poseidon, Jason1, Jason2, and Jason3. The approach involves two steps: estimating sea level trends and identifying breakpoints that indicate trend shifts; and leveraging time lags between breakpoints at various locations to classify water drainage areas according to their degree of influence on each period. By revealing concealed patterns in the altimetry data, this technique can provide insights to understand the impacts of global warming and local climate changes on sea level fluctuations in the Caspian Sea. We hope that our study can facilitate subsequent interdisciplinary research on the intricate interplay between climate change and hydrological processes in inland water bodies.

Can the phase of SNR oscillations in GNSS-IR be used to estimate sea-level height?

In existing global navigation satellite system-interference reflectometry (GNSS-IR) research, only the frequency of signal-to-noise ratio (SNR) oscillations has been used to estimate sea-level height. However, the characteristic parameters of SNR oscillations are not isolated from each other, and a single feature cannot accurately and comprehensively capture the environmental changes of reflecting surface. Our simulation results show that for the nonlinear least squares (NLS), when there is a certain difference between the fitting frequency and the actual frequency of SNR oscillations, the deviation of the phase solution obtained is approximately linear with the frequency difference. Consequently, a linear phase correction GNSS-IR sea-level estimation method is constructed in this study. This method integrates the Lomb–Scargle periodogram (LSP) and NLS to process SNR oscillations, using the phase obtained from NLS to correct the retrieval error of LSP. Through processing SNR data from four sites for nearly half a year, we verified the stability of the relationship between phase and frequency-based retrieval error at different sites in continuous monitoring, and established the relationship model between the two. Then, utilizing the relationship model acquired at different sites, we estimated the sea-level variations for the next 6 months at each site through joint frequency and phase versus reflector height relationships. Experimental results show that the phases acquired from NLS can effectively correct the retrieval error of LSP. Compared with the traditional method using only frequency, the root mean square error and mean absolute error of the retrieval results obtained from the linear phase correction GNSS-IR sea-level estimation method based on LSP-NLS are both reduced by about 60%. This multi-feature fusion technique introduces a new perspective and technical approach for GNSS-IR sea-level estimations.

Global Mean and Relative Sea-Level Changes Over the Past 66 Myr: Implications for Early Eocene Ice Sheets

We estimate ice-volume driven (barystatic; BSL) sea-level changes for the Cenozoic using new Mg/Ca data from 58 to 48 Ma and a revised analysis of Mg/Ca trends over the past 66 Myr. We combine records of BSL, temperature-driven sea level, and long-term ocean basin volume variations to derive a new global mean geocentric sea level (GMGSL; “eustatic”) estimate. Bayesian analysis with Gaussian process priors shows that our BSL estimate shares a component that covaries on the Myr scale with “backstripped” relative sea-level (RSL) estimates (accounting for compaction, loading, and thermal subsidence) from the US Mid-Atlantic Coastal Plain, validating our method and estimates with errors of ±10 m. Peak warmth, elevated GMGSL and BSL, high CO2, and ice-free conditions occurred at times in the Paleocene to Eocene (ca. 64, 57.5, 35 Ma) and in much of the Early Eocene (55–48 Ma). However, our new results show that the Early Eocene was punctuated at specific times by several Myr-scale sea level lowerings (∼20–40 m) that require growth and decay of significant continental ice sheets even in the supposedly “ice-free” world. Continental-scale ice sheets waxed and waned beginning ca. 34 Ma (>50 m BSL changes), with near complete collapse during the Miocene Climate Optimum (17–14.8 Ma). Both the BSL and RSL estimates have markedly higher Oligocene to Early Miocene Myr-scale amplitudes (20–60 m) than recently published δ18O-based estimates (<20 m) and much lower estimates than those of Exxon Production Research (>100 m), leading us to reject those estimates. The US Mid-Atlantic margin RSL was dominated by GMGSL but was overprinted by changes in mantle dynamic topography on the several Myr scale, showing approximately 50 m higher Eocene estimates and regionally propagating Miocene RSL changes.

Multi-constellation GNSS interferometric reflectometry for tidal analysis: mitigations for K1 and K2 biases due to GPS geometrical errors

It has been observed that when using sea levels derived from GPS (Global Positioning System) signal-to-noise ratio (SNR) data to perform tidal analysis, the luni-solar semidiurnal (K2) and the luni-solar diurnal (K1) constituents are biased due to geometrical errors in the reflection data, which result from their periods coinciding with the GPS orbital period and revisit period. In this work, we use 18 months of GNSS SNR data from multiple frequencies and multiple constellations at three sites to further investigate the biases and how to mitigate them. We first estimate sea levels using SNR data from the GPS, GLONASS, and Galileo signals, both individually and by combination. Secondly, we conduct tidal harmonic analysis using these sea-level estimates. By comparing the eight major tidal constituents estimated from SNR data with those estimated from the co-located tide-gauge records, we find that the biases in the K1 and K2 amplitudes from GPS S1C, S2X and S5X SNR data can reach 5 cm, and they can be mitigated by supplementing GLONASS- and Galileo-based sea-level estimates. With a proper combination of sea-level estimates from GPS, GLONASS, and Galileo, SNR-based tidal constituents can reach agreement at the millimeter level with those from tide gauges.

Dating the late Miocene marine sediments around the southern middle Durance valley (Provence, SE France): new evidences for a Tortonian age

The present study aims dating the topmost 50 m of a 115 m-long core retrieved from a valley located in the Cadarache Area (Upper Provence, South East France). Based on burial dating by in situ produced cosmogenic nuclides (10Be, 26Al and 21Ne), and paleomagnetic analyses, a Tortonian age was determined for the sedimentary succession exhibited in the core. In addition, thin sections, grain size analyses and quartz morphoscopy were used to characterize a shallow marine environment and to correlate the sediment core to the surrounding exposed sections. When comparing the studied sedimentary record to global sea level estimates, we establish that the local Tortonian transgression was not synchronous with the global scale sea level high-stand, but happened more likely later, during a global regressive trend. The timing of the Tortonian flooding in Upper Provence was therefore most probably driven by regional tectonic forcing. Finally, the Tortonian shallow marine sediments are topped by lacustrine tight carbonates. These carbonates protect the marine sediments from the following major erosional events resulting from the Messinian sea level drop and from interglacial-glacial fluctuations that both yielded to the present-day valley topography.

Accounting for seasonality in extreme sea-level estimation

Accounting for seasonality in extreme sea-level estimation

Geodynamically corrected Pliocene shoreline elevations in Australia consistent with midrange projections of Antarctic ice loss

The Mid-Pliocene represents the most recent interval in Earth history with climatic conditions similar to those expected in the coming decades. Mid-Pliocene sea level estimates therefore provide important constraints on projections of future ice sheet behavior and sea level change but differ by tens of meters due to local distortion of paleoshorelines caused by mantle dynamics. We combine an Australian sea level marker compilation with geodynamic simulations and probabilistic inversions to quantify and remove these post-Pliocene vertical motions at continental scale. Dynamic topography accounts for most of the observed sea level marker deflection, and correcting for this effect and glacial isostatic adjustment yields a Mid-Pliocene global mean sea level of +16.0 (+10.4 to +21.5) m (50th/16th to 84th percentiles). Recalibration of recent high-end sea level projections using this revised estimate implies a more stable Antarctic Ice Sheet under future warming scenarios, consistent with midrange forecasts of sea level rise that do not incorporate a marine ice cliff instability.

Combined Coastal Sea Level Estimation Considering Astronomical Tide and Storm Surge Effects: Model Development and Its Application in Thermaikos Gulf, Greece

Tide gauge recordings furnish the longest and almost the most continuous data source of sea level monitoring. Traditionally, they are collected using tide gauge instrumentation fixed at seaport locations to provide a time series of sea level estimates relative to a local geodetic benchmark. Sea level tidal observables are distinguished in the astronomical tide component originating from the attraction of the Earth–Moon–Sun gravitational system, and the storm surges ought to have meteorological effects due to wind and atmospheric air pressure variation. This study provides a comprehensive methodological approach and software to compute sea level considering astronomical tides enhanced by storm surge effects. The model is realized and assessed using a long-standing set of 21 consecutive years of tidal and meteorological measurements originating from Thermaikos Gulf, Greece. Analyses show model verification and conclusions about the tidal behavior of the test area, suggesting a satisfactory agreement (86% Willmott Skill factor, 9 cm standard deviation) between predicted and observed sea level estimates, accounting for amplitude and the time shift of skew surges.

Tidal harmonics retrieval using GNSS-R dual-frequency complex observations

Tidal analysis and methods for estimation and prediction of ocean tidal constitutes are essential in a large area of scientific disciplines, for example, navigation, onshore and offshore engineering, and production of green energy. Ground-based Global Navigation Satellite System-Reflectometry (GNSS-R) has been proposed as an alternative method for measuring sea surface height. We use 6 years of GNSS-R observations at In-phase and Quadrature levels from July 2015 to May 2021 obtained from a dedicated receiver and sea-looking left hand circular polarization antenna for estimating sea level (SL). In the first step, the multivariate least-square harmonic estimation (LS-HE) method is applied for SL estimation. Then, final SL time series are generated by combining estimated SL from all satellites at L1 and L2 frequencies in the averaging step. The 6-year root-mean-square error between GNSS-R L12 sea surface heights and a collocated tide gauge (TG) is 5.8 cm with a correlation of 0.948 for a high temporal resolution of 5 min with 15 min averaging window. Afterward, using the univariate LS-HE, we detect tidal harmonics with periods between 30 min to 1 year. The detection results highlight a good match between GNSS-R and TG. Higher harmonics, i.e., the periods shorter than 3 h, show stronger signatures in GNSS-R data. Finally, we estimate the amplitude and phase of standard tidal harmonics from the two datasets. The results show an overall good agreement between the datasets with a few exceptions.

GNSS-Interferometric Reflectometry, spectral artifacts and sea level measurements in the Mediterranean Sea

Tidal sea level variations in the Mediterranean basin, although altered and amplified by resonance phenomena in confined sub-basins (e.g., Adriatic Sea), are generally confined within 0.5 meters and exceptionally up to 1.5 meters. Here we explore the possibility to retrieve sea level measurements using data from GNSS antennas on duty for ground motion monitoring and analyze the spectral outcomes of such distinctive measurements. We estimate one year of GNSS data collected on the Mediterranean coasts in order to get reliable sea level data from all public-available data and compare it with collocated tide gauges. A total amount of eleven stations was suitable for interferometric analysis (as for 2021) and all were able to supply centimeter level sea level estimates. The spectra in the tidal frequency windows are remarkably similar to tide gauges data. We find that the O1 and M2 diurnal and semidiurnal tides and MK3, MS4 shallow sea water tides may be disturbed by aliasing effects.

Polar Ocean Tides—Revisited Using Cryosat-2

With the availability of more than 9 years of Cryosat-2, it is possible to revisit polar ocean tides, which have traditionally been difficult to determine from satellite altimetry. The SAMOSA+ physical retracker is a stable retracker developed particularly for Cryosat-2. Being a physical retracker, it enables the determination of the sea state bias. Correcting for the sea state bias enables more reliable sea level estimates compared with traditional empirical retrackers used before. Cryosat-2 data have been analyzed for residual ocean tides to the FES2014 ocean tide model in the Arctic Ocean and Antarctic Ocean using the response formalism. We utilize data from the sub-cycle of Cryosat-2, which follows a repeating pattern of approximately 28.33 days. This sub-repeat period makes it an advantageous alias period for the majority of significant constituents. This allowed for the estimation and mapping of the major tidal constituents in the open ocean and also in floating ice shelves from data extracted from leads in the sea ice. A novel empirical ocean tide model designed specifically for the polar region, DTU22, is introduced. Our findings reveal substantial enhancements in semi-diurnal tides within the Arctic Ocean and improvement in diurnal constituents within the Southern Ocean. In the Southern Ocean, the diurnal constituents are particularly improved using the empirical model by more than a factor of two to around 3 cm for both constituents compared with FES2014b. These outcomes underscore the significance of incorporating the reprocessed and retracted Cryosat-2 data into tidal modeling, highlighting its pivotal role in advancing the field.

Sea-Level Estimation from GNSS-IR under Loose Constraints Based on Local Mean Decomposition.

The global navigation satellite system-interferometric reflectometry (GNSS-IR) technique has emerged as an effective coastal sea-level monitoring solution. However, the accuracy and stability of GNSS-IR sea-level estimation based on quadratic fitting are limited by the retrieval range of reflector height (RH range) and satellite-elevation range, reducing the flexibility of this technology. This study introduces a new GNSS-IR sea-level estimation model that combines local mean decomposition (LMD) and Lomb-Scargle periodogram (LSP). LMD can decompose the signal-to-noise ratio (SNR) arc into a series of signal components with different frequencies. The signal components containing information from the sea surface are selected to construct the oscillation term, and its frequency is extracted by LSP. To this end, observational data from SC02 sites in the United States are used to evaluate the accuracy level of the model. Then, the performance of LMD and the influence of noise on retrieval results are analyzed from two aspects: RH ranges and satellite-elevation ranges. Finally, the sea-level variation for one consecutive year is estimated to verify the stability of the model in long-term monitoring. The results show that the oscillation term obtained by LMD has a lower noise level than other signal separation methods, effectively improving the accuracy of retrieval results and avoiding abnormal values. Moreover, it still performs well under loose constraints (a wide RH range and a high-elevation range). In one consecutive year of retrieval results, the new model based on LMD has a significant improvement effect over quadratic fitting, and the root mean square error and mean absolute error of retrieval results obtained in each month on average are improved by 8.34% and 8.87%, respectively.