Surface Height Measurements Research Articles

Antarctic ice surface properties inferred from Ka and Ku band altimeter waveforms

Altimetry missions designed for ocean monitoring can also evaluate the Antarctic ice sheet’s mass balance by measuring surface height. However, the returned radar echoes (waveforms) have complex shapes influenced by various snow and ice surface properties at multiple scales. Radar altimeters, operating in different modes and frequencies, interact with these surface properties in diverse ways. In this study, we developed a method to assess Antarctic surface properties using data from SARAL/AltiKa and Sentinel-3A & 3B altimeters for June 2021 and January 2023, respectively. We normalized and averaged the observed waveforms in 5 × 5 km2 grid cells. These were then used to create false-color images, with each grid cell’s average power and time gate represented as different ‘bands’. False-color images were analyzed using Principal Component Analysis (PCA) and ISODATA unsupervised classification to identify regions of Antarctica with similar surface properties. We achieved a percent variance of 73% and 84% for the first three Principal Components (PCs), and 96% and 98% for the first ten PCs with the Sentinel-3 and SARAL/AltiKa datasets, respectively. Finally, we analyzed the Ka and Ku band altimeter waveform shapes for each identified class to better understand snow and ice sensitivity to waveforms.

Improving GNSS-IR Sea Surface Height Accuracy Based on a New Ionospheric Stratified Elevation Angle Correction Model

Approximately 71% of the Earth’s surface is covered by vast oceans. With the exacerbation of global climate change, high-precision monitoring of sea surface height variations is of vital importance for constructing global ocean gravity fields and preventing natural disasters in the marine system. Global Navigation Satellite System Interferometry Reflectometry (GNSS-IR) sea surface altimetry is a method of inferring sea surface height based on the signal-to-noise ratio of satellite signals. It enables the retrieval of sea surface height variations with high precision. However, navigation satellite signals are influenced by the ionosphere during propagation, leading to deviations in the measured values of satellite elevation angles from their true values, which significantly affects the accuracy of GNSS-IR sea surface altimetry. Based on this, the contents of this paper are as follows: Firstly, a new ionospheric stratified elevation angle correction model (ISEACM) was developed by integrating the International Reference Ionosphere Model (IRI) and ray tracing methods. This model aims to improve the accuracy of GNSS-IR sea surface altimetry by correcting the ionospheric refraction effects on satellite elevation angles. Secondly, four GNSS stations (TAR0, PTLD, GOM1, and TPW2) were selected globally, and the corrected sea surface height values obtained using ISEACM were compared with observed values from tide gauge stations. The calculated average Root Mean Square Error (RMSE) and Pearson Correlation Coefficient (PCC) were 0.20 m and 0.83, respectively, indicating the effectiveness of ISEACM in sea surface height retrieval. Thirdly, a comparative analysis was conducted between sea surface height retrieval before and after correction using ISEACM. The optimal RMSE and PCC values with tide gauge station observations were 0.15 m and 0.90, respectively, representing a 20.00% improvement in RMSE and a 4.00% improvement in correlation coefficient compared to traditional GNSS-IR retrieval heights. These experimental results demonstrate that correction with ISEACM can effectively enhance the precision of GNSS-IR sea surface altimetry, which is crucial for accurate sea surface height measurements.

Dynamic three-dimensional measurement and analysis of rotating polygons

Rotating polygons are geometric patterns formed spontaneously by the free surface of a rotating fluid driven by a rotating disk at the bottom of a partially filled cylindrical container. Most previous studies mainly predict the number of polygon apexes as a function of disk rotation speed and initial fluid depth. We propose to experimentally characterize this three-dimensional instability by means of highly accurate measurements of the free surface height using Fourier transform profilometry. For a given initial height of 26 mm in a cylindrical cavity of radius 140 mm, these measurements enabled us to not only revisit quantitatively the previous analysis in the fully developed regime but also extend the analysis to the spin-up regime (starting from rest). This latter regime has not been explored. In addition, we describe the mixed-mode regime at the boundary between two clearly established polygons. Thanks to precise space-time resolved surface height measurements, we propose a decomposition of each azimuthal mode that provides valuable information on the growth and dynamics of rotating polygons and can, therefore, serve as a basis for future numerical simulations and theoretical models.

Mapping geodetically inferred Antarctic ice surface height changes into thickness changes: a sensitivity study

Abstract. Determining recent Antarctic ice volume changes from satellite altimeter measurements of ice surface height requires a correction for contemporaneous vertical crustal deformation. This correction must consider two main sources of crustal deformation: (1) ongoing glacial isostatic adjustment (GIA), that is, the deformational, gravitational, and rotational response to Late Pleistocene and Holocene ice and ocean mass changes and (2) modern ice mass change. In this study, we seek to quantify the uncertainties associated with each of these corrections. Corrections of ice surface height changes for correction 1 have generally involved the adoption of global models of GIA defined by some preferred combination of ice history and mantle viscoelastic structure. We have computed the GIA correction generated from a coupled ice sheet–sea level model and a realistic Earth model incorporating three-dimensional viscoelastic structure. Integrating the difference between this correction and those from recent GIA analyses widely adopted in the literature yields an uncertainty in total present-day ice volume change equivalent to approximately 10 % of Antarctic ice mass loss inferred for the period 2010–2020. This reinforces earlier work indicating that ice histories characterized by relatively high excess ice volume at the Last Glacial Maximum may be introducing a significant error in estimates of modern melt rates. Regarding correction 2, a spatially invariant scaling has commonly been used to convert GIA-corrected ice surface height changes obtained from satellite altimetry to ice volume estimates. We adopt modeling results based on a projection of Antarctic ice mass change over the period 2015–2055 to demonstrate a spatial variability in the scaling of up to 10 % across the ice sheet. Furthermore, using these calculations, we find a systematic error of ∼ 3 % in the projected net ice volume change, with most of the difference arising in areas of West Antarctica above mantle zones of low viscosity.

Evaluation of a 4DVAR Assimilation System in the California Current at the SWOT Calibration/Validation Site

Abstract This study evaluates the feasibility of applying the Estimating the Circulation and Climate of the Ocean (ECCO) data assimilation (DA) framework to a submesoscale-resolving model [Massachusetts Institute of Technology General Circulation Model (MITgcm), at 1-km grid resolution]. This is in preparation for future studies to understand and assimilate the novel swath measurements of sea surface height from the Surface Water and Ocean Topography (SWOT) satellite mission. The model domain is centered at the SWOT calibration/validation (CalVal) site, located 300 km offshore of Monterey Bay, California. We assimilate vertical profiles of temperature and salinity from a linear array of three SWOT prelaunch CalVal moorings, between September and December 2019. Two model solutions are analyzed: 1) a nonassimilating forward simulation termed “first-guess” and 2) an optimized solution that assimilates the in situ observations. Both runs are nested within the global 1/12° Hybrid Coordinate Ocean Model that uses Navy Coupled Ocean Data Assimilation (HYCOM/NCODA) analysis. We evaluate the performance by comparing the two model solutions against assimilated and withheld in situ observations. We show that by assimilating hydrographic data, the model performance over the first-guess solution is improved with an error-to-observation reduction of 30%–45% for temperature, 14%–41% for salinity, and 44%–56% for steric height. Over the study period, the average steric height error at the three assimilated moorings was 1.27 cm for the optimized solution versus 2.6 cm for the first-guess solution. A comparison to withheld glider observations shows that the optimized solution outperforms the first-guess solution with an error-to-observation reduction of approximately 38% in steric height (1.5 versus 2.4 cm). This study indicates, for the first time, that the MITgcm–ECCO framework can be successfully applied to the reconstruction of submesoscale ocean variability, via the nesting of a high-resolution regional domain into a global outer domain.

Learning Sea Surface Height Interpolation From Multi‐Variate Simulated Satellite Observations

AbstractSatellite‐based remote sensing missions have revolutionized our understanding of the Ocean state and dynamics. Among them, space‐borne altimetry provides valuable Sea Surface Height (SSH) measurements, used to estimate surface geostrophic currents. Due to the sensor technology employed, important gaps occur in SSH observations. Complete SSH maps are produced using linear Optimal Interpolations (OI) such as the widely used Data Unification and Altimeter Combination System (duacs). On the other hand, Sea Surface Temperature (SST) products have much higher data coverage and SST is physically linked to geostrophic currents through advection. We propose a new multi‐variate Observing System Simulation Experiment (OSSE) emulating 20 years of SSH and SST satellite observations. We train an Attention‐Based Encoder‐Decoder deep learning network (abed) on this data, comparing two settings: one with access to ground truth during training and one without. On our OSSE, we compare abed reconstructions when trained using either supervised or unsupervised loss functions, with or without SST information. We evaluate the SSH interpolations in terms of eddy detection. We also introduce a new way to transfer the learning from simulation to observations: supervised pre‐training on our OSSE followed by unsupervised fine‐tuning on satellite data. Based on real SSH observations from the Ocean Data Challenge 2021, we find that this learning strategy, combined with the use of SST, decreases the root mean squared error by 24% compared to OI.

Sea Surface Height Measurements Based on Multi-Antenna GNSS Buoys.

Sea level monitoring is an essential foundational project for studying global climate change and the rise in sea levels. Satellite radar altimeters, which can sometimes provide inaccurate sea surface height data near the coast, are affected by both the instrument itself and geophysical factors. Buoys equipped with GNSS receivers offer a relatively flexible deployment at sea, allowing for long-term, high-precision measurements of sea surface heights. When operating at sea, GNSS buoys undergo complex movements with multiple degrees of freedom. Attitude measurements are a crucial source of information for understanding the motion state of the buoy at sea, which is related to the buoy's stability and reliability during its development. In this study, we designed and deployed a four-antenna GNSS buoy with both position and attitude measurement capabilities near Jimiya Wharf in Qingdao, China, to conduct offshore sea surface monitoring activities. The GNSS data were processed using the Precise Point Positioning (PPK) method to obtain a time series of sea surface heights, and the accuracy was evaluated using synchronous observation data from a small sea surface height radar. The difference between the GNSS buoy and the full-time radar was calculated, resulting in a root-mean-square error (RMSE) of 1.15 cm. Concurrently, the attitude of the GNSS buoy was calculated using multi-antenna technology, and the vertical elevation of the GNSS buoy antenna was corrected using the obtained attitude data. The RMSE between the corrected GNSS buoy data and the high ground radar was 1.12 cm, indicating that the four-antenna GNSS buoy can not only acquire high-precision coastal sea level data but also achieve synchronous measurement of the buoy's attitude. Furthermore, the data accuracy was also improved after the sea level attitude correction.

Advancing Sea Surface Height Retrieval through Global Navigation Satellite System Reflectometry: A Model Interaction Approach with Cyclone Global Navigation Satellite System and FengYun-3E Measurements

The measurement of sea surface height (SSH), which is of great importance in the field of oceanography, can be obtained through the innovative technique of GNSS-R for remote sensing. This research utilizes the dataset from spaceborne GNSS-R platforms, the Cyclone Global Navigation Satellite System (CYGNSS) and FengYun-3E (FY-3E), as the primary source of data for retrieving sea surface height (SSH). The utilization of artificial neural networks (ANNs) allows for the accurate estimation of ocean surface height with a precision of meter-level accuracy throughout the period of 1–17 August 2022. As a traditional machine learning method, an ANN is employed to extract pertinent data features, facilitating the acquisition of precise sea surface height estimations. Additionally, separate models are devised for both GNSS-R platforms, one based on constant velocity (CV) and the other on constant acceleration (CA). The Interactive Multiple Model (IMM) is utilized as the main method to combine the four models and convert the likelihood of each model. The transition between the models allows the filters to effectively adapt to dynamic changes and complex environments. This approach relies on the fundamental notion of the Kalman filter (KF), which showcases robust noise handling capabilities in predicting the SSH, separately. The results demonstrate that the model interaction technology is capable of efficiently filtering and integrating SSH data, yielding a Root Mean Square Error (RMSE) of 1.03 m. This corresponds to a 9.84% enhancement compared to the retrieved height from CYGNSS and a 37.19% enhancement compared to the retrieved height from FY-3E. The model proposed in this paper provides a potential scheme for the GNSS-R data fusion of multiple platforms and multiple models. In the future, more data sources and more models can be added to achieve more accurate adaptive fusion.

A review of the BuFeng-1 GNSS-R mission: calibration and validation results of sea surface and land surface

ABSTRACT In this paper, we will conclude the results of Bufeng-1 (BF-1) A/B data processing, calibration workflow, and validation of the calibrated sea surface winds, land surface soil moisture, and sea surface height measurements. Since 2019, the BF-1 mission has operated in-orbit for over 4 years. The Earth reflected delay Doppler maps (DDMs) are continuously collected to perform global sea surface and land observations. At the same time, the intermediate frequency (IF) raw data are also obtained for 12 seconds every pass in diagnostic mode. To begin with, a brief description of the spaceborne Global Navigation Satellite System Reflectometry (GNSS-R) technique will be provided in the introduction. Next, we will present the overview of Chinese BF-1 mission and the data specifications used in our research. In the next section, the BF-1 mission-related spaceborne power calibration and validation are presented to show the support to power DDM observable production for sea surface and land surface applications. Then, the status of Chinese Beidou System (BDS) Equivalent Isotropic Radiated Power (EIRP) acquisition programme is then introduced. Furthermore, the latest sea surface height (SSH) measurements results including two modes (group delay and carrier phase) and wind speed derivation based on machine learning (ML) method will be spatial-temporal aligned and validated with auxiliary datasets including Denmark Technology University (DTU) mean sea surface (MSS) products and European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis. The previous published results of sea surface winds retrieval under Hurricane conditions and soil moisture retrieval are also reviewed for the BF-1 mission applications. Finally, the conclusion of BF-1 derived results will be discussed to draw out ongoing/future works.

Medium-range forecasting of oceanic eddy trajectory

ABSTRACT The capability of continuous eddy tracking has been significantly advanced over the past decades, thanks to the availability of sea surface height measurements routinely collected by satellite altimeters. However, due to the complexity of eddy kinematic mechanisms and underlying oceanic processes, a medium-range forecast of individual eddy trajectories is a challenging task. This study develops an algorithm to effectively achieve a precise prediction of eddy propagation with a ten-day lead time by building a physics-embedded temporal evolution model. The theoretical eddy phase speed, current field, and eddy properties are incorporated as physical constraints. Compared to only considering eddy past/climatological velocities, the forecast accuracy of embedded physics constraints is improved by 21%. Forecasting of 2.3 million altimeter-derived eddy tracks globally shows that trajectory predictions are valid for eddies moving towards any direction, and the forecast error achieves 9.9 km on a ten-day average. After systematically evaluating the global forecast error, we conclude that the forecasting accuracy is geographically correlated and affected by external forcings (topography and wind) and eddy properties (geostrophy and life stage). Achieving accurate eddy trajectory prediction is expected to provide critical guidance for in-situ eddy observations, and bring substantial improvements for understanding oceanic substance transportations and biogeochemical processes.

Inversion method of deflection of the vertical based on SWOT wide-swath altimeter data

The deflection of the vertical (DOV) is the key information in the study of ocean gravity field. However, in most areas, the precision of the prime component of DOV is significantly lower than that of the meridian component. To obtain higher accuracy and resolution of ocean gravity information, researchers have proposed a novel altimeter called the wide-swath altimeter. This altimeter allows for the simultaneous acquisition of high-precision and high-resolution two-dimensional measurements of sea surface height (SSH). In this paper, the Surface Water and Ocean Topography (SWOT) mission with a wide-swath altimeter on board is selected for research. One cycle of SWOT sea surface height data is simulated to inverse the DOV in the Arabian Sea (45°E—80°E, 0°–30°N), and the inversion results are compared with those of conventional altimeter data. The results demonstrate that the difference between the meridian and prime components derived from the inversion of SWOT wide-swath data is minimal, significantly outperforming the inversion results of conventional nadir altimeter data. The advantage of SWOT wide-swath altimeter lies in its ability to use the multi-directional geoid slope at any sea surface measurement point to invert the components in the meridian and prime directions. To investigate the impact of this advantage on inversion precision, this paper employs a method to calculate the gradient of the geoid in multiple directions to invert DOV components. The improvement effect of calculating the gradient of the geoid in multiple directions on the precision of DOV component is analyzed. It is found that the accuracy of DOV inversion has significantly improved with the increase of geodetic gradient calculation direction. In addition, the effects of various errors and grid spacing in SWOT wide sea surface height data on the precision of DOV inversion are also analyzed.

Satellite Evidence for Strengthened M2 Internal Tides in the Past 30 Years

AbstractSatellite altimetry sea surface height measurements from 1993 to 2022 are used to show the strengthened mode‐1 M2 internal tides in the past 30 years. Two mode‐1 M2 internal tide models M9509 and M1019 are constructed using the data in 1995–2009 and 2010–2019, respectively. The results show that the global mean M2 internal tides strengthened by 6% in energy. However, the internal tide strengthening is spatially inhomogeneous. Significantly strengthened internal tides are observed in a number of regions including the Aleutian Ridge and the Madagascar‐Mascarene region. Weakened internal tides are observed in the central Pacific. On global average, M1019 leads M9509 by about 10° (20 min in time), suggesting that the propagation speed of M2 internal tides increased. M9509 and M1019 are evaluated using independent altimetry data. The results show that M9509 and M1019 perform better for the data in 1993–1994 and 2020–2022, respectively.

Identifying atmospheric processes favouring the formation of bubble-free layers in the Law Dome ice core, East Antarctica

Abstract. Physical features preserved in ice cores may provide unique records about past atmospheric variability. Linking the formation and preservation of these features and the atmospheric processes causing them is key to their interpretation as palaeoclimate proxies. We imaged ice cores from Law Dome, East Antarctica, using an intermediate layer core scanner (ILCS) and found that thin bubble-free layers (BFLs) occur multiple times per year at this site. The origin of these features is unknown. We used a previously developed age–depth scale in conjunction with regional accumulation estimated from atmospheric reanalysis data (ERA5) to estimate the year and month that the BFLs occurred, and then we performed seasonal and annual analysis to reduce the overall dating errors. We then investigated measurements of snow surface height from a co-located automatic weather station to determine snow surface features co-occurring with BFLs, as well as their estimated occurrence date. We also used ERA5 to investigate potentially relevant local/regional atmospheric processes (temperature inversions, wind scour, accumulation hiatuses and extreme precipitation) associated with BFL occurrence. Finally, we used a synoptic typing dataset of the southern Indian and southwest Pacific oceans to investigate the relationship between large-scale atmospheric patterns and BFL occurrence. Our results show that BFLs occur (1) primarily in autumn and winter, (2) in conjunction with accumulation hiatuses > 4 d, and (3) during synoptic patterns characterised by meridional atmospheric flow related to the episodic blocking and channelling of maritime moisture to the ice core site. Thus, BFLs may act as a seasonal marker (autumn/winter) and may indicate episodic changes in accumulation (such as hiatuses) associated with large-scale circulation. This study provides a pathway to the development of a new proxy for past climate in the Law Dome ice cores, specifically past snowfall conditions relating to synoptic variability over the southern Indian Ocean.

Spectral wear modelling of rubber friction on a hard substrate with large surface roughness

Soft-hard matter friction is a long-standing tribology problem that remains unclarified, requiring engineers to empirically predict the wear life. To clarify this issue, this study examines the transient running-in regime of rubber friction on a hard rough substrate and models the temporal wear progression using the spectrum curves of surface roughness for both materials. Performing a series of friction tests and three-dimensional surface-height measurements, the time-dependent behaviours of the power spectral densities (PSDs) are divided into two phases, namely the initial non-steady and long-term steady phases. The detailed spectral analyses of worn rubber surfaces in the initial phase lead to a blended PSD function between self-affine and K -correlation surface models, consisting of one variable (the Hurst exponent) that is saturated by the substrate self-affinity. Supported by the Greenwood–Williamson theory concerning rough contact mechanics, the volumetric estimate with the blended PSD function is used to assess the volume rate of wear debris in the steady phase, which is validated experimentally. These findings not only improve the wear predictions of soft materials from the initial measurements of worn surfaces but also help clarify the constrained multiscale mechanism of wear.

Steric heights of submesoscale processes and internal gravity waves in the subtropical northwestern Pacific and northern South China Sea as revealed by moored observations

The Surface Water and Ocean Topography (SWOT) altimeter mission provides a good opportunity to globally detect submesoscale processes (submesoscales) from high-resolution sea surface height (SSH) measurements. However, in addition to the balanced mesoscale eddies and submesoscales, the measured SSH also contains signals of unbalanced internal gravity waves (IGWs) including internal tides (ITs) and supertidal IGWs (IGWs with frequencies of 3–8 cycles per day). Therefore, a quantitative understanding of the contributions of the above multiscale dynamic processes to the SSH is a prerequisite for exploring submesoscales from the SWOT-derived SSH data. Here, this issue was investigated through analyzing one-year moored observation-derived near-surface steric heights (SHs) in the subtropical northwestern Pacific (NWP) and northern South China Sea (SCS) which have different dynamic backgrounds. In the sense of annual mean, the root-mean-squared (RMS) SHs of submesoscales (defined as processes with periods of 2–15 days here) and IGWs in the SCS are 1.30 and 5.54 cm, respectively, while they are only 0.70 and 3.19 cm in the NWP. Seasonally, the RMS SH of submesoscales is larger in winter than summer in both regions; with respect to the IGWs, their RMS SH is larger in summer than winter in the SCS but it is opposite in the NWP. Generally, the SHs of diurnal and semidiurnal ITs are dominated by the stationary component in both regions but the proportion of the nonstationary component is much larger in the NWP than the SCS. The sum of the SHs by nonstationary diurnal and semidiurnal ITs exceeds that of submesoscales except in winter in the SCS. Furthermore, we also found that the SHs of supertidal IGWs are always larger than those of submesoscales in both regions and both seasons. By decomposing the IGWs with frequencies of 1–8 cpd (i.e., cycles per day) into different baroclinic modes, we found that for all of the IGWs bands, the SHs are overwhelmingly attributed to the first mode. The results in this study will provide useful information for the application of SWOT data in regions with active IGWs.

A data-assimilative modeling investigation of Gulf Stream variability

An advanced data-assimilative ocean circulation model is used to investigate Gulf Stream (GS) variability during 2017–2018. The modeling system applies a strong-constraint, 4D variational data assimilation algorithm. It assimilates satellite-based sea surface height and sea surface temperature measurements and in situ temperature and salinity profiles. Model skill assessment metrics along with comparisons of GS position and GS's three-dimensional mean kinetic energy with historical observations are applied to validate the data-assimilative model. The resulting time- and space-continuous ocean state estimates are used to diagnose eddy kinetic energy conversion and cross-stream eddy heat and salt fluxes over the two-year study period. The processes leading to kinetic energy conversion are primarily due to GS meanders. Significant inverse energy cascading (EKE→MKE and EKE→EPE) can occur during GS-eddy interactions, particularly during onshore intrusions or offshore meanderings of the GS. Throughout the two-year study period, the cross-stream eddy heat and salt fluxes off Cape Hatteras were predominantly positive (onshore). Both GS offshore meandering (occurring 44% of the time and associated with shelf/slope water export) and GS intrusion (occurring 56% of the time) contribute to onshore heat and salt transport. Improved understanding of these processes and dynamics requires strong integration of an advanced observational infrastructure that combines remote sensing; fixed, mobile, and shore-based observing components; and high-resolution data assimilative models.

A comparison of contemporaneous airborne altimetry and ice-thickness measurements of Antarctic ice shelves

AbstractEstimates of ice shelf mass loss are typically based on surface height measurements, assuming hydrostatic equilibrium and estimated firn thickness. Recent investigations, however, challenge the assumption that ice shelves are freely floating, particularly in proximity to narrow structures such as basal channels and shear margins. We compare contemporaneous measurements of Antarctic ice shelf thickness, from ice-penetrating radar, to freeboard height, from laser altimetry, acquired during multiple airborne surveys. On average, the hydrostatic thickness differs from observed thickness by at least ~17 ± 98 m, but this difference varies well beyond the propagated error within and among ice shelves, and depends on the corrections applied. We find that uncertainty in firn thickness can account for most, but not all, of the imbalance. Overall, errors in hydrostatic thickness do not significantly impact estimated basal melt rates. Our results indicate that localized approaches to estimating ice shelf thickness and rates of change are not applicable at large scales, and vice versa, and point to the need for more abundant and accurate firn and ice thickness measurements to improve estimates and predictions of ice shelf mass loss.

Crossover adjustment of ICESat-2 satellite altimetry for the Arctic region

The Ice, Cloud, and Land Elevation Satellite-2 (ICESat-2) mission, operated by NASA, was launched in September 2018. The mission aims to obtain height measurements that create a global portrait of Earth’s radial dimension, gathering data to monitor changes of terrain including glaciers, sea ice, forests and more. It is important to understand the error budget of the observations, one component of which is radial orbit error. Apart from the altimetric ranging errors, radial orbit errors directly influence the accuracy of the measurement of sea surface height (SSH). These errors can be assessed by analyzing the difference of SSHs at ground track intersections, so-called crossover differences (XO differences). An effective approach is to model the orbit error by minimizing the residual XO difference by the least-squares method. XO differences are assumed to be caused by the difference of radial orbit errors between ascending and descending arcs, the sea surface variation, mispointing, and measurement errors. Since the sea surface variation in a short time interval and measurement errors can be considered as random variable, these residuals can be reduced by the method of XO adjustment. In our study, the RMS XO differences of ICESat-2 is significantly reduced from 17.2 cm to 8.7 cm in the Arctic region.

SARAL/AltiKa measurements for geodetic applications: Impact of drifting and mispointing phase data

The Indo-French SARAL/AltiKa mission in Ka band has provided valuable information on global oceans to cater the needs of oceanographic community. The SARAL/AltiKa has been operating in three different orbital configurations, viz. Exact Repeat Mission (ERM, March 2013 – July 2016), Drifting Phase (DP, July 2016 – February 2019) and Mispointing Phase (MP, February 2019 – till date). We investigate the utility of the SARAL/AltiKa data for geodetic applications. Global crossover analysis of Sea Surface Height (SSH) measurements from SARAL/AltiKa suggests a stable performance throughout its life with similar range of standard deviations during ERM (5.8 cm), DP (5.9 cm) and MP (5.9 cm) configurations. Two separate Mean Sea Surface (MSS) models were retrieved by adding DP and MP data from SARAL/AltiKa to the ERM stacks of SARAL/AltiKa and Jason satellite series. The quality of MSS models were evaluated based on the crossover differences with the ERM database. It is observed that the crossover adjustments have reduced the deviations in SSH errors by ∼30% for both DP-MSS and MP-MSS models. Analysis of along-track sea surface slopes suggests that 99.9% of data in ERM and DP phases and 93.8% of data in MP phase are well within 1 μrad bound corresponding to an accuracy of ∼1 mGal in free-air gravity anomaly. Further, time-series analysis of Sea Level Anomaly (SLA) from SARAL/AltiKa showed a stable performance with no significant drifts throughout its phases. Deviations in daily SLA for SARAL/AltiKa DP (10 cm) is considerably lower than that of Jason-3 (10.2 cm) and CryoSat-2 (10.2 cm) satellites. However, daily SLA for the MP phase showed slightly larger deviation (10.4 cm), owing to the larger number of outliers, which could be easily removed using a simple median filter. The present study reveals the usefulness of MP data from SARAL/AltiKa for geodetic applications.

Low-Cost BDS Reflectometry for Real-Time Water Surface Retrieval

The official launch of the Chinese BeiDou Navigation Satellite System with global coverage (BDS-3) presents significant opportunities for various applications, including precision agriculture and autonomous driving, among others. With its global spatial coverage and hybrid space constellation comprising geosynchronous Earth orbit (GEO), inclined geosynchronous orbit (IGSO), and medium Earth orbit (MEO) satellites, BDS can significantly contribute to various GNSS remote sensing applications that require real-time, precise water surface height measurements with high temporal and spatial resolution, such as in tidal monitoring. In this paper, we propose a carrier-phase-based method for BDS Reflectometry (BDS-R) to precisely retrieve real-time water surface height. Firstly, the BDS-R altimetry method is introduced, along with a detailed explanation of the data processing procedures. Secondly, a quality control method tailored to the characteristics of low-cost BDS devices is developed. Thirdly, a land altimetry experiment is conducted to evaluate the precision of BDS-R and analyze the specific contribution of the BDS hybrid constellation. Finally, a water surface altimetry experiment validates the real-time monitoring capabilities for low-cost BDS-R. The results indicate that low-cost BDS-R can achieve real-time centimeter-level water level monitoring with a temporal resolution of 1 s in lakefront environments. The performance of BDS-R can be significantly improved by the BDS hybrid constellation, particularly IGSOs. It is concluded that low-cost BDS-R has great potential for promoting ground-based GNSS remote sensing applications.