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.     

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.     

The X-TRACK/ALES multi-mission processing system: New advances in altimetry towards the coast

In the context of the ESA Climate Change Initiative project, a new coastal sea level altimetry product has been developed in order to support advances in coastal sea level variability studies. Measurements from Jason-1,2&3 missions have been retracked with the Adaptive Leading Edge Subwaveform (ALES) Retracker and then ingested in the X-TRACK software with the best possible set of altimetry corrections. These two coastal altimetry processing approaches, previously successfully validated and applied to coastal sea level research, are combined here for the first time in order to derive a 16-year-long (June 2002 to May 2018), high-resolution (20-Hz), along-track sea level dataset in six regions: Northeast Atlantic, Mediterranean Sea, West Africa, North Indian Ocean, Southeast Asia and Australia. The study demonstrates that this new coastal sea level product called X-TRACK/ALES is able to extend the spatial coverage of sea level altimetry data ~3.5 km in the land direction, when compared to the X-TRACK 1-Hz dataset. We also observe a large improvement in coastal sea level data availability from Jason-1 to Jason-3, with data at 3.6 km, 1.9 km and 0.9 km to the coast on average, for Jason-1, Jason-2 and Jason-3, respectively. When combining measurements from Jason-1 to Jason-3, we reach a distance of 1.2–4 km to the coast. When compared to tide gauge data, the accuracy of the new altimetry near-shore sea level estimations also improves. In terms of correlations with a large set of independent tide gauge observations selected in the six regions, we obtain an average value of 0.77. We also show that it is now possible to derive from the X-TRACK/ALES product an estimation of the ocean current variability up to 5 km to the coast. This new altimetry dataset, freely available, will provide a valuable contribution of altimetry in coastal marine research community.     

基于FY-3C/MWHTS观测资料反演中低纬度海面气压

利用风云三号C星（FY-3C）微波温湿探测仪（MWHTS）的实测亮温数据，开展了中低纬度（40°S-40°N）区域海面气压反演研究.MWHTS 118.75GHz氧气通道的辐射亮温测量值与氧气气柱总量密切相关，可用于反演海面气压.根据辐射传输方程分析了MWHTS 8个氧气通道对海面气压的敏感性.结果表明，与位于氧气吸收带中心的通道相比，位于吸收带翼区的探测通道对海面气压的变化更敏感.基于神经网络方法建立了中低纬度海面气压反演算法，通过将反演结果与ERA-Interim再分析数据以及原位观测数据进行对比分析，发现建立的反演算法在中低纬度晴空、云天、雨天条件下，对海面气压的估计精度分别为2.0，3.0和3.5hPa.最后，开展了生成初期热带气旋的反演试验，结果表明反演的海面气压资料对热带低压的判别有一定帮助.      

GPS时间比对数据的Vondrak平滑和三次样条插值处理

介绍了Vondrak平滑方法和三次样条插值方法。利用国家授时中心时间频率基准重点实验室的GPS时间比对数据,先进行预处理和规范化处理,再采用Vondrak平滑方法和三次样条插值方法进行处理,得到的结果表明:在实际中利用Vondrak平滑方法和三次样条插值方法对GPS时间比对数据处理是可行的,减弱了随机噪声的影响。     

微波干涉仪测量羽流电子密度反演方法

利用微波干涉仪进行推进器羽流密度测量的反演方法研究.重点针对羽流等离子体密度反演的Abel逆变换数值求解,采用离散化算法、三次样条插值算法、Hankel-Fourier算法以及Nestor-Olsen算法等四种方法进行仿真分析和比较.通过对这四种方法在无噪声和有噪声两种情况下反演误差的比较,找出适用于实际干涉仪数据处理的方法;通过对采样点数和反演之间的关系分析,给出解决欠采样问题的方法和数值参考;在分析比较的基础上,总结数值处理的必要步骤.利用模拟实验测试数据进行验证并对反演结果进行分析.      

Towards development of a consistent orbit series for TOPEX,Jason-1, and Jason-2

The TOPEX/Poseidon, Jason-1 and Jason-2 set of altimeter data now provide a time series of synoptic observations of the ocean that span nearly 17 years from the launch of TOPEX in 1992. The analysis of the altimeter data including the use of altimetry to monitor the global change in mean sea level requires a stable, accurate, and consistent orbit reference over the entire time span. In this paper, we describe the recomputation of a time series of orbits that rely on a consistent set of reference frames and geophysical models. The recomputed orbits adhere to the IERS 2003 standards for ocean and earth tides, use updates to the ITRF2005 reference frame for both the SLR and DORIS stations, apply GRACE-derived models for modeling of the static and time-variable gravity, implement the University College London (UCL) radiation pressure model for Jason-1, use improved troposphere modeling for the DORIS data, and apply the GOT4.7 ocean tide model for both dynamical ocean tide modeling and for ocean loading. The new TOPEX orbits have a mean SLR fit of 1.79 cm compared to 2.21 cm for the MGDR-B orbits. These new TOPEX orbits agree radially with independent SLR/crossover orbits at 0.70 cm RMS, and the orbit accuracy is estimated at 1.5–2.0 cm RMS over the entire TOPEX time series. The recomputed Jason-1 orbits agree radially with the Jason-1 GDR-C orbits at 1.08 cm RMS. The GSFC SLR/DORIS dynamic and reduced-dynamic orbits for Jason-2 agree radially with independent orbits from the CNES and JPL at 0.70–1.06 cm RMS. Applying these new orbits, and using the latest altimeter corrections for TOPEX, Jason-1, and Jason-2 from September 1992 to May 2009, we find a global rate in mean sea level of 3.0 ± 0.4 mm/yr.     

Comparative analysis of four different single-frequency PPP models on positioning performance and atmosphere delay retrieval

Single-frequency precise point positioning (SF-PPP) has attracted increasing attention due to its high precision and cost effectiveness. With various strategies to handle the dominant error, i.e., ionosphere delay, the ionosphere-float (IF), ionosphere-free-half (IFH), ionosphere-corrected (IC), and ionosphere-weighted (IW) SF-PPP models are certain to possess different characteristics and performance levels. This study is dedicated to assessing and comparing the four models from model characteristics, positioning performance, and atmosphere delay retrieval. The model comparison shows that IC and IW models are full-rank while IF and IFH models have a rank deficiency of size one that will result in biased estimations, which means the better solvability of IC and IW models. The experiments are carried out based on the 7-day Global Positioning System (GPS) observations collected at 57 global Multi-GNSS Experiment (MGEX) stations and Global Ionosphere Map (GIM) products. The results indicate that the IW model can accelerate SF-PPP convergence and achieve higher positioning accuracy compared to the other three SF-PPP models, especially in kinematic mode. With convergence criteria of 0.25 m in horizontal and 0.5 m in vertical, the east/north/up convergence times of IW model are 0.5/15.0/25.0 min and 0.5/16.0/36.5 min for static and kinematic modes, respectively. The IW model is able to achieve an instantaneous positioning accuracy of 0.28/0.35/0.75 m. In addition, a real kinematic test also demonstrates the best positioning solutions of IW model. Regarding troposphere delay retrieval, the IF, IFH, and IW models obtain a comparable daily accuracy of 3.0 cm on average, while the IC model achieves the worst accuracy of 8.0 cm. For precise ionosphere delay estimation, IW model only needs an average initialization time of 34.3 min, but a longer initialization time of 51.6 min is required for IF model. The daily precision of ionosphere delay estimation for IW model can reach up to 10.8 cm. At the present accuracy of GIM products, it is suggested that the IW model should be adopted for SF-PPP first due to its superior performance in positioning and atmosphere delay retrieval.     

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 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.     

Regional in situ validation of satellite altimeters: Calibration and cross-calibration results at the Corsican sites

The in situ validation of the satellite altimeter sea surface heights is generally performed either at a few local points directly flown over by the satellites or using the global tide gauge network. A regional in situ calibration method was developed by NOVELTIS in order to monitor the altimeter data quality in a perimeter of several hundred kilometres around a given in situ calibration site. The primary advantage of this technique is its applicability not only for missions flying over dedicated sites but also for missions on interleaved or non repetitive orbits. This article presents the altimeter bias estimates obtained with this method at the Corsican calibration site, for the Jason-1 mission on its nominal and interleaved orbits as well as for the Jason-2 and Envisat missions. The various regional bias estimates (8.2 cm and 7.4 cm for Jason-1 respectively on the nominal and interleaved orbits in Senetosa, 16.4 cm for Jason-2 in Senetosa and 47.0 cm for Envisat in Ajaccio, with an accuracy between 2.5 cm and 4 cm depending on the mission) are compared with the results obtained by the other in situ calibration teams. This comparison demonstrates the coherency at the centimetre level, the stability and the generic character of the method, which would also be of benefit to the new and future altimeter missions such as Cryosat-2, SARAL/AltiKa, Sentinel-3, Jason-3, Jason-CS.     

Snow depth retrieval by using robust estimation algorithm to perform multi-SNR and multi-system fusion in GNSS-IR

Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) technology provides a new means of snow depth detection. Multi-satellite and multi-Signal-to-Noise Ratio (SNR) provide more data for daily high-precision snow depth retrieval, but also face the problem of data fusion and effective utilization. Therefore, this study proposes a robust estimation algorithm based on multi-satellite and multi-SNR fusion applied to the observations of a GNSS station in Alaska. This study uses four solutions (S_avg, S_med, S_{RE_avg} and S_{RE_med}) to carry out multi-system fusion snow depth inversion and precision comparison research. The S_avg has more obvious disadvantages, which is not suitable for snow depth assessment. The S_{RE_avg} and S_{RE_med} have better snow depth retrieval effects in the snowy periods. The correlation coefficient (R), root mean square error (RMSE) and mean error (ME) of the calculated snow depth using the robust estimation algorithm with respect to the nearest in-situ measurements reached 0.759, 3.7 cm and ?1.4 cm, respectively. Compared with the S_med, the R is increased by 2.0 %, the RMSE corresponds to an improvement of 2.6 %. Moreover, the ME of the snow depth retrievals, as an indicator of the measurement bias, has significantly decreased by 6.7 %. The result also shows that the snow depth inversion by the robust estimation algorithm is more consistent with the in-situ measurements, further extending and advancing the optimal algorithm for snow depth retrieval.     

Initial accuracy and reliability of current BDS-3 precise positioning,velocity estimation,and time transfer (PVT)

The primary system of Chinese global BeiDou satellite system (BDS-3) was completed to provide global services on December 27, 2018; this was a key milestone in the development process for BDS in terms of its provision of global services. Therefore, this study analyzed the current performance of BDS-3, including its precise positioning, velocity estimation, and time transfer (PVT). The datasets were derived from international GNSS monitoring and assessment system (iGMAS) tracking networks and the two international time laboratories in collaboration with the International Bureau of Weights and Measures (BIPM). With respect to the positioning, the focus is on the real-time kinematic (RTK) positioning and precise point positioning (PPP) modes with static and kinematic scenarios. The results show that the mean available satellite number is 4.8 for current BDS-3 system at short baseline XIA1–XIA3. The RTK accuracy for three components is generally within cm level; the 3D mean accuracy is 8.9 mm for BDS-3 solutions. For the PPP scenarios, the convergence time is about 4 h for TP01 and BRCH stations in two scenarios. After the convergence, the horizontal positioning accuracy is better than cm level and the vertical accuracy nearly reaches the 1 dm level. With respect to kinematic scenarios, the accuracy stays at the cm level for horizontal components and dm level for the vertical component at two stations. In terms of velocity estimation, the horizontal accuracy stays at a sub-mm level, and the vertical accuracy is better than 2 mm/s in the BDS-3 scenario, even in the Arctic. In terms of time and frequency transfer, the noise level of BDS-3 time links can reach 0.096 ns for long-distances link NT01–TP02 and 0.016 ns for short-distance links TP01–TP02. Frequency stability reaches 5E–14 accuracy when the averaging time is within 10,000 s for NT01–TP02 and 1E–15 for TP01–TP02.     

结合嵌入可信度的B样条小波边缘检测

边缘检测中，用一个由输入数据得到的模板进行匹配是很有意义的，因为它提供了一种独立测量存在所用边缘模板的可信度的方法。文章充分利用边缘信息的多尺度特性及小波变换的特性，设计三次B样条平滑滤波算子，再结合嵌入可信度方法进行边缘检测，并进一步根据人类视觉系统的敏感性，对噪声严重的图像边缘检测进行了研究。实验结果表明，丈中所给的方法能准确检测出图像边缘，效果较好。     

Comprehensive outage compensation of real-time orbit and clock corrections with broadcast ephemeris for ambiguity-fixed precise point positioning

The main challenge in real-time precise point positioning (PPP) is that the data outages or large time lags in receiving precise orbit and clock corrections greatly degrade the continuity and real-time performance of PPP positioning. To solve this problem, instead of directly predicting orbit and clock corrections in previous researches, this paper presents an alternative approach of generating combined corrections including orbit error, satellite clock and receiver-related error with broadcast ephemeris. Using ambiguities and satellite fractional-cycle biases (FCBs) of previous epoch and the short-term predicted tropospheric delay through linear extrapolation model (LEM), combined corrections at current epoch are retrieved and weighted with multiple reference stations, and further broadcast to user for continuous enhanced positioning during outages of orbit and clock corrections. To validate the proposed method, two reference station network with different inter-station distance from National Geodetic Survey (NGS) network are used for experiments with six different time lags (i.e., 5 s, 10 s, 15 s, 30 s, 45 s and 60 s), and one set of data collected by unmanned aerial vehicle (UAV) is also used. The performance of LEM is investigated, and the troposphere prediction accuracy of low elevation (e.g., 10–20degrees) satellites has been improved by 44.1% to 79.0%. The average accuracy of combined corrections before and after LEM is used is improved by 12.5% to 77.3%. Without LEM, an accuracy of 2–3 cm can be maintained only in case of small time lags, while the accuracies with LEM are all better than 2 cm in case of different time lags. The performance of simulated kinematic PPP at user end is assessed in terms of positioning accuracy and epoch fix rate. In case of different time lags, after LEM is used, the average accuracy in horizontal direction is better than 3 cm, and the accuracy in up direction is better than 5 cm. At the same time, the epoch fix rate has also increased to varying degrees. The results of the UAV data show that in real kinematic environment, the proposed method can still maintain a positioning accuracy of several centimeters in case of 20 s time lag.     

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.     

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.     

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).     

高动态GPS/BD2组合导航信号模拟器关键技术研究

高动态组合导航信号模拟器是高动态组合导航接收机设计验证的高效平台。本文给出了高动态GPS/BD2组合导航信号模拟器关键部分架构和实现方案,重点阐述了高动态信号的产生方法、提高模拟器运算效率的三次样条插值算法、反SINC滤波器补偿方法和保证模拟器通道一致性措施。对这一信号模拟器所产生的GNSS信号进行了验证。     

板料成形的数值分析及程序系统

本文讨论了板料成形的数值分析方法,并介绍一个能在微机上运行的程序系统——CASF(Computer Aided Sheetmetal Forming)01系统。 CASF01系统采用参数三次样条描述板金零件的几何外形,按弹-塑性流动理论用完全拉格朗日有限元法计算成形过程中的应力应变分布。由于参数样条的插值性和分段描述特点与有限元法的结构离散在基本思想和处理方法上的相似性,系统内曲面描述和力学分析程序间数据传递迅速方便。圆板胀形及其汽车零件的计算实例表明了CASF01系统的可靠性和实用性。