The determination of a one year mean sea surface height track from Geosat altimeter data and ocean variability implications

One year (November 1986 to October 1987) of Geosat altimeter data with improved orbits produced at The Ohio State University has been used to define sea surface heights for 22 ERM and one year averaged Geosat track. All sea surface heights were referenced to the single reference track through the application of geoid gradient corrections. The root mean square (RMS) gradient correction was on the order of ±1 cm although it could reach 20 cm with data points in trench areas. 10 values used to form the mean were considered. Although this study was initially driven by a need for a good reference sea surface for geodetic applications the formation of the reference track yields information on the variability of the ocean surface in the first year of the Geosat ERM. The RMS point variability was ± 12.6 cm with only a very small number of values exceeding 50 cm when a depth editing criteria was used. Global plots of the sea surface variability clearly reveal the major ocean currents and their variations in position in the year. Examination of the 1° × 1° averaged sea surface height variations show average and maximum variability values as follows: Gulf Stream (29 and 50 cm); Kurshio Current (24 and 49 cm); Agulhas Current (24 and 52 cm) and the Gulf of Mexico (18 and 31 cm). These magnitudes may be dependent on the radial orbit correction procedure. To investigate this effect sea slope variations were also computed. These results also showed clear current structures but also high frequency gravity field information despite efforts to average out such information. The data described in the paper is available from the authors for numerous other studies, some of which are suggested in the paper.     

The confidence evaluation for airborne GPS data

l lntroductionIn the winter Of l989 Wuhan Technical Universi-ty of Surveying and Mapping COntracted withTrimble Navigation Ltd. to purchase fOur TrimbIe4000SST receivers. They were required tO suit theaeriaI phWetric work without intreducing avelocity limitation. In February, l993 twO of thereceivers were uPgraded to provide two eventrnarker plugfords and one pulse Per second(lPPS) output axkets. The uPgradd receivers canincormrate external event markers, e. g. the shutter.oPening …     

陆海交界区域厘米级精度似大地水准面的确定

为了得到我国某陆海交界区厘米级精度的区域(似)大地水准面,利用43个高精度GPS/水准点和1 045个实测重力点数据对EGM96,WDM94和GFZ计算的局部重力(似)大地水准面进行了比较与评价。结果表明,在该测区用移去-恢复法确定重力(似)大地水准面时,EGM96应该是首选参考重力场模型。该测区处在陆海交界处,海域无GPS/水准数据。经比较发现,采用距离倒数加权平均法将该区重力似大地水准面拟合于GPS/水准数据比在大范围使用的多项式法效果更好。采用该方法计算的测区(似)大地水准面精度优于3cm。     

A kinematic GPS methodology for sea surface mapping,Vanuatu

During the past few decades, satellite altimetry has brought tremendous new knowledge about the spatial and temporal variations of sea surface heights over the Earth’s oceans. However, the precision is limited over short wavelengths and in coastal areas, and other methods such as kinematic GPS may be needed to fill in this information. We present kinematic GPS work aimed at mapping the sea surface height, with special attention to the precision one can expect. Active marine subduction zones, like the Vanuatu archipelago, may present short wavelength, high amplitude undulations of the sea surface height that are difficult to map with satellite altimetry. This paper presents the methodology used around Santo Island, in Vanuatu, to obtain a well-resolved local sea surface map with a precision of 5–15 cm limited by the sea conditions and the distance from the coastal reference station. We present the results of three campaigns in 2004, 2006 and 2007. Careful observation of the ship behaviour along the surveys as well as simultaneous recording of the ship attitude variations is mandatory to obtain reliable results. We show that the ship GPS antenna height varies with the ship’s velocity and we suggest a method to correct this effect. The final precision is estimated using the crossover differences method.     

Precise orbit determination of the Sentinel-3A altimetry satellite using ambiguity-fixed GPS carrier phase observations

The Sentinel-3 mission takes routine measurements of sea surface heights and depends crucially on accurate and precise knowledge of the spacecraft. Orbit determination with a targeted uncertainty of less than 2 cm in radial direction is supported through an onboard Global Positioning System (GPS) receiver, a Doppler Orbitography and Radiopositioning Integrated by Satellite instrument, and a complementary laser retroreflector for satellite laser ranging. Within this study, the potential of ambiguity fixing for GPS-only precise orbit determination (POD) of the Sentinel-3 spacecraft is assessed. A refined strategy for carrier phase generation out of low-level measurements is employed to cope with half-cycle ambiguities in the tracking of the Sentinel-3 GPS receiver that have so far inhibited ambiguity-fixed POD solutions. Rather than explicitly fixing double-difference phase ambiguities with respect to a network of terrestrial reference stations, a single-receiver ambiguity resolution concept is employed that builds on dedicated GPS orbit, clock, and wide-lane bias products provided by the CNES/CLS (Centre National d’Études Spatiales/Collecte Localisation Satellites) analysis center of the International GNSS Service. Compared to float ambiguity solutions, a notably improved precision can be inferred from laser ranging residuals. These decrease from roughly 9 mm down to 5 mm standard deviation for high-grade stations on average over low and high elevations. Furthermore, the ambiguity-fixed orbits offer a substantially improved cross-track accuracy and help to identify lateral offsets in the GPS antenna or center-of-mass (CoM) location. With respect to altimetry, the improved orbit precision also benefits the global consistency of sea surface measurements. However, modeling of the absolute height continues to rely on proper dynamical models for the spacecraft motion as well as ground calibrations for the relative position of the altimeter reference point and the CoM.     

Baltic Sea Level project with GPS

In order to study the Baltic Sea Level change and to unify national height systems a two week GPS campaign was performed in the region in Autumn 1990. Parties from Denmark, Finland, Germany, Poland and Sweden carried out GPS measurements at 26 tide gauges along the Baltic sea and 8 VLBI and SLR fiducial stations with baseline lengths ranging from 230 km to 1600 km. The observations were processed in the network mode with the Bernese version 3.3 software using orbit improvement techniques. To get rid of the scale error introduced by the ionospheric refraction from single-frequency data, the local models of the ionosphere were estimated using L4 observations. The tropospheric zenith corrections were also considered. The preliminary results show average root mean square (RMS) errors of about ±3 cm in the horizontal position and ±7 cm in the vertical position relative to the Potsdam SLR station in ITRF89 system. After transformation of the GPS results to geoid heights using the levelled heights, an absolute comparison with gravimetric geoid heights using the least squares modification of Stokes' formula (LSMS), the modified Molodensky and the NKG Scandinavian geoid 1989 (NGK-89) models gives a standard deviation of the difference of ±7cm to ±9cm for the NKG-89 model and of ±9cm to ±30cm for the LSMS and the modified Molodensky model. The Swedish height system is found to be about 8-37cm higher than those of the other Baltic countries for NKG-89 model.     

A spectral optimally interpolated mean sea surface from satellite radar altimetry

 A technique is presented for the development of a high-precision and high-resolution mean sea surface model utilising radar altimetric sea surface heights extracted from the geodetic phase of the European Space Agency (ESA) ERS-1 mission. The methodology uses a cubic-spline fit of dual ERS-1 and TOPEX crossovers for the minimisation of radial orbit error. Fourier domain processing techniques are used for spectral optimal interpolation of the mean sea surface in order to reduce residual errors within the initial model. The EGM96 gravity field and sea surface topography models are used as reference fields as part of the determination of spectral components required for the optimal interpolation algorithm. A comparison between the final model and 10 cycles of TOPEX sea surface heights shows differences of between 12.3 and 13.8 cm root mean square (RMS). An un-optimally interpolated surface comparison with TOPEX data gave differences of between 15.7 and 16.2 cm RMS. The methodology results in an approximately 10-cm improvement in accuracy. Further improvement will be attained with the inclusion of stacked altimetry from both current and future missions. Received: 22 December 1999 / Accepted: 6 November 2000     

Analysis of some systematic errors affecting altimeter-derived sea surface gradient with application to geoid determination over Taiwan

This paper analyzes several systematic errors affecting sea surface gradients derived from Seasat, Geosat/ERM, Geosat/GM, ERS-1/35d, ERS-1/GM and TOPEX/POSEIDON altimetry. Considering the data noises, the conclusion is: (1) only Seasat needs to correct for the non-geocentricity induced error, (2) only Seasat and Geosat/GM need to correct for the one cycle per revolution error, (3) only Seasat, ERS-1/GM and Geosat/GM need to correct for the tide model error; over shallow waters it is suggested to use a local tide model not solely from altimetry. The effects of the sea surface topography on gravity and geoid computations from altimetry are significant over areas with major oceanographic phenomena. In conclusion, sea surface gradient is a better data type than sea surface height. Sea surface gradients from altimetry, land gravity anomalies, ship gravity anomalies and elevation data were then used to calculate the geoid over Taiwan by least-squares collocation. The inclusion of sea surface gradients improves the geoid prediction by 27% when comparing the GPS-derived and the predicted geoidal heights, and by 30% when comparing the observed and the geoid-derived deflections of the vertical. The predicted geoid along coastal areas is accurate to 2 cm and can help GPS to do the third-order leveling. Received 22 January 1996; Accepted 13 September 1996     

Surface roughness signatures of summer arctic snow-covered sea ice in X-band dual-polarimetric SAR

ABSTRACT

Surface roughness of sea ice is primary information for understanding sea ice dynamics and air–ice–ocean interactions. Synthetic aperture radar (SAR) is a powerful tool for investigating sea ice surface roughness owing to the high sensitivity of its signal to surface structures. In this study, we explored the surface roughness signatures of the summer Arctic snow-covered first-year sea ice in X-band dual-polarimetric SAR in terms of the root mean square (RMS) height. Two ice campaigns were conducted for the first-year sea ice with dry snow cover in the marginal ice zone of the Chukchi Sea in August 2017 and August 2018, from which high-resolution (4 cm) digital surface models (DSMs) of the sea ice were derived with the help of a terrestrial laser scanner to obtain the in situ RMS height. X-band dual-polarimetric (HH and VV) SAR data (3 m spatial resolution) were obtained for the 2017 campaign, at a high incidence angle (49.5°) of TerraSAR-X, and for the 2018 campaign, at a mid-incidence angle (36.1°) of TanDEM-X 1–2 days after the acquisition of the DSMs. The sea ice drifted during the time between the SAR and DSM acquisitions. As it is difficult to directly co-register the DSM to SAR owing to the difference in spatial resolution, the two datasets were geometrically matched using unmanned aerial vehicle (4 cm resolution) and helicopter-borne (30 cm resolution) photographs acquired as part of the ice campaigns. A total of five dual-polarimetric SAR features―backscattering coefficients at HH and VV polarizations, co-polarization ratio, co-polarization phase difference, and co-polarization correlation coefficient ―were computed from the dual-polarimetric SAR data and compared to the RMS height of the sea ice, which showed macroscale surface roughness. All the SAR features obtained at the high incidence angle were statistically weakly correlated with the RMS height of the sea ice, possibly influenced by the low backscattering close to the noise level that is attributed to the high incidence angle. The SAR features at the mid-incidence angle showed a statistically significant correlation with the RMS height of the sea ice, with Spearman’s correlation coefficient being higher than 0.7, except for the co-polarization ratio. Among the intensity-based and polarimetry-based SAR features, HH-polarized backscattering and co-polarization phase difference were analyzed to be the most sensitive to the macroscale RMS height of the sea ice. Our results show that the X-band dual-polarimetric SAR at mid-incidence angle exhibits potential for estimation of the macroscale surface roughness of the first-year sea ice with dry snow cover in summer.     

Heading and Pitch Determination Using GPS/GLONASS

This article describes a single difference approach to estimate heading and pitch with a twin global positoning system (GPS)/GLONASS (GG) receiver system. Augmentation of GPS with GLONASS is not straightforward, however, because the latter system employs the frequency division multiple access technique to distinguish the signals form different satellites, rather than the code division multiple access technique used by GPS. The fact that each GLONASS signal has its own slightly different frequency makes the double difference (DD) of carrier phase observables no longer possible without modification. To get around this problem, the use of the between-receiver single difference (SD) of the carrier phase observables is proposed. In this case, however, receiver clock and other errors do not cancel out. The possibility of using a common external oscillator for the two receivers is explored. Remaining time and other biases are estimated using a low-pass averaging filter. The single difference integer ambiguities can then be resolved and the heading and pitch can be determined with a relatively good level of accuracy. Static and kinematic tests conducted with a pair of GPS/GLONASS receivers are used to validate the approach. Under reduced visibility, the combined GPS/GLONASS approach is shown to yield superior availability. ? 2000 John Wiley & Sons, Inc.     

Models for Fitting Gravimetric Geoids and GPS Results

The aim of this investigation is to study how to use a gravimetric(quasi) geoid for levelling by GPS data in an optimal way.The advent of precise geodetic GPS has made the use of a technique possible,which might be called GPS- gravimetric geoid determination.In this approach,GPS heights above the reference ellipsoid are determined for points whose levelled (orthometric) height H is above sea level people have already surveyed;for these points,we thus have the values of the geoid undulation N.These values are then used to constrain the geoid undulations N‘ obtained from the gravimetric solution.     

The US Gravimetric Geoid of 2009 (USGG2009): model development and evaluation

A new gravimetric geoid model, USGG2009 (see Abbreviations), has been developed for the United States and its territories including the Conterminous US (CONUS), Alaska, Hawaii, Guam, the Commonwealth of the Northern Mariana Islands, American Samoa, Puerto Rico and the US Virgin Islands. USGG2009 is based on a 1′ × 1′ gravity grid derived from the NGS surface gravity data and the DNSC08 altimetry-derived anomalies, the SRTM-DTED1 3′′ DEM for its topographic reductions, and the global geopotential model EGM08 as a reference model. USGG2009 geoid heights are compared with control values determined at 18,398 Bench Marks over CONUS, where both the ellipsoidal height above NAD 83 and the Helmert orthometric height above NAVD 88 are known. Correcting for the ellipsoidal datum difference, this permits a comparison of the geoid heights to independent data. The standard deviation of the differences is 6.3 cm in contrast to 8.4 cm for its immediate predecessor— USGG2003. To minimize the effect of long-wavelength errors that are known to exist in NAVD88, these comparisons were made on a state-by-state basis. The standard deviations of the differences range from 3–5 cm in eastern states to about 6–9 cm in the more mountainous western states. If the GPS/Bench Marks-derived geoid heights are corrected by removing a GRACE-derived estimate of the long-wavelength NAVD88 errors before the comparison, the standard deviation of their differences from USGG2009 drops to 4.3 cm nationally and 2–4 cm in eastern states and 4–8 in states with a maximum error of 26.4 cm in California and minimum of −32.1 cm in Washington. USGG2009 is also compared with geoid heights derived from 40 tide-gauges and a physical dynamic ocean topography model in the Gulf of Mexico; the mean of the differences is 3.3 cm and their standard deviation is 5.0 cm. When USGG2009-derived deflections of the vertical are compared with 3,415 observed surface astro-geodetic deflections, the standard deviation of the differences in the N–S and E–W components are 0.87′′ and 0.94′′, respectively.     

Role of ocean variability and dynamic ocean topography in the recovery of the mean sea surface and gravity anomalies from satellite altimeter data

Procedures to calculate mean sea surface heights and gravity anomalies from altimeter-derived sea surface heights and along-track sea surface slopes using the least-squares collocation procedure are derived. The slope data is used when repeat track averaging is not possible to reduce ocean variability effects. Tests were carried out using Topex, Geosat, ERS-1 [35-day and 168-day (2 cycle)] data. Calculations of gravity anomalies in the Gulf Stream region were made using the sea surface height and slope data. Tests were also made correcting the sea surface heights for dynamic ocean topography calculated from a degree 360 expansion of data from the POCM-4B global ocean circulation model. Comparisons of the anomaly predictions were carried out with ship data using anomalies calculated for this paper as well as others. Received: 19 August 1996 / Accepted: 14 April 1997     

Time and Frequency Transfer Using GPS Codes and Carrier Phases: Onsite Experiments

Recent studies have shown the capabilities of Global Positioning System (GPS) carrier phases for frequency transfer based on the observations from geodetic GPS receivers driven by stable atomic clocks. This kind of receiver configuration is the kind primarily used within the framework of the International GPS Service (IGS). The International GPS Service/Bureau International des Poids et Mesures (IGS/BIPM) pilot project aims at taking advantage of these GPS receivers to enlarge the network of Time Laboratories contributing to the realization of the International Atomic Time (TAI). In this article, we outline the theory necessary to describe the abilities and limitations of time and frequency transfer using the GPS code and carrier phase observations. We report on several onsite tests and evaluate the present setup of our 12-channel IGS receiver (BRUS), which uses a hydrogen maser as an external frequency reference, to contribute to the IGS/BIPM pilot project. In the initial experimental setup, the receivers had a common external frequency reference; in the second setup, separate external frequency references were used. Independent external clock monitoring provided the necessary information to validate the results. Using two receivers with a common frequency reference and connected to the same antenna, a zero baseline, we were able to use the carrier phase data to derive a frequency stability of 6 × 10⁻¹⁶ for averaging times of one day. The main limitation in the technique originates from small ambient temperature variations of a few degrees Celsius. While these temperature variations have no effect on the functioning of the GPS receiver within the IGS network, they reduce the capacities of the frequency transfer results based on the carrier phase data. We demonstrate that the synchronization offset at the initial measurement epoch can be estimated from a combined use of the code and carrier phase observations. In our test, the discontinuity between two consecutive days was about 140 ps. ? 1999 John Wiley & Sons, Inc.     

卫星测高沿轨海面高的精细结构及其应用技术初探

首先介绍了频域和多尺度域中的两种沿轨测高海面高精细结构，进而提出了利用沿轨测高海面高精细结构计算平均海面高与海平面距平的新方法，最后进一步讨论了沿轨平均海面高和海平面距平的频谱和多尺度分解，以及它们随时间的变化特性。     

The value of ocean reflections of GPS signals to enhance satellite altimetry: data distribution and error analysis

The time and space distribution of general reflection altimetry from two satellites (senders and receivers) via the the oceans surface is examined with specific reference to GPS senders and two current receiving satellites. While a considerable enhancement of conventional altimeter coverage is possible in all configurations if the reflection signals can be used, repeating passes of these (with GPS senders) having reasonably small cycle times (days to tens of days) occur only if the receiving orbit is nearly polar. Results of an analysis of the fundamental geometry show that over a large range of reflection angles the error of recovered sea heights depends almost entirely on the errors in the delay signal and the radial error of the receiving satellite (using current estimates of GPS orbit accuracies). The most critical element is the precision of the delay measurement. Both it and the accuracy of the receiving orbit should be below the decimeter level for the technique to achieve its full potential.     

GPS海面反射信号特性仿真分析

利用GPS反射信号遥感陆地和海面的GPS—R技术已经得到日益关注。对海面反射信号的极化特性进行分析,分析结果表明：GPS信号经海面反射后,反射信号同时包含右旋和左旋信号,且两者强度与卫星仰角有直接关系;反射的左旋和右旋信号的功率相差可高达30dB。为海面遥感以及专门的GPS接收机的研制提供了必要的参数支撑。     

Assessment of long-range kinematic GPS positioning errors by comparison with airborne laser altimetry and satellite altimetry

Long-range airborne laser altimetry and laser scanning (LIDAR) or airborne gravity surveys in, for example, polar or oceanic areas require airborne kinematic GPS baselines of many hundreds of kilometers in length. In such instances, with the complications of ionospheric biases, it can be a real challenge for traditional differential kinematic GPS software to obtain reasonable solutions. In this paper, we will describe attempts to validate an implementation of the precise point positioning (PPP) technique on an aircraft without the use of a local GPS reference station. We will compare PPP solutions with other conventional GPS solutions, as well as with independent data by comparison of airborne laser data with “ground truth” heights. The comparisons involve two flights: A July 5, 2003, airborne laser flight line across the North Atlantic from Iceland to Scotland, and a May 24, 2004, flight in an area of the Arctic Ocean north of Greenland, near-coincident in time and space with the ICESat satellite laser altimeter. Both of these flights were more than 800 km long. Comparisons between different GPS methods and four different software packages do not suggest a clear preference for any one, with the heights generally showing decimeter-level agreement. For the comparison with the independent ICESat- and LIDAR-derived “ground truth” of ocean or sea-ice heights, the statistics of comparison show a typical fit of around 10 cm RMS in the North Atlantic, and 30 cm in the sea-ice region north of Greenland. Part of the latter 30 cm error is likely due to errors in the airborne LIDAR measurement and calibration, as well as errors in the “ground truth” ocean surfaces due to drifting sea-ice. Nevertheless, the potential of the PPP method for generating 10 cm level kinematic height positioning over long baselines is illustrated.     

平坦与丘岭地区GPS工程水准的研究

对ＧＰＳ工程水准网的布设、拟合法的模型选择和数据处理进行了探讨。通过实验网的布设和计算发现：在平坦和丘岭地区，控制面积不超出１００ｋｍ＾２时，按三等以上水准测量的精度联测网中６￣８个点，采用最佳三点平面拟合、二次多项式曲面拟合和ｈａｒｄｙ曲面拟合，求得ＧＰＳ工程水准高程的精度可达２￣４ｃｍ。     

The autocorrelation of waveforms generated from ocean-scattered GPS signals

A "waveform" is generated by cross-correlating local copies of a global positioning system (GPS) signal with an ocean-reflected GPS signal, over a range of carrier frequencies and code delays. The shape of this waveform can be inverted to obtain estimates of the ocean surface roughness. To assess the accuracy of these retrievals, a stochastic model for the waveform time series measurements was developed in a previous publication. In this letter, this model is validated by comparing the predicted autocorrelation function of the waveform against the autocorrelation computed from experimental waveforms collected from an airborne receiver. A 1-ms coherent integration time was used at first. Then, blocks of these measurements were concatenated to produce equivalent integration times of up to 5 ms to compare the dependence of model predictions on integration time. Correlation time was estimated by fitting a model Gaussian function to the magnitude or the real part of the autocorrelation function. The magnitude and phase of the complex autocorrelation function from the model were also studied to show the location of the first , and better explain cases in which the Gaussian function did not fit well. The autocorrelation is found to be weakly dependent upon the surface roughness, over a range of moderate wind speeds.